Thesis Title Goes Here

FACTORS AFFECTING THE GROWTH AND FRAGMENTATION OF POLYFERROCENYLSILANE DIBLOCK COPOLYMER MICELLES

Jieshu Qian

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Chemistry University of Toronto

Jieshu Qian

Doctor of Philosophy

Graduate Department of Chemistry University of Toronto

2013 Abstract

Polyferrocenylsilane (PFS) diblock copolymers self-assemble in selective solvents to form

one-dimensional micelles for a broad range of polymer compositions and experimental

conditions, driven by the crystallization of the PFS block that forms the micelle core. The most

striking feature of these micelles is that they remain active for further growth. They can be

extended in length when additional polymer, dissolved in a good solvent, is added to a solution

of the pre-existing micelles. This thesis describes several studies investigating the factors that

affect the growth and fragmentation of PFS diblock copolymer micelles in solution, with a

particular emphasis on polyisoprene-PFS (PI-PFS) diblock copolymers. The goal of my research

was trying to provide deeper understanding of this crystallization-driven self-assembly (CDSA) process.

In an attempt to understand the growth kinetics of the PI-PFS cylindrical micelles, I added tiny amount of short micelle seeds into supersaturated solution of the same polymer, and

followed the micelle growth by light scattering. The data analysis showed that the increase of

micelle length could be described by an expression with two exponential decay terms. In another

ii attempt to examine the factors that may affect the growth behavior of the PI-PFS micelles, I found that PI-PFS long micelles underwent fragmentation when they were subjected to external stimuli, e.g. addition of polar solvent, or heating. During the course of studying the effect of heating on the micelles, I developed a new approach to generate cylindrical micelles with controllable and uniform length, a one-dimensional analogue of self-seeding of crystalline polymers. I carried out a systematic study to investigate the self-seeding behavior of PFS block copolymers.

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Acknowledgements

This thesis would not have been possible without the support, guidance, patience and encouragement of a great scientist, my supervisor Prof. Mitchell A. Winnik. I am truly indebted and thankful for that he teaches me how to be not only a better scientist but also a better person. The knowledge, skills, and experience I have acquired under his supervision will benefit me all through my career and life. I would like to express my gratitude and appreciation to Prof. Ian Manners from University of Bristol for his valuable suggestions, discussions and collaboration throughout my doctoral research. I also would like to thank Prof. Wenbing Hu from Nanjing University and Prof. Eugenia Kumacheva from University of Toronto for their fruitful suggestions.

I owe sincere and earnest thankfulness to my colleagues and friends in the Winnik group. Particularly, I want to thank Dr. Yijie Lu for his enormous help on my research, Mr. Graeme Cambridge for providing polymer materials for my research, Dr. Gerald Guerin and Dr. Mohsen Soleimani for their helpful discussions, Ms. Anselina Chia for participating in part of my research. I am also much obliged to Mr. Meng Zhang, Dr. Chun Feng, Mrs. Wanjuan Lin, Mr. Guangyao Zhao, Mr. Peng Liu, Dr. Yi Hou, Dr. Lin Jia, Mr. Lemuel Tong, Dr. Nicolas Illy and all other members of the Winnik group for not only discussing science and also sharing happiness in life.

In the end, I would like to express my gratitude to my beloved parents for their love and support during my whole life. This thesis is dedicated to them. I also would like to thank all my family members for their kind support, especially my cousin Xinyang Zhang for his help on data analysis. I am also deeply indebted to my dear wife Mrs. Min Feng for her long time support and making my life enjoyable.

Table of Contents

Abstract………………………………………………………………………………………… ii

Acknowledgements……………………………………………...………..…….…………...... iv

Table of Contents……………………………………………………………………………… v

List of Tables…………………………………………………………………………………... x

List of Schemes and Figures………………………………………………………………... xiii

List of Appendices…………………………………………………………………………... xix

Chapter 1. Introduction: Nanofiber Micelles from the Self-assembly of Block Copolymers in Solution………………………………………………………………………………… 1

1.1 Introduction: Self-assembly of Block Copolymers…………………………………………. 1 1.2 The Energy Landscape for Block Copolymer Self-assembly………………………………. 3 1.3 Theories of Nanofiber Micelle Formation by Block Copolymers………………………….. 4 1.4 Examples Classified by the Nature of the Block Copolymers……………………………… 5 1.4.1 Coil-coil Block Copolymers………………………………………………………………….. 7 1.4.2 Rod-coil Block Copolymers………………………………………………………………….. 12 1.4.3 Crystalline-coil Block Copolymers…………………………………………………………... 15 1.4.3.1 PFS Block Copolymers………………………………………………………………... 15 1.4.3.2 Non-PFS Block Copolymers………………………………………………………….. 23 1.4.4 Nanofibers from Disk-like Building Blocks and Other Examples…………………………… 29 1.5 Summary……………………………………………………………………………………. 32 1.6 Research Objectives and Thesis Outline……………………………………………………. 33 References………………………………………………………………………………………. 34

Chapter 2. Experimental: Material, Instrumentation, Method and Protocol……………... 40

2.1 Material……………………………………………………………………………………... 40 2.1.1 Solvents……………………………………………………………………………………….. 40 2.1.2 Polymers……………………………………………………………………………………… 40 v

2.2. Instrumentation…………………………………………………………………………….. 42 2.2.1 Transmission Electron Microscopy (TEM)…………………………………………………... 42 2.2.2 Light Scattering……………………………………………………………………………….. 42 2.2.3 Gel Permeation Chromatography (GPC)……………………………………………………... 43 2.2.4 Atomic Force Microscopy (AFM)……………………………………………………………. 43 2.2.5 Nuclear Magnetic Resonance (NMR)………………………………………………………… 43 2.2.6 Heating Bath and Temperature Control………………………………………………………. 44 2.2.7 Sonication…………………………………………………………………………………….. 44 2.3 Image Analysis Method…………………………………………………………………….. 44 2.3.1 Image Analysis……………………………………………………………………………….. 44 2.3.2 PDI……………………………………………………………………………………………. 46 2.3.2.1 Example 1...…………………………………………………………………………… 46 2.3.2.2 Example 2……………………………………………………………………………... 47 2.3.2.3 Example 3……………………………………………………………………………... 47 2.3.2.4 Example 4……………………………………………………………………………... 48 2.3.2.5 Example 5……………………………………………………………………………... 49 2.3.2.6 Example 6……………………………………………………………………………... 49 2.4 Experimental Protocol: Seeded Growth…………………………………………………….. 50 References………………………………………………………………………………………. 54

Chapter 3. Solvent-induced Fragmentation of Fiber-like PI1000-PFS50 Block Copolymer Micelles……………………………………………………………………………………. 55

3.1 Introduction…………………………………………………………………………………. 55 3.2 Experimental………………………………………………………………………………... 59 3.2.1 Seeded Growth of PI-PFS Block Copolymer Micelles………………………………………. 59 3.2.2 Adding THF into Micelle in Decane Solutions………………………………………………. 60 3.2.3 Adding Decane into Polymer in THF Solutions……………………………………………… 60 3.2.4 Test of the Supersaturation for Micellization………………………………………………… 60 3.3 Results and Discussion……………………………………………………………………… 61 3.3.1 Seeded Growth of PI-PFS Block Copolymer Micelles………………………………………. 61 3.3.2 Effect of Adding THF into Micelle in Decane Solutions…………………………………….. 64 3.3.3 Kinetics of CLD Evolution Induced by the Addition of THF………………………………... 68 vi

3.3.4 Effect of Adding Decane into Polymer in THF Solutions……………………………………. 70 3.3.5 Test of Supersaturation Region for Micellization…………………………………………….. 73 3.4 Conclusion………………………………………………………………………………….. 75 References………………………………………………………………………………………. 76

Chapter 4. Growth Kinetics of Fiber-like PI1000-PFS50 Block Copolymer Micelles……….. 77

4.1. Introduction………………………………………………………………………………… 77 4.2 Experimental………………………………………………………………………………... 82 4.2.1 Preparation of Micelle Seed Solution………………………………………………………… 82 4.2.2 Preparation of Micelle Solutions for the Correlation of Scattering Intensity with Micelle Length…………………………………………………………………………………………. 82 4.2.3 Study of Micelle Growth Kinetics……………………………………………………………. 83

4.2.4 Diffusion Coefficient of PI800-PFS20 Polymer Chains in decane/THF Mixture……………… 85 4.3 Results and Discussion……………………………………………………………………… 85 4.3.1 Static Light Scattering Theory………………………………………………………………... 87 4.3.2 A Simple Growth Model……………………………………………………………………… 89 4.3.3 Correlation of Scattering Intensity with Micelle Length……………………………………... 91 4.3.4 Kinetics Data of Trial V10T11M05…………………………………………………………... 95 4.3.5 Fitting of the Kinetics Data of Trial V10T11M05……………………………………………. 99 4.3.6 Additional Kinetics Experiments…………………………………………………………..... 101 4.3.7 Kinetics Models Leading to Double Exponential Decay Kinetics…………………………... 109 4.3.8 A Model for Diffusion Controlled Micelle Growth…………………………………………. 114 4.3.9 Experiments at Higher Unimer Concentrations……………………………………………... 118 4.4 Conclusion…………………………………………………………………………………. 125 References……………………………………………………………………………………… 127 Appendix I to Chapter 4……………………………………………………………………...… 129 Appendix II to Chapter 4………………………………………………………………………. 139 AII-4.1 Dynamic Light Scattering Theory………………………………………………………… 139

AII-4.2 Experimental Correlation between Rh,app and length L……………………………………. 142

AII-4.3 Evolution of Rh,app Over Time for Kinetics Experiments…………………………………. 144

AII-4.4 Analysis of Evolution of Rh,app Over Time………………………………………………... 146 References…………………………………………………………………………………………. 148 vii

Chapter 5. Self-seeding of Fiber-like Micelles Formed by PFS Block Copolymers……… 149

5.1 Introduction……………………………………………………………………………….... 149 5.2 Experimental……………………………………………………………………………….. 152

5.2.1 Self-seeding of PI1000-PFS50………………………………………………………………….. 152

5.2.2 Effect of Good Solvent on Self-seeding Behavior of PI1000-PFS50………………………...… 152

5.2.3 Using Solvent to Perform Self-seeding of PI1000-PFS50…………………………………….... 153

5.2.4 Effect of Pre-annealing on Self-seeding Behavior of PI1000-PFS50………………………...… 153 5.2.5 Self-seeding of Other PFS Block Copolymers in Selective Solvents……………………….. 154 5.3 Results and Discussion…………………………………………………………………..… 155

5.3.1 Self-seeding of PI1000-PFS50………………………………………………………………….. 156

5.3.2 Effect of Good Solvent on Self-seeding Behavior of PI1000-PFS50…………………………... 164

5.3.3 Using Solvent to Perform Self-seeding of PI1000-PFS50……………………………………… 167

5.3.4 Effect of Pre-annealing on Self-seeding Behavior of PI1000-PFS50…………………………... 171 5.3.5 Self-seeding of Other PFS Block Copolymers in Selective Solvents……………………..… 174 5.4 Conclusion…………………………………………………………………………………. 187 References…………………………………………………………………………………….... 188 Appendix to Chapter 5…………………………………………………………………………. 189

Chapter 6. Polyferrocenylsilane Crystals in Nanoconfinement: Fragmentation, Dissolution, and Regrowth of Cylindrical Block Copolymer Micelles…………………………...… 203

6.1 Introduction……………………………………………………………………………….... 203 6.2 Experimental……………………………………………………………………………….. 207 6.3 Results and Discussion…………………………………………………………………..… 208 6.3.1 Effect of Heating on the L-1250 nm Micelle Sample……………………………………..… 209 6.3.2 Effect of Heating on the L-250 nm Micelle Sample and Comparison with L-1250……….... 212 6.3.3 Fragmentation and Dissolution upon Heating, Regrowth upon Cooling……………………. 215 6.3.4 Preparation and Effects of Heating on 1250 nm and 250 nm Micelle Mixtures…………….. 217 6.4 Conclusion…………………………………………………………………………………. 223 References……………………………………………………………………………………... 226 Appendix to Chapter 6…………………………………………………………………………. 228

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Chapter 7. Summary and Future Work…………………………………………………….. 232

7.1 Summary…………………………………………………………………………………… 232 7.1.1 Fragmentation Behavior of the Fiber-like PFS Block Copolymer Micelles……………….... 232 7.1.2 Growth Kinetics of Fiber-like PFS Block Copolymer Micelles…………………………..… 233 7.1.3 Self-seeding of PFS Block Copolymer Micelles…………………………………………….. 234 7.2 Future Work……………………………………………………………………………...… 235 7.2.1 Growth Kinetics…………………………………………………………………………….... 235 7.2.2 Self-seeding………………………………………………………………………………...... 236

List of Tables

Chapter 2……………………………………...……………………………………………….. 40

Table 2.1. Values of Mn and PDI of all PFS block copolymers examined in this thesis…………………….... 41

Chapter 3……………………………………...……………………………………………….. 55

Table 3.1. Estimated CMC values for PI1000-PFS50 for different solvent compositions………………………. 67

Chapter 4……………………………………...……………………………………………….. 77

Table 4.1. Experimental parameters of each trial of the kinetic experiments………………………………… 84 Table 4.2. Values of micelle lengths obtained from TEM and LS measurements for each of the four kinetic experiments……………………………………………………………………………………………... 107 Table 4.3. Values of fitting parameters of kinetic data from each experiment..…………………………...… 107 Table 4.4. Values of different parameters calculated based on the values of fitting parameters in Table 4.3.. 114 Table 4.5. Fitting parameters for Trial V10T11M20…………………………..…………………………..… 121 Table 4.6. Fitting parameters for Trial V10T14M25…………………………..………………………….… 124 Appendix I to Chapter 4……………………………………………………………………...… 129 Table AI-4.1. Experimental parameters and TEM measurements of the eighteen micelle reference solution. 129 Table AI-4.2. Experimental parameters and LS measurements of the micelle reference solution…………... 130 Appendix II to Chapter 4……………………………………………………………..………... 139

Table AII-4.1 Values of Ltheoretical, final micelle length values LScattering and LRh,90 for different trials of kinetics experiments.…………...... 146

Chapter 5……………………………………...………………………………………………. 149

Table 5.1. Values of dn and dw/dn for all of the as-prepared micelle samples.…………...………………..… 176 Appendix to Chapter 5…………………………………………………………………………. 189

Table A5.1. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.…...……………………………………………………………………………..… 194

Table A5.2. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle fragments and micelles formed solutions of the micelle fragments in decane were annealed at 70.0 oC for different times followed by cooling to room temperature..…...………………………………………………………………………...………. 195

Table A5.3. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelles formed after solutions of the micelle fragments in decane were annealed at 80.0 oC for different times followed by cooling to room temperature...…...………………………………………………………………………...…………….. 195

Table A5.4. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle fragments and micelles formed after the solution of the fragments in decane with different amount of THF was annealed at different temperatures for 30 min followed by cooling to room temperature...………………………………………...... ……. 196

Table A5.5. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelles formed after the evaporation of THF vs.

the volume fractions of THF in the PI1000-PFS50 fragment decane solutions before the evaporation...… 197

Table A5.6. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle fragments and fragments that have been pre-annealed at different temperatures for 24 hrs and micelles formed after the solution of the these fragments in decane was heated at different temperatures for 30 min followed by cooling to room temperature.…………………………………………………………………………………………..…. 198

Table A5.7. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI637-PFS53 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.……………………………………………………………………………………. 199

Table A5.8. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS60-PDMS660 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.…...………………………………………………………………………. 199

Table A5.9. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS90-PDMS900 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.…...………………………………………………………………………. 200

Table A5.10. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS30-P2VP300 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.…...………………………………………………………………………. 201

Table A5.11. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI637-PFS53 micelles formed after solutions of the micelle fragments in decane were annealed at 64.0 oC for different times followed by cooling to room temperature…...……………………………………………………………………………...………….. 201

Table A5.12. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS60-PDMS660 micelles formed after solutions of the micelle fragments in decane were annealed at 75.0 oC for different times followed by cooling to room temperature……………………………………………………………………………...…...………….. 202

Table A5.13. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS90-PDMS900 micelles formed after solutions of the micelle fragments in decane were annealed at 88.0 oC for different times followed by cooling to room temperature………………………………………………………...………………………...………….. 202

Table A5.14. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS30-P2VP300 micelles formed after solutions of the micelle fragments in 2-propanol were annealed at 68.0 oC for different times followed by cooling to room temperature……………………………………………………………...…………...... 202

Chapter 6……………………………………...………………………………………………. 203

Appendix to Chapter 6………………………………………………………………………… 228

Table A6.1. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle sample L-1250 with Ln ≈ 1250 nm and micelles formed after the micelle solution in decane was annealed at 55.0 oC for different lengths of time followed by cooling to room temperature………………..…………………………………………..… 228

Table A6.2. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle sample L-1250 with Ln ≈ 1250 nm and micelles formed after the micelle solution in decane was annealed at 70.0 oC for different lengths of time followed by cooling to room temperature………………..…………………………………………..… 228

Table A6.3. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle sample L-1250 with Ln ≈ 1250 nm and micelles formed after the micelle solution in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.……..…………...………………………………………..… 229

Table A6.4. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle sample L-250 with Ln ≈ 250 nm and micelles formed after the micelle solution in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.……..…………...………………………………………..… 229

Table A6.5. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 mixture sample L-Mix3/1, containing L-250 and L-1250 with number ratio of 3:1 and micelles formed after the micelle solution in decane was annealed at different temperatures for 30 min followed by cooling to room temperature...….……………………. 230

Table A6.6. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 mixture sample L-Mix1/1, containing L-250 and L-1250 with number ratio of 1:1 and micelles formed after the micelle solution in decane was annealed at different temperatures for 30 min followed by cooling to room temperature...….…………………..… 230

Table A6.7. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 mixture sample L-Mix1/3, containing L-250 and L-1250 with number ratio of 1:3 and micelles formed after the micelle solution in decane was annealed at different temperatures for 30 min followed by cooling to room temperature...….……………..……… 231

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List of Schemes and Figures

Chapter 1………………………………………………………………………………………. 1

Scheme 1.1. Chemical structures of the polymer blocks mentioned in Chapter 1……………………….…… 6 Figure 1.1. Phase diagrams and selected examples of filamentous micelles formed by coil-coil block copolymers……………………………………………………………………………………………….. 11 Figure 1.2. Drawings and selected examples of filamentous micelles formed by rod-coil block copolymers……………………………………………………………………………………………….. 14 Figure 1.3. Selected examples of filamentous micelles formed by PFS block copolymers I…...... 18 Figure 1.4. Selected examples of filamentous micelles formed by PFS block copolymers II………………... 22 Figure 1.5. Selected examples of filamentous micelles formed by non-PFS crystalline-coil block copolymers……………………………………………………………………………………………….. 28 Figure 1.6. Selected examples of filamentous micelles formed by disk-like building blocks………………... 31

Chapter 2……………………………………...……………………………………………….. 40

Scheme 2.1. Structures of block copolymers PI1000-PFS50, PI800-PFS20, PI637-PFS53, PFS90-PDMS900, PFS60-

PDMS660 and PFS30-P2VP300…………………………………………………………………………….. 42

Figure 2.1. An example of TEM image of fiber-like micelles formed by the self-assembly of PI1000-PFS50 block copolymer in decane…………………………………………………...... 45 Figure 2.2. Histograms of micelle length distribution for Example 1-6………………………...... 48

Figure 2.3. TEM images and length distribution histograms showing the seeded growth of PI1000-PFS50 micelles……………………………………………………………………………...... 52 Figure 2.4. Mean length of the micelles obtained by seeded growth versus the mass of polymer added...…... 53

Chapter 3……………………………………...……………………………………………….. 55

Figure 3.1. TEM image and length distribution histogram of the micelle seeds formed by adding PI1000-PFS50 as a powder to decane and sonicating the mixture for two 10 min intervals………………...…………... 61 Figure 3.2. Representative TEM images and length distribution histograms of the micelles from the mother

solution, formed by adding 0.150 mL of PI1000-PFS50 in THF (c = 2.00 mg/mL) to 3.00 mL of seed

micelles (c = 0.0200 mg/mL of PI1000-PFS50) in decane………………………………………………… 63

Figure 3.3. Length distribution histograms of PI1000-PFS50 micelles formed by seeded growth in decane/THF followed by addition of additional THF…………………………………………………………………. 65

Figure 3.4. Evolution of the scattering intensity at 90°, evolution of number average length Ln and weight

average length Lw, evolution of σ/Ln, and evolution of mass percentage of polymer in the micelles,

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following the addition of different amounts of THF to solutions of PI1000-PFS50 micelles formed by seeded growth……………………………………………………………………………………………. 66

Figure 3.5. Length distribution histograms of PI1000-PFS50 micelles at different times after the addition of 0.24

mL THF into 2.10 mL of the PI1000-PFS50 mother solution of micelles…………………………………. 69

Figure 3.6. Evolution of number-averaged length Ln and weight-averaged length Lw of the micelles, and

evolution of σ/Ln versus logarithm of time after the addition of 0.24 mL THF to 2.1 mL of the mother

solution of PI1000-PFS50 micelles………………………………………………………………………… 70 Figure 3.7. Evolution of the scattering intensity at 90° of each sample as the increased amount of decane added

into nine bathes of PI1000-PFS50 in THF solutions……………………………………………………….. 71

Figure 3.8. TEM images of the solutions prepared by adding various amounts of decane into PI1000-PFS50 in THF solutions…………...……………………………………………………………………………….. 72 Figure 3.9. Evolution of the scattering intensity at 90° versus the THF volume fraction in solution……….... 73

Figure 3.10. TEM images of the samples by adding small amount of short PI1000-PFS50 micelles in decane (5

μL, c = 0.020 mg/mL) as shown in Figure 3.1 into PI1000-PFS50 in decane/THF mixture solutions with different solvent compositions…………………………………………………………………………… 74

Chapter 4……………………………………...……………………………………………….. 77

Scheme 4.1.Chemical structure of peptide C16-W3K and illustration of the formation of elongated micelles by the attachment of spherical micelles to the ends of the growing micelles……………………………….. 80

Figure 4.1. TEM image and length distribution histogram of the PI1000-PFS50 micelle seeds………………… 86 Figure 4.2. A simple model illustrating the micelle growth…………………………………………………... 90 Figure 4.3. TEM images and length distribution histograms of micelles formed in four reference solutions... 92

Figure 4.4. Number-averaged length Ln of the micelles obtained from the TEM images in the reference solutions versus unimer-to-seed ratios, and representative Holtzer-Casassa plots for micelles formed in four reference solutions………………………………………………………………………………….. 94 Figure 4.5. Plots of scattering intensities versus the micelle lengths based on the reference solutions………. 95 Figure 4.6. Kinetic data of Trial V10T11M05………………………………………………………………... 98 Figure 4.7. Fitting of the kinetics data of Trial V10T11M05………………………………………………... 100 Figure 4.8. Scattering intensities of solutions from Trial V10T11M02, V10T11M10, and V25T11M12.5 at angles of 30o, 60o and 90o for a period of ca. two weeks (2×104 min)………………………………….. 103

Figure 4.9. Number-averaged length Ln of the micelles obtained from the TEM images in the six reference

solutions versus the unimer-to-seed ratio. And plot of scattering intensity versus Ltheoretical of micelles for the six reference solutions………………………………………………………………………………. 105 Figure 4.10. Evolution of micelle length L(calc) over time of Trial V10T11M02, V10T11M10, and V25T11M12.5 for a period of two weeks (2×104 min)…………………………….…………………... 106 Figure 4.11. Fitting of the kinetic data in Figure 4.10……………………..………………………………… 108 xiv

Figure 4.12. Illustrations of two sequential growth models for PI1000-PFS50 block copolymer micelles……. 111 2 Figure 4.13. Plot of inverse of relaxation time (decay rate Γ) of the autocorrelation function versus q for PI800-

PFS20 block copolymer in decane/THF (φTHF = 0.11) solution…………………………………………. 116 Figure 4.14. Evolution of scattering intensities over time of solutions from Trial V10T11M20 and Trial V10T14M25…………………………………………………………………………………………….. 118 Figure 4.15. Data analysis for Trial V10T11M20………..…………………………………………………... 119 Figure 4.16. Data analysis for Trial V10T14M25……………………………………………………………. 123 Appendix I to Chapter 4……………………………………………………………………….. 129

Figure AI-4.1. Number-averaged length Ln of the micelles obtained from the TEM images of the reference solutions versus the unimer-to-seed ratios…………………………………………………………..….. 133 Figure AI-4.2. A TEM image and corresponding width distribution of the micelles at the growth time of ca. 2 weeks for Trial V10T11M05………………………………………………………………………….... 133 Figure AI-4.3. CONTIN plot of the distribution of the decay time for the data of Trial V10T11M05……... 134 Figure AI-4.4. Representative TEM images and the corresponding length distribution histograms of the micelles for Trial V10T11M02, Trial V10T11M10; and Trial V25T11M12.5.……………………..… 135 Figure AI-4.5. DLS measurement of the supersaturated solution with unimer concentration of 0.10 mg/mL at angle of 20o……………………………………………………………………………………………... 136

Figure AI-4.6. Plot of the diffusion coefficient of the micelles Dm, of six of the 18 reference solutions versus

the length (LTEM) of the micelles……………………………………………………………………..… 136 Figure AI-4.7. TEM results of the competitive micelle growth……………………………………………... 137 Figure AI-4.8. Representative TEM images and the corresponding length distribution histograms of the micelles for Trial V10T11M20 and Trial V10T14M25……………………………………………….. 138 Appendix II to Chapter 4…………………………………………………..…………………... 139

Figure AII-4.1. Correlation of Rh,app values versus the theoretical micelle length (Ltheoretical) of the eighteen reference solutions at angles of 30o, 60o, and 90o……………………………………………………… 143

Figure AII-4.2. Evolution of Rh,app values over time for different trials of kinetic experiments…………..… 145

Figure AII-4.3. Evolution of micelle length (LRh,90) over time for different trials of kinetics experiments…. 147

Chapter 5……………………………………...………………………………………………. 149

Figure 5.1. RI and UV (420 nm) signal of GPC chromatographs of PI1000-PFS50 micelles before sonication and micelle fragments formed by sonication for 20 min……………………………………………………. 155

Figure 5.2. A TEM image, length distribution histogram and width distribution histogram of the PI1000-PFS50 micelle fragments used in the experiments described in section 5.3.1…………………………………. 156

Figure 5.3. TEM images of micelles formed after annealing PI1000-PFS50 micelle fragment solutions for 30 min at different temperatures as indicated in each image and cooling to room temperature………………... 158

Figure 5.4. Two AFM height images and the corresponding height scan profiles along the white line in each

image of the PI1000-PFS50 micelles from the same sample as shown in Figure 5.3I……………………. 159

Figure 5.5. Mean micelle length Ln of PI1000-PFS50 micelles in decane versus heating temperature for micelle

fragment solutions annealed for 30 min. And fraction of surviving seeds in decane solutions of PI1000-

PFS50 micelle fragments versus heating temperature………………………………………………….... 161 o Figure 5.6. TEM images of PI1000-PFS50 solution of micelle fragments annealed at 80.0 C for 30 min……. 162

Figure 5.7. Time dependence of micelle length Ln formed from solutions of PI1000-PFS50 micelle fragments after being annealed at different temperatures and then cooled to room temperature in air……………. 163

Figure 5.8. The proposed self-seeding mechanism for fiber-like PI1000-PFS50 micelles in decane solution…. 164

Figure 5.9. Mean micelle length Ln of micelles obtained by heating the PI1000-PFS50 fragment decane solutions for 30 min with the presence of different volume fractions of THF versus the heating temperatures. And a

semilogarithmic plots of fraction of surviving seeds in solution of PI1000-PFS50 micelle fragments with different volume fractions of THF versus dissolution temperatures……………………………………. 165 Figure 5.10. 1H NMR spectra of a decane and THF (THF vol 20 %) mixture before and after the evaporation of THF in a desiccator under mild vacuum (ca. 10 Torr) for 12 hours……………………………………. 169

Figure 5.11. Mean length Ln of micelles formed after the evaporation of THF versus the volume fractions of

THF in the PI1000-PFS50 fragment solutions before the evaporation of THF. And a plot of fraction of

surviving seeds in solution of PI1000-PFS50 micelle fragments versus the volume fraction of THF……. 171

Figure 5.12. Mean length Ln of micelles obtained by heating the PI1000-PFS50 fragment decane solutions and solutions which have been annealed at different temperatures for 24 hrs versus the heating temperatures.

And a semilogarithmic plot of fraction of surviving seeds in solution of PI1000-PFS50 micelle fragments versus heating temperatures……………………………………………………………………………. 174 Figure .5.13. Micelles formed by different PFS block copolymers.…………………………………………. 176 Figure 5.14. TEM images and length distribution histograms of each micelle fragment……………………. 178 Figure 5.15. Representative TEM images of micelles formed after annealing each block copolymer micelle fragments solutions for 30 min at different temperatures and cooling to room temperature…………… 180 Figure 5.16. Length distribution histograms of the micelles obtained by heating each micelle fragments at different temperature for 30 min, and cooling to room temperature……………………………………. 181

Figure 5.17. TEM images of PI637-PFS53, PFS60-PDMS660, and PFS30-P2VP300 micelles formed after annealing the fragment in solutions for 30 min at different temperatures and cooling………………………….... 182

Figure 5.18. Mean micelle length Ln versus heating temperatures for PI637-PFS53, PFS60-PDMS660, PFS90-

PDMS900 and PFS30-P2VP300 fragment solutions annealed for 30 min. And semilogarithmic plots of

fraction of surviving seeds in solution of PI637-PFS53, PFS60-PDMS660, PFS90-PDMS900 and PFS30-

P2VP300 micelle fragments versus heating temperatures………………………………………….…… 183

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Figure 5.19. Time dependence of micelle length Ln formed from decane solutions of PI637-PFS53, PFS60-

PDMS660, PFS90-PDMS900 and 2-propanol solution of PFS30-P2VP300 micelle fragments after being annealed at the temperatures indicated in the plots and then cooled to room temperature in air……….. 185 Appendix to Chapter 5…………………………………………………………………………. 189

Figure A5.1. TEM images of micelles formed after annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at different temperatures and cooling to room temperature. And width distribution histogram of the dark centers and non-center regions of the micelles as formed…………………………………. 189 Figure A5.2 Length distribution histograms of the dark centers of the micelles and the whole micelles formed

after annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at different temperatures and cooling to room temperature……………………………………………………………………………. 190

Figure A5.3. Representative TEM images and length distribution histograms of the PI1000-PFS50 micelle fragments used in the experiments in Section 5.3.4…………………………………………………….. 191

Figure A5.4. Representative TEM images and corresponding width distribution histograms of PI637-PFS53

micelles formed in decane, PFS60-PDMS660 micelles formed in decane, PFS90-PDMS900 micelles formed

in decane, and PFS30-P2VP300 micelles formed in 2-propanol………………………………….……... 192

Figure A5.5. More TEM images of the PFS90-PDMS900 micelle formed by annealing the micelle fragment in decane solutions for 30 min at 96 oC and cooling to room temperature……………………………….. 193

Figure A5.6. RI and UV (420 nm) signals of GPC chromatographs of PFS90-PDMS900……………………. 193

Chapter 6……………………………………...……………………………………………..... 203

Figure 6.1. Drawing of the experimental design…………………………………………………………….. 209

Figure 6.2. TEM image and length distribution histogram of PI1000-PFS50 micelle sample L-1250 as prepared and sample L-1250 after being annealed at 55.0 oC for different times…………………………...……. 210 Figure 6.3. TEM images of sample L-1250 after being annealed at 55 oC for different lengths of time…….. 210 Figure 6.4. TEM image of sample L-1250 after being annealed at 70 oC for 30 min, and length distribution histograms of L-1250 after being annealed at 70 oC for different times…………………………………212

Figure 6.5. TEM images and length distribution histograms of PI1000-PFS50 micelle sample L-250 as prepared, and L-250 after being annealing at 55.0 oC and 70.0 oC for 30 min…………………………………….. 213

Figure 6.6. Mean length Ln versus heating temperatures for L-250 and L-1250 annealed for 30 min………. 214

Figure 6.7. Ratio of the initial Ln value for the micelle sample to that obtained (final Ln) after annealing for 30 min at the temperature indicated, followed by cooling to 23 °C. And the number concentration of micelles present in samples L-1250 and L-250 after they were heated for 30 min and cooled to 23 °C………… 216

Figure 6.8. TEM images of PI1000-PFS50 micelle samples L-Mix3/1, L-Mix1/1 and L-Mix1/3 as prepared and after being annealed at different temperatures for 30 min…………………………………………….... 218 Figure 6.9. Histograms of the length distribution of the corresponding micelles as shown in Figure 6.8…… 219

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Figure 6.10. Mean micelle length Ln versus heating temperatures for L-Mix3/1, L-Mix1/1, and L-Mix1/3 (L- 250/ L-1250) solutions annealed for 30 min…………………………………………………………… 220

Figure 6.12. Plots of the measured value of Ln vs the number fraction of L-1250 micelles (f(L-1250)) in the L- 1250/L-250 micelle mixture following annealing at 23 and 40 °C…………………………………….. 223

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List of Appendices

Chapter 4……………………………………...……………………………………………….. 77

Appendix I to Chapter 4……………………………………………………………………...… 129 Appendix II to Chapter 4…………………………………………………..…………………... 139

Chapter 5……………………………………...………………………………………………. 149

Appendix to Chapter 5…………………………………………………………………………. 189

Chapter 6……………………………………...……………………………………………..... 203

Appendix to Chapter 6………………………………………………………………………… 228

xix

Chapter 1

INTRODUCTION: NANOFIBER MICELLES FROM THE SELF-

ASSEMBLY OF BLOCK COPOLYMERS IN SOLUTION

Micelles are formed when block copolymers are dissolved in solvents selective for one of the blocks. In contrast to micelles formed by surfactants, block copolymer micelles are generally more robust, and this opens the door to many applications. Different structures can be generated by the self-assembly of block copolymers: spheres, cylinders or fibers, lamellar bilayers and vesicles. Since my main research interest is focused on fiber-like micelles, in this Introduction chapter to my thesis, I will examine the formation and structure of fiber-like or filamentous micelles, with cross-sections of nanometer dimensions. These fascinating objects are currently under investigation for drug delivery applications, as impact modifiers for plastics, as templates for the deposition of metal nanoparticles and as precursors to nanoscale ceramics. Moreover, in some cases, studies of their formation and fragmentation are beginning to provide insight into the generation of protein fibers, such as actin or amyloid fibers, derived from soluble cytosolic protein precursors. The major content of this chapter is adopted from a review paper I co- authored, published in the journal of Trends in Biotechnology [1] (Qian, J. S.; Zhang, M.; Manners, I.; Winnik, M. A. Trends in Biotechnology 2010, 28, 84-92), which covers a broad range of examples of fiber-like micelles formed by the self-assembly of block copolymers. At the same time, I expand some of the sections to accommodate recent progress in this field and particularly, studies that are closely related to my research are examined with more details.

1.1 Introduction: Self-assembly of Block Copolymers

Block copolymers consist of chemically distinct polymers connected by a covalent bond. In the bulk state, block copolymers undergo microphase separation because their constituent blocks are generally immiscible. The self-assembly of block copolymers in the bulk state gives rise to long-range ordering and the formation of structures such as cubic array of spheres, hexagonally packed cylinders, bicontinuous structures or lamellae. Factors that are influencing the characteristic sizes and morphologies of these nanostructures include the degree of polymerization, the volume fraction of each of the blocks, and the Flory-Huggins parameter 2 between them. However, the topic of self-assembly of block copolymers in the bulk state is not a major concern in my thesis. Detailed information about the self-assembly of block copolymers in the bulk state, including both the theoretical and experimental aspects, can be found in the review articles by Bates and Fredrickson [2], and the book by Hamley [3].

Like traditional surfactants, block copolymers are amphiphilic. When block copolymers are dissolved in a selective solvent, a good solvent for one of the blocks and a poor solvent for the other, the polymer molecules self-assemble into micelle-like objects, with a core formed by the insoluble block, surrounded by a corona of the solvent-swollen soluble block. As with surfactants, a variety of different structures can form in this way, including spheres, cylinders or fibers, lamellar bilayers and vesicles. There are number of excellent reviews about the self- assembly of block copolymers in solution by Piirma [4], Tuzar and Kratochvil [5], Webber et al. [6], Riess [7] and Gohy [8].

Since my doctorate research has been focused on the study of fiber-like micelles, I will only review block copolymers that self-assemble in solution to form long (> 1 μm) fiber-like structures of uniform diameter, with widths of a few to tens of nanometers. Such structures have been referred to as worm-like micelles, cylindrical micelles, filamentous micelles or, if the micelles are relatively rigid, as rod-like micelles. One reason for interest in this topic is that it is part of a broader and growing interest in nanofiber formation in solution by the self-assembly of molecular building blocks. For example, some surfactants in water can form worm-like micelles that are in rapid equilibrium with their amphiphilic components [9,10]. These micelles are useful rheology modifiers in applications such as enhanced oil recovery. In the surfactant literature, they are referred to as ‘living’ micelles because they constantly break and reform, particularly when subjected to shear [11]. By contrast, micelles prepared from the self-assembly of block copolymers with a higher molar mass generally possess much higher stability, which can be advantageous for many applications, such as those described below. While various research groups have studied block copolymer micelles for decades, the idea that one could manipulate polymer and/or solvent composition to obtain non-spherical micelles began with the seminal studies of Eisenberg in the mid-1990s [12]

In bioscience and medicine, there is interest in the mechanism of the formation of protein fibers from soluble protein precursors [13]. For example actin fibers are important for cell movement and amyloid fibers are associated with disease processes. While there are many 3 outstanding studies of protein fiber formation [e.g. 14,15,16], fiber growth is accompanied by partial reversibility and other complicating features, such as the complex response of fiber growth and degradation to sonication. Chemists often take the view that simpler systems can be studied in greater detail, and that these can serve as models for developing a mechanistic understanding of the formation of fiber-like structures by self-assembly.

Filamentous block copolymer micelles are also of interest because of a growing list of potential applications, some well on the way to being realized. For example, filamentous block copolymer micelles have been used for drug delivery to cells in vitro [10] and in animal models [17]. Other worm-like block copolymer micelles have shown promise as impact modifiers to reduce brittleness and suppress crack propagation in epoxy resins [18]. Filamentous nanotubes obtained through block copolymer self-assembly have been used as templates for the deposition of metal nanoparticles [19,20], creating fascinating structures with a regular linear array of metal nanoparticles that could have important applications as catalysts. Fiber-like micelles in which the core polymer contains an Fe atom in the repeat unit have been positioned on GaAs wafers using a liftoff process and converted to nanoscale ceramic features [21].

1.2 The Energy Landscape for Block Copolymer Self-assembly

The term “self-assembly” describes a process in which a disordered system of components forms an organized structure as a result of specific, localized interactions among the components, following rules governed by the underlying thermodynamics. Nature uses this approach, based upon the non-covalent interaction of building blocks, to create complex functional materials and systems in which the functions of the whole are greater than the sum of the parts [9]. An attractive goal of self-assembly is to be able to construct increasingly complex nanostructures in a simple manner [22].

It is important to realize that kinetic factors as well as thermodynamics play an important role in the self-assembly process. Block copolymer micelles are often trapped during their formation in a kinetically frozen state, either because the core polymer is in its glassy state or because the polymer chains that form the core are too insoluble in the solvent for polymer molecules to exchange among different micelles on any experimentally accessible time scale [23]. Frozen structures are particularly common when micelles are prepared by adding a poor solvent for one block to a polymer sample dissolved in a common good solvent. In a recent 4 review, Lee et al. [9] commented that the experimental conditions required to obtain nanofibers or other types of aggregates are unique to each system. As in the case of protein folding [13], there is an energy landscape for self-assembly which may have many local minima, and the trajectory that self-assembly will follow on this landscape is highly dependent on a variety of experimental conditions. For example, PCL24-PEO45 (the subscripts refer to the average number of repeat units) formed long uniform fibrous micelles when excess water was added to a solution of this polymer dissolved in acetone, whereas similar experiments with the polymer dissolved in dimethylformamide (DMF) or tetrahydrofuran (THF) led to spherical micelles [24]. Thus, the variables one has to consider in order to control block copolymer self-assembly include the choice of solvent or solvent mixtures, the way the components are combined, and the variation in temperature, in addition to the structure and length of each block.

1.3 Theories of Nanofiber Micelle Formation by Block Copolymers

Because the packing of the core-forming blocks within the micelles plays such an important role, people usually classify the block copolymers in terms of the nature of this block. In most of the cases, the non-core-forming block is solvent-swollen and stretched beyond its random coil dimensions in the selective solvent. As a result, block copolymers are referred to as “coil-coil” copolymers when the core-forming blocks form an amorphous phase and behave as a random coil. The term “rod-coil” refers to those block copolymers in which the core-forming block is rigid and extended, while “crystalline-coil” polymers are those block copolymers for which the insoluble blocks crystallize in the core of the micelles.

Micelle dimensions for coil-coil block copolymers are determined by an interplay of three contributors to the overall free energy of the system: the free energy required to stretch the insoluble chains to fill the core, the interfacial free energy between the core block and the solvent, and the repulsive interactions between the solvent-swollen corona chains. Long corona chains promote high curvature. For coil-coil block copolymers, high curvature leads to small spherical star-like micelles. When the core-forming block is a rigid rod, or when it crystallizes, these factors can influence how the chains pack in the micelle core.

For coil-coil block copolymers with short corona chains that lead to micelles in which the thickness of the swollen corona is less than the radius of the core (‘crew-cut’ micelles), the factors that affect micelle morphology are subtle. Extension of chains in both the corona and in 5 the core depends upon the area per chain, determined by a balance of the elastic energy of the corona and the surface energy of the core. The corona chain preference for a spherical geometry weakens with decreasing length. Therefore transitions between the different morphologies are driven by the core chains that prefer elongated fiber-like or lamellar morphologies as they allow lower extension of the core block [25].

The theory of micelle formation by rod-coil block copolymers and coil-crystalline block copolymers is much less advanced. Rod-coil polymers are predicted to form disk-like micelles with a parallel alignment of the rigid blocks. Recent molecular-dynamics simulations [26] using a very simple ball-and-spring model showed how a weakening of the attractive interaction between rods or introducing a degree of flexibility to the rods or increasing the length of the corona chains could lead instead to a string-like morphology with the rods aligning and packing with a helical twist along the string as depicted in Figure 1.2B.

Theoretical models of micelles with a crystalline core stress the tendency of crystalline polymers to form a folded lamellar structure. These micelles are characterized by two different interfacial energies, one at the surface from which the corona chains enter the solution, and one at the edges, where the core polymer is directly exposed to solvent [27]. When the corona chains are long, strong repulsive interactions can impose curvature on the structure and lead to elongated structures.

1.4 Examples Classified by the Nature of the Block Copolymers

In the sections that follow, I will examine which block copolymers have been used to form fiber-like micelles and the properties of these micelles that make them attractive. I first consider coil-coil block polymers. Next I consider rod-coil polymers, followed by an examination of crystalline-coil polymers. Finally, I consider a few examples of polymers that do not fall neatly into these categories, including polymers that form disk-like structures that stack to form fiber- like micelles. The chemical structures of the components of the various polymer block copolymers described in this chapter are presented in Scheme 1.1. 6

PEO PPO PI PB O O n n mno mn

PS PMA PAA PMMA PLA PE n n O n O n n O O n COOH O O

P4VP P2VP O PAN PCL PDMS O n n O O n n PMCL Si n N O Me CN n Me N

PFS PFG PMVS PBLG O H O N Me Fe Me Fe Si n n Si Ge O n n Me Me Me O

PtBA PGMA PCEMA

O OC(CH3)3 n n O O(CH2)2OOCCH2 CH n O OCH2 CH CH2 HO OH OPV OOF C H C H P3HT R2 8 17 8 17 R1

R S n 2 n R1 n

Scheme 1.1 Chemical structures of the polymer blocks mentioned in this chapter. Notation: PEO: poly(ethylene oxide); PPO: poly(propylene oxide); PI: polyisoprene; PB: polybutadiene; PE: polyethylene; PS: polystyrene; PMA: poly(methyl acrylate); PAA: poly(acrylic acid); PMMA: poly(methyl methacrylate); PLA: poly(lactic acid); P4VP: poly(4-vinyl pyridine); P2VP: poly(2-vinyl pyridine); PAN: polyacrylonitrile; PCL: poly(ε-caprolactone); PMCL: poly(4-methyl caprolactone); PDMS: polydimethylsiloxane; PFS: poly(ferrocenyldimethylsilane); PFG: poly(ferrocenyldimethyl- germane); PMVS: poly(methyl vinyl siloxane); PBLG: poly(γ-benzyl L-glutamate); PtBA: poly(t-butyl acrylate); PGMA: poly(glycerol methacrylate); PCEMA: poly(cinnamoylethyl methacrylate); OPV: oligo(phenylene vinylene) R1=C6H13, R2=H (ref 57,58), R1=R2=OC8H17 (ref 59); OOF: oligo(9,9’- dioctyl- 2,7-fluorene); P3HT: poly(3-hexyl thiophene). Reprinted from Ref [1] with permission.

7 1.4.1 Coil-coil Block Copolymers

Most synthetic polymers are amorphous, with random coil dimensions in the bulk state and swollen coil dimensions in a good solvent. Thus most diblock and triblock copolymers can be thought of as coil-coil block copolymers. Interest in fiber-like structures for this class of polymers was given a major boost by a report by the Bates group of giant wormlike micelles formed in water by a polybutadiene-poly(ethylene oxide) PB-PEO diblock copolymer [28]. This polymer, PB45-PEO55, formed fiber-like structures with a width of 7 nm and lengths greater than 1 µm. From the low glass transition temperature of the polymer and from the low modulus determined by linear viscoelastic measurements for a 1 wt % solution of the polymer in water, the authors inferred that these micelles had liquid-like cores. In Figure 1.1A, I present an example of a morphology phase diagram from Jain and Bates [23] for aqueous solutions of two series of PB-PEO block copolymers that differ by a factor of four in the length (NPB) of the PB block. Only a very narrow range of compositions near 50 wt % PEO forms cylinders (C). For the sample with the shorter PB block, there is a wider range of compositions in which cylinders and vesicles (C+B) coexist, as well as a range of compositions where cylinders and spheres (C+S) coexist. An unexpected structure appears for the polymers with the longer PB block. Here cylinders often appear with Y-branches (CY) in the form of bulbous spherical end-caps and loops (Figure 1.1C) [29]. Another informative example from Cheng’s laboratory (Figure 1.1B) describes morphology as a function of polymer concentration and solvent composition for a polystyrene-PEO block copolymer (PS962-PEO227) in dimethylformamide-acetonitrile mixtures [ 30 , 31 ]. Here one sees a very narrow range of solvent compositions in which long one- dimensional micelles are formed (Figure 1.1D), and other compositions where cylinders are accompanied by spheres or vesicles. One of the major points raised by Jain and Bates is that the micelles formed in their system exist in kinetically frozen states, which might explain the prevalence of the multiple morphologies seen in Figure 1.1A (and also in Figure 1.1B) compared with the general absence of multiple morphologies in most surfactant solutions.

For systems close to thermodynamic equilibrium that do not involve mixed solvents, the theory of block copolymer micelle formation is well developed. Consideration of the energy and geometric factors makes it possible to construct a theoretical morphology phase diagram for specific well-defined cases such as polystyrene-polyisoprene block copolymers (PS-PI) in heptane [25]. Solvent penetration into the core affects the interfacial energy, and the degree of 8 core swelling can vary with temperature. LaRue et al. showed that, by choosing a polymer

(PS198-PI88) with a composition close to the sphere-cylinder phase boundary, a small increase in temperature (from 25°C to 35°C) caused a slow, but striking, reversible transition from worm- like fiber-like micelles to spheres as shown in Figure 1.1E [32].

Over the past several years, a large number of publications from the Discher group have explored potential biomedical applications of filamentous micelles in aqueous media. They drew analogies to the shapes of filamentous viruses and argued that such long thin flexible structures would pass more easily through blood capillaries than spherical block copolymer micelles [17]. To characterize their self-assembled structures, the authors used video fluorescence microscopy to visualize individual micelles in which a highly fluorescent hydrophobic dye was dissolved (Figure 1.1F) [33]. Dalhaimer et al. [34] used this technique to compare the flexibility of PB- PEO block copolymer micelles to that of their crosslinked analogs. Persistence lengths were calculated from analysis of sequential images, and this approach was also used to describe stretching of the micelles under flow. These fluorescence images also allowed a histogram to be constructed of the micelle length distribution, for those micelles long enough (contour length L ≥ 2 µm) to be detected by optical microscopy. The histogram they built confirmed the presence of an exponentially broad length distribution, as predicted by the theory of one-dimensional self- assembly [35].

The Discher group has shown that PEO-based wormlike micelles had limited adhesion in flow to cells in human blood, and, by modifying the hydrophilic termini of the diblock copolymers with biotin, these micelles could target specific cells [10]. As model experiments, they showed that hydrophobic drugs can be dissolved in the hydrophobic core of these micelles [36]. Recent experiments employed wormlike micelles constructed from polycaprolactone-PEO

(e.g. PCL58-PEO110) [37]. These micelles, when injected into the tail vein of rats, could circulate in vivo for up to one week, much longer than corresponding spherical micelles. PCL undergoes spontaneous hydrolysis in water. Thus the micelles degraded over time, promoting release of the hydrophobic drug from the carriers. One of the challenges of using PCL for the core-forming block is that, in bulk, PCL is highly crystalline, and, for the applications described above, the micelle core must remain amorphous and fluid.

In a recent study, the Discher group investigated the self-assembly of a set of semicrystalline PEO-PCL diblock copolymers in water by hydration of a chloroform solution of 9 the polymer at room temperature with slow evaporation of chloroform, forming micelles with various morphologies including worm-like micelles [38]. I consider this example here in the “coil-coil block copolymers” section because the authors established that the crystallization of the PCL took place after micelle formation. Micelle morphology was determined by composition features characteristic of coil-coil block copolymers. The subsequent crystallization of PCL affected the self-assembly phase diagram but was not the driving force for the micelle formation. The crystallization of the PCL core was expected to increase the rigidity of the micelles. Interestingly, the authors found that the worm-like micelles obtained were either entirely flexible with dynamic thermal undulations or fully rigid, as visualized directly by video fluorescence microscopy; only a few worms appeared to be rigid at room temperatures, indicating suppression of crystallization by both curvature of the cylindrical core and the presence of water molecules in the PCL core. The authors commented that, for biomedical applications such as delivery of entrapped drugs or flow through the vasculature, the presence of rigid assemblies, even in small numbers, will limit functionality. They avoided this problem by incorporating 10% D,L-lactide within the PCL block. I will revisit this example in Section 1.4.3 when I talk about other examples of PEO-PCL block copolymer micelles reported by a different research group.

Crystallization of the PCL plays a very important role in the polymer self-assembly process [24,39]. Instead of incorporating D,L-lactide within the PCL block to disrupt the crystallinity as reported by the Discher group [38], the same goal could be achieved by introducing tacticity via a pendant substituent. A paper by Hillmyer and Bates [ 40 ] showed that PEO-poly(4- methylcaprolactone) with the proper weight fraction of PEO will form worm-like micelles, and the tacticity introduced by the methyl substituent disrupted crystallization of the core-forming block.

Liu and coworkers have been interested in wormlike micelles from a different perspective. They explored new methods for structure control and the use of these structures as templates, for example, to support catalytically active metal nanoparticles. They focused on triblock copolymers such as poly(t-butyl acrylate-b-cinnamoylethyl methacrylate-b-glycerol methacrylate) (e.g. PtBA107-PCEMA193-PGMA115) [41] and PI-PCEMA-PtBA. Much of their research was designed to take advantage of the photodimerization of cinnamate ester groups. Photoirradiation of fiber-like micelles containing PCEMA as an insoluble block crosslinked the 10 core, providing robust filamentous structures for further transformation [42,43]. These and other examples were described in more detail in the review of nanotube formation published by Liu [44].

The discovery of new structures, particularly those obtained by manipulation of the processing conditions, continues to fascinate scientists interested in polymer self-assembly. One such surprise concerns worm-like micelles of a poly(4-vinylpyridine)-polystyrene triblock copolymer (P4VP43-PS260-P4VP43) in a 4:1 (w/w) mixture of dioxane-water. Yu and Jiang [45] reported that these filamentous structures cyclized to form closed circular structures when subjected to shear, as shown in Figure 1.1G. Another interesting example by Chen et al. [46] reported a simple and continuous production of PS170-PI140 fiber-like micelles using nanopore extrusion-induced transition from spherical micelles.

Figure 1.1. Phase diagrams and selected examples of filamentous micelles formed by coil-coil block copolymers. (A) A phase diagram showing how the shape of the micelles formed by PB-PEO block copolymers in water varies with their composition. The x-axis represents the weight fraction of PEO

(wPEO) in each block copolymer sample. The upper set of points is for a second set of block copolymers that differ by a factor of four in the length (NPB) of the PB block. Different morphologies are denoted by the letters B (bilayers or lamellae), C (cylindrical), CY (cylinders with Y-branches), and N (network).

[23]. (B) A phase diagram showing how the shape of the micelles formed by PS962-PEO227 varies with polymer concentration and solvent composition in dimethylformamide/acetonitrile mixtures [31]. (C) CryoTEM image of a network structure (N, see Figure 1.1A) comprising cylindrical struts that loop and show Y-branches (CY), with bulbous spherical end-caps formed by a PB-PEO sample in water [29]. (D)

TEM image of long fiber-like micelles formed by PS962-PEO227 in a very narrow range of solvent compositions as shown in Figure 1.1B [31]. (E) AFM height micrographs of PS198-PI88 micelles from heptane showing the reversible transition from worm-like micelles to spheres induced by an increase in temperature from 25°C to 35°C [32]. (F) Fluorescence microscopy image of an individual PAA45-PB107 micelle captured at different times, demonstrating the flexibility of the micelles [33]. (G) SEM images of worm-like micelles (left) formed by a P4VP43-PS260-P4VP43 triblock copolymer in a 4:1 (w/w) mixture of dioxane-water, and the closed-circular structures that formed (right) when the solution was subjected to shear [45]. Reprinted from Ref [1,23,29,31,32,33,45] with permission.

12 1.4.2 Rod-coil Block Copolymers

The term rod-coil block copolymer refers to a polymer in which one block has a rigid and elongated shape. This rigidity can be due to π-conjugation along the backbone, or to secondary structure, as for helical polypeptide derivatives. The self-assembly of rod-coil block copolymers in the bulk state and in solution were well described in the review by Olsen and Segalman [47]. Theoretical considerations [48] for rod-coil polymer self-assembly in solution have already been presented in section 1.3.

Figure 1.2A shows the theoretical prediction of the morphology and geometry of the molecular packing of such rod-coil block copolymers, with different rod/coil block ratio [48]. The Lin group used molecular dynamic simulation to simulate the chain conformations in the rod-like micelle formed by PBLG-PEG (PBLG: poly(γ-benzyl-L-glutamate)) block copolymer, where the PBLG is a rigid block. Figure 1.2B shows how such polymer can assemble to form rod-like micelle with the PBLG block adopting a twisted structure with α-helix conformation in the core [26,49].

In thin films, various block copolymers with rigid π-conjugated oligomers or polymer blocks form microphase-separated morphologies consisting of long thin fibers that are thought to arise from π-stacking of the conjugated block. Examples for the conjugated block include oligophenylenevinylene [ 50 ], regioregular poly(3-hexylthiophene) [ 51 , 52 , 53 ], oligo(9,9- dioctylfluorene) [54] and oligo(para-phenyleneethynylene) [55 ]. These oligomers and their corresponding polymers are of particular interest for their optical and electronic properties for uses in light-emitting diodes and flexible conducting plastics, respectively [56].

In contrast, there are very few examples of long, uniform fiber-like micelles formed by these polymers in solution. The classic example of such micelles is that of oligophenylenevinylene attached either to polyethylene oxide (OPV-PEO, PEO-OPV-PEO) [57] (Figure 1.2C) or to poly(propylene oxide) (OPV-PPO) [58]. The function of the two n-hexyl substituents on an alternating backbone of phenylene groups was to lower the melting temperature of the rigid block and enhance its solubility in organic solvents. Even so, the block copolymer with 45 EO units in the PEO block has limited solubility in tetrahydrofuran (THF) and was rapidly self-assembled when small amounts of water were added to a THF solution of the polymer. The structures formed were long nanofibers, with a uniform diameter of the order 13 of 8 nm, an elliptical cross-section and lengths well over 1 µm. Small changes in the structure of the rod block, however, can complicate the self-assembly process. For example, an OPV-PEO block copolymer with different pendant substituents attached to the OPV block, under seemingly similar self-assembly conditions, formed elongated structures that were at most a few hundred nanometers in length [59].

It is not clear at this time why there are so few examples of long fiber-like micelles formed from rod-coil block copolymers in solution. Thus it is noteworthy that two recent reports provided examples where introducing a rigid spacer between two flexible coil blocks can transform the nature of self-assembly from spheres to cylinders [60] or to nanotubes [61]. There are also examples in which the rod block is an α-helix of PBLG. Several different PBLG rod- coil block copolymers formed very long fibers in toluene solution, a solvent selective for the non-PBLG block [62]. The fibers formed were so long that the solutions appeared to gel at polymer concentrations of only 0.3 to 3 wt %. A combination of atomic force microscopy and small angle X-ray scattering established that these structures were in fact ribbons, approximately 2 nm thick, with widths ranging from 10 to 20 nm that depended linearly on the length of the PBLG helix (Figure 1.2D and 1.2E). More recent experiments with a higher molecular weight polymer (PEO1300-PBLG630) in ethanol-CHCl3 mixtures yielded elongated micelles of rather low aspect ratio (ca. 200 nm long, 100 nm wide) which may be short fibers or ribbons [49]. The width of the each ribbon was approximately equal to the length expected for the PBLG helix. Nevertheless, it is difficult to assert at this time which structural features of rod-coil block copolymers and what choice of self-assembly conditions will lead to long fiber-like micelles.

Another important group of rod-coil block copolymers that form fiber-like micelles contains regioregular poly(3-alkylthiophene) as the core-forming block, typically poly(3- hexylthiophene) (P3HT), in which the self-assembly is driven by the π-stacking of P3HT block. The first example that showed the formation of fiber-like micelles by a P3HT block copolymer,

P3HT67-PS183, was reported by McCullough [51]. They obtained nanowires (Figure 1.2F) spaced laterally by 30-40 nm (which corresponds to a fully extended P3HT block), with lengths on the order of several micrometers, in thin and ultrathin films casted from P3HT67-PS183 toluene solution. At that time, these authors were not concerned about whether the P3HT core is crystalline or not. According to a later study [52] about fiber-like micelles formed by other P3HT block copolymers, the P3HT block crystallizes in the core of the micelles. As a result, I 14 believe that the micelles obtained by McCullough [51] and shown in Figure 1.2F had a crystalline core. Nevertheless, I still present the McCullough example in this section. As for other results about fiber-like micelles formed by P3HT block copolymers where the P3HT block is shown to crystallize in the core, I prefer to describe them in the section of crystalline-coil block copolymers although one might still consider them as rod-coil block copolymers. One can see that the distinction between rod-coil block copolymers and crystalline-coil block copolymers can be arbitrary.

A B C

twisted structure D E F PFS38‐PBLG95 ribbons

500 nm 500 nm

Figure 1.2. Drawings and selected examples of filamentous micelles formed by rod-coil block copolymers. (A) Drawing from ref. [48] showing the lamellar bilayer structure predicted for micelles of rod-coil polymers with short corona chains and the corona-chain repulsion that becomes important for polymers with longer corona chains. (B) Drawing from ref. [49] of the core of a twisted-string micelle, showing how the rod blocks align locally but twist in their orientation to allow the corona chains to

minimize their repulsive interactions. (C) TEM image from of fiber-like micelles formed by OPV6-

PEG45 in THF/water mixed solvent [57]. (D) AFM height mode image of PFS38-PBLG95 nanoribbons (obtained from a 0.1 wt % gel solution in toluene, a good solvent for PFS [62]. (E) A schematic representation of this nanoribbon structure (2 nm high) in which 14.2 nm indicates the calculated length

of the PBLG helix. (F) AFM phase mode image of a thin film of P3HT67-PS183 fiber-like micelles, casted from toluene solution [51]. Reprinted from Ref [1,48,49,51,57,62] with permission.

15 1.4.3 Crystalline-coil Block Copolymers

In this section, I focus upon block copolymers that form fiber-like micelles with a crystalline core. Early examples of self-assembly of crystalline-coil block copolymers in solution described the formation of raft-like planar structures [27,63,64]. In these examples, the crystalline block was PEO (crystalline in hydrocarbon solvents) or polyethylene, and the results were consistent with the theoretical model described in section 1.3. An overview of crystalline- coil block copolymers will be presented in more detail compared to the previous sections because my doctoral research focuses on understanding of the behavior of fiber-like micelles formed by the self-assembly of one family of crystalline-coil block copolymers, the poly(ferrocenyldimethylsilane) (PFS) block copolymers.

1.4.3.1 PFS Block Copolymers

The study of fiber-like micelles formed by self-assembly of PFS block copolymers in solution dates back to 1998 [65], from the collaboration of the Manners and Winnik research groups. Their early papers have shown that a number of PFS block copolymers, including

PFS50-PDMS300 [65], PFS75-PDMS370 [66] and PI320-PFS53 [67], formed long uniform fiber-like micelles in alkane solvents (e.g. Figure 1.3A) for a broad range of polymer compositions and block ratios that one expected to form spherical micelles [ 68 ]. This surprising result was attributed to the semicrystalline nature of the PFS core. The most telling evidence that crystallinity played an important role in the formation of these fiber-like structures came from wide-angle X-ray scattering (WAXS) measurements that showed Bragg peaks (Figure 1.3B) [69]. These corresponded to the peaks in the spectrum of the semicrystalline PFS homopolymer [70]. Further evidence that the crystallization of the PFS core was crucial for the formation of fiber-like micelles was the observation that other poly(ferrocenylsilane) block copolymers (e.g. PFMES-PDMS, PFMES = poly(ferrocenyl-methyl-ethyl-silane)) only formed spherical micelles [66], where the ability to crystallize of the core-forming block was destroyed by the asymmetric substituents on the silicon atom.

To describe those self-assembly processes for which the crystallization of the core-forming block is the driving force for micelle formation, we use the term “crystallization-driven” self- assembly (CDSA). For some micelle systems, crystallization of the core block is observed but takes place after the micelles are formed. We do not consider this as CDSA, because 16 crystallization is not the driving force for self-assembly. One important example has been reported by the Discher group [38] for the fiber-like micelles formed by PCL-PEO block copolymers. This example was described above in the coil-coil section of this chapter. In this example, the PCL block crystallized after micelle formation.

Since the PFS block forms semicrystalline domains in the core of the micelles, an important consideration is the shape of the cross section of the micelles formed by these PFS block copolymers. Previous report by Lotz and Kovacs [71] showed that block copolymers with a PEO crystalline block formed raft-like lamellar micelles. Such plate-like or ribbon-like structures have also been observed for PFS block copolymer micelles when the soluble PI or PDMS block was equal to or shorter than the PFS block (Figure 1.3C, [67]). For plate-like or ribbon-like micelles, the shape of the cross section can be portrayed as in Figure 1.3D. However, when the PI or PDMS block was much longer than the PFS block, fiber-like micelles were formed. The long corona chains must impose curvature on the micelle structure, affecting the morphology of the micelle core. From the fiber-like structures as seen from the TEM image (Figure 1.3A), a rectangular or circular cross section is possible, as illustrated in Figure 1.3D. We have evidence about the cross section shape of PFS micelles for only one example reported by Wang et al. [72]. They prepared PI250-PFS50 micelles in hexane solution and then chemically cross-linked the PI corona via a Pt-catalyzed hydrosilylation reaction to improve the stability of the micelles. A film formed by these micelles with a cross-linked corona could be microtomed without destroying the original morphology. A TEM image of the cryosectioned micelle sample in Figure 1.3E shows a circular cross section of these micelles. However, I think this result is not convincing due to the poor contrast of the TEM image. In my thesis, I will show some width distribution analysis from TEM images with high magnification of the PFS block copolymer micelles, which might provide further insight about the morphology and structure of the micelle cores.

In 2007, Wang et. al. [73] reported the most remarkable feature of these fiber-like PFS micelles. This paper showed that the rod-like PFS block copolymer micelles can be extended in length when additional polymer, dissolved in a small amount of common solvent, was added to a solution of the micelles in a selective solvent. Micelles present in the solution acted as seeds for the epitaxial deposition of the newly added PFS block copolymer. For example, addition of

PI320-PFS53 in THF to a solution of its micelles (Ln = 96 nm, Lw/Ln = 1.49) in decane caused the 17 micelles to grow longer (Figure 1.3F). The authors examined micelles of PI264-PFS48 in decane using static light scattering and found that the micelle length increased linearly with the amount of added polymer, whereas the mass per unit length, deduced from multiangle static light scattering measurements, remained constant (Figure 1.3G). We sometimes refer to this growth process as “living self-assembly”, analogous to classical angstrom-scale living polymerization reaction. This seeded growth process is unprecedented for polymer self-assembly and emphasized the crystallization-driven nature of the self-assembly. The living growth mechanism predicts that PFS block copolymers with a chemically different coil block could grow from the ends of existing micelles to generate a new kind of self-assembled structure, a three-block comicelle. For example, these authors [73] also showed the growth of PFS-PDMS cylinders and PFS-PMVS cylinders (PMVS, poly(methylvinylsiloxane)) from both ends of PI-PFS rod-like seed micelles. I am particularly interested in the growth kinetics of this living self-assembly process, and as a result, I chose this topic as part of my doctoral research.

In 2007, Wang et. al. [74 ] reported the synthesis of PFS-P2VP (P2VP = poly(2- vinylpyridine)) block copolymers, which underwent self-assembly in alcohol solvents to form micelles with a PFS core. The PFS-P2VP block copolymer micelles also display the seeded growth feature [ 75 ]. The authors first prepared fiber-like PFS17-P2VP170 block copolymer micelles in 2-propanol and then partially methylated the P2VP corona to introduce positive charges in the corona. After that, more PFS17-P2VP170 polymer dissolved in THF was added into seeds micelles, which were obtained by sonicating the quaternized micelles, to grow from the pre-existed micelles. In this way, an A-B-A triblock structure bearing spatially controlled corona charge was obtained. When these triblock co-micelles in aqueous 2-propanol were treated with anionically charged gold nanoparticles, the particles became bound only to the cationically charged middle block, as shown in Figure 1.4A.

PI -PFS A PI320-PFS53 B 6.42 C 30 60

PI320-PFS53 Intensity

250 nm 250 nm 2θ 10 20 30 E PI250-PFS50 D Ribbon-like Rectangular Circular

60 nm

900 G F PI320-PFS53 TEM 600 SLS

300

500 nm Length (nm) 500 nm 0 00.4 Conc. (mg/mL)

Figure 1.3. Selected examples of filamentous micelles formed by PFS block copolymers I. (A) TEM image of PI320-PFS53 micelles from THF/hexane mixture (2/8, v/v) showing their rod-like structure [67]. (B) WAXS spectrum of a film of these micelles [69]. (C) TEM image of raft-like micelles formed by

PI30-PFS60 from THF/hexane mixture (3/7, v/v) [67]. (D) Schematic drawing showing the possible shapes of the cross section of the PFS block copolymer micelles. When the soluble blocks are very short, the PFS chains prefer folded lamellar structure in the crystalline core of raft-like micelles, with a ribbon-like cross section. When the soluble blocks are long, the curvature imposed by corona chain repulsion leads to rectangular or spherical cross section of the PFS crystalline core. (E) TEM image of a cryosectioned sample of a film of PI250-PFS50 micelles in which the corona chains were chemically cross-linked [72].

(F) TEM images showing the seeded growth of the fiber-like micelles of PI320-PFS53, when more polymer dissolved in THF was added to sonicated PI320-PFS53 micelle seeds (left), longer micelles were obtained

(right) [73]. (G) Plot of the number average length Ln of PI264-PFS48 micelles formed by adding additional polymer dissolved in THF to a solution of seed micelles in decane; SLS refers to values obtained by static light scattering [73]. Reprinted from Ref [1,67,69,72,73] with permission.

19 There are interesting similarities in the fiber growth process of PFS block copolymer micelles and amyloid protein fibers. Both types of structures are formed by a nucleated growth mechanism [16,73], and they grow bidirectionally from seed nuclei formed by sonication [14,75]. The protein fibers are relatively rigid and easily fractured into short pieces by sonication. Perhaps the most important lesson to be learned by comparing these different entities comes from the fact that while both types of structures are similar in overall length and stiffness.

One of the striking features of the triblock PFS17-P2VP170 co-micelles shown in Figure 1.4A is the resemblance to amyloid fibers shown in Figure 1.4B by Lindquist et. al. [14]. These authors used amyloid fiber formed by NM region (N: N-terminal; M: middle), the prion-determining region of the Sup35p protein from the yeast Saccharomyces cerevisiae, and decorated seed NM fibers (top figure in Figure 1.4B) with gold nanoparticles to demonstrate that amyloid fiber growth for this system is primarily bidirectional, with soluble macromolecules condensing at both ends of preformed fibers (two bottom figures in Figure 1.4B).

One of the most remarkable achievements of the Manners-Winnik collaboration was finding conditions to obtain micelles with a very narrow length distribution [76]. The seeded growth of PFS fiber-like micelles begins with micelle solutions that are sonicated to produce short fragments, used as seeds for epitaxial micelle growth. In order to obtain micelles with a very narrow length distribution, Gilroy et al. [76] prepared very small uniform PFS28-PDMS560 crystallites (Ln = 23 nm, Lw/Ln = 1.04, Figure 1.4C) as seed initiators by using intense or prolonged sonication. Intense sonication was necessary because the fracture rate of the fiber-like micelles was shown to be very sensitive to fiber length L (increasing as L2.6) [77]. After addition of PI550-PFS50 polymer dissolved in THF into a solution of uniform seed micelles in hexane, monodisperse (Lw/Ln ≈ 1.01) nanoscale fibers of variable lengths (between 200 nm to 2 mm) were obtained (Figure 1.4D). Figure 1.4E shows the plot of micelle length versus the unimer-to- seed ratio, which indicates that in their self-assembly conditions, 100 % of the additional PI550-

PFS50 polymer added uniformly onto the existing PFS28-PDMS560 seed micelles. I would like to comment that this is a fantastic result with regards to the fine control of one-dimensional nanoscale structure.

Another example showing that the Manners and Winnik groups have achieved precise control over the one-dimensional micelle structure was reported in 2011 [78], when they made fiber-like micelles with a light-emitting “barcode” structure. He et. al. [78] used the uniform 20 fiber-like micelles (Ln ≈ 500 nm) formed by a triblock copolymer PFS30-P2VP300-PDEHPV13 (PDEHPV = poly(2,5-di(2’-ethylhexyloxy)-1,4-phenylvinylene) [ 79 ] in 2-propanol as a precursor, then sequentially added controlled amount of diblock copolymer PFS30-P2VP300, and, at intervals of 24 hr, added additional aliquots of PFS30-P2VP300-PDEHPV13, PFS30-P2VP300 and PFS30-P2VP300-PDEHPV13. In this way, uniform fiber-like multiblock co-micelles up to 6 μm long were obtained. What is special about this co-micelle structure is that the PDEHPV block is highly fluorescent with a quantum yield near 20 %. This characteristic of PDEHPV block enabled the co-micelles to be visible under laser confocal fluorescence microscopy, showing a banded light-emitting “barcode” structure with fluorescent segments of triblock copolymer (PFS30-P2VP300-PDEHPV13) separated by non-emissive segment made up of the diblock copolymer (PFS30-P2VP300) in 2-propanol (Figure 1.4F, [78]).

In addition to rod-like micelles, platelet micelle can also be used as seeds for the growth of the PFS fiber-like micelles. For example, Gädt et. al. [80] showed that the growth of the PI342-

PFS57 fiber-like micelles could be initiated from the exposed PFS edge of the plate-like structure formed by PI76-PFS76, resulting in scarf-like structures as shown in Figure 1.4G.

The living growth of the PFS block copolymer micelles via epitaxial crystallization of the PFS block has also been extended to heteroepitaxial growth. Gädt et. al. [80] showed that a polyferrocenylgermane (PFG) block copolymer, PI336-PFG59 with a core block different from

PFS, could grow uniform fiber-like micelles from the ends of PI342-PFS57 seeds in hexane

(Figure 1.4H) or from the exposed PFS edge of PI76-PFS76 platelets, also forming a scarf-like structure (Figure 1.4I). What is impressive about this result is the uniformity of the PI-PFG structures formed from the heteroepitaxial growth. In the absence of the PI-PFS seeds, PI336-

PFG59 in alkane solvents self-assembled to give elongated but irregularly shaped micelles. This result emphasizes the importance of epitaxial crystallization in the self-assembly process.

Very recently, Rupar et. al. [81] extended the state of the art of CDSA of PFS block copolymers to non-centrosymmetric cylindrical micelles by unidirectional growth. The authors first prepared uniform cylindrical micelles formed by PFS60-PDMS660 (Ln ~ 150 nm) in hexane and then added a concentrated THF solution containing PI1424-PFS63 polymer. The process yielded uniform B-A-B type cylindrical block co-micelles. The PI corona was then cross-linked by Karstedt’s catalyst to inhibit the CDSA process from the two ends of the B-A-B triblock co- micelles. Afterwards, the authors removed the center PFS60-PDMS660 block by dispersing the 21 triblock co-micelles in a decane/toluene mixture (v/v 3/5), forming uniform cross-linked PI1424-

PFS63 micelles (Ln ~ 130 nm). Upon removal of the toluene from the solution through selective evaporation, the dissolved PFS60-PDMS660 unimers grew back onto only one side of the cross- linked PI1424-PFS63 micelles, presumably off the end that was originally bound to the PFS60-

PDMS660 domain. In such way, a non-centrosymmetric structure: A-B diblock co-micelles were obtained. A representative TEM image of these A-B diblock co-micelles are presented in Figure 1.4J. The A-B diblock co-micelles were also active for further CDSA. For example, by adding a 2-propanol solution containing a third different block copolymer PFS-P2VP into the A-B diblock co-micelles, the authors obtained non-centrosymmetric A-B-C triblock co-micelles. The obtained A-B-C triblock co-micelles were later shown to self-assemble into hierarchical supermicelles. Pochan [82] commented on these methods developed by Rupar et. al. to be “well beyond self-assembly” and “ The combined use of covalent chemistry, crystallization, and partial dissolution, in addition to self-assembly and directed assembly, is an example of a new hierarchical paradigm for soft nanomaterial solution construction”.

The research described above serves as background to my Ph.D research. What interested me about this system was the idea of trying to develop a deeper fundamental understanding of living crystallization-driven self-assembly. When I started my research, there were many questions without answers. For examples, what is the growth kinetics of these fiber-like micelles? How will these fiber-like micelles behave when they are exposed to external stimuli, e.g. different solvent composition, temperature variation? Is there any alternative way to control the length of these fiber-like micelles? I started my Ph.D. research with the motivation trying to answer some of these questions, and I hope my work will contribute to the further understanding of this system. 22

A PFS17-P2VP170 B Seeds C PFS28-PDMS560

Au NPs

100 nm 500 nm 100 nm

D PI550-PFS50 F 2000 E (nm) 1000 Length 0 500 nm 0 20 40 2 μm munimers/mseeds

G H I PI -PFG J PI342-PFS57 336 59 PFS60-PDMS660 PI76-PFS76

PI1424-PFS63 PI76-PFS76

500 nm 500 nm 200 nm 500 nm

Figure 1.4. Selected examples of filamentous micelles formed by PFS block copolymers II. (A) Gold nanoparticle-decorated PFS17-P2VP170 micelles demonstrating micelle growth by condensation of new polymer, added as in THF solution to partially quaternized seeds micelles [75]. (B) Gold nanoparticle- decorated amyloid fibers demonstrating amyloid fiber growth by condensation of protein onto the ends of the central seed segments (the top figure) [14]. (C) Very small monodisperse PFS28-PDMS560 as seeds for preparation of monodisperse micelles [76]. (D) Monodisperse PI550-PFS50 fiber-like micelles grown from uniform seeds in (C) [76]. (E) Plot of number average length Ln of PI550-PFS50 micelles grow from the small monodisperse seeds as shown in (C) versus the unimer-to-seed ratio [76]. (F) Laser confocal fluorescence microscopy image of 9-segment barcode co-micelles formed by sequential addition of

PFS30-P2VP300 (dark) and PFS30-P2VP300-PDEHPV13 (fluorescent) in 2-propanol [78]. (G) Scarf-like micelles from addition of PI342-PFS57 to platelet micelles of PI76-PFS76 [80]. (H) PI336-PFG59 micelles grown in hexane from PI342-PFS57 seed micelles [80]. (I) Scarf-like micelles obtained by the heteroepitaxial growth of PI336-PFG59 from PI76-PFS76 plates [80]. (J) Non-centrosymmetric A-B diblock co-micelles, forming by the growth of PFS60-PDMS660 from cross-linked PI1424-PFS63 [81]. Reprinted from Ref [1,14,75,76,78,80,81] with permission. 23 1.4.3.2 Non-PFS Block Copolymers

Since our publication in Science in 2007 [73], a number of other research groups have reported the examples of fiber-like micelles formed by other crystalline-coil block copolymers.

As I mentioned above in the rod-coil section of this chapter, block copolymers containing a P3HT block can also self-assemble to from fiber-like micelles in solution. However, the McCullough group [51], who showed the first example of fiber-like micelle formation by a

P3HT67-PS183 block copolymer, did not comment on the crystalline structure of the P3HT core. In this section, I start by revisiting several recent examples of the formation of fiber-like micelle by P3HT block copolymers, in which the micelles have a crystalline core. Most importantly, it appears that the crystallization of the P3HT block is the driving force for the self-assembly process.

In 2011, Winnik and Manners [52] reported the formation of fiber-like micelles by

P3HT48-PDMS550 in a toluene-ether mixture (Figure 1.5A). These micelles had a crystalline P3HT core, confirmed by DSC and WAXS measurements. The prominent feature of their system was that when more polymer dissolved in toluene was added into the sonication- shortened micelles (Ln = 38 nm) in a mixed toluene-ether solution, longer micelles with a narrow length distribution were obtained. These results indicate a living CDSA process. The evidence showing that the P3HT48-PDMS550 micelle formation was driven by the crystallization of the P3HT block was acquired from the UV-vis absorption spectra of the micelle solution, which showed significant red shift in the absorption maxima (475-505 nm) relative to a solution of P3HT48-PDMS550 unimers (450 nm) (Figure 1.5B); moreover, the appearance of low energy absorption bands in the 600-625 nm region was indicative of crystalline P3HT aggregates in solution. As a result, one can monitor the crystallization of P3HT using UV-vis spectra. However, there is much more that needs to be understood for this system. For example, their control of micelle length was limited to around 300 nm; and their data showed that the efficiency of the micelle growth process was very low, only ca. 5 % of the newly added polymer grew onto the ends of the existing micelles. The fate of the rest 95 % of the unimers that have been added remained unknown.

Another recent example concerning P3HT block copolymers was reported by Emrick and Hayward [53] on the helical nanowires of all-conjugated polythiophene diblock copolymers. In 24 their diblock copolymers, one block of the diblock polymer had nonpolar (hexyl) side chains (P3HT), while the other block had polar (triethylene glycol, TEG) side chains (P3(TEG)T). The large contrast in solubility between the two blocks made it possible for the block copolymer to self-assemble into fiber-like micelles in methanol, as a polar selective solvent. Interestingly, in the presence of the salt KI in the system, the complexation of K+ ions with the TEG side chains drove the formation of helical ribbons, which further associated into superhelical structures, single-, double-, and multi-stranded helices (Figure 1.5C). According to many classification systems, since the both blocks are rigid conjugated polymer, it seems more reasonable to refer to them as “rod-rod” block copolymers. However, in the reported system, the P3(TEG)T block is soluble in methanol and might show similar behavior to that of a normal coil block.

The Park group [83] investigated the self-assembly of a series of P3HT20-PEO block copolymers in water and methanol. The PEO chains in these polymers had 16, 48, and 108 EO units. Interestingly, all these block copolymers were shown to form fiber-like micelles regardless the length of the PEO block, but the length of the micelles obtained depended on the length of the PEO block; the shorter the PEO block, the longer the micelles that were obtained. These results suggest that the packing of the P3HT block was the driving force for the self- assembly. The authors also showed that the packing structure and properties of the P3HT in the micelles were not affected significantly by the variation of the PEO block length. The P3HT- PEO fibers were then further used as building blocks to form hierarchical assemblies of nanofibers. By adding P3HT20-PEO48 block polymers to preformed P3HT200 homopolymer nanofibers in anisole, followed by the addition of water, micelles with branched superstructures were obtained (Figure 1.5D).

In the coil-coil section of this chapter, I presented several examples of fiber-like micelles of PCL-PEO block copolymers reported by the Discher group [37,38]. I also mentioned that the Discher group believed that the crystallization of the PCL block subsequent to the self-assembly interfered with drug delivery applications, because the crystallization of the PCL core introduced rigidity to the micelles.

In this section, I present other examples from the Xu group [39,84] showing fiber-like micelles formed by PCL-PEO block copolymers, where the PCL block crystallized in the micelle core. The authors examined the self-assembly of a series of PCL-PEO block copolymers in aqueous solution and observed a variety of different morphologies as the block ratio was 25 varied. They reported that for a subgroup of the PCL-PEO block copolymers with the PEO repeat unit fixed at 44, the micellar morphology changed from spherical, rod-like, fiber-like, to lamellar, as the length of the PCL block increases. Figure 1.5E shows a TEM image of fiber-like micelles of PCL59-PEO44 with a crystalline PCL core. These authors later [84] showed that the micellar morphology can also be affected by the crystallization temperature, for example, at a higher crystallization temperature, spherical or fiber-like micelles with large aspect ratio were formed, while lamellar and cylindrical micelles with small aspect ratio were preferred at a lower crystallization temperature.

In the Xu’s example, although the crystallization of the PCL block has been shown to play an important role in determining the structure and morphology of the micelles, I would like to offer my opinion that crystallization was not the driving force for the micelle formation. I am convinced about the fact that PCL block formed crystalline domains in the micelle core, as established by the electron diffraction pattern [39]. Nevertheless, in Xu’s study, when the block ratio of the PCL-PEO polymer was varied, a full phase diagram of spheres/rods/worms/lamella transformation was obtained, pure worm-like micelles were only obtained for one polymer composition. These results suggest that the micelle morphology was strongly influenced by the composition characteristics of the block copolymer, rather than dominated by one factor, the crystallization of the PCL block. In my opinion, if the formation of the worm-like micelles was crystallization-driven, worm-like micelles should have been obtained for a broader range of polymer compositions. As a result, I believe that in the examples reported by the Xu group, the micelle formation of PCL-PEO polymers was not driven by the crystallization of the PCL block, and that the crystallization happened after micellization.

The Lazzari group has been interested in block copolymers containing a polyacrylonitrile (PAN) block. PAN is unusual because it is an atactic polymer that has crystalline-like properties in the solid state. Lazzari and coworkers reported that PAN-PS (Figure 1.5F) and PAN-PMMA formed long fiber-like micelles in solvents selective for PS or PMMA [85,86]. For these PAN block copolymers, the change of the block ratios in the PAN/PS (or PMMA) from 1/3 to 1/13 was shown to have little effect on the micelle shape, implying a CDSA process [85]. Interestingly, the authors showed that the micelle length could be changed using by different solution conditions. For example, direct dissolution of PAN20-PS177 in the selective solvent chloroform resulted in short rod-like micelles (100-200 nm). In contrast, slow addition of the 26 chloroform to the polymer PAN20-PS210 in DMF solution led to the formation of much longer worm-like micelles. The Lazzari group took advantage of a special property of PAN, which itself is carbonized upon pyrolysis in a vacuum, and showed that filamentous PAN20-PS210 micelles formed carbon nanofibers when pyrolyzed, a very impressive result [86]. Lazzari has recently reviewed their work with details in the context of crystalline-coil block copolymers [87].

Stereoregular poly(lactic acid), sometimes called polylactide (PLA), is a semicrystalline polymer. Both poly(L-lactic acid) (PLLA) and poly(D-lactic acid) (PDLA) are semicrystalline polymers, and have the unusual property of forming a 1:1 crystalline complex in solution. Portinha et al. found cylindrical micelles formed by a co-crystallization process when they mixed a block copolymer containing a poly(L-lactic acid) block (PLLA36-PCL59) with a similar polymer (PDLA42-PCL69) containing a poly(D-lactic acid) block in THF (Figure 1.5G) [88].

Another example of one-dimensional micelles formed by PLA-containing block copolymers was reported recently by the O’Reilly’s group [89]. The authors showed that the direct dissolution of PAA-PLA (PAA = poly(acrylic acid)) containing enantiopure homochiral poly(lactide) (e.g. PAA220-PDLA42 or PAA265-PLLA32) in water resulted in rod-like micelles with a semicrystalline PLA core. While in contrast, block copolymers PAA240-PLA33 containing amorphous atactic PLA cores only formed spherical micelles. This indicates a CDSA process. These authors also showed that they could vary the length and dispersity of the cylindrical micelles by using different dissolution temperatures for the micelle formation; however, their control of length was limited to the range from tens of nanometers to ca. 200 nm.

Earlier in this chapter I mentioned early experiments on polyethylene-containing diblock copolymers [63,64]. These polymers formed plate-like micelle with a semicrystalline PE core.

Recently, Schmaltz and coworkers have looked at micellization of a triblock copolymer PS39-

PE21-PMMA40 with a PE middle block. This samples formed fiber-like micelles with a patchy corona of PS and PMMA (Figure 1.5H) [90]. In a more recent publication [91], they provided a thorough investigation of the fundamental parameters influencing the self-assembly process of both a symmetrical ABA (PS380-PE880-PS390) and a non-symmetrical ABC (PS340-PE700-

PMMA360) block copolymers. The authors showed that they could selectively produce either spherical or worm-like crystalline-core micelles (Figure 1.5I, [91]) from the same block copolymer by tuning the solvent quality. In dioxane, a poor solvent for PE, the PE blocks 27 collapsed upon cooling, forming spherical micelles with an amorphous core that later crystallized. Under these conditions, the PE crystallized in the pre-formed spherical confinement. Thus this was not a CDSA process. However when experiments were carried out in toluene, a good solvent for the PE block, the block copolymer chains were molecularly dissolved above the crystallization temperature. Upon cooling, worm-like micelles with a crystalline core were formed through a nucleation and growth mechanism (a CDSA process), with the length controlled by the crystallization temperature.

In the same paper [91], Schmaltz and coworkers used light scattering to study the formation kinetics of the PS340-PE700-PMMA360 fiber-like micelles in toluene (Figure 1.5I). They first heated the concentrated polymer toluene solution (2 g/L) to 80 °C to ensure complete melting of the PE blocks. After cooling to the desired crystallization temperatures, they monitored the scattering intensity of the polymer solutions as a function of time. They showed that the scattering intensity increased as the micelle formation proceeded until a plateau was reached, indicating complete micelle formation. However, they only extracted qualitative information from the light scattering data. Quantitative analysis needs additional parameters such as the particle form factor. This is not easy to obtain for their system.

The growing number of examples in which fiber-like micelles are formed by CDSA of block copolymers emphasizes the need for a deeper theoretical analysis of this process. My goal in this thesis is to look at some of the underlying physics behind the self-assembly process of crystalline-coil block copolymers. I hope that my work will contribute to the progress of understanding in field.

1.0 509 nm A P3HT48-PDMS550 B C 0.8 450 nm 0.6

0.4 607 nm

0.2 Absorbance

0.0 500 nm 400 500 600 700 200 nm Wavelength (nm)

D E PCL59-PEO44 F PAN 20-PS210

200 nm 200 nm 500 nm

G H I

200 nm 200 nm 200 nm

Figure 1.5. Selected examples of filamentous micelles formed by non-PFS crystalline-coil block copolymers. (A) Fiber-like micelles of P3HT48-PDMS550 formed in 85% (v/v) Et2O/toluene solution

[52]. (B) UV-vis absorption spectra of free P3HT48-PDMS550 unimers (blue line) in toluene and

P3HT48-PDMS550 micelles formed in 85% (v/v) Et2O/toluene solution (red line) [52]. (C) Multi- stranded helices structure formed by the association of self-assembled P3HT34-P3(TEG)T12 fiber-like micelles in methanol with the presence of KI salt. Inset: TEM image and schematic showing association of double helices into quadruple superhelices (scale bar, 100 nm) [53]. (D) Branched structure composed of P3HT200 nanofibers decorated with longer P3HT20-PEO48 nanofibers formed at a molar ratio of 250:1 (P3HT20-PEO48/ P3HT200) [83]. (E) PCL59-PEO44 micelles from aqueous solution in which the PCL core chains crystallized [39]. [F] TEM image of PAN20-PS210 fiber-like micelles formed in chloroform solution [85]. (G) Tapping mode AFM image of rod-like micelles formed by a co-crystallization process in a mixture of PLLA36-PCL59 and a similar polymer PDLA42-PCL69 in

THF, spin-coated on a silicon wafer [88]. (H) Fiber-like micelles formed in toluene solution by PS39-

PE21-PMMA40 [90]. (I) Fiber-like micelles formed in toluene solution by PS340-PE700-PMMA360 [91].

Reprinted from Ref [1,39,52,53,83,85,88,90,91] with permission. 29 1.4.4 Nanofibers from Disk-like Building Blocks and Other Examples

A number of impressive recent descriptions of filamentous micelle formation involve polymers that do not fit neatly into the three categories described above [92-95]. The research groups of Pochan and Wooley are engaged in an ongoing collaboration to explore ways of creating block copolymer micelles with internal structure or with unusual periodic shapes. Many of these experiments involve poly(acrylic acid)-poly(methyl acrylate)-polystyrene (PAA-PMA- PS) triblock copolymers, often in the presence of various concentrations of diamines. The PS block is hydrophobic. The PAA block is hydrophilic, especially when complexed with diamines, and the PMMA block is a spacer of intermediate polarity. This combination offers many degrees of freedom with which to explore a complex self-assembly landscape. For example, when

PAA94-PMA103-PS44 in THF was treated with 2,2'-(ethylenedioxy)diethylamine (EDDA, one amine per carboxylic acid group) followed by the addition of water, fiber-like micelles formed with the unique nanostructures shown in Figure 1.6A. The periodic stripes perpendicular to the fiber axes indicate alternating layers of hydrophilic PAA/EDDA complex and hydrophobic PMA-PS domains [22,93]. This unusual structure can be thought of as formed from face-to-face assembly of disk-like building blocks (Figure 1.6B). Alternatively, with triethylenetetramine in combination with PAA94-PMA103-PS88 at a much higher ratio of amine to acid (15:1) at the same water content, single-stranded or double-stranded helical micelles with extremely regular superstructures were obtained [94]. Recently, Pochan and coworkers [95] investigated the solution assembly of a blend of unlike block copolymers (PAA-PS and PAA-PB, PS dislikes PB), with the presence of EDDA. Relying on kinetic trapping of the two polymers into the same nanoparticles, the authors not only made nanoparticles with multiple internal compartments of a desired size, but also made nanoparticles of hybrid geometries (a blend of cylindrical and spherical geometries). Other examples of micelles that have the shapes of twisted cylinders [96] and of double helices and triple helices [92] have been reported by Liu and coworkers.

Worm-like micelles have also been reported to form from self-assembly of a cyclic diblock copolymer. Minatti et al. synthesized a heterodifunctional linear PS290-PI110, and, through a chemical reaction between the end-groups, produced a cyclic polymer with the same degree of polymerization as the linear precursor [97,98]. In heptane solution, over a range of different polymer concentrations, the linear polymer formed spherical micelles with a PS core. The cyclic polymer also formed aggregates at low concentrations (0.1, 1 mg/ml) that appeared circular in 30 AFM images. At 5 mg/ml, relatively stiff fiber-like micelles formed (Figures 1.6C and 1.6D). The authors speculated that the circular objects seen at low concentration are ‘sunflower micelles’ that stack at higher concentrations to form nanofibers.

As I have mentioned in Section 1.2, kinetic factor plays an important role in the self- assembly process of block copolymers. Due to kinetic obstacles, trapping of metastable species can occur, preventing well-defined solution of low polydispersity on an appropriate time scale. Inspired by the precise folding of peptides in biology, which involves prefolded intermediates before furnishing monodisperse proteins, Müller and coworker recently [99] reported a precise hierarchical self-assembly of multicompartment A-B-C triblock copolymer micelles (e.g. PS- PB-PMMA). Such precise control was achieved by a step-wise restriction of the degrees of freedoms along a directional energy landscape. Using suitable solvents (N,N-dimethylacetamide, non solvent for PB), the authors first constructed well-defined micellar subunits with a collapsed but dynamic B core and a mixed corona of blocks A/C (first reduction of conformation freedom). Afterwards, by lowering the solvent quality for block A (dialysis against a acetone/2-propanol 60/40 v/v mixture), these subunits serve as bricks for the next-level assembly into various well- defined spherical micelles with A core, B patches and C corona (second reduction of conformation freedom). Interestingly, the authors defined conditions for which cylindrical micelles with alternating A and B segments form via step-growth polymerization from spherical micellar subunits (Figure 1.6E). Their work represents a milestone for the rational design of new generations of tunable and functional multicompartment solution-based hierarchies. 31

A C E

50 nm

200 nm 200 nm (ABA)2

B anisotropic D 40 nm growth (ABA)x

50 nm

> 1 µm

Figure 1.6. Selected examples of filamentous micelles formed by disk-like building blocks. (A) TEM image of uranyl acetate stained PAA94-PMA103-PS44 micelles from 67% THF/water solution in the presence of EDDA (1:1mole ratio of amine to acid groups) [93]. (B) Schematic drawing of the nanofiber micelle cross section and the growth mechanism. The PMA-PS stripes are illustrated as gray and dark blue bands. Light blue bands denote the PAA concentrated area. This fiber structure is formed by stacking of disk micelles. (C) Tapping mode AFM image of fiber-like structures formed by cyclic PS290-

PI110 in heptane at c = 5 mg/mL [97]. (D) Schematic drawing showing that linear PS290-PI110 forms spherical micelles, whereas the cyclic polymer forms sunflower micelles that stack to form the elongated structures. [E] Schemes and TEM images showing the colloidal polymerization of PS283-PB596-PMMA304 micellar subunit into segmented worms [99]. PS grey, PB black and PMMA not visible. Reprinted from Ref [1,93,97,99] with permission.

1.5 Summary

Fiber-like or filamentous micelles formed by block copolymers are promising nanoscale, cylindrical core-shell materials with a range of potential applications. A key asset is their relative stability. For example, they are often resistant to dissociation at high dilution and can be fabricated by standard solution processing methods such as evaporative spin-coating. Moreover, using core or corona crosslinking strategies, access to cylinders with controlled flexibility and swellability, and even complete stability in common solvents for both blocks, can be achieved [28,72]. These features help explain much of the current intense interest in their applications in both biotechnology and nanoscience.

Significantly, in the past few years, a series of key and complementary preparative advances have been reported that offer potentially profound improvements in the ability to control the structure of fiber-like micelles. For example, cylinders with a crystalline core have been shown to undergo extension reactions that allow control of fiber length and the formation of segmented ‘block comicelle’ architectures. There are similarities between this micelle growth mechanism and that of protein fibers that need to be better understood. Although this type of growth has only been demonstrated for a limited range of synthetic polymers, broader applicability to other systems with potentially crystallizable core-forming blocks appears highly likely. For example, as it is already feasible for one to control the preparation of fiber-like micelles from polymers in which the core-forming block were a conducting polymer such as P3HT [52], one would have a colloidal suspension of nanowires that could be incorporated into microelectronic devices by liquid processing conditions such as microfluidics or spin coating.

Other approaches, such as the use of kinetic control, pre-assembly in bulk, and segregation of polymer chains in the micelle corona have been shown to permit access to a range of remarkable, periodic and asymmetric fiber-like structures [73,80,93,100]. The ability to create structures with controlled length and narrow size dispersity, tunable flexibility and spatially defined functionality should offer many new and diverse opportunities in the future for both improved performance and also new applications. 33 1.6 Research Objectives and Thesis Outline

I came to University of Toronto to join Prof. Mitchell A. Winnik’s group in 2008 after I obtained my master degree in Physical Chemistry from Nanjing University in China. With my physical chemistry background, I was asked to learn the light scattering technique and focus on the physical aspects of the self-assembly process of PFS block copolymers in solutions.

This thesis contains seven chapters.

In Chapter 2, I describe the general experimental details for my doctoral research, including the materials, solvents, instrumentation, and general image analysis method to obtain the length distributions of micelles from TEM images. I also describe a general experimental protocol for the seeded growth of PFS block copolymer micelles.

In Chapter 3, I report the solvent-induced fragmentation of the fiber-like PI1000-PFS50 block copolymer micelles and a solvent composition supersaturated for the micellization.

In Chapter 4, I describe how I used the solvent combination as found in Chapter 3 to study the growth kinetics of the PI1000-PFS50 fiber-like micelles using light scattering.

In Chapter 5, I present an alternative way to control the length of PFS block copolymer, self-seeding. I also describe how this self-seeding approach is affected by various experimental parameters.

In Chapter 6, I describe the fragmentation of the fiber-like PI-PFS induced by heating, as well as the interesting behavior of the PFS crystals under one-dimensional confinement.

In Chapter 7, I summarize my research and make suggestions for future research. 34

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Chapter 2

EXPERIMENTAL: MATERIAL, INSTRUMENTATION,

METHOD AND PROTOCOL

In this chapter, I describe the experimental details related to this thesis, including the material, instrumentation, image analysis method and the general experimental protocol for seeded growth.

2.1 Material

2.1.1 Solvents

All solvents used in experiments described in this thesis were received from Sigma-Aldrich Co. and used without further purification. These include decane (≥99%, ReagentPlus), tetrahydrofuran (THF, ≥99.5%, spectrophotometric grade), hexane (≥99%, ReagentPlus), heptane (>99%, biotech grade) and 2-propanol (≥99.5%, ACS grade).

2.1.2 Polymers

All the PFS block copolymers examined in this thesis were synthesized by sequential anionic polymerization by other students in the Winnik and Manners groups.

The PI1000-PFS50, PI800-PFS20 and PI637-PFS53 block copolymers were synthesized by sequential anionic polymerization in THF as described for other PI-PFS [1] samples. The PI1000-

PFS50 and PI800-PFS20 samples were synthesized by Graeme Cambridge and the characterization of the samples were described in ref. [2] and [3], respectively. The PI637-PFS53 sample was synthesized by Dr. Paul A. Rupar and the characterization of the sample was described in ref. [4].

The PFS90-PDMS900 and PFS60-PDMS660 block copolymers were synthesized by sequential anionic polymerization in THF as described for other PFS-PDMS [5] samples. The PFS90-

PDMS900 sample was synthesized by Dr. Jose Raez and the characterization of the sample was 41 described in ref. [6]. The PFS60-PDMS660 sample was also synthesized by Dr. Paul A. Rupar and the characterization of the sample was described in ref. [4].

The PFS30-P2VP300 block copolymer was synthesized by sequential anionic polymerization in THF as described for other PFS-P2VP [7] samples. The sample was synthesized by Dr. Feng He and the characterization of the sample was described in ref. [8]

My notation here for these block copolymers reflects the sequence of synthetic steps when the block copolymers were synthesized, i.e. the anionically polymerized PI block was the precursor block for PI-PFS, while for PFS-PDMS and PFS-P2VP, the PFS block was synthesized first. The number averaged molecular weight and the polydispersity of all the PFS block copolymers as mentioned above are listed in Table 2.1. The structures of these block copolymers are shown in Scheme 2.1.

Table 2.1. Values of Mn and PDI of all PFS block copolymers examined in this thesis

Polymer Mn (g/mol) PDI = Mw/Mn

PI1000-PFS50 [2] 81,500 1.02

PI800-PFS20 [3] 60,000 1.03

PI637-PFS53 [4] 56,300 1.01

PFS90-PDMS900 [6] 88,400 1.01

PFS60-PDMS660 [4] 14,800 1.06

PFS30-P2VP300 [8] 30,400 1.17

PIn-PFSm n = 1000, m = 50 or n = 800, m = 20 or n = 637, m = 53

PFSm-PDMSn m = 60, n = 660 or m = 90, n = 900

PFSm-P2VPn m = 30, n = 300

Scheme 2.1. Structures of block copolymers PI1000-PFS50, PI800-PFS20, PI637-PFS53, PFS90-PDMS900,

PFS60-PDMS660 and PFS30-P2VP300.

2.2 Instrumentation

2.2.1 Transmission Electron Microscopy (TEM)

TEM images were taken using a Hitachi H-7000 TEM instrument. The operation voltage and current were 100 kV and 10 mA, respectively. Samples were prepared by placing a drop of sample solution onto a carbon-coated copper TEM grid. TEM measurements were performed one day after the sample preparation to let the solvent evaporate completely.

2.2.2 Light Scattering

Static (SLS) and dynamic light scattering (DLS) measurements were performed using a wide-angle light scattering photometer from ALV-Laser GmbH, Deutschland. The light source is a JDS Uniphase He-Ne laser (λ = 632.8 nm, 35 mW) emitting vertically polarized light. The sample cell was placed into the ALV/DLS/SLS-5000 Compact Goniometer System. The cell 43 was surrounded by thermostated toluene, which matches the refractive index of the glass cell. The angular range of the goniometer is 12 - 155°. The scattered light was detected by a Dual ALV-High Q.E. APD avalanche photodiode module. This detector is interfaced to the ALV- 5000/EPP multiple tau digital correlator. All measurements were performed at 20.0 °C. Autocorrelation functions were analyzed by the ALV-Correlator Software v3.0 [9].

2.2.3 Gel Permeation Chromatography (GPC)

The degradation effect of PI1000-PFS50 block copolymer micelle in decane caused by sonication was investigated by GPC. Rotary evaporation was performed on the micelle decane solution after sonication in order to evaporate the solvent decane, then GPC measurements were performed by dissolving the solid in THF and injecting the solution into Viscotek GPCMax GPC equipped with a Viscotek 2501 UV/VIS detector (wavelength of 420 nm), TDA302 triple detector array, and Visotek GMHHRH and GMHHR-M Viscogel GPC columns (kept at 35 °C). The flow rate was maintained at 0.6 mL/min using a VE2001 solvent/sample module. The system was calibrated with polystyrene standards.

2.2.4 Atomic Force Microscopy (AFM)

The PI1000-PFS50 block copolymer micelle was also characterized by AFM. The AFM measurements were carried out with a commercial instrument (Digital Instruments, Dimension 5000, Nanoscope IIIa). Silicon nitride cantilevers with spring constant 40 N/m, resonance frequency 320 kHz, (NanoWorld, Switzerland) were used for tapping-mode AFM. Height and phase images were captured and viewed using the Nanoscope software (Digital Instruments, Nanoscope (R) III v5.31R1).

2.2.5 Nuclear Magnetic Resonance (NMR)

In order to examine the amount of THF in the decane solution, 1H NMR measurements were preformed. The 1H NMR (400 MHz) spectra were recorded on a Varian Mercury 400 spectrometer. Chemical shifts were referenced to tetramethylsilane (TMS) in CDCl3. All spectra were collected as 64 transients with a delay time of 5 seconds.

44 2.2.6 Heating Bath and Temperature Control

All heating experiments were performed by placing the sample containing vial in silicon oil bath on top of a hot plate. The vials were sealed with Teflon tape to prevent the solvent evaporation. The temperature of the oil bath is controlled by an IKATRON ETS-D5 (Germany) thermometer with a rated temperature fluctuation of 0.1 °C.

2.2.7 Sonication

All sonication experiments were performed by placing the sample containing vial in the center of a water sonication bath from Branson Ultrasonics Corp. USA, model 1510R-MT, with a sonication power of 70 W. The vials were sealed with Teflon tape.

2.3 Image Analysis Method

Throughout my thesis, the most valuable information about each micelle sample was obtained from the quantitative analysis of TEM images of each sample. This method was employed in the experiments described in every chapter of my thesis. Consequently, I describe this general method in this chapter. Other characterization methods are not described here and will be introduced in the content where they are employed.

2.3.1 Image Analysis

Length information of each micelle sample was obtained by TEM image analysis, which was performed by hand using the software program ImageJ from the National Institutes of Health, USA. After taking several TEM images of each micelle sample, I used the software to trace every micelle in the image and measured its contour length. A typical TEM image of the fiber-like micelles formed by the self-assembly of PI1000-PFS50 block copolymer in decane is shown in Figure 2.1. Generally, for each micelle sample that had average length shorter than 1 μm, I traced 200-400 micelles in several TEM images from the same sample for statistic analysis. If the sample had an average length longer than 1 μm, I traced 100-200 micelles. All micelles that appeared in the field of view in the TEM images were traced without any bias. However, objects that were obviously different from those fiber-like micelles were considered as contamination of the copper grid and ignored, as shown in the dashed circles in Figure 2.1. 45

PI1000-PFS50

500 nm

Figure 2.1 An example of TEM image of fiber-like micelles formed by the self-

assembly of PI1000-PFS50 block copolymer in decane. Objects that appear in the dashed circles are considered as contamination and ignored.

In order to obtain the length information of each sample, I collected the length values of all individual micelles Li, and calculated the number average micelle length (Ln) and weight average micelle length (Lw) using eq. 2.1,

N N 2 ∑ nLii ∑ nLii i=1 i=1 Ln = N Lw = N (2.1) ∑ ni ∑ nLii i=1 i=1 where N is the total number of micelles examined in each sample, ni is the number of micelles that have the length value of Li. Here, since each micelle was measured accurately, no two

N micelles have exactly the same length value, as a result, ni ≡1 , and also, ∑nNi = . When i=1 constructing the length distribution histogram for each sample, the bin width h was chosen following the Scott’s normal reference rule (eq. 2.2), 3.5σ h = N1/3 (2.2) where σ is the standard deviation of the micelle length distribution 46 There is variety of different ways to characterize the distribution of the micelle length. I chose two of them suitable for symmetric distribution, i.e. Lw/Ln and σ/Ln. Similar to the characterization of the molecule weight distribution of polymer molecules [10], I also refer to

Lw/Ln as the polydispersity index (PDI) of the micelle length distribution. Values of Lw, Ln, PDI, and σ are correlated through eq. 2.3,

1/2 σ 1/2 ⎛⎞L =−=−()PDI 11⎜⎟w (2.3) LLnn⎝⎠

2.3.2 PDI

In this section, I describe how PDI (Lw/Ln) characterizes the length distribution of the micelles. Strictly speaking, only biological systems can produce monodisperse (PDI = 1.00) macromolecules or large building blocks, such as DNA, proteins. For polydisperse systems, the PDI is always larger than 1.00 [11]. Synthetic polymers can be narrow distributed in length with PDI values that are very close to 1, but never reach 1. Here, I would like to use some examples to show how the PDI value reflects the polydispersity of the micelle length. In the following examples, each system contains the same number of micelles, 100, but with different length. To simplify the calculation, the unit of the length is ignored, because the unit does not affect the PDI value.

2.3.2.1 Example 1

In this system, the length values of the 100 micelles are 1, 2, 3, …, 100. The length distribution histogram is shown in Figure 2.2A. It is not difficult to imagine that this is a very broad distribution.

N nL ∑ ii 1+++ 2 3 ... + 100 L ==i=1 =50.5 n N 100 ∑ ni i=1

N nL2 ∑ ii 1223++++ 2 3 ... 100 2 100(100+ 1)(2 × 100 + 1) / 6 L ==i=1 = =67 w N 1+++ 2 3 ... + 100 5050 ∑nLii i=1 47 As a result, PDI = 1.33.

2.3.2.2 Example 2

In this system, 1 micelle has length value of 100, other 99 micelles have length value of 1. The length distribution histogram is shown in Figure 2.2B.

N nL ∑ ii 100+× 99 1 L ==i=1 =1.99 n N 100 ∑ ni i=1

N nL2 ∑ ii 10022+× 99 1 L ==i=1 =50.7 w N 100+× 99 1 ∑ nLii i=1

As a result, PDI = 25.5. Comparing this PDI value with that in Example 1, we can see that a very small population with a large value of length has huge effect on the PDI value.

2.3.2.3 Example 3

In this system, 1 micelle has length value of 1, other 99 micelles have length value of 100. The length distribution histogram is shown in Figure 2.2C.

N nL ∑ ii 1+× 99 100 L ==i=1 =99.01 n N 100 ∑ ni i=1

N nL2 ∑ ii 122+× 99 100 L ==i=1 =99.99 w N 1+× 99 100 ∑ nLii i=1

As a result, PDI = 1.01. From this example, we can see that small population with small length value has little effect on the PDI value. 48

By comparing example 2 and 3, we can see that the Lw overweighs the contribution of large species, resulting a larger PDI value.

A B C 1.0 1.0 0.10 0.8 0.8 0.08

0.06 0.6 0.6

0.04 0.4 0.4

0.02 0.2 0.2

0.00 Normalized Frequency Normalized 0.0 0.0 0 20406080100 0 20406080100 0 20406080100 Length (nm) Length (nm) Length (nm) 0.6 D 0.4 E 0.4 F

0.3 0.3 0.4 0.2 0.2 0.2 0.1 0.1

Normalized Frequency 0.0 0.0 0.0 0 20406080100 0 20406080100 1000 1020 1040 1060 1080 1100 Length (nm) Length (nm) Length (nm)

Figure 2.2 (A-F) Histograms of micelle length distribution for Example 1-6. The solid lines in (E) and (F) represent the fit for Gaussian distribution.

2.3.2.4 Example 4, a bimodal distribution

In this system, 50 micelles have length value of 1, other 50 micelles have length value of 100. The two populations have very different length values, but same numbers. The length distribution histogram is shown in Figure 2.2D. We can also imagine that this is a system with very broad overall distribution

N ∑ nLii i=1 50×+ 1 50 × 100 L == =50.5 (Note: this value is the same as Ln in Example 1.) n N 100 ∑ ni i=1

N nL2 ∑ ii 50×+ 122 50 × 100 L ==i=1 =99.02 w N 50×+ 1 50 × 100 ∑ nLii i=1 49 As a result, PDI = 1.96. This is a system with very broad length distribution, but the PDI value is much smaller than that in Example 2.

2.3.2.5 Example 5

In this system, the lengths of the 100 micelles follow a quasi-Gaussian distribution. The distribution function for Gaussian distribution is expressed in e.q. 2.4,

()x−μ 2 − 1 2σ 2 fx()= e (2.4) 2πσ where μ is the value of the central peak (mean value), σ is the standard deviation. In this system, I set μ = 50, σ = 10. For Gaussian distribution, the population in (μ-σ, μ+σ) is around 68 %, the population in (μ-1.96σ, μ+1.96σ) is around 95 %, the population in (μ-2.58σ, μ+2.58σ) is around 99 %.

It is not necessary to build a system with micelle lengths that satisfy e.q. 2.4 strictly. For convenience, I set the 100 micelles with the following length values, 1 micelle of 23, 2 micelles of 28, 13 micelles of 35, 34 micelles of 45, 34 micelles of 55, 13 micelles of 65, 2 micelles of 72, 1 micelles of 77. The length distribution histogram is shown in Figure 2.2E.

In this system, Ln = 50, Lw = 52.2, σ = 10, as a result, PDI = 1.04. This PDI value indicates a narrow length distribution.

2.3.2.6 Example 6

In this system, the lengths of the 100 micelles also follow a quasi-Gaussian distribution, but with different values from those in Example 5. Suppose the 100 micelles in Example 5 grow longer simultaneously, all length values increase by 1000 (The peak value increases by 1000, μ = 1050), but the shape of the distribution does not change (σ = 10). The histogram of the length distribution is presented in Figure 2.2F. Here, Ln = 1050, Lw = 1050.1, σ = 10, as a result, PDI = 1.0001. This PDI value tells one that this system is almost homogeneous. It is interesting to compare this system with the one in Example 5, the two systems have the same shape in length distribution histogram but very different PDI value because of the difference in mean length, as shown by e.q. 2.3. 50 2.4 Experimental Protocol: Seeded Growth

In this section, I describe the experimental procedures to perform seeded growth, which serves as the standard protocol to obtain monodisperse micelles with desirable length. Generally, seeded growth experiment is carried out by adding additional polymer, dissolved in a small amount of common solvent (THF), to a solution of preexisting micelles in a selective solvent. In this process, the number of micelles remains constant because all the additional polymer grows onto the ends of preexisting micelles, and no new micelles form. As a consequence, based on the initial length of the preexisting micelles, we are able to obtain micelles with expected length by controlling the ratio of additional polymer to preexisting polymer [12].

Since longer micelles are grown from existing micelles, the length distribution of the initial micelles will affect that of the final micelles. Because of this, we have learned to use intense or prolonged sonication to create very small micelle fragments. Subsequent addition of new polymers to these micelle fragments leads to micelles with a very narrow length distribution [11]. We refer to the micelle fragments for the later growth experiment as “seed micelles”.

In this section, I use the PI1000-PFS50 block copolymer as an example to demonstrate how I obtained PI1000-PFS50 block copolymer micelles of controllable length, and with narrow length distribution (PDI < 1.03).

I started the experiments by adding PI1000-PFS50 block copolymer 0.162 mg in selective solvent decane 1.62 mL with a concentration of 0.100 mg/mL in a 20 mL vial. The vial containing the polymer/decane mixture was placed in oil bath on top of a hot plate at the temperature of 100 °C. After 30 min, the heating was turned off to let the solution cool back to room temperature slowly (cooling rate was around 1.5 °C/min). In this way, the PI1000-PFS50 block copolymer self-assembled to form long fiber-like micelles with length over 10 μm and uniform width. A representative TEM image of PI1000-PFS50 block copolymer micelle in decane is shown in Figure 2.3A.

The long micelles were then subjected to sonication in water bath for two 10 min intervals in room temperature. A TEM image of the micelles after sonication is presented in Figure 2.3B, where one can see the short fragments of the micelles, as we called “seeds” micelles. The length distribution histogram of the micelle seeds is shown in Figure 2.3C, the seeds were 51 characterized by Ln = 58 nm, Lw = 64 nm, Lw/Ln = 1.11, and σ/Ln = 0.328. Here I want to emphasize that this is only one representative batch of the seeds sample, micelle seeds with slightly different length and length distribution were produced in different experiments. I will specify the characteristics of the seeds sample used in each experiment in the following chapters.

The 0.100 mg/mL PI1000-PFS50 micelle seeds solution was diluted with decane to c = 0.020 mg/mL before the seeded growth experiments. Three portions of 3.00 mL 0.020 mg/mL PI1000-

PFS50 micelle seeds solutions were transferred into three new vials for seeded growth experiments. Three 0.15 mL THF solutions containing 0.210 mg, 0.710 mg, and 1.20 mg PI1000-

PFS50 polymers were added into the three seeds solutions separately. All the three solutions were allowed to age in dark for a week before diluting with decane again to c = 0.020 mg/mL. After the dilution, copper grids were prepared for the samples for TEM measurements. Representative TEM images of the three samples are shown in Figure 2.3D, E, and F. One can see that, after the addition of more polymer materials, longer micelles than the initial seeds with narrow length distribution were obtained, as shown by their corresponding length distribution histograms in Figure 2.3G, H, and I. The more polymers that were added, the longer the micelles were obtained. The first sample with the addition of 0.210 mg polymer was characterized by Ln = 256 nm, Lw = 263 nm, Lw/Ln = 1.03, and σ/Ln = 0.160; the sample that

0.710 mg polymer was added into was characterized by Ln = 752 nm, Lw = 763 nm, Lw/Ln = 1.01, and σ/Ln = 0.121; the last sample with addition of 1.20 mg polymer was characterized by Ln =

1243 nm, Lw = 1258 nm, Lw/Ln = 1.01, and σ/Ln = 0.109.

In Figure 2.4, I plot the mean length Ln of the micelles after the seeded growth experiments versus the amount of polymer I added. Error bars represent the standard deviation σ of the length distribution of each data point. The dash line is the theoretical prediction of the micelle length Ltheoretical based on the assumptions that (i) all additional polymer grow onto the pre- existing seed micelles without forming new micelles; and (ii) the linear aggregation number (number of molecules per unit length) does not change during the growth, which could be expressed by:

M unimer Ltheoretical =+×(1)Lseed (2.5) M seed 52 where Lseed is the mean length of the micelle seeds, in this case, Lseed = 58 nm; Munimer is the mass of polymer that was dissolved in THF for seeded growth; and Mseed is the mass of polymer that was present in the micelle seeds, in this case, Mseed = 0.060 mg. From Figure 2.4, one sees that the micelles all grew to their theoretical predicted lengths.

A B 0.30 C 0.25 0.20 0.15 0.10 0.05

Normalized Frequency 0.00 0 255075100125 Length (nm) D E F

0.5 0.3 G H 0.3 I 0.4 0.2 0.2 0.3

0.2 0.1 0.1 0.1

0.0 0.0 Normalized Frequency Normalized 0.0 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 Length (nm) Length (nm) Length (nm)

Figure 2.3 (A) TEM image of fiber-like micelles formed by the self-assembly of PI1000-PFS50 block copolymer in decane, formed by heating the polymer decane solution to 100 °C for 30 min and cooling to room temperature. (B) TEM image of micelle fragments obtained by sonicating the micelles as shown in (A) for 10 min + 10 min in room temperature. (C) Length distribution histogram of micelle fragments as

shown in (B), Ln = 58 nm, Lw = 64 nm, Lw/Ln = 1.11, and σ/Ln = 0.328. (D-F) TEM images of micelles after seeded growth experiments using micelle fragments in (B) as seeds. (G-I) Length distribution

histograms of micelles as shown in (D-F). (G) Ln = 256 nm, Lw = 263 nm, Lw/Ln = 1.03, and σ/Ln = 0.160.

(H) Ln = 752 nm, Lw = 763 nm, Lw/Ln = 1.01, and σ/Ln = 0.121. (I) Ln = 1243 nm, Lw = 1258 nm, Lw/Ln =

1.01, and σ/Ln = 0.109. Scale bars are all 500 nm.

1500

1200

900

600 Length (nm) Length 300

0 0.0 0.3 0.6 0.9 1.2 1.5 Mass of Polymer Added (mg)

Figure 2.4. Mean length of the micelles obtained by seeded growth experiment versus the mass of polymer added. Error bars represent the standard deviation σ of the length distribution of each data point. The dash line represents the predicted maximum lengths based on the assumptions that (i) all additional polymer grow onto the pre-existing seed micelles without forming new micelles and (ii) the linear aggregation number does not change during the micelle growth.

The length and length distribution of these micelles obtained by the seeded growth method as shown in Figure 2.4 were very stable for a long period of at least one year. These micelles of different lengths, but with narrow length distribution were ready for later study. In chapter 5, I will describe the experiments that investigated the effect of heating on the micelle samples as shown in Figure 2.3D and 2.3F. Because of the Ln values of the two samples, I referred to the sample in Figure 2.3D as L-250, and the sample in Figure 2.3F as L-1250. 54

References

1 Cao, L.; Manners, I.; Winnik, M. A. Macromolecules 2002, 35, 8258-8260. 2 Cambridge, G.; Guerin, G.; Manners, I.; Winnik, M. A. Macromol. Rapid Commun. 2010, 31, 934-938. 3 Cambridge, G. Ph.D. thesis, University of Toronto, 2012. 4 Rupar, P. A.; Cambridge, G.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2011, 133, 16947-16957. 5 Massey, J.; Power, K. N.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 1998, 120, 9533- 9540. 6 Raez, J.; Zhang, Y. M.; Cao, L.; Petrov, S.; Erlacher, K., Wiesner, U., Manners, I., Winnik, M. A. J. Am. Chem. Soc. 2003, 125, 6010-6011. 7 Wang, H.; Winnik, M. A.; Manners, I. Macromolecules 2007, 40, 3784-3789. 8 He, F.; Gädt, T.; Jones, M.; Scholes, G. D.; Manners, I.; Winnik, M. A. Macromolecules 2009, 42, 7953-7960. 9 Guerin, G.; Raez, J.; Manners, I.; Winnik, M. A. Macromolecules 2005, 38, 7819-7827. 10 Rubinstein, M.; Colby, R. H. Polymer Physics. 2003, Oxford University Press, Oxford. 11 Gilroy, J. B.; Gädt, T.; Whittell, G. R.; Chabanne, L.; Mitchels, J. M.; Richardson, R. M.; Winnik, M. A.; Manners, I. Nat. Chem. 2010, 2, 566-570. 12 Wang, X. S.; Guerin, G.; Wang, H.; Wang, Y. S.; Manners, I.; Winnik, M. A. Science 2007, 317, 644-647. 55

Chapter 3

SOLVENT-INDUCED FRAGMENTATION OF FIBER-LIKE

PI1000-PFS50 BLOCK COPOLYMER MICELLES AND

DISCOVERY OF SUPERSATURATION FOR MICELLIZATION

In this chapter, I first describe experiments showing that the addition of tetrahydrofuran

(THF) to a solution of PI1000-PFS50 micelles in decane induced the fragmentation of the micelles. The content is from the paper which has been published in 2010 [1] (Qian, J. S.; Guerin, G.; Cambridge, G.; Manners, I.; Winnik, M. A. Macromol. Rapid Commun. 2010, 31, 928-933).

Later in this chapter, I show that addition of decane to PI1000-PFS50 THF solution induced micelle formation. A supersaturation region for PI1000-PFS50 micelle formation was discovered.

3.1 Introduction

For the self-assembly systems of small amphiphilic molecules, e.g. surfactants, Israelachvili has derived the fundamental thermodynamic equations for the different self- assembly structures [2]. For system under thermodynamic equilibrium,

N XNX=−exp⎡μμ00 / kT⎤ N{ 11⎣()N⎦} (eq. 3.1)

0 where XN and μ N represents the concentration and chemical potential of molecules in 0 aggregates of number N, when N = 1, X1 and μ 1 correspond to isolated molecules or monomers in solution. As a result, the total solute concentration C can be expressed as

∞ CX=+++=123 X XL ∑ XN (eq. 3.2) N =1

0 0 Depending on how the free energies μ 1, μ N are defined, the dimensionless concentration C and XN can be expressed in volume fraction or mole fraction units. Note that C and XN can never exceed unity. 56 For the simplest shaped structures, rods or fibers (one-dimensional), discs or sheets (two- dimensional), and spheres (three-dimensional), the interaction free energy of the molecules can be expressed as

μμ00=+αkT N ∞ N p (eq. 3.3) where α is a positive constant dependent on the strength of the intermolecular interactions and p is a number that depends on the shape of dimensionality of the aggregates. For rods or fibers, p 0 = 1; for discs or sheets, p = 1/2; for spheres, p = 1/3. μ ∞ is the “bulk” energy of a molecule in an infinite aggregate.

Incorporation of eq. 3.3 into eq. 3.1 and eq. 3.2 gives the distribution of molecules in aggregates of N molecules

N ⎡p ⎤ XNXN =−{1 exp⎣α (1 1/ N )⎦} (eq. 3.4)

From eq. 3.4, the critical micelle concentration (CMC) is expressed by

X =≈−−CMC exp[μμ00 /kT ] ≈ e−α ()11crit ( N ) for all p. (eq. 3.5)

For one-dimensional self-assembly aggregates, e.g. rods or fiber-like micelles, p = 1, so eq. 3.4 can be rewritten as,

N ⎡⎤α −α XNXeeN = ⎣⎦1 (eq. 3.6)

The total concentration of molecules is given by inserting eq. 3.6 into eq. 3.2 as

∞∞ ααN − α2 CX==∑∑N NXeeXXe[]11 =− /(11) (eq. 3.7) NN==11

∞ where we use ∑ NxN =− x/(1 x )2 . Thus the solution of eq. 3.7 gives N =1 57

(1+−+ 2Ceα ) 1 4 Ceα X = (eq. 3.8) 1 2Ce2α

α Note that, at low concentrations C where Ce <<1 , this gives X1 ≈ C , whereas at high concentrations, well above the CMC such as Ceα >> 1, eq. 3.8 is simplified to

X ≈−11/ Ceα e−−αα ≤ e 1 ( ) (eq. 3.9)

that is X1 ≈ CMC as expected. Above the CMC, the distribution of molecules in aggregates of N molecules is given by inserting eq. 3.9 into eq. 3.6, giving

N α XN=−11/ Ceeαα−− ≈ NeNCe/ N ( ) for large N. (eq. 3.10)

This function peaks at ∂∂=XNN / 0 , which occurs at

α NMCemax == (eq. 3.11) where M is the mean aggregation number. From eq. 3.11, the expectation value of N, defined by

NNXXNX==∑∑∑NN// NC, is given by

αα NCeCe=+14 ≈ 2 = 2M above the CMC. (eq. 3.12)

Finally, the density distribution of aggregates above the CMC is

− N / M XNConsteN /.= for N > M. (eq. 3.13)

Eq. 3.12 and eq. 3.13 provide two very interesting predictions of the theory of equilibrium one-dimensional self-assembly to describe the formation of rod-like or fiber-like micelles by molecules that can undergo monomer exchange with the aggregates. The first is that, at concentrations above the onset of micellization (C > CMC), the number average micelle length

Ln (proportional to N in eq. 3.12) should increase with the square root of the concentration of the solute. The second is that the number distribution of aggregates is very broad, the concentration 58 of aggregates first increases with N for small aggregates and then decays gradually to zero at large N, as expressed by eq. 3.13. The mean aggregation number M is a characteristic decay number and also concentration dependent.

For coil-coil block copolymer systems at equilibrium, such as the micelles formed in heptane by polystyrene-polyisoprene (PS-PI) block copolymers [3], the current theory of the self-assembly appears to describe adequately the phase diagram of structure vs polymer composition, even as temperature was varied. For other structures, such as micelles formed by polybutadiene-poly(ethylene oxide) (PB-PEO) in water, there was very strong evidence that the micelles formed were kinetically frozen, so that no exchange of monomers among micelles took place on normal time scales [4]. Nevertheless, direct mixing with water under agitation led to structures that can be described by a phase diagram not too different from thermodynamic considerations alone.

What is interesting about the one-dimensional block copolymer micelle system is that the contour length distribution (CLD) of the micelles, in the few cases that have been reported, appeared to follow the distribution as expressed in eq. 3.13, even though the micelles were not formed under strictly equilibrium conditions. For example, Dalhaimer et al. [ 5 ] used fluorescence video microscopy to study filamentous micelles in flow formed by PB45-PEO55 in water. They showed that these micelles were characterized by an exponentially broad contour length distribution, following the distribution described by eq. 3.13. Our group reported [6] an example of seeded growth of PI264-PFS48 micelles in decane using seeds with a relatively broad length distribution. While the CLDs that were measured from transmission electron microscopy (TEM) images were narrower than that reported by Dalhaimer et al. [5], they could still be fitted to eq. 3.13. However, in our report [6], we showed that when we added increasing concentration

C of block copolymer to seed micelles in solution, the number average length Ln of the fiber-like micelles increased as C, instead of the square root of C, as described by eq. 3.12.

The case of fiber-like micelles formed by polymers in which the core block can crystallize is particularly challenging to understand. The earliest examples of micelles formed by crystalline-coil block copolymers led to planar raft-like structures [7,8,9]. The theoretical analysis of Vilgis and Halperin, which assumed that the crystalline block formed a folded lamellar structure, was consistent with these results, but did not make quantitative predictions. More recent examples, however, in which the corona forming coil block is much longer than the 59 block that crystallizes, describe high-aspect-ratio fiber-like structures, often very uniform in width [10,11,12,13]. The most prominent examples involve PFS block copolymers such as PI- PFS, PFS-PDMS, and PFS-P2VP [14,15,16]. These polymers form stiff rod-like micelles for a broad range of compositions in which the corona-forming coil block is longer than the PFS block.

One anticipates for micelles formed by block copolymers containing a crystalline block that the crystallization process is a high energy event (lattice energy, ΔH >> kT), and the crystalline core should affect the equilibrium process, as it involves melting-recrystallization events.

In this chapter I examine the seeded growth of PI-PFS micelles for a polymer sample with a very long PI block, PI1000-PFS50. In decane solution and in decane containing small amounts of THF, I obtained micelles with a very narrow CLD. Then I added increasing amounts of THF to these solutions, with the hope of finding the equilibrium state of the self-assembly of these fiber- like micelles. My results showed that large volume fractions of THF (e.g. 17 %) caused the micelles to dissolve. Modest amounts of THF lead to a broadening of the CLD, but with a very different distribution than that predicted by e.q. 3.13. I conclude that THF promoted micelle fragmentation rather than a transition to equilibrium micelle formation. Later in this chapter I describe the experiments showing that addition of decane to the PI1000-PFS50 THF solution induced micelle formation when the THF volume fraction was lower than 10 %. Based on these results, a supersaturation region of solvent composition for micellization was discovered.

3.2 Experimental

3.2.1 Seeded Growth of PI-PFS Block Copolymer Micelles

The PI1000-PFS50 block copolymer micelle seeds for the seeded growth experiments were prepared by a slightly different method from that has been described in detail in Chapter 2. For this work, a micelle seed solution was prepared by immersing a vial (20 mL) with decane 8.75 mL containing PI1000-PFS50 block polymer 0.175 mg (c = 0.0200 mg/mL) into a 70 watt ultrasonic cleaning bath and sonicating the polymer/decane mixture for two 10 min intervals at 23 °C. I would like to emphasize that the polymer/decane mixture had not been heated before 60 the sonication treatment. A separate solution of this polymer was prepared by dissolving 0.382 mg of polymer in 0.19 mL THF (c = 2.00 mg/mL).

Seeded growth of the block copolymer micelles was performed by adding 0.150 mL of the c = 2.00 mg/mL THF solution into 3.00 mL c = 0.0200 mg/mL seed solution. Then, additional mixed solvent with the ratio of decane:THF = 20:1 was added to adjust the final concentration to c = 0.0200 mg/mL. I refer to this sample as the “mother solution”. As a result, the mother solution contained THF with the volume fraction of 4.8 %.

3.2.2 Adding THF into Micelle in Decane Solutions

To investigate the effect of adding THF into micelle solutions, seven equivalent batches with volume V = 2.10 mL were transferred from the mother solution to new vials (20 mL), and then different amounts of THF (0.040, 0.080, 0.12, 0.16, 0.20, 0.24, 0.30 mL) were added at once into each of the seven vials. The vials were capped and sealed using Teflon tape to prevent solvent evaporation and allowed to age for three weeks before examining the solutions by light scattering and by TEM. For one solvent composition, the kinetics of the solvent-induced micelle transformation was investigated, where 0.24 mL THF was added to 2.10 mL of the mother solution.

3.2.3 Adding Decane into Polymer in THF Solutions.

A sample of PI1000-PFS50 block copolymer 1.024 mg was dissolved in THF (10.24 mL, c = 0.100 mg/mL) in a 20 mL vial. Nine equivalent batches with volume V = 1.00 mL were transferred from the THF solution to new vials. Then different amount of decane (4.00, 5.00, 5.71, 6.67, 8.00, 10.00, 15.67, 19.00, 24.00 mL) were added at once into each of the nine vials. The vials were also capped and sealed using Teflon tape to prevent solvent evaporation and allowed to age for one week before examining the solutions by both light scattering and TEM.

3.2.4 Test of the Supersaturation for Micellization.

A sample of PI1000-PFS50 block copolymer 0.509 mg was dissolved in THF (5.09 mL, c = 0.100 mg/mL) in a 20 mL vial. Five equivalent batches with volume V = 1.00 mL were transferred to new vials, different amount of decane (5.00, 5.71, 6.67, 8.00, 10.00 mL) were added at once into each of the five vials. Ten minutes later, one drop (≈ 5 μL) of sonicated 61 micelle seeds in decane (c = 0.020 mg/mL) was added into each solution. One day later, the solutions were checked by TEM.

3.3 Results and Discussion

3.3.1 Seeded Growth of PI-PFS Block Copolymer Micelles

The experiments reported in this chapter employed a PFS block copolymer with a very long, soluble PI block PI1000-PFS50 (Mn = 81,500 g/mol, Mw/Mn = 1.02, details see Chapter 2). By sonicating the polymer/decane mixture with a 70 watt ultrasonic cleaning bath for two 10 min intervals, I obtained seed micelles characterized by Ln = 85 nm, and Lw/Ln = 1.09. A TEM image of these seed micelles and their length distribution histogram are presented in Figure 3.1. Additional polymer (0.150 mL, 2.00 mg/mL) in THF was added to 3.00 mL of micelle seeds (c = 0.0200 mg/mL), and then additional solvent (decane:THF = 20:1) was added to adjust the polymer concentration to 0.0200 mg/mL. After the solution was allowed to age at room temperature for a week, TEM images (Figure 3.2A) showed that the micelles were much longer, with Ln = 645 nm, Lw = 658 nm. Thus Lw/Ln = 1.02. After 3 weeks (Figure 3.2B), Ln and Lw values increased slightly, yielding Ln = 691 nm, Lw = 705, but the distribution remained narrow with Lw/Ln = 1.02 (histograms of both samples are shown in Figure 3.2C and D).

A 0.40 B

0.30

0.20

0.10 Normalized Frequency Normalized 0.00 500 nm 0 50 100 150 200 250 Length distribution (nm)

Figure 3.1. TEM image (A) and length distribution histogram (B) of the micelle seeds formed by adding

PI1000-PFS50 as a powder to decane and sonicating the mixture for two 10 min intervals. I identify the wider objects circled in dashed black as amorphous aggregates. The uniform rod-like structures are

micelle seeds. The micelle seeds possess Ln = 85 nm, Lw = 93 nm, Lw/Ln = 1.09 and σ/Ln = 0.306. Reprinted from Ref [1] with permission.

62 A curious feature of the micelles I obtained is that their length increased by 7% as the sample aging time increased from 1 week to 3 weeks. This result suggests that there was a source of polymer in the system that slowly condensed onto the ends of micelles present in solution. Close inspection of TEM images of the micelle seed solution (e.g., Figure 3.1A) shows that in addition to rod-like seeds there were amorphous aggregates, indicated by the black dash circles in Figure 3.1A. Unlike typical seeded growth experiments I described in chapter 2, in which seed micelles were initially prepared by heating the polymer/decane mixture to 90 or 100

°C, cooling and then sonicating, the seed solution employed here was prepared by adding PI1000-

PFS50 powder to decane at room temperature and sonicating the mixture directly. The results from the work of Shen et al. [17] suggested that amorphous aggregates can act as a reservoir for PFS block copolymer molecules, leading to very slow growth in length of fiber-like micelles over time. These authors examined PFS-P2VP micelles in ethanol. That sample initially formed amorphous spherical micelles that evolved over a year to form very long, uniform fiber-like micelles. Unlike the obvious aggregates indicated in Figure 3.1A, the amorphous aggregates of

PI1000-PFS50 are probably too small and too few in number to be seen in the micelles formed by seeded growth (see Figure 3.2A and 3.2B). They may, however, be the source of polymer for the small growth observed when the sample was checked three weeks after the seeded growth. 63

A 0.20 C

0.15

0.10

0.05

Normalized Frequency 0.00 500 nm 0 200 400 600 800 1000 1200 Length (nm) B 0.20 D

0.15

0.10

0.05

Normalized Frequency Normalized 0.00 500 nm 0 200 400 600 800 1000 1200 Length (nm)

Figure 3.2. (A and B) Representative TEM images of the micelles from the mother solution, formed by adding 0.150 mL of PI1000-PFS50 in THF (c = 2.00 mg/mL) to 3.00 mL of seed micelles (c = 0.0200 mg/mL of PI1000-PFS50) in decane. Then, additional mixed solvent (decane:THF = 20:1) was added to adjust the final concentration to c = 0.0200 mg/mL. (A) after aging one week and (B) after aging three weeks at room temperature. (C and D) Length distribution histogram of the micelles from the mother solution after aging (C) one week with Ln = 645 nm, Lw = 658 nm, Lw/Ln = 1.02, and σ/Ln = 0.142 and

(D) three weeks with Ln = 691 nm, Lw = 705 nm, Lw/Ln = 1.02, and σ/Ln = 0.146 after the sample preparation. These data are taken from TEM images of the same solutions shown in (A) and (B), respectively. Reprinted from Ref [1] with permission..

3.3.2 Effect of Adding THF into Micelle in Decane Solutions

In order to test the hypothesis that there is an equilibrium state of the self-assembly of the PI-PFS block copolymer under certain solvent composition, I transferred seven equivalent batches (volume of 2.1 mL) of micelle mother solutions into new vials and added different amounts of THF to each of the solution. These solutions were then allowed to age three weeks at room temperature. Aliquots were taken for TEM analysis, and the light scattering intensity of at each solution at 90° was monitored. Histograms of the length distribution are plotted in Figure 3.3. Figure 3.4A presents the scattering intensity of different samples normalized by the sample concentration to account for the dilution that occurred upon addition of different amounts of THF. These data are meaningful, because the index of refraction of THF (1.407) is nearly identical to that of decane (1.41), leading to very similar predicted values of dn/dc for the two solvents.

The data in Figure 3.4A show that addition of small amounts of THF (up to 8.3 vol %) lead to a small increase in scattering intensity, but that at higher THF concentrations, there is a decrease in scattering intensity. At 17 vol % THF and above, the micelles dissolve completely. The histograms of the length distribution show that the distributions are symmetrical and remain narrow for the samples with 6.5, 8.3, and 9.9 vol % THF. Calculated values of Ln and Lw show a small increase (Figure 3.4B), consistent with the change in light scattering, and no significant change in Lw/Ln ≈ 1.02. When larger amounts of THF were added, however, values of Ln and Lw decreased and more pronounced changes in the contour length distribution took place. For the solutions with 11.5, 13.0 and 14.5 vol % THF, the distributions became much broader.

Another measure of the width of the CLD is the ratio σ/Ln, where σ is the standard deviation of contour length distribution. Values of σ/Ln calculated for these distributions are plotted against solvent composition in Figure 3.4C, which shows that the width of the CLD remained almost unchanged with the addition of THF when THF vol % was lower than 10% but changed significantly with the addition of THF when higher amounts of THF were present.

0.250 A, 6.5% 0.200 B, 8.3%

y 0.200 0.150 0.150 0.100 0.100

0.050 0.050 Normalized Frequency Normalized Frequenc 0.000 0.000 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm)

0.200 D, 11.5% C, 9.9% 0.150 y 0.150 0.100

0.100

0.050 0.050 Normalized Frequency Normalized FrequencNormalized 0.000 0.000 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm) 0.150 0.150 E, 13.0% F, 14.5% y

0.100 0.100

0.050 0.050 Normalized Frequenc Normalized Frequency Normalized 0.000 0.000 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm)

Figure 3.3. Length distribution histograms of PI1000-PFS50 micelles formed by seeded growth in decane/THF followed by addition of additional THF. The final solvent compositions are indicated by the vol % THF % (A) 6.5%, (B) 8.3%, (C) 9.9%, (D) 11.5%, (E) 13.0%, (F) 14.5%. The lines in A, B, and C represent Gaussian fits of the histograms. Reprinted from Ref [1] with permission.

A L 1.0 B w 800 759 762 705 722 727 713 690 737 0.8 691 708 740 600 693 654 609 0.6 L 400 n 0.4 Intensity Length (nm) Length 200 0.2

0.0 0 4 6 8 10121416184 6 8 10121416 THF fraction %(v/v) THF fraction % (v/v)

0.40 C 100 D 0.35 90 0.30 80 n 0.25 L / σ

70 0.20

0.15 60

0.10 Mass% in micelles ofpolymer 50 4 6 8 10121416 8101214 THF fraction % (v/v) THF fraction % (v/v)

Figure 3.4. (A) Evolution of the scattering intensity at 90° following the addition of different amounts of

THF to solutions of PI1000-PFS50 micelles formed by seeded growth. (The intensities were normalized for

changes in concentration.) (B) Evolution of number average length Ln and weight average length Lw with

the addition of different amounts of THF. (C) Evolution of σ/Ln with the addition of THF. (D) Evolution of mass percentage of polymer in the micelles with the addition of THF, based upon the assumption that the number of micelles in solution did not change. Reprinted from Ref [1] with permission..

The decrease in scattering intensity at 11.5, 13.0 and 14.5 vol % THF in Figure 3.4A suggests that some of the polymer dissolved as the fraction of good solvent in the medium was increased. One way to interpret this data is to hypothesize that number of micelles in the solution as well as their linear aggregation number remained constant at all THF concentrations up to sample dissolution. This hypothesis means that the decrease of the micelle length as shown in Figure 3.4B was due to the dissolution of some of the polymer materials from the ends of the micelles. Based on this idea, I assume that the micelles characterized by the largest values of Ln and Lw, formed in 9.9 % THF (Ln = 740 nm and Lw = 762 nm), contained all of the polymer 67 molecules present in the micelles, without free polymer chains existing in the solution. Then, I calculated the mass fraction of polymer present in the micelle for the samples that contained more than 10 vol % THF via mass%/= Ln 740× 100%. The plot of mass fraction of polymer present in the micelle versus the THF volume fractions is presented in Figure 3.4D.

From the loss of material associated with the decrease in Ln as shown in Figure 3.4D, and the assumption that this represents the equilibrium concentration of free chains in solution, I can equate these concentrations with the CMC of the polymer. The values of the CMC calculated in this way are presented in Table 3.1.

Table 3.1. Estimated CMC values for PI1000-PFS50 for different solvent compositions assuming that the changes in Ln are due only to dissolution of polymer molecules from the ends of existing micelles.

THF (vol %) 11.5 % 13.0 % 14.5 %

CMC (mg/L)a 1.3 2.3 3.5

102 × CMC (μmol/L) a 1.6 2.9 4.4 a. Since the number of micelles in the system is not constant, these values represent an upper limit of the CMC values.

However, there are problems with assuming that the number of micelles in solution remained constant in solvents with elevated THF compositions. In Figure 3.3, although one sees the appearance of shorter micelles in the length distribution histograms, very few micelles are shown to have increased in length. Thus there was little evidence that polymer can both dissolve off the ends of some micelles and deposit onto the ends of other micelles. If the system evolved toward equilibrium formation of micelles, one would expect histograms with a long tail decaying gradually to zero at large L as predicted by e.q. 3.13. From the length distribution histograms in Figure 3.3, I also do not observe the formation of large numbers of short micelles that might be expected if new micelles were nucleated. Instead, I find a broadened distribution with a tail decreasing to zero at small L. Distributions similar to those observed for the samples 68 at 11.5, 13.0 and 14.5 vol % THF were observed in a study of the length distribution of PI-PFS block copolymer micelles in decane subjected to the shear forces of ultrasonic irradiation [18]. Sonication caused these fiber-like micelles to fragment. For the case of sonication, the rate of micelle fracture increased strongly with increasing micelle length. From this perspective, it appears that the effect of adding additional THF into the micelle solution is not only to increase the solubility of the polymer but also to promote fragmentation of existing micelles.

3.3.3 Kinetics of CLD Evolution Induced by the Addition of THF

To study the rate at which changes in the CLD take place, I carried out a kinetic study for the case of 13.0 vol % THF in decane. At time t = 0, I added an aliquot of THF 0.24 mL to 2.1 mL of the mother solution of PI1000-PFS50 micelles (Ln = 691 nm, Lw = 705 nm, and Lw/Ln = 1.02), and then periodically removed aliquots for TEM analysis. Figure 3.5 shows the histogram of micellar length distribution at different times after the addition of THF into the mother solution. One sees that the broadening of the length distribution takes place over the first hour. Subsequently the micelle CLD remained relatively stable.

Figure 3.6A shows the evolution of Ln and Lw at different times after the addition of THF to the micelle solution. After only a few minutes, the micelle length began to decrease. This process continued for somewhat less than an hour. At approximately 30 min, the values of Ln and Lw appear to pass through a shallow minimum, but this effect is very small compared to the breadth of the distribution, and is unlikely to be real. Over this time, the breadth of the length distribution increased significantly, as measured by the increase in σ/Ln shown in Figure 3.6B.

These relatively rapid changes, coupled with the observation that the final CLD is very different from that predicted for an equilibrium self-assembly process support the idea that the primary role of THF in perturbing the contour length distribution is to promote fragmentation of the micelles. It is curious that this process does not continue over the time scales I investigated. This result suggests that the influence of increased solvency for the PI-PFS polymer does not occur uniformly along the micelle. One possible interpretation of this result is that there are defects along the semicrystalline core, which results in a distribution of crystallinity of the micelle core. The regions that have lower crystallinity may be the sites of fragmentation in the micelles. 69

A: 1 min B : 5 m i n 0.15 0.15

0.10 0.10

0.05 0.05 Normalized Frequency 0.00 Normalized Frequency 0.00 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm) C: 10 min D: 30 min 0.15 0.15

0.10 0.10

0.05 0.05 Normalized Frequency Normalized Normalized Frequency Normalized 0.00 0.00 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm) E : 2 h r F: 24 hr 0.15

0.10 0.10

0.05 0.05 Normalized Frequency Normalized Normalized Frequency Normalized 0.00 0.00 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Length distribution (nm) Length distribution (nm)

Figure 3.5. Length distribution histograms of PI1000-PFS50 micelles at different times after the addition of

0.24 mL THF into 2.10 mL of the PI1000-PFS50 mother solution of micelles (Ln = 691 nm, Lw = 705 nm, and Lw/Ln = 1.02). Reprinted from Ref [1] with permission.

800 A 0.50 Lw B 639 644 0.45 538 571 600 559 0.40 621 609 521 507 479 0.35 400 462 468 474 433 n 0.30 L / σ L 0.25 Length (nm) 200 n 0.20

0.15 0 0.1 1 10 100 1000 0.1 1 10 100 1000 log(time (min)) log (Time (min))

Figure 3.6. (A) Evolution of number-averaged length Ln and weight-averaged length Lw of the micelles vs the logarithm of time after the addition of 0.24 mL THF to 2.1 mL of the mother solution of PI -PFS micelles, the final solution contained 13.0 vol % THF. (B) Evolution of 1000 50 σ/Ln versus logarithm of time for this solution. Reprinted from Ref [1] with permission.

3.3.4 Effect of Adding Decane into Polymer in THF Solution

The experiments results described in Section 3.3.2 showed that the addition of THF can dissolve the micelle completely when the THF volume fraction is larger than 17 %. In this section, I describe experiments to examine the behavior of PI1000-PFS50 block copolymers when the polymer solution is prepared in an opposite way, e.g. adding decane into polymer THF solution. I expected to observe micelle formation when the THF volume faction is below 17 %.

The experiments were carried out by adding different amounts of decane (4.00, 5.00, 5.71,

6.67, 8.00, 10.00, 15.67, 19.00, 24.00 mL) into nine PI1000-PFS50 THF solutions (1.00 mL, c = 0.100 mg/mL). I allowed a relative long period of time, one week, for the solution to age in room temperature. Aliquots were taken for TEM analysis, and the light scattering intensity of each sample at 90o was measured. In Figure 3.7, I plot the scattering intensity at 90o of each solution as a function of the volume fraction of THF that is present in each solution. The scattering intensities were also normalized by the sample concentration to account for the dilution that occurred upon addition of decane into the block copolymer THF solutions. 71

1.0

0.8 micelles form 0.6

0.4

0.2 Solvent

Normalized Scattering Intensity Scattering Normalized 0.0 2 6 10 14 18 THF (vol %)

Figure 3.7. Evolution of the scattering intensity at 90° of each sample as the increased

amount of decane added into nine batches of PI1000-PFS50 in THF solutions (1.00 mL, c = 0.100 mg/mL), measured one week after the sample preparation. (The intensities were normalized for changes in concentration, the dashed line in the bottom corresponds to the

scattering intensity of the solvent decane.)

From the data in Figure 3.7, one sees that as the volume fraction of THF decreased from 19 % to 9 %, the light scattering intensity only increased slightly. The scattering intensities of these solutions were very close to that of pure solvent decane. However, when the THF volume fraction further decreased to 6 %, a sharp increase of scattering intensity was observed, which continued to increase substantially with the decrease of THF volume fraction to 4 %.

Aliquots of each solution were removed for TEM measurements one week after the sample preparation. Representative TEM images of these solutions are shown in Figure 3.8. One can see that no micelles were observed in the solutions with THF volume fraction ≥ 9 % (Figure 3.8A-E). These results are consistent with the light scattering measurements that the scattering intensities of these solutions were only slightly larger than pure solvent decane. When the THF volume fraction was 6 %, fiber-like micelles were observed in TEM measurement, as shown in Figure 3.8F. This result also agrees with the observation in light scattering measurements that the scattering intensity of this solution (THF vol 6 %) is significantly higher than that of those solutions with higher THF volume fractions. 72

A THF v % = 16.7 % B THF v % = 14.9 % C THF v % = 13.0 %

500 nm 500 nm 500 nm

D THF v % = 11.1 % E THF v % = 9.1 % F THF v % = 6.0 %

500 nm 500 nm 500 nm

Figure 3.8. TEM images of the solutions prepared by adding various amounts of decane into PI1000-PFS50 in THF solutions (1 mL, c = 0.100 mg/mL). After the addition of decane, the THF volume factions are indicated in each figure. All samples are allowed to age for one week after the preparation before TEM measurements.

I then combine the two curves of the evolution of scattering intensity versus the volume fraction of THF in Figure 3.4A and 3.7 together in Figure 3.9. One sees an obvious hysteresis with regards to solvent composition for the formation of PI1000-PFS50 micelles. When THF was added into PI1000-PFS50 micelle solutions (decane), the micelles were completely dissolved when the THF volume fraction reached 17 % (dashed line in Figure 3.9). However, when decane was added into polymer THF solution, micelles formed only when the THF volume fraction was lower than 9 % (solid line in Figure 3.9). As a result, I now identify the solvent composition regions with THF volume fraction between 9-15 % as the supersaturated condition for the micelle formation, when the solution is prepared by adding decane into the polymer THF solution. 73

1.0 Add THF to decane

0.8

super- 0.6 saturation region 0.4

0.2

Add decane to THF Normalized Intensity Scattering 0.0 2 6 10 14 18 THF (vol %)

Figure 3.9. Evolution of the scattering intensity at 90° versus the THF volume fraction in solution. Solid line represents the solutions prepared by adding decane to the PI -PFS THF solutions, and dashed line 1000 50 represents the solutions prepared by adding of THF to the PI1000-PFS50 micelle solutions (decane).

3.3.5 Test of the Supersaturation Region for Micellization

It is well known that when a solution is supersaturated, adding external nuclei can initiate crystallization [19]. In this section, I describe the experiments that examined the behavior of the supersaturated polymer solution by adding micelle seeds. The experiments started with the preparation of five polymer solutions with THF volume fractions of 9 %, 11 %, 13 %, 15 %, and 17 %, by adding various amounts of decane (5.00, 5.71, 6.67, 8.00, 10.00 mL) into five polymer THF solutions (1.00 mL, c = 0.100 mg/mL). Ten minutes later, a small amount (one drop, ~ 5

μL) of short micelle solution (decane, the sample as shown in Figure 3.1, Ln = 85 nm, c = 0.020 mg/mL), was added to each of the five solutions. One day later, aliquots of these solutions were removed for TEM measurements.

In Figure 3.10, I present the TEM images of the samples one day after the addition of short micelle solution. One sees that long micelles (> 1 μm) are observed in the solutions in which the THF volume fractions were 15 %, 13 %, 11 %, and 9 % (see Figure 3.10B-E). However, no micelles are observed in the solution that contained the largest volume fraction of THF (17 %), interestingly, even the short micelles as added were hardly observed in the TEM image (see Figure 3.10A). 74

The TEM results in Figure 3.10 show that adding micelle seeds (Ln = 85 nm) into the polymer solutions that contain THF volume fraction from 15 % to 9 % can initiate the growth of the fiber-like micelles, forming longer micelles (> 1 μm). These results, combining with the results shown in Section 3.3.4, confirm that solvent mixtures of decane/THF with certain compositions (THF vol % ranging from 15 % to 9 %) are supersaturated conditions for PI1000-

PFS50 block copolymer.

A THF v % = 16.7 % B THF v % = 14.9 % C THF v % = 13.0 %

500 nm 500 nm 500 nm

D THF v % = 11.1 % E THF v % = 9.1 %

500 nm 500 nm

Figure 3.10. TEM images of the samples by adding small amount of short PI1000-PFS50 micelles in decane

(5 μL, c = 0.020 mg/mL) as shown in Figure 3.1 into PI1000-PFS50 in decane/THF mixture solutions with different solvent compositions, prepared by adding various amounts of decane into the polymer THF solutions. The THF volume factions are indicated in each figure.

3.4 Conclusion

In this chapter, I describe the effect of adding increasing amounts of THF, a common good solvent, to a solution of fiber-like PI1000-PFS50 micelles in decane. Once the volume fraction of THF in the mixed solvent exceeded 0.1, the micelles became shorter and the contour length distribution broadened significantly. The shape of the CLD was not consistent with the idea that block copolymer micelles dissociated reversibly form the micelles. Rather, it appears that the polar solvent promoted the fragmentation of the micelles. I speculated that the solvent-induced fragmentation was partially due to the non-uniformity of core crystallinity. A kinetic study showed, for one THF/decane solvent mixture, that the evolution of the CLD took place on a relatively short time scale (30 min) and then the mean micelle length and it CLD became relatively stable. However, when the volume fraction of THF reached 17 %, the micelles were dissolved completely.

Later in this chapter, I showed that addition of decane into the PI1000-PFS50 block copolymer dissolved in THF solutions induced the micelle formation, however, only when the THF volume fraction was lower than 9 %. Consequently, I identify the solvent composition with THF volume fraction in the range of 9 % to 15 % as the supersaturated condition for micellization of PI1000-PFS50 block copolymer. I also showed that adding small amount of short micelles into the supersaturated solutions initiated the growth of fiber-like micelles.

The discovery of the supersaturated condition for PI1000-PFS50 allowed me to separate the nucleation stage of the micelle formation from the growth stage. In Chapter 4, I will describe the experiments showing the study of the growth kinetics of the PI1000-PFS50 block copolymer micelles using light scattering by adding micelle seeds into supersaturated polymer solutions.

References

1 Qian, J. S.; Guerin, G.; Cambridge, G.; Manners, I.; Winnik, M. A. Macromol. Rapid Commun. 2010, 31, 928-933. 2 Israelachvili, J. (ed) Intermolecular and Surface Force, 1992, Academic Press, Amsterdam. 3 LaRue, I.; Adam, M.; Pitsikalis, M.; Hadjichristidis, N.; Rubinstein, M.; Sheiko, S. S. Macromolecules 2006, 39, 309-314. 4 Jain, S.; Bates, F. S. Macromolecules 2004, 37, 1511-1523. 5 Dalhaimer, P.; Bates, F. S.; Discher, D. E. Macromolecules, 2003, 36, 6873-6877. 6 Wang, X. S.; Guerin, G.; Wang, H.; Wang, Y. S.; Manners, I.; Winnik, M. A. Science 2007, 317, 644-647. 7 Lin, E. K.; Gast, A. P. Macromolecules 1996, 29, 4432-4441. 8 Richter, R.; Schneiders, D.; Monkenbusch, M.; Willner, L.; Fetters, L. J.; Huang, J. S.; Lin, M.; Mortensen, K.; Farago, B. Macromolecules 1997, 30, 1053-1068. 9 Vilgis, T.; Halperin, A. Macromolecules 1991, 24, 2090-2095. 10 Lazzari, M.; Scalarone, D.; Hoppe, C. E.; Vazquez-Vazquez, C.; Lòpez-Quintela, M. A. Chem. Mater. 2007, 19, 5818-5820. 11 Lazzari, M.; Scalarone, D.; Vazquez-Vazquez, C.; Lòpez-Quintela, M. A. Macromol. Rapid Commun. 2008, 29, 352-357. 12 Schmalz, H.; Schmelz, J.; Drechsler, M.; Yuan, J. Y.; Walther, A.; Schweimer, K.; Mihut, A. M. Macromolecules 2008, 41, 3235--3234. 13 Du, Z. X.; Xu, J. T.; Fan, Z. Q. Macromolecules 2007, 40, 7633-7637. 14 Cao, L.; Manners, I.; Winnik, M. A. Macromolecules 2002, 35, 8258-8260. 15 Massey, J.; Power, K. N.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 1998, 120, 9533- 9540. 16 Wang, H.; Winnik, M. A.; Manners, I. Macromolecules 2007, 40, 3784-3789. 17 Shen, L.; Wang, H.; Guerin, G.; Wu, C.; Manners, I.; Winnik, M. A. Macromolecules, 2008, 41, 4380-4389. 18 Guerin, G.; Wang, H.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 2008, 130, 14763- 14771. 19 Sperling, L. H. Introduction to physical polymer science: 2006, John Wiley & Sons, Inc. 77

Chapter 4

GROWTH KINETICS OF FIBER-LIKE PI1000-PFS50 BLOCK

COPOLYMER MICELLES

In this chapter, I describe experiments that study the growth kinetics of fiber-like PI1000-

PFS50 block copolymer micelles by measuring the increase of the scattering intensity of the micelle solution over time. The data analysis showed that the growth kinetics of the fiber-like micelles could be described by an expression with two exponential decay terms.

4.1 Introduction

Fiber-like micelles, with cross-sections of nanometer dimensions, formed by the self- assembly of block copolymers have attracted much research interest because of their potential applications in many fields. For example, these objects are currently under investigation for drug delivery applications [ 1 ], as impact modifiers for plastics [ 2 ], as templates for the deposition of metal nanoparticles and as precursors to nanoscale ceramics [3]. Moreover, in some cases, studies of their formation and fragmentation are beginning to provide insight into the generation of protein fibers, such as actin or amyloid fibers [4]. As a result, it is important to understand the formation mechanism of these fiber-like micelles. In Chapter 1, I presented the theories describing micelle formation by different classes of block copolymers including coil- coil, rod-coil, and crystalline-coil block copolymers. For micelle formation by crystalline-coil block copolymers, there is only preliminary theory and it predicts a lamellar structure for these kinds of micelles [5].

Our group has been interested in the fiber-like micelles formed by the self-assembly of a family of crystalline-coil block copolymers containing a PFS block, which forms semicrystalline domains in the core of the micelles. We use the term “crystallization-driven” self- assembly (CDSA) to describe those self-assembly processes for which the crystallization of the core-forming block is the driving force for micelle formation. The CDSA of PFS block copolymers has been studied for several years. However, there has been no quantitative study about the growth kinetics of these fiber-like micelles, and the mechanism of the CDSA process 78 is still unknown. I was interested in understanding the formation mechanism of these PFS fiber- like micelles when I started my Ph.D., so I chose to study the growth kinetics of the fiber-like micelles formed by a block copolymer PI1000-PFS50 as part of my Ph.D. research.

PFS fiber-like micelles share common features with amyloid fibers formed by the aggregation of misfolded amyloid β-proteins [6] in biological systems. Both types of structures are formed by a nucleated growth mechanism [7,8], and they grow bidirectionally from seed nuclei formed by sonication [9,10]. There are substantial studies focused on the formation mechanism of amyloid fibers, due to the researchers’ desire to design targets for treatment of a class of diseases known as amyloidoses, which includes Alzheimer’s, Parkinson’s, type II diabetes, and the transmissible spongiform encephalopathies, all of which are associated with amyloid fiber formation. The mechanism of amyloid fiber formation is very complex. Recently, the Dobson group [11] presented an analytical treatment of a set of coupled kinetic equations that govern this process. The authors showed that the kinetics of amyloid growth can be even dominated by secondary nucleation events (fragmentation) rather than primary nucleation events. This feature makes it difficult to study the growth of amyloid fibers experimentally.

Several experimental techniques have been employed for the study of growth kinetics of amyloid fibers. The most commonly used technique employs thioflavin T (ThT) fluorescence [12]. ThT is a fluorescent dye that binds to β-sheet structures. When the ThT molecules bind to amyloid fibers, they become strongly fluorescent. Thus the formation of amyloid fibers can be followed by measuring the time profile of fluorescence intensity. This method is effective in quantifying the amount of protein molecules that transform from unimers to fibers, but not so useful for measuring the lengths of these fibers. Using ThT fluorescence, the Goto group developed a technique based on total internal reflection fluorescence microscopy to monitor the growth of individual fibers directly [13,14].

Light Scattering (LS) techniques, including Static Light Scattering (SLS) and Dynamic Light Scattering (DLS), are powerful tools for the study of the formation of amyloid fibers. Early in 1993, the Murphy group [15] used both SLS and DLS to study the formation kinetics of aggregates by the amine-terminal fragment β(1-28) of the β-amyloid peptide. These authors found that both the molecular weight (from SLS data) and apparent hydrodynamic radius (Rh,app, a radius indicative of the apparent size of the particle and calculated from the diffusional property of the particles from DLS data) increased as the fibers grew. However, in the late stage 79 of growth (e.g. after 48 hrs), the measured Rh,app no longer increased, although evidence from TEM measurements showed that the fibers were still growing. A similar methodology was adopted by the Teplow group [16], who also used DLS at 90° to study the kinetics of fiber formation of Aβ(1-40) by measuring the evolution of Rh,app over time.

The main challenge for studying the growth kinetics of fiber-like structures is that it is almost impossible to control the nucleation process. For example in the field of amyloid fibers, researchers have found that there is a large variation in nucleation rate among macroscopically identical samples, which results in poor reproducibility of the kinetics data [17]. A recent paper from the Linse group [18] shows how they appear to have overcome this problem by developing a recombinant expression system for the production of large amounts of highly pure Aβ(1-42). These samples allowed them to obtain reproducible kinetics data based on ThT fluorescence. Another factor that adds complexity to the kinetic study of amyloid fibers is that secondary nucleation processes, such as fragmentation, occur during the growth process. Chemists often take the view that simpler systems can be studied in greater detail. However, compared to the number of papers that describes studies of amyloid fiber formation, there are fewer studies investigating the growth kinetics of fiber-like micelles formed by synthetic block copolymers.

Peptide amphiphiles (PA), comprising hydrophilic peptides with hydrophobic alkyl tails, are a class of surface active molecules that are able to form micelles in water. These micelles have various morphologies depending on the volume and length of the alkyl tail and surface area of the peptide, similar to micelles formed by traditional surfactants [19,20]. Controlling the nano- and microstructures of these PA assemblies to give specific bioactivity of worm-like micelle is very much demanded in tissue regenerative therapies. As a result, understanding the formation mechanism is very important for further application of PA self-assembling materials. Recently, the Shimada group [21] used Small-angle Neutron Scattering (SANS) and Atomic Force Microscopy (AFM) to study the formation of the worm-like micelles formed by W3K- C16 PA (structure shown in Scheme 4.1A), a molecule with a simple structure and slow micelle formation kinetics. The authors showed that transient spherical micelles form in the early stage, and that elongated micelles are formed by attachment of spherical micelles to the ends of growing micelles, as illustrated in Scheme 4.1B. The different shapes of the micelles were distinguished from the fitting parameters of the neutron scattering data. A limitation of this approach is that when worm-like micelles grow to lengths over 20 nm, one is not able to obtain 80 quantitative information about the micelle length from SANS data. Quantitative analysis of the kinetics of the fiber-like micelle formation remains challenging.

Scheme 4.1. (A) Chemical structure of the peptide amphiphile C16-W3K. (B) Illustration of the formation of elongated micelles by the attachment of spherical micelles to the ends of the growing micelles. Reprinted from Ref [21] with permission.

The Schmalz group [ 22 ] has been interested in fiber-like micelles formed by block copolymers that contain a semicrystalline polyethylene (PE) block. They recently [23] reported a study of the formation kinetics of cylindrical micelles in toluene by the triblock copolymer

PS340-PE700-PMMA360 (PS: polystyrene, PMMA: polymethyl methacrylate). As part of that study, they examined growth kinetics by light scattering. Concentrated solutions of the polymer in toluene (2 g/L) were first heated to 80 °C to ensure complete melting/dissolution of the PE block. After cooling solutions to different crystallization temperatures, the authors monitored the 90° scattering intensity of the polymer solutions as a function of time. Their results showed that the scattering intensity increased as micellization proceeded until a plateau was reached, indicating complete micelle formation. Unfortunately, only qualitative information was available from the light scattering data. To obtain more quantitative information, the authors would need additional information about parameters such as the particle form factor and the number concentration of micelles in solution. This information is difficult to obtain for their system. 81 One study reporting some aspects of the formation kinetics of PFS block copolymer micelles was published by the Vancso group [24]. They used light scattering to study the time profile of the change in scattering intensity for fiber-like micelles formed by PFS50-PMMA341 in acetone, a good solvent for the PMMA block and a nonsolvent for the PFS block. The authors claimed that there was a rod-to-sphere transition at around 60 °C for the cylindrical micelles. As a result, they heated the polymer acetone solution to 65 °C, at where there was low scattering intensity. Then they quenched the solution to 55 °C and monitored the light scattering intensity over time. They found that the evolution of the scattering intensity had a sigmoidal shape, an exponential growth of scattering intensity at early stage and a linear growth after ~1000 s until the full development of the fiber-like micelles. Due to the complexity of the system, the authors were not able to draw quantitative information of the micelle growth kinetics from the light scattering measurements.

Until now, there have been no quantitative studies of the growth kinetics of fiber-like micelles formed by CDSA of block copolymers. The main limitation has been the difficulty in controlling the nucleation step. In addition, one has to know and control the number density of micelles. In Chapter 1, I described that under certain conditions, PFS block copolymer can grow onto pre-existing micelles without forming new micelles. The number of micelles remains constant and is determined by the number of micelles that were originally present in the solution. This feature of the PFS micelles gives one opportunity to separate the nucleation and the growth events. As a result, an alternative for studying the growth kinetics of PFS micelles is to use preformed micelle fragments as seed nuclei to eliminate the nucleation step and investigate the pure growth events of these fiber-like micelles.

In this chapter, I describe experiments that examine the growth kinetics of fiber-like micelles of PI1000-PFS50 block copolymer. The growth experiments were carried out by adding micelle seeds (in decane solution) into supersaturated polymer solutions (decane/THF mixtures). The growth of the micelles was monitored by measuring the evolution of scattering intensity of the solution at angles of 30o, 60o and 90o over a period of several weeks. The data analysis required a correlation of the scattering intensities versus the micelle lengths. This correlation was established by preparing a number of micelle solutions containing the same number concentration of micelles but with different lengths, and measuring the scattering intensity of each solution versus the micelle length. The kinetic results obtained showed that the increase of 82 micelle length can be described by an expression with two exponential decay terms. A model is then proposed to explain the kinetic results. In this model, we assumed that there exist two populations of polymer chains in the solution with different PFS conformations. One set of polymer molecules have a PFS block with a random coil conformation. These undergo rapid addition to the growing micelles. The other polymer is in a form that cannot add directly to the micelles, but must first undergo a slow relaxation. This “slow form” might be a small aggregate of unimers that must first undergo dissociation to free unimer, or it might be in the form of a unimeric micelle with a partially folded PFS (crystalline) block. These aggregates or unreactive unimer conformations lead to a slow rate constant when they add onto the micelles. We also examined various hypothesis about the nature of this class of unimers.

4.2 Experimental

4.2.1 Preparation of Micelle Seed Solution

The micelle seed solution was prepared by adding PI1000-PFS50 block copolymer (0.820 mg) to decane (1.64 mL, c = 0.500 mg/mL) in a 20 mL vial. The vial was placed in an oil bath at 90 °C for 30 min, followed by cooling slowly (ca. 1.5 °C/min) to room temperature. One day later, the vial was placed into a 70 watt ultrasonic cleaning bath and sonicated for 10 min at 23 °C followed by an additional 10 min at 23 °C.

4.2.2 Preparation of Micelle Solutions for the Correlation of Scattering Intensity with Micelle Length

In order to establish a correlation of scattering intensity with micelle length, I prepared a number of micelle solutions which contained the same number concentration of micelles, but of different lengths using the seeded growth approach as described in Chapter 2. I refer to these solutions as “reference solutions”. Eighteen reference solutions were prepared by adding 18 batches (20 μL, c = 0.500 mg/mL) of micelle seed solution (each contained 0.010 mg polymer) into 18 decane solutions (1.78 mL). After that, 18 batches of THF solutions (0.22 mL) containing different amounts of block copolymer were added into each of the 18 decane solutions. The amounts of polymer that were dissolved in the THF solutions of all these samples are listed in Table AI-4.1 in the Appendix I to this chapter. 83 Subsequently, I prepared another set of six reference solutions in which the number concentrations of micelles were doubled compared to those described above. The six reference solutions for a different correlation curve were prepared by adding six batches of 25 μL (c = 0.500 mg/mL) micelle seed solutions into six decane (0.89 mL) solutions, followed by addition of six batches of THF solutions (0.11 mL) containing different amounts of block copolymer (0.025, 0.050, 0.75, 0.100, 0.125, 0.150 mg).

In all reference solutions, the volume fraction of THF was 11 % (φTHF = 0.11), the same solvent composition as that used for the kinetics experiments. All the reference solutions were prepared in 7 mL vials and the vials were capped and sealed using Teflon tape to line the threads of the vials to prevent solvent evaporation. The solutions were allowed to age for four weeks before examining them by both TEM and light scattering.

4.2.3 Study of Micelle Growth Kinetics

The growth kinetics experiments for the PI1000-PFS50 micelles started with the preparation of supersaturated polymer solutions, followed by addition of a small amount of seed solution. In Table 4.1, I list all experimental parameters for each trial of the kinetics experiments, including the amount of polymer (Mpolymer mg), the volume of THF (VTHF mL), the volume of decane

(Vdecane mL), and the volume of seed solution (Vseed μL). For example, for Trial V10T11M02 as shown in Table 4.1, the supersaturated solution was prepared by dissolving block copolymer (0.020 mg) in THF (0.11 mL) in a 7 mL vial, followed by adding decane (0.89 mL) into the THF solution. Ten minutes later, micelle seed solution (10 μL) was added into the supersaturated solution. A series of six different kinetics experiments were carried out.

Immediately after the addition of micelle seed solution into the supersaturated polymer solution, the vial was agitated briefly and then placed in the sample holder of the light scattering apparatus. The scattering intensities of the solution at angles of 30o, 60o and 90o were monitored over a period of weeks. During the first day of the micelle growth, the acquisition time for each data point was 5 s. After one day, the acquisition time for each data point was increased to 10 s, three measurements were performed at each angle. The light scattering instrumentation was described in Chapter 2.

Table 4.1. Values of the volume of seed solution Vseed, the volume of THF VTHF, the volume of decane Vdecane, volume fraction of THF φTHF, and the mass mpolymer and molar concentration

Mpolymer of polymer in the supersaturated solutions of each trial of the kinetic experiments. V V V Trial a seed THF decane 100×φ c m (mg) M (mol/L) (μL) b (mL) c (mL) c THF polymer polymer V10T11M02 10 0.11 0.89 11 0.020 2.50×10-7 V10T11M05 10 0.11 0.89 11 0.050 6.24×10-7 V10T11M10 10 0.11 0.89 11 0.100 1.25×10-6 V10T11M20 10 0.11 0.89 11 0.200 2.50×10-6 V10T14M25 10 0.14 0.86 14 0.250 3.12×10-6 V25T11M12.5 20 0.11 0.89 11 0.125 1.56×10-6

a. The notation of each trial. For example, V10T11M02, 10 represents the volume of seed solution Vseed (μL),

11 represents the volume fraction of THF φTHF multiplied by 100, 02 represents the mass of polymer (mg) multiplied by 100 in the supersaturated solution. b. The seed solution had a polymer concentration of 0.500 mg/mL. c. The total volume of solvent for each trial was 1.00 mL.

Before the addition of seed solution, I carried out DLS measurements on two supersaturated solutions with unimer concentration of 0.10 mg/mL and 0.20 mg/mL, as well as pure solvent. The DLS experiments were performed at both 90o and 20o. DLS measurements at low angles are more sensitive to scattering objects. At 90o, both supersaturated solutions showed indistinguishable autocorrelation decays from the solvent. At 20o, we were able to obtain distinguishable autocorrelation decay from the supersaturated solutions with unimer concentration of 0.10 mg/mL (the acquisition time was 600s), however the signal is extremely low, which is only 20 % of scattering intensity of the pure solvent. For the supersaturated solution with unimer concentration of 0.20 mg/mL, we could see sparking species in the light path. The number of those sparking species increased as the solution aged. Due to the existence of sparking species, we were not able to obtained meaningful autocorrelation decay of the solution.

4.2.4 Diffusion Coefficient of PI800-PFS20 Polymer Chains in decane/THF Mixture

A solution was prepared by dissolving PI800-PFS20 block copolymer (4.857 mg) in a decane/THF mixture (1.00 mL, THF vol % = 11 %). The characteristics of this polymer were described in Chapter 2. The solution was filtered through a 0.2 μm PTFE membrane before the DLS measurements, which were carried out at 30°, 60°, 90°, 120°, and 150°. At each angle, the acquisition time was 120 s.

4.2.5 Competitive Seeded Growth of Micelles with Different Lengths

PI1000-PFS50 micelles with average length of ca. 250 nm and ca. 1250 nm were prepared via the seeded growth approach as described in Chapter 2. Two THF solutions (0.15 mL) containing

PI1000-PFS50 polymer (0.210 mg and 1.20 mg) were added into two decane solutions (3 mL) of sonication-shortened PI1000-PFS50 micelle seeds (Ln = 58 nm, Lw/Ln = 1.10, c = 0.020 mg/mL), respectively. 0.5 mL of each solution was taken out and mixed together to obtain a mixture solution, which contains both micelles of ca. 250 nm and ca. 1250 nm with the same number concentration. The mixture solution was diluted by decane to c = 0.020 mg/mL. Afterwards, competitive seeded growth was carried out by adding two aliquots of THF solutions (0.030 mL and 0.050 mL) containing PI1000-PFS50 polymer (c = 0.179 mg/mL) into two micelle mixture solutions (1.00 mL).

4.3 Results and Discussion

In Chapter 3, I described the preparation of supersaturated solutions of PI1000-PFS50 block copolymer in decane/THF mixtures. The preparation started with dissolving polymer in THF, followed by addition of decane to the THF solution. When the THF volume fraction fell into the range of 9-15 %, the block copolymer did not spontaneously form micelles. However, when I added aliquots of seed micelles in decane solution (average length of ca. 50 nm) into those solutions, I observed that much longer micelles (> 1 μm) formed. The results suggested that the addition of micelle seeds initiated micelle growth. Based on these observations, I identified this range of decane/THF solvent compositions as supersaturation conditions for the PI1000-PFS50 block copolymer. 86 In this chapter, I describe experiments that measured the kinetics of micelle growth when seed micelles were added to these supersaturated solutions. I used Static Light Scattering (SLS) to monitor the scattering intensities of the solution at angles of 30o, 60o and 90o after the addition of micelle seeds into the supersaturated polymer solution. To establish a correlation of scattering intensity with micelle length, I prepared a series of reference solutions which contained equal number concentration of micelles but with different lengths, and measured the scattering intensities of these reference solutions at angles of 30o, 60o and 90o. Based on the correlation of scattering intensity with micelle length, I translated the evolution of scattering intensity over time obtained in the kinetic experiments to the evolution of micelle length over time. I also show my attempts of using different models to analyze the kinetic data.

In Figure 4.1 I present a representative TEM image and the corresponding length distribution histogram of the PI1000-PFS50 micelle seeds in decane solution (c = 0.500 mg/mL) that were used in the experiments described in this chapter. The micelle seeds were characterized by Ln = 48 nm, Lw = 53 nm, and Lw/Ln = 1.12. The length and length distribution of the seeds remained constant over months.

A Seeds, c = 0.500 mg/mL 0.30 B 0.25 0.20 0.15 0.10 0.05

100 nm Normalized Frequency 0.00 0 50 100 150 200 Length (nm)

Figure 4.1. (A) TEM image and (B) length distribution histogram of the PI1000-PFS50 micelle seeds (c =

0.500 mg/mL). The micelle seeds were characterized by Ln = 48 nm, Lw = 53 nm, Lw/Ln = 1.12 and σ/Ln = 0.345.

87 4.3.1 Static Light Scattering Theory

In Static Light Scattering (SLS), one obtains structural and dimensional information about the scattering objects by measuring the angular dependence of the excess absolute scattering intensity (the Rayleigh ratio, ΔRθ, which is linear proportional to the scattering intensity I). For dilute solutions, Rθ is related to the concentration of the scattering objects c, the second viral coefficient A2, the weight-averaged molecular weight Mw of the scattering objects, and the form factor P(q) (P(q) = ΔRθ/ΔRθ=0) by

Kc ⎡⎤1122⎡1⎤ =⎢⎥ +++=2Ac23 3 Ac ... ⎢ +++2Ac23 3 Ac ...⎥ (4.1) ΔRθ ⎣⎦ Mww Pq() Pq()⎣ M ⎦

2 2 2 4 where K = 4π ns (dn/dc) /(NAλ ), NA is Avogadro’s number, λ is the incident wavelength (632.8 nm), ns is the refractive index of solvent (in my study, the refractive index of decane is 1.41, which is almost identical to that of THF (1.407), thus, I consider the ns value of the decane/THF mixture to be 1.41); dn/dc is the refractive index increment. The dn/dc value of each block of

PI1000-PFS50 in decane/THF was calculated using the Dale-Gladstone relation: (dn/dc)block ≈ (np - ns)/ρp, where np is the refractive index of the polymer block and ρp is the density of the polymer block. The error in the approximation of (dn/dc)block has been estimated to be less than 5 % [25]. 3 To calculate (dn/dc)block, I used a density of 1.26 g/cm and a refractive index of 1.68 for the PFS block, and a density of 0.92 g/cm3 and a refractive index of 1.52 for the PI block. From these values, I calculated the (dn/dc) of PFS and PI in decane/THF mixture to be (dn/dc)PFS ≈

0.214 mL/g and (dn/dc)PI ≈ 0.120 mL/g. The overall PI1000-PFS50 copolymer (dn/dc)tot was calculated from the weighted sum of the polymer blocks

ddnndn ()=+ww () () (4.2) ddcctot PFS PFS PIdc PI

where wPFS is the weight fraction of the PFS block wPFS = 0.151, and wPI is the weight fraction of the PI block wPFS = 0.849. Thus, I calculated the (dn/dc)tot for PI1000-PFS50 in decane/THF to be 0.134 mL/g.

When qRg < 1 (where q is the scattering vector qn= (4πλs / )sin( θ / 2) , and Rg is the radius

2 2 of gyration of the scattering objects), the form factor of the scattering object P(q) = 1-(q R g)/3. 88 In this case, P(q) is independent of the shape of the scattering objects, and eq. 4.1 can be rewritten as

Kc ⎡⎤11⎡ ⎤ A cAc22 qR2 =++++⎢⎥2323 ...1⎢ g ⎥ (4.3) ΔRMθ ⎣⎦w ⎣ 3 ⎦

2 Based on eq. 4.3, a Zimm Plot can be built by plotting Kc/ΔRθ versus sin (θ/2)+αc (α is an arbitrary constant). From the Zimm Plot, Rg can be evaluated from the slope of the plot for data extrapolated to c = 0; the weight-averaged molecular weight Mw of the scattering objects can be calculated from the intercept at θ = 0 of the plot for data extrapolated to c = 0.

For long thin cylindrical objects, the mass per unit length of the objects can be calculated without making any preliminary assumptions [26], using a Holtzer-Casassa (HC) representation

[27,28]. For my case of long fiber-like micelles formed by PI1000-PFS50 block copolymers with a narrow molecular weight distribution, I used a slightly modified form of the Holtzer-Casassa equation, and plot qRθ/πM0Kc as a function of q. Here M0 is the polymer molecular weight, and c is the weight concentration of polymer in the micelles. As in the traditional HC plot, the curve reaches a plateau value at high q, and, the magnitude of the plateau value is equal to the number of polymer molecules per unit length. I refer to this value as the linear aggregation number,

Nagg/L.

The rationale for studying the growth of one-dimensional micelles by monitoring the scatting intensity can be seen by expressing eq. 4.1 as

I ∝ ΔRθ ≈ P(q)KcMw (4.4)

If I assume that during the micelle growth, the linear aggregation number Nagg/L remains constant, then elongation of the micelles leads to a linear increase in both Mw and c. When the micelles are monodisperse in length L, then

2 I ∝ ΔRθ ∝P(q)L (4.5) which theoretically describes the correlation of scattering intensity I with the length of the fiber- like micelles L. 89 4.3.2 A Simple Growth Model

The growth of elongated objects in solution can in principle be very complex. For example very recently, Winnik and Ozin [29] examined the formation of ultrathin crystalline Bi2S3 nanowires in solution. In their system, the number concentration of nanowires decreased during the reaction, but the concentration of available Bi and S were approximately constant throughout the reaction. The authors derived a rate equation based on a model in which there are two major events for the elongation of nanowires, (i) addition of monomer to the ends of the nanowires, and (ii) “end-to-end” coupling of nanowires. Their model also assumed negligible termination and no initiation during fiber growth.

PFS block copolymer micelles display seeded growth as described in Chapter 1. When additional polymer dissolved in good solvent is added into a solution of micelles, these fiber- like micelles grow longer; but the number of micelles remains constant. The number of micelles in the solution is determined by the number of micelles that were originally present at the start of the experiment. We also found that the linear aggregation number remained constant. Based on this information, I present a simple model of micelle growth in Figure 4.2. This model assumes that (i) the elongation of the micelles is due only to the deposition of unimer (free polymer chains) onto the active ends of pre-existing micelles; (ii) the deposition of unimer onto micelle open end is irreversible, there is no dissociation of the already formed micelles; (ii) all unimers are identical; (iv) each growing micelle has two active ends, and all growing sites have equal activity towards monomer deposition. Thus, all micelles grow in parallel.

I can write the propagation of the micelles as:

••k ~~ MMx +⎯⎯→ ~~ Mx+1 where M is a unimer (a single polymer molecule in solution), M• is the active growing site for the propagation, and k is the rate constant for the propagation. The unimer concentration at time t is represented as [M]t with units of mol/L. The concentration of the growth sites (active chain ends) is expressed as [M•] with units of mol/L. Since there are two active ends per micelle, the value of [M•] = 2×[micelles], where [micelles] is the concentration of micelles with units of mol/L. The values of both [M•] and [micelles] remain constant during growth. 90

polymer chains in deposition and supersaturated solution growth seeds in all micelles grow suspension in parallel

Figure 4.2. A simple model illustrating the micelle growth. In this model, the number of micelles remains constant; the free polymer molecules in the supersaturated solution are identical and only grow from the

ends of the pre-existing micelle seeds, without forming new micelles.

Assuming that the growth of the micelles is a simple second-order reaction, the rate equation for the micelle growth can be written as:

-1 -1 Rate (mol·L ·s ) = -d[M]t/dt = k·[M]t·[M•] (4.6)

where at t = 0, the initial concentration of the monomer is [M]0, and rate constant k has units of L·mol-1·s-1.

Since the concentration of active growing sites [M•] remains constant during the growth, Equation 4.6 describes pseudo first-order kinetics equation:

-1 -1 Rate (mol·L ·s ) = -d[M]t/dt = k’·[M]t (4.7) where k’ = k·[M•] and k’ is the pseudo first-order rate constant with units of s-1.

Integration of eq. 4.7 gives

-k’t [M]t = [M]0·e (4.8) which suggests that the depletion of monomer follows first-order exponential decay kinetics. 91

At growth time t, the concentration of unimer is [M]t, thus, the concentration of unimer that has been consumed is [M]0 - [M]t. Supposing that the linear aggregation of the micelles remains constant during the growth, the length increment can be represented by

[]MM0 − []t Δ=LL0 (4.9) []M s

where [M]s is the concentration of polymer present in the initial micelle seeds, and L0 is the number-averaged length of the micelle seeds. Thus, the micelle length Lt at the growth time t can be expressed by:

[]MM00− []t [] ML0−kt' LLt =+00LL=+0(1 − e ) (4.10) []MMss[] suggesting that the increase of the micelle length can be described by an equation with an exponential decay term.

4.3.3 Correlation of Scattering Intensity with Micelle Length

The growth of the micelles was monitored using light scattering by measuring the scattering intensities of the solution at three different angles (30o, 60o and 90o) at different growth times. In Section 4.3.1, I presented the theoretical description of how scattering intensity varies with micelle length. In this section, I describe the experiments that establish an experimental correlation of scattering intensity with micelle length. I first prepared 18 reference micelle solutions via the seeded-growth method, by adding 18 batches (20 μL, c = 0.500 mg/mL) of micelle seed solutions into 18 decane solutions (1.78 mL), followed by addition of 18 batches of THF (0.22 mL) containing various amounts of polymers (from 0.002 to 0.4 mg). These reference solutions contained equal number concentration of micelles but with different mean lengths. One month after the preparation of these reference solutions, these solutions were examined by both TEM and SLS.

In Figure 4.3A-D, I show four representative TEM images of the micelles formed in four reference solutions. The corresponding length distributions of each sample are shown in Figure 4.3E-H. The ratio indicated in each TEM image represents the ratio of amount of polymer (unimer) dissolved in THF to the amount of polymer in the micelle seeds (0.010 mg). One sees 92 that as the unimer-to-seed ratio was increased, longer micelles with narrow length distributions were obtained. Values of Ln, Lw/Ln and σ/Ln obtained from the TEM image of all the 18 reference samples are collected in Table AI-4.1 in the Appendix I to this chapter. In Figure 4.4A,

I plot the number-average length Ln of these micelles obtained from their TEM images versus the unimer-to-seed ratio. This plot shows a linear dependence of the micelle length on the unimer-to-seed ratio. The dashed line in Figure 4.4A represents the theoretical values of the micelle length for seeded growth experiments. The theoretical length is evaluated using eq. 2.5

M unimer { Ltheoretical =+×(1)Lseed } in Chapter 2. Comparing the Ln values obtained from TEM M seed measurements with Ltheoretical for each sample, I estimate the average growth efficiency of unimer onto the micelles for the reference solutions to be ca. 90 %. In Figure AI-4.1 in the Appendix I to this chapter, I show a plot of Ln versus the unimer-to-seed ratio, in which the ratio values vary from 0 to 5, from the same data in Figure 4.4A.

A: 1.8:1 B: 2.4:1 C: 3.5:1 D: 4.4:1

0.4 0.3 0.25 E 0.3 F G H 0.3 0.20 0.2 0.2 0.15 0.2 0.10 0.1 0.1 0.1 0.05 0.0 0.0 0.00 Normalized Frequency Normalized 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Length (nm) Length (nm) Length (nm) Length (nm)

Figure 4.3. (A-D) TEM images and (E-H) corresponding length distribution histograms of micelles formed in four reference solutions, which were prepared by the seeded growth method. The ratio indicated in each figure represents the ratio of amount of polymer dissolved in THF to the amount of polymer in the

micelle seeds. (E) Ln = 111 nm, Lw = 115 nm, Lw/Ln = 1.04 and σ/Ln = 0.189; (F) Ln = 138 nm, Lw = 143

nm, Lw/Ln = 1.04 and σ/Ln = 0.199; (G) Ln = 195 nm, Lw = 200 nm, Lw/Ln = 1.03 and σ/Ln = 0.172; (H) Ln

= 228 nm, Lw = 235 nm, Lw/Ln = 1.03 and σ/Ln = 0.180. Scale bars are 500 nm.

93 SLS measurements were carried out on these reference solutions, in which the unimer-to- seed ratios ranged from 0.2 to 5. In Figure 4.4B, I show four representative Holtzer-Casassa plots of qRq/πM0Kc as a function of q, for the four reference solutions that are shown in Figure 4.3. The solid lines correspond to the best fit of the data to

fq()= qPqM ()w / M0π (4.11)

where Mw is the molecular weight of the micelles and Mw = L×Nagg,L×M0, and P(q) is the form factor for rigid rods monodisperse in length [30]:

2 ⎡⎤⎛⎞⎛⎞qLSLS cos( x ) ⎢⎥sin ⎜⎟ π /2 ⎜⎟Jsin()qR x ⎢⎥⎝⎠2 1 ()SLS PqL(,SLS , R SLS )=× 2 ⎜⎟× ×sin()dx x (4.12) ∫0 qLcos( x ) ⎢⎥⎜⎟SLS qRSLS sin( x ) ⎢⎥⎜⎟ ⎣⎦⎝⎠2

here the fitting parameters LSLS represents the weight-averaged length of the micelles and RSLS represents the radius of the cross section of the micelles. The plateau at high q value in the plots in Figure 4.4B indicates the presence of elongated objects in the solution. The magnitudes of the plateau values, from which the linear aggregation number Nagg/L can be calculated, were obtained as a fitting parameter for all of the samples. The data fitting was performed by computer automatically using software Matlab, the code for the data fitting was developed based on the Gauss-Newton iteration method by my cousin Mr. Xinyang Zhang. The data analysis method and the code are described in the Appendix I to this chapter. The values of the fitting parameters of LSLS, RSLS, and Nagg/L for each sample are listed in Table AI-4.2 in the Appendix I to this chapter. One sees that micelles from the reference solutions were characterized by radius values RSLS ranging from 20 nm to 34 nm, with an average value of RSLS

= 27 nm for the cross section. The average value of the linear aggregation number Nagg/L was ca.

1.6 molecules/nm. A previous paper from our group reported a Nagg/L value of 1.9 molecules/nm for the micelles formed by the same polymer PI1000-PFS50 in pure decane [31].

In an attempt to investigate the influence of polydispersity in the length of the micelles, I re-fitted the data for the first two samples, which were characterized by the largest Lw/Ln values (1.08 and 1.07, as determined from the TEM measurements) by taking into account the polydispersity in length of the micelles by incorporating a Zimm-Schulz distribution into eq. 4.12: 94 bz+1 wL()= LzbL e− (4.13) z!

where b = (z+1)/Lw, and z = 1/[(Lw/Ln)-1]. However, no change of the fitting parameters was observed from the data fitting after taking the polydispersity (Lw/Ln = 1.08, z = 12.5) in micelle length into account.

o o o 30 60 90 2000 1.5 A B 1500 theoretical

(nm) length 1.0 Kc n o L

1000 M / π q 0.5 4.4:1

500 qR 3.5:1

Length 2.4:1 1.8:1 0 0.0 010203040 0 5 10 15 20 25 q (μm-1) munimer/mseed

Figure 4.4. (A) Number-averaged length Ln of the micelles obtained from the TEM images in the reference solutions versus unimer-to-seed ratios. The error bars represent the standard deviations σ of the length distribution as determined from the length distribution histograms. The dashed line represents the theoretical length evaluated from eq. 2.5. (B) Representative Holtzer-Casassa plots for micelles formed in four reference solutions as shown in Figure 4.3, with different unimer-to-seed ratios (as indicated in the plot).

In Figure 4.5A, I plot the scattering intensities I of the 18 reference solutions at different angles (30o, 60o, and 90o) versus the theoretically predicted lengths of each sample, with micelle lengths up to ca. 2000 nm. The same data with the micelle lengths from 50 to 300 nm is represented in Figure 4.5B. The scattering angles are indicated in the plots. The solid lines represent the best fit of these scattering intensity data points at each angle to eq. 4.5: {I ∝ P(q)L2} with fitting equations of

2 I = 0.00125×P(q,LSLS,RSLS)×L (4.14) 95 o obtained by setting RSLS = 27 nm as the radius of the cross sections of micelles. For data at 30 , q = 7.25 μm-1; for data at 60o, q = 14.0 μm-1; for data at 90o, q = 19.8 μm-1. The goodness of fit for data points at each angle are all R2 = 0.99. The goodness of fit is represented by a statistics term, the coefficient of determination R2, which is defined by

2 ∑()yfii− 2 (4.15) R ≡−1 i 1 n ∑∑()yyii− iin

where yi is the observed value, fi is the predicted value, and n is the number of data points. The plots in Figure 4.5 describe an experimental correlation of scattering intensity vs micelle length.

1200 100 A B 30° 30° 900 75 60°

600 50 60° 90° 300 25 90° 0 Scattering Intensity (kHz) 0 Scattering Intensity (kHz) 0 500 1000 1500 2000 0 50 100 150 200 250 300 Micelle length (nm) Micelle length (nm)

Figure 4.5. (A) Plot of scattering intensities versus micelle lengths (50-2000 nm) based on the 18 reference solutions. (B) Plot of scattering intensities versus micelle lengths (50-300 nm) of 15 reference solutions, from the same data in (A). Solid lines represent the best fit of each set of the data points to eq. 2 4.14 with {I = 0.00125×P(q,LSLS,RSLS)×L , with RSLS = 27 nm}. The scattering angles are indicated in the plots.

4.3.4 Kinetics Data of Trial V10T11M05

In this section, I describe one characteristic experiment that illustrates key features of the micelle growth kinetics. In this experiment, a seed solution (10 μL, decane, c = 0.500 mg/mL) was added into 1.00 mL of supersaturated polymer solution (decane/THF, c = 0.0500 mg/mL,

φTHF = 0.11). In my notation for this experiment Trial V10T11M05, 10 represents the volume of 96 the seed solution Vseed (μL), 11 represents the volume fraction of THF in the solution expressed as a percent, 05 represents the mass of polymer (0.05 mg) multiplied by 100 in the supersaturated solution. Due to the addition of seed solution, the total volume of the solution increased from 1.00 mL to 1.01 mL; φTHF decreased from 0.11 to 0.109. I consider these slight changes in total volume and solvent composition to be negligible.

In Figure 4.6A, I show the evolution of scattering intensities of the solution at angles of 30o, 60o and 90o over a period of ca. 5 weeks for Trial V10T11M05. The error bars for the scattering intensity data points starting from ca. 1×103 min represent the standard deviations of three measurements at each angle. One sees that the scattering intensities of the solution increased substantially over the first two days (3×103 min) and continued for more than five weeks (5.5×104 min). The scattering intensities after one week’s growth (1×104 min) increased much more slowly than during the early stage. In order to convert the plot of scattering intensities versus time in Figure 4.6A to a plot of micelle lengths versus time, I need the correlation between scattering intensities and micelle lengths, as shown in Figure 4.5. However, it is impossible to obtain an analytic solution of the fitting equation 4.14 {I = 2 0.00125×P(q,LSLS,RSLS)×L } due to the complicated P(q) expression. Thus, I used a set of high order polynomial equations to approximate the numerical solutions:

For data at 30o,

L (nm) = 27.62491 + 8.21472×I - 0.251015×I2 + 6.12398×10-3×I3 - 8.54898×10-5×I4 + 6.1674×10-7×I5 - 1.77939×10-9×I6 when I < 98;

L (nm) = 62.4808 + 3.43841×I - 0.014811×I2 + 5.34221×10-5×I3 - 9.02282×10-8×I4 + 7.18923×10-11×I5 when I ≥ 98 (4.16a)

For data at 60o,

L (nm) = 25.29322 + 9.27463×I - 0.34998×I2 + 0.01136×I3 - 2.10464×10-4×I4 + 2.04022×10-6×I5 - 7.94872×10-9×I6 when I < 71;

L (nm) = -30.47566 + 5.18429×I - 0.01129×I2 + 3.90995×10-5×I3 - 6.39167×10-8×I4 + 3.98352×10-11×I5 when I ≥ 71; (4.16b)

97 For data at 90o,

L (nm) = 25.63545 + 9.334×I - 0.31204×I2 + 0.00935×I3 - 1.3247×10-4×I4 + 7.68228×10-7×I5 when I < 51;

L (nm) = 30.3897 + 5.40794×I - 0.00144×I2 + 1.00254×10-5×I3 - 2.93444×10-8×I4 + 3.0767×10-11×I5 when I ≥ 51 (4.16c)

The precision of this set of numerical solutions is better than 0.1 %.

In Figure 4.6B, I present the evolution of micelle length L(calc) versus time, calculated based on the scattering intensities in Figure 4.6A through eq. 4.16. The error bars for data points during the early 1×103 min represent the standard deviations of the L values calculated from the three different angles, while the error bars at longer time represent the standard deviations of the L values calculated from nine measurements (three measurements at each angle). The dashed line in Figure 4.6B represents the theoretical predicted micelle length Ltheoretical = 528 nm evaluated by eq. 2.5. The data in Figure 4.6B show that the length of the micelles increased over a period of several weeks (5.5×104 min). At the growth time of ca. 2 weeks (2×104 min), the micelle length reached a measured value of 559±40 nm, which is slightly larger than the predicted maximum length. Three weeks later (at the growth time of 5.5×104 min), the micelle length L(calc) had increased slightly to 580±40 nm. During the last three weeks (growth time from 2×104 min to 5.5×104 min), the increase of micelle length as determined by the light scattering intensity was ca. 3.5 %, which is smaller than the experimental error (ca. 7 %). For the light scattering data at of 30o, 60o and 90o at the growth time of ca. two weeks, I also fitted the data to eq. 4.4 by using a LSLS value of 559 nm and a RSLS value of 27 nm, I obtained a Nagg,L value of 1.65 molecules/nm, which is very close to the value that obtained from the reference solutions as shown in Table AI-4.2.

An aliquot of the solution of Trial V10T11M05 taken after two weeks (2×104 min) was examined by TEM. In Figure 4.6C and D, I show a representative TEM image and the corresponding length distribution histogram of the micelles of this sample. One sees that the longer micelles formed had uniform length and width. These micelles were characterized by Ln

= 551 nm and Lw = 558 nm, thus, Lw/Ln = 1.01, a very narrow length distribution. The length value obtained by the TEM measurements is very close to that obtained from the light scattering measurements (559 nm) at the same growth time (2×104 min). The consistency of the final 98 length value obtained from different characterization methods provides confidence in the kinetic data as shown in Figure 4.6B. In Figure AI-4.2 in Appendix I to this chapter, I show a magnified TEM image of this sample and the corresponding width distribution histogram of the PFS core.

One sees that the obtained micelles had very uniform core and were characterized by dn = 10.0 nm, dw = 10.1 and dw/dn = 1.01.

300 A 600 B 30° 250 500 200 400 60° 150 300

100 (calc)(nm) 200 90° L 50 100

Scattering Intensity(kHz) 0 0 0 102030405060 0 102030405060 3 Time (×10 min) Time (×103 min)

C D 0.3

0.2

0.1

Normalized Frequency 0.0 0 300 600 900 1200 1500 Length (nm)

Figure 4.6. Kinetic data of Trial V10T11M05. The sample examined was obtained by adding 10 μL (c =

0.500 mg/mL) seed solution into 1.00 mL supersaturated polymer solution (c = 0.050 mg/mL, φTHF = 0.11). (A) Evolution of scattering intensities over time for a period of ca. five weeks. The error bars of the scattering intensity data points starting from ca. 1×103 min represent the standard deviations of three measurements at each angle. (B) Evolution of micelle length L(calc) over time, calculated from the data in (A) through eq. 4.16. The error bars for data points during the first 1×103 min represent the standard deviations of the L values calculated from the three different angles, while the error bars for longer times represent the standard deviations of the L values calculated from nine measurements (three measurements

at each angle). The dashed line represents the value Ltheoretical evaluated by eq. 2.5. (C and D) TEM image and the corresponding length distribution histogram of the micelles at the growth time of ca. 2 weeks. The

scale bar is 500 nm. The micelles in (C) were characterized by Ln = 551 nm, Lw = 558 nm, Lw/Ln = 1.01.

99 4.3.5 Fitting of the Kinetics Data of Trial V10T11M05

In this section, I describe the fitting of the kinetic data for Trial V10T11M05 as shown in Figure 4.6B. In Section 4.3.2, I derived a simple model of the micelle growth, which predicts that the increase of micelle length should follow first-order exponential decay growth to a maximum value. As a result, I first tried to fit the kinetics data in Figure 4.6B to the equation

Lt()=+× A B e−t /τ (4.17) which is a simplified form of eq. 4.10. In Figure 4.7A, I show a best fit of first-order exponential decay to the data by setting the boundary condition that L(t→∞) = A = 559 nm, where I consider the micelle length at the growth time of two weeks as the final length. The solid line in Figure 4.7A represents the fitting equation of L = 559 - 426×e(-t/2438), which gives R2 = 0.92. One sees that the fitting line reaches the plateau of 559 nm at growth time of ca. 2×103 min, much shorter than the experimental time to reach the plateau at 559 nm (2×104 min). In Figure 4.7B, I show the same plot on a logarithmic time scale. One sees that the fitting equation also does not fit the early stage of the growth. The plots in Figure 4.7A and B indicate that the data cannot be fitted by a simple first-order exponential decay equation.

An interesting question is whether the growth kinetics are best fit with a sum of exponential terms describing discrete steps or by a broad distribution of rates or relaxation times f(τ). If the data are of sufficient quality, one can distinguish these descriptions through an inverse Laplace transform of the decay kinetics. We used a CONTIN analysis [32] to fit the kinetics data of Trial V10T11M05 to the expression

LL− ∞ 1(−=t 1 f τ )exp( −td/ττ) (4.18) ∫0 LLf − 1

where L1 is the initial value of length of micelles as determined by light scattering (L1 = 74 nm);

Lt is the length of micelles at time t, Lf is the final length of micelles as determined by light scattering (Lf = 559 nm). In Figure AI-4.3 in Appendix I to this chapter, I present the CONTIN plot of the distribution f(τ) of decay time τ. One sees that there are two main decay times, one has a mean value of ca. 400 min, and another has a mean value of ca. 7800 min. Because of the ill-posed nature of eq. 4.18 and the presence of noise and error in the kinetic data, it is difficult to determine accurately the magnitude of the individual decay rates by the CONTIN analysis. 100 However, one can still clearly see that micelle growth is not described by a broad unimodal distribution of rates. A sum of fast and slow processes, differing by about an order of magnitude in rate, provides a better description of the growth kinetics.

600 600 500 500 400 400 300 300 200 200 (calc) (nm) (calc) (calc) (nm) (calc) Length (nm) Length (nm) L L 100 100 0 0 0 102030405060 1 10 100 1000 10000 Time (×103 min) Time (min)

600 C 600 D 500 500 400 400 300 300

200 (nm) (calc) 200 (calc) (nm) (calc) Length (nm) L Length (nm) L 100 100 0 0 0 102030405060 1 10 100 1000 10000 Time (×103 min) Time (min)

Figure 4.7. Fitting of the kinetics data of Trial V10T11M05 as shown in Figure 4.6B. The fitting equations are (A,B) L = 559 - 426×e(-t/2438), R2 = 0.92, (A) on normal time scale, (B) on logarithmic time scale; (C,D) L = 559 - 197×e(-t/337)- 275×e(-t/6975), R2 = 0.99, (C) on normal time scale, (D) on logarithmic time scale.

To proceed, I fit the data for this experiment to a sum of two exponential decay terms.

Lt()=+× A B e−−tt//τ12 +× C e τ (4.19) with the boundary condition that L(t→∞) = A = 559 nm. This expression fits the data very well. In Figure 4.7C, I show the best fit of the kinetic data to the equation of

L = 559 - 197×e(-t/337)- 275×e(-t/6975) (4.20) 101 which gives R2 = 0.99. In Figure 4.7D, I show the same plot on a logarithmic time scale. One sees that the equation fits the experimental results well over the entire course of the measurement. The two decay times from the data fitting (337 and 6975 min) are close to the values of the CONTIN analysis (~ 400 min and ~ 7800 nm)

A mechanistic interpretation of the two exponential decay fitting would suggest that there are two parts to the micelle growth, a fast part with a relaxation time of 337 min, and a slower part with a relaxation time of ca. 7000 min. The pre-factor of the fast part is 197 nm, and the pre-factor of the slow part is 275 nm. These results suggest that the first 197 nm of the micelle growth (ca. 42 %) was due to the rapid part, which occurred over in the first day of the micelle growth; while other 275 nm of the micelle growth (ca. 58 %) was due to the slower part, which continued for a period of two weeks.

If the double exponential fit is mechanistically meaningful, it means that at least one of the assumptions that led to the predictions of eq 4.17 is incorrect. Later in the paper, I remove the assumption that there is only one class of unimer in solution whose addition to the micelle ends could be described with a single rate constant. This leads to models that predict that micelle growth should follow a sum of two exponential decay terms. Before presenting these models, I describe additional experiments to test whether kinetics experiments run with different ratios of unimer to seed micelles also fit a sum of two exponential decay terms.

4.3.6 Additional Kinetics Experiments

The experimental data I describe in this section were obtained from Trial V10T11M02, Trial V10T11M10, and Trial V25T11M12.5. For Trial V10T11M02, seed solution (10 μL, decane, c = 0.500 mg/mL) was added into 1.00 mL supersaturated polymer solution -7 (decane/THF, c = 0.0200 mg/mL = 2.50×10 mol/L, φTHF = 0.11). For Trial V10T11M10, seed solution (10 μL) was added into 1.00 mL supersaturated polymer solution (c = 0.100 mg/mL = -6 1.25×10 mol/L, φTHF = 0.11). For Trial V25T11M10, seed solution (25 μL) was added into -6 1.00 mL supersaturated polymer solution (c = 0.125 mg/mL = 1.56×10 mol/L, φTHF = 0.11). Based on the information obtained from Trial V10T11M05 in Section 4.3.4 that the increase of micelle length from growth time of two weeks to five weeks was only 3.5 %, I considered that the micelle growth was nearly complete after a growth time of two weeks. As a result, for the 102 experiments described in this section, I stopped measuring the scattering intensities at the growth time of ca. two weeks for each trial.

In Figure 4.8, I present the increase of scattering intensities at angles of 30o, 60o and 90o of solutions from Trial V10T11M02, V10T11M10, and V25T11M12.5 for a period of ca. two weeks. The scattering angles for each measurement are indicated on the plots. The error bars of the scattering intensity data points starting from ca. 1×103 min represent the standard deviation of three measurements at each angle. One sees that for all the three trials, the scattering intensities of the solutions increased substantially over the first two days (3×103 min). After that, the increase of scattering intensities slowed down, but continued for two weeks (2×104 min).

The conversion of the evolution of scattering intensities over time to the evolution of micelle length over time needs correlation of scattering intensity with micelle length. For the data from Trial V10T11M02 and V10T11M10 in Figure 4.8A and B, I used the same set of equations 4.16, because the concentration of micelle seeds in these solutions (the reference solutions and the solutions in Trial V10T11M02 and V10T11M10) were the same, and thus all these solutions contained the same number concentration of micelles. However, for Trial V25T11M12.5, in which larger amount of seed solution (25 μL) was added into 1.00 mL supersaturated polymer solution, a new correlation curve is needed.

In order to build a new correlation curve suitable for Trial V25T11M12.5, I prepared another set of six micelle reference solutions via seeded growth method by adding six batches of micelle seed solution (25 μL) into six decane (0.89 mL) solutions, followed by addition of six batches of THF solutions (0.11 mL) containing different amounts of block copolymer (0.025, 0.050, 0.75, 0.100, 0.125, 0.150 mg). These solutions were allowed to age at room temperature for one month before examining then both by LS and TEM. 103

A : T r ial V 10T11M02 B: Trial V10T11M10 75 600 500 30° 30° 50 400 60° 300 90° 60° 25 200 100 90° 0 0 cteigIntensityScattering (kHz) Scattering Intensity (kHz) 0 5 10 15 20 0 5 10 15 20 25 Time (×103 min) Time (×103 min) C: Trial V25T11M12.5 600 500 30° 400 300 60° 200 90° 100 0 Scattering Intensity (kHz) 0 5 10 15 20 25 Time (×103 min)

Figure 4.8. Scattering intensities of solutions from (A) Trial V10T11M02, (B) V10T11M10, and (C) V25T11M12.5 at angles of 30o, 60o and 90o for a period of ca. two weeks (2×104 min). The error bars of the scattering intensity data points starting from ca. 1×103 min represent the standard deviations of three

measurements at each angle.

In Figure 4.9A, I plot the number-averaged length Ln obtained from TEM images of the micelles from the six reference solutions versus the unimer-to-seed ratio. The dashed line represents the theoretical lengths Ltheoretical of the micelles based on eq. 2.5. One sees that the lengths of the micelles from each sample reached the predicted maximum value; all micelles were characterized by very narrow length distribution, as indicated by the small error bars σ (standard deviation of length distribution) of each data point. In Figure 4.9B, I show the correlation curve based on the six reference solutions by plotting the scattering intensities at 104 o o o angles of 30 , 60 and 90 versus the Ltheoretical for each sample. The scattering angles are indicated on the plots. The solid lines represent the best fit of these scattering intensity data points at each angle to eq. 4.5 {I ∝ P(q)L2 (4.5)} with fitting equations

2 I = 0.003125×P(q,LSLS,RSLS)×L (4.21)

obtained by setting RSLS = 27 nm as the radius of the cross sections of the micelles.. The goodness of fit for the data points at each angle are all R2 = 0.99. In order to calculate the length values of the micelles based on the scattering intensity, I also used a set of numerical equations to approximate the eq. 4.21:

For data at 30o,

L (nm) = 27.62379 + 3.28609×I - 0.04017×I2 + 3.92059×10-4×I3 – 2.18955×10-6×I4 + 6.31924×10-9×I5 – 7.29384×10-12×I6 when I < 246;

L (nm) = 101.88717 + 0.96063×I – 8.22032×10-4×I2 + 8.05063×10-7×I3 – 2.21709×10-10×I4 when I ≥ 246 (4.22a)

For data at 60o,

L (nm) = 27.83522 + 3.31353×I - 0.03712×I2 + 3.397×10-4×I3 – 1.55474×10-6×I4 + 2.81415×10-9×I5 when I < 178;

L (nm) = 406.81641 - 3.58387×I + 0.0244×I2 – 4.92104×10-5×I3 + 3.54232×10-8×I4

when I ≥ 178 (4.22b)

For data at 90o,

L (nm) = 25.6367 + 3.73335×I – 0.04992×I2 + 5.9838×10-4×I3 – 3.38987×10-6×I4 + 7.86272×10-9×I5 when I < 128;

L (nm) = -343.32871 + 8.86923×I – 0.04328×I2 + 1.18124×10-4×I3 – 1.15976×10-7×I4 when I ≥ 128 (4.22c)

The precision of this set of numerical solutions is better than 0.1 %. 105

800 A 600 B 30° 600

(nm) 400

n 400

L 60° 200 200 90° Length

0 Scattering Intensity(kHz) 0 0.0 4.0 8.0 12.0 0 200 400 600 Micelle Length (nm) munimer/mseed

Figure 4.9. (A) Number-averaged length Ln of the micelles obtained from the TEM images in the six reference solutions versus the unimer-to-seed ratio. The error bars represent the standard deviations σ of the length distribution as determined from the length distribution histograms. The dashed line represents

the theoretical length evaluated from eq. 2.5. (B) Plot of scattering intensity versus Ltheoretical of micelles for the six reference solutions in (A). Solid lines represent the best fit of the data points from the same

2 angle to eq. 4.21 with {I = 0.003125×P(q,LSLS,RSLS)×L , with RSLS = 27 nm}.

Based on eq. 4.16 and 4.22 of the correlation between scattering intensity and micelle length, I calculated the micelle length based on the data of evolution of scattering intensities in Figure 4.8. The results are presented as evolution of L(calc) versus time in Figure 4.10. The error bars for data points during the early 1×103 min represent the standard deviations of the L values calculated from the three different angles, while the error bars at longer time represent the standard deviations of the L values calculated from nine measurements (three measurements at each angle). The dashed line in each plot represents the theoretical predicted maximum length

Ltheoretical evaluated based on eq. 2.5. For Trial V10T11M02 in Figure 4.10A, one sees that after two weeks (2×104 min) growth, the micelles length L(calc) reached 250±15 nm, which is close to the theoretical predicted maximum length of 240 nm. For Trial V10T11M10, after more than two weeks (2.5×104 min) growth, the micelle length L(calc) reached 1086±80 nm, which is slightly larger than the theoretical predicted maximum length of 1008 nm. For Trial V25T11M12.5, after two weeks (2×104 min) growth, the micelle length L(calc) reached 514±25 nm, which is also very close to the theoretical predicted maximum length of 528 nm.

106

300 1200 Theoreticalmaximum Theoreticalmaximum 250 1000 200 800 150 600

100 (nm) (calc) 400 Length (nm) Length (calc) (nm) (calc) Length (nm) L L 50 A: Trial V10T11M02 200 B: Trial V10T11M10 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (×103 min) Time (×103 min)

600 TheoreticalMaximum

400

200 Length (nm) (calc) (nm) (calc) L C: Trial V25T11M12.5 0 0 5 10 15 20 25 Time (×103 min)

Figure 4.10. Evolution of micelle length L(calc) over time of (A) Trial V10T11M02, (B) V10T11M10, and (C) V25T11M12.5 for a period of two weeks (2×104 min), calculated from the data in Figure 4.8. The error bars for data points during the early 1×103 min represent the standard deviation of the L values calculated from the three different angles, while the error bars at longer time represent the standard deviation of the L values calculated from nine measurements (three measurements at each angle). The dashed line represents the theoretical maximum length evaluated based on eq. 2.5.

At the end of each experiment (two weeks), I took aliquots of each sample for examination by TEM. In Figure AI-4.4 in the Appendix I to this chapter, I show representative TEM images of each micelle sample and their corresponding length distribution histograms. One can see that after ca. two weeks growth, long micelles with uniform length and uniform width were obtained.

I list the values of Ln, Lw and Lw/Ln obtained from TEM measurements of the micelles from Trial V10T11M02, V10T11M10, V25T11M12.5, and also V10T11M05 in Table 4.2, where I also present the values of Ltheoretical and length L(calc) obtained from light scattering measurements of each trial for comparison. Data in Table 4.2 show that for each trial of the 107 kinetic experiments, the final micelle lengths obtained from TEM measurements and light scattering measurements are within 10 % of the theoretical length Ltheoretical. This set of data provides confidence on the validity of the kinetics results shown in Figure 4.10.

Table 4.2. Value of Ltheoretical, Ln, Lw and Lw/Ln obtained from TEM measurements, and length

L(calc) calculated from light scattering (LS) intensity of PI1000-PFS50 micelle samples for each of the four trials of kinetic experiments.

TEM LS L Trial theoretical (nm) Ln (nm) Lw (nm) Lw/Ln L(calc) (nm) σ (nm)

V10T11M02 240 239 245 1.02 250 15

V10T11M05 528 551 558 1.01 559 40

V10T11M10 1008 937 945 1.01 1086 80

V25T11M12.5 528 514 521 1.01 514 25

I then fitted the kinetic data (L(calc) vs. t) for these three experiments to eq 4.19 with two exponential decay terms. We used the boundary conditions that L(t→∞) = A = 250 nm for the data in Figure 4.10A, that L(t→∞) = A = 1086 nm for the data in Figure 4.10B, and that L(t→∞) = A = 514 nm for the data in Figure 4.10C. The fits of these data to eq. 4.19 are shown in Figure 4.11. The values of fitting parameters and the goodness of fitting parameters for each trial are listed in Table 4.3.

Table 4.3. Values of fitting parameters of kinetic data from Trial V10T11M02, V10T11M02, V25T11M12.5, and V10T11M10 to eq. 4.19, and the goodness of fit. Boundary Trial B (nm) τ (min) C (nm) τ (min) R2 L(t→∞) (nm) 1 2 V10T11M02 250 59 334 126 5806 0.99

V10T11M05 559 197 337 275 6975 0.99

V25T11M12.5 514 145 116 233 3815 0.98

V10T11M10 1086 293 196 676 4611 0.99

108

300 300

250 250

200 200

150 150 (calc) (nm) (calc) (nm) (calc) 100 100 L L Length (nm) Length Length (nm) 50 50 A: Trial V10T11M02 B: Trial V10T11M02 0 0 0 5 10 15 20 25 1 10 100 1000 10000 Time (×103 min) Time (min) 600 600

400 400 (calc) (nm) (calc) (calc) (nm) (calc)

L 200 200 L Length (nm) Length (nm) Length

C: Trial V25T11M12.5 D: Trial V25T11M12.5 0 0 0 5 10 15 20 25 1 10 100 1000 10000 Time (×103 min) Time (min) 1200 1200 1000 1000 800 800 600 600 (calc) (nm) (calc) (calc) (nm) (calc) L L

400 Length (nm) 400 Length (nm) Length 200 200 E: Trial V10T11M10 F: Trial V10T11M10 0 0 0 5 10 15 20 25 1 10 100 1000 10000 Time (×103 min) Time (min)

Figure 4.11. Fitting of the kinetic data in Figure 4.10. (A and B) Trial V10T11M02, fitted by L = 250 - 59×e(-t/334)- 126×e(-t/5806), R2 = 0.99; (C and D) Trial V25T11M12.5, fitted by L = 514 - 145×e(-t/116)- (-t/3815) 2 (-t/196) (-t/4611) 2 233×e , R = 0.98; (E and F) Trial V10T11M10, fitted by L = 1086 - 293×e - 676×e , R = 0.99.

109 4.3.7 Kinetic Models Leading to Double Exponential Decay Kinetics

In the sections above, I showed that fitting the micelle growth kinetics from all four experiments requires a sum of two exponential decay terms, which suggests that the growth of the micelles involves two steps, a fast step and a slower step. In this section, I present two sequential kinetic models that predict a sum of two exponential decay terms of the growth. To develop a model that predicts fast and slow steps in the micelle growth, we have to relax the assumption that there is only one type of unimer present in the solution. Some of the unimer must be trapped in an unproductive state such as an aggregate. DLS measurements at 90° on supersaturated solutions of unimer at concentrations up to 0.20 mg/mL in 11 % THF in decane showed autocorrelation decays indistinguishable from the solvent. Since DLS measurements at low angles are more sensitive to the scattering objects, as well as the presence of aggregates, we carried out additional measurements at 20° for the supersaturated solutions of unimer at concentration of 0.10 mg/mL (see autocorrelation function in Figure AI-4.5A in Appendix I to this chapter). The CONTIN analysis (Figure AI-4.5B) showed that the polymer chains were characterized by a mean hydrodynamic radius of ca. 8 nm. Based on the scattering intensity of the supersaturated solution with unimer concentration of 0.10 mg/mL at angle of 20o, I calculated the molecular weight of the scattering species in the solution. For my system, the excess Rayleigh ratio Rθ of the solution is calculated via:

I scat 2 sinθ 2 RRsolution− solvent ⎛⎞ nsolvent Iinc −5 ⎛⎞1.41 RRθ ==Rstd ⎜⎟ −5 ×1.35× 10 ×⎜⎟ Rnstd ⎝⎠std 5.27× 10 ⎝1.4969 ⎠ (4.23) I =×0.2273scat sinθcm−1 Iinc -5 -1 where RRstd = 1.35×10 cm is Rayleigh ratio of the standard solvent toluene, nstd = 1.4969 is -5 the refractive index of toluene, Rstd = 5.27×10 is a constant related to our apparatus, Iscat represents the scattering intensity of the solution, Iinc represents the intensity of the incident beam, θ represents the scattering angle. Thus for the supersaturated solution with unimer concentration of 0.1 mg/mL, I calculated the molecular weight of the scattering species via: I M ==×RKc/ 0.2273scat. sinθ / (1.457 × 10−−722cmgmolmgmL ×0.1 / ) θ I inc. (4.24) -7 2 -2 Where K is the optical constant with value of 1.457×10 cm g mol. In my experiment, Iscat =

Isolution - Isolvent = 31.3 kHz - 24.5 kHz = 5.8 kHz, while Iinc = 404,000, inserting these values into 110 eq. 4.24 gives M ≈ 90 kDa. The molecular weight M0 of the PI1000-PFS50 polymer is ca. 80 kDa. These results suggest that there is no aggregate in the supersaturated solution with unimer concentration of 0.1 mg/mL. In the attempt to carry out DLS measurements at 20° for the supersaturated solution of unimer at concentrations of 0.20 mg/mL, we saw sparking species, whose number increased as the solution aged, in the light path. Due to this reason, we were not able to acquire meaningful autocorrelation function. we infer that at such unimer concentration, self-nucleation occurred in the supersaturated solution. In measurements that I will describe in more detail below, we also carried out DLS measurements on a sample of PI800-PFS20, which does not form micelles in this solvent. To obtain the diffusion coefficient of this polymer (i.e., to detect signal from free molecules), we had to examine solutions with a much higher concentration, ca. 5 mg/mL. Small aggregates would not be detected by scattering experiments at polymer concentrations no greater than 0.20 mg/mL.

In deriving the kinetic equations for a model in which only a fraction of the unimers are in a productive state for addition to growing micelles, we note that there is a kinetically equivalent model which does not involve aggregates. In this model, one hypothesizes that a fraction of the unimers are kinetically trapped in an unproductive state. In protein chemistry, there is substantial current interest in proteins, commonly enzymes, that are kinetically trapped in unproductive conformations and are slow to rearrange to active forms [33].These kinetically trapped states often arise as newly synthesized protein molecules are transformed into the properly folded state with biological activity [6]. This situation is unknown for synthetic polymers. For completeness, we include this idea in our basic kinetic model presented in Figure 4.12.

In this model, a fraction of the unimer in the initially prepared supersaturated polymer solution is present as free molecules. We depict this polymer in a random coil conformation and refer to them as Mpro, i.e., “productive” unimers. They are able to add directly to the ends of micelle seeds or growing micelles with a second order rate constant kadd. In the upper left, we depict small aggregates of unimer also present in the initially prepared supersaturated polymer solution. Unimer can dissociate from the aggregates with a first order rate constant kd to form productive unimer. We also include the idea of a fraction of unimer kinetically trapped in an unproductive state that unfolds slowly (with first order rate constant ku) to form Mpro. Since we 111 have evidence against the presence of aggregates in the supersaturated solution, this process can serve as an alternative explanation for the slow step in micelle growth.

A: Dissociation Model k d small PFS aggregate

k add B: Unfolding PI Model k u Mpro

unproductive conformation

Figure 4.12. Illustrations of two sequential growth models for PI1000-PFS50 block copolymer micelles. For both models, one population of the polymer chains are kinetically trapped in “unproductive” state, the other population of the polymer chains are in the “productive” state. (A) Dissociation Model: the “unproductive” state is small aggregate of several molecules; (B) Unfolding Model: the “unproductive” state is the polymer chain with the PFS block partially folded. Polymer chains in the “unproductive” state cannot grow onto micelles directly, they must first transform themselves to the “productive” state, which can add onto micelles directly.

Below is the derivation of kinetic equations based on the two sequential growth models depicted in Figure 4.12. For both models, I use Mpro to represent the “productive” unimer that can add to micelle directly with rate constant kadd; I use Munpro to represent the “unproductive” unimer that either in small aggregate or in folded state. Since the models are kinetically equivalent, we employ ku to refer to the slow first order step for the transformation of unimers from the Munpro state to the Mpro state.

The growth of micelles involves:

••kadd ~~ M x +⎯⎯⎯MMpro → ~~ x+1 (4.25a) 112

ku MMunpro ⎯⎯→ pro (4.25b)

The rate equations for Mpro and Munpro can be written separately as:

-1 -1 RateMpro (mol·L ·s ) = -d[Mpro]t/dt = kadd·[Mpro]t·[M•] – ku·[Munpro]t (4.26a)

-1 -1 RateMunpro (mol·L ·s ) = -d[Munpro]t/dt = ku·[Munpro]t (4.26b)

-1 -1 Note that kadd is a second-order rate constant with unit of L·mol ·s , while ku is first-order rate -1 constant with unit of s . The initial total concentration of unimer is [M]0 = [Mpro]0 + [Munpro]0. Since the concentration of active growing sites [M•] is a constant and [M•] = 2×[micelles].

Eq. 4.26a can be rewritten as:

-1 -1 RateMpro (mol·L ·s ) = -d[Mpro]t/dt = k1’·[Mpro]t – ku·[Munpro]t (4.27)

-1 where we can define the pseudo-first-order rate constants k1’ with units of s :

k1’ = kadd·[M•] (4.28)

Integration of eq. 4.26b gives:

−ktu [][]MMunpro t= unpro 0 e (4.29)

Insertion of eq. 4.29 into eq. 4.27 and integration gives:

k'[][][ M−− kM kM ] kM [ ] 10pro u pro 0 u unpro 0−kt1 ' u unpro 0−ktu []M pro t =+ee (k1’ ≠ ku) kk11''−−uukk (4.30)

The total concentration of unimer is given by [M]t = [Mpro]t + [Munpro]t. Setting [Mpro]0 = x×[M]0, [Munpro]0 = (1-x)×[M]0, then:

xk1 '− ku −kt1 ' 1− x −ktu []MMt =+ []{0ek1'e} (4.31) kk11''−−uu kk

Thus, the increase of micelle length could be expressed by inserting eq. 4.31 into eq. 4.9: 113

[]Mxkkx01 '− u −kt1 ' 1− −ktu LLt =+00 L[1 − e − k1' e ] (4.32) []Mkkkksu11 '−− ' u

where L0 is the length of the seed micelles at t = 0, [M]s is the concentration of polymer present in the initial micelle seeds, with units of mol/L, and x is the fraction of micelle growth of due to the deposition of molecules that originally exist in the “productive” state. Eq. 4.32 suggests that the increase of micelle length could be described by an expression with two exponential decay terms. Eq. 4.32 can be rewritten in a general form as { Lt()=+× A B e−−tt//τ12 +× C e τ , eq. 4.19}.

Eq. 4.32 relates the fitting parameters of the kinetic data in terms of eq. 4.19 (Table 4.3), to mechanistically meaningful rate constants. From values of τ1 (τ1 = 1/k1’) and τ2 (τ2 = 1/ku) I obtained the pseudo-first-order rate constants k1’ and first-order rate constant ku for the two growth steps. The fraction x of growth due to the fast step k1’ can be calculated from the pre- factors of two exponentials terms (B and C). These values are listed in Table 4.4. There is consistency among the different experiments in the values of the rate constants and fractional contribution of the fast and slow steps to the micelle growth process. I can also use Eq. 4.28 to obtain the second-order rate constants kadd through known [M•] value, where [M•] = 2×[micelles]. To calculate the molar concentration of micelles [micelles], I assume that the micelle seeds were characterized by the same linear aggregation number (Nagg/L ≈ 1.6 molecules/nm) as that determined by SLS for the micelles in the reference solutions. The micelle seed sample had Ln = 48 nm. For Trials 1, 2 and 3, the mass concentration of micelle seeds in the solution was 5×10-3 g/L; thus I calculate:

510× −3 gL / []M •= ×21.6310 ≈ × −9 mol / L (4.33) 80100g / mol×× 48 nm 1.6 molecules / nm

By introducing this value, I obtain the values of the second-order rate constants kadd that are also listed in Table 4.4. These values show a remarkable consistency for the four kinetic experiments.

114 Table 4.4. Values of unimer concentration [M], concentration of active growing site [M•], pseudo first-order rate constant k1’ and first-order rate constant ku, second-rate constants kadd, and fraction x of micelle growth due to the fast step for each trial of the kinetics experiments, based on the two sequential growth models.

-1 -1 -1 -1 Trial [M] (mol/L) [M•] (mol/L) k1’ (s ) ku (s ) kadd (L·mol ·s ) x

V10T11M02 2.50×10-7 1.63×10-9 5.0×10-5 2.8×10-6 3.1×104 0.36

V10T11M05 5.24×10-7 1.63×10-9 4.9×10-5 2.4×10-6 3.0×104 0.45

V10T11M10 1.25×10-6 1.63×10-9 8.5×10-5 3.6×10-6 5.2×104 0.33

V20T11M10 1.25×10-6 3.26×10-9 14.4×10-5 4.4×10-6 4.4×104 0.40

Average N/A N/A N/A 3.3×10-6 4.0×104 0.39

Based on the two sequential growth models and data in Table 4.4, we suggest that there are two components of the micelle growth, a fast step and a slow step. The fast step is due to the direct addition of “productive” unimer onto micelles with a second-order rate constant of ca. 4.0×104 L·mol-1·s-1. The slow step is due to the transformation of “unproductive” unimer to “productive” one with a first-order rate constant of ca. 3.3×10-6 s-1. The fraction of micelle growth due to the attachment of “productive” unimer in the fast step is ca. 40%.

4.3.8 A Model for Diffusion Controlled Micelle Growth

According to the data presented above, it appears that micelles grow via two steps that take place at different rates. It is important to examine whether the fast step is limited by the mass transport of unimers to the active growing ends, the so-called diffusion controlled limit. In this section, I describe a model of micelle growth, in which the rate-determining step is the diffusion of unimers to the growing ends. My goal is to calculate the magnitude of kdiff, the rate constant one would obtain if the micelle growth was a diffusion-controlled reaction, and compare its magnitude with kadd for the fast step of micelle growth (Table 4.4). I approach this problem through the theory of diffusion-controlled reaction.

I rewrite the propagation of the micelles as:

••kdiff ~~ MMx +⎯⎯⎯→ ~~ Mx+1 (4.34) 115

If the micelle growth step is diffusion-controlled, the rate constant kdiff can be expressed as [34]: 4π N kDDR=+AV ()(+R) (4.35) diff 1000 u m u m

In this expression, Du is the diffusion coefficient of the unimer; Dm is the diffusion coefficient of the micelle; Ru is the capture cross section of the unimer; and Rm is the capture cross section of the micelle. I take the capture cross section of the micelle to be that of the PFS core with Rm ~ 5 nm, which is obtained from the TEM measurement as shown in Figure AI-4.2. I also assume that it is much larger than Ru for the unimer. The most important parameter for evaluating Eq.

4.33 is the diffusion coefficient of the unimer Du in solution, which should be much larger than

Dm for the micelles.

In order to measure the diffusion coefficient Du of the unimer in the solution, I chose to use a block polymer PI800-PFS20, which has a slightly smaller molecular weight but a much shorter

PFS block than the polymer PI1000-PFS50 as used in the kinetics experiments. This polymer does not form micelles at high concentration under the same solvent composition as the micelle growth experiments described above. The solution was prepared by dissolving PI800-PFS20

(4.857 mg) in a decane/THF mixture (1.00 mL, φTHF = 0.11). DLS measurements were carried out at angles of 30°, 60°, 90°, 120°, and 150°. The results are presented as a plot of the inverse of relaxation time (the decay rate Γ) of the autocorrelation function versus q2 in Figure 4.13. From the slope of the plot in Figure 4.13, I calculated the diffusion coefficient of the unimer to -7 2 -1 be Du = 4.1×10 cm ·s via the equation:

Γ = D×q2. (4.36) 116

) 20 -1 >(ms

Γ 10 <

0 0 200 400 600 800 2 -2 q (μm )

Figure 4.13. Plot of inverse of relaxation time (decay rate Γ) of the autocorrelation function versus q2 for

PI800-PFS20 block copolymer in decane/THF (φTHF = 0.11) solution at the concentration of 4.875 mg/mL. The solid line represents the best linear fit of the data. From the slope of the line, the diffusion coefficient

D = 4.1×10-7 cm2·s-1 of the polymer was calculated.

The information of diffusion coefficient Dm of the micelles with different lengths was obtained from the DLS measurements of the reference solutions as shown in Figure 4.4. In Figure AI-4.6 in the Appendix I to this chapter, I plot the diffusion coefficient of the micelles, which was calculated via eq. 4.36, versus the length (LTEM) of the micelles from six of the reference solutions. One can see that the diffusion coefficient Dm decreases as the micelles grow -8 2 -1 longer. The diffusion coefficient of the micelle was Dm = 4.7×10 cm ·s for micelles with

LTEM = 58 nm. When the length of micelles increases to LTEM = 1166 nm, the value of diffusion -8 2 -1 coefficient decreased to be Dm = 1.8×10 cm ·s . All these Dm values are at least one magnitude smaller than the diffusion coefficient of the unimer Du. As a result, I consider Du >>

Dm.

Based on eq. 4.35, I calculated the rate constant for diffusion-controlled micelle growth:

23− 1 4π ×× 6.023 10 mol −72−− 1 6 1−1 kdiff =×()4.1 10 cm× s(5 nm)≈ 1.5× 10 L× mol× s (4.37) 1000

The kdiff value is about two orders of magnitude larger than the rate constant kadd for the fast addition process. 117 There are examples in the literature where rotational diffusion of rod-like molecules plays a role in reducing the rate of a diffusion controlled reaction [35].As an additional test of whether this influences micelle growth, we carried out a competition experiment to test whether short micelles, which undergo more rapid rotational diffusion, undergo more rapid extension under seeded growth. We prepared a 1:1 (by number) mixture of two micelle samples at c = 0.020 mg/mL in decane, one with Ln,TEM = 250 nm and the other with Ln,TEM = 1250 nm. We then added a small amount of a solution of PI1000-PFS50 in THF to the solution to see if both types of micelles reacted at the same rate. As the experimental results described in Figure AI-4.7 in Appendix I to this chapter, both micelles increased in length by similar lengths. We conclude that micelle growth is also not influenced by rotational diffusion rates of the micelles.

It is not surprising that epitaxial condensation of the PFS block onto the micelle ends is an activated process if we consider micelle growth in the context of models for polymer crystallization. In the classic theory to address the kinetics of spherulitic growth in crystallizing polymers developed by Keith and Padden [36], the growth rate G, can be described by the equation

Δ−ΔERT// FRT GGe= 0 e (4.38) where ΔF is the free energy of formation of a surface nucleus of critical size, and ΔE is the free energy of activation for a chain crossing the barrier to the crystal. Eq. 4.38 shows that the growth of a polymer crystal is determined by both the nucleation process and the growth process. In the case of our micelle growth experiments, added micelle seeds served as the nuclei, and no new micelles were formed. Consequently, the growth rate of the micelles depends solely on the rate at which unimers add to the growth fronts of the micelle seeds. The driving force for unimers crossing the barrier to the seeds was provided by the supersaturation condition. The unimers grew onto the seeds via chain folding of the PFS block. A theory proposed by Yoon and Flory [37] suggests that for a lamellar polymer crystal in process of growth, a sequence of a certain minimum length is required for its deposition in the growth layer via conformational rearrangements. We speculate that in the “Unfolding” sequential growth model, the folded PFS block needs to unfold to reach the required size for deposition, resulting in a slower growth rate than for the unimers with the PFS block in the form of a random coil. The unfolding takes place in solution prior to interaction with the micelle. Our kinetic data demand that this 118 conformational rearrangement is time-consuming, and in solution the two populations of unimers are slow to equilibrate.

4.3.9 Experiments at Higher Unimer Concentrations

In this section, I describe two additional experiments carried out at higher unimer concentrations. In Trial V10T11M20, seed solution (10 μL) was added into 1.00 mL -6 supersaturated polymer solution (decane/THF, c = 0.200 mg/mL = 2.5×10 mol/L, φTHF = 0.11). In Trial V10T14M25, seed solution (10 μL) was added into 1.00 mL supersaturated polymer -6 solution (decane/THF, c = 0.250 mg/mL = 3.12×10 mol/L, φTHF = 0.14).

A : Tri al V 10T11M20 B: Trial V10T14M25 1200 1200 30° 30° 900 900 60° 600 600 60°

300 300 90° 90° 0 0 Scattering Intensity (kHz) Scattering Intensity (kHz) Scattering Intensity (kHz) 0 5 10 15 20 Scattering Intensity (kHz) 0 1020304050 Time (×103 min) Time (×103 min)

Figure 4.14. Evolution of scattering intensities over time of solutions from (A) Trial V10T11M20 for a period of ca. two weeks (2×104 min), and from (B) Trial V10T14M25 for a period of ca. one month (5×104 min). The error bars of the scattering intensity data points starting from ca. 1×103 min represent the standard deviations of three measurements at each angle as indicated in the plot.

In Figure 4.14, I present the increase of scattering intensities at angles of 30o, 60o and 90o of the solution from Trial V10T11M20 (Figure 4.14A) over a period of ca. two weeks (2×104 min), and from Trial V10T14M25 (Figure 4.14B) over a period of more than one month (5×104 min). The error bars of the scattering intensity data points starting from ca. 1×103 min represent the standard deviations of three measurements at each angle. One sees that for Trial V10T11M20 in Figure 4.14A, the scattering intensities reached a plateau at growth time of ca. one week (1×104 min). While for Trial V10T14M25 in Figure 4.14B, the increase of scattering intensities continued for a very long period of more than one month (5×104 min). 119

2500 Theoretical maximum 1000 30° 2000 800

1500 TEM length 600 60° 1000 400 (calc) (nm) (calc)

app 90°

L 500 200 A (kHz) Intensity B 0 0 Corrected Scattering Scattering Corrected 0 5 10 15 20 0 5 10 15 20 Time (×103 min) Time (×103 min) 2000 2000

1500 1500 TEM length 1000 1000 (calc) (nm) (calc) (calc) (nm) (calc) Corrected app Corrected 500 500 L app L C D 0 0 0 5 10 15 20 1 10 100 1000 10000 Time (×103 min) Time (min)

Figure 4.15. Data for Trial V10T11M20. (A) Evolution of micelle length over time, calculated from the data in Figure 4.14A through 4.16. The upper dashed line represents the theoretical predicted maximum

length Ltheoretical evaluated based on eq. 2.5. The lower dashed line represents the final micelle length obtained from TEM measurement. (B) Evolution of corrected scattering intensity over time, by dividing the scattering intensity in Figure 4.14A by 1.24. (C) Evolution of corrected micelle length over time, calculated from the data in corrected plot in (B) through eq. 4.16. The dashed line represents the final micelle length obtained from TEM measurement. (D) Fitting of the kinetic data in (C) on a logarithmic time scale. The fitting equation is L = 1579 - 689×e(-t/121)- 709×e(-t/1994), R2 = 0.99. In (A, C, and D), the error bars for data points during the early 1×103 min represent the standard deviations of the L values obtained from the three different angles, while the error bars for longer time represent the standard deviations of the L values obtained from nine measurements (three measurements at each angle).

Based on the eq. 4.16 showing the correlation between scattering intensity and micelle length, I calculated the micelle length Lapp(calc) from the scattering intensity in Figure 4.14A

(Trial V10T11M20) and present the evolution of micelle length Lapp(calc) versus time in Figure 4.15A. The error bars for data points during the early 1×103 min represent the standard deviations of the L values calculated from the three different angles, while the error bars at 120 longer time represent the standard deviations of the L values calculated from nine measurements (three measurements at each angle). The upper dashed line represents the theoretical maximum length Ltheoretical = 1968 nm, which is evaluated based on eq. 2.5. One can see that after ca. 2 weeks growth, the calculated micelle length reached an apparent value of Lapp(calc) = 1960±200 nm, which is close the predicted maximum length. The lower dashed line represents the length of micelles that were characterized by the TEM measurement, which was performed at the growth time of ca. two weeks (2×104 min). In Figure AI-4.8 in the Appendix I to this chapter, I show a representative TEM image and the corresponding length distribution histogram of the micelle sample. One can see that, long micelles with uniform length and uniform width were obtained. The micelles were characterized by Ln = 1579 nm, Lw = 1591 nm, Lw/Ln = 1.01. This length value obtained from TEM measurements is smaller than the value obtained from the light scattering measurements Lapp(calc). These results indicate that new factors operate in this experiment, and complicate analysis of the kinetic data shown in Figure 4.15A for Trial V10T11M20.

I was curious about the reasons why the values of micelle length obtained from both LS and TEM measurements are smaller than Ltheoretical. I began the analysis by comparing the experimental conditions in Trial V10T11M20 with those in other trials (V10T11M02, V10T11M05, and V10T11M10) described above. In all these experiments, the volume of the seed solution and the solvent compositions were the same, but the unimer concentration in the supersaturated solution varied. In Trial V10T11M20, a higher unimer concentration (0.200 mg/mL or 2.5×10-6 mol/L) was used. I speculate that due to the increase of the unimer concentration, self-nucleation may have occurred during the growth, resulting in an increase of the number of micelles in the solution. By TEM measurement, I showed that the Lw/Ln value of the final micelles was only 1.01, indicating micelles with very narrow length distribution. Therefore, new nucleation had to happen at very early times in the experiment. The increase of micelle number also caused the increase of scattering intensity. However, the calibration curve I used to connect scattering intensity to micelle length assumed a constant and known concentration of micelles.

In order to test my hypothesis about Trial V10T11M20, I now assume that the deviation of values of the micelle length obtained from both LS and TEM was because of the increase of micelle number. Thus, based on the length value determined from TEM (LTEM = 1579 nm) and 121

LS (Lapp(cal) = 1960 nm), there were 1960/1579 = 1.24 times the amount micelles present in the solution compared to that in the seed solution. I then corrected the scattering intensity of the solution (divided by 1.24) as shown in Figure 4.14A to normalized the data to the number of micelles equivalent to that present in the seed solution. The time profile of scattering intensity after correction is shown in Figure 4.15B. I then calculated the micelle length Lapp(calc) based on the new plot of scattering intensity over time to a plot of micelle length over time, through eq. 4.16. The result is shown in Figure 4.15C. One sees that after data correction, the final micelle length (corrected Lapp(calc)) calculated from scattering intensities is 1579 nm, which is the value of LTEM (Ln = 1579 nm).

For the results of Trial V10T11M20, I used an equation with a sum of two exponential decay terms { Lt()=+× A B e−−tt//τ12 +× C e τ (4.19)} to fit the corrected data in Figure 4.15C. I used the boundary condition that L(t→∞) = A = 1579 nm, which is the corrected final length

Lapp(calc) value calculated from scattering intensities before data correction. The fit of data in Figure 4.15A is shown in Figure 4.15D in logarithmic time scale. The values of fitting parameters and the goodness of fitting parameters are listed in Table 4.5. I interpret these values of the fitting parameters based on the two sequential growth models as described in Section

4.3.7. From values of the fitting parameters τ1 and τ2, I calculated the values of pseudo first-order rate constants k1’ and first-order rate constant ku. I calculated the fraction x of growth due to the fast step from the pre-factors of two exponential terms. I also calculated the values of second- order rate constants kadd, via equation 4.26, based on presumed values of [M•], where [M•] = 2×[micelles]. The values of these parameters are also listed in Table 4.5.

Table 4.5. Trial V10T11M20, values of fitting parameters, the goodness of fit, values of concentration of unimer [M] and active growing site [M•], pseudo first-order rate constants k1’ and first-order rate constants ku, second-order rate constants kadd and fraction x of micelle growth due to the fast step, based on the two sequential growth models Boundary Trial B (nm) τ (min) C (nm) τ (min) R2 L(t→∞) (nm) 1 2 V10T11M20 1579 689 121 709 1994 0.99

a -1 -1 -1 -1 a [M] (mol/L) [M•] (mol/L) k1’ (s ) ku (s ) kadd (L·mol ·s ) x

2.50×10-6 2.02×10-9 1.4×10-4 8.4×10-6 6.8×104 0.52

a. This value takes into account the 24% additional seeds formed by self nucleation. 122 The data in Figure 4.15 and Table 4.5 show the growth of micelles can still be well fitted by an equation with two exponential decay terms. The second-order rate constant for the fast step (8.6×104 L·mol-1·s-1) and first-order rate constant for the slow step (8.4×10-6 s-1) have the same magnitude as the values that were obtained for the trials described in previous sections (4.0×104 L·mol-1·s-1 and 3.3×10-6 s-1, respectively). The fraction of micelle growth due to the fast step is 0.52 for Trial V10T11M20, which is slightly larger than the reported value for other experiments.

For Trial V10T14M25, I also calculated the micelle lengths based on the scattering intensities in Figure 4.14B via eq. 4.16. In Figure 4.16A, I present the time profile of micelle 3 length Lapp(calc). The error bars for data points during the early 1×10 min represent the standard deviations of the L values calculated from the three different angles, while the error bars at longer time represent the standard deviations of the L values calculated from nine measurements (three measurements at each angle). The upper dashed line represents the theoretical maximum length Ltheoretical = 2448 nm, which is evaluated via eq. 2.5. One can see that after ca. 5 weeks growth, the micelle length reached an apparent calculated value of

Lapp(calc) = 2150±200 nm, which is ca. 12 % smaller than the predicted maximum length. The lower dashed line represents the length of micelles that were characterized by the TEM measurement, which was performed at the growth time of more than one month (5×104 min). In Figure AI-4.8 in the Appendix I to this chapter, I show a representative TEM image and the corresponding length distribution histograms. One can see that, long micelles with uniform length and uniform width were obtained. The micelles were characterized by Ln = 1768 nm, Lw

= 1791 nm, Lw/Ln = 1.01. This length value is smaller than the values obtained by the light scattering measurements (Lapp(calc) = 2150); and both experimental values of final length deviate from Ltheoretical. These results suggest that there are also factors that operate in this experiment and complicate analysis of the kinetic data in Figure 4.16A for Trial V10T14M25.

I was also interested in the reasons why the values of micelle length obtained from both LS and TEM measurements are smaller than Ltheoretical for Trial V10T14M25. In this experiment, the volume fraction of THF was increased to 14 %, while other experimental conditions remained the same as those used in Trial V10T11M20. I suspect that due to the high volume fraction of THF in the mixture solvent, the CMC of the polymer might not be negligible, and only a fraction of the unimer could grow onto the micelles, leading to shorter micelles than expected. 123 In order to test this hypothesis, after five weeks growth of the sample, I selectively evaporated the THF in the solution and carried out TEM measurement on the sample again. The results showed that the micelles were characterized by Ln = 1407 nm, Lw = 1436 nm and Lw/Ln = 1.02, which was even smaller than the value (Ln = 1768 nm) before THF evaporation. This result implies that my hypothesis is wrong. Right now, I do not have a reasonable explanation for the results of Trial V10T14M25.

3000 2500 Theoreticalmaximum 2500 2000 2000 1500 1500 TEM length

(calc) (nm) (calc) (nm) (calc) 1000 Length (nm)

app 1000 app L L Length (nm) Length 500 500 A B 0 0 0 1020304050 1 10 100 1000 10000 Time (×103 min) Time (min)

Figure 4.16. Data analysis for Trial V10T14M25. (A) Evolution of micelle length Lapp(calc) over time, calculated from the data in Figure 4.14B through eq. 4.16. The upper dashed line represents the theoretical

predicted maximum length Ltheoretical evaluated based on eq. 2.5. The lower dashed line represents the final micelle length obtained from TEM measurement. (B) Fitting of the kinetic data in (A) on logarithmic time scale. The fitting equation is L = 2150 - 479×e(-t/592)- 1530×e(-t/11131), R2 = 0.99. The error bars for data points during the early 1×103 min represent the standard deviations of the L values calculated from the three different angles, while the error bars for longer time represent the standard deviations of the L values calculated from nine measurements (three measurements at each angle).

The interpretation of data from Trial V10T14M25 may be complicated, but it is also interesting to see that the micelles obtained after more than one month (5×104 min) growth were characterized by a very narrow length distribution (Lw/Ln = 1.01). As a result, I also used the equation with a sum of two exponential decay terms { Lt()=+× A B e−−tt//τ12 +× C e τ (4.19)} to fit the data in Figure 4.16A. I used the boundary condition that L(t→∞) = Lapp(calc) (t→∞) = A = 2150 nm. The fit of data in Figure 4.16A is shown in Figure 4.16B for the logarithmic time scale. The values of fitting parameters and the goodness of fitting parameters are listed in Table 124 4.6. I interpret these values of the fitting parameters based on the two sequential growth models as described in Section 4.3.7. From values of the fitting parameters τ1 and τ2, I calculated the values of pseudo first-order rate constants k1’ and first-order rate constant ku. I calculated the fraction x of growth due to the fast step from the pre-factors of two exponential terms. I also calculated the values of second-order rate constants kadd, via equation 4.26, based on presumed values of [M•], where [M•] = 2×[micelles]. The values of these parameters are also listed in Table 4.6.

Table 4.6. Trial V10T14M25, values of fitting parameters, the goodness of fit, values of concentration of unimer [M] and active growing site [M•], pseudo first-order rate constants k1’ and first-order rate constants ku, second-order rate constants kadd and fraction x of micelle growth due to the fast step, based on the two sequential growth models Boundary Trial B (nm) τ (min) D (nm) τ (min) R2 L(t→∞) (nm) 1 2 V10T11M20 2150 479 592 1530 11131 0.99

-1 -1 -1 -1 [M] (mol/L) [M•] (mol/L) k1’ (s ) ku (s ) kadd (L·mol ·s ) x

3.12×10-6 1.63×10-9 2.8×10-5 1.5×10-6 1.7×104 0.26

Probably the most important message that one can obtained from the data in Figure 4.16 and Table 4.6 for Trial V10T14M25 is that the growth of micelles can still be well fitted by an equation with two exponential decay terms. The second-order rate constant for the fast step is 1.7×104 L·mol-1·s-1 and the first-order rate constant for the slow step is 1.5×10-6, both of them are slightly smaller than the average values (4.0×104 L·mol-1·s-1 and 3.3×10-6 s-1, respectively) calculated from other experiments in Section 4.3.7. The fraction of micelle growth due to the fast step is only 0.26 for Trial V10T14M25.

Although it is difficult to interpret the data from Trial V10T11M20 and V10T14M25, I can still make a qualitative observation from comparing their results of evolution of scattering intensity over time as shown in Figure 4.14. One can see that with a larger volume fraction of THF present in the solution, the increase of scattering intensity (the growth of micelles) slowed down. For Trial V10T11M20 with φTHF = 0.11, the scattering intensity reached a plateau in about one week (Figure 4.14A), however, when φTHF = 0.14 for Trial V10T14M25, while other experimental conditions remained unchanged, the increase of scattering intensity continued for more than five weeks (Figure 4.14B) and finally reached similar values as that in Trial 125 V10T11M20. This observation is consistent with a previous study from our group by Wang et. al. [38], showing that the addition of THF to solutions of PI250-PFS50 in decane slowed the rate of micelle formation. Based on the values of rate constant for both the fast and slow processes, I infer that the slowing down of micelle formation is associated with the diminished importance of the fast step (for Trial V10T14M25, x = 0.26), and the increased importance of the slow step in the growth process.

4.4 Conclusion

In this chapter, I describe the experiments showing that addition of tiny amounts of PI1000-

PFS50 micelle seeds (in decane solution) into supersaturated solutions of this polymer (in a decane/THF mixture) initiates the growth of fiber-like micelles. I took advantage of this phenomenon to study the growth kinetics of these micelles using a combination of light scattering and electron microscopy.

The growth of the fiber-like micelles was monitored by measuring the evolution of the scattering intensity of each solution at angles of 30o, 60o and 90o over time. In order to correlate the scattering intensity with the micelle length, I prepared a series of reference solutions, which contained the same number concentration micelles but with different uniform lengths, and then measured the scattering intensity of these solutions. In this way, I was able to translate the measured increases in scattering intensity into plots of micelle length versus time. TEM measurements on micelles obtained at the end of the growth stage gave results consistent with final lengths obtained from SLS measurements.

Micelle growth appeared to take place over two time scales, a relatively rapid increase in length over about 24 h, followed by slower growth that continued for two weeks. The data analysis showed that the increase of the micelle length could be fitted by an expression with two exponential decay terms. Since the micelle concentration in each experiment remained constant, these results imply that there were two different populations of PI1000-PFS50 unimer in the supersaturated polymer solution that added to the open ends of the micelles at different rates. Our hypothesis is that one type of unimer is in “productive” state that adds directly to the growing micelles, and that the other type of unimer is kinetically trapped in a “unproductive” state and has to transform itself to “productive” state before attaching onto micelles. 126 We propose two closely related sequential growth kinetic models that predict this double exponential growth kinetics. In the “Dissociation” model, the “unproductive” state of unimer is the small amorphous aggregate. In the “Unfolding” model, the “unproductive” state of unimer has PFS block partially folded. Both models lead to the same kinetic equations. All four kinetic experiments gave similar values for the individual rate constants. However, our light scattering experiments provide evidence against the “Dissociation” model.

The most important conclusion from this study is that micelle growth is characterized by both a fast process and a slow process that differ in their rates by an order of magnitude. The more rapid process is 100 times slower than diffusion controlled, consistent with the idea that crystal growth is an activated process. We explain the two different rates in terms of two distinct states of the unimer in solution that are slow to equilibrate.

In the end of the chapter, I described two more trials of the kinetics experiments which were carried out at higher unimer concentration. However, the TEM measurements of the samples showed inconsistent length values with that obtained from LS measurements. Based on the results, I made a qualitative conclusion from those two trials, e.g. with larger fraction of THF present in the solution, the growth of the micelles was slowed down.

The data analysis described in this chapter is based on the information of scattering intensity versus time. In the Appendix II to this chapter, I described an alternative way of analyzing the kinetic data, based on the information of apparent hydrodynamic radius versus time. 127

References

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Appendix I to Chapter 4

Table AI-4.1. The amounts of polymer that were dissolved in THF, the unimer-to-seed ratios, the theoretical length values Ltheoretical of the micelles, values of Ln, Lw/Ln and σ/Ln obtained from

TEM measurements of the 18 PI1000-PFS50 micelle reference solutions containing a number concentration of 4.9×1011 mL-1 (0.82×10-9 mol/L) of micelles. These samples were measured by TEM one month after the sample preparation.

TEM Polymer Unimer-to- Ltheoretical (mg) seed ratio (nm) Ln (nm) Lw/Ln σ/Ln 0.002 0.2:1 58 65 1.08 0.285 0.005 0.5:1 72 71 1.07 0.266 0.008 0.8:1 86 80 1.05 0.225 0.010 1.0:1 96 80 1.05 0.228 0.012 1.2:1 106 94 1.04 0.206 0.014 1.4:1 115 103 1.06 0.238 0.016 1.6:1 125 108 1.05 0.221 0.018 1.8:1 134 111 1.04 0.189 0.020 2.0:1 144 136 1.04 0.192 0.024 2.4:1 163 138 1.04 0.199 0.030 3.0:1 192 169 1.04 0.191 0.035 3.5:1 216 195 1.03 0.172 0.040 4.0:1 240 201 1.02 0.154 0.044 4.4:1 259 228 1.03 0.180 0.050 5.0:1 288 258 1.03 0.136 0.233 23.3:1 1166 1081 1.01 0.099 0.290 29.0:1 1440 1356 1.01 0.099 0.393 39.3:1 1934 1846 1.01 0.076 130

Table AI-4.2. The unimer-to-seed ratios, Ltheoretical, values of LSLS, Nagg/L, and RSLS obtained from 2 2 the data fitting, and fitting goodness (R and χ ) of the LS results of the 18 PI1000-PFS50 micelle reference solutions containing a number concentration of 4.9×1011 mL-1 (0.82×10-9 mol/L) of micelles. These samples were measured by LS one month after the sample preparation. a,d

Unimer LS L -to-seed theoretical (nm) L σ b N σ b R σ b ratio SLS agg/L SLS R2 χ2 (nm) (nm) (nm-1) (nm-1) (nm) (nm) 0.2:1 58 116 46 1.75 0.68 24 27.6 0.997 0.037

0.5:1 72 107 41 1.66 0.60 33 26.6 0.997 0.035

0.8:1 86 111 44 1.45 0.56 32 26.5 0.996 0.035

1.0:1 96 116 43 1.50 0.55 34 20.9 0.997 0.023

1.2:1 106 141 21 1.53 0.22 27 10.8 0.998 0.017

1.4:1 115 144 24 1.45 0.21 31 12.4 0.993 0.060

1.6:1 125 154 27 1.49 0.24 27 14.0 0.992 0.078

1.8:1 134 173 21 1.49 0.17 23 13.5 0.992 0.068

2.0:1 144 178 17 1.69 0.15 32 8.6 0.990 0.075

2.4:1 163 198 14 1.69 0.10 29 6.6 0.987 0.088

3.0:1 192 253 9 1.64 0.04 20 4.5 0.980 0.101

3.5:1 216 266 10 1.56 0.05 21 4.8 0.968 0.128

4.0:1 240 278 10 1.59 0.04 22 4.6 0.964 0.131

4.4:1 259 318 9 1.64 0.02 24 2.6 0.944 0.141

5.0:1 288 311 8 1.65 0.02 25 2.1 0.963 0.097

23.3:1c 1166 1166 N/A 1.65 N/A 27 N/A N/A N/A

29.0:1c 1440 1440 N/A 1.62 N/A 27 N/A N/A N/A

39.3:1c 1934 1934 N/A 1.62 N/A 27 N/A N/A N/A 131 a. The data fitting was performed automatically by computer software Matlab using a code developed based on the Gauss-Newton iteration method. This method is one of the most commonly-used methods to solve non-linear least square problems. The Gauss-Newton algorithm is derived by linearly approximating the fitting equation 4.11 using Taylor’s theorem, and used to fit to the SLS data by minimizing the sum of squares of errors between the data and model's predictions. The iteration number for each analysis is 100. The rate of convergence of the Gauss-Newton algorithm can approach quadratic. b. The values of σ for each fitting parameter were generated by the software when setting the confidence level of the data fitting at a typical value of 95 %. From the σ values for each fitting parameter, one can see that as the micelle length increases, the accuracy of each fitting parameter increases. c. For the longest three samples, LS measurements were only carried at 30, 60, and 90°. In

fitting the data, I fixed the LSLS as the value obtained from TEM and also fixed the RSLS = 27

nm, which is the average RSLS value of other fifteen samples. In such way, I was able to

obtain meaningful Nagg/L value for the longest three samples. d. The Matlab code for the data fitting: function fitfunc clc; Data=load('Data.txt'); xdata=Data(:,1); ydata=Data(:,2); x0=[1.7500,0.0202,0.30]; options=statset('TolX',1e-0); [x,r,J,cov]=nlinfit(xdata,ydata,@myfun,x0,options); x ci=nlparci(x,r,'Jacobian',J); ci(1,3)=(ci(1,1)+ci(1,2))/2; ci(2,3)=(ci(2,1)+ci(2,2))/2; ci(3,3)=(ci(3,1)+ci(3,2))/2; ci figure; hold on; Data=load('Data.txt'); F=myfun(x,xdata); sum=0; for counter=1:130 sum= sum+ydata(counter,1); end 132 average=sum/130; t2=0; t5=0; for counter=1:130 t(counter,1)=ydata(counter,1)-F(counter,1); t1(counter,1)=t(counter,1).^2; t2=t2+t1(counter,1); t3(counter,1)=ydata(counter,1)-average; t4(counter,1)=t3(counter,1).^2; t5=t5+t4(counter,1); end m3=0; for counter=1:130 m(counter,1)=ydata(counter,1)-F(counter,1); m1(counter,1)=m(counter,1).^2; m2(counter,1)=m1(counter,1)./F(counter,1); m3=m3+m2(counter,1); end R=1-t2/t5 %R^2 X=m3 %X^2 plot(Data(:,1),Data(:,2),'or','MarkerSize',3) plot(Data(:,1),F,'-b') function F=myfun(x,xdata) for counter = 1:130 t(counter,1) = y(x,xdata(counter,1)); end F=t; function y=y(x,xdata) stepSize = pi/10000; z = stepSize:stepSize:(pi/2-stepSize); y=(trapz(z,((((4*(sin((xdata*x(3)*cos(z))./2))./xdata./x(3)./cos(z)).*(real(besselj(1,xdata*(sqrt(x (2))^2)*sin(z))/xdata/(sqrt(x(2))^2)))).^2)./sin(z))))*(xdata*x(1)*x(3)/pi);

133

300 theoretical length

(nm) 200 n L

100 Length Length

0 0.000.0 0.011.0 0.022.0 0.033.0 4.0 0.04 5.0 0.05 Free Polymer added (mg) munimer/mseed

Figure AI-4.1. Number-averaged length Ln of the micelles obtained from the TEM images of the reference solutions versus the unimer-to-seed ratios. The error bars represent the standard deviations σ of the length distribution as determined from the length distribution histograms. The solid line represents the linear best fit of the data. The dashed line represents the theoretical length evaluated from eq. 2.5.

A B 0.3

0.2

0.1

0.0 Normalized Frequency 048121620 100 nm Width (nm)

Figure AI-4.2. (A) A TEM image and (B) corresponding width distribution of the micelles at the growth time of ca. 2 weeks for Trial V10T11M05.

134

~ 7800 min 1.0

0.8 ~ 400 min

0.6 f(t) 0.4

0.2

0.0

1 10 100 1000 10000 100000 Decay time (min)

Figure AI-4.3. CONTIN plot of the distribution of the decay time for the kinetics data of Trial V10T11M05. 135

A: Trial V10T11M02 B: Trial V10T11M02 0.3

0.2

0.1 Normalized Frequency Normalized 0.0 0 300 600 900 1200 1500 Length (nm)

C: Trial V10T11M10 D: Trial V10T11M10 0.4

0.3

0.2

0.1

Normalized Frequency 0.0 0 300 600 900 1200 1500 Length (nm)

E: Trial V25T11M12.5 F: Trial V25T11M12.5

0.3

0.2

0.1

0.0 Normalized Frequency Normalized 0 300 600 900 1200 1500 Length (nm)

Figure AI-4.4. Representative TEM images and the corresponding length distribution histograms of the micelles at the growth time of ca. 2 weeks for (A and B) Trial V10T11M02; (C and D) Trial V10T11M10; and (E and F) Trial V25T11M12.5. Scale bars are 500 nm. The micelles in (A) were characterized by Ln = 239 nm, Lw = 245 nm, Lw/Ln = 1.02; the micelles in (C) were characterized by Ln =

937 nm, Lw = 945 nm, Lw/Ln = 1.01; the micelles in (E) were characterized by Ln = 514 nm, Lw = 521 nm,

Lw/Ln = 1.01.

136

0.05 A 1.0 B 0.04 0.8

/A 0.03 ) 0.6 -A ) τ

( 0.02 0.4 (2) Intensity G ( 0.01 0.2

0.00 0.0 0.01 0.1 1 10 0.1 1 10 100 1000

τ (ms) Rh (nm)

Figure AI-4.5. DLS measurement of the supersaturated solution with unimer concentration of 0.10 mg/mL at angle of 20o, the acquisition time was 600s. (A) Intensity-intensity autocorrelation function. One sees that the signal is extremely low. (B) CONTIN plot of the hydrodynamic radius of the polymer chain in the supersaturated solution. The peak value is ca. 8 nm.

4 /s) /s) 2

cm 3 -8 -8 10

× 2 (

Diffusion Coefficient Diffusion 1 0 300 600 900 1200

Micelle Length (nm)

Figure AI-4.6. Plot of the diffusion coefficient of the micelles Dm, of six of the 18 reference solutions that -9 contained 0.82×10 mol/L micelles, versus the length (LTEM) of the micelles.

137

A 0.4 B

0.3

0.2

0.1

0.0 Normalized Frequency 0 300 600 900 1200 1500 1800 500 nm Length (nm) 0.4 C D 0.3

0.2

0.1

Normalized Frequency 0.0 500 nm 0 300 600 900 1200 1500 1800 Length (nm) 0.3 E F

0.2

0.1

Normalized Frequency Normalized 0.0 500 nm 0 300 600 900 1200 1500 1800 2100 Length (nm)

Figure AI-4.7. (A and B) A representative TEM image and the corresponding length distribution histogram of a micelle mixture containing equal number concentration of short micelles and long micelles in decane solution (c = 0.020 mg/mL). The micelle in (A) is characterized by Ln = 759 nm, Lw = 1097 nm,

Lw/Ln = 1.44, σ = 507 nm. The population of short micelle is characterized by Ln1 = 268 nm, σ1 = 36 nm.

The population of long micelle is characterized by Ln2 = 1271 nm, σ2 = 92 nm; (C and D) A representative TEM image and the corresponding length distribution histogram of the micelle mixture after adding 0.03 mL THF solution (polymer c = 0.179 mg/mL) into 1.00 mL micelle solution as shown in (A). The micelle in (C) is characterized by Ln = 953 nm, Lw = 1226 nm, Lw/Ln = 1.29, σ = 512 nm (ΔL = 194 nm). The population of short micelle is characterized by Ln1 = 455 nm, σ1 = 51 nm (ΔL1 = 187 nm). The population of long micelle is characterized by Ln2 = 1461 nm, σ2 = 113 nm (ΔL2 = 190 nm); (E and F) A representative TEM image and the corresponding length distribution histogram of the micelle mixture after adding 0.05 mL THF solution (polymer c = 0.179 mg/mL) into 1.00 mL micelle solution as shown in

(A). The micelle in (E) is characterized by Ln = 1117 nm, Lw = 1384 nm, Lw/Ln = 1.24, σ = 504 nm (ΔL =

358 nm). The population of short micelle is characterized by Ln1 = 627 nm, σ1 = 69 nm (ΔL1 = 359 nm).

The population of long micelle is characterized by Ln2 = 1618 nm, σ2 = 101 nm (ΔL2 = 347 nm). 138

A: Trial V10T11M20 B: Trial V10T11M20 0.5

0.4

0.3

0.2

0.1

Normalized Frequency 0.0 0 500 1000 1500 2000 2500 3000 Length (nm)

C: Trial V10T14M25 D: Trial V10T14M25 0.5

0.4

0.3

0.2

0.1 Normalized Frequency 0.0 0 500 1000 1500 2000 2500 3000 Length (nm)

Figure AI-4.8. Representative TEM images and the corresponding length distribution histograms of the micelles for (A and B) Trial V10T11M20 at the growth time of ca. 2 weeks; (C and D) Trial V10T14M25 at the growth time of ca. 5 weeks. Scale bars are 500 nm. The micelles in (A) were characterized by Ln =

1579 nm, Lw = 1591 nm, Lw/Ln = 1.01; the micelles in (C) were characterized by Ln = 1768 nm, Lw = 1791 nm, Lw/Ln = 1.01.

139

Appendix II to Chapter 4

In this Appendix, I describe an alternative method of data analysis for the kinetic experiments in Chapter 4. The analysis described here is based on the information of apparent hydrodynamic radius (Rh,app) instead of the information of scattering intensity. The information of Rh,app was obtained from the dynamic light scattering (DLS) measurements of the samples.

AII-4.1 Dynamic Light Scattering Theory

(2) In a DLS measurement, the measured intensity-intensity time-correlation function g (tc), (1) where tc is the delay time, is related to the normalized electric field correlation function g (tc), representative of the motion of the particles, by the Siegert relation [1]:

(2) (1) 2 g (tc) = 1 + β×| g (tc)| (AII-4.1) where β (<1) is a correction factor that depends on the geometry and alignment of the laser (1) beam in the light scattering setup. As tc increases, g (tc) decays. This decay contains information about the diffusion of the particles in solution. For monodisperse spherical objects (1) undergoing Brownian motion, g (tc) can be described by a single exponential expression:

(1) g (tc) = exp(-Г×tc) (AII-4.2)

where Γ is the decay rate and related to the mutual diffusion coefficient Dmut of the diffusing species as:

2 Γ = q ×Dmut (AII-4.3)

2 Thus, a plot of Γ vs q should be linear with slope Dmut and pass through the origin. For data extrapolated to zero concentration and zero angle, Dmut approaches D0, which is the center of mass diffusion coefficient. The real hydrodynamic radius Rh can be calculated from D0 through the Stokes-Einstein equation:

Rh = kBT/(6πηsD0) (AII-4.4)

where kB is the Boltzmann constant, T is the temperature, ηs is the viscosity of the solvent. For data from finite concentration and scattering angles > 0, the value of hydrodynamic radius 140 obtained is called apparent hydrodynamic radius Rh,app, which can also be calculated from Dmut through the Stokes-Einstein equation:

Rh,app = kBT/(6πηsDmut) (AII-4.5)

(1) For polydisperse or rigid extended systems, g (tc) cannot be described by a single decay (1) rate Γ, but a continuous distribution of decay rates G(Γ). In this case, g (tc) can be described as the Laplace transform of G(Γ) via the expression:

∞ gt(1) ()=− G()exp(ΓΓt )dΓ c∫0 c (AII-4.6)

(1) The analysis of g (tc) was performed by the ALV correlator software in terms of a (1) cumulant expansion to second (2-CUM) order of the logarithm of g (tc),

(1) ⎛⎞μ2 2 lngt (cc ) =−Γ1t +⎜⎟tc ⎝⎠2! (AII-4.7)

where Γ1 is the average value of Γ and also known as the first cumulant, while μ2 is the second cumulant, which allows one to evaluate the polydispersity of distribution of decay rates.

For rigid rods, the translational diffusion coefficient parallel to the rod axis, D||, that perpendicular to the rod axis, D⊥, and the rotational diffusion coefficient, Dr, all influence the evolution of the first cumulant as a function of q. For a dilute solution of rigid rods, when the translational and rotational motions are coupled, Maeda and Fujime have shown that the reduced 2 cumulant, Γ1/q , can be expressed by [2]

2 2 Γ1/q = D + (L /12) ×Dr×f1(qL/2) – (D|| – D⊥) ×(1/3 – f2(qL/2)) (AII-4.8) where L is the length of the rod and D is the overall translational diffusion coefficient of the rod, defined as D = (2 D⊥+ D||)/3. f1(qL/2) and (1/3 – f2(qL/2)) are weighting factors which depend on qL/2 and are given by Maeda and Fujime [2]. When q approaches to 0, f1(qL/2) = 0 and 2 f2(qL/2) = 1/3; then, according to eq AII-4.8, Γ1/q approaches to the overall translational diffusion coefficient, D0. Note that eq. AII-4.8 applies to low concentration (c) where Γ is not influenced by c. 141 The translational and rotational diffusion coefficients can be expressed as a function of the ratio of the rod length L to the cross-sectional diameter d, L/d, and the solvent viscosity ηs. A recent study by Dr. Guerin [3] from our group shows that the PFS fiber-like micelles can be described as cylinders with flat caps, a model developed by Aragon and Flamik [ 4 ]. For cylinders with flat caps, the translational diffusion coefficients, D⊥ and D|| are given by

D⊥ = (kT/4πηsL) × (ln(L/d) + X⊥) (AII-4.9a)

D|| = (kT/4πηsL) × (2×ln(L/d) + X||) (AII-4.9b) where

1/2 2 X⊥(L/d) = 0.86609 – 0.650602/(L/d) + 1.2839/(L/d) – 0.397905/(L/d) – 0.18332×ln(L/d)/(L/d)2 (AII-4.10a)

1/2 2 X||(L/d) = -0.234963 – 3.14268/(L/d) + 4.29031/(L/d) + 0.197913/(L/d) – 1.96581×ln(L/d)/(L/d) (AII-4.10b)

while rotational diffusion coefficient, Dr is

3 Dr = (3kT/πηsL ) × (ln(L/d)+Xr) (AII-4.11)

Where

1/2 3 4 Xr(L/d) = -0.480483 – 1.40056/(L/d) + 3.91903/(L/d) – 2.4528/(L/d) – 0.587033/(L/d) – 2.58127×ln(L/d)/(L/d)2 (AII-4.12)

Aragon and Flamik have shown that these expressions for D⊥, D||, and Dr are valid when the ratio L/d is larger than 1, they also showed that the precision of their numerical expression is better than 0.05 %.

The combination of equation AII-4.5, AII-4.8, AII-4.9, AII-4.10, AII-4.11, and AII-4.12 gives the theoretical correlation between the apparent hydrodynamic radius Rh,app and the length L for monodisperse PFS fiber-like micelles. 142

AII-4.2 Experimental Correlation between Rh,app and length L

The micelle samples considered here are the same as those described in the main text of Chapter 4. They were prepared in decane/THF mixtures with THF volume fraction of 11 %. The viscosity of the solvent mixture is estimated via an expression developed by Arrhenius [5]:

logηs = X1×logη1 + X2×logη2 (AII-4.13)

here X1 and η1 represent the mole fraction and viscosity of component 1, while X2 and η2 represent the mole fraction and viscosity of component 2. At experimental temperature (ca. 20 o C), the viscosity of decane is η1 = 0.92 mPa×s, and the viscosity of THF is η2 = 0.48 mPa×s. For decane/THF mixture solvent with THF volume fraction of 11 %, the mole fraction of decane

X1 = 0.77 and THF X2 = 0.23. Thus, I calculate the viscosity of the mixture solvent to be η = 0.79 mPa×s.

In Figure AII-4.1, I present the experimental correlation between the values of Rh,app obtained from the DLS measurements and the theoretical micelle length (Ltheoretical) of the eighteen reference solutions at angles of 30o, 60o, and 90o, as described in Section 4.3.3. The error bars in Figure AII-4.1C represent the error of Rh,app values (ca. 8 %) determined from the DLS measurements. The solid line in each plot represents the best fit of each set of the data point to equations AII-4.5, AII-4.8, AII-4.9, AII-4.10, AII-4.11, and AII-4.12, by setting the diameter of the micelles d = 72 nm. Note that this value of the diameter of the micelles is significantly larger than that was evaluated from the SLS experiments (54 nm), as described in Section 4.3.3. The recently study by Dr. Guerin [3] shows a similar result for the same polymer in decane that, the diameter of the cross section of the micelles obtained by DLS (80 nm) is also much larger than the diameter deduced from the SLS fitting (48 nm). The authors attributed the difference to a consequence of the density distribution of the corona in the radial direction. As the corona chains protrude from the core surface in the radial direction, they become more diffuse, more swollen by the solvent. Thus, the corona is expected to be denser close to the center of the micelle than at its fringe, while the denser part of the micelle is emphasized in SLS experiments. These effects result in a larger value of the diameter obtained by DLS than that by SLS. The data fitting was preformed by my colleague Dr. Yijie Lu. The goodness of fit for each set of data is R2 = 0.99. 143

250 A: 30° 250 B: 60° 200 200

150 150 (nm) (nm) 100 100 h,app h,app R R 50 50

0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 Length (nm) Length (nm)

250 C: 90° 200

150 (nm) 100 h,app R 50

0 0 500 1000 1500 2000 Length (nm)

Figure AII-4.1. Correlation of Rh,app values versus the theoretical micelle length (Ltheoretical) of the eighteen reference solutions at angles of (A) 30o, (B) 60o, and (C) 90o. Solid lines represent the best fit of each set of the data point to equations AII-4.5, AII-4.8, AII-4.9, AII-4.10, AII-4.11, and AII-4.12, by setting the

diameter of the micelles d = 72 nm. The error bars in (C) represent the error of Rh,app values (ca. 8 %) determined from the DLS measurements.

Another feature about the data in Figure AII-4.1 could be observed by looking at one plot o carefully. For example at 90 , when the micelle length reaches ca. 300 nm, the Rh,app value is ca.

90 nm. However, when the micelle growth to 2000 nm (more than six times longer), the Rh,app value only increases to ca. 200 nm (two times larger). This suggests that the increase of the

Rh,app value is slower than the increase of the micelle length. This feature could be represented by the theoretical description for rigid thick rod, where the true Rh value is related to the length L and diameter d via [6]

Rh = L/(2×ln(L/d)) (AII-4.14) 144

AII-4.3 Evolution of Rh,app Over Time for Kinetics Experiments

In Section 4.3.4 and Section 4.3.7, I showed the results of the evolution of scattering intensity over time from several trials of the kinetic experiments, and I also showed that very interesting results were obtained from the information of scattering intensity over time. In this section, I present the information of apparent hydrodynamic radius Rh,app over time for Trial

V10T11M02, V10T11M05, and V10T11M10 and describe the data analysis based on Rh,app.

For Trial V10T11M02, V10T11M05, and V10T11M10, the values of Rh,app at each time point were also acquired through the DLS measurements. However, it is very difficult to obtain o meaningful values of Rh,app from low angle DLS measurements, especially at 30 . For example, I o present a plot of the evolution of Rh,app values obtained from 30 DLS measurement over a period of ca. two weeks (2×104 min) for Trial V10T11M02 in Figure AII-4.2A, one can see that 3 in the early stage of micelle growth (1×10 min), I obtained both very large Rh,app values (ca. 90 nm) and very small Rh,app values (ca. 50 nm). I infer that the data in Figure AII-4.2A are not meaningful. However, the time profile of scattering intensity at 30o (see the evolution of scattering intensity at 30o over time for Trial V10T11M02 as shown in Figure 4.8A). For this o reason, I carried out analysis only on the Rh,app values obtained from the 90 DLS measurements, where the data were more stable.

o In Figure AII-4.2B, C, and D, I present the evolution of Rh,app values obtained from the 90 DLS measurements (hollow cubes) for Trial V10T11M02 (B), V10T11M05 (C), and

V10T11M10 (D). One sees that for each trial, the Rh,app value increased significantly in early 3 3 stage (2×10 min) of the micelle growth. The increase of Rh,app slowed down after 2×10 min. The time profiles of the apparent hydrodynamic radius are very similar to the corresponding time profiles of the scattering intensity for each trial, as shown in Figure 4.6A (V10T11M05), Figure 4.8A (V10T11M02), and Figure 4.8B (V10T11M10). In Figure AII-4.2B, C, and D, I also present the corresponding evolution of micelle length (L(intensity 90o)) over time, obtained by the scattering intensity at 90o and represented by hollow spheres. One can see that in early 3 stages (2×10 min), the increases of Rh,app and micelle length seem to overlap. However, in late stages of the micelle growth, the measured Rh,app values seem to level off even though the micelle length continues to increase. 145

A: V10T11M02, 30° B: V10T11M02, 90°

90 90 250 80 ) (nm) o 75 200 (nm) (nm) 70 150

h,app 60 h,app

60 R R 50 100 (intensity 90 45 40 50 L 0 5 10 15 20 0 5 10 15 20 Time (×103 min) Time (×103 min)

C: V 1 0 T11M05, 9 0 ° D: V10T11M10, 90° 120 500 1000 150 100 400 ) (nm) ) (nm) o 125 750 o

(nm) 300 80 (nm) 100 500 h,app

200 h,app 75 R 60 R 250 50 (intensity 90

100 90 (intensity L 40 25 0 L 02468 0 5 10 15 20 25 Time (×103 min) Time (×103 min)

Figure AII-4.2. (A-D) Evolution of Rh,app values over time for different trials of kinetic experiments. (A) o o Rh,app values from 30 DLS measurements of Trial V10T11M02; (B) Rh,app values (hollow cubes) from 90 o DLS measurements of Trial V10T11M02, (C) Rh,app values (hollow cubes) from 90 DLS measurements o of Trial V10T11M05; and (D) Rh,app values (hollow cubes) from 90 DLS measurements of Trial V10T11M10. In (B-D) The length of the micelles over time, obtained by the scattering intensity at 90o

and represented by hollow spheres, are also plotted for comparison. The error bars for both the Rh,app and

length values starting from ca. 1×103 min represent the standard deviations of three measurements.

Here I would like address a note that for Trial V10T11M05, the evolution of scattering intensity was monitored until the growth time of ca. 5 weeks (5×104 min), as shown in Figure

4.6A. However, the evolution of Rh,app for this trial in Figure AII-4.2C is only shown over a 3 period of 8×10 min because the original data containing the information of Rh,app in the later stages of the growth were lost. 146

AII-4.4 Analysis of Evolution of Rh,app Over Time

I then converted the evolution of Rh,app over time as shown in Figure AII-4.2B, C, and D to the evolution of micelle length L over time, based on the experimental correlation curve of Rh,app o versus L at 90 as shown in Figure AII-4.1C. In order to calculate the micelle length LRh based on the values of Rh,app, I refitted the correlation curve in Figure AII-4.1C to a second-order polynomial equation:

2 2 LRh = -133.3 + 0.4475×Rh,app + 0.04994×Rh,app , R = 0.99 (AII-4.15)

The results are shown in Figure AII-4.3. One sees that for Trial V10T11M02 (Figure AII-4.3a), after ca. two weeks’ (2×104 min) growth, the length of micelles reached 180±40 nm; for Trial V10T11M05 (Figure AII-4.3b), the micelle length reached 387±80 nm after ca. five days (8×103 min); for Trial V10T11M10 (Figure AII-4.3c), the micelle length reached 747±140 nm after more than two weeks (2.5×104 min). In Table AII-4.1, I summarize these micelle length values that are obtained from the Rh,app (LRh,90) for each trial and I also show the corresponding values of

Ltheoretical, and the final length values that were obtained from the scattering intensity LScattering for comparison. One sees that for each trial, the micelle length values obtained from the conversion of Rh,app (LRh,90) are much smaller than the length values obtained from the conversion of scattering intensity (LScattering). Based on my analysis in Chapter 4, the LScattering values of all these trials are consistent with both the length values obtained from TEM and Ltheoretical, thus, the

LScattering values should reflect the true length of the micelles. Thus, I infer that the length values that are obtained from the translation of Rh,app (LRh,90) are systematically too small.

Table AII-4.1. Values of Ltheoretical, final micelle length values obtained from the scattering o intensity LScattering, and final micelle length values (LRh,90) obtained from Rh,app at 90 for different trials of kinetics experiments.

Trial Ltheoretical (nm) LScattering (nm) LRh,90 (nm)

V10T11M02 240 250±15 180±36

V10T11M05 528 450±30 a 387±77 a

V10T11M10 1008 1086±80 747±150 a. The length values are obtained at the growth time of 8×103 min, the micelle growth is not yet complete, thus, it is not meaningful to compare them with the Ltheoretical. 147

A: V10T11M02 B: V10T11M05 500 200 400 160 (nm) 300 (nm) 120 Rh,90 200 L Rh,90 L 80 100

40 0 0 5 10 15 20 02468 Time (×103 min) Time (×103 min) C: V10T11M10 800

600 (nm) 400 Rh,90 L 200

0 0 5 10 15 20 25 Time (×103 min)

Figure AII-4.3. Evolution of micelle length (LRh,90) over time for different trials of kinetics experiments, o converted from the Rh,app values at 90 in Figure AII-4.2B, C, and D through eq. AII-4.15. The error bars starting from ca. 1×103 min represent the error of length values propagated from the calculation, based on

the error of Rh,app values (8 %).

Another interesting aspect of the data can be observed by looking at the length values in o Table AII-4.1. The values of micelle length that are obtained from the Rh,app values at 90 (LRh,90) have errors of ca. 20 %, which is much larger than the error (ca. 7 %) of LScattering. This is because the increase of scattering intensity is sensitive to the increase of micelle length L {ΔRθ ~ 2 L (4.5)}, while the increase of Rh,app value is not sensitive to the increase of micelle length {Rh = L/(2×ln(L/d)) (AII-4.14)}, especially when the length of micelle is larger than 300 nm. A small error of Rh,app values (ca. 8 %) leads to a large error of LRh,90 (ca. 20 %). 148 Based on the previous results, I conclude that the analysis based on the information of

Rh,app values is not as precise as the analysis based on the scattering intensity. My colleague Dr.

Yijie Lu is currently systematically investigating the behavior of Rh,app versus micelle length at different q regions.

References

1 Jakeman, E. In Photon Correlation and Light Beating Spectroscopy; Cummins, H. Z., Pike, E. R., Eds; Plenum Press: New York, 1974. 2 Maeda, T.; Fujime, S. Macromolecules 1984, 17, 1157-1167. 3 Guerin, G.; Qi, F.; Cambridge, G.; Manners, I.; Winnik, M. A. J. Phys. Chem. B 2012, 116, 4328-4337. 4 Aragon, S. R.; Flamik, D. Macromolecules 2009, 42, 6290-6299. 5 Arrhenius, S. Z. Physik. Chem. 1887, 1, 285. 6 Wu, C.; Li, M.; Kwan, S.C.M.; Liu, G.J. Macromolecules 1998, 31, 7553-7554. 149

Chapter 5

SELF-SEEDING OF FIBER-LIKE MICELLES FORMED BY PFS

BLOCK COPOLYMERS

In this chapter, I examine the behavior of PFS block copolymer micelle fragments under self-seeding condition. Part of the content in this chapter is from the paper published in 2011 [1] (Qian, J. S.; Guerin, G.; Lu, Y. J.; Cambridge, G.; Manners, I.; Winnik, M. A. Angew. Chem. Int. Ed. 2011, 50, 1622-1625).

5.1 Introduction

Polymer crystals are different from crystals formed by small molecules [2]. Crystallization of small molecules leads to the formation of a uniform crystal lattice that displays a sharp melting temperature even if the crystals themselves contain defects. In contrast, polymers have difficulty in crystallizing. In most of the cases, only part of each polymer chain can be accommodated in the crystal lattice. As a result, polymers form crystals with lamellar structures bound by surfaces containing chain folds [3]. If long chains have to be integrated into the crystal in a short time, they will do so at the expense of lower crystallinity. The degree of the chain order (crystallinity) depends on the rate at which the crystal was grown, the age of the crystal, and its thermal history. As a consequence, polymer crystals inevitably consist of regions with different chain order and conformational entropy, thus, display a broad range of melting temperatures whose values depend upon the details of the crystallization process [4].

These features serve as the underlying physics for a strategy to grow polymer single crystals known as “self-seeding”. The term refers to a process in which a crystalline polymer in the bulk state is heated slightly above its normal melting point (as determined, for example by differential scanning calorimetry, DSC), or a crystalline polymer suspended in a solvent is heated slightly above its apparent dissolution temperature, so that no residual crystals can be detected optically or spectroscopically. Cooling this melt or solution leads to the formation of polymer single crystals, normally in the form of thin plates uniform in size and thickness. These 150 single crystals are thought to be initiated by submicroscopic nuclei that survived the annealing procedure.

Self-seeding was discovered in the 1960s and examined in detail by the research groups of Kovacs and Keller [5] as a means of controlling the nucleation step of polymer crystallization without the need for external nucleating agents [6]. Later, Lotz and Kovacs [7] also found that the crystalline component of diblock copolymers with one crystalline block (e.g., poly(styrene- b-ethylene oxide), PS-PEO) could also be induced to form single crystals by self-seeding. For example, in crystals grown from ethylbenzene at 25 °C, the PEO component crystallized as thin square monolayer crystals. Upon drying these crystalline films were sandwiched between layers of amorphous PS. These were the first results to suggest that coil-crystalline block copolymers formed planar raft-like micelles in solvents selective for the non-crystalline block.

Over the past several years, there has been a renewed interest in the self-seeding of polymer crystallization to obtain uniform polymer single crystals. For example, the Cheng group [8] has been interested in understanding how polymers crystallize in confined environments. Using PEO as an example, they used self-seeding to generate single crystals of PEO from PS- PEO block copolymers in solution. As formed, these thin, square single PEO crystals had PS chains attached to their upper and lower faces. Upon drying this suspension, the single-crystal PEO layers became encapsulated by a continuous glassy PS matrix. These single crystals became the substrates for subsequent studies of melting and recrystallization in a confined geometry. These samples could be heated above the melting temperature of PEO (51-60 °C) without softening the PS matrix (Tg ≈ 62-80 °C), and the authors were able to study how confinement imposed by the matrix affected the PEO crystal orientation upon cooling. Samples prepared by self-seeding allowed them to investigate how the crystallization temperature, thickness of the confinement layer, and reduced tethering density on the PEO crystal affected the crystallization process.

The Li group [9] has been interested in self-seeding as a strategy for synthesizing Janus or patchy nanoparticles. In their approach, they used self-seeding in solution to generate uniform single crystals of PEO containing a thiol end group. Exposure of gold nanoparticles (AuNPs) to a suspension of these crystals led to attachment of the nanoparticles to the thiol groups confined to the crystal surface. The surface area of the AuNPs not in contact with the PEO was then functionalized with other thiol-containing molecules. After dissolution of the PEO and 151 separation of the products, the authors obtained AuNPs with PEO chains confined to the patch that had been in contact with the planar crystals. This method appeared to be general, and was used for other crystallizable polymers such as polycaprolactone (PCL) and polyethylene(PE)-b-

PEO to functionalize Fe3O4 magnetic nanoparticles and CdSe/ZnS core-shell quantum dots [9c].

In 2009, Reiter and coworkers [2] examined the mechanism of self-seeding in the melt for single crystals formed by P2VP-PEO block copolymers and for PFS homopolymer single crystals. They found a correlation in molecular orientation between a starting single crystal and the regenerated crystal clones formed through the self-seeding process. They also showed for both systems that the number density of the regenerated crystals decreased exponentially with the increase of the heating temperature but did not vary with the heating time. Their experiments established that single crystal growth by self-seeding operates under thermodynamic control, consistent with the idea that upon heating, the less perfect crystals will melt and more perfect crystallites will survive [10]. It is not a kinetic effect associated with polymer conformational memory effects [11].

In this chapter, I examine the one-dimensional analogue of self-seeding for fiber-like PFS block copolymer micelles. First, I describe experiments in which sonication-shortened PI1000-

PFS50 block copolymer micelles (ca. 50 nm) in decane, were subjected to typical self-seeding conditions: heating the solutions to temperatures at which the micelles started to disappear, followed by slow cooling to room temperature, where the dissolved polymer crystallized at the ends of the remaining fragments. As a result, I obtained longer micelles with a narrow length distribution in which the length was very sensitive to the heating temperature. Later, I show the effect of tiny amount of good solvent (THF) on the self-seeding behavior of PI1000-PFS50 block copolymer micelles in decane, and further show that the selective dissolution of micelle fragments could be controlled by the amount of THF instead of heating temperature. This is the first example of performing self-seeding by varying solvent composition. Afterwards, I show that the self-seeding behavior of PI1000-PFS50 block copolymer micelles in decane can also be affected by pre-annealing the micelle fragments. At the end of this chapter, I describe the extension of the self-seeding protocol to other fiber-like micelles formed by several different crystalline-coil block copolymers, PI637-PFS53 in decane, PFS60-PDMS660 and PFS90-PDMS900 in decane, and PFS30-P2VP300 in 2-propanol. The structures and characteristics of these block copolymers are described in Chapter 2. 152 5.2 Experimental

5.2.1 Self-seeding of PI1000-PFS50

A solution of PI1000-PFS50 micelles (c = 0.100 mg/mL) was prepared by heating polymer (0.415 mg) in decane (4.15 mL) in a 20 mL vial at 90 °C for 30 min in an oil bath on top of a hot plate. Then the heater was turned off and the solution was allowed to cool slowly (cooling rate ~ 1.5 °C/min) to room temperature. One day later, the solution was placed in 70 watt ultrasonic cleaning bath and sonicated for 10 min at 23 °C followed by an additional 10 min at 23 °C. The solution of micelle fragments was diluted with decane to c = 0.0200 mg/mL. To investigate the effect of temperature, 13 equivalent batches (0.5 g) of this solution were annealed in an oil bath at different temperatures. After 30 min, each sample was taken out of the oil bath and allowed to cool to room temperature in air. Grids for TEM measurements were prepared after the solution cooled to room temperature for at least one day. Another batch (0.5 g) of this solution was annealed at 80.0 oC. After 30 min, a drop of the hot solution was placed directly onto a carbon-coated copper TEM grid, and 10 sec later, the excess solution was wicked away with a piece of filter paper. To investigate the effect of annealing time on micelle elongation at a given temperature, two sets of three PI1000-PFS50 micelle fragment solutions (0.5 g) were annealed in the oil bath at 70.0 oC and 80.0 oC, respectively, for different times: 10 min, 2 hr, 24 hr. After aging, each sample was taken out of the oil bath and allowed to cool to room temperature in air.

5.2.2 Effect of Good Solvent on Self-seeding Behavior of PI1000-PFS50

A micelle solution of PI1000-PFS50 was prepared in a similar way by heating polymer (0.373 mg) in decane (3.73 mL, c = 0.100 mg/mL) in a 20 mL vial at 100 °C for 30 min in oil bath on top of a hot plate. One day later, the solution in decane was placed in 70 watt ultrasonic cleaning bath and sonicated for two 10 min intervals at 23 °C. After sonication, the PI1000-PFS50 fragment solution was diluted with decane c = 0.0200 mg/mL. Four equivalent batches (3.00 mL, c = 0.0200 mg/mL) of the fragments solutions were transferred to four new 7 mL vials, followed by addition of different amounts of THF, 0 μL, 9 μL, 18 μL, and 30 μL. As a result, the four fragment solutions in decane contain THF volume fractions of 0 %, 0.3 %, 0.6 %, and 1.0 %. A control experiment was performed by preparing a fragment solution in decane containing 1.0 % 153 hexane. To investigate the effect of good solvent THF on self-seeding, a number of equivalent batches with 0.3 g of fragment solutions with different THF volume fractions were transferred to new vials (7 mL) and then annealed in oil bath at various temperatures. After 30 min, each sample was taken out of the oil bath and allowed to cool to room temperature in air. Grids for TEM measurements were prepared after the solution cooled to room temperature.

5.2.3 Using Solvent to Perform Self-seeding of PI1000-PFS50

A similar protocol was applied to generate PI1000-PFS50 fragments in decane solution with c = 0.0200 mg/mL. Ten equivalent batches (1.00 mL) of the fragment solution were transferred to new vials (7 mL), followed by the addition of different amounts of THF, 0 μL, 110 μL, 124 μL, 136 μL, 149 μL, 163 μL, 176 μL, 190 μL, 205 μL, and 220 μL. As a result, these solutions contained different THF volume fractions, 0 %, 10 %, 11 %, 12 %, 13 %, 14 %, 15 %, 16 %, 17 %, 18 %. Two hours after the addition of THF, the ten vials were placed in desiccators under mild vacuum (ca. 10 Torr) with a cap on top of each vial, but not tightened, for 12 hrs to evaporate the THF. Another vial contained a solvent mixture of decane and THF (THF vol 20 %) without polymer. It was treated similarly in the desiccator in order to check whether THF had completely evaporated. 1H NMR measurements showed no detectable THF. Grids for TEM measurements were prepared after the complete evaporation of the THF.

5.2.4 Effect of Pre-annealing on Self-seeding Behavior of PI1000-PFS50

PI1000-PFS50 micelle fragments in decane were prepared in the same way as described above. To investigate the effect of pre-annealing, three equivalent batches of micelle fragment solutions (3.00 mL, c = 0.0200 mg/mL) were transferred to new vials and annealed for 24 hrs in an oil bath at three different temperatures 45.0 °C, 50.0 °C, and 55.0 °C. Each sample was then taken out of its oil bath and allowed to cool to room temperature in air for 24 hours. Next, the self-seeding protocol described above was applied to these solutions by heating aliquots (0.3 g) of each sample at different temperatures (65.0°C, 70.0°C, 74.0°C, 78.0°C, 80.0°C, 82.0°C) for 30 min. Copper grids for TEM measurements were prepared at least one day after each solution cooled to room temperature.

154

5.2.5 Self-seeding of Other PFS Block Copolymers in Selective Solvents

Micelle solutions of other PFS block copolymers were prepared in a similar way as described for PI1000-PFS50 in the previous sections. A micelle solution of PI637-PFS53 was prepared by heating polymer (0.552 mg) in decane (5.52 mL, c = 0.100 mg/mL) in a 20 mL vial at 100 °C for 30 min in an oil bath on top of a hot plate. A micelle solution of PFS60-PDMS660 was prepared by dissolving polymer (0.567 mg) in decane (5.67 mL, c = 0.100 mg/mL) in a 20 mL vial at 100 °C for 30 min. A micelle solution of PFS90-PDMS900 was prepared by dissolving polymer (0.399 mg) in decane (3.99 mL, c = 0.100 mg/mL) in a 20 mL vial at 100 °C for 30 min.

A micelle solution of PFS30-P2VP300 was prepared by dissolving polymer (0.260 mg) in 2- propanol (2.60 mL, c = 0.100 mg/mL) in a 20 mL vial at 80 °C for 30 min. After heating these solutions for 30 min, the heater was turned off and the solutions were allowed to cool slowly to room temperature (the cooling rate was approximately 1.5 °C /min). One day later, each solution in turn was placed in a 70 watt ultrasonic cleaning bath and sonicated for 10 min at 23 °C followed by an additional 10 min at 23 °C. All of the fragment solutions were diluted with decane or 2-propanol to c = 0.0200 mg/mL.

To investigate the self-seeding behavior of these block copolymers, a number of equivalent batches with 0.3 g fragment solutions of each sample were transferred to new vials (7 mL). These solutions were then annealed in an oil bath at various temperatures. After 30 min, each sample was taken out of the oil bath and allowed to cool to room temperature in air. Grids for TEM measurements were prepared at least one day after the solution cooled to room temperature.

To investigate the effect of annealing time, three 0.3 g PI637-PFS53 fragment solutions were annealed in the oil bath at 64.0 oC for different lengths of time, 10 min, 2 hr, and 24 hr. Similar o experiments were carried out for the PFS60-PDMS660 fragment solutions annealing at 75.0 C, o the PFS90-PDMS900 fragment solutions annealing at 88.0 C, and the PFS30-P2VP300 fragment solutions annealing at 68.0 oC for different times.

155 5.3 Results and Discussion

In this chapter, the self-seeding experiments described were all carried out on short micelles with an average length of 50-80 nm. These short micelles were prepared by a similar protocol: dissolving the polymer in a selective solvent at a high temperature in an oil bath followed by cooling slowly (ca. 1.5 oC/min) to room temperature to produce elongated micelles (> 1 μm). The long micelles were then shortened by sonication in a water bath for two 10 min intervals at room temperature. I refer to these sonication-shortened micelles as “micelle fragments”. A typical experiment describing the formation of PI1000-PFS50 block copolymer micelles in decane and the preparation of micelle fragments by sonication was described in Chapter 2. The characteristics of the micelle fragments obtained by the same experimental protocol, i.e. the average length and length distribution, varied from batch to batch. I will specify the characteristics of the micelle fragments employed in each experiment in the following sections.

It is possible that the sonication treatment of the block copolymer micelles caused chemical degradation of the block copolymer molecules. In order to examine the possible degradation of the PI1000-PFS50 molecules caused by the 20 min sonication, a sample of micelle fragments was dissolved in THF and analyzed by GPC. The GPC traces, RI and UV signals, of the PI1000-PFS50 block copolymer before and after the sonication treatment are shown in Figure 5.1, where one sees the appearance of signal from molecules with lower mass after the sonication. These results suggest a slight degradation of the polymer caused by the sonication. By normalizing and integrating the peak area, the fraction of degraded polymer is estimated to be less than 5 %.

1.00 1.00 A B

0.75 0.75 PI-PFS PI-PFS fragments fragments 0.50 (sonicated 0.50 (sonicated PI-PFS micelles for 20 min) PI-PFS micelles for 20 min) (before sonication) (before sonication) Normalized RI Normalized 0.25 0.25

0.00 nm 420 at UV Normalized 0.00 51015205101520 Retention Volume (mL) Retention Volume (mL)

Figure 5.1. (A) RI and (B) UV (420 nm) signal of GPC chromatographs of PI1000-PFS50 micelles before sonication (black solid line) and micelle fragments formed by sonication for 20 min (red solid line).

156

5.3.1 Self-seeding of PI1000-PFS50

In this section I describe self-seeding experiments on micelle fragments of PI1000-PFS50 (in decane, c = 0.0200 mg/mL). A representative TEM image of the micelle fragments used in the experiments described in this section is shown in Figure 5.2A. The corresponding length distribution and width distribution histograms of these fragments are shown in Figure 5.2B and

5.2C, respectively. These fragments were characterized by Ln = 52 nm, Lw = 59 nm, Lw/Ln =

1.13, and σ/Ln = 0.365; and dn = 13.6 nm, dw = 13.9 nm, dw/dn = 1.02, and σ/dn = 0.147. The width distribution histogram shows that the fragments had a very narrow width distribution. In order to investigate the effect of heating temperature, I annealed aliquots of the micelle fragment solution in an oil bath at different temperatures for 30 min and then allowed these solutions to cool in air back to room temperature. TEM and AFM images were taken after the cooled solutions were allowed to age at least 24 hr at room temperature.

A 0.25 B 0.4 C

0.20 0.3 0.15 0.2 0.10 0.1 0.05 0.00

Normalized Frequency Normalized 0.0 100 nm 20 40 60 80 100 120 Frequency Normalized 0 5 10 15 20 25 Length distribution (nm) Width Distribution (nm)

Figure 5.2. (A) A TEM image of the PI1000-PFS50 micelle fragments used in the experiments described in section 5.3.1. (B) Length distribution histogram and (C) width distribution histogram of the micelle fragments shown in (A).

In Figure 5.3, I show representative TEM images of nine micelle samples, with the heating temperature indicated in each image. One sees that as the heating temperature was increased, micelles of increased but uniform length and uniform width were obtained. However, an interesting feature of the micelles shown in Figure 5.3G, H, and I can be observed: the centers of some micelles seem to be wider and darker than the two ends. In Figure A5.1A and D in the Appendix to this chapter, I selectively show magnified TEM images of the two samples in Figure 5.3G and I (heating at 80 oC and 86 oC) and measure the widths of the wide centers and the thin remainder of the those micelles. The width distribution histograms are also shown in 157 Figure A5.1. One sees that for the micelles that were obtained after heating at 80 oC for 30 min

(Figure A5.1A, B, and C), the wide centers of the micelles were characterized by dn = 25.3 nm, dw = 26.0 nm, dw/dn = 1.03, and the thin remainder of these micelles were characterized by dn =

13.3 nm, dw = 13.5 nm, dw/dn = 1.02; while for the micelles that were obtained after heating at 86 oC for 30 min (Figure A5.1D, E, and F), the wide centers of the micelles were characterized by dn = 23.8 nm, dw = 24.4 nm, dw/dn = 1.03, and the thin remainder of these micelles were characterized by dn = 13.4 nm, dw = 13.7 nm, dw/dn = 1.02. These results suggest that the wide centers of both samples had similar width values, which are larger than the width of the initial micelle seeds as shown in Figure 5.2; the remainder of the micelles from both samples had very similar width values that are also close to the width of the initial micelle seeds.

It is also interesting to look at the length of the wide centers for the both micelle samples as shown in Figure 5.3G (80 oC) and I (86 oC). In Figure A5.2A and C, I present the corresponding length distribution histograms of the wide centers for each sample, while the total length distribution histograms of each sample are also shown in Figure A5.2B and D for comparison. One sees that for the micelles that were obtained after heating at 80 oC for 30 min, the wide centers were characterized by Ln = 69 nm, Lw = 71 nm, and Lw/Ln = 1.03, which is slightly larger than the length of the initial micelle fragments and occupy ca. 10 % of length of the entire micelle. For the micelles that were obtained after heating at 86 oC for 30 min, the wide centers were characterized by Ln = 132 nm, Lw = 136 nm, and Lw/Ln = 1.03, which is clearly larger than the length of the initial micelle fragments and occupy ca. 8 % of length of the entire micelle. The electron contrast of the micelles with the carbon film on the copper grid is provided by the iron-containing PFS block, thus the differences in electron density between the dark/wide center and thin remainders of the micelles in Figure 5.2G and H imply differences in the thickness of the PFS core. 158

A: 50 °C B: 60 °C C: 65 °C

D: 70 °C E: 74 °C F: 78 °C

G: 80 °C H: 82 °C I: 86 °C

Figure 5.3. TEM images of micelles formed after annealing PI1000-PFS50 micelle fragment solutions (decane) for 30 min at different temperatures as indicated in each image and cooling to room temperature.

All scale bars are 500 nm.

In order to measure the thickness of the micelles, my friend Dr. Weiqing Shi performed AFM measurements on the same sample as shown in Figure 5.3I. Two AFM height images and the corresponding height scan profiles along the white line in each image are presented in Figure 5.4. One sees that the centers of two micelles (as indicated by the green triangles) were both ca. 11 nm in height, while the remainder of the micelles (as indicated by the red triangles) had a measured height of ca. 5 nm. However, the height values obtained from AFM measurements include the contributions from both the PFS core and the PI corona, thus, it is impossible to measure the height of the PFS core alone. Nevertheless, the AFM results in Figure 5.4 are 159 consistent with the TEM results in Figure 5.3I that the micelles had a center thicker than the remainder.

A 10 11 nm 0

Height (nm) Height -10 5 nm 02.55.0 Length (μm) B 10

Height (nm) Height -10 5 nm 11 nm 02.55.0 Length (μm)

Figure 5.4. (A) and (B) Two AFM height images and the corresponding height scan profiles along the

white line in each image of the PI1000-PFS50 micelles from the same sample as shown in Figure 5.3I, obtained by heating the micelle fragments at 86 °C for 30 min and cooling to room temperature. Scale bars in (A) and (B) are both 1 μm.

In Figure 5.5A, I plot the number-averaged length Ln of micelles in each sample vs the heating temperature. One sees that for solutions heated above 60 °C, there was dramatic increase in length. The micelle fragments that initially were ca. 50 nm long were transformed into micelles that could be greater than 1 μm long. For these samples, the size distribution remained very narrow, as shown by the error bars (σ) for each point, where σ is the standard deviation of the length distribution and values of σ were calculated from histograms of the micelle length distributions. The values of Ln, Lw, Lw/Ln, and σ/Ln for all of these samples are presented in Table A5.1 in the Appendix to this chapter. When the heating temperature was too high (≥ 95 oC), the micelles formed were too long to get accurate length information from TEM 160 image analysis, and the structures seen on these TEM grids resembled those of the initially prepared micelle samples as shown in Chapter 2.

In order to explain these results, I begin by pointing out two important features of the experiment. First, heating and cooling did not change the number of polymer molecules in the sample; each solution contained an equal mass of polymer M. Second, the critical micelle concentration for this polymer in decane at room temperature is undetectably small, as I showed in Chapter 3. Thus there was a negligible amount of free polymer in solution at room temperature, and I can assume that all of the polymer present in each sample was incorporated into the micelles. As a consequence, the average length of the micelles Ln is connected to the number N of micelles present as

Ln = (1/ML)(M/N) (5.1)

where ML is the mass per unit length of the micelles. This equation ignores the contribution to

ML of the thicker centre of the micelle.

Data in Figure 5.5A show that, as the heating temperature increased (> 60 °C), longer micelles were obtained. Combining this observation with the two features I described above, I conclude that the increase of the micelle length must be due to a decrease of the micelle number. Based upon this idea, I used eq. 5.1 to calculate the fraction of micelle fragments remaining after annealing at each temperature. These results are shown in Figure 5.5B. This calculation took account of the initial length of the fragment micelles before annealing and the final length after annealing at different temperatures. From Figure 5.5B, one sees that, as the heating temperature was increased in the range of 70 to 90 oC, the fraction of surviving seeds decreased exponentially. This is one of the key characteristics of the self-seeding phenomenon as reported in ref [2].

The thermodynamic argument for self-seeding supposes that it is the polymer less perfectly incorporated into the semicrystalline PFS core that dissolves at a given dissolution temperature, and that higher temperatures lead to dissolution and disappearance of a greater fraction of the remaining micelle fragments. As these fragments dissolve, they form free polymer in solution. The surviving fragments serve as seed crystals. As the solution is cooled, the polymer molecules in solution condense epitaxially onto the ends of these seed crystals, and the length of the micelles formed is determined by the number of seed crystals that survive the dissolution 161 process. Here I would like to address a comment about the wide/dark centers of the micelles as observed in Figure 5.3G and 5.3I. At these high annealing temperatures (> 80 oC), the fraction of surviving seeds was less than 5 % (as shown in Figure 5.5B), which represent the most stable seeds. It is possible that the stability of the seeds is associated with the thickness of the PFS core, it is the most thickest fragments that have the highest stability. I showed that the wide centers of the micelles in Figure 5.3G and 5.3I were characterized by an average width of > 20 nm, however, fragments with width larger than 20 nm were not observed in the initial sample, as shown in the width distribution histogram in Figure 5.2C. Based on this information, I suspect that during the annealing process, the PFS chain in the stable fragments rearranged and these stable crystals thickened. During the cooling process, the dissolved polymer chains grow onto the ends of the thick centers, but the width of the remainder of the micelles is smaller than the centers and is almost identical to that of the initial fragments (ca. 14 nm).

2000 100 A B 1500

1000 10

Length (nm) 500

0 1 40 50 60 70 80 90 seeds surviving Percent 40 50 60 70 80 90 o T ( C) Dissolution Temperature ( oC)

Figure 5.5. (A) Mean micelle length Ln of PI1000-PFS50 micelles in decane versus heating temperature for micelle fragment solutions annealed for 30 min (the error bars are the standard deviations σ of the length

distribution). (B) Fraction of surviving seeds in decane solutions of PI1000-PFS50 micelle fragments versus heating temperature. The solid line represents the linear best fit for the six points of highest T. Reprinted from [1] with permission.

To establish when the micelle growth occurred, I placed a drop of hot solution, annealed at 80 °C, on a TEM grid. The TEM image of this sample in Figure 5.6A shows a mixture of short cylinders (Ln ≈ 120 nm) and likely amorphous materials, as indicated in dashed circles. This is very different from the long micelles obtained after letting the solution cool to room temperature and age for one day, as shown in Figure 5.6B. These results suggest that micelles grew during or after cooling to room temperature, the amorphous materials as identified in Figure 5.6A are 162 probably aggregates of PI1000-PFS50 molecules, which may be the source of polymer for the growth during or after cooling.

A B

500 nm 500 nm

Figure 5.6. A comparison of TEM images of PI1000-PFS50 solution of micelle fragments (c = 0.020 mg/mL) annealed at 80.0 oC for 30 min. (A) Short micelles were observed when a drop of the hot solution (80 oC) was placed directly on the grid, dashed circles indicate amorphous materials. (B) Longer micelles formed after the solution was allowed to cool to room temperature and let to crystallize for one day before placing a drop on the TEM grid. The difference between the two figures indicated that the micelle grew during or after cooling to room temperature. Reprinted from [1] with permission.

The thermodynamic argument for self-seeding implies that size of the polymer crystals that are obtained by self-seeding depends only upon the annealing temperature and not on the annealing time [2]. I carried out experiments to examine whether this argument is applicable for the PI1000-PFS50 block copolymer micelles generated by self-seeding experiments. Aliquots of the micelle fragment solutions were annealed for different lengths of time at two temperatures, 70.0 and 80.0 °C. Samples annealed for 10, 120, and 1440 min were examined by TEM after cooling back to room temperature. In Figure 5.7, I plot the mean length Ln of the micelle versus the annealing time. One sees that neither Ln nor σ varied with annealing time, the micelle length only depended on the annealing temperature. The values of Ln, Lw, Lw/Ln, and σ/Ln for all of these samples are collected in Table A5.2 and A5.3 in the Appendix to this chapter. These data indicate that the length of the micelles obtained after the self-seeding experiments depended only on the annealing temperature, rather than the annealing time. 163

800 80.0 oC 600

400

Length (nm) 70.0 C 200

0 10 100 1000 Annealing Time (min)

Figure 5.7. Time dependence of micelle length Ln formed from solutions of PI1000-PFS50 micelle fragments after being annealed at the temperatures indicated in the plots and then cooled to room temperature in air. (The solid lines are a guide for the eye.) Reprinted from [1] with permission. The

results suggest that the self-seeding of PI1000-PFS50 micelle is not a kinetic-controlled process.

In summary, short fragments of rod-like PFS block copolymer micelles in decane, ca. 50 nm in length, rearranged when the solutions were heated above a characteristic temperature (T > 60 °C) and then cooled to room temperature. The net result was fewer micelles of increased length, of a similar uniform width, and a narrow length distribution. The overall process appeared to involve selective dissolution of the micelle fragments of the lowest degree of crystallinity, with the surviving submicroscopic seeds serving as nuclei for the growth of micelles upon cooling. This process is irreversible. A cartoon illustrating the proposed mechanism is presented in Figure 5.8. The length of the micelles obtained (up to 1.5 μm) increased exponentially over the operative temperature range, implying that the number of surviving seeds decreased exponentially with temperature. The process operated under thermodynamic rather than kinetic control. These are the features of self-seeding of polymer crystals, and these experiments demonstrated that a typical self-seeding protocol can be used to generate one-dimensional micelles with controlled length. 164

Figure 5.8. The proposed self-seeding mechanism for fiber-like PI1000-PFS50 micelles in decane solution. Reprinted from [1] with permission.

5.3.2 Effect of Good Solvent on Self-seeding Behavior of PI1000-PFS50

The underlying physics for the polymer self-seeding experiments is that polymer crystal consists of regions of different crystallinity. As a result, factors that affect the crystallinity of the polymer crystals, such as solvent composition, might influent their self-seeding behavior.

In this section, I describe experiments investigating the effect of the presence of small amount of THF on the self-seeding behavior of the PI1000-PFS50 micelle fragments in decane.

THF is a good solvent for both the PFS and PI blocks. The PI1000-PFS50 micelle fragments (in decane, c = 0.0200 mg/mL) used in the experiments described this section were characterized by

Ln = 57 nm, Lw = 64 nm, Lw/Ln = 1.12, and σ/Ln = 0.333. I started the experiments by preparing four fragment solutions containing different volume fractions of THF (0 %, 0.3 %, 0.6 %, and 1.0 %) by adding various amounts of THF, 0 μL, 9 μL, 18 μL, and 30 μL, into four equivalent fragment decane solutions (V = 3.00 mL). The addition of tiny amount THF (up to 1 vol %) did not cause any changes to the number-averaged length Ln and the standard deviation σ of the length distribution of the micelle fragments, as shown in Table A5.4 in the Appendix to this chapter. Aliquots of ca. 0.3 mL of each solution were transferred to new vials, with caps on the vials to prevent solvent evaporation, and heated in an oil bath at various temperatures for 30 min and then allowed to cool in air back to room temperature. To make sure that THF did not evaporate during the experiments, I weighed each vial before heating and after cooling, and no 165 mass change was observed. TEM images were taken after the cooled solutions were allowed to age at least one day at room temperature.

4000 100 A B 1.0 % 3000 0.6 % 0.3 % 0.0 % 2000 10

1000 0.0 % Length (nm) Length 0.3 % 0.6 % 1.0 %

0 Percent Surviving Seeds 1 50 55 60 65 70 75 80 85 50 55 60 65 70 75 80 85 Temperature (oC) Temperature (oC)

Figure 5.9. (A) Mean micelle length Ln of micelles obtained by heating the PI1000-PFS50 fragment decane solutions for 30 min with the presence of different volume fractions of THF versus the heating

temperatures. (B) Semilogarithmic plots of fraction of surviving seeds in solution of PI1000-PFS50 micelle fragments with different volume fractions of THF versus dissolution temperatures. (The solid lines represent the linear best fits for the highest several data points.)

In Figure 5.9A, I plot the number-averaged lengths (Ln) of the micelles obtained after the heating and cooling process versus the heating temperatures. Values of Ln, Lw, Lw/Ln, and σ/Ln of all these samples are collected in Table A5.4 in the Appendix to this chapter. Data in Figure 5.9A show that after aliquots of each fragment solution were heated above 60 °C for 30 min and cooled to room temperature, the longer micelles obtained had lengths that were sensitively dependent both on the heating temperatures as well as the volume fraction of THF that was present in the solution. The length distribution of these samples remained very narrow, as shown by the standard deviation (error bars σ) for each point. For the same heating temperature, the presence of THF led to the formation of longer micelles compared to the micelles obtained by heating the fragments in pure decane; the higher the volume fraction of THF present in the fragment solution, the longer the micelles that were obtained after the heating and cooling process.

The elongation of the micelles was due to the decrease of micelle number caused by the heating process. In section 5.3.1, I described the use of eq. 5.1 to calculate the fraction of 166 surviving fragments at each temperature based on the final length of the micelles and initial length of the fragments. The calculation took into account three features of the self-seeding process, (i) the mass of polymer in each solution is constant; (ii) the CMC of the polymer is negligible at room temperature; and (iii) the mass per unit length of the micelles ML does not change. For the experiments described in this section, the mass of polymer in each solution also remained constant, and I also assume that ML remained constant. In Chapter 3, I showed that small amounts THF (up to 1 vol %) in decane did not lead to a measureable CMC of the polymer at room temperature. Consequently, I could use eq. 5.1 to translate the data in Figure 5.9A to the plot in Figure 5.9B, where I show the percentage of surviving fragments versus the heating temperature in the presence of various amounts of THF. One sees that for each fragment solution with certain THF volume fraction, the percentage of surviving fragments decreased exponentially as the increase of the heating temperature. One can also see that at the same heating temperature, the presence of THF resulted in smaller fractions of surviving fragments compared to fragments in pure decane solution; the more THF present in the fragment solution, the fewer fragments survived the heating process. In other words, the temperature required to dissolve equal fraction of fragments shifted to a smaller value when the volume fraction of THF increased. For example, the temperature required to dissolve 97 % micelle fragments (3 % fragments surviving) shifted from ca. 82 °C (fragments in pure decane) to ca. 78 °C (with the presence of 1 vol % THF in decane).

The Data in Figure 5.9 show that the presence of small amounts of THF in decane helped to dissolve the micelle fragments. THF is a good solvent for the PFS block, the presence of good solvent THF in decane results in a smaller value of the Flory-Huggins parameter χ than that when the polymer is in pure decane, which in turn would lead to a depression of the melting point of the polymer crystals (the crystalline core of the micelles in our case) [12].

In order to examine the effect of the presence of a volatile non-polar solvent at a similar volume fraction on the behavior of PI1000-PFS50 micelle fragments under self-seeding conditions,

I carried out a control experiment by annealing the same PI1000-PFS50 fragment decane solution containing 1.0 vol % hexane at 70 °C for 30 min. After cooling to room temperature, the micelles obtained were characterized by Ln = 336 nm, Lw = 345 nm and Lw/ Ln = 1.03, which were almost identical to the micelles obtained by annealing the PI1000-PFS50 fragments in pure decane solution at 70 °C for 30 min. These results establish that the presence of a non-polar 167 solvent hexane, at the same tiny volume fraction of 1 %, has no effect on the self-seeding behavior of the PI1000-PFS50 micelle fragments.

In this section, I described the self-seeding experiments of PI1000-PFS50 micelle fragment in decane solution in the presence of small amount of THF (vol 0.3-1.0 %), a good solvent for both PFS and PI blocks. The results showed that with the presence of a small amount of THF, the temperature required to dissolve equal fraction of micelle fragments shifted to a lower value. I conclude that the THF helped dissolve the micelle fragments upon heating, resulting in fewer surviving fragments, and thus longer micelles were obtained after the solutions were cooled. In contrast, the presence of a non-polar solvent hexane (1 vol %) in the decane solution showed no effect on the self-seeding behavior of PI1000-PFS50 micelle fragments.

5.3.3 Using Solvent to Perform Self-seeding of PI1000-PFS50

Previous studies of polymer self-seeding in solution use an increase in temperature to reduce the fraction of surviving polymer nuclei. In this section, I describe the experiments showing an alternative approach to manipulating solvent composition to dissolve the micelle fragments. Experiments in Section 5.3.2 showed that the presence of ting amount of THF (1 vol %) in the PI1000-PFS50 micelle fragment solutions helped to disrupt the crystallinity of the PFS crystalline core. The experiments described in this section were designed in the way that more THF was added into the PI1000-PFS50 micelle fragment solution to dissolve fraction of surviving fragments at room temperature, micelles were expected to grow after the volatile THF evaporates. All experiments described in this section were carried out at room temperature.

The PI1000-PFS50 micelle fragments (c = 0.0200 mg/mL) used in the experiments described in this section were characterized by Ln = 57 nm, Lw = 64 nm, Lw/Ln = 1.13, and σ/Ln = 0.351. Note that although the fragments were characterized by the same length values as that described in Section 5.3.2, they came from different batches (see the slight difference of the σ/Ln values). I transferred nine equivalent batches of PI1000-PFS50 fragment solutions in decane (V = 1.00 mL) into new vials (7 mL) and then added different amounts of THF into each of the solution to prepare solutions containing various THF volume fractions ranging from 10 % to 18 % in increments of 1 %. Two hours after the addition of THF, all vials were placed inside a desiccator under vacuum. The cap was put on top of each vial, but not tightened. Twelve hours later, the vials were removed from the desiccator and the cap was tightened on each vial. 168 Another vial containing a mixture of decane and THF (1.25 mL, THF 20 vol %) was treated similarly. It was placed in the desiccator at the same time, for the purpose of monitoring the evaporation of THF by 1H NMR. All samples were allowed to age for one day before the TEM measurements.

In Figure 5.10A, I show the 1H NMR spectrum of the mixture solution of decane and THF before it was put in the desiccator. The peaks at chemical shift of 0.7-1.4 ppm correspond to the signals of decane, while the peaks at 3.6-3.8 ppm and 1.8-1.9 ppm correspond to the signals of THF. By comparing the peak integrals, the molar ratio of THF to decane was calculated to be 0.56:1.0. This corresponds to a THF volume fraction of ca. 19 %, which is close to the target value of 20 % (error of 5 %). After the vial with the un-tightened cap on top was placed in the desiccator under mild vacuum (ca. 10 Torr) for 12 hours, the solution was examined again by 1H NMR. The 1H NMR spectrum of the solution is shown in Figure 5.10B. One sees that the THF signals at 3.6-3.8 ppm and 1.8-1.9 ppm nearly disappeared. The molar fraction of THF in the solution was estimated to be less than 1 %, which corresponds to a THF volume fraction lower than 0.4 %. These results suggest that only a trace amount of THF was left after subjecting the solutions in the desiccator to mild vacuum for 12 hours. 169

B B B B A A A B B B B

D D C C

D C AB

B B B B A B A B B B B O D D C C D C AB

Figure 5.10. 1H NMR spectra of a decane and THF (THF vol 20 %) mixture (A) before and (B) after the evaporation of THF in a desiccator under mild vacuum (ca. 10 Torr) for 12 hours. The THF volume fraction after evaporation is below 0.5 %, which is calculated by comparing the peak integrals of THF

(3.6-3.8 ppm and 1.8-1.9 ppm) and those of decane (0.7-1.4 ppm).

170

In Figure 5.11A, I plot the mean micelle length Ln of the micelles obtained after the evaporation of THF versus the volume fractions of THF that was present in the PI1000-PFS50 fragment solutions before evaporation. Values of Ln, Lw, Lw/Ln, and σ/Ln for all of these samples are presented in Table A5.5 in the Appendix to this chapter. From Figure 5.11A, one sees that after the evaporation of THF, longer micelles up to ca. 2200 nm with narrow length distribution were obtained, as indicated by the small error bar (standard deviation σ of length distribution) of each data point. The length of the micelles obtained depends sensitively on the volume fraction of THF that was originally present in the solution; the larger the volume fraction of THF present before evaporation, the longer the micelles that were obtained. When even larger amounts of THF was added into the fragment solution in decane (e.g. THF vol 18 %), no micelles were observed from the TEM images of the sample. After the evaporation of THF, the micelles obtained were too long to get accurate length information from TEM image, and their structures resembled those of initially prepared micelles as shown in Chapter 2.

The elongation of the micelles after the selective evaporation of THF resembles a self- seeding event. To draw an analogy to polymer self-seeding upon heating, I infer that the addition of THF increased the CMC of the block copolymer in solution and thus dissolved a fraction of micelle fragments with low crystallinity; higher THF volume fractions in the solution led to the dissolution and disappearance of a greater fraction of the micelle fragments. When the THF evaporated, the CMC of the polymer molecules decreased, the free polymer molecules grew back onto the surviving fragments, forming longer micelles with uniform length. In Figure 5.11B, I show the plot of the fraction of surviving seeds versus the volume fraction of THF that was initially present in the solution before evaporation, which was calculated via eq. 5.1, based on the initial length of the fragments and the final length of the micelles. One can see that as the THF volume fraction was increased (from 10 % to 17 %), the fraction of surviving seeds decreased. When the volume fraction was 17 %, the fraction of surviving seeds was only 2 %. These results suggest that one can manipulate the solvent composition to control the dissolution of polymer nuclei, instead of increasing temperature. 171

100 2500 A B

2000

1500 10 1000 Length (nm) 500

0 Seeds Surviving Percent 1 9 101112131415161718 9 101112131415161718 THF Volume Fraction (%) THF Volume Fraction (%)

Figure 5.11. (A) Mean micelle length Ln of micelles formed after the evaporation of THF versus the

volume fractions of THF in the PI1000-PFS50 fragment solutions before the evaporation of THF. (B) Plots of fraction of surviving seeds in solution of PI -PFS micelle fragments versus the volume fraction of 1000 50 THF.

In this section, I described the experiments showing that, self-seeding experiments of

PI1000-PFS50 micelle fragments could be carried out by addition of a good solvent THF for the crystalline polymer followed by slow selective evaporation of this solvent. The results showed that the volume fraction of THF in the solution affected the fraction of surviving micelle fragments and thus the final length of the micelles when THF evaporated; the higher the volume fraction of THF present in the solution, the fewer the micelle fragments survived; the longer the micelles that were obtained after the evaporation of THF.

5.3.4 Effect of Pre-annealing on Self-seeding Behavior of PI1000-PFS50

It is well known that annealing polymer crystals below their melting point improves their crystallinity [3]. In one of the first reports, Peterlin showed that annealing semicrystalline polyethylene in the bulk state led to an increase in crystal thickness and an increase of melting temperature. The rate of thickening was temperature dependent and faster at higher T [13].

In this section, I describe self-seeding experiments on PI1000-PFS50 micelle fragments and fragments that were pre-annealed at temperatures below the dissolution temperature of the micelle fragments. The pre-annealing treatment on micelle fragments is expected to improve the 172 crystallinity of the core and stability of the micelle, thus affect the self-seeding behavior of the micelle fragments.

The experiments included in this section were performed by a summer student Ms.

Anselina Chia under my supervision. The PI1000-PFS50 micelle fragments (in decane, c = 0.0200 mg/mL) used in the experiments described in this section came from the same batch as in

Section 5.3.3 and were characterized by Ln = 57 nm, Lw = 64 nm, Lw/Ln = 1.13, and σ/Ln = 0.351.

Three equivalent batches of the PI1000-PFS50 micelle fragment solutions (V = 3.00 mL) were transferred to new vials and annealed for 24 hours in an oil bath at three different temperatures 45 °C, 50 °C, and 55 °C, followed by cooling to room temperature. The choice of annealing temperatures was based on the data shown in Figure 5.5, where one sees that annealing at these temperatures does not dissolve the micelle fragments.

We first checked whether the annealing treatment on these micelle fragments led to any changes in micelle length and width. In Figure A5.3A-D in the Appendix to this chapter, I show representative TEM images of the initial non-annealed PI1000-PFS50 micelle fragments and fragments that were pre-annealed for 24 hours at different temperatures. One can hardly see any differences among the micelle fragments in the TEM images. We carried out analyses of the length and width distributions on each sample. The corresponding length distribution histograms of these samples are shown in Figure A5.3E-H. One sees that the annealing treatment led to small changes in the average length and length distribution of micelle fragments. The initial micelle fragments were characterized by Ln = 57 nm and Lw/Ln = 1.13. After annealing the fragments at 45 °C for 24 hrs, the fragments were characterized by Ln = 58 nm and Lw/Ln = 1.11.

These values continued to change slightly to Ln = 60 nm and Lw/Ln = 1.15 after annealing at

50 °C for 24 hrs, and Ln = 57 nm and Lw/Ln = 1.12 after annealing at 55 °C for 24 hrs. Also in Figure A5.3H-L, I present the width distribution histogram of each sample. The results show that the initial non-annealed fragments were characterized by a mean width value of dn = 13.8 nm and width distribution of dw/dn = 1.03. The values of dn and dw/dn for other three fragment samples after annealing for 24 hours were: dn = 13.5 nm and dw/dn = 1.04 (45 °C), dn = 13.2 nm and dw/dn = 1.03 (50 °C), dn = 13.5 nm and dw/dn = 1.03 (55 °C). These results show no prominent change of the widths of these micelle fragments caused by the annealing treatment.

Self-seeding experiments were then carried out on the three pre-annealed fragment samples in parallel with a sample of non-pre-annealed micelle fragments. Aliquots of each sample were 173 heated at various temperatures for 30 min, followed by cooling to room temperature. In Figure

5.12A, I plot the average lengths Ln of the micelles obtained after heating the PI1000-PFS50 fragment solutions and cooling versus the heating temperature. One sees that heating the solutions at temperatures above 60 °C, longer micelles up to ca. 2600 nm were obtained. These micelles had narrow length distributions, as indicated by the small error bars (standard deviation σ of the length distribution) of these points. The lengths of the micelles depended sensitively on the heating temperature and whether the micelle fragments had been pre-annealed, as well as the pre-annealing temperature. The pre-annealing treatment of the micelle fragments led to micelles of shorter length after the self-seeding experiments. In other words, at each heating temperature, the micelles obtained after the self-seeding experiments had a shorter average length if the fragments were pre-annealed; the higher the pre-annealing temperature, the shorter the micelles that were obtained. For example, at the highest heating temperature that was investigated 82 °C, micelles of average length ca. 2600 nm were obtained from the non-pre-annealed fragments. In contrast, the micelles obtained by the pre-annealed fragments (55 °C) were characterized by an average length of only ca. 1200 nm. The values of Ln, Lw, Lw/Ln, and σ/Ln for all of these samples are collected in Table A5.6 in the Appendix to this chapter. These results indicate that the pre-annealing treatment had prominent effects on the self-seeding behavior of the PI1000-

PFS50 micelle fragments.

In order to further show the effect of pre-annealing, I used eq. 5.1 to calculate the fraction of surviving seeds at each heating temperature of these samples, based on the final lengths of the micelles and initial length of the fragments before heating. The results are shown in Figure 5.12B. One sees that for each fragment sample, as the increase of the heating temperature, the fraction of surviving seeds deceased exponentially. While at the same heating temperature, the fraction of surviving seeds of the pre-annealed sample was larger than that of the non-pre- annealed sample; pre-annealing at a higher temperature led to larger fraction of surviving seeds. For example, at the heating temperature of 65 °C, the fraction of surviving seeds increased from 40 %, of the initial non-pre-annealed sample, to 70 % for the fragments that have been pre- annealed at 45 °C for 24 hrs; while for the other two fragment samples that have been pre- annealed at 50 °C and 55 °C for 24 hrs, 100 % seeds survived the heating at 65 °C. Comparing the data for the non-pre-annealed fragments and the fragments after being pre-annealed at 55 °C for 24 hrs in Figure 5.12B, one can see that the dissolution temperature of the micelle fragments 174 was shifted ca. 5 °C to higher value. These results imply that the stability of the micelle fragments was improved by the pre-annealing treatment.

3000 A 100 B 2500 2000 55 oC 1500 N/A 50 oC o 10 45 C o o 45 C 1000 50 C 55 oC N/A Length (nm) Length 500 0 1 20 30 40 50 60 70 80 90 Percent Surviving Seeds 20 30 40 50 60 70 80 90 Temperature (oC) Temperature (oC)

Figure 5.12. (A) Mean micelle length Ln of micelles obtained by heating the PI1000-PFS50 fragment decane solutions and solutions which have been annealed at different temperatures for 24 hrs versus the heating temperatures. N/A means that the micelle fragment for self-seeding was not pre-annealed. (B)

Semilogarithmic plots of fraction of surviving seeds in solution of PI1000-PFS50 micelle fragments versus heating temperatures. (The solid lines represent the linear best fits for the highest several data points.)

In this section, I described the self-seeding experiments of PI1000-PFS50 micelle fragments that had been pre-annealed for 24 hours at several temperatures below the fragment dissolution temperature. The results show that pre-annealing affected the self-seeding behavior of these micelle fragments. Fragments that were pre-annealed led to micelles of shorter length after the self-seeding experiments; the higher the pre-annealing temperature, the shorter the micelles that were obtained after the self-seeding experiments. I conclude that the pre-annealing treatment helped to stabilize the micelle fragments in solution by improving their crystallinity, thus increasing the dissolution temperature of the fragments.

5.3.5 Self-seeding of Other PFS Block Copolymers in Selective Solvents

In the previous sections, I described self-seeding experiments of PI1000-PFS50 micelle fragments and several factors that affect the self-seeding process. In this section, I describe self- seeding experiments carried out on several other PFS block copolymer micelle samples and investigate the influence of polymer composition on the self-seeding process. The block 175 copolymer samples investigated in this section include PI637-PFS53 micelles in decane, PFS60-

PDMS660 micelles in decane, PFS90-PDMS900 micelles in decane and PFS30-P2VP300 micelles in 2-propanol.

A solution of PI637-PFS53 micelles was prepared by adding polymer (0.552 mg) to decane (5.52 mL), heating the polymer/decane mixture to 100 °C for 30 min, and then cooling the solution slowly (ca. 1.5 °C/min) to room temperature. This process yielded fiber-like micelles, as seen in the TEM image in Figure 5.13A, with lengths on the order of 10 μm. I show a magnified TEM and the width distribution histogram of the PI637-PFS53 micelles in Figure A5.4A and B in the Appendix to this chapter, one sees that the micelles had a uniform core width of dn = 14.1 nm and dw/dn = 1.02. A similar treatment of PFS60-PDMS660 (0.567 mg) in decane (5.67 mL), after heating to 100 °C for 30 min, led to similar long micelles with lengths on the order of 10 microns (Figure 5.13B). A magnified TEM image and the width distribution histogram of the PFS60-PDMS660 micelles are shown in Figure A5.4C and D in the Appendix to this chapter, showing that the micelles had a uniform core width of dn = 11.4 nm and dw/dn =

1.03. A micelle solution of PFS90-PDMS900 with lengths on the order of 10 μm (Figure 5.13C) was prepared by dissolving polymer (0.399 mg) in decane (3.99 mL) in a 20 mL vial at 100 °C for 30 min, followed by slow cooling to room temperature. A magnified TEM image and the width distribution histogram of the PFS90-PDMS900 micelles are shown in Figure A5.4E and F in the Appendix to this chapter, showing that the micelles had a uniform core width of dn = 23.2 nm and dw/dn = 1.02. A micelle solution of PFS30-P2VP300 with lengths on the order of 2 to 3 μm (Figure 5.13D) was prepared by adding of polymer (0.260 mg) to 2-propanol (2.60 mL), heating to 80 °C for 30 min and then slow cooling to room temperature. A magnified TEM image and the width distribution histogram of the PFS30-P2VP300 micelles are shown in Figure A5.4G and H in the Appendix to this chapter, showing that the micelles had a uniform core width of dn = 23.6 nm and dw/dn = 1.02. 2-propanol was chosen as solvent for PFS30-P2VP300 micelle formation because 2-propanol is good solvent for the P2VP block but a non-solvent for the PFS block. The values of dn and dw/dn for all of the as-prepared micelle samples are summarized in Table 5.1.

176

Table 5.1. Values of dn and dw/dn for all of the as-prepared micelle samples.

Sample dn (nm) dw/dn

PI637-PFS53 14.1 1.02

PFS60-PDMS660 11.4 1.03

PFS90-PDMS900 23.2 1.02

PFS30-P2VP300 23.6 1.02

A PI637-PFS53 B PFS60-PDMS660

C PFS90-PDMS900 D PFS30-P2VP300

Figure 5.13. (A) PI637-PFS53 micelles formed by dissolving polymer 0.552 mg in decane (5.52 mL, c = 0.100 mg/mL) in a 20 mL vial at 100 °C for 30 min, followed by slow cooling (1.5 °C/min) to room

temperature. (B) PFS60-PDMS660 micelles formed by dissolving polymer 0.567 mg in decane 5.67 mL in a

20 mL vial at 100 °C for 30 min, followed by slow cooling to room temperature. (C) PFS90-PDMS900 micelles formed by dissolving polymer 0.399 mg in decane 3.99 mL in a 20 mL vial at 100 °C for 30 min,

followed by slow cooling to room temperature. (D) PFS30-P2VP300 micelles formed by dissolving polymer 0.260 mg in 2-propanol 2.60 mL in a 20 mL vial at 80 °C for 30 min, followed by slow cooling to room temperature. All scale bars are 500 nm.

177 Fragments of these micelles were prepared by sonicating each micelle solution in turn for two 10 min intervals using a 70 watt ultrasonic cleaning bath. In Figure 5.14A-D, I show representative TEM images of the micelle fragments obtained from sonicating the long micelles of PI637-PFS53, PFS60-PDMS660, PFS90-PDMS900 and PFS30-P2VP300, respectively. From histograms of their length distributions (Figure 5.14E-H), I calculated the Ln, Lw and Lw/Ln of each micelle fragment sample. Fragments of PI637-PFS53 micelles were characterized by Ln = 63 nm and Lw/Ln = 1.29; Fragments of PFS60-PDMS660 micelles were characterized by Ln = 47 nm and Lw/Ln = 1.12; Fragments of PFS90-PDMS900 micelles were characterized by Ln = 55 nm and

Lw/Ln = 1.22; and Fragments of PFS30-P2VP300 micelles were characterized by Ln = 66 nm and

Lw/Ln = 1.23.

I then annealed aliquots of the these fragment solutions in an oil bath at different temperatures for 30 min and allowed these solutions to cool back to room temperature in air. In Figure 5.15, I show representative TEM images for the four block copolymer micelle fragments annealed at different temperatures (PI637-PFS53 fragments in decane annealed at 55 °C (Figure

5.15A), 60 °C (5.15B), and 64 °C (5.15C); PFS60-PDMS660 fragments in decane annealed at 65

°C (5.15D), 70 °C (5.15E), and 75 °C (5.15F); PFS90-PDMS900 fragments in decane annealed at

88 °C (5.15G), 92 °C (5.15H), and 96 °C (5.15I) and PFS30-P2VP300 fragments in 2-propanol annealed at 65 °C (5.15J), 70 °C (5.15K), and 75 °C (5.15L)). One sees that after heating the micelle fragment solutions and cooling to room temperature, I obtained longer micelles than the initial micelle fragments of each sample. 178

0.4 A PI637-PFS53 Seeds E PI637-PFS53 Seeds

0.3

0.2

0.1

Normalized Frequency Normalized 0.0 0 50 100 150 200 250 Length (nm)

B PFS60-PDMS660 Seeds 0.5 F PFS60-PDMS660 Seeds 0.4

0.3

0.2

0.1

Normalized Frequency Normalized 0.0 0 50 100 150 200 Length (nm) G C PFS90-PDMS900 Seeds PFS90-PDMS900 Seeds

0.3

0.2

0.1

0.0 Normalized Frequency Normalized 0 40 80 120 160 200 Length (nm)

D PFS30-P2VP300 Seeds H PFS30-P2VP300 Seeds 0.4

0.3

0.2

0.1

0.0 0 50 100 150 200 Normalized Frequency Length (nm)

Figure 5.14. (A-D) PI637-PFS53, PFS60-PDMS660, PFS90-PDMS900, and PFS30-P2VP300 micelle fragments obtained by sonicating the corresponding long micelles as shown in Figure 5.13 for two 10 min intervals. All scale bars are 500 nm. (E-H) Corresponding length distribution histograms of each micelle fragments as shown in (A-D).

179

More information can be acquired from the TEM images in Figure 5.15. For PI637-PFS53 sample (Figure 5.15A-C), the micelles obtained had uniform width that is identical to the initially prepared micelles as shown in Figure 5.13A. There was very little indication of a thicker center for the micelles in any of the images for this sample. The micelles were also characterized by a narrow length distribution. A representative length distribution histogram of the sample in Figure 5.15C is shown in Figure 5.16A, the sample was characterized by Ln = 943 nm, Lw = 952, Lw/Ln = 1.01. For PFS60-PDMS660 sample (Figure 5.15D-F), the micelles obtained also had uniform width that is identical to the initially prepared micelles as shown in Figure 5.13B. There was also very little indication of a thicker center for the micelles in any of the images for this sample. These micelles were characterized by a narrow length distribution. In Figure 5.16B, I show a representative length distribution histogram of the sample in Figure

5.15F; the sample was characterized by Ln = 848 nm, Lw = 870, Lw/Ln = 1.02. For PFS30-

P2VP300 sample (Figure 5.15J-L), longer micelles were also obtained as the heating temperature was increased. A representative length distribution histogram of the sample in Figure 5.15L is shown in Figure 5.16D, the micelles are characterized by Ln = 572 nm, Lw = 609, Lw/Ln = 1.06, a relative narrow length distribution.

For PFS90-PDMS900 sample (Figure 5.15G-I), a somewhat different behavior was observed. One sees that longer micelles were obtained as the heating temperature was increased; however, the micelles seem to have very different lengths. For instance, in Figure 5.15I, micelles with lengths of ca. 300 nm as well as micelles of lengths over 1 μm can be seen. I construct the length distribution histogram of this sample in Figure 5.16C, where one can see that the lengths of the micelles range from 100 nm to 2400 nm. These micelles are characterized by Ln = 1309 nm, Lw = 1601, Lw/Ln = 1.22, a very broad length distribution. These micelles also have a non- uniform width as seen from the TEM image in Figure 5.15I. More TEM images showing the non-uniform width of this sample are presented in Figure A5.5 in the Appendix to this chapter. 180

o o o A: PI637-PFS53 , 55.0 C B: PI637-PFS53 , 60.0 C C: PI637-PFS53 , 64.0 C

o o o D: PFS60-PDMS660 , 65.0 C E: PFS60-PDMS660 , 70.0 C F: PFS60-PDMS660 ,75.0 C

o o o G: PFS90-PDMS900 ,88.0 C H: PFS90-PDMS900 , 92.0 C I: PFS90-PDMS900 ,96.0 C

o o o J: PFS30-P2VP300 ,65.0 C K: PFS30-P2VP300 , 70.0 C L: PFS30-P2VP300 ,75.0 C

Figure. 5.15. Representative TEM images of micelles formed after annealing each block copolymer micelle fragments (as indicated in each figure) solutions for 30 min at different temperatures (as indicated in each figure) and cooling to room temperature. More TEM images showing the non-uniform width of sample in (I) are presented in Figure A5.5 in the Appendix to this chapter. All scale bars are 500 nm. 181

o o A: PI -PFS , 64.0 C B: PFS60-PDMS660 , 75.0 C 0.5 637 53 0.4

0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 Normalized Frequency Normalized Normalized Frequency Normalized 0 500 1000 1500 2000 0 500 1000 1500 2000 Length (nm) Length (nm)

o o C: PFS90-PDMS900 , 96.0 C D: PFS30-P2VP300 , 75.0 C 0.15 0.35 0.30 0.25 0.10 0.20 0.15 0.05 0.10 0.05 0.00 0.00 Normalized Frequency Normalized 0 500 1000 1500 2000 2500 Frequency Normalized 0 500 1000 1500 2000 Length (nm) Length (nm)

Figure 5.16. (A-D) Length distribution histograms of the micelles obtained by heating each micelle fragments (as indicated in each image) at different temperature (as indicated in each image) for 30 min,

and cooling to room temperature. (A) Ln = 943 nm, Lw = 952, Lw/Ln = 1.01; (B) Ln = 848 nm, Lw = 870,

Lw/Ln = 1.02; (C) Ln = 1309 nm, Lw = 1601, Lw/Ln = 1.22; (D) Ln = 572 nm, Lw = 609, Lw/Ln = 1.06.

Interesting results were obtained by heating the PI637-PFS53, PFS60-PDMS660, and PFS30-

P2VP300 micelle fragment solutions (all at c = 0.02 mg/mL) at high temperature. For example, o when the PI637-PFS53 micelle fragments solution was heated at 75 C for 30 min, the micelles obtained were too long to get accurate length information from TEM image analysis. Also the structures seen on these TEM grids (Figure 5.17A) are very similar to those shown in Figure

5.13A for the initially prepared micelle samples. For PFS60-PDMS660 sample, when the solution was heated at 80 oC, the micelles obtained had lengths values ranging from ca. 100 nm to 3 μm, o as shown in Figure 5.17B. For PFS30-P2VP300 sample, when heated 30 min at 80 C, the micelles obtained show aggregated structures with very strange branched morphologies, as shown in Figure 5.17C. 182

o o o A: PI637-PFS53, 75 C B: PFS60-PDMS660, 80 C C: PFS30-P2VP300, 80 C

Figure 5.17. TEM images (A) of PI637-PFS53 micelles formed after annealing the fragment in decane

solutions for 30 min at 75 °C and cooling; (B) PFS60-PDMS660 micelles formed after annealing the

fragments in decane solutions for 30 min at 80 °C and cooling; (C) PFS30-P2VP300 micelles formed after annealing the fragments in 2-propanol solutions for 30 min at 80 °C and cooling. All Scale bars are 500 nm.

In Figure 5.18A-D, I plot number-averaged length Ln of each sample versus the annealing temperature for each micelle polymer composition, Figure 5.18A for PI637-PFS53 in the heating temperature range from 50-70 °C , Figure 5.18B for PFS60-PDMS660 (55-77 °C), Figure 5.18C for PFS90-PDMS900 (60-98 °C), and Figure 5.18D for PFS30-P2VP300 (40-75 °C). The values of

Ln, Lw, Lw/Ln, and σ/Ln for all of these samples are collected in Tables A5.7 (PI637-PFS53), A5.8

(PFS60-PDMS660), A5.9 (PFS90-PDMS900) and A5.10 (PFS30-P2VP300) in the Appendix to this chapter. These results show that when the temperature was above a certain value (60 °C for

PI637-PFS53, 65 °C for PFS60-PDMS660, 80 °C for PFS90-PDMS900, and 60 °C for PFS30-

P2VP300), there was a dramatic increase in the length of the micelles obtained. For the PI637-

PFS53 and PFS60-PDMS660 samples, I obtained micelles with narrow length distributions (Lw/Ln < 1.04), as indicated by the small standard deviation σ of the length distribution for each data point. For the PFS90-PDMS900 sample, micelles obtained at heating temperature below 94 °C were chacterized by narrow length distributions, while micelles obtained at heating temperatures above 94 °C were characterized by very broad length distributions. For the PFS30-P2VP300 samples, the data point at T = 75 °C in Figure 5.18D shows a relatively broad length distribution

(Lw/Ln = 1.06; σ/Ln = 0.257) of the sample, while the length distribution for the other data points below 75 °C are small (Lw/Ln < 1.04; σ/Ln < 0.2). 183

3000 100 A: PI637-PFS53 2500

2000 1500 10 1000 Length (nm) Length 500 E: PI637-PFS53 0 1

45 50 55 60 65 70 75 Seeds Surviving Percent 45 50 55 60 65 70 75 1600 100 B: PFS60-PDMS660 1200

800 10 Length (nm) Length 400

F: PFS60-PDMS660 0 1 50 55 60 65 70 75 80 Seeds Surviving Percent 50 55 60 65 70 75 80 2500 100 C: PFS90-PDMS900 2000

1500 10 1000 Length (nm) Length 500 G: PFS90-PDMS900 0 1

50 60 70 80 90 100 Seeds Surviving Percent 50 60 70 80 90 100 800 D: PFS30-P2VP300 100 600

400 10

Length (nm) Length 200 H: PFS30-P2VP300 0 1 40 50 60 70 80 Seeds Surviving Percent 40 50 60 70 80 Temperature (oC) Temperature (oC)

Figure 5.18. (A)-(D) Mean micelle length Ln versus heating temperatures for (A) PI637-PFS53, (B) PFS60-

PDMS660, (C) PFS90-PDMS900 and (D) PFS30-P2VP300 fragment solutions annealed for 30 min. (E)-(H)

Semilogarithmic plots of fraction of surviving seeds in solution of (E) PI637-PFS53, (F) PFS60-PDMS660,

(G) PFS90-PDMS900 and (H) PFS30-P2VP300 micelle fragments versus heating temperatures. (The solid lines represent the linear best fits for the highest several data points.) 184 Based on the knowledge I acquired in the previous sections, I attribute the elongation of the micelles to the decrease of micelle number in solution when the PI637-PFS53, PFS60-PDMS660,

PFS90-PDMS900, and PFS30-P2VP300 micelle fragment solutions were treated under self-seeding conditions. Heating these micelle fragment solutions selectively dissolved a fraction of the micelle fragments with lower crystallinity, with surviving fragments serving as nuclei for micelle growth upon cooling. The process resulted in fewer micelles of increased length. Based on the data in Figure 5.18A-D, I used eq. 5.1 to calculate the fraction of surviving seeds at different heating temperatures for each sample. The results are shown in Figure 5.18E (PI637-

PFS53), 5.18F (PFS60-PDMS660), 5.18G (PFS90-PDMS900) and 5.18H (PFS30-P2VP300), where one sees that as the annealing temperature was increased, the fraction of surviving seed fragments decreased exponentially. This is the one of the key characteristics of self-seeding of polymer crystals as reported by ref.[2].

Data in Figure 5.18 also suggest that for the micelle fragments of PI637-PFS53, PFS60-

PDMS660 and PFS30-P2VP300, self-seeding experiments can be carried out as a means of generating longer micelles (up to 2500 nm for PI637-PFS53, up to 1400 nm for PFS60-PDMS660, and up to 500 nm for PFS30-P2VP300) with narrow length distributions (Lw/Ln < 1.06) and uniform width. For PFS90-PDMS900, longer micelles (up to 500 nm) with Lw/Ln value of ca. 1.15 were obtained at heating temperature below 94 °C; however, when the heating temperature was above 94 °C, longer micelles (up to 1500 nm) can be obtained, but with a very broad length distribution (Lw/Ln > 1.20).

Right now I do not have a clear explanation for the strange behavior of PFS90-PDMS900. A possible reason could be due to the age (ca. 10 years) of this polymer. This polymer was synthesized by Dr. Jose Raez [14] from our group, and was reported to be characterized by a very narrow molecular weight distribution of PDI = Mw/Mn = 1.01. In order to investigate whether the chemical composition of this polymer has changed, the polymer was dissolved in

THF (ca. 1 mg/mL) and analyzed by GPC. I present the GPC traces (RI and UV) of the PFS90-

PDMS900 sample in Figure A5.6 in the Appendix to this chapter. From both the RI and UV traces, one can see the appearance of shoulder-like signal from molecules with high mass. Unfortunately, details of the original characterization for this polymer do not appear in Dr.

Raez’s Ph.D. thesis. However, I speculate that the strange behavior of PFS90-PDMS900 under 185 self-seeding conditions is associated with the possible change of the chemical composition of the polymer.

In order to investigate the effect of annealing time on the micelle length, aliquots of each

PI637-PFS53, PFS60-PDMS660, PFS90-PDMS900 and PFS30-P2VP300 fragment solutions were annealed at a fixed temperature for different lengths of time. TEM images were taken after the solutions were cooled back to room temperature. The results are shown in Figure 5.19. The values of Ln, Lw, Lw/Ln, and σ/Ln of each sample are collected in Table A5.11 (PI637-PFS53),

Table A5.12 (PFS60-PDMS660), Table A5.13 (PFS90-PDMS900) and Table A5.14 (PFS30-P2VP300) in the Appendix to this chapter. One sees that the lengths of the micelles obtained were independent of the annealing time and depended only on the annealing temperature, consistent with the results for PI1000-PFS50 sample as shown in Figure 5.7 in Section 5.3.1. This is another key characteristic of self-seeding of polymer crystals as reported in ref.[2].

1600 1600 O O A: PI637-PFS53, 64.0 C B: PFS60-PDMS660, 75.0 C 1200 1200

800 800

Length (nm) Length 400 400

0 0 10 100 1000 10 100 1000 400 600 O O C: PFS90-PDMS900, 88.0 C D: PFS30-P2VP300, 68.0 C 300 400

200

200 100 Length (nm) Length

0 0 10 100 1000 10 100 1000 Annealing Time (min) Annealing Time (min)

Figure 5.19. Time dependence of micelle length Ln formed from decane solutions of (A) PI637-PFS53, (B)

PFS60-PDMS660, (C) PFS90-PDMS900 and 2-propanol solution of (C) PFS30-P2VP300 micelle fragments after being annealed at the temperatures indicated in the plots and then cooled to room temperature in air. (The solid lines are a guide for eye.)

186

In this section, I describe the behaviors of PI637-PFS53, PFS60-PDMS660, PFS90-PDMS900, and PFS30-P2VP300 micelle fragments when their solutions were subjected to self-seeding conditions. Short micelle fragments (ca. 60-80 nm) were transformed into longer micelles when the fragment solutions were heated above a characteristic temperature and then cooled to room temperature. The longer micelles of PI637-PFS53 in decane, PFS60-PDMS660 in decane, and

PFS30-P2VP300 in 2-propanol as obtained had narrow length distribution (Lw/Ln < 1.06) and uniform width. However, for PFS90-PDMS900 in decane, longer micelles were obtained, but with broad length distributions (Lw/Ln > 1.15) and a non-uniform width. Nevertheless, all four polymers displayed self-seeding behavior: (i) the fraction of surviving seeds depended sensitively on the heating temperature and decreased exponentially with the increase of temperature, and (ii) the process operated under thermodynamic control rather than kinetic control. 187

5.4 Conclusion

In this chapter, I describe experiments showing that fiber-like PI1000-PFS50 block copolymer micelles in decane exhibited self-seeding behavior: when solutions their fragments (< 100 nm) were heated and then cooled to room temperature, longer micelles (1-2 μm) with narrow length distributions were obtained. The overall process involved selective dissolution of the micelle fragments of the lowest degree of crystallinity, with the surviving seeds serving as nuclei for the growth of micelles upon cooling. The length of the micelles obtained increased exponentially over the operative temperature range, implying that the number of surviving seeds decreased exponentially with temperature. The process operated under thermodynamic rather than kinetic control.

Later in this chapter, I describe a systematic investigation of the effect of presence of a good solvent (THF) as well as a pre-annealing treatment on the self-seeding behavior of the

PI1000-PFS50 micelle fragments in decane. The results show that the presence of THF in the decane solutions disrupted the stability and promoted the dissolution of the PI1000-PFS50 micelle fragments. In contrast, pre-annealing helped improve the crystallinity of the micelle fragments. I also show that self-seeding of PI1000-PFS50 micelle fragments could be carried out by addition of various amounts of THF into the decane solutions, followed by slow selective evaporation of THF.

In the last part of this chapter, I describe the self-seeding behavior of micelle fragments of

PI637-PFS53 in decane, PFS60-PDMS660 in decane, PFS90-PDMS900 in decane and PFS30-P2VP300 in 2-propanol. Short fragments of these micelles, 60-80 nm in length, rearranged when their solutions were heated above a characteristic temperature (60 °C for PI637-PFS53, 65 °C for

PFS60-PDMS660, 80 °C for PFS90-PDMS900, and 60 °C for PFS30-P2VP300) and then cooled to room temperature, forming longer micelles. For PI637-PFS53, PFS60-PDMS660 and PFS30-

P2VP300 samples, the long micelles obtained were characterized by a narrow length distribution

(Lw/Ln < 1.06) and uniform width for operative temperature ranges. However for PFS90-

PDMS900 sample, the long micelles obtained were characterized by broad length distributions

(Lw/Ln > 1.15) and non-uniform width. The reason for this phenomenon is unknown. 188

References

1 Qian, J. S.; Guerin, G.; Lu, Y. J.; Cambridge, G.; Manners, I.; Winnik, M. A. Angew. Chem. Int. Ed. 2011, 50, 1622-1625. 2 Xu, J. J.; Yu, M.; Hu, W. B.; Rehahn, M.; Reiter, G. Nat. Mater. 2009, 8, 348-353. 3 Wunderlich, B. Macromolecular Physics, vol. 1: Crystal Structure, Morphology, Defects Ch. III: Academic, 1973. 4 Strobl, G. Prog. Polym. Sci. 2006, 31, 398-442. 5 a) Blundell, D. J.; Keller, A.; Kovacs, A. J. J. Polym. Sci. B. 1966, 4, 481-486; b) Blundell, D. J.; Keller, A. J. Macromol. Sci. –Phys. B 1968, 2, 301-336. 6 a) Sperling, L. H. Introduction to physical polymer science: John Wiley & Sons, Inc. 2006; b) Wunderlich, B. Macromolecular Physics, vol. 2: Crystal Nucleation, Growth, Annealing Ch. V: Academic, 1976. 7 a) Lotz, B.; Kovacs, A. J. Kolloid Z. Z. Polymere 1966, 209, 97-114; b) Lotz, B.; Kovacs, A. J.; Bassett, G. A.; Keller A. Kolloid Z. Z. Polymere 1966, 209, 115-128. 8 a) Zhu, L.; Calhoun, B. H.; Ge, Q.; Quirk, R. P.; Cheng, S. Z. D.; Thomas, E. L.; Hsiao, B. S.; Yeh, F. J.; Liu L. Z.; Lotz, B. Macromolecules 2001, 34, 1244-1251; b) Hsiao, M. S.; Chen, W. Y.; Zheng, J. X.; Horn, R. M. V.; Quirk, R. P.; Ivanov, D. A.; Thomas, E. L.; Lotz, B.; Cheng, S. Z. D. Macromolecules 2008, 41, 4794-4801; c) Hsiao, M. S.; Zheng, J. X.; Horn, R. M. V.; Quirk, R. P.; Thomas, E. L.; Chen, H. L.; Lotz, B.; Cheng, S. Z. D. Macromolecules 2009, 42, 8343-8352. 9 a) Li, B.; Ni, C. Y. J. Am. Chem. Soc. 2007, 129, 12-13; b) Li, B.; Ni, C. Y.; Li, C. Y. Macromolecules 2008, 41, 149-155. c) Wang, B. B.; Li, B.; Ferrier, R. C. M.; Li. C. Y. Macromol. Rapid Commun. 2010, 31, 169-175. 10 Lorenzo, A. T.; Arnal, M. L.; Sanchez, J. J.; Müller, A. J. J. Polym. Sci. B 2006, 44, 1738- 1750. 11 a) Massa, M. V.; Lee, M. S. M.; Dalnoki-Veress, K. J. Polym. Sci. B 2005, 43, 3438-3443; b) Maus, A.; Hempel. E.; Thurn-Albrecht, T.; Saalwächter, K. Eur. Phys. J. E 2007, 23, 91-101. 12 Mandelkern, L.; Garrett, R. R.; Flory, P. J. J. Am. Chem. Soc. 1952, 74, 3949-3951. 13 Peterlin, A. J. Poly. Sci., Part B: Poly. Lett. 1963, 1, 279-284. 14 Raez, J. Ph.D. Thesis, University of Toronto, 2002. 189

Appendix to Chapter 5

0.4 0.6 A: 80 ℃ B: 80 ℃ C: 80 ℃ 0.5 0.3 0.4 0.2 0.3 0.2 0.1 0.1 0.0 0.0 Normalized Frequency Normalized Frequency 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Width of Micelle Center (nm) Width of Non-center (nm) D: 86 ℃ 0.4 E: 86 ℃ 0.7 F: 86 ℃ 0.6 0.3 0.5 0.4 0.2 0.3 0.1 0.2 0.1 0.0 0.0 Normalized Frequency Normalized Frequency 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Width of Micelle Center (nm) Width of Non-center (nm)

Figure A5.1. (A) TEM image of a micelle formed after annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at 80 oC and cooling to room temperature, scale bar is 100 nm. (B) Width distribution histogram of the dark centers of the micelles in sample as shown in (A), the centers of the micelles were characterized by dn = 25.3 nm, dw = 26.0 nm, and dw/dn = 1.03. (C) Width distribution histogram of the non- center regions of the micelles in sample as shown in (A), which were characterized by dn = 13.3 nm, dw = 13.5 nm, and dw/dn = 1.02. (D) TEM image of micelles formed after annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at 86 oC and cooling to room temperature, scale bar is 100 nm. (E) Width distribution histogram of the dark centers of the micelles in sample as shown in (D), the centers of the micelles were characterized by dn = 23.8 nm, dw = 24.4 nm, and dw/dn = 1.03. (F) Width distribution histogram of the non-center regions of the micelles in sample as shown in (D), which were characterized by dn

= 13.4 nm, dw = 13.7 nm, and dw/dn = 1.02. 190

0.6 A: 80 ℃ B: 80 ℃ 0.30 0.5 0.4 0.20 0.3

0.10 0.2 0.1

0.00 Normalized Frequency 0.0 Normalized Frequency 0 50 100 150 200 250 0 500 1000 1500 2000 2500 Length of Micelle Centers (nm) Length (nm)

0.5 0.30 C: 86 ℃ D: 86 ℃ 0.4 0.25 0.3 0.20 0.15 0.2 0.10 0.1 0.05 0.0 0.00 Normalized Frequency Normalized Frequency 0 50 100 150 200 250 0 500 1000 1500 2000 2500 Length of Micelle Centers (nm) Length (nm)

Figure A5.2. (A and B) Length distribution histograms of the (A) dark centers of the micelles and (B) the o whole micelles formed after annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at 80 C and cooling to room temperature; the length of the dark centers were characterized by Ln = 69 nm, Lw = 71 nm, and Lw/Ln = 1.03; the micelles were characterized by Ln = 718 nm, Lw = 728 nm, and Lw/Ln = 1.01. (C and D) Length distribution histogram of the (C) dark centers of the micelles and (D) the whole micelles formed after o annealing PI1000-PFS50 micelle fragments decane solutions for 30 min at 86 C and cooling to room temperature; the length of the dark centers were characterized by Ln = 132 nm, Lw = 136 nm, and Lw/Ln = 1.03; the micelles were characterized by Ln = 1744 nm, Lw = 1754 nm, and Lw/Ln = 1.01. 191

A: N/A 0.25 E: N/A 0.35 I: N/A 0.20 0.30 0.25 0.15 0.20 0.10 0.15 0.10 0.05 0.05 0.00 0.00 Normalized Frequency Normalized Frequency 0306090120150 0 5 10 15 20 25 Length (nm) Width (nm)

B: 45 °C 0.30 F: 45 °C 0.35 J: 45 °C 0.25 0.30 0.20 0.25 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 Normalized Frequency Normalized FrequencyNormalized 0 306090120150 0 5 10 15 20 25 Length (nm) Width (nm) C: 50 °C 0.25 G: 50 °C 0.35 K: 50 °C 0.20 0.30 0.25 0.15 0.20 0.10 0.15 0.10 0.05 0.05 0.00 0.00 Normalized Frequency 0 30 60 90 120 150 Normalized Frequency 0 5 10 15 20 25 Length (nm) Width (nm) D: 55 °C 0.25 H: 55 °C 0.35 L: 55 °C 0.20 0.30 0.25 0.15 0.20 0.10 0.15 0.10 0.05 0.05 0.00 0.00 Normalized Frequency Normalized 0306090120150Normalized Frequency 0 5 10 15 20 25 Length (nm) Width (nm)

Figure A5.3. (A)-(D) Representative TEM images of the PI1000-PFS50 micelle fragments used in the experiments in Section 5.3.4. (A) N/A represents the fragments without pre-annealing. (B-D) the fragments in (A) after being annealed for 24 hours at different temperatures indicated in each image. All scale bars are 100 nm. (E-H) Corresponding length distribution histograms of the fragments shown in (A-D). (I-L) Corresponding width distribution histograms of the fragments shown in (A-D). 192

A: PI637-PFS53 E: PI637-PFS53 0.4

0.3

0.2

0.1

Normalized Frequency Normalized 0.0 0 5 10 15 20 25 30 35 40 Width (nm)

B: PFS60-PDMS660 F: PFS60-PDMS660 0.4

0.3

0.2

0.1

0.0 Normalized Frequency Normalized 0 5 10 15 20 25 30 35 40 Width (nm)

C: PFS90-PDMS900 0.4 G: PFS90-PDMS900

0.3

0.2

0.1

Normalized Frequency Normalized 0.0 0 5 10 15 20 25 30 35 40 Width (nm)

D: PFS30-P2VP300 0.4 H: PFS30-P2VP300

0.3

0.2

0.1

0.0 Normalized Frequency Normalized 0 5 10 15 20 25 30 35 40 Width (nm)

Figure A5.4. Representative TEM images (A-D) and corresponding width distribution histograms (E-H) of

PI637-PFS53 micelles formed in decane (A and E), PFS60-PDMS660 micelles formed in decane (B and F),

PFS90-PDMS900 micelles formed in decane (C and G), and PFS30-P2VP300 micelles formed in 2-propanol (D and H). All scale bars are 100 nm. PI637-PFS53 micelles were characterized by dn = 14.1 nm, dw = 14.4 nm, and dw/dn = 1.02; PFS60-PDMS660 micelles were characterized by dn = 11.4 nm, dw = 11.7 nm, and dw/dn =

1.03; PFS90-PDMS900 micelles were characterized by dn = 23.2 nm, dw = 23.6 nm, and dw/dn = 1.02; PFS30-

P2VP300 micelles were characterized by dn = 23.6 nm, dw = 24.1 nm, and dw/dn = 1.02.

193

o o A: PFS90-PDMS900 , 96.0 C B: PFS90-PDMS900 , 96.0 C

Figure A5.5. (A and B) More TEM images of the PFS90-PDMS900 micelle formed by annealing the micelle fragment in decane solutions for 30 min at 96 oC and cooling to room temperature, the same sample as shown in Figure 5.15I. Scale bars are 500 nm.

1.00 1.00 A B 0.75 0.75

0.50 0.50

0.25 0.25 Normalized RI Normalized 0.00 0.00

5 10152025Normalized UV at 420 nm 5 10152025 Retention Volume (mL) Retention Volume (mL)

Figure A5.6. (A) RI and (B) UV (420 nm) signals of GPC chromatographs of PFS90-PDMS900. From both the RI and UV traces, one can see the appearance of shoulder-like signal from molecules with high mass. The GPC measurements were carried out ca. 10 years after the polymer was synthesized.

194

Table A5.1 Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature. Reprinted from [1] with permission.

Sample Ln (nm) Lw (nm) Lw/Ln σ/Ln Fragments 52 59 1.13 0.365 45.0 oC 67 74 1.10 0.328 50.0 oC 65 74 1.13 0.369 55.0 oC 61 68 1.12 0.344 60.0 oC 79 84 1.06 0.253 65.0 oC 113 117 1.04 0.186 70.0 oC 168 172 1.02 0.155 74.0 oC 323 329 1.02 0.130 78.0 oC 570 580 1.02 0.126 80.0 oC 718 728 1.01 0.116 82.0 oC 1009 1020 1.01 0.107 86.0 oC 1744 1754 <1.01 0.0751 195

Table A5.2 Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelles formed after solutions of the micelle fragments in decane were annealed at 70.0 oC for different times followed by cooling to room temperature. Reprinted from [1] with permission.

Sample Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 163 167 1.03 0.166

2 hr 163 167 1.03 0.160

24 hr 160 163 1.02 0.138

Table A5.3 Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelles formed after solutions of the micelle fragments in decane were annealed at 80.0 oC for different times followed by cooling to room temperature. Reprinted from [1] with permission.

Sample Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 790 800 1.01 0.114

2 hr 803 814 1.01 0.119 24 hr 797 808 1.01 0.122

196

THF v% 0 % 0.3 % 0.6 % 1.0 %

L L L L L L L L Temp. n w L /L σ/L n w L /L σ/L n w L /L σ/L n w L /L σ/L (nm) (nm) w n n (nm) (nm) w n n (nm) (nm) w n n (nm) (nm) w n n Fragments 57 64 1.12 0.333 60 65 1.09 0.295 58 63 1.09 0.299 58 64 1.09 0.307

50.0 oC 55 59 1.07 0.273 62 67 1.09 0.290 68 75 1.10 0.309 69 75 1.09 0.304

60.0 oC 91 96 1.05 0.220 89 93 1.05 0.225 104 109 1.05 0.221 114 118 1.04 0.202

65.0 oC 162 166 1.02 0.154 168 173 1.03 0.173 166 171 1.03 0.175 209 215 1.03 0.172

70.0 oC 336 344 1.02 0.149 383 392 1.02 0.151 432 442 1.02 0.155 524 535 1.02 0.147

74.0 oC 616 625 1.01 0.125 855 865 1.01 0.109 979 989 1.01 0.103 1214 1226 1.01 0.100

78.0 oC 1107 1120 1.01 0.108 1384 1405 1.01 0.124 1439 1455 1.01 0.105 1823 1847 1.01 0.114

80.0 oC 1625 1634 1.004 0.068 2164 2193 1.01 0.116 2096 2115 1.01 0.095 2475 2494 1.01 0.090

82.0 oC 2088 2116 1.01 0.115 2484 2497 1.01 0.098 3052 3078 1.01 0.092 3379 3400 1.01 0.080 197

Table A5.5. Values of Ln, Lw, Lw/Ln, and σ/Ln of PI1000-PFS50 micelles formed after the evaporation of THF versus the volume fractions of THF in the PI1000-PFS50 fragment decane solutions before the evaporation of THF.

THF v % Ln (nm) Lw (nm) Lw/Ln σ/Ln

Fragments 57 64 1.13 0.351

10.0 % 81 88 1.08 0.284

11.0 % 92 97 1.05 0.228

12.0 % 118 122 1.04 0.186

13.0 % 162 167 1.03 0.179

14.0 % 274 281 1.03 0.168

15.0 % 429 436 1.02 0.131

16.0 % 935 950 1.02 0.126

17.0 % 2284 2308 1.01 0.103

198

Pre-anneal No Pre-annealing 45 °C, 24 hr 50 °C, 24 hr 55 °C, 24 hr T. L L L L L L L L Temp. n w L /L σ/L n w L /L σ/L n w L /L σ/L n w L /L σ/L (nm) (nm) w n n (nm) (nm) w n n (nm) (nm) w n n (nm) (nm) w n n Fragments 57 64 1.13 0.351 58 65 1.11 0.328 60 69 1.15 0.383 57 64 1.12 0.351

65.0 oC 146 151 1.04 0.192 83 86 1.04 0.193 59 63 1.08 0.288 53 58 1.09 0.302

70.0 oC 328 337 1.03 0.162 193 200 1.04 0.197 113 118 1.04 0.204 71 74 1.05 0.225

74.0 oC 654 664 1.02 0.125 376 382 1.02 0.128 281 289 1.03 0.167 194 199 1.03 0.170

78.0 oC 1459 1474 1.01 0.099 988 999 1.01 0.107 675 685 1.02 0.126 452 460 1.02 0.135

80.0 oC 1677 1691 1.01 0.092 1453 1469 1.01 0.105 1269 1278 1.007 0.085 769 780 1.01 0.118

82.0 oC 2614 2629 1.01 0.077 2504 2522 1.007 0.084 1825 1840 1.008 0.091 1193 1205 1.01 0.101 199

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln Fragments 63 81 1.29 0.540

50.0 oC 88 98 1.12 0.341 55.0 oC 142 146 1.03 0.169 60.0 oC 426 434 1.02 0.138

62.0 oC 504 512 1.01 0.119 64.0 oC 943 952 1.01 0.100 66.0 oC 1417 1427 1.007 0.083

70.0 oC 2556 2571 1.006 0.076

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln Fragments 47 52 1.12 0.340

55.0 oC 47 50 1.07 0.255 60.0 oC 67 72 1.07 0.269 65.0 oC 120 129 1.07 0.267

70.0 oC 222 237 1.07 0.268 72.0 oC 479 489 1.02 0.148 75.0 oC 848 870 1.02 0.158

77.0 oC 1420 1432 1.007 0.089

200

Table A5.9. Value of Ln, Lw, Lw/Ln, and σ/Ln of PFS90-PDMS900 micelle fragments and micelles formed after the solution of the fragments in decane was annealed at different temperatures for 30 min followed by cooling to room temperature.

Sample Ln (nm) Lw (nm) Lw/Ln σ/Ln Fragments 55 67 1.22 0.473

60.0 oC 44 51 1.15 0.386 80.0 oC 64 69 1.08 0.281 85.0 oC 129 139 1.08 0.287

88.0 oC 219 251 1.15 0.384 90.0 oC 239 281 1.17 0.418 92.0 oC 360 419 1.16 0.406

94.0 oC 482 529 1.10 0.315 95.0 oC 1072 1373 1.28 0.531 o 96.0 C 1309 1601 1.22 0.474 98.0 oC 1583 1868 1.18 0.426

201

Table A5.10. Values of Ln, Lw, Lw/Ln, and σ/Ln of PFS30-P2VP300 micelle fragments and micelles formed after the solution of the fragments in 2-propanol was annealed at different temperatures for 30 min followed by cooling to room temperature.

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln

Fragments 66 81 1.23 0.470

40.0 oC 66 72 1.09 0.303

50.0 oC 74 92 1.25 0.500

60.0 oC 128 139 1.09 0.297

65.0 oC 209 217 1.04 0.201

68.0 oC 329 336 1.02 0.143

70.0 oC 384 396 1.03 0.182

75.0 oC 572 609 1.06 0.257

Time Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 879 887 1.01 0.100

2 hr 927 940 1.01 0.119 24 hr 924 936 1.01 0.116

202

Time Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 809 844 1.04 0.208

2 hr 798 808 1.01 0.110

24 hr 831 842 1.01 0.114

Sample Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 211 233 1.10 0.322

2 hr 221 253 1.15 0.380

24 hr 216 242 1.12 0.347

Time Ln (nm) Lw (nm) Lw/Ln σ/Ln 10 min 339 347 1.02 0.153

2 hr 329 336 1.02 0.143

24 hr 347 354 1.02 0.138

Reference

1 Qian, J. S.; Guerin, G.; Lu, Y. J.; Cambridge, G.; Manners, I.; Winnik, M. A. Angew. Chem. Int. Ed. 2011, 50, 1622-1625. 203

Chapter 6

POLYFERROCENYLSILANE CRYSTALS IN

NANOCONFINEMENT: FRAGMENTATION, DISSOLUTION,

AND REGROWTH OF CYLINDRICAL BLOCK COPOLYMER

MICELLES

In this chapter, I describe the experiments examining the behavior of PFS crystals in nanoconfinement when two solutions of PI-PFS block copolymer micelles with different but uniform length as well as their solution mixture were heated at various temperatures. The content in this chapter is from the paper published in 2012 [1] (Qian, J. S.; Lu, Y. J.; Cambridge, G.; Guerin, G.; Manners, I.; Winnik, M. A. Macromolecules 2012, 45, 8363-8372).

6.1 Introduction

In the past decades, interests in polymer crystallization have broadened from the crystallization of homopolymer in the bulk towards the crystallization of crystalline-amorphous block copolymers because the incompatibility of the two blocks adds more complexity. In the melt of crystalline-amorphous block copolymer, the microphase separation can happen prior to the crystallization if the order-disorder transition temperature (TODT) is higher than the melting temperature (Tm) [ 2 ]. Various nanoscale morphologies can be generated by microsphase separation in the melt such as spheres, cylinders, bicontinuous structures or lamellae [3].

In the cases that the segregation force of the block copolymer is weak, and both blocks are well above the glass transition temperatures, the morphology that was created from the phase separation could be easily destroyed when the crystalline block crystallizes, known as “breakout”, which has been investigated extensively by Register and Ryan [4]. For instance, by using time-resolved small- and wide-angle X-ray scattering (SAXS and WAXS) to examine the crystallization of a weakly segregated melt of polyethylene- polypropylene (PE-PP), where TODT is ca. 125 °C and Tm of PE block is around 115 °C, Rangarajan et al. found that the 204 crystallization of PE block induced simultaneous rearrangement of the preformed microphase domains and the final morphology was sensitive to thermal history due to melt segregation, which served as barrier to the microdomain reorganization [4a].

However, when the segregation force of the block copolymer is strong or/and the amorphous block is in its glassy state, the crystallization might happen in those regions with predefined morphologies dictated by the microphase separation, known as “confinement”. In this case, TODT of the block copolymer is higher than the glass-transition temperature of the amorphous block Tg; both of them are higher then Tm of the crystallizable block. Study of such confinement effect on crystalline-glassy block copolymer was pioneered by Lotz on poly(ethylene oxide)-polystyrene (PEO-PS) system in later 1960s [5]. In the early 2000s, the Register group carried out systematic studies of crystallization under nanoconfinement in one-, two-, or three-dimensions [6]. For example, Loo et al. [6b] examined the crystallization of polyethylene-poly(vinylcyclohexane) (PE-PVCH), where TODT is ca. 260 °C, Tg of PVCH is ca.

135 °C, and Tm of PE is around 100 °C, by using transmission electron microscopy (TEM), dilatomerty, and SAXS. They used glassy VCH matrix to effectively restrict the crystallization of PE block in different geometries such as spheres, cylinders, gyroid channels, or lamellae, which formed by the microphase separation in the melt before crystallization. They found that the dimension of confinement greatly affected the crystallization kinetics, for spherical and cylindrical confinements, homogenous nucleation and first-order crystallization kinetics were observed, while conventional sigmoidal kinetics applied for gyroid confinement. Lamellar confinement resulted in two-step crystallization behavior.

The Cheng group has been interested in understanding the crystal orientation with respect to the microdomain interfaces when crystallizing under confinement [7]. For many years, they have focused on the PEO-PS system, where Tg of the phases formed by the PS block was in the range of 60-70 °C and Tm of PEO was in the range of 50-60 °C. They investigated intensively the orientation of PEO chains within the lamellar structure confined by two glassy PS layers. By using two-dimensional WAXS and SAXS measurements, they found [7a] that as the increase of the crystallization temperature (Tc), the orientation of the c-axis in the PEO crystals varied from random to perpendicular, then to inclined, and finally to parallel (homeotropic configuration) to the lamellar surface. Later for the same system, they [7c] studied the effects of the confined PEO dimension (the thickness of the PEO layer, dPEO) and the reduced tethering density (σ ) on the 205 PEO orientation change in the lamellar confinement. On one hand, the onset temperature for the crystal orientation change (Tonset) was found to decrease with an increase in the dPEO, which indicated that the confined layer thickness lead to a compression of the overall PEO chain conformation, and thus, favored the c-axis of the PEO crystals adopting homogeneous PEO orientation. On the other hand, the increase of σ resulted in a decrease in the Tonset value because the segmental orientation of PEO chains parallel to the layer normal near the PS interface facilitate the homeotropic orientation of the c-axis of the PEO crystals.

Comparing to the number of papers in the field of crystallization of block copolymers under confinement in the bulk, there are fewer studies about the effects of nanoconfinement on the crystallization of block copolymer in solution. Several research groups have reported examples of one-dimensional micelles formed by block copolymers containing one crystallizable block, such as poly(ε-caprolactone) [ 8 ] and polyacrylonitrile [ 9 ], but little attention has been paid to the understanding of the effects of the one-dimensional nanoconfinement on the crystalline core.

Very recently, the Schmalz group [ 10 ] used a triblock copolymer containing a semicrystalline polyethylene (PE) middle block to examine the crystallization under confinement in solution. They found that when the triblock copolymer was molecularly dissolved at temperatures higher than the crystallization temperature of the PE block, worm-like micelles formed via a nucleation and growth process with length controllable by varying the crystallization temperature. However, if the spherical micelles with the amorphous PE core preformed before crystallization, crystallization took place in the confinement of the precursor micelles, thus spherical micelles were formed. The authors took advantage of this mechanism to achieve the production of nanoparticles with tunable dimensions and surface structures. As a part of their study, the authors also investigated the effect of annealing on the crystalline core of worm-like micelles formed by one triblock copolymer PS340-PE700-PMMA360 (PMMA = poly methyl methacrylate) in toluene. The Micro Differential Scanning Calorimetry (μDSC) annealing experiments on a 10 g/L toluene solution of the polymer showed that non-annealed worm-like micelles exhibited a broad melting peak ranging from 35 to 55 °C with a maximum value of 48.9 °C; while an intense and sharp peak at 50.4 °C was observed for the worm-like micelles after annealing the solution at 45 °C for 3 hrs. The authors attributed the increase of the main peak of melting temperature to the increase of the crystal thickness, which can be 206 described by the Gibbs-Thomson equation. Moreover, the melting peak became much narrower after annealing, indicating a more uniform distribution of crystal thickness.

Our group has been interested in the properties of semicrystalline polyferrocenylsilane (PFS) polymers confined to the core of one-dimensional (1D) block copolymer micelles in solution for many years. In selective solvents, the PFS crystals are formed through a crystallization-driven self-assembly (CDSA) process in the nanoconfinement provided by the other amorphous block. These PFS block copolymer micelles are useful platform to study the nanoconfinement effects on polymer crystals. In chapter 1, I have described the properties of the CDSA process of PFS block copolymers in solution.

In this chapter, I describe the behavior of rigid-rod block copolymer micelles of PI1000-

PFS50 when dilute solutions of these micelles were annealed at various temperatures in decane. I compare two micelle samples of different but uniform length. An initial micelles solution was obtained by heating the polymer in decane to ca. 100 °C for 30 min. Over time, upon cooling, it formed long (5 to 20 µm) thin micelles with a uniform core width (TEM) of ca. 15 nm. After sonication to form fragments, followed by seeded growth, the two micelle samples were obtained. One was characterized by Ln ≈ 250 nm (Lw/Ln = 1.03), which I refer to as L-250, and a second sample with Ln ≈ 1250 nm (Lw/Ln = 1.01), which I refer to as L-1250. The details of the preparation methods and the characteristics of the two samples were described in Chapter 2.

One anticipates that when these solutions of uniform micelles in decane are heated at high enough temperatures, the micelles will dissolve completely. New micelles will form upon cooling, with a different length and very different length distribution than the sample before heating. I find that this does indeed occur for solutions of PI1000-PFS50 micelles heated above 90 °C. Upon cooling, these solutions produced micelles that resembled the initial preparation. When dilute solutions of L-250 and L-1250 micelles were heated at somewhat lower temperatures and then cooled, the behavior was more complex and much more interesting. At moderate temperatures (e.g., 55 °C), fragmentation was the dominant process, leading to shorter micelles with a broad length distribution. The length distribution for these samples was reminiscent of solvent-induced fragmentation of similar micelles as I described in Chapter 3. At somewhat higher temperatures, for example, 65 to 75 °C, the micelles that formed upon cooling had a narrow length distribution that not only depended upon the annealing temperature, but 207 differed for the L-250 sample and the L-1250 sample. The change in length of the micelles is a clear indication that fragmentation was accompanied by partial dissolution of the polymer at these intermediate temperatures, followed by epitaxial deposition of the polymer on the surviving fragments as the solution cooled. A careful analysis of these data indicates the most surprising result, that fragments formed from the longer micelles had, on average, a higher dissolution temperature than those of the shorter micelles.

6.2 Experimental

A micelle solution of PI1000-PFS50 was prepared by heating a polymer sample (0.162 mg) in decane (8.10 mL, c = 0.0200 mg/mL) in a 20 mL vial at 100 °C for 30 min in oil bath on top of a hot plate. The temperature of the oil bath was controlled by an IKATRON ETS-D5 (Germany) thermometer. After heating the solutions for 30 min, the heater was turned off and the solutions were allowed to cool slowly to room temperature (the cooling rate was approximately 1.5 °C /min). One day later, the solution was placed in 70 watt ultrasonic cleaning bath and sonicated for 10 min at 23 °C followed by an additional 10 min at 23 °C. In this way, I obtained shorter micelles characterized by Ln = 58 nm and Lw/Ln = 1.10. I refer to the solution obtained after sonication as the “seeds” solution.

In the seeded growth experiments, micelles of number-averaged length of about 1250 nm were prepared by injecting a THF solution (0.15 mL) containing PI1000-PFS50 polymer (1.20 mg) into a PI1000-PFS50 seeds solution (3 mL, c = 0.0200 mg/mL). Similarly, micelles of number- averaged length of about 250 nm were obtained by adding another THF solution (0.15 mL) containing PI1000-PFS50 polymer (0.210 mg) into a PI1000-PFS50 seeds solution (3 mL, c = 0.0200 mg/mL). These two samples are referred to as L-1250 and L-250. These solutions were allowed to age in the dark for a week. Aliquots of the two solutions were transferred to new vials and diluted with decane to c = 0.0200 mg/mL. Aliquots (0.5 mL) of these micelle solutions were then heated at different temperatures for 30 min in an oil bath followed by slow cooling to room temperature. For a kinetics study, aliquots of the L-1250 solutions were heated at 55 oC and 70 oC (± 0.3°C) for different lengths of time.

For preparation of micelle mixtures, 0.50 mL of each L-250 and L-1250 solution was taken out and mixed together to obtain a mixture solution, denoted as L-Mix1/1, which contains both micelles of 250 nm and 1250 nm with the same number concentration. Similarly, solution of L- 208 Mix3/1 was obtained by mixing 0.6 mL L-250 with 0.2 mL L-1250, which contains micelles of 250 nm and 1250 nm with number ratio of 3:1, solution of L-Mix1/3 was obtained by mixing 0.2 mL L-250 with 0.6 mL L-1250, which contains micelles of 250 nm and 1250 nm with number ratio of 1:3. All the mixture solutions were diluted by decane to c = 0.0200 mg/mL, followed by heating at different temperatures for 30 min in an oil bath.

6.3 Results and Discussion

In the sections below, I describe the effect of thermal annealing on dilute solutions of two samples of rod-like PI1000-PFS50 block copolymer micelles, both with a narrow length distribution. These samples were prepared by seeded growth as described in the Experimental section. A sample of PI1000-PFS50 block copolymer was suspended in decane, heated to ca. 100 °C to dissolve the polymer and then cooled to room temperature. The micelles formed in this way had a uniform width (dn = 15.4 nm, dw = 15.7 nm) with lengths on the order of 5 to 10 μm. By sonicating the solution with a 70 W ultrasonic cleaning bath, I obtained shorter micelles characterized by Ln = 58 nm and Lw/Ln = 1.10 used as seeds for the subsequent growth of PI1000-

PFS50 block copolymer micelles of controlled length.

A TEM image of the micelle seeds and their length distribution histogram were presented in Chapter 2. In order to obtain the L-1250 micelles, additional block copolymer (1.20 mg) dissolved in THF (0.150 mL, 8.00 mg/mL) was added to a micelle seed solution (3 mL, c = 0.0200 mg/mL) in decane at room temperature and allowed to age for 1 wk. The L-250 micelle sample was prepared similarly, by adding a smaller amount of PI1000-PFS50 block copolymer (0.210 mg) in THF (0.150 mL, 1.40 mg/mL) to an identical micelle seed solution (3 mL, c = 0.0200 mg/mL). Both samples were then diluted with decane to give solutions with an identical polymer concentration, c = 0.0200 mg/mL.

My experimental design for the thermal annealing experiments is summarized in Figure 6.1. Solutions of L-1250 or L-250 micelle samples, or their mixtures, were heated at a given temperature, ranging from 40 to 90 °C for 30 min, and then allowed to cool to room temperature and age for one day. In some instances the annealing time was varied. The micelles present in the solution following this treatment were analyzed by TEM. It is useful to keep in mind, when considering the results described below, that the solubility of PI1000-PFS50 in decane increases 209 dramatically with increasing temperature, but that the concentration of free polymer molecules in solution at room temperature (ca. 23 °C) is undetectably small, as I described in Chapter 3.

Figure 6.1. Drawing of the experimental design. Reprinted from Ref. [1] with permission.

6.3.1 Effect of Heating on the L-1250 nm Micelle Sample

In order to investigate the effect of mild heating on the L-1250 nm micelle samples, I took four aliquots of a solution at c = 0.0200 mg/mL, annealed each at 55 °C for a different time (10 min, 30 min, 2 hr, and 24 hr) and then allowed the solutions to cool to room temperature. A representative TEM image of the L-1250 micelle sample prior to heating is shown in Figure 6.2A, and a length distribution histogram obtained from multiple TEM images is presented in

Figure 6.2B. These micelles are characterized by Ln = 1243 nm and Lw/Ln = 1.01. TEM images of these four L-1250 samples annealed at 55 °C are shown in Figure 6.3. In these figures, one sees that the number of short micelles present on the TEM grids increased as heating time increased. 210

Figure 6.2. (A) TEM image and (B) length distribution histogram of PI1000-PFS50 sample L-1250 as prepared. Scale bar: 500 nm. Ln = 1243 nm, Lw/Ln = 1.01, σ/Ln = 0.109. (C-E) Length distribution o histograms of L-1250 after being annealed at 55.0 C for (C) 10 min (Ln = 1153 nm, Lw/Ln = 1.02, σ/Ln =

0.158), (D) 30 min (Ln = 1014 nm, Lw/Ln = 1.09, σ/Ln = 0.307), and (E) 24 hr (Ln = 752 nm, Lw/Ln = 1.16,

σ/Ln = 0.400). (F) Time dependence of micelle length Ln of sample L-1250 micelle after being annealed at 55 oC. (The error bars are the standard deviations σ in length for each sample as determined from the length distribution histograms. The solid line is a guide for eye.) Reprinted from Ref. [1] with permission.

A: 10 min B: 30 min

C: 2 hr D: 24 hr

Figure 6.3. (A) to (D) Representative TEM images of sample L-1250 after being annealed at 55 oC for different lengths of time: (A) 10 min; (B) 30 min; (C) 2 hr; (D) 24 hr. All scale bars are 500 nm. Reprinted from Ref. [1] with permission.

211 In order to obtain quantitative information about the length distributions of these samples as shown in Figure 6.3, I measured the lengths of all of the micelles in field of view from multiple TEM images for each sample. Histograms obtained in this way are presented in Figure 6.2. After 10 min annealing (Figure 6.2C), the changes in the length distribution were small, with the appearance of a small shoulder located at shorter micelle lengths. After 30 min of annealing (Figure 6.2D), the main population of micelles broadened considerably. There are two peaks in the length distribution, at ca. 1300 nm and at 800 nm as well as a significant number of micelles with lengths ranging from 300 to 600 nm. It is likely that the part of the distribution with a peak at ca. 1300 nm corresponds to the initial sample. I also note that there a small number of micelles with lengths greater than 1500 nm. Upon prolonged heating (24 h, Figure 6.2E), One sees that there were very few surviving long micelles. The main population of micelle lengths is centered at ca. 600 nm, while the micelle distribution broadened significantly (Lw/Ln = 1.16). In none of the images, however, did I observe micelles with lengths shorter than 200 nm.

These kinetics measurements are summarized in Figure 6.2F, where I plot the decrease in Ln values over time as well as the changes in the standard deviation (shown as error bars in the plot) of the length distribution. The values of Ln, Lw, Lw/Ln, and σ/Ln for all four samples are presented in Table A6.1 in the Appendix to this chapter. Here σ refers to the standard deviation of the length distribution.

The behavior of the sample at 70 °C is different. Not only have the micelles grown in length, but the length distribution has narrowed. This can be seen for the sample annealed for 30 min in the TEM image presented in Figure 6.4A and the corresponding histogram of the length distribution in Figure 6.4B. In addition, the mean length and the width of the length distribution are almost independent of annealing time. After 10 min annealing, Ln ≈ 1500 nm, and this increased only slightly to ca. 1670 nm at longer times. A histogram of the length distribution for

24 h annealing is presented in Figure 6.4C, and the time evolution of Ln and σ are presented in

Figure 6.4D. For all of these samples, I find Lw/Ln = 1.01. Full details are collected in Table A6.2 in the Appendix to this chapter.

212

A: L‐1250, 70 oC, 30 min 0.3 B: L-1250, 70 °C, 30 min

0.2

0.1

0.0 0 500 1000 1500 2000 2500 Normalized Frequency Normalized Length (nm) C: L-1250, 70 °C, 24 hr D: L-1250, 70 °C 2000 0.3 1500 0.2 1000

0.1 500 Length (nm)

0.0 0 0 500 1000 1500 2000 2500 0 1 10 100 1000 Normalized Frequency Normalized Length (nm) Time (min)

o Figure 6.4. (A) TEM image of PI1000-PFS50 sample L-1250 after being annealed at 70 C for 30 min. Scale bar: 500 nm. (B,C) Length distribution histograms of L-1250 after being annealed at 70 oC for (B) 30 min

(Ln = 1686 nm, Lw/Ln = 1.01, σ/Ln = 0.098), and (C) 24 hr (Ln = 1661 nm, Lw/Ln = 1.01, σ/Ln = 0.087). (D) o Time dependence of micelle length Ln of sample L-1250 micelle after being annealed at 70 C. (The error bars are the standard deviations σ in length for each sample as determined from the histograms of the length distribution. The solid line is a guide for eye.) Reprinted from Ref. [1] with permission.

6.3.2 Effect of Heating on the L-250 nm Micelle Sample and Comparison with L-1250

A TEM image and the length distribution histogram of the L-250 sample are shown in

Figures 6.5A and 6.5D. The sample is characterized by Ln = 256 nm and Lw/Ln = 1.03. Representative TEM images of the L-250 sample after being annealed at 55 °C and 70 °C for 30 min are shown in Figures 6.5B and 6.5C, while the corresponding histograms of length distribution are shown in Figures 6.5E and 6.5F. For the sample annealed 30 min at 55 °C, one sees some fragmentation, but it is much less significant than for the longer L-1250 micelle sample. In the histogram of the length distribution, one also sees evidence for the formation of 213 some micelles longer than those in the initial sample, suggesting that some of the polymer dissolved at this temperature and deposited on the ends of remaining micelles as the solution was cooled. As one saw for the L-1250 micelle sample, annealing at the L-250 sample at 70 °C for 30 min led to an increase in micelle length as well as a narrowing of the length distribution.

A: L‐250 B: L‐250, 55 oC C: L‐250, 70 oC

D: L-250 E: L-250, 55 °C, 30 min F : L - 250, 7 0 ° C, 3 0 m i n 0.5 0.4 0.3

0.4 0.3 0.2 0.3 0.2 0.2 0.1 0.1 0.1

0.0

Normalized FrequencyNormalized 0.0 0.0 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 Length (nm) Length (nm) Length (nm)

Figure 6.5. (A-C) TEM images of PI1000-PFS50 micelle sample L-250 as prepared, and L-250 after being annealing at (B) 55.0 oC and (C) 70.0 oC for 30 min. Scale bars are 500 nm. (D-F) Histograms of the

length distribution of the corresponding micelles are shown in (A-C). (D) Ln = 256 nm, Lw/Ln = 1.03, σ/Ln

= 0.160, (E) Ln = 245 nm, Lw/Ln = 1.06, σ/Ln = 0.249, (F) Ln = 542 nm, Lw/Ln = 1.02, σ/Ln = 0.149. Reprinted from Ref. [1] with permission.

To compare the results for the L-1250 and L-250 nm micelle samples, I plot Ln (and σ) versus annealing temperatures (30 min at 40 - 75 °C) in Figure 6.6 and compare these values to those of the initial samples at room temperature. For this experiment, the annealed samples were aged for one day at room temperature before samples were taken for TEM analysis. One can see that when the micelle solutions were heated at 40 °C, changes in length and length distribution were negligible. At 55 °C, shorter micelles with a broader length distribution were obtained, and this effect was much more prominent for the longer micelles. When the solutions were heated at higher temperatures (65-75 °C) longer micelles were obtained with a very narrow length 214 distribution. When experiments were carried out at higher annealing temperatures, (≥ 80 oC), longer micelles formed, but they were too long to obtain accurate length information from their TEM images.

In Table A6.3 in the Appendix to this chapter, I have compiled values of Ln, Lw, Lw/Ln, and

σ/Ln for the L-1250 samples, as prepared and after annealing at each of the six temperatures shown in Figure 6.6. Corresponding values for the L-250 samples are presented in Table A6.4 in the Appendix.

1000 2500 A: L-250 B: L-1250 800 2000 600 1500 400 Length (nm)Length Length (nm) Length 1000 200 20 30 40 50 60 70 80 20 30 40 50 60 70 80 T (oC) T (oC)

Figure 6.6. Mean micelle length Ln versus heating temperatures for (A) L-250 and (B) L-1250 annealed for 30 min. The error bars are the standard deviations σ for each sample calculated from the histograms of the length distributions. Reprinted from Ref. [1] with permission.

In Chapter 5, I described the behavior of solutions of the PI1000-PFS50 micelle fragments themselves when solutions in decane were annealed at various temperatures ranging from 40 to 90 °C followed by cooling to room temperature. In those experiments, I found that long micelles were formed, with Ln values that increased sensitively with even small increases in annealing temperature, and with a narrow length distribution for each sample. To explain this increase in length, I draw an analogy to the phenomenon of “self-seeding” of crystalline polymers [11,12,13] and hypothesize that the small micelles of the original sample were characterized by a distribution of dissolution temperatures. As the temperature was increased, more polymer dissolved, accompanied by the disappearance of a larger fraction of the original short micelles. Upon cooling the sample, the polymer in solution grew epitaxially onto the ends of the remaining micelle seeds. Fewer seeds led to longer micelles. In keeping with recent findings 215 about the self-seeding behavior of semicrystalline polymers [13], I found that there was an exponential decrease in the fraction of remaining seeds with an increase in annealing temperature. I also found that the mean length of the micelles and its length distribution were independent of the annealing time. Thus this one-dimensional self-seeding growth process, like the more conventional crystalline polymer systems studied by Reiter and coworkers [13], operated under thermodynamic, rather than kinetic control.

6.3.3 Fragmentation and Dissolution upon Heating, Regrowth upon Cooling

The results in Figure 6.2 and Figure 6.4 show that when longer micelles are subjected to self-seeding conditions, two processes operate in parallel. The micelles undergo kinetically driven heat-induced fragmentation along with thermodynamically driven dissolution of polymer molecules. The signature of polymer dissolution is that, upon cooling the solution, some of the micelles become longer than in the initial sample. There is a suggestion in Figure 6.2D that some polymer dissolved at 55 °C. I imagine that at 70 °C, fragmentation is more rapid than at 55 °C, but it is accompanied by polymer dissolution. The increase in micelle length and narrowing of the length distribution indicates that a large fraction of the micelle fragments dissolved completely, leaving a smaller number of seeds for micelle growth upon cooling of the solution.

In their 1968 classic study of self-seeding, Blundell and Keller [11] showed an example of a polyethylene single crystal in xylene that fragmented as the solution was reheated. Thus they were the first to report the temperature-induced fragmentation of crystals during a self-seeding experiment. Our results on the fragmentation of PI1000-PFS50 block copolymer micelles, with a semicrystalline PFS core should be viewed in this context. I find, for example, that fragmentation of PI1000-PFS50 micelles is very sensitive to their length: The seed micelles obtained by sonication showed no signs of fragmentation upon heating. For the L-250 sample, fragmentation was detected but was not particularly prominent. But for the L-1250 sample, fragmentation was significant when the micelle solutions were annealed at 55 °C. These results are consistent with a sonication study of the fragmentation rate (kf) for PFS48-PI264 block 2.6 copolymer micelles, which showed that kf ~ L [14], i.e., a strong decrease in fragmentation rate with a decrease in micelle length.

Deeper insights are possible into the fragmentation-dissolution process on heating and subsequent micelle regrowth on cooling. To obtain this information, we plot in Figure 6.7 the 216 ratio of the initial Ln values for the L-250 and L-1250 samples to the values obtained (final Ln) after annealing at different temperatures. The values of 1.0 at 25 and 40 °C are consistent with no change in the sample under these mild conditions. Values greater than 1 at 55 °C for L-250 and at 55, 60 and 65 °C for L-1250 indicate that there were more micelles of overall shorter length. That is to say that fragmentation dominated over polymer dissolution under these conditions. At higher temperatures, longer micelles (with a narrow length distribution) were formed and this ratio decreased substantially.

Figure 6.7. (A) Ratio of the initial Ln value for the micelle sample to that obtained (final Ln) after annealing for 30 min at the temperature indicated, followed by cooling to 23 °C. (B) The number concentration of micelles present in samples L-1250 and L-250 after they were heated for 30 min and cooled to 23 °C. For all samples, the total polymer concentration c = 0.0200 mg/mL. Reprinted from Ref. [1] with permission.

In Chapter 5, I argued that in this type of self-seeding experiment, all of the polymer that dissolved upon heating became incorporated into the micelles on cooling. This argument was based on findings that the critical micelle concentration for these PI1000-PFS50 block copolymer 217 micelles at room temperature was undetectably small, as I have shown in Chapter 3. From this perspective and the known value of the mass per unit length of the micelles (1.9 polymer molecules/nm) [15], we can calculate from Ln the number concentration of micelles present in each solution. These values are plotted in Figure 6.7B.

The data in Figures 6.7A and 6.7B make it clear that the presence of longer micelles formed on cooling is a direct consequence of fewer micelles in the sample. During the heating stage, micelles fragment, polymer dissolves, and the number of fragments that can serve to nucleate micelle growth decreases. This effect is particularly prominent for samples annealed at T > 60 °C. We imagine that there is a distribution of degrees of crystallinity among the fragments, and that this translates into a distribution of dissolution temperatures. Annealing at elevated temperatures leads to an increase in the fraction of the fragments that dissolve, and a decrease in the number of fragments that survive. One can read the y-axis in Figure 6.7B as a measure of the number concentration of micelle fragments in the sample that survive annealing at each temperature and serve as nuclei or seeds for micelle growth when the solution is cooled.

From this perspective, one gets a very interesting insight into the difference in behavior of the L-1250 and L-250 micelle samples. The curve for L-1250 in Figure 6.7A is shifted to about 5 °C higher temperature than that for L-250. There is a similar effect in Figure 6.7B. The implication of this shift is that the distribution of dissolution temperatures for L-1250 micelles and their fragments is shifted by about 5 °C to higher temperatures compared to that for L-250 micelles and their fragments. This result suggests that the longer micelles have a somewhat higher degree of crystallinity than their shorter counter parts.

6.3.4 Preparation and Effects of Heating on 1250 nm and 250 nm Micelle Mixtures

In order to test some of the ideas presented above and to obtain further insights into the behavior of PI1000-PFS50 block copolymer micelles when subjected to self-seeding conditions, I examined mixtures of the L-250 and L-1250 micelle samples in decane. At room temperature I prepared three mixtures of the two types of micelles. These solutions contain different number ratios (3:1, 1:1, and 1:3) of L-250 and L-1250 micelles. I refer to these solutions as L-Mix3/1 (L-250/L-1250 = 3:1), L-Mix1/1, and L-Mix1/3, respectively. All solutions were then diluted with decane to c = 0.0200 mg/mL. Representative TEM images of these samples before and 218 after heating are presented in Figure 6.8, with corresponding histograms in Figure 6.9. The images obtained from the newly prepared mixtures show the coexistence of L-250 and L-1250 micelles. I constructed histograms of the length distributions from these images, and calculated mean values and length distributions of the mixtures, obtaining Ln = 518 nm and Lw/Ln = 1.72 for the L-Mix3/1 sample, Ln = 735 nm and Lw/Ln = 1.47 for the L-Mix1/1 sample, and Ln = 1041 nm and Lw/Ln = 1.17 for L-Mix1/3. The Ln values of these mixtures are very close to the theoretical number average length due to the mixing of the L-250 and L-1250 samples. These micelle solutions were very stable. I did not observe any noticeable change in the length or the length distribution of these samples stored at room temperature over a time scale of months.

A: L‐Mix3/1 B: L‐Mix3/1, 55 oC C: L‐Mix3/1, 70 oC

D: L‐Mix1/1 E: L‐Mix1/1, 55 oC F: L‐Mix1/1, 70 oC

G: L‐Mix1/3 H: L‐Mix1/3, 55 oC I: L‐Mix1/3, 70 oC

Figure 6.8. (A-C) TEM images of PI1000-PFS50 micelle sample (A) L-Mix3/1 as prepared, and L-Mix3/1 o o after being annealing at (B) 55.0 C and (C) 70.0 C for 30 min. (D-F) TEM images of PI1000-PFS50 micelle sample (D) L-Mix1/1 as prepared, and L-Mix1/1 after being annealing at (E) 55.0 oC and (F) 70.0 o C for 30 min. (G-I) TEM images of PI1000-PFS50 micelle sample (G) L-Mix1/3 as prepared, and L- Mix1/3 after being annealed at (H) 55.0 oC and (I) 70.0 oC for 30 min. All scale bars are 500 nm. Reprinted from Ref. [1] with permission.

219

A: L-Mix3/1 B: L-Mix3/1, 55 °C C: L-Mix3/1, 70 °C 0.6 0.3 0.5 0.5 0.4 0.4 0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.1 Normalized Frequency Normalized 0.0 0.0 0.0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Length (nm) Length (nm) Length (nm)

D: L-Mix1/1 E : L - Mix1/1, 5 5 ° C F: L-Mix1/1, 70 °C 0.3 0.4 0.3

0.2 0.3 0.2

0.2 0.1 0.1 0.1 Normalized Frequency Normalized 0.0 0.0 0.0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Length (nm) Length (nm) Length (nm)

G: L-Mix1/3 H : L-Mix1/3, 55 ° C I: L-Mix1/3, 70 °C 0.15 0.3 0.2 0.10 0.2

0.1 0.05 0.1 Normalized Frequency Normalized 0.0 0.00 0.0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Length (nm) Length (nm) Length (nm)

Figure 6.9. (A-I) Histograms of the length distribution of the corresponding micelles as shown in Figure

6.8. (A) Ln = 518 nm, Lw/Ln = 1.72, σ/Ln = 0.851, (B) Ln = 644 nm, Lw/Ln = 1.31, σ/Ln = 0.557, (C) Ln =

1056 nm, Lw/Ln = 1.01, σ/Ln = 0.091, (D) Ln = 735 nm, Lw/Ln = 1.47, σ/Ln = 0.683, (E) Ln = 756 nm, Lw/Ln

= 1.24, σ/Ln = 0.492, (F) Ln = 1248 nm, Lw/Ln = 1.01, σ/Ln = 0.111, (G) Ln = 1041 nm, Lw/Ln = 1.17, σ/Ln =

0.410, (H) Ln = 944 nm, Lw/Ln = 1.17, σ/Ln = 0.409, (I) Ln = 1493 nm, Lw/Ln = 1.01, σ/Ln = 0.089.

Reprinted from Ref. [1] with permission.

Samples of these mixtures were then heated at different temperatures for 30 min and then allowed to cool to room temperature and age for one day. Representative TEM images of the three micelle mixture solutions after being annealed at 55 °C and 70 °C are shown in Figure 6.8 with the corresponding histograms of length distribution shown in Figure 6.9. I summarize these results on the effect of the heating for each of the micelle mixtures in Figures 6.10A-C, where I plot Ln versus heating temperature. The values of Ln, Lw, Lw/Ln, and σ/Ln for these samples after being annealed at each temperatures are presented in Table A6.5 (L-Mix3/1), Table A6.6 (L- Mix1/1) and Table A6.7 (L-Mix1/3) in the Appendix of this chapter. 220

2000 A: L-Mix3/1 2000 B: L-Mix1/1 1500 1500 1000 1000

500 Length(nm) 500 Length(nm)

0 0 20 30 40 50 60 70 80 20 30 40 50 60 70 80 2500 C: L-Mix1/3 T (oC) 2000

1500

1000

500 Length(nm)

0 20 30 40 50 60 70 80 T (oC)

Figure 6.10. (A-C) Mean micelle length Ln versus heating temperatures for (A) L-Mix3/1, (B) L-Mix1/1,

and (C) L-Mix1/3 (L-250/ L-1250) solutions annealed for 30 min. The error bars are the standard deviations σ for each sample calculated from the histogram of the length distributions. In (A-C), at low temperatures (25 oC and 40 oC), the samples contains two sharp populations with narrow length distribution. The open circles with no error bar represent the mean length calculated for these bimodal samples. Reprinted from Ref. [1] with permission.

A number of key observations can be made from the data in Figure 6.10. The first is that at 25 °C and 40 °C, the bimodal populations remain intact. This observation indicates that neither fragmentation nor polymer dissolution takes place to any significant extent at these temperatures. The second important observation comes from the results at 55 °C. Here one observes a merging of the micelle length distributions. From the histograms of the length distribution presented in Figures 6.9B, E, H, one can see that this broadening is primarily a consequence of the fragmentation of the L1250 sample. At 60 °C, the distributions are still broad but they start to narrow. The contour length distributions sharpened considerably at 65 °C, for all three mixtures and remained sharp at higher temperatures. Values of Ln increased strongly for higher annealing temperatures. 221 To obtain deeper insights into the behavior of the mixed samples upon annealing, in Figure

6.11 we plot values of Ln against the number fraction f(L-1250) of L-1250 micelles in the sample. Separate curves are plotted for data obtained annealing temperatures of 65, 70 and 75 °C. In Figure 6.11A, the x-axis describes the number fraction of L-1250 micelles in the mixture as prepared at room temperature before annealing. The values at x = 0 refer to the L-250 sample itself, and the values at x = 1 refer to the L-1250 sample. One of our goals in carrying out this analysis is to test the idea that micelles and fragments from the L-1250 sample and from the L- 250 sample had different distributions of dissolution temperatures. If the number fraction of L-

1250 in the L-1250/L-250 mixtures was not temperature dependent, one would expect Ln to be a linear function of f(L-1250). For example, values of Ln calculated from the bimodal mixtures of L-1250 and L-250 depicted at 25 and 40 °C in Figure 6.12 vary linearly with initial sample composition.

When one examines the lines drawn through the data points in Figure 6.11A, the fits are not very good. We obtain correlation coefficients of R2 = 0.973 at 65 °C, 0.954 at 70 °C, and 0.875 at 75 °C. It appears that curved lines would give a better fit to these data. An alternative approach to plotting these data involves calculating values of f(L-1250)T at each temperature from the data in Figure 6.7B. f(L-1250)T refers to the fraction of fragments at temperature T that were formed from the L-1250 sample. This calculation assumes, as I have shown above, that the number concentration after cooling is equal to the number of surviving seeds at the annealing

T T temperature before cooling. Using these new values of f(L-1250) , we replot Ln vs f(L-1250) in Figure 6.11B.

The plots in Figure 6.11B provide better linear fits (R2 = 0.989 at 65 °C, 0.988 at 70 °C and 0.969 at 75 °C) than those in Figure 6.11A. The enrichment of each mixture in fragments from the sample L-1250 is also emphasized by the dashed lines that plotted in Figure 6.11B. These lines slope to the right and indicate the extent to which the magnitude of f(L-1250)T increased as the annealing temperature was varied from 65 to 75 °C.

222

2500 A 2000

1500 75 °C (nm) n L 1000 70 °C

500 65 °C 0 00.20.40.60.81 f(L-1250) as mixed 2500 B 2000

1500

(nm) 75 °C n L 1000 70 °C 500 65 °C 0 0 0.2 0.4 0.6 0.8 1 T f(L-1250)f(L-1250)at at the the annealing annealing temperature temperature

Figure 6.11. Plots of the measured value of Ln vs the number fraction of L-1250 micelles (f(L-1250)) in the L-1250/L-250 micelle mixture in decane following annealing at 65, 70, and 75 °C, In A, the value of f(L- 1250) was calculated for the sample as prepared. In B, the value of f(L-1250)T was calculated from the data in Figure 5B as described in the text. The lines are intended as guides for the eye. In B, the dashed lines indicate the change in the value of f(L-1250) as a consequence of annealing the sample at each particular temperature. Reprinted from Ref. [1] with permission.

223

A: 23 °C, 30 min B: 40 °C, 30 min 1500 1500

1200 1200

900 900 (nm)

n 600 600 L 300 300

0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 f (L-1250) f (L-1250)

Figure 6.12. Plots of the measured value of Ln vs the number fraction of L-1250 micelles (f(L-1250)) in the L-1250/L-250 micelle mixture following annealing at (A) 23 and (B) 40 °C. Reprinted from Ref. [1]

with permission.

6.4 Conclusion

The block copolymer PI1000-PFS50 forms fiber-like micelles in decane with a semicrystalline PFS core of uniform width (ca. 15 nm) surrounded by a corona of PI chains. I examined the properties of two micelle samples of uniform length, L-250 characterized by Ln =

256 nm and Lw/Ln = 1.03, and L-1250, characterized by Ln = 1243 nm and Lw/Ln = 1.01 when dilute solutions of the micelles in decane were annealed at various temperatures between 40 and 75 °C and then allowed to cool to room temperature. The micelles were stable at room temperature and at 40 °C. At 55 °C, the micelles in the longer sample underwent kinetically controlled fragmentation to form shorter micelles with a broader length distribution. At this temperature, fragmentation of the L-250 sample could be detected, but was less prominent. Heating to higher temperatures, from 65 to 75 °C, led to the formation of longer micelles with a narrow length distribution. Here the micelle length depended sensitively on annealing temperature, but not on the annealing time.

This thermodynamic control of micelle length in the range of 65 to 75 °C is consistent with the process of self seeding, in which micelle fragments have a distribution of dissolution temperatures, and a larger fraction of the polymer sample dissolved as the annealing temperature 224 was increased. When the samples were cooled, the polymer that dissolved when the samples were heated condensed on the ends of the remaining fragments, which acted as seed micelles for epitaxial growth. Because the CMC of the polymer is undetectably small at room temperature, we infer that all of the polymer in the sample became incorporated into the elongated micelles. The formation of longer micelles implied the survival of few fragments to act as seeds.

Assuming that the mass per unit length of these micelles (ca. 2 block polymer molecules per nm) is independent of their length, we could calculate from the micelle length the number of micelles present in each sample after annealing. By inference, the number corresponds to the number of micelle fragments present at the annealing temperature prior to cooling. This analysis led to the surprising result that the dissolution temperature for the fragments formed from the shorter (L-250) micelles was about 5 °C lower that that of the fragments formed by the longer (L-1250) micelle sample. Each sample is characterized by a distribution of dissolution temperatures, and the proper conclusion is that the distribution of dissolution temperatures is shifted by about 5 °C to lower temperatures for the shorter micelles. To confirm this idea, I subjected three mixtures of the L-250 and L-1250 micelles to the self-seeding conditions. Again these results indicated a lower dissolution temperature for the micelles or micelle fragments of the shorter micelle sample.

I summarize the view of the fragmentation-dissolution process in Figure 6.13, depicted for a 1:1 mixture of the L-250 and L-1250 micelles. While the longer micelles fragment at 55 °C, it is likely that both types of micelles undergo more extensive fragmentation at higher temperature. Regrowth takes place when the samples are cooled. The final length of the micelles is determined by the number of fragments that persist at the annealing temperature and the total concentration of polymer in the sample (constant for all samples). 225

Figure 6.13. Fragmentation and dissolution of a 1:1 mixture of L-250 and L-1250 PI1000-PFS50 micelles when their solution in decane is heated to 70 °C and then cooled to room temperature. The longer micelles fragment extensively at 55 °C, and I imagine that both micelles fragment at 70 °C, accompanied by dissolution of the least crystalline fragments. Upon cooling, all of the polymer in the sample grows epitaxially off the ends of the surviving seeds. Reprinted from Ref. [1] with permission.

We do not have a definitive answer to the question of why fragments of the longer micelles have a higher dissolution temperature than those of the shorter micelles. As a hypothesis for future consideration, we propose that the dissolution temperature is related to the length of the micelle fragments, and that the fragments formed by the L-1250 micelle sample are longer at each temperature than those of the L-250 sample. As a qualitative test of this idea, we compared my findings reported here with the dissolution temperatures found for the initial seed micelle sample with Ln = 58 nm and Lw/Ln = 1.10. Here the distribution of dissolution temperatures appeared to be a few degrees lower than that of the L-250 sample, consistent with my hypothesis. More definitive insights may become available from quantitative modeling of the fragmentation-regrowth process. 226

References

1 Qian, J. S.; Lu, Y. J.; Cambridge, G.; Guerin, G.; Manners, I.; Winnik, M. A. Macromolecules 2012, 45, 8363-8372. 2 Zhu, L.; Chen, Y.; Zhang, A.; Calhoun, B. H.; Chun, M.; Quirk, R. P.; Cheng, S. Z. D.; Hsiao, B. S.; Yeh, F.; Hashimoto, T. Phys. Rev. B 1999, 60, 10022-10031. 3 (a) Bates, F. S.; Fredrickson, G. H. Annu. Rev. Phys. Chem. 1990, 41, 525-557; (b) Hamley, I. W. The Physics of Block Copolymers. 1998, Oxford Science Publications. 4 (a) Rangarajan, P.; Register, R. A.; Fetters, L. J.; Bras, W.; Naylor, S.; Ryan, A. J. Macromolecules 1995, 28, 4932-4938; (b) Rangarajan, P.; Register, R. A.; Adamson, D. H.; Fetters, L. J.; Bras, W.; Naylor, S.; Ryan, A. J. Macromolecules 1995, 28, 1422-1428; (c) Ryan, A. J.; Hamley, I. W.; Bras, W.; Bates, F. S. Macromolecules 1995, 28, 3860-3868; (d) Ryan, A. J.; Fairclough, J. P. A.; Hamley, I. W.; Mai, S. M.; Booth, C. Macromolecules 1997, 30, 1723-1727; (e) Quiram, D, J.; Register, R. A.; Marchand, G. R. Macromolecules 1997, 30,

4551-4558. 5 Lotz, B. Ph.D. Thesis, 1963, Universite´ de Strasbourg. 6 (a) Loo, Y. L.; Register, R. A.; Ryan, A. J. Phy. Rev. Lett. 2000, 84, 4120-4123; (b) Loo, Y. L.; Register, R. A.; Ryan, A. J.; Dee, G. T. Macromolecules 2001, 34, 8968-8977; (c) Loo, Y. L.; Regster, R. A.; Ryan, A. J. Macromolecules 2002, 35, 2365-2374. 7 (a) Zhu, L.; Cheng, S. Z. D.; Calhoun, B. H.; Ge, Q.; Quirk, R. P.; Thomas, E. L.; Hsiao, B. S.; Yeh, F. J.; Lotz, B. J. Am. Chem. Soc. 2000, 122, 5957-5967; (b) Zhu, L.; Cheng, S. Z. D.; Calhoun, B. H.; Ge, Q.; Quirk, R. P.; Thomas, E. L.; Hsiao, B. S.; Yeh, F. J.; Lotz, B. Polymer 2001, 42, 5829-5839. (c) Hsiao, M. S.; Chen, W. Y.; Zheng, J. X.; Van Horn, R. M.; Quirk, R. P.; Ivanov, D. A.; Thomas, E. L.; Lotz, B.; Cheng, S. Z. D. Macromolecules 2008, 41, 4794- 4801; (d) Hsiao, M. S.; Zheng, J. X.; Horn, R. M. V.; Quirk, R. P.; Thomas, E. L.; Chen, H. L.; Lotz, B.; Cheng, S. Z. D. Macromolecules 2009, 42, 8343-8352; (e) Hsiao, M. S.; Zheng, J. X.; Leng, S. W.; Van Horn, R. M.; Quirk, R. P.; Thomas, E. L.; Chen, H. L.; Hsiao, B. S.; Rong, L. X.; Lotz, B.; Cheng, S. Z. D. Macromolecules 2008, 41, 8114-8123. 8 Du, Z. X.; Xu, J. T.; Fan, Z. Q. Macromol. Rapid Commun. 2008, 29, 467-471.

227

9 (a) Lazzari, M.; Scalarone, D.; Hoppe, C. E.; Vazquez-Vazquez, C.; Lopez-Quintela, M. A. Chem. Mater. 2007, 19, 5818-5820; (b) Lazzari, M.; Scalarone, D.; Vazquez-Vazquez, C.; Lopez-Quintela, M. A. Macromol. Rapid Commun. 2008, 29, 352-357. 10 Schmelz. J.; Karg, M.; Hellweg, T.; Schmalz, H. ACS Nano 2011, 5, 9523-9534. 11 a) Blundell, D. J.; Keller, A.; Kovacs, A. J. J. Polym. Sci. B 1966, 4, 481-486; b) Blundell, D. J.; Keller, A. Macromol. Sci. - Phys. B 1968, 2, 301-336. 12 a) Lotz, B.; Kovacs, A. J. Kolloid Z. Z. Polymere 1966, 209, 97-114; b) Lotz, B.; Kovacs, A. J.; Bassett, G. A.; Keller, A. Kolloid Z. Z. Polymere 1966, 209, 115-128. 13 Xu, J. J.; Ma, Y.; Hu, W. B.; Rehahn, M.; Reiter, G. Nat. Mater. 2009, 8, 348-353. 14 Guerin, G.; Wang, H.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 2008, 130, 14763- 14771. 15 Cambridge, G.; Guerin, G.; Manners, I.; Winnik, M. A. Macromol. Rapid Commun. 2010, 31, 934-938. 228

Appendix to Chapter 6

Time Ln (nm) Lw (nm) Lw/Ln σ/Ln

10 min 1153 1181 1.02 0.158 30 min 1014 1109 1.09 0.307

2 hr 923 1048 1.13 0.368

24 hr 752 971 1.16 0.400

Time Ln (nm) Lw (nm) Lw/Ln σ/Ln

10 min 1491 1502 1.01 0.086 30 min 1686 1702 1.01 0.098

24 hr 1661 1674 1.01 0.087

229

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln 23.0 oC 1243 1258 1.01 0.109

40.0 oC 1231 1242 1.01 0.093

55.0 oC 1014 1109 1.09 0.307

60.0 oC 1082 1147 1.06 0.246 65.0 oC 1143 1163 1.02 0.133

70.0 oC 1686 1702 1.01 0.098

75.0 oC 2289 2309 1.01 0.093

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln 23.0 oC 256 263 1.03 0.160

40.0 oC 252 259 1.03 0.167

55.0 oC 245 260 1.06 0.249

60.0 oC 275 284 1.04 0.189 65.0 oC 302 310 1.03 0.162

70.0 oC 542 555 1.02 0.149

75.0 oC 880 890 1.01 0.109

230

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln 23.0 oC 518 892 1.72 0.851

40.0 oC 524 856 1.63 0.800

55.0 oC 644 844 1.31 0.557

60.0 oC 837 899 1.07 0.274 65.0 oC 615 622 1.01 0.112

70.0 oC 1056 1065 1.01 0.091

75.0 oC 1649 1657 1.005 0.070

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln 23.0 oC 735 1077 1.47 0.683

40.0 oC 722 1023 1.42 0.648

55.0 oC 756 938 1.24 0.492

60.0 oC 740 801 1.08 0.286

65.0 oC 791 804 1.02 0.130

70.0 oC 1248 1263 1.01 0.111

75.0 oC 1950 1966 1.01 0.091 231

Temperature Ln (nm) Lw (nm) Lw/Ln σ/Ln 23.0 oC 1041 1215 1.17 0.410

40.0 oC 1039 1209 1.16 0.405

55.0 oC 944 1101 1.17 0.409

60.0 oC 1101 1146 1.04 0.203 65.0 oC 1052 1068 1.01 0.123

70.0 oC 1493 1504 1.01 0.089

75.0 oC 2271 2281 1.004 0.068

232

Chapter 7

SUMMARY AND FUTURE WORK

In this chapter, I summarize my doctoral research work and make some suggestions for future research in the field that is related to my work.

7.1 Summary

My doctoral research has focused on understanding the physical aspects of the self- assembly of the PFS block copolymers in solution. I summarize my research in the following several aspects.

7.1.1 Fragmentation Behavior of the Fiber-like PFS Block Copolymer Micelles

As the first project of my Ph.D. research, I studied the effect of adding increasing amounts of THF to a solution of fiber-like PI1000-PFS50 micelles in decane. My results showed that once the volume fraction of THF in the mixed solvent exceeded 0.1, the micelles became shorter and the contour length distribution broadened significantly. It appeared that polar solvent promoted the fragmentation of the micelles. I speculated that the solvent-induced fragmentation was partially due to the non-uniformity of core crystallinity. A kinetic study showed, for one THF/decane solvent mixture, that the evolution of the CLD took place on a relatively short time scale (30 min) and then the mean micelle length and its CLD became relatively stable. However, when the volume fraction of THF reached 17 %, the micelles were dissolved completely. These results were described in Chapter 3.

Later in a different project, I showed that these fiber-like PI1000-PFS50 micelles also underwent kinetically controlled fragmentation to form shorter micelles with a broader length distribution when they were subjected to heating treatment at mild temperatures (ca. 55 °C ). The fragmentation was more significant for long micelles than short micelles. These results were described in Chapter 6.

233 7.1.2 Growth Kinetics of Fiber-like PFS Block Copolymer Micelles

In the end of the first project, I found a supersaturated condition for PI1000-PFS50 block copolymers. Addition of a small amount of PI1000-PFS50 micelle seeds (in decane solution) into supersaturated polymer solutions (decane/THF mixture, THF 11 vol %) initiated the growth of fiber-like micelles. This discovery allowed me to separate the nucleation stage of the micelle formation from the growth stage and study the growth kinetics of the PI1000-PFS50 fiber-like micelles. The growth of the fiber-like micelles was followed by light scattering by measuring the scattering intensity of the solution at angles of 30o, 60o and 90o over time. In order to correlate the scattering intensity with the micelle length, I prepared a number of reference solutions, which contained the same number concentration of micelles but with different average lengths, and then measured the scattering intensity of these solutions. Based on the experimental correlation of scattering intensity between micelle length, the kinetic data, obtained as the evolution of scattering intensity versus time, were converted to the evolution of micelle length versus time. The micelles at the end of the growth were also investigated by TEM measurements, which showed similar final length values of micelles with those obtained from LS measurements.

The increase of the micelle length was shown to be well fitted by an expression with two exponential decay terms. The fitting parameters from four different kinetics experiments were very similar. These results indicated that the growth of the micelles involved two separate steps, a fast step with rate constant of the magnitude of 104 Lmol-1s-1, and a slow step with rate constant of 103 Lmol-1s-1. Both of the two rate constant values were smaller than that expected for a diffusion-controlled reaction (106 Lmol-1s-1), implying that both growth processes were reaction-controlled.

To explain the two different rates, we hypothesized that the two processes in the micelle growth were due to the existence of two different populations of PI1000-PFS50 molecules in the supersaturated solution that are slow to equilibrate. One population of the polymer chain is in the “productive” state, while the other population is in the “unproductive” state which has to transform itself into the “productive” state before attaching onto micelles.

The results concerning the growth kinetics were described in Chapter 4. 234 7.1.3 Self-seeding of PFS Block Copolymer Micelles

For the purpose of investigating the behavior of the PFS block copolymer micelles under heating, I found that these fiber-like micelles exhibited self-seeding behavior. For example, when solutions of PI1000-PFS50 block copolymer micelle fragments (ca. 60 nm) in decane were heated and then cooled to room temperature, longer micelles (1-2 μm) with narrow length distributions (Lw/Ln < 1.03) were obtained. The process involved selective dissolution of the micelle fragments of the lowest degree of crystallinity, with the surviving seeds serving as nuclei for the growth of micelles upon cooling. The length of the micelles obtained increased exponentially over the operative temperature range, implying that the number of surviving seeds decreased exponentially with temperature. This process operated under thermodynamic rather than kinetic control.

Later, systematic experiments were carried out to investigate the effect of the presence of a good solvent (THF) as well as a pre-annealing treatment on the self-seeding behavior of the

PI1000-PFS50 micelle fragments in decane. I found that the presence of THF in the decane solutions disrupted the stability and promoted the dissolution of the PI1000-PFS50 micelle fragments. In contrast, pre-annealing helped improve the crystallinity of the micelle fragments. I also showed that self-seeding experiments of PI1000-PFS50 micelle fragments could be carried out by addition of various amounts of THF into the decane solutions, followed by slow selective evaporation of THF.

I also described the self-seeding behavior of micelle fragments of PI637-PFS53 in decane,

PFS60-PDMS660 in decane, PFS90-PDMS900 in decane and PFS30-P2VP300 in 2-propanol. Short fragments of these micelles, 60-80 nm in length, rearranged when their solutions were heated above a characteristic temperature (60 °C for PI637-PFS53, 65 °C for PFS60-PDMS660, 80 °C for

PFS90-PDMS900, and 60 °C for PFS30-P2VP300) and then cooled to room temperature, forming longer micelles. For PI637-PFS53, PFS60-PDMS660 and PFS30-P2VP300 samples, the long micelles obtained were characterized by a narrow length distribution (Lw/Ln < 1.06) and uniform width for operative temperature ranges. However for PFS90-PDMS900 sample, the long micelles obtained were characterized by broad length distributions (Lw/Ln > 1.15) and non-uniform width. The reason for this phenomenon is unknown.

These results as mentioned above were described in Chapter 5. 235

In Chapter 6, I described a self-seeding study on two PI1000-PFS50 micelle samples of uniform length, L-250 characterized by Ln = 256 nm and Lw/Ln = 1.03, and L-1250, characterized by Ln = 1243 nm and Lw/Ln = 1.01. At temperatures in the range of 65 to 75 °C, the micelles that formed upon cooling had a narrow length distribution that not only depended upon the annealing temperature, but differed for the L-250 sample and the L-1250 sample. This thermodynamic control of micelle length in the range of 65 to 75 °C is consistent with the process of self-seeding, in which micelle fragments have a distribution of dissolution temperatures, and a larger fraction of the polymer sample dissolved as the annealing temperature was increased. When the samples were cooled, the polymer that dissolved when the samples were heated condensed on the ends of the remaining fragments, which acted as seed micelles for epitaxial growth. The data analysis led to a surprising result that the dissolution temperature for the fragments formed from the shorter (L-250) micelles was about 5 °C lower that that of the fragments formed by the longer (L-1250) micelle sample. Each sample is characterized by a distribution of dissolution temperatures, and the proper conclusion is that the distribution of dissolution temperatures is shifted by about 5 °C to lower temperatures for the shorter micelles. The reason for such phenomenon is unknown.

7.2 Future Work

7.2.1 Growth Kinetics

Studying the growth kinetics of these fiber-like PFS block copolymer micelles is extremely important for the understanding of the crystallization-driven self-assembly process of PFS block copolymers. I have provided the first quantitative study of the growth kinetics of PI1000-PFS50 block copolymer micelles in decane/THF mixture. However, my results only represent preliminary efforts on this important project. There are many aspects needed to be studied in order to further understand the mechanism of the self-assembly process:

(i) Kinetics experiments could be carried out on other PI-PFS block copolymers with different block ratios. This will allow us to understand the effect of length of each block on the growth process.

(ii) Kinetics experiments could be extended to other PFS block copolymers in various solvents, such as PFS-PDMS in alkane solvents, and PFS-P2VP in alcohols. This will 236 allow us to understand the effect of chemical composition of block copolymers and solvent on the growth process.

(iii) Kinetics experiments could be carried out at different temperatures, above or below room temperatures. This will allow us to investigate the influence of temperature on the growth process.

The three aspects mentioned above only represent my personal suggestions for future efforts on this project. Based on personal experience, the kinetics experiments are very delicate, those who want to continue on this project should be very careful about the experiment design before carrying on any experiments.

7.2.2 Self-seeding

My research represents the first one-dimensional analogy of self-seeding as a means of generating uniform fiber-like micelles with a crystalline core in solution. Although I have carried out systematic studies of the self-seeding behavior of PI1000-PFS50 block copolymer micelles in decane and I have also shown preliminary results on extending the self-seeding experiments on other PFS block copolymers, there is still much to be done on this topic.

(i) The self-seeding experiments could be also applied to other fiber-like micelles formed by different crystalline-coil block copolymers and block copolymers that contain a π- conjugated block, such as P3HT block copolymers.

(ii) Some physical aspects of the self-seeding experiments could also be studied. For

example in Chapter 5, I showed that some of the PI1000-PFS50 micelles obtained after self-seeding experiments had thicker centers. One might be interested in the molecular origin (crystal packing) of this phenomenon.

(iii) My colleague Dr. Guerin has suggested that self-seeding experiments could be carried out on mixtures of different block copolymer micelles. This will allow us to generate uniform fiber-like micelles that are composed by different block copolymers