331: Soft Materials Kenneth R. Shull Department of Materials Science and Engineering Northwestern University October 9, 2020 Contents 1 Catalog Description4 2 Course Outcomes5 3 331: Soft Materials5 4 Introduction5 4.1 Synthetic Polymers.......................... 7 4.2 Understanding Polymer Chemistry................. 10 5 Polymerization Reactions 13 5.1 Step-Growth.............................. 14 5.2 Interfacial Polymerizations...................... 16 6 Mol. Wt. Distributions 18 6.1 Number Average ........................... 19 6.2 Weight Average............................ 20 6.3 Step Growth.............................. 23 7 Non-Linear Step Growth 28 7.1 Gelation ................................ 29 7.2 Prepolymers.............................. 29 7.3 Corothers Theory........................... 30 8 Chain-Growth 33 8.1 Mechanisms.............................. 33 8.2 Reactive Species............................ 34 8.3 Initiation................................ 35 8.4 Termination .............................. 36 1 CONTENTS CONTENTS 8.5 Intramolecular Chain Transfer.................... 38 8.6 Dienes ................................. 39 8.7 Living Polymerizations........................ 40 8.8 Tacticity................................. 41 9 Common Polymers 42 9.1 Add. to a Double Bond........................ 42 9.2 Ring Opening............................. 49 9.3 Step Growth.............................. 50 10 Crosslinking 55 11 Copolymers 56 12 The Glass Transition 57 12.1 Free volume.............................. 58 12.2 Enthalpy and Heat Capacity..................... 62 12.3 DSC................................... 62 13 Amorphous Polymers 63 13.1 End-to-end Vector........................... 64 13.2 1D Random Walk........................... 64 13.3 Average of a Function ........................ 66 13.4 Averages for Random Walks..................... 67 13.5 3D Random Walks .......................... 68 14 Chain Dimensions 72 14.1 General Considerations........................ 73 14.2 Freely Jointed Chain Model..................... 75 14.3 Freely Rotating Chain Model .................... 75 14.4 Bond Angle Restrictions....................... 77 14.5 Characteristic Ratio.......................... 78 14.6 Self-Avoiding Random Walks.................... 80 14.7 Deformation of a Single Polymer Molecule ............ 81 15 Elasticity 83 15.1 Fundamental Definitions....................... 83 15.2 Rubber Elasticity ........................... 89 16 Viscoelasticity 95 16.1 Relaxation Modulus ......................... 97 16.2 Boltzmann Superposition Principle................. 98 16.3 Idealized Relaxation Curves..................... 101 16.4 Temperature Dependence ...................... 102 16.5 Dynamic Moduli ........................... 104 2 CONTENTS CONTENTS 17 Semicrystalline Polymers 110 17.1 Structural Hierarchy in Semicrystalline Polymers . 111 17.2 The Structural Repeat Unit...................... 111 17.3 Helix Formation............................ 112 17.4 Crystalline unit cells ......................... 114 17.5 Single Crystal Stiffness........................ 117 17.6 Chain Folding............................. 117 17.7 Spherulitic morphologies ...................... 119 17.8 Birefringence.............................. 121 17.9 Growth of a Lamellar Crystallite .................. 122 17.10Density................................. 124 18 Liquid Crystals 125 18.1 Nematic Liquid Crystals....................... 126 18.2 Nematic Liquid Crystals - Texture . 126 18.3 Liquid Crystal Displays ....................... 127 19 Solutions and Blends 127 19.1 Chemical Potentials.......................... 128 19.2 Ideal Entropy of Mixing for Polymers . 132 19.3 Idealized Enthalpy of Mixing .................... 132 19.4 Flory-Huggins............................. 136 19.5 Binodal and Spinodal......................... 137 19.6 Critical Point.............................. 139 19.7 Spinodal Decomposition....................... 140 19.8 Phase Diagrams............................ 141 19.9 Chemical Potentials.......................... 142 19.10Osmotic Pressure ........................... 145 19.11Equilibrium Swelling......................... 153 20 Surfaces and Interfaces 156 20.1 Equilibrium Contact Angle ..................... 156 20.2 Interfacial Energy........................... 157 20.3 Block Copolymer Morphologies................... 160 21 Case Study: Triblock Gels 163 21.1 Introduction.............................. 163 21.2 Gelcasting ............................... 165 21.3 Solid/Liquid Transition ....................... 166 21.4 Glass Transition............................ 169 21.5 Gel Modulus.............................. 172 21.6 Hydrogels: Water as the Solvent .................. 174 22 Summary 178 22.1 Classification Scheme......................... 178 22.2 Molecular Weight Averages..................... 178 3 1 CATALOG DESCRIPTION 22.3 Polymerizations............................ 178 22.4 Chain Dimensions........................... 179 22.5 Crystallization............................. 180 22.6 Rubber Elasticity ........................... 181 22.7 Viscoelasticity............................. 182 22.8 Solutions and Blends......................... 183 22.9 Interfaces................................ 184 23 Review Questions 184 23.1 Polymer Synthesis........................... 184 23.2 Molecular Weight Distributions................... 184 23.3 Gels and Elastomers ......................... 185 23.4 Glass transition ............................ 185 23.5 Chain dimensions of amorphous polymers . 185 23.6 Rubber Elasticity ........................... 186 23.7 Viscoelasticity............................. 186 23.8 Semicrystalline Polymers....................... 186 23.9 Solution Thermodynamics...................... 187 23.10Interfaces and Self-Assembly .................... 188 24 331 Problems 188 25 Appendix 1: MATLAB scripts 210 25.1 Symbolic Math............................. 210 25.2 Solution to a Nonlinear Equation.................. 210 26 Appendix 2: Data Tables 211 26.1 Dynamic Moduli ........................... 211 27 Other Resources 215 27.1 Polymer Synthesis........................... 215 1 Catalog Description Different kinds of polymeric materials. Relationships between structure and physical properties; rubber elasticity, the glassy state, crystallinity in polymers. Lectures, laboratory. Prerequisites: 301 or equivalent; 314 or CHEM 342 1. 4 4 INTRODUCTION 2 Course Outcomes 3 331: Soft Materials At the conclusion of the course students will be able to: 1. Given the chemical structure of a common polymer, draw the chemical structures of the monomer(s) from which it was made. 2. Given the chemical structure of a monomer (or monomers), draw the chemical structure polymers that can be synthesized from it (or them). 3. Understand, describe and calculate the structural parameters of poly- meric materials including monomer units, molecular weight, tacticity, coil dimension, crystallinity, and morphology. 4. Describe the relationship between the above structural parameters and the mechanical and thermal properties of polymeric materials. 5. Describe how the structure and mechanical properties of polymeric ma- terials change at the glass transition temperature and at the melting tem- perature. 6. Describe how the molecular structure of a surfactant determines its mi- celle structure. 7. Describe how surfactant molecules and aggregates affect the optical prop- erties, viscosity and surface tension of polymer solutions. 8. Calculate the intermolecular and surface forces for molecules and col- loids of different geometries. 9. Design strategies to stabilize or destabilize colloidal systems. 10. Identify a soft material application in daily life, such as in arts, music, sports or food, and explain how material advancement has imporved the application. 4 Introduction Since the title of this book is ’Soft Materials’, it makes sense to define what we really mean by ’soft’. Here are two ways to think about it: 5 4 INTRODUCTION 1. Soft Materials have Low Elastic Moduli. By ’low’ we mean significantly lower than the moduli of crystalline met- als and ceramics. The jellyfish shown in Fig. 4.1 is obviously ’soft’ in this sense. Metals and ceramics typically have moduli in the range of 100 MPa (see Fig. 4.2). While the strength of metals can be adjusted by a variety of mechanisms that affect the nature of dislocation motion in these systems, the modulus is set by the nature of the interatomic poten- tials and there nothing that can really be done to significantly affect the modulus of a given material. Polymers are different, however, and have a much broader range of elastic moduli. The stiffest of these (Kevlar™for example) have elastic moduli in at least one direction that are compara- ble to the modulus of steel. 2. Thermal Fluctuations Matter in Soft Materials. At a molecular level, the relevant energy scale that determines a variety of important properties is the thermal energy, kBT , where kB is Boltz- mann’s constant and T is the absolute temperature. If different molec- ular arrangements within a material differ in energy by an amount that of the order of kBT or less, than these different arrangements will all be experienced by the material. When the free energy of a material is dom- inated by the entropy associated with the accessibility of these different arrangements, it is possible to calculate the elastic properties of the ma- terial from the molecular structure with considerable accuracy. The best example of this is our discussion of Rubber Elasticity.