Controlling Gold Nanoparticle Assembly Through Particle

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CONTROLLING GOLD NANOPARTICLE ASSEMBLY THROUGH PARTICLE-

PARTICLE AND PARTICLE-SURFACE INTERACTIONS

Dissertation

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Doctor of Philosophy in Engineering

John Joseph Kelley, M.S.

Dayton, Ohio

August, 2018 CONTROLLING GOLD NANOPARTICLE ASSEMBLY THROUGH

PARTICLE-PARTICLE AND PARTICLE-SURFACE INTERACTIONS

Name: Kelley, John Joseph

APPROVED BY:

______Erick S. Vasquez, Ph.D. Donald Klosterman, Ph.D. Advisory Committee Chairman Committee Member Assistant Professor, Department of Associate Professor, Department of Chemical and Materials Engineering Chemical and Materials Engineering

______Andrey Voevodin, Ph.D. P. Terrence Murray, Ph.D. Committee Member Committee Member Adjunct Professor, Department of Adjunct Professor, Department of Chemical and Materials Engineering Chemical and Materials Engineering

______Richard A. Vaia, Ph.D. Research Advisor Technical Director, Air Force Research Laboratory

______Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering Professor School of Engineering

ii ABSTRACT

CONTROLLING GOLD NANOPARTICLE ASSEMBLY THROUGH PARTICLE-

PARTICLE AND PARTICLE-SURFACE INTERACTIONS

Name: Kelley, John Joseph University of Dayton

Advisor: Dr. Erick S. Vasquez

Two-dimensional assemblies of colloidal gold nanoparticles were deposited via electrostatic self-assembly onto silicon substrates modified with aminopropyltriethoxysilane. Assemblies were tuned by systematically adjusting the pH and ionic strength of the nanoparticle solutions and the fraction of adsorbed aminosilane molecules on the silicon surfaces. The nanoparticles were characterized by their size distribution, solution stability and electrokinetic properties. The resulting two-dimensional assemblies varied in particle surface coverage, interparticle separation and lateral organization. Increasing solution pH intensified interparticle repulsions and reduced the charge density of the aminosilane substrate, thus decreasing the fractional monolayer coverage of particles. Additionally, increasing ionic strength reduced interparticle separations, which were described by radial distribution functions, and consequently produced denser particle assemblies. At long adsorption times, surface coverage approaches a maximum which was constrained by the extent of interparticle repulsion and

iii particle-surface interactions. With strong surface attraction of the pure aminosilane surface, the particles were incapable of lateral rearrangement during the adsorption process and, at best, organized into liquid-like structures, in agreement with the random sequential adsorption model for colloidal monolayers. In an effort to circumvent this issue, non- binding alkylsilanes were incorporated into the modified surfaces, thereby reducing the aminosilane surface density and weakening the attractive potential of the surface. These mixed silane surfaces were characterized to reveal their chemical and interfacial energetic properties. At a particular threshold of reduced aminosilane density, nanoparticle coverage fell considerably and two-dimensional order degraded. The local geometries of particle assemblies were evaluated by Voronoi tessellation which provided indication of structural transformations with changing solution and surface conditions. As a result, optimal processing parameters were described for obtaining monolayers of gold nanoparticles with varying degrees of surface coverage and two-dimensional arrangement. The results from this study expands the understanding of the underlying chemical and physical mechanisms behind colloidal stability and particle adsorption. This progresses towards the realization of arrays of highly-ordered and densely packed nanoparticles of diverse chemistries largely assembled in parallel onto assorted surfaces using minimal processing.

iv DEDICATION

Dedicated to my support group.

For all that we have endured together.

This accomplishment would not have been possible without you.

v ACKNOWLEDGEMENTS

Above all, I must thank my family: Caryn, Jack, Sam, my parents, my in-laws and anyone else who suffered yet still supported me during this arduous journey. Whether it was through gentle words of encouragement or punitive threats, you did what was necessary to light a fire under my butt and push me across the finish line. You were the inspiration for me to finish that I might not have had on my own.

I would also like to thank my friends who have encouraged me along the way, but more importantly, provided me with necessary distractions to help maintain my sanity, whether it be a couple jokes, a few (or more) beers or a good old gripe session. You definitely helped to keep me grounded and not to take life too seriously. I am also grateful for having Jen DeCerbo as my partner-in-crime throughout grad school. Thank you for keeping me awake during class and making the journey as enjoyable as possible.

Furthermore, I am grateful to those who have contributed to my research, whether through technical assistance, imparted knowledge or much-needed guidance. At the front of the pack is Rich Vaia, who has educated and guided me substantially for over a decade.

He has also shown considerable patience with me while working on this dissertation, probably more than I deserve. I would also like to thank Hilmar Koerner for being my first mentor at AFRL and helping to establish my skillset in materials research. I also greatly valued the mentorship and friendship of Mike Jespersen, who showed me the ropes with

vi nanoparticle assemblies and surface modifications (it’s all your fault!). Additionally, Mike supported my research with useful XPS data, even when he had more important things to do. I also appreciate the assistance and interactions from all of the researchers and technicians at the AFRL Materials and Manufacturing directorate that I’ve had the pleasure to work with at some capacity, a list which is surely too long to include.

I would also like to thank all of my professors at UD as well as my committee:

Erick Vasquez, Terry Murray, Andrey Voevodin and Don Klosterman. Their knowledge and support have been quite beneficial during my time at UD.

Lastly, I would like to thank myself for persevering and seeing this dissertation through to the end, despite all the grief it has imparted over the years. You are my rock.

You are my inspiration. You are my hero.

vii TABLE OF CONTENTS

ABSTRACT ……………………………………………………………………………iii DEDICATION ...... v ACKNOWLEDGEMENTS ...... vi LIST OF FIGURES ...... xi LIST OF TABLES ...... xviii LIST OF ABBREVIATIONS AND NOTATIONS ...... xix CHAPTER 1. INTRODUCTION ...... 1 1.1 The Rise of Nanotechnology ...... 1 1.2 Nanoparticle Assemblies for Technology ...... 2 1.3 Dissertation Overview ...... 7 1.4 Research Objectives ...... 8 CHAPTER 2. BACKGROUND ...... 10 2.1 Nanoscale Structures ...... 10 2.2 Functional Surfaces for Nanoparticle Assembly ...... 11 2.2.1 Self-assembled Monolayers on Two-dimensional Surfaces ...... 12

2.2.2 Self-assembled Monolayers on SiO2 Surfaces ...... 13 2.3 Gold Nanoparticles ...... 26 2.3.1 History and Properties...... 26 2.3.2 Synthesis and Purification...... 29 2.4 Particle Interactions and Stability ...... 34 2.4.1 Interaction Potentials ...... 35 2.4.2 Zeta Potential ...... 38 2.4.3 Acid-base Chemistry ...... 39 2.4.4 Ionic Environment ...... 43 2.5 Electrostatic Adsorption of Nanoparticles ...... 44 2.5.1 Theory and Simulations ...... 44 2.5.2 Experimental Examples ...... 46 CHAPTER 3. EXPERIMENTAL ...... 48

viii 3.1 Materials and Chemicals ...... 48 3.2 Substrate Functionalization ...... 48 3.2.1 Single Silane Solution Deposition ...... 49 3.2.2 Co-adsorption of Organosilane SAMs ...... 50 3.2.3 Sequential Adsorption of Organosilane SAMs ...... 51 3.3 Gold Nanoparticle Synthesis and Purification ...... 51 3.3.1 Citrate-stabilized Gold Nanoparticles ...... 53 3.3.2 MPS-stabilized Gold Nanoparticles ...... 54 3.3.3 Buffered Gold Nanoparticle Solutions ...... 55 3.4 Gold Nanoparticle Assembly ...... 56 3.5 Characterization ...... 57 3.5.1 Scanning Electron Microscopy ...... 57 3.5.2 Transmission Electron Microscopy ...... 58 3.5.3 UV-Vis Spectrophotometry ...... 58 3.5.4 Zeta Potential & Dynamic Light Scattering ...... 59 3.5.5 X-ray Photoelectron Spectroscopy ...... 60 3.5.6 Contact Angle Goniometry ...... 61 3.5.7 Radial Distribution Function...... 62 3.5.8 Voronoi Tessellation ...... 62 CHAPTER 4. RESULTS & DISCUSSION: PH AND IONIC STRENGTH MODULATED GOLD NANOPARTICLE ASSEMBLY ...... 64 4.1 Gold Nanoparticle Assembly ...... 64 4.2 Acid/Base Chemistry ...... 66 4.3 Electrostatics ...... 69 4.4 Colloidal Stability of AuNP Solutions ...... 70 4.4.1 UV-vis Spectroscopy ...... 71 4.4.2 Zeta Potential ...... 73 4.5 Assembly of AuNPs ...... 76 4.6 Two-dimensional Structures of AuNP Assemblies ...... 80 4.6.1 Radial Distribution Function...... 81 4.6.2 Voronoi Tessellation ...... 88 CHAPTER 5. RESULTS & DISCUSSION: SURFACE CHEMISTRY REGULATED ASSEMBLY OF GOLD NANOPARTICLES ...... 93 5.1 Mixed Silane Surfaces for the Assembly of Gold Nanoparticles ...... 93 5.2 Characterization of Mixed Silane Surfaces ...... 94

ix 5.2.1 Co-adsorbed Mixed Silanes Self-assembled Monolayers ...... 94 5.2.2 Gradient Mixed Silane Self-assembled Monolayers ...... 105 5.3 Effect Surface Chemistry on Nanoparticle Coverage and Structure ...... 112 5.3.1 Nanoparticle Areal Density ...... 113 5.3.2 Two-dimensional Structure of Nanoparticle Assemblies ...... 119 CHAPTER 6. CONCLUSIONS ...... 127 6.1 Effect of pH and Ionic Strength ...... 127 6.2 Effects of Surface Composition ...... 130 CHAPTER 7. FUTURE WORK...... 134 REFERENCES ...... 139 APPENDICES A. Additional Figures and Equations ...... 151 Ionic Strength ...... 151 Ion Speciation ...... 152 UV-vis Spectra of Gold Nanoparticles ...... 161

Hard-sphere Approximation of aeff ...... 162 Hydrodynamic Diameter ...... 163 Radial Distribution Functions of AuNP Assemblies ...... 163 Contact Angle ...... 168 AuNP Assemblies on Mixed Silanes ...... 169 B. MATLAB Code ...... 171 Radial Distribution Function...... 171 Voronoi Analysis ...... 172 C. Reprint Permissions ...... 175

x LIST OF FIGURES

Figure 1. Electrostatic deposition of charged nanoparticles on charged substrates...... 12

Figure 2. Schematic of SAM showing the head group, alkyl chain and functional terminal group ...... 13

Figure 3. Schematic of chemical reactions of tri-functional silanes with a SiO2 surface. 14

Figure 4. Structures of various alkyl-silanes...... 16

Figure 5. Structures of various amino-silanes...... 18

Figure 6. Self-catalysis of APTES molecules ...... 19

Figure 7. Polymerization of APTES on a silica surface...... 20

Figure 8. Possible conformations of APTES on a silica surface ...... 20

Figure 9. Vapor diffusion deposition of aminosilane molecules across an activated substrate ...... 22

Figure 10. Controlled rate infusion and backfill method for creating gradient surfaces of mixed silanes ...... 23

Figure 11. Top left: pH variation with variation in χAu; Top right: relative reactivity of dominant Au3+ complexes and their associated pH values; Bottom: schematic of two reaction pathways for the synthesis of citrate-reduced AuNPs...... 32

xi Figure 12. SPR peak wavelengths of AuNPs as function of the ratio of gold and citrate concentrations ...... 33

Figure 13. Schematic of a continuous diafiltration setup ...... 34

Figure 14. Potential energy of two particles as a function of separation distance ...... 37

Figure 15. Diagram of a gold colloid and the electrical potential as a function of distance from the particle surface and the charge layer to which it corresponds...... 38

Figure 16. Schematic representation of pH-dependent stabilization of negatively- charged AuNPs and adsorption onto a positively-charged amine- terminated surface ...... 42

Figure 17. Illustrations of AuNPs stabilized by electrostatically bound citrate molecules and covalently bound mercaptopropanesulfonate ligands...... 43

Figure 18. Schematic representation of random sequential adsorption of particles onto planar surfaces ...... 45

Figure 19. Phase diagrams of ordered and disordered surface structures for a volume fraction of 0.01 and a Debye screening parameter κa =1 ...... 46

Figure 20. Various precursors for organosilane SAMs ...... 49

Figure 21. Top left: pH variation with variation in χAu; Top right: relative reactivity of the dominant Au3+ complexes and their associated pH values; Bottom: schematic of two reaction pathways for the synthesis of citrate-reduced AuNPs...... 52

Figure 22. SPR peak wavelengths of AuNPs as function of the ratio of gold and citrate concentrations...... 53

Figure 23. TEM image and particle size distribution for as-synthesized Au-Cit and Au-MPS...... 54

xii Figure 24. (a) Schematic illustration of AuNP self-assembly process and (b) SEM micrographs displaying uniform, large area coverage for Au-Cit NPs deposited at pH ≈ 5.6 and I = 1 mM...... 65

Figure 25. (a) Ion speciation plots for citrate (blue lines) and MPS ligands (red lines) along with Si/APTES surfaces (green lines). (b) Mean charge 푍 of chemical species for citrate, MPS and Si/APTES molecules...... 67

Figure 26. Images of Au-Cit and Au-MPS solutions with increasing pH at I = 1, 3 and 5 mM ...... 70

Figure 27. UV-Vis spectra for Au-Cit (a, c) and Au-MPS NPs (b, d) at various pH and ionic strengths of 1 mM and 5 mM...... 71

Figure 28. Top: Wavelengths at extinction maxima for AuNPs as a function of solution pH at various ionic strengths: (a) Au-Cit and (b) Au-MPS. Bottom: Absorbance ratios (Rads = A520 / A600) as a function of solution pH at various ionic strengths: (c) Au-Cit and (d) Au-MPS ...... 73

Figure 29. Particle charge data for 11 nm AuNPs as a function of pH at various ionic strengths (I = 0.1 – 10 mM). Top: Zeta potentials for (a) Au-Cit NPs and (b) Au-MPS NPs. Bottom: Charge densities for (c) Au-Cit NPs and (d) Au-MPS NPs ...... 76

Figure 30. SEM micrographs of AuNP assemblies at various pH values with I = 3 mM: (a) Au-Cit and (b) Au-MPS ...... 77

Figure 31. Particle coverage for (a) Au-Cit and (b) Au-MPS as a function of pH for I = 0.1 – 10 mM and (c) their respective pH inflection points as a function of ionic strength ...... 78

Figure 32. SEM micrographs of (a) Au-Cit and (b) Au-MPS NPs (a = 5.7 nm) assembled at pH ≈ 5.6 with I = 0.1 – 10 mM...... 79

Figure 33. Structural diagrams of AuNP assemblies at varying pH and ionic strength: (a) Au-Cit and (b) Au-MPS NPs ...... 81

xiii Figure 34. (a) plot of g(r) vs. r for assemblies of Au-Cit and Au-MPS deposited at pH ≈ 5 with I = 0.1 – 10 mM (a = 5.7 nm), and g(r) plotted against r/r1 for (b) Au-Cit and (c) Au-MPS...... 83

Figure 35. Average center-center particle separation r1 for (a) Au-Cit and (b) Au-MPS NPs as a function of pH at various ionic strengths...... 86

Figure 36. Maximum surface coverage θ as a function of κa for Au-Cit and Au-MPS NPs for various pH/ionic strength combinations ...... 87

Figure 38. Fractions of 6-sided Voronoi cells, f6, as a function of pH at I = 0.1 – 10 mM for (a) Au-Cit and (b) Au-MPS, and (c) the pH values at maximum f6 versus ionic strength for Au-Cit and Au-MPS assemblies...... 92

Figure 39. Schematic representations for tuning AuNP density and structure via modulation of APTES surface concentration ...... 95

Figure 40. Images of water contact angles for (a) UVO-clean Si/SiO2 and SAMs of (b) APTES, (c) PTES and (d) OTCS...... 97

Figure 41. Static contact angles for APTES surfaces co-adsorbed with PTES and OTCS at various molar fractions of APTES...... 98

Figure 42. (Top) Static contact angles for co-adsorbed APTES and F3PTES surfaces at various molar fractions of APTES. (Bottom) Solutions of APTES + F3PTES after ~ 1 day ...... 100

Figure 43. XPS spectra for APTES on Si/SiO2...... 102

Figure 44. XPS data for mixed APTES + PTES SAMs...... 103

Figure 45. XPS data for mixed APTES + OTCS SAMs...... 103

xiv Figure 46. Comparison of χAS before (in solution) and after (on surface) adsorption of APTES mixtures with PTES and OTCS...... 104

Figure 47. Images of water contact angles for OTCS gradients backfilled with APTES at various relative distances from the starting edge of infusion (xr = 0.0) to the opposite end (xr = 1.0)...... 107

Figure 48. Static contact angles for PTES gradient backfilled with APTES...... 108

Figure 49. Static contact angles for OTCS gradients backfilled with APTES: a) contact angles after various rates (ml/min) of OTCS infusion and b) the change in contact angle as a function of infusion rate...... 109

Figure 51. XPS data for PTES→APTES gradient SAMs...... 112

Figure 52. Particle coverage data for Au-Cit NPs adsorbed onto SAMs of APTES

mixed with PTES or OTCS as a function of APTES molar fraction (χAS) ... 114

Figure 53. SEM images of AuCit assemblies on SAMs of APTES mixed with PTES or OTCS ...... 116

Figure 54. Particle coverage data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr) . 117

Figure 55. Particle coverage data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with OTCS as a function of relative distance (xr) ...... 119

Figure 56. Structural data for Au-Cit NPs adsorbed onto PTES + APTES mixed monolayers with respect to APTES molar fraction (xAS) at ionc strengths of 0.5 and 3 mM ...... 122

xv Figure 57. Structural data for Au-Cit NPs adsorbed onto PTES + APTES and OTCS + APTES mixed monolayers with respect to APTES molar fraction (xAS), for I = 0.5mM ...... 124

Figure 58. Structural data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr)...... 126

Figure 59. Ion speciation plots for citrate (blue lines) and MPS ligands (red lines) along with Si/APTES surfaces (green lines)...... 158

Figure 60. Buffer capacity of various buffering systems used in this work ...... 158

Figure 61. Fractional speciation of citric acid (H3Cit) and APTES with respect to solution pH...... 159

Figure 62. Fractional speciation of 3-mercaptopropanesulfonic acid (H–MPS) and APTES with respect to solution pH...... 160

Figure 63. Fractional speciation of phosphoric acid (H3PO4) with respect to solution pH...... 160

Figure 64. Fractional speciation of carbonic acid (H2CO3) with respect to solution pH...... 160

Figure 65. UV-Vis spectra for Au-Cit NPs at various pH and ionic strengths of 1, 3, 5 and 10 mM...... 161

Figure 66. UV-Vis spectra for Au-MPS NPs at various pH and ionic strengths of 0.1, 1, 3 and 5 mM...... 162

Figure 67. Radial distribution functions of Au-Cit assemblies at various pH values for I = 1 – 10 mM ...... 164

Figure 68. Radial distribution functions of Au-MPS assemblies at various pH values for I = 0.1 – 5 mM ...... 165

xvi Figure 69. Average locations the primary (g1(r)) and secondary peaks (g2(r)) in the radial distribution functions for Au-Cit and Au-MPS assemblies as a function of pH at various ionic strengths...... 165

Figure 70. Average surface coverage for Au-Cit and Au-MPS assemblies calculated from Equation A.21 using aeff = r0/2...... 166

Figure 71. Plots of interparticle separation (r) vs. pH at different ionic strengths for Au- Cit assemblies ...... 167

Figure 72. Primary peak (r1) vs. interparticle separation from NP density (r0) for assemblies of (a) Au-Cit and (b) Au-MPS at various ionic strengths. The dotted line represents r0 = r1...... 168

Figure 73. Schematic representation of contact angles between a planar surface and a liquid drop ...... 168

Figure 74. Controlled-rate infusion setup demonstrating the vapor phase above the solution meniscus...... 169

Figure 75. AuNP adsorption data for PTES → APTES gradients with respect to relative distance (xr) ...... 169

Figure 76. AuNP adsorption data for PTES → OTCS gradients with respect to relative distance (xr)...... 170

Figure 77. Particle coverage compared to contact angle data for AuCit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr) ...... 170

xvii LIST OF TABLES

Table 1. Processing details for various SAM combinations with silicon and gold-based surfaces...... 25

Table 2. Various morphologies, compositions and physical properties of nanoparticles which are altered from the bulk scale ...... 27

Table 3. Various synthetic methods for spherical AuNPs ...... 30

Table 4. Colloidal stability as a function of the absolute value of the zeta potential...... 39

Table 5. Recipes for mixed silane solutions combined from aliquots of 50 mM stock solutions ...... 50

Table 6. pH values of Au-Cit and Au-MPS solutions for each ionic strength...... 57

Table 7. Structures, pKa values and chemical species for citrate and MPS stabilized AuNPs and Si/SiO2 surfaces modified with APTES...... 66

Table 8. Static contact angles of organosilane SAMs on Si/SiO2 with varying carbon chain lengths and terminal functionalities ...... 97

Table 9. Acid/base speciation data for ligand, adsorbate and buffer molecules...... 156

Table 10. Changes in pKa for various ion species with increasing ionic strength and increasing temperature ...... 159

xviii LIST OF ABBREVIATIONS AND NOTATIONS

Symbols a particle radius aeff affective particle radius AuNP gold nanoparticle ci concentration of ion i d diameter fn fraction of n-sided Voronoi cells g(r) radial distribution function

Gaggr aggregation ratio for radial distribution function I ionic strength

Ka acid-dissociation constant kB Boltzman constant

LB Bjerrum length lm meniscus travel distance

NA Avogadro’s number pKa logarithm of acid-dissociation constant r center-center interparticle separation r’ expected interparticle separation r0 interparticle distance normalization constant

Rabs absorbance ratio (UV-Vis) T temperature distance of position relative to length of xr substrate zi valence of ion i 푍̅ mean charge

αi fraction of species i Γ areal nanoparticle coverage (NP/μm) surface free energies at the solid/liquid, γSL, γSV and γLV solid/vapor and liquid/vapor interfaces ε molar extinction coefficient

ε0 vacuum permittivity

xix εr relative permittivity ζ zeta potential θ fractional surface coverage

θjam surface coverage jamming limit

θmax maximum theoretical surface coverage

θC, θA and θR static, advancing and receding contact angles κ inverse Debye length κ-1 Debye length κa Debye screening parameter λ Coulomb potential fitting parameter

λSPR surface plasmon peak wavelength σ surface charge density

σAPS surface coverage of APTES molecules

χAu molar fraction of HAuCl4 to Na3Cit

χAS molar fraction of aminosilane (APTES) Molecules APTES 3-aminopropyltriethoxysilane Au-Cit citrate-capped gold nanoparticle 3-mercaptopropanesulfonate-capped gold Au-MPS nanoparticle DTS dodecyltrichlorosilane

HAuCl4 hydrochloroaurate ETMS ethyltrimethoxysilane

Na3Cit tri-sodium citrate

NH2 amine + NH3 protonated amine (ammonium ion) OTCS octyltrichlorosilane OTES octyltriethoxysilane OTS octadecyltrichlorosilane RSH alkanethiol SAM self-assembled monolayer

Si/SiO2 silicon with native oxide surface Si/APTES APTES modified silicon

SiO2/APTES Si/SiO2 substrate functionalized with APTES – SO3 sulfonate ion

xx Methods AFM atomic force microscopy CRI controlled-rate infusion DLVO Derjaguin-Landau-Verwey-Overbeek theory Standard Cleaning methods SC-1/SC-2 for RCA silicon RSA random sequential adsorption SEM scanning electron microscopy TEM transmission electron microscopy UVO ultraviolet-ozone XPS x-ray photoelectron spectroscopy

xxi CHAPTER 1

1. INTRODUCTION

1.1 The Rise of Nanotechnology

State-of-the-art technology has been continuously pushing the limits with respect to capabilities and size. It was only a futuristic concept in 1959 when Richard Feynman discussed in his seminal lecture1 “There’s Plenty of Room at the Bottom” how the scale of engineered materials and devices could be miniaturized down to the atomic level and possibly even beyond. Today, that concept is a thriving reality, as devices have become increasingly functional and efficient while simultaneously reducing their dimensions.

Daunting tasks that used to be performed 50 years ago on computers the size of an entire room can now be executed almost instantly on devices the size of one’s hand! Over the past 15 years, we have seen smartphones become a primary tool for communication, computation and entertainment, all while fitting in our pockets. In fact, a quarter century ago, it would have required more than ten separate devices to perform the same tasks a smartphone does today,2 not to mention they all paled in comparison with respect to its memory, processing power, efficiency and sophisticated interface, amongst other attributes.

Over the past two decades, the need for smaller and more efficient electronic and optical devices has driven the progression of nanoscience and nanotechnology from the synthesis of the individual building blocks to their assembly into larger nanostructured

1 devices. Nanoparticles, i.e. ultrafine clusters of atoms with dimensions between 1 – 100 nm, are excellent candidates for constructing such assemblies and can be fabricated with various sizes, shapes, material properties and surface chemistries. They have size and morphology dependent properties that are significantly altered from their bulk material, thereby creating avenues for increasingly efficient and functional nanostructures that can be fashioned into macroscopic devices while exhibiting properties that differ constructively from those of the bulk material.3

1.2 Nanoparticle Assemblies for Technology

The organization of nanoparticles at solid interfaces is enabling for numerous technologies such as sensing,4-5 nanoelectronics,6-7 biotechnology,7-8 tribology,9 catalysis,10-11 photovoltaics,12 and nanophotonics.13 Coupling between adjacent nanoparticles, the substrate and the surroundings determine electron and phonon transport, as well as result in unique catalytic, optical and excitonic properties. However, many applications requiring local, nanoscale access within an array (memory or pixels) or signal enhancement via a collective response (meta-surfaces). These necessitate uniform local organization across macroscopic scales, rather than a few idealized structures or disordered assemblies. Such hierarchical nanostructures with high precision and excellent reproducibility are commonly fabricated by top-down lithographic techniques, such as electron beam lithography,14-15 nano-imprint lithography or dip-pen nanolithography.16

Surface roughness and polycrystallinity of the subsequently evaporated inorganic films compromise optical and plasmonic performance. This creates challenges in the use of these techniques in many applications17 such as flex devices, biochemical optical detectors and meta-surfaces. Alternatively, bottom-up methods, such as templated assembly of

2 colloids,13, 17 Langmuir-Blodgett deposition,18 electrophoretic deposition,19 or direct patterning techniques,20-21 provide a lower cost alternative with the potential to radically expand accessible composition, size, and substrate shape. However, these nanoparticle- based approaches seldom achieve uniform organization, require narrow processing windows, or rely upon post-processing steps that increase cost or decrease accessible structures.

Scalable bottom-up approaches for solid interfaces focus on engineering of the interaction potentials between particle, solvent and substrate using environmentally friendly solvents, and the absence of structure directing additives. Electrostatically stabilized colloids12, 22-34 provide many of these features. Like-charges on particles promote solution stability while simultaneously facilitating attraction to an oppositely- charged surface. The interparticle separation is determined by the thickness of the electric double layer (Debye length, κ-1) surrounding the particles and can be adjusted by varying the ionic strength I of the solution.27-29, 33-34 The mechanisms of structure evolution, including defect formation and annihilation, depend on a myriad of process parameters that control particle deposition rate, particle exchange rate between solution and surface, defect stability, and in-plane and out-of-plane particle mobility.

Surprisingly, the details of electrostatic assembly and how it is influenced by particle size is still under investigation. At one extreme, random sequential adsorption

(RSA) considers particles as hard disks with strong attraction to the surface that adsorb sequentially, irreversibly, and at random positions across the surface.29, 34-42 This self- limiting adsorption affords a random particle arrangement with a limiting fractional coverage (a.k.a. jamming limit). In reality, the Debye length contributes to the effective

3 radii of the particles and the fractional coverage for a colloidal assembly will be less than the jamming limit. Furthermore, due to the irreversibility of adsorption, these configurations at best have a liquid-like structure, with interparticle separations greater than those in solution.33 The Debye length, however, depends on the solution environment, i.e., ionic strength and dielectric constant.24, 37 The similar scale of the particle radius and

Debye length along with the tunability of electrostatic interaction implies that the potential structures achievable via electrostatic assembly of nanoparticles could be much richer than random arrays.

Computer simulations have indicated that particle ordering develops as adsorption strength decreases, particle repulsion increases, and particle volume fraction increases.38,

42-45 The order/disorder transition is predicted to occur when particles gain lateral mobility, i.e., where particle potentials are low and surface potentials are high or vice-versa.

Numerous experimental studies have explored facets of this complex processing space.24,

27-29, 31, 34, 37-41 For example, Semmler et al.29 and Kooij et al.27 concluded that long-time maximum surface coverage was independent of particle concentration but strongly dependent upon ionic strength; that is, surface organization was governed by the strength of the particle-surface interaction and the repulsion among charged particles. The impact of pH, though, has not been as extensively examined.17-19, 29 Variation of pH through the isoelectric point of the adsorbate will decrease the strength and even reverse particle- surface or particle-particle interactions. Furthermore, the synergy between ionic strength and pH on interactions, surface charge density, maximum coverage, and in-plane order of the nanoparticle assemblies is still uncertain.

Although pH and ionic strength affect particle coverage and arrangement during adsorption, these outcomes can be influenced by altering the surface prior to adsorption.

Specifically, the density of particle-binding surface molecules can be adjusted to modulate the interaction strength between the surface and particles. Therefore, to possibly mitigate the constraint of irreversible adsorption, the density can be lowered to a threshold where the interaction energy is strong enough for particle adsorption but sufficiently weak to permit in-plane particle mobility. As a consequence, adsorbed particles would be able to rearrange into structures of higher density and greater order.29

Methods for achieving surfaces of tuned adsorbate density include co-adsorption of mixed self-assembled monolayers (SAMs)46-49 or gradient deposition of SAMs23, 50-54, to name a few. In the former case, adsorbate density and dispersion are governed by a predetermined ratio of constituent molecules and the competition between their adsorption mechanisms. The effects of the ratio are explored in a serial manner. On the other hand, gradient SAMs provide a continuum of adsorbate densities along a single substrate which facilitates particle assemblies that spend less time to process and are subject to less systematic error. While both of these methods have been well explored, little has been done to compare them and evaluate their implications upon nanoparticle assembly, specifically coverage and structure.

In this dissertation, two main approaches are taken to explore the influences of tuning interactions among particles and surfaces on particle assembly. First, the coupling between simultaneous modifications of electrolyte concentration and pH was elucidated by determining the processing-structural space in the strongly bound regime of self-limiting monolayer assemblies of functionalized gold nanoparticles (AuNPs) on amine-terminated

5 silicon wafers. This strongly bounded regime establishes the baseline for future understanding of structure formation at intermediate and weak particle-surface potentials.

Specifically, the most ordered assemblies of densely-packed isolated particles occurred between pH 3.5 – 8.1 for ionic strengths between 0.1 – 5 mM with liquid-like in- plane organization. At higher pH values, particle-surface interactions diminished and coverage decreased significantly. On the other hand, increased ionic strength further reduced the repulsion among particles, thus affording particle assemblies with smaller separations. At the highest ionic strengths and/or extreme pH, particles destabilized and formed aggregates in solution and on the surface. These results agreed with predictions that considered the ionic content of particle solutions and the acid/base interactions between the particles and surface. Furthermore, exchange of native citrate molecules on the particle surfaces with mercaptopropanesulfonate (MPS) led to more clustered assemblies within the same conditions as a result of reduced particle charge density and consequently colloidal stability.

Second, the deposition behavior of charge-stabilized gold nanoparticles onto bifunctional silicon substrates was investigated as a function of adsorbate chemistry, molar ratio and processing. The derivatized substrates are characterized by surface energetics and surface chemistry. The ensuing nanoparticle assemblies are described by particle surface coverage, interparticle separation and two-dimensional structure. Substrates with pure aminosilane films promoted strong surface attraction (i.e., electrostatic, polar and hydrogen bond interactions) where the particles are incapable of lateral rearrangement during the adsorption process, as suggested by the random sequential adsorption (RSA) model for colloidal monolayers. In an effort to improve the structural order of nanoparticle

6 assemblies, aminosilane molecules were partially replaced by non-binding n-alkylsilanes of various chain lengths (5 – 18 carbon atoms). This decreased the interaction strength between the functional surface and the nanoparticles, possibly enough to allow rearrangement of the particles. Therefore, it was crucial to determine the minimum molar fraction of alkylsilane molecules that afforded saturated nanoparticle coverage while also facilitating lateral diffusion into more ordered structures.

Decreasing the aminosilane concentration on silicon surfaces also reduced the surface charge density, consequently decreasing the fractional monolayer coverage of particles. At best, liquid-like structures were achieved, as the RSA model suggests.29, 34, 36,

41-42 At very low concentrations of aminosilane, adsorbed AuNPs were more prone to aggregation, suggesting either lateral diffusion of particles or clustering onto aminosilane domains dispersed within a sea of alkylsilane molecules. Structural evaluation by radial distribution functions and Voronoi tessellations revealed changes in interparticle separation and local geometry of assemblies at certain fractions of mixed silanes, which was altered by the chemical nature of the adsorbates or the ionic content of the deposition solution.

Control of nanoparticle assembly through modulation of ionic strength, pH and surface functionality can help further enable the production of nanostructured surfaces through facile and safe methods such as direct printing or dip-coating.

1.3 Dissertation Overview

This work differs from previous nanoparticle assembly work in several ways. First, few have systematically investigated the simultaneous effects of pH and ionic strength on the immobilization colloidal nanoparticles onto functional surfaces. Several characteristics

7 of the nanoparticle assemblies are affected such as areal density, interparticle separation and two-dimensional organization (i.e. “order”). Second, no experiments to knowledge have compared the behavior of colloidal assembly between self-assembled monolayers of co-adsorbed mixed silanes and sequentially adsorbed mixed silane gradients. Additionally, very few have studied the particular silane combinations used in this study. Furthermore, none have investigated the structural organization nanoparticle assemblies on these mixed silane surfaces.

1.4 Research Objectives

This main goal of this work is to determine specific regimes where particle-particle and particle-surface interactions influence the organization of colloidal nanoparticles onto functionalized surfaces into highly-ordered assemblies. Two underlying objectives seek to establish these parameters:

1. Control nanoparticle assembly through simultaneous modulation of pH and

ionic strength. Synergistically tuning interparticle repulsion and spacing,

particle-surface attraction and particle chemistry provides better insight on the

processing regimes required to achieve highly-ordered assemblies of isolated

nanoparticles.

2. Control nanoparticle assembly by reducing the particle-surface interaction

strength. By diluting the surface concentration of particle-binding molecules

and subsequently weakening the surface attraction, adsorbed particles may gain

sufficient in-plane mobility to rearrange from assemblies of short-range, liquid-

like order to those of extended-range, crystalline structure.

By better understanding the underlying chemical and physical mechanisms behind colloidal stability and particle adsorption, large arrays of highly-ordered and densely packed nanoparticles of diverse chemistries can be easily assembled in parallel onto assorted surfaces using simple laboratory setups, without the assistance of templates or patterns.

CHAPTER 2

2. BACKGROUND

2.1 Nanoscale Structures

Nanoscale structures can be generated by either top-down or bottom-up approaches. The former are destructive methods that utilize controlled removal of material from substrates to generate structures with precise spacing and geometry. Examples include as electron beam lithography,14-15 nano-imprint lithography or dip-pen nanolithography.16 Although these methods can be highly reproducible, they suffer from high surface roughness and crystallographic defects along with significant time and fabrication costs. On the other hand, bottom-up methods are constructive, adding nanomaterial onto almost any type of surface. Nanostructures can be manufactured on large scales with significant reductions in time and equipment. Examples include templated assembly of colloids,17, 22-34, 55-58 deposition assisted by external fields (e.g., Langmuir-

Blodgett deposition18 or electrophoretic deposition19) and direct pattering techniques20-21

(e.g. drop-on-demand, electrospray or nanoparticle ink printing). These methods require specialized equipment or post-processing steps and inherently lack the high degree of structural order to render them useful in technological applications. In this dissertation, the electrostatic assembly of colloidal nanoparticles onto functional planar substrates will be the primary focus.

2.2 Functional Surfaces for Nanoparticle Assembly

The process of nanoparticle self-assembly is regulated by the interactions (e.g. van der Waals, electrostatic and entropic) of particles with the surface energetics of supporting substrates, which are either native to the material or achieved through physical or chemical modification. One of the most common methods for chemically modifying surface energetics is through the formation of SAMs on technologically applicable surfaces.

Through the use of SAMs, various routes for tuning the particle-surface interactions within nanoparticle assemblies are obtained primarily by controlling the surface chemistry.

Below, an in-depth understanding is provided for the preparation, formation and structure of SAMs on two-dimensional surfaces as foundations for nanoparticle assemblies.

In the vast library of nanoparticle assemblies on two-dimensional solid surfaces,

23, 30, 56-57, 59 30, 56, 59 28, 60 some of the more common substrates used are Si/SiO2, glass, gold ,

47 29, 31 61-62 63 Al2O3, mica , various forms of carbon and polymers films . These surfaces can have different topographies, such as planar,23, 28-31, 47, 56-57, 59-60, 62 rough/textured61, 63 or even porous64. Nanoparticles can be directly deposited upon these surfaces, although many times the substrate requires modification to achieve a desired surface charge or chemical compatibility. For example, positively-charged latex colloids can be directly deposited upon negatively-charged mica sheets29, 31 via electrostatic interactions (Figure 1a), while negatively-charged gold nanoparticles (AuNPs) can only successfully assemble onto

Si/SiO2 substrates (negatively-charged) that are functionalized with a positively-charged coupling layer (e.g., an amine-terminated silane in aqueous solution) prior to deposition

(Figure 1b).23, 30, 56-57, 59 Such planar surfaces with grafted molecular layers are of particular interest for nanoparticle assemblies in this work.

+ + + + + + + + + + + + (a) + + + + + + + + + + + + + + ------+ - - - - -+ - - - O O O O O O O O Aqueous O O O O O O O O Latex NPs (+) mica mica

------(b) - - - - - Aqueous ------Amino-silane Au NPs (–) +- + + + -+ + + O O O O O O O O NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH3 NH3 NH3 NH3 NH3 NH3 NH3

Si/SiO2 Si/SiO2 Si/SiO2

Figure 1. Electrostatic deposition of charged nanoparticles on charged substrates: (a) positively-charged latex on negatively-charged mica and (b) negatively-charged gold nanoparticles on positively-charged aminosilane/SiO2. 2.2.1 Self-assembled Monolayers on Two-dimensional Surfaces

In the past 30 years, the formation of self-assembled monolayers has been one of the most prolific applications in surface and interfacial science. SAMs are ordered assemblies of functional molecules adsorbed onto a solid, energetically-active surface.

SAMs can be highly ordered and contain a variety of functional groups both within the alkyl chain and at the termini.65 The concept of SAMs was first realized by Bigelow et al. in 1946 when they adsorbed various polar organic molecules onto metallic and non- metallic surfaces from a number of non-polar solvents.66 It took nearly forty years, though, for SAMs to become a mainstream interest, after the seminal study by Allara et al. on alkanethiol SAMs adsorbed onto gold surfaces67. Since then, numerous combinations of molecules, surfaces and reaction media have generated a vast library of supported SAMs.

The process of creating SAMs is generally quite facile and can produce large areas of ordered, functional molecules. SAM formation is less intensive than other methods of monolayer formation, e.g. Langmuir-Blodgett or molecular beam epitaxy.68 SAMs are important not only for the engineering of surface energy and interfacial properties (e.g. wetting, adhesion, friction), but also for activating surfaces for the attachment of other

12 molecules and particles.65 In turn, SAMs are especially appealing for surface engineering and technological applications.

Equatorial Axial Tilted R Functional group

Alkyl chain

θ Head group Substrate

Figure 2. Schematic of SAM showing the head group (circle), alkyl chain and functional terminal group (R). Alkyl chains can have equatorial, axial or tilted orientations. One of the most commonly studied surfaces for supporting NP assemblies on SAMs is SiO2, either in bulk form or as a thin layer on top of silicon. In choosing an appropriate molecule for tethering NPs, one must consider its terminal functionalities. Surfaces of specific material and even crystallographic orientation will have distinct affinities for particular chemical moieties. For instance, trichloro- and trialkoxy-silanes are well known

47, 54, 57, 65, 69-73 for their abilities to graft to SiO2 surfaces via hydrolysis and condensation reactions.47, 65 These types of molecules are vital to the engineering of surface energetics through modulation of chemical functionalities of their SAMs.

2.2.2 Self-assembled Monolayers on SiO2 Surfaces

23, 30, 56-57, 59 Although most commonly used for functionalization of Si/SiO2, organosilanes can also be grafted onto other common oxide surfaces, e.g., glass,30, 56, 59

47 73 Al2O3, and GeO2, through similar surface chemical reactions. To demonstrate, a general reaction of trialkoxysilanes ((R’O)3–Si–R) or trichlorosilanes (Cl3–Si–R) with a SiO2 surface is illustrated in Figure 3. First, the substrate must be cleaned and hydroxylated

(activated) to generate surface silanol groups (–SiOH), through which the silanes

13 chemically bind to the surface. This is usually achieved by treatment with strongly-

70, 74 69, 74-75 oxidizing acids (7:3 H2SO4:H2O2) or bases (1:1:5 NH4OH:H2O2:H2O) or with ultraviolet-ozone plasma (UVO)23, 57, 59. Before the silanes are grafted, they are first hydrolyzed, exchanging the alkoxy- or chloro- groups with hydroxyl groups while producing R’OH or HCl as byproducts. Then, the silanols self-condense in the presence of water to form polysiloxanes, which in turn, adsorb to the hydroxylated surface via intermolecular attractions, such as hydrogen bonding (physisorption). Finally, water is removed, hydrogen bonds are broken and the condensed silanes chemically graft to the surface (chemisorption).

Figure 3. A schematic of chemical reactions of tri-functional silanes with a SiO2 surface: a) hydrolysis, b) self-condensation, c) physical adsorption and d) chemical adsorption (R = any functional group and R’ = short alkyl chain).

During these reactions, the first silane layer is strongly anchored to the SiO2 surface through silanol moieties (Si–O bond strength ≈ 128 kcal/mol); however, subsequent layers are physically and weakly deposited onto the first layer at the solid-liquid interface.47 These additional layers are generally undesirable and can be removed by rinsing or

14 ultrasonication in an appropriate solvent. In order to generate high-quality silane SAMs, the water concentration and temperature of the solution must be carefully controlled. In the absence of water, incomplete monolayers are formed, while excess water promotes polymerization of the silanes in solution and results in the deposition of oligomers onto the surface, which are less prone to dense packing and ordering.65, 76-77 Furthermore, temperature affects the balance of reactions of the silanes with each other and with the surface; as temperature decreases, the balance favors reaction with the surface.65

In addition to reaction conditions, the chemistry of the silane head groups, alkyl chains and termini will also affect the quality of SAMs. First, the underlying structure of the polysiloxane network can determine the packing and ordering of the alkyl chains of the grafted silanes, which can be oriented equatorially, axially or tilted, as shown in Figure 2.

For the polysiloxane, the oxygen atoms and the alkyl chain occupy the equatorial and axial positions, respectively. Second, the separation and degree of tilt of the alkyl chains are ultimately determined by the magnitude of van der Waals forces acting among them, which is greater for longer chains.65, 78 Last, the reactivity of terminal groups can also drive order/disorder within the SAM. For example, silanes terminated with polar amino groups will form more disordered monolayers due to acid-base interactions with surface silanol groups.65, 79 Thus, careful selection of the silane chemistry will greatly affect the SAMs from which they are produced. The knowledge base of silane SAMs is extensive and to review all types is beyond the scope of this research. Therefore, the two relevant classes of silane SAMs, i.e., alkylsilane and aminosilane, will be discussed.

2.2.2.1 Alkylsilane SAMs

The simplest forms of silane SAMs are comprised of organosilanes containing alkyl chains of varying numbers of methylene units (n = 1 – 17) and have the basic structure X3–

Si–(CH2)n–CH3 (X = Cl or RO). Some common alkylsilanes are shown in Figure 4.

Terminated only by methyl groups, these molecules are hydrophobic and minimally reactive toward other functional groups. Alkylsilane SAMs are attractive for technological applications due to their chemical compatibility with semiconducting silicon and insulating silica surfaces and their ability to be structurally and compositionally tuned. For example,

SAMs of dodecyltrichlorosilane (DTS) or octadecyltrichlorosilane (OTS) are useful in micro- and nano-electromechanical systems (MEMS/NEMS), where they are used as antistiction lubricants for polysilicon switching devices.80-81 This results from a work of adhesion several orders of magnitude lower for these hydrophobic SAMs compared to unmodified hydrophilic SiO2. Additionally, the mechanical and tribological properties of the SAM can be modified by adjusting the length of the alkyl chain. For example, octadecylmethylsilane (n = 17) versus octyldimethylsilane (n = 7) monolayers on Si/SiO2 provide higher adhesive and friction forces but considerably better wear resistance.82-83

(a) (b)

(C1) (C8)

(c)

(C12)

(d)

(C18)

Figure 4. Structures of various alkyl-silanes: (a) methyltrimethoxysilane (MTMS), (b) octyltriethoxysilane (OTES), (c) dodecyltrichlorosilane (DTS) and (d) octadecyltrichlorosilane (OTS).

Alkylsilanes react with SiO2 surfaces via hydrolysis and condensation reactions, as previously mentioned (refer to Figure 3). The density to which these molecules self- assemble is regulated by the length of the alkyl chain (n + 1) and the chemistry of the head group (X). Stronger van der Waals forces exist between longer alkyl chains which facilitate greater silane packing. Also, the reactivity of the head groups will also influence packing density. Head groups with smaller hydrolysis rates will promote slower cross-linking and thus denser packing of silane molecules. Trichlorosilanes are more reactive than trialkoxysilanes and therefore hydrolyze rather quickly, which can lead to fast growth and island formation.84 Among trialkoxysilanes, steric hindrance reduces the hydrolysis rates and therefore larger substituents will promote slower SAM formation. Thus, the order of

85 reactivity for silane head groups is Cl ≫ OCH3 > OCH2CH3 > OCH2CH2CH3. In addition to the differences in reactivity, alkyoxy groups are larger than chlorine atoms and therefore add to steric restriction on the packing of silane molecules, especially if some of the alkoxy groups are unhydrolyzed. Ultimately, choice of alkyl chain length and head group composition can greatly affect the structure of silane SAMs on SiO2.

2.2.2.2 Amino-silane SAMs

Some of the most extensively researched organosilane SAMs are those containing amino terminal groups (–NH2). The most commonly studied amino-silanes are 3- aminopropyltrimethoxysilane (APTMS)47, 54, 70, 74, 86 and 3-aminopropyltriethoxysilane

(APTES)22, 54, 56-57, 69-70. Other derivatives of these molecules have also been studied, such as N,N-diethyl-3-aminopropyltrimethoxysilane (DEAPTMS)54, N-(2-aminoethyl)-3- aminopropyltrimethoxysilane (AEAPTMS)54, 70, (n-alkyl)-3-aminopropyltrimethoxysilane

54, 70 and p-aminophenyltrimethoxysilane (APhTMS)86, which are shown in Figure 5.

(a) (b) (c)

(d) (e) (f)

Figure 5. Structures of various amino-silanes: (a) 3-aminopropyltrimethoxysilane (APTMS), (b) 3- aminopropyltriethoxysilane (APTES), (c) N-(2-aminoethyl)-3-aminopropyltrimethoxysilane (AEAPTMS), (d) N,N-diethyl-3-aminopropyltrimethoxysilane (DEAPTMS), (e) (n-alkyl)-3-aminopropyltrimethoxysilane and (f) p-aminophenyltrimethoxysilane (APhTMS).

The formation of aminosilane SAMs on Si/SiO2 surfaces implements the same silane grafting mechanism previously demonstrated in Figure 3. However, compared to other alkylsilane/SiO2 surfaces, the amine functionality introduces additional complexity to adsorption mechanism. The extent of interaction between –NH2 groups and the surface

–OH groups (e.g. hydrogen bonding) makes the formation of ordered SAMs increasingly difficult. Additionally, the lone electron pair of the basic –NH2 group can act as a self- catalyst for the hydrolysis of alkoxy-70, 76, 87 and chloro-silanes.54, 88 Also, it can catalyze siloxane bond formation, both intra- and inter-molecularly,70, 87 as illustrated in Figure 6.

Intramolecular catalysis involves the coordination of the –NH2 group to the Si atom of the same molecule, forming a cyclic intermediate which then facilitates the covalent attachment of the molecule to the SiO2 surface. Intermolecular catalysis, on the other hand, entails the coordination of the –NH2 group of one silane molecule to the Si atom of a different, nearby silane molecule. The self-catalysis of aminosilanes can enhance the reaction time of monolayer formation but with the cost of exaggerated self-polymerization and ultimately incomplete monolayer formation.69, 76

The efficiency at which aminosilanes react with surface silanol groups can be optimized by maximizing hydrolysis and limiting self-condensation. This efficiency depends on the number of available reactive amines, steric or electronic hindrance of these sites and the degree of amine substitution. Studies investigating the effect of the number of amines of aminosilanes on the condensation reaction rates found that diamines and triamines react similarly but are both considerably faster than monoamines.54, 89 Also, investigations on the catalytic effects of substituted aminosilanes demonstrated that the rate of condensation followed the order of primary > secondary > tertiary amine. The authors also note that bulkier substituents on the amine generally slow the reaction rate by hindering self-condensation. The decreasing rate is a product of increased steric hindrance resulting from additional and/or larger substituents on the amine.54, 90 Thus, the rate at which aminosilanes form can be easily tuned by the adjusting the number of amines and substituents present in the molecule.

Figure 6. Self-catalysis of APTES molecules by coordination of amine group to Si atom of same molecule (intra-molecular) or nearby molecule (inter-molecular) followed by covalent attachment to SiO2 surface. As mentioned earlier, silanes are capable of cross-linking to each other via Si–O–

Si bonds that can extend vertically or horizontally (Figure 7). Vertical polymerization leads

19 to formation of disordered multilayers and islands while horizontal polymerization tends to produce dense monolayers.70-71 The type and extent of polymerization is quite sensitive to the water content in the reaction, and as a result, the reproducibility can vary considerably.

70 Aminosilanes can take on various conformations once grafted onto a SiO2 surface, as shown in Figure 8. Conformations that are upright (a) or tilted (b) result from interactions between the terminal amine and surface silanol groups. The molecules may also be physisorbed to the surface through hydrogen-bonding between the surface silanol and either the silane ethoxy or hydroxyl group (c and d) or the terminal amino group (e). These weakly bound molecules can be removed after grafting by either rinsing or sonicating in

77 solvent. The various conformations of amino-silanes on SiO2 present quite a challenge for producing quality SAMs with high density and good stability.

Figure 7. Polymerization of APTES on a silica surface: (a) vertical and (b) horizontal.

Figure 8. Possible conformations of APTES on a silica surface: (a) upright, (b) tilted or hydrogen-bonded through (c) ethoxy, (d) hydroxyl or (e) amine moieties.

2.2.2.3 Mixed Silane SAMs

Additionally, silicon surfaces can be modified with multiple organosilanes to accommodate particular applications that require various terminal functionalities. For example, the assembly of AuNPs onto silicon are traditionally facilitated by silanes terminated by amines or thiols. By replacing some of the binding silanes with non-binding silanes (e.g., alkylsilanes), the density and/or structure of adsorbed AuNPs can be significantly altered.46 These mixed silane SAMs can made by mixing two or more silanes in solution prior to deposition (co-adsorption) or by applying one partial silane layer after the other (sequential adsorption). Numerous studies have investigated the co-adsorption of

46, 48 49 47 aminosilanes and alkylsilanes onto SiO2, Si/SiO2, and Al2O3 surfaces while noting the effects of initial mixing fractions and competitive adsorption on the final surface composition. All of these studies concluded that the final compositions are not entirely predictable and do not necessarily equate the initial solution concentrations. This may be attributed to the differences in reaction rates, alkyl chain length and solvent compatibility between the two adsorbates.91

Additionally, mixed silane SAMs can be fabricated as sequential chemical gradients, most notably by lateral vapor diffusion23, 50-51, 57 or controlled-rate infusion

(CRI)52-54. The former is the simpler method, in which a clean, hydroxylated surface is simply placed in proximity of a reservoir of pure or diluted liquid silane that vaporizes and diffuses across the substrate, as shown in Figure 9. When deposited, the adsorbed silane molecules form a concentration gradient with higher concentrations being closest to the source. An enclosure is utilized to confine the diffusing vapor to a maximum vertical distance from the substrate. An inert gas (i.e., nitrogen or argon) can also be injected into

21 the setup to assist the flow of vapor across the substrate. The concentration and quality of the adsorbed silane film will depend upon time, the distance between the substrate and the silane source, the concentration of the silane in the reservoir, gas flow, temperature and humidity.

Figure 9. Vapor diffusion deposition of aminosilane molecules across an activated substrate (e.g., Si/SiO2). The molecules vaporize from the reservoir across the substrate (1), creating a concentration gradient (2). The empty sites (gray) on this substrate can be subsequently backfilled (3) with another silane (e.g., alkylsilane) to create a gradient with varying characteristics (4). On the other hand, CRI is carried out in the liquid phase, where the length of a substrate is gradually exposed to a dilute silane solution. As demonstrated in Figure 10, an activated substrate is positioned vertically inside an empty syringe which is attached to a programmable pump. The silane solution is injected into the reaction vessel at a predetermined rate. Once the solution front reaches the top of the substrate, the reaction is terminated. Thus, the surface density of silane molecules is directly related to time of exposure of the substrate to the solution, with the bottom having the greatest and the top

22 having the least. The shape and extent of the ensuing gradient can be controlled by the concentration and the rate of injection of the silane solution.

Figure 10. Controlled rate infusion and backfill method for creating gradient surfaces of mixed silanes, e.g., amino- and alkyl-silanes. Important parameters include reaction time, injection rate and the meniscus distance (lm). 2.2.2.4 Fabrication of Organosilane SAMs

The effects of reaction conditions on the attachment and structure of organosilane SAMs onto SiO2 substrates has been the focus of a multitude of studies.69-70, 74, 76-77, 87, 92 Key parameters include time, temperature, silane concentration and rinsing and curing procedures. Although procedures for creating amino-silane SAMs vary widely across the literature, most have very similar structures.

Table 1 reveals organosilane deposition parameters from multiple references.

Deposition from solution and vapor phases is the primary route to creating silane SAMs, which generally follows these main steps:

1. Substrate preparation – Substrates are cleaned and activated with one or a

combination of organic solvents (e.g. acetone, methanol or isopropanol),

70, 74 mixtures of strongly-oxidizing acids (7:3 H2SO4:H2O2) or bases (1:1:5

69, 74-75 23, 57, 59 NH4OH:H2O2:H2O) or with ultraviolet-ozone plasma (UVO) .

Solution-based cleaning may also be assisted by elevated temperatures and

sonication. These processes also ensure that the surface is fully hydroxylated,

which is necessary for the condensation of silane molecules onto SiO2.

2. Silane deposition – Substrates are either immersed into a dilute silane solution

(generally ≤ 2% v/v in anhydrous organic solvent) or exposed to silane vapor

(from solution or pure silane) for prescribed times (few minutes to many

hours) and temperatures (20 º – 120 ºC). Longer times and lower temperatures

generally lead to thicker, more disordered silane layers.69-70 Deposition can

also be performed in a dry, oxygen-free atmosphere to ensure greater control

of surface moisture of the substrate.

3. Post-deposition processing – Excess and weakly bound silanes are removed

from the substrates by thorough rinsing or sonication with organic solvents.

The substrates are then dried in a stream of nitrogen or argon and then

annealed at 100 º – 120 ºC to ensure the silane layer has fully condensed.

Thus, it is evident that multiple approaches can be taken to generate organosilane SAMs.

Although the main processing steps are fairly similar, many small differences among the vast library of procedures can produce SAMs of the same molecule(s) but with varying structure, density and robustness.

Table 1. Processing details for various SAM combinations with silicon and gold-based surfaces.

69 93 74 70 54 92 92 76

Ref.

IR,

AFM, AFM, AFM, AFM,

XPS

AFM AFM

RAIRS RAIRS

AFM, XPS, XPS, AFM, XPS, XPS, XPS

XPS, SIMS, SIMS, XPS,

ellipsometry ellipsometry

ellipsometry,

contact angle, contact angle, contact angle,

chemical/atomic chemical/atomic

FM, angle contact FM,

Characterization

rinse rinse rinse

Post

water)

30 30 min

ethanol, ethanol,

(toluene)

for 5 min for 5 min

(ethanol);

methanol, methanol,

processing

rinse, sonicat rinse (toluene, rinse (toluene,

rinse rinse (ethanol) rinse (toluene)

(bicyclohexyl)

110°C, 15 min

anneal, 120°C, 120°C, anneal,

water); anneal, water); anneal,

70°C 20°C 70°C 20°C 60°C 80°C

reflux

Temp. 20, 50,

25, 75°C

Reaction

min

4 4 h

48 48 h 15 h

Time

10 10 min 20

2 min 2 min

variable

1, 24, 72 1,72 24,

1, 3, 24 h 1,24 3,

Reaction

2 2 2

------

purged

Dry N Dry N Dry N

vacuum

glovebox

Atmosphere

8% 8% 5% 1%

33% 33%

(v/v) (v/v) (v/v) (v/v) (v/v) (v/v) (v/v) (v/v)

0.5% 0.2%

1, 10, 1, 10,

0.1 % 0.1 % 100%

Conc.

Silane Silane

exyl exyl

(vap)

(vap) (vap)

(soln) (soln) (soln) (soln) (soln)

anhyd. anhyd. anhyd. anhyd.

toluene toluene toluene ethanol toluene toluene

(phase)

Solvent Solvent

water vapor

xylene xylene

bicycloh

- -

)

or or or

(s)

)

2 2

) )

2 2

(CH

(CH (CH

2 2

APTES APTES APTES APTES APTES

APTMS

APTMS, R APTMS, R APTMS,

- -

(CH

Molecule

APTES (R = (R APTES = (R APTES =

NH NH

R R

O, O,

HF, HF,

RCA RCA RCA

ozone,

plasma

piranha piranha piranha piranha

piranha, piranha, piranha,

Method

HF/H

Cleaning Cleaning

2 2 2 2 2 2 2 2

Si/SiO Si/SiO Si/SiO Si/SiO Si/SiO Si/SiO Si/SiO Si/SiO

Substrate(s)

Self-assembled monolayers have been established as ideal candidates for building the platforms for various nanostructures, such as nanoparticle assemblies. They are simplistic in the fact that they can generate ordered, nanostructured materials through facile methods without external intervention. On the other hand, many experimental factors, either inherent to the molecules or related to the processing environment, can greatly alter the mechanisms and integrity of their self-assembly. Small variations in solution composition, temperature and moisture content can be the difference between the formation of dense, well-ordered monolayers and patchy, disordered multilayers or aggregates.

Although planar substrates have been primarily discussed, SAMs can be applied to surfaces of any geometry or dimension, thereby providing a versatile avenue for interfacial modification with molecular precision. In addition, SAMs can control the surface energetics and electrostatic interactions that facilitate the addition and organization of functional nanostructures (e.g. nanoparticles, macromolecules and biomolecules), which in turn can be connected to more complex systems, such as biological systems, mechanical components or electronic devices. Although nanoscience and nanotechnology has progressed considerably in the past 20 years, their advancement is still dependent upon the development and optimization of interfacial properties of both surfaces and nanostructures.

2.3 Gold Nanoparticles

2.3.1 History and Properties

Nanoparticles are ultrafine clusters of atoms, typically having dimensions in the range of 1 – 100 nm, that have size and morphology dependent properties that are significantly different than their bulk material. When matter becomes small enough (i.e.

26 nanoscale), it stops obeying the laws of classical physics and starts demonstrating quantum effects. For example, bulk gold has a familiar lustrous yellow hue, while nano-sized gold can appear red, blue or even brown in solution. This phenomenon is related to the aspect ratio of the nanoparticle and how it interacts with light. Additionally, one of the characteristics of nanoparticles commonly exploited in nanotechnology is the high surface area to volume ratio, which allows more interfacial interaction within nanoparticle systems.

For instance, given a volume of spherical particles, those with a radius of 10 nm would have 10 times the surface area of those with a radius of 100 nm. This characteristic provides nanomaterials with tunable thermal, mechanical, electronic and catalytic properties.

Nanoparticles come in a wide variety of morphologies and compositions.3, 94

Geometries include, but are not limited to, spheres, polyhedral, rods, plates, ellipsoids, core/shell, nanocages and dumbbells. These nanoparticles have been commonly made from a variety of materials, such as metals, ceramics, semiconductors, inorganic salts, inorganic carbon and polymers, to name a few. Despite the large library of nanoparticles available, gold nanoparticles are of particular interest in this study.

Table 2. Various morphologies, compositions and physical properties of nanoparticles which are altered from the bulk scale. 3, 94

Morphology Composition Altered Properties low aspect ratio high aspect ratio spheres rods metals thermal ellipsoids wires ceramics mechanical cubes pillars semiconductors electronic rods tubes inorganic salts catalytic wires belts inorganic carbon photonic plates helices polymers core/shell nanocages dumbbells

The simplest and arguably the most widely studied nanoparticles are gold nanospheres (AuNPs). Their applications date back several thousands of years when they

27 were incorporated into colored enamels and stained glasses. Brilliant shades of yellow, red and purple could be obtained by varying the synthesis procedure. The famous 4th century

Lycurgus cup contained glass with embedded AuNPs, and the perceived color changed whether the light was being reflected or transmitted.95 A 16th century alchemist, Paracelsus, also claimed to make an “elixir of life,” dubbed Aurum Potible, which was believed to cure various ailments and to boon mental and physical capabilities. In the mid-17th century, the colorant “Purple of Cassius” was developed by Andreas Cassius, with colors ranging from pink to maroon, and was commonly used in the manufacture of ruby glass and red enamels.

Later, in the 18th century, ruby gold was known in China and had been used as a porcelain enamel.96

In 1857, British scientist Michael Faraday synthesized the first pure sample of

96,97 colloidal gold by reducing aqueous NaAuCl4 with phosphorous in carbon disulfide. In fact, Faraday’s study on colloids of gold and other metals developed the fundamental concept of how particle size determines the color perceived from various colloidal dispersions. In his conclusion, Faraday stated that the dimensions of the particles were very minute, in fact undetectable by the microscopes of that era. It wasn’t until about 100 years later that scientists utilized electron microscopes to evaluate AuNPs formed by Faraday’s synthetic route, which were approximately 6 nm in size.98-99 The particles were also very stable, as one of Faraday’s original suspensions remains stable to date.96

Curiosity about colloidal gold production continued to grow with Zsigmondy’s new synthetic route around the turn of the 20th-century100 – the first colloidal gold produced in dilute solution. He used a method similar to Faraday’s (although originally unaware of it) in which he reduced gold chloride with formaldehyde in a weak alkaline solution. This

28 produced stable red colloidal solutions as opposed to the purple colloids known previously.

Zsigmondy also developed the ultramicroscope to view the size and motion of AuNPs.100

Subsequent contributions from Svedburg101 (ultracentrifuge) and Mie102 (light-scattering theory) also helped to bolster the understanding of colloidal chemistry and physics.

Beginning in the 1950’s, the synthesis of AuNPs became rather simple, as demonstrated by Turkevich et al.103 and later by Frens.104-105 The study of gold nanoparticles (of all geometries) became mainstream around the mid-1990’s and continues to flourish to this date.

2.3.2 Synthesis and Purification

To date, AuNPs are produced by a vast number of synthetic methods (see Table 3), most of which focus on simple procedures that have high control over uniformity and size monodispersity. The majority of methods utilize solutions of tetrachloroauric acid

98-99, 103-106 (HAuCl4) but vary in reducing agent(s) used (e.g. trisodium citrate , sodium ascorbate 106-107, white phosphorus 96, 107, formaldehyde 100, ethanol and tannin107), order of reagent addition and synthetic conditions (temperature, mixing rate and concentration), all on which the resulting particle size and shape depend. Most common particle sizes obtained range from 3 – 30 nm, although methods exist that extend the range from 1 – 150 nm.107

The final particle diameter is governed by the rate of icosahedral nuclei formation compared to shell condensation.107 The more rapidly a reductant works, the greater number of nuclei will be formed. Therefore, much of the available gold ions will be spent, and growth by condensation will be limited. The converse is true for slow-acting reductants.

These variables, among others, allow for good selectivity of particle size and shape in

AuNP syntheses.

Table 3. Various synthetic methods for spherical AuNPs

Method Reducing Agents Stabilizers Other Reagents/ Particle Size References Processing (nm) 103-104, Citrate reduction tri-sodium citrate citrate tannic acid 3 - 120 106-107 TOAB, thiols, Brust-Schiffrin NaBH4 1 - 5 108 amines, carboxylates

UV-irradiation tri-sodium citrate citrate UV (366 nm) 106

Ascorbate ascorbic acid ascorbate 30 - 70 106 reduction ultrasound (200 Ultrasonication 2-propanol 30 - 70 109 kHz, 20-200 W)

Thermolysis heat alkyl molecules 180°C 5 - 50 110

Microwave microwaves green tea extract 10 - 15 111 irradiation (100W) tannic acid, plant Green synthesis Varies 112-114 extracts, biomass

In this dissertation, a variation106 of the citrate reduction method developed by

Frens was used to create small AuNPs. To describe, a solution of HAuCl4 (0.01% w/v) is brought to a boil with rapid stirring and a solution of trisodium citrate (1% w/v) is added quickly. The solution goes through color changes of grey to light purple to red within 1 –

3 minutes. A constant volume is required for controlling particle diameter, and thus necessitates refluxing or water replacement to avoid a change in solution concentration.

This method produces AuNPs 10 – 12 nm in diameter with good size dispersion (20% variation).115

The desired diameter d of AuNPs can be calculated from Equation (2.1, where N is the number of atoms in a spherical particle and ρ and M represent the density (19.3 g/cm3) and the atomic mass of gold (197 g/mol).116

휋 휌푑3 (2.1) 푁 = = 30.89602 ∗ 푑3 6 푀

For a given mass of HAuCl4, the amount Na3Cit is determined from the molar ratio χAu of the precursors:

푚표푙 HAuCl4 (2.2) 휒퐴푢 = 푚표푙 Na3Cit where smaller ratios produce smaller particles and vice versa. This behavior is explained by the growth mechanism of AuNPs, where upon mixing, Au seeds are formed and begin

– growing based upon concentrations of AuCl4 and citrate ions. When more citrate ions are present, they quickly surround the AuNPs and the growth is quenched relatively quickly.

– Conversely, when the molar ratio favors AuCl4 , the citrate molecules take longer to cover the AuNPs, thus allowing them more time to grow and ripen. Moreover, a smaller χAu will favor a more basic solution affording more hydroxylated Au3+ complexes and strongly ionized citrate molecules (Figure 11), thus retarding seed nucleation and promoting slow particle growth. On the other hand, a larger χAu will acidify the reaction mixture due to the abundance of chlorinated Au3+ complexes and the citrate molecules will partially ionize resulting in faster seed agglomeration and particle ripening.116

Figure 11. Top left: pH variation with variation in χAu (decreases left to right); Top right: relative reactivity of the dominant Au3+ complexes and their associated pH values; Bottom: schematic of two reaction pathways for the synthesis of citrate-reduced AuNPs. (Reprinted with permission; Ref 116) Furthermore, Kimling et al. mapped out the diameters obtained for citrate-stabilized

AuNPs via thermal reduction at various concentrations of gold precursor.106 As seen in

Figure 12, particle diameters follow a polynomial trend for a given precursor ratio and tend to produce more predictable sizes at smaller ratios. They also revealed the importance of

– limiting the AuCl4 concentration below 0.8 mM to generate AuNPs of more spherical shape, low size dispersion and stability, all of which are also related to the passivation role of citrate.

Figure 12. SPR peak wavelengths of AuNPs as function of the ratio of gold and citrate concentrations. The different symbols mark the gold concentration of the reaction (■ – less than 0.8 mM; ○ – 1 mM; – 1.2 mM). The lines are a guide to the eye. (Modified and reprinted with permission; Ref 106). Traditionally, centrifugation has been employed to purify AuNPs of excess reactants, stabilizing molecules and particles of undesirable sizes. In this process, containers of AuNP solutions are spun at very high velocities and centripetal force separates particles and molecules by mass. The supernatant liquid contains mostly solvent

(e.g., water), small particles and free molecules and is removed. The remaining concentrated particle solution is then redispersed in solvent and the process can be repeated numerous times for further purification. After purification, the particles can subsequently be redispersed and altered by ligand exchange reactions (e.g., alkylthiol for citrate) to modify particle stability and/or reactivity. Unfortunately, centrifugation is time consuming due to necessary repetitions and hinders the efficiency of particle synthesis and characterization. Alternatively, diafiltration117 is a one-step process that combines purification and size separation. The process utilizes a reusable, semi-permeable tangential flow membrane, where the size of the pores dictates the retention and elution of materials from the solution. Figure 13 illustrates the process, where the AuNP solution is fed into the

33 system through the reservoir and pumped through the diafiltration membrane. Here, particles and molecules larger than the pore size are retained and re-cycled through the system while smaller particles and molecules permeate through the membrane and are removed from the system. Pure solvent (e.g., water) can be added to the reservoir to maintain solution volume or the system can run until a desired concentrated solution is achieved. Thus, diafiltration is capable of purifying and concentrating a particle solution in a fraction of the time centrifugation takes (nearly 20 times faster) all in one simple process.

Figure 13. Schematic of a continuous diafiltration setup. Components include the retentate reservoir, peristaltic pump and semipermeable membrane. The expanded view demonstrates how the membrane retains particles larger than the pores while smaller particles and molecules permeate through the membrane and are removed from the solution. (Reprinted with permission; Ref 117) 2.4 Particle Interactions and Stability

The chemistry of colloidal solutions is crucial for tailoring interparticle interactions and preventing unwanted aggregation. Since background electrolyte solutions span a wide

34 range of pH values and ionic strengths, the stability and interaction of colloidal nanoparticles are greatly influenced by the pKa of their stabilizing molecules (i.e. ligands or free ions) and the concentration of ions in solution. The pH determines the number of charges on a particle while ionic strength screens those charges to a certain extent.

2.4.1 Interaction Potentials

The interactions of colloids are commonly described by the Derjaguin, Landau,

Verwey, and Overbeek (DLVO) theory118-120, which employs attractive van der Waals

(Vattr, Equation (2.3 and repulsive electrostatic interactions (Vrep, Equation (2.4) to explain nanoparticle stability121:

퐴 2푎2 2푎2 푟2 − 4푎2 (2.3) 푉 (푒푉) = − 푘 푇 [ + + ln ( )] 푎푡푡푟 6 퐵 푟2 − 4푎2 푟2 푟2

2 푉푟푒푝(푒푉) = 2휋휀푟휀0휓0푎푘퐵푇 ln[1 + exp(−휅푟)] (2.4) where the inverse Debye length is

1000푒2푁 (2퐼) (2.5) 휅(m−1) = 퐴 휀푟휀0푘퐵푇

In these equations, A is the Hamaker constant, kB is the Boltzman constant, T is the temperature in Kelvin (kBT is the thermal energy of the system), a and r are the particle radius and the interparticle separation, respectively, in meters, εr is the relative dielectric constant of the liquid, εo is the permittivity of the vacuum, ψ0 is the surface potential of the particles, e is the elementary charge, NA is Avagadro’s number, and I is the ionic strength of the solution in mol/L. Put simply, in the case of aqueous nanoparticles, Vattr is primarily determined by size and composition while Vrep is largely influenced by pH and ionic strength. Figure 14a shows various types of interaction potentials between two particles as a function of their separation. As particle separation decreases, Vrep increases exponentially

35 and Vattr decreases by a power law. The sum of these potentials (Vtotal), reveals a few features121:

1. the primary maximum (Vrep ≫ Vattr) – the maximum potential which correlates to

the energetic barrier that particles must overcome to approach contact (r ≈ 0). For

highly-charged surfaces in weak electrolyte, this barrier is large (many kBT).

2. the primary minimum (Vrep ≪ Vattr) – the potential energy at contact, where the

van der Waals forces completely dominate. If the energy barrier is large, then it

is difficult for the energy to reach this minimum and the particles are considered

kinetically stable.

3. the secondary minimum (Vrep < Vattr) – the minimal potential energy before the

energy barrier as r→0. Particles may form weak attractions but can be easily

redispersed. The minimum becomes more pronounced with higher ionic strength.

Stability exists when the energy barrier is above V = 0, which is usually the case for particles with high surface charge and/or low electrolyte concentration. Below this threshold, particles begin to aggregate and are considered unstable, which commonly happens for particles with low surface charge and/or high electrolyte concentration. The potentials for particles with varying pH and electrolyte content are displayed in Figure 14b.

Here, it is evident that the potential and the energy barrier decrease with increasing ionic strength and/or decreasing pH, and the particles eventually become unstable (red curve).

As the surface charge minimizes, the potential approaches that of pure van der Waals interaction, and the particles strongly attract each other at all separations.

Figure 14. Potential energy of two particles as a function of separation distance: (a) electrostatic repulsion (Vrep), van der Waals attraction (Vattr) and the total potential (Vtotal); (b) effect of increasing pH and ionic strength on particle potential. For a given type of colloid, the van der Waals interactions will remain mostly constant. On the other hand, the electrostatic forces can be empirically regulated through pH and ionic strength (these properties are discussed in future sections). These repulsive interactions are manifested in the electrical double layer,118-120 as demonstrated in Figure

15. Here, charges are present on the surface of the particle which are balanced by ions of opposite charge that are loosely bound to the surface through Coulomb forces and serve to electrically screen the surface charges. The mobility of these ions is constrained only by electrostatic attraction and thermal motion, and therefore the outer layer is considered the

“diffuse layer”. The slipping plane separates the inner layer (Stern layer) and the diffuse layer and is approximately where the colloid’s electrokinetic potential (or zeta potential, ζ) can be measured. The bottom plot in Figure 15 exhibits the particle potential as a function of distance and also correlates the surface, Stern and zeta potentials to their positions within the colloid.

Figure 15. Diagram of a gold colloid composed of a hard core of radius a with an electrical double layer of thickness κ-1 (Debye length). The bottom plot shows the electrical potential as a function of distance from the particle surface and the charge layer to which it corresponds. 2.4.2 Zeta Potential

The zeta potential ζ (V) is the only practical way to characterize the magnitude of particle charge since surface potential and Stern potential are not accessible to measurement. Even so, the zeta potential is only approximated from electrophoretic

119 mobility μe using a zeta potential analyzer via electrophoresis. During electrophoresis, an external electrical field of strength E (V/m) is applied across a colloidal solution where the diffuse ions move along the field at a velocity v (m/s) against the particles while experiencing drag due to the viscosity η (N∙s/m2) of the dispersant. The electrophoretic velocity is measured by a laser Doppler anemometer and is proportional to μe by: 푣 휇 = (2.6) 푒 퐸

By applying the electrophoretic model of Smoluchowski122, the zeta potential is related to the measured μe via:

m2 휀 휀 휁 (2.7) 휇 ( ) = 푟 0 푒 V ⋅ s 휂

This model is valid for most aqueous systems where κ-1 is only a few nm. The model breaks down when the ionic strength reaches that of water. As seen in Table 4, the magnitude of the zeta potential can provide an indication of colloidal stability – a greater potential in either the positive or negative direction signifies greater stability, while a small potential implies instability or even aggregation.

Table 4. Colloidal stability as a function of the absolute value of the zeta potential.

Zeta potential [mV] Colloid stability (absolute value) 0 – 5 Rapid aggregation 10 – 30 Poor stability / emergent instability 30 – 40 Moderate stability 40 – 60 Good stability > 60 Excellent stability

2.4.3 Acid-base Chemistry

Colloidal particles are significantly affected by the pH of the suspending medium.

The acidity (pH < 7) or alkalinity (pH > 7) of a colloidal solution greatly affects the ability of the particles to remain suspended in solution as well as react with other particles and surfaces. Changes in pH will affect the amount of ionization on surfaces or in polar molecules, typically by the release or capture of hydrogen ions (or protons, H+), which are in a dynamic state of equilibrium. Solutions of weak acids and bases follow the reaction:

퐾 푎 + − (2.8) 퐻퐴 + 퐻2푂 ⇔ 퐻3푂 + 퐴

– + where HA and A are the conjugate acid/base pair and the hydronium ion (H3O ) is a solvated hydrogen ion. For strong acids and bases, pH is calculated from the negative logarithm of the hydrogen (hydronium) ion concentration (mol/L):123

+ + 푝퐻 = − log [퐻 ] = − log [퐻3푂 ] (2.9)

In the case of weak acid/base solutions (e.g. buffers), pH is more precisely determined by the Henderson-Hasselbalch equation:

[퐴−] (2.10) 푝퐻 = 푝퐾 + log ( ) 푎 [퐻퐴] where the acid dissociation rate constant Ka is defined as

[퐻+][퐴−] (2.11) 퐾 = 푎 [퐻퐴]

(see Appendix A for derivation of rate constants). Thus, the pKa (–log Ka) identifies the pH where the concentrations of HA and A– are equivalent. This is useful for determining pH ranges of buffer solutions or estimating the concentrations of charged and neutral organosilane molecules on a surface.

As an example, an aqueous solution of citric acid (H3Cit) can contain a combination of ions depending upon the solution pH, given by the equilibrium

퐾 퐾 퐾 1 − 2 2− 3 3− 퐻3퐶𝑖푡 ⇔ 퐻2퐶𝑖푡 ⇔ 퐻퐶𝑖푡 ⇔ 퐶𝑖푡 where K1 – K3 are the acid-dissociation rate constants:

[ +][ −] 퐻 퐻2퐶𝑖푡 −4 퐾1 = = 7.41 x 10 (푝퐾1 = 3.13) (2.12) [퐻3퐶𝑖푡]

[퐻+][퐻퐶𝑖푡2−] –5 (2.13) 퐾2 = − = 1.74 x 10 (푝퐾2 = 4.76) [퐻2퐶𝑖푡 ]

[퐻+][퐶𝑖푡3−] 퐾 = = 3.98 x 10–7 (푝퐾 = 6.40) (2.14) 3 [퐻퐶𝑖푡2−] 3

Being a weak acid and having three pKa values makes citric acid a great buffering agent, i.e., it is resistant to large pH change when small amounts of strong acid or base is added.

A buffer maintains constant pH in the range of pKa ± 1. Therefore, citric acid buffers well for pH = 2.1 – 7.4, since the buffer regions for each pKa overlap.

In addition to pH and pKa, the fraction of an ion specie α is important for evaluating the charge character of a surface or molecule. With the use of the rate equilibrium equations and the mass balance equation for all ion species of a molecule (see Appendix A for derivations), α can be determined solely as a function of pH (i.e., [H+] = 10–pH). For example, the fraction of monohydrogen citrate is

2− + [퐻퐶𝑖푡 ] 퐾1퐾2[퐻 ] (2.15) 2− 훼퐻퐶푖푡 = = + 3 + 2 + [퐻3퐶𝑖푡]0 [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 where [H3Cit]0 is the total concentration of all citric acid species. At a given pH, the fraction of all species can be calculated and their contributions to the mean charge 푍̅. For example, the mean charge of citrate anions is

̅ − ( ) 2− ( ) 3− (2.16) 푍퐶푖푡 = 훼퐻2퐶푖푡 ∗ −1 + 훼퐻퐶푖푡 ∗ −2 + 훼퐶푖푡 ∗ (−3)

Thus, the charge character of a molecule can be readily determined at a given pH.

The impact of pH on particle adsorption is portrayed in Figure 16. In this example, negatively-charged AuNPs are adsorbed onto positively-charged APTES surfaces. Here, three main pH regimes exist:

1. below pH 4, the AuNPs and APTES surface are mostly protonated – although

there is strong attraction to the surface, there is little repulsion among the particles

to keep them isolated on the surface. This results in a high density of aggregated

particles.

2. above pH 8, the AuNPs and APTES surface are mostly deprotonated – although

there is plenty of interparticle repulsion, there is little attraction to the mostly

neutral APTES surface. This results in sparse coverage of isolated particles.

3. from pH 4 – 8, interparticle repulsion increases while surface attraction decreases.

In this range, though, these interactions are balanced to afford dense assemblies

of isolated particles.

Thus, the density and structure of adsorbed particles can be tuned by the pH of the particle solution and the pKa’s of the particle stabilizing molecules and the functionalized surface.

Figure 16. Schematic representation of pH-dependent stabilization of negatively-charged AuNPs and adsorption onto a positively-charged amine-terminated surface. As pH increases, interparticle repulsion increases while particle-surface attraction decreases.

Figure 17. Illustrations of AuNPs stabilized by electrostatically bound citrate molecules and covalently bound mercaptopropanesulfonate ligands. 2.4.4 Ionic Environment

Along with pH, the concentration and nature of ions greatly influence the stability of colloids. The extent of ion influence is quantified by the ionic strength (I):

푛 1 (2.17) 퐼 = ∑ 푐 푧2 2 푖 푖 푖=1 where ci and zi are the concentration (mol/L) and valence of ion i in solution, respectively.27-28 Ionic strength differs from ion concentration in that the charges of the ions can have significant influence. For monovalent electrolytes, such as NaCl, the ionic strength simply equals the total ion concentration, but for multivalent ions, the charge has a parabolic effect (z2). Thus, at the same total ion concentration, a divalent electrolyte such as CuSO4 would have an ionic strength four times greater than that of NaCl. Furthermore, for an aqueous solution at room temperature, ionic strength can be easily related to the

Debye length121 by κ-1 (nm) = 0.3/√I. Lastly, ionic strength not only affects charged colloids but charged surfaces as well. For example, surfaces covered in amine-terminated

43 organosilanes will protonate more with increasing ionic strength.124 Thus, for colloidal assembly, ionic strength can alter both interparticle stability and particle-surface attraction.

2.5 Electrostatic Adsorption of Nanoparticles

2.5.1 Theory and Simulations

The details of electrostatic assembly and how it is influenced by particle size, interparticle repulsion and particle-surface attraction has long been under investigation.

The adsorption of charged particles to planar surfaces have been classically described by random sequential adsorption (RSA),29, 34-42 which is illustrated in Figure 18. Here, particles are simply considered hard disks with strong attraction to the surface that adsorb at random positions across the surface in a sequential and irreversible manner. If an adsorption attempt results in an overlap, it is rejected. Initially, the surface is filled quickly, but as the fractional area coverage θ increases, the rate of successful adsorption attempts rapidly decreases (Figure 18b). The process continues until no more particles can be adsorbed and the coverage has reached an upper limit (i.e., the jamming limit, θjam) which for 2D disks is approximately 0.547. If the particles are polydisperse, θjam will increase since smaller particles can fit in the spaces between larger particles. These random configurations generally have broad, normally-distributed interparticle separations and a strongly damped radial distribution function (i.e. they lack higher-order peaks).36 Also, due to the irreversibility of the adsorption, the mean in-plane interparticle separation is larger than 2κ-1 for the particles in solution.33 For small particles (diameter < 50 nm), κ-1 is on the same order of magnitude as a and therefore contributes substantially to the effective particle radius. Thus, for immobilized nanoparticles (NPs), θ can be less than θjam.

However, κ-1 depends on the environment, i.e. the concentration electrolytes surrounding

24, 37 the particles and the dielectric constant (εr) of the dispersing medium. These comparable length scales of a and κ-1 and the large extent to which electrostatic attraction and repulsion can be tuned suggests that potential structures achieved by electrostatic assembly of nanoparticles could expand beyond random arrays.

Figure 18. Schematic representation of random sequential adsorption of particles onto planar surfaces. (a) The circles represent approaching particles (yellow) and adsorbed particles (red). Dashed arrows denote where adsorption was rejected. The top diagrams depict the solution/surface interface while the bottom diagrams depict the resulting particle assembly structure. (b) The kinetic evolution of particle coverage and adsorption rate. Computer simulations have attempted to map out the richness of this intermediate space.38, 42-45 Studies of charged spherical particles on homogenous or patterned surfaces with opposite charge reveal that coverage and in-plane order of the particles are primarily regulated by the relative magnitude of particle-particle and particle-surface interactions, as well as particle volume fraction in solution. For example, Gray and Bonnecaze performed

Brownian motion simulations to map out the synergy of these interactions for colloids in determining coverage and structural order.42 Figure 19 displays the order/disorder transition of adsorbed colloids for various particle and surface (wall) potentials. When particle-surface interactions are sufficiently strong (> 5 – 10 kBT), lateral mobility of adsorbed particles is inhibited and in plane ordering along with annihilation of packing defects are restricted.24, 41, 45 Surface coverage is shown to increase with either increasing ionic strength or increasing volume fraction of particles in solution. The order/disorder

45 transition is also impacted by volume fraction and is predicted to occur where particles potentials are low and surface potentials are high or vice-versa.

Figure 19. Phase diagrams of ordered and disordered surface structures for a volume fraction of 0.01 and a Debye screening parameter κa =1. (Reprinted with permission; Ref 42) 2.5.2 Experimental Examples

Numerous empirical investigations have furthered the quantitative understanding of electrostatic deposition of nanoparticles.24, 27-29, 31, 34, 37, 39-41 For example, Semmler et al. investigated surface coverage and deposition kinetics of positively-charged latex particles on negatively-charged mica surfaces, and concluded that long-time maximum surface coverage is independent of particle concentration (several orders of magnitude lower than for simulations) but strongly dependent upon ionic strength.29 In addition, Kooij et al. found similar results for small charge-stabilized gold nanoparticles deposited onto amine-modified silicon substrates, noting that the spatial distribution of nanoparticles

(normalized by particle area) at moderate ionic strengths is universal.27 They also established that surface organization is governed by the strength of the particle-surface interaction and the repulsion among charged particles. More recently, Nepal and co- workers extended these concepts to hierarchical one-dimensional gold nanorod assemblies

46 on chemical contrast patterns, demonstrating the local alignment relative to the underlying pattern and nanoparticle spacing along the pattern is related directly to the Debye length.17

All of these studies are in agreement with prior models describing the impact of ionic strength. The impact of pH, though, has not been as extensively examined. The pH of the colloidal solution will affect both interparticle repulsion and particle-surface interaction,

23, 26, 32, 58 depending on the relative pKa of the particle and surface. Variation of pH through the isoelectric point of the constituents will decrease the strength and even reverse particle- surface or particle-particle interactions.

Furthermore, several studies have demonstrated the impact of tuning surface potential on nanoparticle adsorption by the use of aminosilane gradients.20-21 They found that the density of adsorbed AuNPs reduced as the aminosilane surface concentration decreased down the gradient. Although they determined that reduced surface charge resulted in less particle coverage, they made no assessments about the microstructure of the particle assemblies.

Ultimately, the synergy among ionic strength, pH and surface charge density and its effect upon interactions (particle-particle and particle-surface), maximum particle coverage and in-plane order of the nanoparticle assemblies remains to be thoroughly established.

CHAPTER 3

3. EXPERIMENTAL

3.1 Materials and Chemicals

All chemicals were used as received without any further purification and stored in a desiccator. Sodium citrate dihydrate (Na3Cit, 99%), hydrogen tetrachloroaurate trihydrate

(HAuCl4, 99.999%), sodium 3-mercapto-1-propanesulfonate (NaMPS, 90%), citric acid

(H3Cit, >99%), disodium hydrogen phosphate heptahydrate (Na2HPO4, >99%), sodium carbonate (Na2CO3, >99%), sodium hydrogen carbonate (NaHCO3, >99%) and 3- aminopropyltriethoxysilane (APTES, >99%) were obtained from Sigma-Aldrich (St.

Louis, MO). Alkyl-silanes n-pentyltriethoxysilane (PTES, 99%), n-octyltrichlorosilane

(OTCS, 99%) and n-octadecyltrichlorosilane (OTS, ≥90%) were obtained from Gelest

(Morrisville, PA). All other chemicals and solvents were of analytical grade and purchased from Fisher Scientific. Aqueous solutions were prepared with deionized water purified by a Millipore reverse osmosis system (18.2 MΩ·cm). Polished silicon wafers with a 100 orientation and a 13 – 18 μm thick native oxide layer (herein simply referred to as “silicon”) were purchased from MEMC Electronic Materials (USA).

3.2 Substrate Functionalization

To activate surfaces for nanoparticle assembly, layers of organosilane molecules

(3-aminopropyltriethoxysilane and n-alkyl silanes with chloro-, methoxy- or ethoxy- head groups, Figure 20) were self-assembled onto silicon substrates from either solution or vapor

48 phases. Concentration, purity, time and environment are all crucial factors for consistently creating high-quality monolayers on silicon substrates.

3.2.1 Single Silane Solution Deposition

The solution deposition of organosilane SAMs on silicon substrates used in this study has been previously described.22, 24-25, 27, 32, 55, 70 Silicon wafers were diced into 1 cm wide chips with lengths of 1 – 4 cm. To remove organic contaminants, glassware and substrates were sonicated in a dilute detergent solution (1% Alconox®), followed by acetone and water for at least 5 min, and then finished with a thorough rinsing with water.

Afterward, the substrates were treated in an ultraviolet-ozone cleaner (Novascan PSD,

USA) for 20 min to promote the hydroxylation of the SiO2 surface, thus creating anchoring sites for hydrolyzed silane molecules.

(a) (b) (C5)

3-aminopropyltriethoxysilane n-pentyltriethoxysilane (APTES) (PTES)

(c)

(C8)

n-octyltrichlorosilane (OTCS)

(d)

(C18) n-octadecyltrichlorosilane (OTS)

Figure 20. Various precursors for organosilane SAMs: a) 3-aminopropyltriethoxysilane, b) pentyltriethoxysilane, c) octyltrichlorosilane and d) octadecyltrichlorosilane. Next, the cleaned substrates were incubated in a 1% v/v (43mM) solution of silane in anhydrous toluene in a closed glass jar at room temperature for approximately 1 h. After

49 incubation, the substrates were sonicated in toluene, ethanol and water, respectively, for 5 min to remove physisorbed silane molecules, rinsed with water and dried in a stream of N2.

Finally, the silane-modified silicon substrates were annealed in a vacuum oven at 120°C and 50 Torr for 1 h to remove reactions byproducts (i.e. H2O, alcohol or HCl) and drive silane chemisorption. The substrates were then stored in a desiccator to mitigate environmental exposure prior to AuNP adsorption.

3.2.2 Co-adsorption of Organosilane SAMs

Surfaces with two different organosilane SAMs were made in the same manner as the previous section, but instead using a mixture of alkyl- and amino-silanes. Solutions of predetermined APTES molar fractions (χAS) were made by combining aliquots of 50 mM alkyl- and amino-silane solutions to maintain a total silane concentration of 43 mM.

Recipes for various χAS are shown in Table 5. Exposure to moisture was minimized during handling and mixing by keeping containers closed as much as possible.

Table 5. Recipes for mixed silane solutions combined from aliquots of 50 mM stock solutions. Final volumes and concentrations are 43 mM and 5 ml, respectively.

APTES Alkyl-silane Molar Fraction Aliquot Concentration Aliquot

(χAS) (mol) (ml) (mM) (mol) (ml) 1.000 2.15  10-4 5.000 43.0 0 0.000 0.800 1.72  10-4 4.000 34.4 4.30  10-5 1.000 0.600 1.29  10-4 3.000 25.8 8.60  10-5 2.000 0.400 8.60  10-5 2.000 17.2 1.29  10-4 3.000 0.200 4.30  10-5 1.000 8.60 1.72  10-4 4.000 0.100 2.15  10-5 0.500 4.30 1.94  10-4 4.500 0.080 1.72  10-5 0.400 3.44 1.98  10-4 4.600 0.060 1.29  10-5 0.300 2.58 2.02  10-4 4.700 0.040 8.60  10-6 0.200 1.72 2.06  10-4 4.800 0.020 4.30  10-6 0.100 0.860 2.11  10-4 4.900 0.010 2.15  10-6 0.050 0.430 2.13  10-4 4.950 0.000 0 0 0 2.15  10-4 5.000

3.2.3 Sequential Adsorption of Organosilane SAMs

In an effort to obtain a surface with a continuous gradient of χAS, SAMs of APTES were deposited onto a substrate via a controlled rate infusion method adapted from Kannan et al.53-54 As seen in Figure 10, a clean silicon chip (10 mm x 40 mm) was placed vertically inside a clean vial, which was then sealed and purged with nitrogen. A syringe pump injected the silane solution into the vial at a controlled rate (0.5 ml/min) until the substrate was completely submerged (i.e., solvent front reached the top of the substrate). At this point, the injection was stopped and the substrate was retrieved, rinsed and sonicated in toluene. Next, the substrate was incubated in the alkylsilane solution (1% v/v in toluene) for approximately 1 hr to backfill any unoccupied sites on the surface. Lastly, the substrate was rinsed, sonicated, dried and annealed as described in Section 3.2.1.

3.3 Gold Nanoparticle Synthesis and Purification

The synthesis of citrate-stabilized gold nanoparticles (Au-Cit) was based upon the

Turkevich method refined by Frens.103, 105-106 The desired diameter d of AuNPs can be calculated from Equation (2.1, where N is the number of atoms in a spherical particle and

ρ and M represent the density (19.3 g/cm3) and the atomic mass of gold (197 g/mol).116

휋 휌푑3 (3.1) 푁 = = 30.89602 ∗ 푑3 6 푀

For a given mass of HAuCl4, the amount Na3Cit is determined from the molar ratio χAu of the precursors:

푚표푙 퐻퐴푢퐶푙4 (3.2) 휒퐴푢 = 푚표푙 푁푎3퐶𝑖푡 where smaller ratios produce smaller particles and vice versa. This behavior is explained by the growth mechanism of AuNPs, where upon mixing, Au seeds are formed and begin

– growing based upon concentrations of AuCl4 and citrate ions. When more citrate ions are present, they quickly surround the AuNPs and the growth is quenched relatively quickly.

– Conversely, when the molar ratio favors AuCl4 , the citrate molecules take longer to cover the AuNPs, thus allowing them more time to grow and ripen. Furthermore, a smaller χAu will favor a more basic solution affording more hydroxylated Au3+ complexes and strongly ionized citrate molecules (Figure 11), thus retarding seed nucleation and promoting slow particle growth. On the other hand, a larger χAu will acidify the reaction mixture due to the abundance of chlorinated Au3+ complexes and the citrate molecules

Figure 21. Top left: pH variation with variation in χAu (decreases left to right); Top right: relative reactivity of the dominant Au3+ complexes and their associated pH values; Bottom: schematic of two reaction pathways for the synthesis of citrate-reduced AuNPs. (Reprinted with permission; Ref 116) will partially ionize resulting in faster seed agglomeration and particle ripening.116 Kimling et al. mapped out the diameters obtained for citrate-stabilized AuNPs via thermal reduction

52 at various concentrations of gold precursor.106 As seen in Figure 22, particle diameters follow a polynomial trend for a given precursor ratio and tend to produce more predictable

- sizes at smaller ratios. They also revealed the importance of limiting the AuCl4 concentration below 0.8 mM to generate AuNPs of more spherical shape and low size dispersion; the same practice was employed in this study.

Figure 22. SPR peak wavelengths of AuNPs as function of the ratio of gold and citrate concentrations. The different symbols mark the gold concentration of the reaction (■ – less than 0.8 mM; ○ – 1 mM;  – 1.2 mM). The lines are a guide to the eye. (Reprinted with permission; Ref 106) 3.3.1 Citrate-stabilized Gold Nanoparticles

Prior to the reaction, all glassware was cleaned with a 3:1 mixture of fuming nitric and hydrochloric acids followed by copious rinsing with deionized water. For the synthesis of 11 nm Au-Cit NPs, 100 mg (0.25 mmol) of HAuCl4 was added to 380 mL of boiling water in a round bottom flask and maintained at ~100°C with stirring. Next, 588 mg (2.00 mmol) of Na3Cit dissolved in 5 mL of water was added to the precursor. The citrate solution was warmed before addition to maintain a consistent reaction temperature. Heating was maintained for 15 minutes during which several color transitions transpired including clear, black, purple and finally ruby red. Next, the heat was removed and stirring was continued

53 while the solution cooled to room temperature. Once cooled, the solution was filtered through a 0.45 μm pore size polypropylene syringe filter to remove any aggregates. In order to remove excess free ligands and ions, the particle solution was concentrated to 20 mL and purified by a diafiltration process117 using a 70 kDa tangential flow filtration membrane

(Pall Life Sciences, USA) and 10 volume equivalents of water. The purified solution was concentrated to 20 mL and used as a stock solution for future Au-Cit NP solutions. The concentration of AuNPs were determined from UV-Vis spectroscopy. The size distribution of particle diameters was 11.4 ± 1.0 nm (RSD = 9%) as determined by TEM measurements

(Figure 23a,b) and the average hydrodynamic diameter was calculated as 18.4 ± 0.7 nm

(RSD = 4%) by DLS measurements. The UV-Vis spectrum displayed a maximum absorbance peak around 520 nm corresponding to the surface plasmon resonance (SPR) for spherical AuNPs (Figure 23c).

Figure 23. TEM image and particle size distribution for as-synthesized Au-Cit (a, b) and UV-Vis spectra (c) for Au-Cit and Au-MPS. The vertical line at 520 nm indicates the theoretical SPR for spherical AuNPs. 3.3.2 MPS-stabilized Gold Nanoparticles

AuNPs capped with 3-mercaptopropanesulfonate (Au-MPS) were obtained by ligand exchange of Au-Cit NPs, where MPS was added at a 10:1 ratio of incoming thiols to available sites on the nanoparticle surfaces.125-126 The required mass of MPS salt needed is approximated from

2 4휋푎퐴푢푁푃 (3.3) 푚푀푃푆(𝑔) = (푐퐴푢푁푃 푉퐴푢푁푃 푀푊푀푃푆) × 10 퐴푀푃푆 where cAuNP, VAuNP and aAuNP are the molar concentration, volume and radius of Au-Cit NPs

2 126 in solution, and AMPS is the footprint of a MPS molecule (0.214 nm ) and MWMPS is the molecular weight of the MPS salt. In this study, 8.9 mg of NaMPS were added to a solution

-8 of 11.4 nm Au-Cit NPs (cAuNP = 1.88  10 M and VAuNP = 0.075 L) and magnetically stirred for 24 h to allow for complete ligand exchange. The solution was purified of excess

MPS molecules and concentrated by the diafiltration process described in the previous section.

3.3.3 Buffered Gold Nanoparticle Solutions

To create AuNP solutions of known pH and ionic strength, stock AuNP solutions were suspended in buffer solutions of citrate/phosphate (pH 2.2 – 8.0; pKa = 3.13, 4.76,

6.40, 7.20) or bicarbonate/carbonate (pH 9.2 – 10.8; pKa = 10.33) conjugate pairs, depending on the desired pH. Buffers were made by mixing calculated volumes of conjugate acid/base solutions to obtain a specific pH and the ionic strength was adjusted to

100 mM with 4 M NaCl.127 The pH was estimated by the Henderson-Hasselbalch equation, as previously described in Section 2.4.3,

[퐴−] (2.10) 푝퐻 = 푝퐾 + log ( ) 푎 [퐻퐴] and the ionic strength I (in mol/L) was calculated from

푛 1 (2.17) 퐼 = ∑ 푐 푧2 2 푖 푖 푖=1

Detailed expressions for ionic strengths of buffer molecules are shown in Appendix A.

The buffer was then diluted to make solutions of 0.1, 1, 3, 5 and 10 mM (κa = 0.19,

0.58, 1.04, 1.34 and 1.81). Citrate/phosphate buffers were made from mixtures of 0.1 M

H3Cit and 0.2 M Na2HPO4 while carbonate buffers were made from 0.1 M Na2CO3 and 0.1

M NaHCO3. Stock Au-Cit and Au-MPS NP solutions were diluted with the desired buffer solution to obtain a particle concentration of ~ 4 nM. The pH values of the buffered AuNP solutions were recorded as the average of at least three measurements using a digital pH meter (Corning 140) and a liquid-filled, polymer-body electrode (Aldrich).

3.4 Gold Nanoparticle Assembly

A colloidal self-assembly process was used to decorate functional planar surfaces with AuNPs. In brief, native oxide silicon (Si/SiO2) wafers were modified with 3- aminopropyltriethoxysilane (APTES) self-assembled monolayers (SAMs) to generate positively-charged sites for the electrostatic assembly of negatively-charged AuNPs (11.4

± 1.0 nm) stabilized by either citrate or 3-mercaptopropanesulfonate molecules (herein denoted as Au-Cit and Au-MPS). AuNP solutions were made by redispersing concentrated

AuNPs in either citrate/phosphate or bicarbonate/carbonate buffers in order to maintain constant ionic strength (0.1 – 10 mM) while varying solution pH. The APTES- functionalized substrates (Si/APTES) were subsequently incubated at room temperature in aqueous AuNP solutions with pH values ranging from 3 – 10 and ionic strengths of 0.1 –

10 mM to produce AuNP assemblies of various particle density, interparticle separation and arrangement. The substrates were vertically aligned in the AuNP solution to avoid artifacts from sedimentation. The adsorption process proceeded for approximately 16 h to facilitate maximum particle coverage. Upon completion of AuNP deposition, the substrates were removed from solution, thoroughly rinsed and sonicated (5 min) in deionized water

56 to remove weakly bound particles and blown dry in a stream of nitrogen. Lastly, the samples were stored in a desiccator prior to characterization.

Table 6. pH values of Au-Cit and Au-MPS solutions for each ionic strength. Ionic strengths of 10 mM and 0.1 mM are for only Au-Cit and Au-MPS, respectively. Solutions marked by “*” signify the use of bicarbonate/carbonate buffers instead of citrate/phosphate.

Ionic Strength pH of pH of (mM) Au-Cit NPs Au-MPS NPs 4.94, 5.12, 5.54, 6.01, 6.07, 0.1 -- 6.24, 6.31 3.99, 4.37, 5.06, 5.89, 6.44, 3.88, 4.18, 4.8, 5.91, 6.53, 1 7.04, 7.42, 7.28*, 7.41*, 7.57* 7.06, 7.31, 7.15*, 7.43*, 7.51* 3.55, 3.89, 4.61, 5.71, 6.52, 3.45, 3.81, 4.52, 5.62, 6.54, 3 7.22, 7.55, 7.57*, 7.70*, 7.94* 7.24, 7.62, 7.80*, 8.15*, 8.25* 3.33, 3.7, 4.45, 5.50, 6.48, 3.3, 3.65, 4.37, 5.47, 6.45, 5 7.24, 7.66, 7.85*, 8.09*, 8.22* 7.25, 7.76, 8.03*, 8.89*, 9.72* 3.09, 3.47, 4.33, 5.41, 6.4, 10 -- 7.26, 7.85, 8.20*, 9.23*, 9.59*

3.5 Characterization

3.5.1 Scanning Electron Microscopy

Scanning Electron Microscopy (SEM) utilizes a focused beam of energized electrons that rasters across the surface of a specimen, generating many secondary electrons. These electrons are detected and processed into high-magnification, high- resolution images. Micrographs of nanoparticle assemblies were obtained by a Sirion field- emission SEM (FEI Company, USA) using secondary electrons accelerated at 10 kV and collected by an in-lens detector. High-resolution images for magnifications ≥ 2,000x were taken in ultra-high-resolution mode using an immersive electromagnetic field. Images were processed by ImageJ software (National Institute of Health, USA) to generate binary images of nanoparticle assemblies. A particle circularity cutoff of 0.5 – 1.0 ensured only spherical and ellipsoidal nanoparticles were counted. Particle analysis of the binary images was used to assess particle number density and area fraction of nanoparticle assemblies.

3.5.2 Transmission Electron Microscopy

Transmission Electron Microscopy (TEM) utilizes a focused beam of highly- energized electrons to produce images of various materials at very high magnifications with sub-nanometer resolution. TEM differs from SEM in that the signal is collected from electrons that are transmitted through the sample rather than scattered from the surface.

Due to the high resolution of TEM, very accurate measurements of individual nanoparticles and nanoparticle arrays can be obtained. Morphology and mean size of AuNPs were assessed by a CM200 LaB6 TEM (FEI-Philips, USA) at 200kV in brightfield mode.

Samples were prepared by applying 50 μL of a diluted nanoparticle solution (10% v/v in water) to a carbon coated copper grid (400-mesh, Ted Pella, Inc., Redding, CA). Excess solution was removed with filter paper, and the sample was allowed to dry. Images of nanoparticles were analyzed by ImageJ (US National Institutes of Health) to obtain a size average and distribution of at least 500 particles.

3.5.3 UV-Vis Spectrophotometry

UV-Visible spectrophotometry measures the absorbance (or transmittance) of monochromatic light as it passes through a medium, e.g., nanoparticles dispersed in a solution or dried on a glass slide. The amount and wavelength of absorbed light relates to the number density and extinction cross-section of the dispersant.128 Therefore, in the case of nanoparticles, the concentration and size can be ascertained. Additionally, absorbance spectra can be used to monitor kinetic stability of particle dispersions.

UV-Vis spectra were acquired with a Cary 300 Bio UV-Vis-NIR spectrophotometer (Varian Inc., USA) from 200 – 800 nm at a scan rate of 0.5 nm/s. All spectra were collected in disposable methacrylate cuvettes (path length = 1.0 cm) and

AuNP concentrations were chosen to produce optical densities of approximately 1. The surface plasmon peak (λSPR) was determined as the wavelength at maximum absorbance near 520 nm. The absorbance at 600 nm was also monitored as a measure of particle instability due to the direct correlation. The spectra were taken within a few minutes of combining AuNP solutions with buffers. The spectra at longer times are not included, although a peak shift to larger wavelengths could be observed in less stable solutions.

The extinction coefficient εext of the AuNPs is estimated from the relation described by Liu et al. 128

ln 휀 = 푘 ln 푑 + 푎 (3.4) where the diameter d is determined from TEM and the fitting parameters k = 3.32111 and a = 10.80505 are taken from literature. Rearranging the Beers-Lambert equation, the solution concentration cAuNP is calculated as

퐴 (3.5) 푐 = 푆푃푅 퐴푢푁푃 휀푏 where ASPR is the absorbance of the SPR peak and b is the path length of the cell. For a particle with d = 11.4 nm and ASPR = 1.0, the calculated extinction coefficient and

8 −1 −1 -9 concentration are ε = 1.58  10 M cm and cAuNP = 6.33  10 M.

3.5.4 Zeta Potential & Dynamic Light Scattering

Effective particle surface charges can be approximated from zeta potentials measured by an electrophoretic analyzer (refer to Section 2.4.2). Zeta potentials of greater magnitude indicate more surface charge and consequently greater stability of particles dispersed in solution. Zeta potentials were determined from the electrophoretic mobilities of approximately 1 nM AuNP solutions at 20°C using a Zetasizer Nano ZS with integrated

20 mW HeNe laser with λ = 633 nm (Malvern Instruments Ltd, UK) using folded capillary cells (DTS 1060). Averages of at least three replicate measurements were fit according to the Smoluchowski model.

Dynamic light scattering (DLS) uses a laser to scatter light off of nanoparticles in solution. Due to Brownian motion, the distance between scatter events are constantly changing with time. The scattered light is either constructively or destructively interfered by surrounding particles, and the detected intensity fluctuations are processed by autocorrelation functions. Analysis of this data provides the hydrodynamic radii (or diameters) of the particles as well as their polydispersion. The hydrodynamic diameters and polydispersion indices were acquired for AuNP solutions in UV-Vis cuvettes using a

Malvern Zetasizer. Averages were taken from at least three separate measurements.

3.5.5 X-ray Photoelectron Spectroscopy

X-ray photoelectron spectroscopy (XPS) detects the relative amounts of elements on a planar surface. It operates based on the photoelectric effect by exciting core electrons on a sample surface and recording both the number and energy of the ejected electrons.

Since the energy of the ejected electrons is specific to an element, the identity of the element as well as electronic transitions can therefore be determined.

XPS measurements were acquired with a Kratos AXIS Ultra X-ray photoelectron spectrometer (Kratos Analytical Ltd., UK) using a monochromatic Al Kα x-ray source at

1486.7 eV, oriented at 35° relative to the sample surface. Low-resolution survey spectra were acquired between 0 eV and 1000 eV binding energies with 1 eV steps. High- resolution spectra were collected for O 1s (531 eV), N 1s (398 eV), C 1s (285 eV), Si 2p

(99 eV) and Au 4f7/2 (84 eV) peaks with pass energy 20 eV and 0.1 eV step size. The XPS

60 binding energies were calibrated with respect to the peak position of the C 1s peak at 285 eV. The sample chamber was maintained at ~ 5 x 10-9 Torr. A low-energy electron flood source was utilized for charge compensation. Data analyses were performed using the

Kratos Vision data reducing processing software (Kratos Analytical Ltd.) and Casa XPS

(Casa Software Ltd., v2.3.15). Peak areas were determined using a Shirley background subtraction and were corrected by the appropriate relative sensitivity factors to obtain elemental composition.

3.5.6 Contact Angle Goniometry

Contact angle goniometry offers information relating to the meso-scale homogeneity of a modified surface. In this process, a drop of liquid is placed upon a surface and, using a video camera and imaging software, the angle of contact between the surface and the outside of the drop (θC) is measured. Depending upon the free energy at the surface, liquid and vapor interfaces (γSL, γSV and γLV), the drop will either wet the surface or form a bead, and the surfaces are considered hydrophilic (θC < 90°) or hydrophobic (θC > 90°), respectively. Chemical heterogeneity for a mixed SAM can be assessed by the difference of its contact angle from the values for the individual adsorbates.

The static contact angles of silane-functionalized surfaces were determined with an

Attension contact angle goniometer (Biolin Scientific, Stockholm, Sweden) using the sessile-drop method. Approximately 2 μl drops of water were placed on the substrate and the left and right contact angles were measured after two seconds, once the drop had stabilized. Baselines were automatically determined unless mismatches were clearly obvious, in which case manual baselines were drawn. Averages were taken over at least 5 random areas on single-silane and co-adsorbed silane surfaces. For gradient surfaces,

61 averages were taken over three spots at each distance interval, one at the center and one each 3 mm to the left and the right of center.

3.5.7 Radial Distribution Function

As a measure of two-dimensional order, the radial distribution function (RDF) determines the probability of finding the center of particle i at a given distance r from the center of a neighboring particle. RDFs (g(r)) were calculated using a custom MATLAB

(MathWorks, USA) code taking the form

푁 1 푁(푟 ) (3.6) 𝑔(푟) = ∑ 푖 푁 푛2휋푟푖(푑푟푖) 푖=1 where N(r) represents the number of particles within an annulus of width dr and n is the overall surface density of particles over the image with area A (n = N/A).27 See Appendix

B for code. The primary peaks (maximum g(r)) represent the most probable interparticle separations and were chosen to evaluate the global structure of AuNP assemblies.

Statistical data were generated from at least five SEM micrographs for each pH/ionic strength combination and averaged to produce plots of g(r) vs. interparticle separation.

3.5.8 Voronoi Tessellation

Voronoi tessellation can provide insight into the local structure of an assembly. For this process, cells are created around each particle where the vertices correspond to the centers of triangulation with two neighboring particles and the edges bisect the mid-points between particle pairs.36 The cells indicate regions where all points are closer to a particular particle center than any other. A close-packed structure will produce cells that are regular hexagons, while a random configuration consists of polygons with various numbers of edges, edge lengths and vertex angles. Therefore, statistics on these polygons can provide

62 useful information for characterizing the structure of particle assemblies and determining the extent of 2D order.

To support previous structural analysis, Voronoi tessellation diagrams of AuNP assemblies were created using a custom MATLAB code (see Appendix B). To mitigate artifacts due to edge effects, particle data from the perimeters of the images (10% width and 10% height) were omitted and only the inner portions were analyzed. The diagrams and their relevant statistics (cell count, number of edges per cell, edge length, etc.) were generated from at least five SEM micrographs for each pH/ionic strength combination.

CHAPTER 4

RESULTS & DISCUSSION:

4. PH AND IONIC STRENGTH MODULATED GOLD NANOPARTICLE ASSEMBLY

The simple deposition of charge-stabilized gold nanoparticles onto aminosilane

derivatized silicon substrates is investigated as function of solution pH and ionic strength.

The nanoparticles are characterized by their size distribution, solution stability and

electrokinetic properties. The resulting two-dimensional assemblies were assessed by their

particle surface coverage, interparticle separation and lateral organization. As a result,

optimal processing parameters are described below for obtaining monolayers of gold

nanoparticles with varying degrees of surface coverage and two-dimensional arrangement.

4.1 Gold Nanoparticle Assembly

Figure 24 summarizes the colloidal self-assembly process and demonstrates the

structural uniformity of AuNPs achieved across large areas. In brief, native oxide silicon

(Si/SiO2) wafers were modified with 3-aminopropyltriethoxysilane (APTES) self-

assembled monolayers (SAMs) to generate positively-charged sites for the electrostatic

assembly of negatively-charged AuNPs (11.4 ± 1.0 nm) stabilized by either citrate or 3-

mercaptopropanesulfonate molecules (Au-Cit and Au-MPS, respectively). AuNP solutions

were made by redispersing concentrated AuNPs in either citrate/phosphate (pH 2.4 – 8.1;

pKa = 3.13, 4.76, 6.40, 7.20) or bicarbonate/carbonate (pH 9.1 – 10.6; pKa = 10.33) buffers

in order to maintain constant ionic strength (0.1 – 10 mM) while varying solution pH. The

64 use of buffers was chosen over titration with HCl or NaOH26, 32 since adding different amounts of strong acid or base is required to achieve various pH values and therefore gives rise to inconsistent ionic strengths across a broad pH range. The APTES-functionalized substrates (Si/APTES) were subsequently incubated in aqueous AuNP solutions with pH values ranging from 3 – 10 and ionic strengths of 0.1 – 10 mM to produce AuNP assemblies of various particle density, interparticle separation and arrangement. The adsorption process proceeded for approximately 16 h, which is sufficient time to allow maximum particle coverage.25 Upon completion of AuNP deposition, the substrates were removed from solution, thoroughly rinsed and sonicated in deionized water to remove weakly bound particles and blown dry in a stream of nitrogen. By following this procedure, we are examining only AuNP assemblies that are dry and strongly bound to the surface.

Figure 24. (a) Schematic illustration of AuNP self-assembly process and (b) SEM micrographs displaying uniform, large area coverage for Au-Cit NPs deposited at pH ≈ 5.6 and I = 1 mM.

Table 7. Structures, pKa values and chemical species for citrate and MPS stabilized AuNPs and Si/SiO2 surfaces modified with APTES.

Molecule Structure pKa Species

H3Cit 3.13 (pKa1) – 129 H2Cit Citrate 4.76 (pKa2) HCit2– 6.40 (pKa3) 3– Cit

MPS-H MPS 130 2.90 MPS–

+ NH3 APTES 23, 26, 93 7.5 NH2

4.2 Acid/Base Chemistry

During self-assembly, negatively-charged AuNPs electrostatically bind to a

Si/APTES surface through the protonated amine groups. The extent of protonation and thus electrostatic attraction is reflected by the pKa values of the functional groups on the substrate and particles, i.e. the negative logarithm of the acid dissociation constants (pKa =

– log Ka), which are provided in Table 7. To recall from Section 2.4.3, pKa can be related to pH by the Henderson-Hasselbalch equation

[퐴−] (2.10) 푝퐻 = 푝퐾 + log ( ) 푎 [퐻퐴]

– and therefore, the pKa identifies the pH where the concentrations of HA and A are equivalent. For example, the pKa of APTES grafted to Si/SiO2 is approximately 7.5, i.e.,

+ the pH where [NH3 ] = [NH2]. When pH < 7.5, the majority of APTES molecules are

+ protonated ([NH3 ] > [NH2]) while for pH > 7.5, the neutral species dominate ([NH2] >

+ + – [NH3 ]). Furthermore, knowing that Ka = [H ][A ]/[HA] and taking into account the mass

+ balance of all species (e.g., [APTES] = [NH3 ] + [NH2]), the fraction α of charged APTES molecules on a surface can be calculated from the pKa and the pH of the solution as

[퐻+] 1 (4.1) 훼 + = = 푁퐻3 + 푝퐻−푝퐾 [퐻 ] + 퐾푎 1 + 10 푎

The fractions for all species of a molecule can be determined in similar fashion and must sum up to unity (see Appendix A for derivations). The ionization profile of APTES in Figure 25a (green lines) shows a rapid decrease in 훼 + between pH 6 – 9, where the 푁퐻3 amine groups convert entirely from protonated (cationic) to deprotonated (neutral) moieties. Consequently, the particle-surface attraction and thus density of adsorbed AuNPs

+ should decrease through this range due to the diminished number of –NH3 sites.

Figure 25. (a) Ion speciation plots for citrate (blue lines) and MPS ligands (red lines) along with Si/APTES surfaces (green lines). The dotted line represents α = 0.50 which correlates to the pKa values for each equilibrium. (b) Mean charge 푍̅ of chemical species for citrate, MPS and Si/APTES molecules.

In concert, changes in pH will also alter the charge-charge repulsion between functionalized AuNPs. As pH rises, an increasing fraction of ligands on the AuNPs deprotonate and become negatively charged, as seen in the charge distributions in Figure

25b. The mean charge 푍̅ of a molecule is determined by summing the products of the fractions of all ion species and their charges at a given pH. For all citrate, MPS and APTES species, the mean charges are calculated as

̅ − ( ) 2− ( ) 3− (4.2) 푍퐶푖푡 = 훼퐻2퐶푖푡 ∗ −1 + 훼퐻퐶푖푡 ∗ −2 + 훼퐶푖푡 ∗ (−3)

푍푀푃푆̅ = 훼푀푃푆− ∗ (−1) (4.3)

푍̅ = 훼 + ∗ (+1) (4.4) 퐴푃푇퐸푆 푁퐻3

For example, MPS molecules bound to AuNPs (red lines) behave as monoprotic acids. They are mostly deprotonated (anionic) when pH > 2.9, bearing up to a single negative charge per molecule (푍̅ = -1). On the other hand, citrate molecules (blue lines) are polyprotic and 푍̅ decreases monotonically down to -3 over pH 2 – 8. In addition, citrate molecules are known to adsorb as multilayers around AuNPs due to hydrogen bonding.131

Therefore, above pH 3.7, Au-Cit NPs should have higher charge densities than Au-MPS

NPs. As a result, Au-Cit NPs are anticipated to have stronger interparticle repulsion

(greater stability) and greater attraction to charged APTES surfaces (higher surface coverage). Moreover, the mean charge distributions reveal that the greatest absolute charges for AuNPs and Si/APTES lie between pH ≈ 3 – 7, i.e., above the pKa’s of Au-Cit and Au-MPS and below the pKa of Si/APTES. Therefore, in this pH range, interparticle repulsion and particle-surface attraction are optimized.

Furthermore, three main pH regimes exist for the interactions of AuNPs and

Si/APTES, which were previously illustrated in Figure 16 (Section 2.4.3). To recall, at low

68 pH (< 4), protonation minimizes charge repulsion among the particles and maximizes the density of charged amino groups on the surface. The lack of surface charge on the particles causes them to aggregate and weakly bind to the highly-attractive surface. On the other hand, at high pH (> 8), deprotonation maximizes the number of negative charges on the particles but significantly decreases the charges density of the surface. Consequently, the particles strongly repel one another and weakly bind to the surface, therefore few or no particles adsorb to the surface. At pH values in between these extremes (4 – 8), a balance of interparticle repulsion and particle-surface interaction exists to afford a dense coverage of isolated AuNPs.

4.3 Electrostatics

In addition to pH, the ionic strength of a solution of AuNPs has a profound effect on their self-assembly onto functional surfaces. According to the DLVO theory,118-120 an increase in ionic strength screens the charges surrounding the nanoparticles, thus shortening the Debye length κ-1 of the electric double layer and ultimately decreasing interparticle separation r. The Debye length (in meters) is calculated from the relation

(4.5) −1 휀푟휀0푘퐵푇 휅 (푚) = √ 2 3 2푁퐴푒 퐼 ∗ 10 where εr and ε0 are the relative and vacuum permittivities, respectively, kB is the Boltzmann constant, T is the absolute temperature, NA is Avogadro’s number, e is unit charge and I is ionic strength in mol/L (Equation (2.17). The dimensionless Debye screening parameter

κa (or a/κ-1) is used to universally compare particles of various radii and ionic environments.27-29, 41 For colloids with κa ≫ 1, the Debye length is much smaller than the radius a, and the particles come into near contact due to weak repulsion (hard interaction).

On the other hand, when κa ≤ 1, the Debye length is on the same order or larger than the radius and the particles are repelled from one another, although some overlap exists among their double layers (soft interaction).41 Thus, modulation of ionic strength can effectively tune the interactions among colloidal particles and their subsequent self-assembly onto surfaces. In this work, the ionic strengths of AuNP solutions are pre-determined primarily by the ion composition of the buffers into which they are dispersed.

4.4 Colloidal Stability of AuNP Solutions

As a demonstration of stability, Figure 26 shows AuNP solutions as a function of pH and ionic strength within 30 minutes after mixing. Both Au-Cit and Au-MPS NPs show good stability above pH 5 for I = 1, 3 and 5 mM, while for solutions below pH 5 and above

3 mM, AuNPs begin to aggregate and blue shift in color. Eventually, over the course of hours to days, AuNPs at high ionic strength and low pH precipitate out of solution.

Figure 26. Solutions of Au-Cit and Au-MPS NPs with increasing pH at I = 1, 3 and 5 mM. At low pH and high ionic strength AuNPs begin to aggregate as seen by the blue-shifting in color.

4.4.1 UV-vis Spectroscopy

Initially, the relative stability of the AuNP solution as a function of pH and ionic strength was considered, which is macroscopically assessed via UV-vis spectroscopy.

Figure 27 displays example spectra for Au-Cit and Au-MPS solutions for various pH values and ionic strengths of 1 mM and 5 mM (additional spectra are provided in Appendix A).

Figure 27. UV-Vis spectra for Au-Cit (a, c) and Au-MPS NPs (b, d) at various pH and ionic strengths of 1 mM and 5 mM.

A maximum peak near λSPR = 520 nm corresponds to the local surface plasmon resonance

(SPR) mode of small isolated AuNPs33, 132 and is maintained for nearly all pH/ionic strength combinations for Au-Cit and Au-MPS NPs. The absorption maxima for Au-Cit

NPs intensify with increasing ionic strength while those for Au-MPS NPs remain consistent. As particle aggregation occurs, the SPR peak broadens and the maximum at

600 nm increases, as seen with Au-MPS NPs at 5 mM/pH 3.3.

Furthermore, Figure 28 displays peak wavelengths and absorbance ratios for Au-

Cit (a, c) and Au-MPS (b, d) solutions as a function of pH for various ionic strengths. The ratio of absorbances at 520 nm and 600 nm (Rabs = A520/A600) is used to qualitatively

132-133 evaluate the stability of AuNP solutions. For Rabs ≥ 3.5, AuNPs are well dispersed and stable against aggregation; between 2.0 and 3.0, they are well dispersed but eventually aggregate over time. As Rabs approaches zero, the AuNPs destabilize and precipitate out of solution. Between pH 3 – 10, consistent values of λSPR ≈ 520 nm and Rabs ≥ 2.5 indicate stable solutions of isolated AuNPs. For Au-Cit, Rabs increases with pH as a result of the rising number of negative charges at the NP surfaces. In addition, a greater positive slope results from increasing the ionic strength up to 10 mM. This suggests that NP stability is more sensitive to changes in pH where there is a higher degree of charge screening. On the other hand, Rabs is nearly constant (slope ≈ 0) for Au-MPS at all combinations except for 5 mM at pH ≤ 5.5 where Rabs begins to decline. Here, instability results from the reduced number of negative charges due to low pH and the diminished electrostatic screening due to higher ionic strength. Furthermore, the post-derivatization of Au-Cit NPs with MPS have shown to reduce NP stability, as evidenced by red-shifting and attenuation of the SPR

134 peak. The difference in slopes for Rabs between Au-Cit and Au-MPS may be attributed to the charge characters and pKa’s of their respective ligands. As seen in Figure 25b, the mean charge for MPS is mostly constant at –1 for pH > 3 while the mean charge for citrate steadily decreases across pH 2 – 7. Thus, the solution stability of the AuNPs is reflective of their mean charges over a given pH range.

Figure 28. Top: Wavelengths at extinction maxima for AuNPs as a function of solution pH at various ionic strengths: (a) Au-Cit and (b) Au-MPS. The dotted line represents λSPR = 520 nm. Filled symbols signify AuNP solutions made with citrate/phosphate buffers while open symbols denote the use carbonate buffers. Bottom: Absorbance ratios (Rads = A520 / A600) as a function of solution pH at various ionic strengths: (c) Au-Cit and (d) Au-MPS. The colored lines are meant to guide the eye. 4.4.2 Zeta Potential

In addition, zeta potentiometry provides insight on the charge character of AuNPs and their stability in solution. When κa ≳ 0.5, the surface charge density σ is related to the zeta potential ζ via119

휀휀 푘 푇 푍̅푒휁 4 푍̅푒휁 (4.6) 휎 = 0 퐵 휅 [2푠𝑖푛ℎ ( ) + 푡푎푛ℎ ( )] 푍̅푒 2푘퐵푇 휅푎 4푘퐵푇 where κ is the inverse Debye length and 푍̅ is the mean charge of the ligands at a given pH, as previously described (Equations (2.16 and (4.3). Figure 29 summarizes the zeta potentials and the calculated surface charge densities as a function of pH for various ionic

73 strengths. The magnitudes of the zeta potentials, |ζ|, for AuNPs (Figure 29a-b) at nearly all pH values and ionic strengths are above 30 mV (except Au-MPS/5 mM below pH 4), which indicate colloidal stability.32 This observation, though, does not ensure stability over time since AuNP solutions at the lowest pH values and high ionic strength (e.g., Au-Cit/10 mM and Au-MPS/5 mM) demonstrate aggregation over the course of a few hours to several days, as seen by color transitions from red to purple to blue (see Figure 26).

In general, as solution pH increased, |ζ| rose due to an increasing fraction of deprotonated anions at the AuNP surface (e.g., citrate or sulfonate) and surrounding the

AuNP (e.g., citrate, phosphate, carbonate and OH–),25, 32 thus increasing the overall surface charge density and interparticle repulsion. For Au-Cit NPs, |ζ| exhibited an increase with ionic strength at a given pH value, with the exception of 10 mM solutions above pH 5

(Figure 29a). This observation suggested that at a high enough ionic strength, stability of

Au-Cit NPs as a function of pH begins to diminish. Contrary to the aforementioned trend,

|ζ| for Au-MPS NPs decreased with ionic strength at a given pH value (Figure 29b). This behavior was expected since larger ionic strengths screen charges more effectively and subsequently reduce |ζ|. The difference in |ζ| trends between Au-Cit and Au-MPS NPs can be explained by the nature of the ligands. MPS molecules covalently bind to AuNPs and form a single ligand layer. Consequently, the maximum σ for Au-MPS NPs is fixed and will primarily respond to the ionic environment of their respective buffers. Also, layers of short-chain mercaptoalkanesulfonates are prone to disorganization on AuNPs, thus leading to low surface coverage135 which decreases σ and |ζ|. Citrate molecules, on the other hand, interact with AuNP surfaces through electrostatic charges and form multilayers though hydrogen-bonding.131 As a result, the surface charge density is dynamic – it depends upon

74 the solution pH as well as the equilibrium of citrate molecules at the surface and in the solution. Therefore, at higher ionic strengths, the surface density of citrate molecules rises, thereby increasing σ and |ζ|. In addition, the higher magnitudes and steeper slopes of σ for

Au-Cit NPs (Figure 29c) are attributed to their greater mean charges (|푍̅| = 0 – 3) at a given pH compared to those of Au-MPS NPs (|푍̅| = 0 – 1) (refer to Figure 25b).

Moreover, the zeta potentials of both types of AuNPs formed “s”-shaped curves that appear to flatten out near the middle of the pH ranges at each ionic strength, thus suggesting their correlation to the strength of the buffer in which the AuNPs are dispersed

– since buffers are most resistant to change in the middle of their respective pH ranges, the zeta potentials will behave similarly. Furthermore, decreasing the ionic strength of the

AuNP solutions affords steeper slopes of the zeta potentials due to lower buffering strength

(i.e., greater changes over a given pH range). In conclusion, Au-Cit and Au-MPS NPs demonstrate greater stability and higher charge densities at higher pH values but show opposing trends when adjusting ionic strength. This will facilitate dense, isolated AuNP assemblies to a positively-charged surface, which will tend to destabilize (aggregate) at high ionic strength.

Figure 29. Particle charge data for 11 nm AuNPs as a function of pH at various ionic strengths (I = 0.1 – 10 mM). Top: Zeta potentials for (a) Au-Cit NPs and (b) Au-MPS NPs. The error bars represent the standard deviations of at least three measurements. Bottom: Charge densities for (c) Au-Cit NPs and (d) Au-MPS NPs. Filled symbols signify AuNP solutions made with citrate/phosphate buffers while open symbols denote the use carbonate buffers. 4.5 Assembly of AuNPs

As an example of the surface assembly, Figure 30 summarizes the AuNP structures as a function of pH at low ionic strength. Here, AuNPs were deposited from 3 mM solutions ranging from about pH 4 – 8. When pH is below the pKa of APTES (< 7.5), –

+ NH3 moieties dominate the APTES surface coverage (Figure 25), thus rendering a surface

6 + 2 with a highly positive charge density of approximately 1 – 2 x 10 NH3 /μm as determined from XPS (see Experimental section). When considering the cross-sectional area of an 11.4 nm AuNP, this density provides approximately 100 – 200 binding sites available to each

76 particle. At the same time, AuNPs become increasingly charged with higher pH, and as a result, a high degree of interaction between the particles and surface affords dense AuNP coverage. Alternatively, when pH > pKa ≈ 7.5, –NH2 moieties dominate and the surface charge begins to neutralize. Despite the high fraction of negatively charged AuNPs, particle-surface interactions are reduced and AuNP coverage decreases significantly.

Figure 30. SEM micrographs of AuNP assemblies at various pH values with I = 3 mM: (a) Au-Cit and (b) Au-MPS. As pH increases, AuNPs become more negatively charged while Si/APTES becomes less positively charged resulting in lower particle density. Trends in AuNP coverage are displayed in Figure 31a-b, demonstrating high density around pH 3 – 4 which steadily decreases to about pH 7 – 8, after which a sharp

+ transition occurs between pH 7.5 – 9.5. This range is about half the width of the NH3 ↔

NH2 transition for APTES (pH 5.5 – 9.5), suggesting that even a half-charged surface is capable of facilitating high coverage from stable AuNP solutions. Bhat et al. observed a similar trend for small Au-Cit NPs deposited onto amine-functionalized silicon surfaces.23

They rationalized that the narrower pH transition is due to the disparity between the sizes

+ of AuNPs and –NH3 sites, i.e., as particle size increases, the inflection points of the curves

+ will shift to higher pH relative to the surface pKa since fewer –NH3 groups are needed to achieve 50% surface coverage.

Figure 31. Particle coverage for (a) Au-Cit and (b) Au-MPS as a function of pH for I = 0.1 – 10 mM and (c) their respective pH inflection points as a function of ionic strength. The dashed vertical lines in (a) and (b) represent the inflection points for each curve. The solid gray line in (c) represents the pKa of APTES at a given ionic strength. The curves and inflection points were obtained by fitting the data in (a) and (b) with a Boltzmann sigmoidal function. In addition, changes in AuNP assembly while altering ionic strength were observed.

When increasing ionic strength of the AuNP solutions and holding pH constant, the particle

Debye lengths are shortened and interparticle separation is reduced. This behavior is reflected in Figure 32, where interparticle separation at pH ≈ 5.6 decreases as ionic strength

78 increases from 1 – 10 mM (Au-Cit, (a)) or 0.1 – 5 mM (Au-MPS, (b)). This pH range is ideal since it renders AuNPs highly stable in solution across most ionic strengths and promotes full protonation of APTES surfaces. At lower ionic strengths, the interparticle repulsion is sufficiently high to promote the assembly of isolated particles, while at higher ionic strength, the electric double layer becomes thin and particle clusters begin to form, consistent with solution stability verified by UV-vis data.

Figure 32. SEM micrographs of (a) Au-Cit and (b) Au-MPS NPs (a = 5.7 nm) assembled at pH ≈ 5.6 with I = 0.1 – 10 mM. As ionic strength increases, particle separation decreases and eventually leads to aggregation. Ideal κa values are calculated based upon ionic strength for each AuNP solution. As a result of decreased interparticle separation, the densities of AuNP assemblies increase with higher ionic strength. Figure 31 also summarizes the number and fractional coverage of (a) Au-Cit and (b) Au-MPS assemblies as a function of pH and ionic strength.

The plots reveal a general increase in AuNP density achieved by increasing ionic strength over pH 3 – 10, with coverage decreasing in more alkaline conditions. At pH > 7.5, the

+ AuNP coverage becomes significantly reduced due to the small fraction of –NH3 sites.

The changes in coverage with respect to pH were quantitatively assessed by the inflection points in the particle coverage curves (Figure 31c), which were obtained by taking the best

79 fit the data using a Boltzmann sigmoidal function. The pH values at these inflection points resemble the apparent pKa of APTES at the given solution conditions. For Au-Cit assemblies progressing from 1 mM to 10 mM, coverage steadily declines between pH 3 –

8 and the inflection points linearly shift to higher pH values (7.5 – 9.5), correlating fairly well to the pKa of APTES. This shift is expected since increasing ionic strength will

136 increase the apparent pKa of a cationic acid. Inflection points for Au-MPS assemblies behave very similarly up to 3 mM, but afterwards they begin to decline due to solution destabilization. An inflection point for the 0.1 mM curve could not be determined due to its narrow pH range (4.9 – 6.5) which falls below the pKa of APTES. Additionally, it should be noted that a moderate degree of uncertainty lies within the determination of the inflection points due to the lack of data points at high pH where the NP densities approach zero, but this does not significantly affect the observed trends. Thus, it is revealed that stable solutions of Au-Cit and Au-MPS NPs across a wide pH range produce assemblies whose densities follow a pattern similar to the ion speciation behavior of APTES surfaces.

4.6 Two-dimensional Structures of AuNP Assemblies

In addition to changes in NP density, variation of pH and ionic strength also affects the local structures of AuNP assemblies, which is summarized in Figure 33. Assemblies of

Au-Cit and Au-MPS NPs were assessed from SEM micrographs and categorized as structures containing isolated particles, clustered particles or mixtures of isolated and clustered particles with or without fused particles. The underlying micrographs provide visual examples of relevant structures. The estimated boundaries between structures are similar between Au-Cit and Au-MPS. Assemblies from both Au-Cit and Au-MPS NPs demonstrate structural transformation from isolated particles to clusters/aggregates when

80 ionic strength is increased at a given pH. For example, at pH ≈ 4 Au-Cit structures change from isolated particles to a mixture of isolates and clusters to clusters and fused particles at ionic strengths of 3, 5 and 10 mM, respectively. Au-MPS assemblies show similar transitions but at lower ionic strengths, thus reiterating the diminished stability of Au-MPS

NPs to higher ion concentrations. Since Au-MPS solutions were not made above 5 mM, no particle fusion was observed at low pH. Therefore, from these diagrams, we can conclude that assemblies of well-dispersed isolated AuNPs can be best obtained above pH

4 and low ionic strengths (≤ 5 mM).

Figure 33. Structural diagrams of AuNP assemblies at varying pH and ionic strength: (a) Au-Cit and (b) Au-MPS NPs. The yellow lines represent estimated boundaries between different structures. The underlying SEM images provide visual examples of relevant structures. 4.6.1 Radial Distribution Function

Although microscopic methods (e.g., SEM and AFM) can visually provide a qualitative assessment of nanoparticle structures, more quantitative methods are required to evaluate the effects of particle-particle interactions on both global (average) and local

(nearest-neighbor) structures. Numerous studies have generated two-dimensional radial distribution functions g(r) to statistically analyze the global structure of nanoparticle

81 assemblies.27, 31, 34, 41-42 In this process, the local surface density of particle centers

(extracted from micrographs) are calculated and normalized by the average surface density.

Thus, g(r) provides the probability of finding neighboring particles whose centers are separated by a specific distance r.

As an example, the plots in Figure 34 display g(r) for assemblies of Au-Cit and Au-

MPS NPs deposited at pH ≈ 5.6 and various ionic strengths. Additional g(r) plots for other pH values are provided in Figure 67 and Figure 68 of Appendix A. The peaks in g(r) provide a wealth of information on the structure of colloidal self-assembly. First, the number of peaks signifies the range of particle interaction within the assembly, i.e., the more peaks, the longer the range of interaction. As interparticle separation increases, the features dampen while g(r) approaches unity. In Figure 34a, we observe large primary peaks (r1) along with small secondary peaks (r2) for Au-Cit (1 – 10 mM) and Au-MPS (0.1

– 3 mM) assemblies, which suggests a high degree of short-range order and some extended-

34, 42 range order (see Figure 71 in Appendix A for plots of r2 vs. pH). These features are consistent with prior reports of various nanoparticle assemblies, e.g., 13 nm Au-Cit NPs on Si/APTES27, 10 nm Au-Cit NPs on Au/octanedithiol28 and 116 nm latex NPs on mica.34

Alternatively, assemblies produced from unstable AuNP solutions (e.g., Au-MPS/5 mM) are prone to aggregation which results in the growth of peaks near r = 2a (i.e., minimal interparticle separation) and the reduction of peaks at extended range. The trend of less surface structure with increasing ionic strength (or κa) has also been observed in Brownian dynamics simulations on the assembly of charged particles.42, 44

Figure 34. (a) plot of g(r) vs. r for assemblies of Au-Cit and Au-MPS deposited at pH ≈ 5 with I = 0.1 – 10 mM (a = 5.7 nm). The vertical line represents the center-center spacing for touching AuNPs (r = 11.4 nm). The arrows point to the approximate locations of secondary peaks (r2). Additionally, g(r) is plotted against r/r1 for (b) Au-Cit and (c) Au-MPS. The overlap of the curves demonstrates the consistency of the adsorption mechanism across all ionic strengths used. Second, the height and width of the peaks describe the extent and the dispersion in g(r) at a given separation. For example, the primary peak for Au-Cit at 1 mM is taller than that of Au-MPS by approximately 9% (Figure 34a), indicating greater order of Au-Cit NPs within the first shell of neighboring particles. In fact, this difference grows as ionic strength increases from 1 mM to 5 mM, thus further illustrating the greater structural integrity of

Au-Cit assemblies in a given ionic environment. In addition, the primary peaks for Au-Cit and Au-MPS have widths of ~20 nm which relate to size dispersion34 of the AuNPs (a =

5.7 ± 0.5 nm). Third, the existence of peak-splitting beyond the primary peak qualitatively suggests the presence of hexatic or crystalline structures.38, 42, 45 For stable assemblies of

Au-Cit and Au-MPS, no peak-splitting is observed which implies that these structures are

83 liquid-like in the dried state, thus demonstrating consistency with two-dimensional RSA assembly of colloids.27-29, 34, 41-42

Lastly, the position of the primary peak r1 indicates the predominant interparticle separations of AuNP assemblies, which steadily decrease as ionic strength increases, as anticipated from DLVO theory.120 The combination of a large primary peak and a shallow minimum near 1.5r1 is in good agreement with RSA simulations of adsorbed colloids with

“soft” interactions, i.e., when κ-1 ≳ a.34, 41, 43 Furthermore, when g(r) for each ionic strength is normalized by r1 (Figure 34b-c), the plots overlap one another. This demonstrates that universal spatial distributions are achieved for Au-Cit and Au-MPS NPs within I = 0.1 –

10 mM and that the same mechanism governs their assembly regardless of ionic strength.27

Moreover, the experimental r1 values closely agreed with the estimated particle separations

(r0) calculated from NP density for most pH/ionic strength combinations (see r1 vs r0 plots in Figure 72 in Appendix A). This demonstrates the good predictability of interparticle separation from the NP density, which itself, can be estimated from pH, ionic strength and particle size.

Figure 35 summarizes the mean interparticle separations for Au-Cit (a) and Au-

MPS (b) assemblies averaged over at least five micrographs for all pH/ionic strength combinations. As pH rises, r1 for both Au-Cit and Au-MPS assemblies increase due to greater interparticle repulsion. The same result is obtained when increasing ionic strength.

The dotted lines denote the expected separations r’ in solution for 11.4 nm AuNPs, which are twice the effective NP radius, i.e.,

−1 푟’ = 2푎푒푓푓 = 2(푎 + 휅 ) (4.7)

For example, 11.4 nm AuNPs in a 1 mM solution yield κ-1 = 9.5 nm and r’ = 30.4 nm.

Interestingly, calculated values of r1 begin to increasingly deviate from expected separations as ionic strength decreases. For example, the separations for Au-Cit NPs near pH 4 are only underestimated by 2% at 10 mM but are overestimated by 43% at 1 mM.

33 Jiang et al. also noticed larger differences between r1 and r’ for assemblies of 13 nm Au-

Cit NPs on Si/APTES when ionic strength decreased from 16.6 mM to 0.5 mM at constant pH (they observed r1 > r’ for all I). They suggested that the disparity in interparticle separations for particles in solution versus adsorbed particles is due to the alteration of the shape and charge distribution of the double layer caused by contact of the AuNPs with the underlying positively-charged substrate. The larger discrepancy with decreasing ionic strength may result from the overlap of electrical double layers between soft particles at

29, 34, 41, 43 low ionic strengths. Furthermore, our data shows that r1 > r’ primarily when I ≥

3 mM and pH > 7 and that r1 < r’ mostly when I ≤ 5 mM and pH < 7, thus demonstrating a dependence upon pH that was not accounted for in the model by Jiang et al. This dependence is rationalized as the reduction of r1 when pH drops and interparticle repulsion decreases; conversely, when pH rises, interparticle repulsion increases and r1 lengthens.

In addition, standard deviations in r1 for AuNP assemblies become larger when pH

≥ 7 or at low particle density (e.g., Au-MPS/0.1 mM). As pH increases, AuNP density decreases while the interparticle repulsions increase steadily. Therefore, with decreasing coverage, interparticle repulsions become less influential on the spatial organization of

AuNPs and pH becomes more responsible for variations in r1 at a given ionic strength.

Furthermore, the large deviations in r1 at lower coverage provide evidence that adsorbed

AuNPs do not rearrange into spatially uniform monolayers, thus demonstrating that the

85 observed adsorption process is random and the particle-surface interactions are strong, as the RSA model predicts.29, 34-42

Figure 35. Average center-center particle separation r1 for (a) Au-Cit and (b) Au-MPS NPs as a function of pH at various ionic strengths. The dotted lines represent the expected interparticle separation r’ (r’ = 71.5 nm for Au-MPS/0.1 mM – not shown for clarity). The second vertical axis displays r1 scaled by the particle radius a. Filled symbols signify AuNP solutions made with citrate/phosphate buffers while open symbols denote the use carbonate buffers. For particle deposition regulated by RSA, the surface coverage θ follows a universal trend for all κa and is calculated27, 29 from:

푎 2 (4.8) 휃 = 휃푗푎푚 ( ) 푎푒푓푓 where aeff = r1/2 and in this study a = 5.7 nm. The surface coverages for Au-Cit and Au-

MPS NPs in Figure 36 were calculated using the r1 values from Figure 35 and plotted

86 against κa. Additionally, plots of θ vs. pH reveal the same trends (inverse) as Figure 35

(see in Figure 70 Appendix A). Generally, when κa ≫ 1, the surface coverage is constrained by the jamming limit, θjam = 0.547, while for small κa, interparticle repulsions

27, 29, 41 dominate and the surface coverage is well below θjam. The data in Figure 36 demonstrate that for I ≥ 3 mM, the calculated surface coverage closely follows the theoretical coverage θmax where aeff is approximated by a hard-sphere model for charge-

29, 119 saturated colloids (see Appendix A for derivation of aeff for hard-spheres). The data shows that θ and θmax correspond better around pH 4 – 8 where interparticle repulsion and surface attraction are well balanced. For lower ionic strengths, θ is slightly larger than θmax, which is a common occurrence at low κa values29, 34, 39, 43 and might indicate that the interparticle repulsions are overestimated. Again, this is likely due to electric double layer overlap at low ionic strengths.

Figure 36. Maximum surface coverage θ as a function of κa for Au-Cit (filled symbols) and Au-MPS NPs (open symbols) for various pH/ionic strength combinations. The solid line represents the theoretical 29 coverage θmax based on an effective hardsphere model with charge saturation and the dashed line represents the physical jamming limit, θjam = 0.547

4.6.2 Voronoi Tessellation

From the radial distribution functions calculated above, we found that the structures of AuNP assemblies are liquid-like at best, in agreement with RSA. This implies that these assemblies have a certain degree of randomness to their local structures, which was characterized by Voronoi tessellation of particle centers. The furnished statistics provided useful information for characterizing the structure of particle assemblies and determining the extent of 2D order.

Examples of Voronoi diagrams for Au-Cit and Au-MPS assemblies at pH ≈ 5.6 and

I = 0.1 – 10 mM are presented in Figure 37a. The color scale differentiates the number of edges n for each cell: six-sided cells (n = 6) are white and correlate to ideal close-packed structures while cells that are not six-sided (n ≠ 6) are colored, signifying “defects” in an ideal crystal structure. Occurrences of cells with nine or more edges (n ≥ 9) are few and therefore are treated as one statistic. The fraction of cells fn with n edges is a useful tool for describing the geometry of particle assemblies. Figure 37b compares the distributions in fn for Au-Cit and Au-MPS assemblies (colored bars) and RSA configurations (horizontal bars). In the latter case, Hinrichsen et al. simulated RSA configurations of hard disks at the jamming limit and revealed that fn is centered about n = 5, 6 and 7 with a normal distribution, contributing to approximately 24%, 50% and 22% of the polygons,

36 respectively (f5,6,7 ≈ 0.96 total). They concluded that the configurations were randomly packed and lacked any long-range order (i.e., liquid-like). For our AuNP assemblies, fn is distributed similarly to RSA, but a fraction of n = 6 cells is reallocated to smaller and larger cells. This trend is more pronounced with increasing ionic strength, particularly for Au-

MPS, and suggests degradation in local structure of the assemblies, which is a result of the

88 large extent of aggregation due to increased charge screening. Alternatively, fn distributions for Au-Cit assemblies at I = 1 – 10 mM correlate rather well to RSA simulations for all n, thus confirming the liquid-like structures of the assemblies from stable AuNP solutions.

For Au-MPS assemblies, it is evident that a structural transition occurs somewhere between

1 mM and 3 mM, but no major changes in local order can be distinguished between 0.1 mM and 1 mM. Additionally, f6 values correlating to transitions between crystalline (f6 ≥

0.98), hexatic (0.98 > f6 ≥ 0.75) and liquid (f6 < 0.75) phases have been reported for spherical diblock copolymer assemblies at various annealing temperatures.137 From these boundaries, it is apparent that RSA configurations (and consequently AuNP assemblies) are well below the hexatic/liquid transition and are incapable of forming highly-ordered structures.

Figure 37. (a) Voronoi tessellation diagrams for Au-Cit and Au-MPS NPs assembled at pH ≈ 5.6 and various ionic strengths. (b) The fractional distribution fn of Voronoi cells with n edges for Au-Cit (solid bars) and Au-MPS (striped bars) at pH ≈ 5.6. The error bars represent the standard deviations in fn from at 36 least five images. The horizontal bars represent the expected RSA distribution of hard disks at θjam.

Furthermore, the effect of pH on f6 at each ionic strength is evaluated in Figure 38.

The data suggest a mild to strong influence of pH on f6, depending upon the ionic strength of the solution as well as the surface chemistry of the AuNPs. For Au-Cit assemblies

(Figure 38a), f6 is mostly consistent across pH 3 – 7 when I = 1 – 10 mM and decreases quickly above pH 7. However, when I > 5 mM, f6 decreases across pH 7 down to pH 3 due to the destabilizing effects of both low pH and high ionic strength. Alternatively, f6 values for Au-MPS assemblies (Figure 38b) are smaller than those for Au-Cit assemblies at each ionic strength and are more pH sensitive when I ≥ 3 mM. These behaviors coincide well with their respective trends in solution stability (Figure 28) and particle coverage (Figure

31) between pH 3 – 10. Similar to the results in Figure 37, the values of f6 are lower for

AuNP assemblies at various pH/ionic strength combinations than for RSA simulations of hard disks36 (dashed lines), thus confirming their optimal structures to be liquid-like.

Furthermore, the decline of f6 at high pH values is a result of sub-monolayer coverage due to decreasing particle-surface interaction. Hence, a correlation can be made between the charge state of the surface (pH/pKa) and the structure of the particle assembly. Therefore, to optimize structural order, it is imperative to maximize surface attraction in addition to interparticle repulsion.

Additionally, Figure 38c reveals the pH values where f6 is maximized for Au-Cit and Au-MPS assemblies, indicating the approximate pH that produces the most locally- ordered structures for each ionic strength. This result suggests that AuNP assemblies are most ordered somewhere between pH 4.4 – 6.4 for Au-Cit and pH 4.9 – 7.8 for Au-MPS when I = 0.1 – 10 mM. Thus, Voronoi analysis reaffirms the ideal parameters for generating assemblies of Au-Cit or Au-MPS NPs with predictable coverage and optimized structure.

Figure 38. Fractions of 6-sided Voronoi cells, f6, as a function of pH at I = 0.1 – 10 mM for (a) Au-Cit and (b) Au-MPS. The dashed line represents f6 = 0.504 for an RSA configuration. (c) The pH values at maximum f6 versus ionic strength for Au-Cit and Au-MPS assemblies.

CHAPTER 5

RESULTS & DISCUSSION:

5. SURFACE CHEMISTRY REGULATED ASSEMBLY OF GOLD NANOPARTICLES

Herein, processes are described for obtaining monolayers of gold nanoparticles

with varying degrees of surface coverage and two-dimensional arrangement on surfaces

passivated by silanes of mixed functionalities. The functional surfaces were evaluated for

surface energetics and surface composition. The AuNP assemblies supported by these

surfaces were assessed for particle coverage, interparticle separation and 2D structural

order. The processing parameters and results are described in detail below.

5.1 Mixed Silane Surfaces for the Assembly of Gold Nanoparticles

The self-assembly of buffered Au-Cit NPs on mixed silane surfaces followed the

same procedure as those on APTES-only surfaces from Chapter 4, holding pH constant

and, in a few instances, adjusting ionic strength. The deposition of mixed silanes onto

silicon substrates, though, was slightly different. In brief, native oxide silicon (Si/SiO2)

wafers were modified with self-assembled monolayers (SAMs) of 3-

aminopropyltriethoxysilane (APTES), n-alkylsilane (4 – 18 carbons; trichloro-,

trimethoxy- or triethoxy- head groups) or a combination of the two to generate surfaces of

varying surface charge densities. The silane-functionalized substrates were subsequently

incubated in buffered AuNP solutions to produce assemblies of various particle density,

interparticle separation and arrangement. The adsorption process ensued for approximately

16 h, after which the substrates were removed from solution, thoroughly rinsed and sonicated in deionized water to remove weakly bound particles and blown dry in a stream of nitrogen. By following this procedure, we are examining only AuNP assemblies that are dry and vary in binding strength to the surface.

5.2 Characterization of Mixed Silane Surfaces

5.2.1 Co-adsorbed Mixed Silanes Self-assembled Monolayers

The process for the co-adsorption of amino- and alkyl-terminated organosilanes is nearly identical to the process for only APTES surfaces. The only difference is the composition of the adsorbate solution, where the silanes are mixed to specific molar ratios of aminosilane (χAS) with a total silane concentration of 43 mM (1% v/v). See Section 3.2.2 for solution recipes and processing details. The concept is depicted in

Figure 39. After functionalization, the mixed-silane substrates were subsequently characterized for surface energetics and surface chemistry.

Figure 39. Schematic representations for tuning AuNP density and structure via modulation of APTES surface concentration: (top) an increase in surface charge and particle-surface interaction with increasing concentration aminosilane molecules (green); (bottom) a decrease in particle-surface interaction with dilution of APTES concentration with alkylsilane molecules (red). Ideally, a specific concentration range of aminosilane molecules will bind AuNPs while allowing in-plane lateral mobility (shaded yellow). 5.2.1.1 Surface Energy

Contact angle goniometry was utilized to assess the surface energetics of the mixed organosilane films as discussed in Section 3.5.6. Images and data for water contact angles of variably functionalized surfaces are shown in Figure 40 and Table 8. The static contact angles of organosilane SAMs on Si/SiO2 demonstrate increasing hydrophobicity (lower surface energy) with increasing carbon chain length, which can be attributed to the greater van der Waals attraction between aliphatic chains and consequently tighter packing of the adsorbed molecules.65 Additionally, the size of the silane head group also influences the

95 molecular packing – bulkier head groups (e.g. alkoxy vs. chloro) restrict the packing density of adsorbed silanes, which reduces the overall van der Waals interactions and leads to less ordered SAMs. Also, due to inductive effects, the more electronegative chlorine atoms would render the head groups more reactive. Thus, a trichlorosilane would ideally be capable of a more ordered and more hydrophobic surface than and trialkoxysilane of the same carbon chain length at a faster rate. On the other hand, trialkoxysilanes are less sensitive to humidity and react in a more controllable manner.138 Furthermore, the terminal functionality has a great influence on the surface interaction. In Table 8, the first three molecules (APTES, BTMS and F3PTMS) have the same backbone length (three carbons) but different terminal functional groups (–NH2, –CH3 and –CF3, respectively) also show the same trend. The decreased surface energy between the amino and alkyl silanes is due to the decrease in polarity of the terminal groups; the decreased surface energy of the trifluoroalkyl silane over the alkyl silane results from the greater repulsive interactions of

139 the –CF3 versus –CH3 groups.

Table 8. Static contact angles of organosilane SAMs on Si/SiO2 with varying carbon chain lengths and terminal functionalities. Averages and standard deviations are provided from at least five separate measurements. Wide ranging values demonstrate the variability in the preparation of these surfaces.

Molecule APTES F3PTMS BTMS PTES OTCS DTCS OTS Si/SiO2 Si/SiO2 (clean) (UVO) Aliphatic 3 3 4 5 8 12 18 -- -- carbons Terminal –NH2 –CF3 –CH3 –CH3 –CH3 –CH3 –CH3 –O– –OH group Static C.A. (°) Literature 59 95 102 75 104 110 110 61 < 5 Min 58.1 66.2 62.4 74.6 102.6 110.5 108.3 52.0 5.0 Max 72.7 74.9 75.4 81.4 111.4 110.5 111.9 64.1 17.2 Average 65.5 70.6 68.9 77.3 107.9 110.5 110.1 57.9 9.1 Std.Dev. 0.9 1.0 0.6 0.3 0.5 -- 0.2 0.7 1.3

Figure 40. Images of water contact angles for (a) UVO-clean Si/SiO2 and SAMs of (b) APTES, (c) PTES and (d) OTCS. The images demonstrate the differences in surface energy among different functional groups (a – c) and different carbon chain length (c and d). The trend demonstrates increasing hydrophobicity and decreasing surface charge from left to right. Static contact angles for surfaces of APTES co-adsorbed with PTES and OTCS at various molar fractions are displayed in Figure 41. At very low molar fractions, the alkyl silane dominates the surface chemistry, as reflected by the contact angles which are very close to the theoretical values for the pure silanes. The curve for the OTCS mixture is much steeper due to the greater difference in contact angles (~ 30°) of pure silane compared to

PTES. As the molar fractions increase, the contact angles decrease towards the theoretical

97 value for pure APTES. For PTES, the decline is gradual for χAS = 0 → 1, while for OTCS, the curve sharply declines when χAS > 0.02. Deviations from the trends might suggest that the final surface chemistries are not completely predictable and do not necessarily equate the initial solution concentrations. This may be attributed to the differences in reaction rates between the two adsorbates, as noted for co-adsorbed silane surfaces of APTES and ethyltrimethoxysilane46, n-propyltriethoxysilane,47 octadecyltrimethoxysilane48 and (2- cyano)ethyltriethoxysilane.49 Additionally, differences in solvent compatibility between the adsorbates may also have an impact, as demonstrated by computations for mixed alkanethiol SAMs.91

Figure 41. Static contact angles for APTES surfaces co-adsorbed with PTES (red) and OTCS (blue) at various molar fractions of APTES. The contact angle monotonically decreases from χAS = 0 (alkyl only) to χAS = 1 (APTES only). The solid lines are meant to guide the eye to the trends. The dashed lines represent theoretical contact angles for pure silane SAMs: APTES (– · –), PTES (- - -) and OTCS (– – –).

Interestingly, the mixed SAMs of APTES and F3PTMS do not follow the same trend as the previous two. Instead, the trend is more parabolic, starting from contact angles of 66.2° for χAS = 0, up to 90.4° for χAS = 0.005 and back down to 63.5° for χAS = 1. This strange result may result from a chemical interaction between the terminal groups or a catalytic effect of one terminal group upon other silane molecules. The bottom image in

Figure 42 clearly demonstrates a concentration-dependent polymerization or aggregation of the silane mixtures, as the opacity of the solutions increase from χAS = 0 to 0.1. APTES molecules are capable of self-catalyzing the hydrolysis of the organosilanes due to the lone

70 pair of electrons of the terminal amine. The F3PTMS molecules may do the same given the three lone electron pairs of the –CF3 terminus. Unfortunately, evidence of reactions between –NH2 and –CF3 functionalities is lacking in the literature. Additional analysis of the precipitated solid, e.g. infrared spectroscopy or gel permeation chromatography, is crucial to identify the precipitate as either oligomerized APTES, F3PTMS or a combination of the two.

Figure 42. (Top) Static contact angles for co-adsorbed APTES and F3PTES surfaces at various molar fractions of APTES. The contact angle monotonically decreases from χAS = 0 (F3PTES only) to χAS = 1 (APTES only). The line is meant to guide the eye. (Bottom) Solutions of APTES + F3PTES after ~ 1 day, which increase in opacity with increasing χAS, up to 0.1. 5.2.1.2 Surface Chemistry

X-ray photoelectron spectroscopy was utilized to assess the chemical composition of the mixed organosilane SAMs as discussed in Section 3.5.5. The main peaks of interest are O 1s (531 eV), N 1s (398 eV), C 1s (285 eV) and Si 2p (99 eV). Survey and high- resolution spectra for an APTES SAM is displayed in

Figure 43. The Si and O peaks dominate the survey spectrum due to the signal of the underlying Si/SiO2 substrate in addition to the silane SAM. With either greater surface concentration or longer backbone of alkyl silanes, the C 1s ratio will increase. Additionally, a greater surface concentration of amino silanes will likewise enhance the N 1s ratio. The

100 ratio of these signals, as well as compared to O 1s and Si 2s, can provide some insight on the relative amounts of alkyl- or amino-silane molecules adsorbed to a substrate. Initially, it is assumed that the adsorptivity of the aminosilane and alkylsilane to the substrate was not altered and that the mole fraction was maintained at the surface.46

Figure 44 and Figure 45 show XPS data for APTES co-adsorbed with either PTES or OTCS, respectively. In general, the N 1s atomic concentrations increase with χAS with the exception of a few deviations. The green boxes signify the regions of steepest change in nitrogen content which may suggest a more pronounced kinetic dependence on adsorption due to a specific molar fraction of amino silane. For the OTCS mixture, this region is shifted to higher χAS than for the PTES mixture which might indicate that APTES adsorbs less competitively with OTCS than with PTES. The difference could be related to either the steric and inductive effects of the different head groups (SiCl3 vs Si(OCH2CH3)3), the different alkyl chain lengths or a combination of all the effects. Moreover, aminosilanes are known to adsorb faster than alkyl silanes in mixed-silane monolayers, which is attributed in part to the hydrophilicity of aminosilanes.46-48 Additionally, the data in Figure

46 demonstrates the inequality of χAS between the silane solutions prior to adsorption and the resulting surfaces. Such behavior has also been described in other mixed silane

47 91 48 experiments and molecular models. In this case, the surface χAS was calculated from the N 1s and C 1s data as such:

%퐶(APTES) = %푁(total) ∗ 3 (5.1)

%퐶(alkylsilane) = %퐶(total) − %퐶(APTES) (5.2)

%퐶(APTES)/3 (5.3) 휒 (surf.) = 퐴푆 %퐶(alkylsilane)/푛

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The carbon concentration for APTES is assumed to be thrice that of the nitrogen concentration (3 C atoms to 1 N atom per molecule) while the carbon concentration for the alkylsilane (with n aliphatic carbons) is the remainder from the total concentration. The surface χAS is then the ratio of carbon concentrations from the aminosilane and alkylsilane.

In the plot, the trends for both PTES and OTCS mixtures show enrichment of aminosilane on the surface compared to the initial solution χAS, demonstrating that APTES appears to adsorb more competitively than OTCS and even more so than PTES. This data is not entirely accurate, though, since the calculation assumes that there is no contamination and that all the silane head groups completely hydrolyze and do not contribute any carbon, both cases which are not very likely.

Figure 43. XPS spectra for APTES on Si/SiO2. Top: survey scan from 0 – 1200 eV; Bottom: high- resolution regions for Si 2p, C 1s, N 1s and O 1s with fitting and peak deconvolution.

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Figure 44. XPS data showing N-1s atomic % and APTES surface coverage () for mixed APTES + PTES SAMs. Additionally, experimental (■) and theoretical (- - -) nitrogen to carbon ratios are displayed. The green regions signify the steepest part of the experimental curves, i.e. the most significant change in composition. The solid lines are meant to guide the eye.

Figure 45. XPS data for mixed APTES + OTCS SAMs.

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Figure 46. Comparison of χ before (in solution) and after (on surface) adsorption of APTES mixtures AS with PTES (●) and OTCS (■). The dashed line represents 1:1 relationship. The orange curves represent the nitrogen to carbon ratios (N/C) for the experimental data (squares) and the theoretical values (dashed line), respectively. The experimental N/C was simply calculated as the ratio of atomic concentrations for N 1s and

C 1s peaks, while the theoretical N/C ratio was calculated from

휒 mol 푁 (5.4) 푁/퐶 (푡ℎ푒표푟. ) = 퐴푆 3휒퐴푆 mol 퐶 + 푛(1 − 휒퐴푆) mol 퐶 where every mol of APTES contributes 1 mol of N and 3 mol of C and each mol of alkyl silane contributes n mol of C, n being the number of aliphatic carbons. For the PTES mixture, the experimental and theoretical N/C ratios only seem to agree when χAS approaches 1 (i.e. pure APTES) while the trends seem to be more closely related for the

OTCS mixture than the PTES mixture. Additionally, the experimental N/C curve shifts to lower χAS for the PTES mixture as compared to the OTCS mixture, although to a greater extent than the theoretical curves suggest. There could be a number of explanations for discrepancies: 1) the N 1s concentration is inflated due to amino-silane molecules forming multilayers; 2) the signals for C 1s, O 1s and Si 2p are partially obstructed by N 1s signal

104 generated from the tops of the SAMs, especially in the case of multilayers; 3) the take-off angle – a larger angle will sample more of the subsurface while a small angle will sample more of the top layers; or 4) the presence of other nitrogen-containing molecules. The better fit of the data to theory for the OTCS mixture may suggest better quality films were produced than for the PTES mixture.

Thus, the XPS data suggests that OTCS forms better quality mixed-silane films with APTES than with PTES, despite the chemical similarity between APTES and PTES.

As expected, the contact angle data additionally demonstrate greater heterogeneity in surface energetics (which may or may not be desirable depending on the application) for the OTCS mixture over the PTES mixture mainly due to the greater difference in alkyl chain length (and consequently total van der Waals interactions) and the greater packing density for smaller head groups. To fortify these arguments, it is essential to analyze analogous APTES mixtures with varying head group chemistries (e.g. trichloro, trimethoxy, triethoxy and alkyl-alkoxy) and carbon chain lengths (n = 2 – 18), such as pentyltrichlorosilane and octyltriethoxysilane.

5.2.2 Gradient Mixed Silane Self-assembled Monolayers

Unfortunately, the fabrication of co-adsorbed silane surfaces is a serial process and is therefore time-consuming to arrange a statistically-relevant set of samples with a discrete number of concentrations. Also, inconsistencies arise when handling numerous substrates thus increasing the likelihood of empirical error. Therefore, it is advantageous to create a single substrate with a continuous set of APTES concentrations, which is attained through molecular gradients. Several methods can be employed to deposit gradient silane SAMs, such as lateral vapor diffusion23, 50-51, 57 and controlled-rate infusion (CRI)52-54, as described

105 in Chapter 2. In this work, gradients were fabricated via CRI using the setup illustrated in

Figure 10. Particularly, a clean silicon wafer was positioned vertically inside an empty syringe which was attached to a programmable pump. The silane solution was injected into the reaction vessel at a predetermined rate. Once the solution front reached the top of the wafer, the reaction was terminated and the substrate was quickly rinsed of excess silane solution and subsequently sonicated to remove physisorbed silane molecules. After annealing the substrate was used either for AuNP adsorption or surface characterization

(refer back to Section 3.2.3 for complete details). After functionalization, the mixed-silane substrates were subsequently characterized for surface energetics and surface chemistry.

The characterization of these surfaces is discussed in the following sections.

5.2.2.1 Surface Energy

Contact angle goniometry was utilized to assess the surface energetics of the mixed- silane films formed by CRI. Static contact angles (θc) were determined for gradient surfaces of either PTES or OTCS backfilled with APTES (PTES→APTES or OTCS→APTES) at various relative distances (xr), i.e. the distances traveled from the beginning of the gradients compared to the total length of the substrate. Figure 47 portrays contact angles of water droplets at various distances for OTCS→APTES surfaces. Going down the length of the substrate, the contact angle decreases and the water droplet increasingly wets the surface due to greater interfacial energies. This clearly demonstrates that the concentration profile

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Figure 47. Images of water contact angles for OTCS gradients backfilled with APTES at various relative distances from the starting edge of infusion (xr = 0.0) to the opposite end (xr = 1.0). The OTCS solution was infused at 1.0 ml/min. The trend demonstrates decreasing hydrophobicity (smaller contact angles) from left to right. goes from OTCS dominant to APTES dominant as xr goes from 0 to 1. The APTES dominant end displays contact angles characteristic of the pure silane while the OTCS end exhibits contact angles more than 15° lower than that of the pure silane. This indicates that: a) given the rate of infusion, the OTCS molecules do not have enough time to completely occupy the surface and leave open sites for either APTES molecules to fill or to be left devoid or b) fewer OTCS molecules are adsorbing with vertical alignments thus limiting their packing density. The PTES→APTES gradients display similar behavior although the profile is much shallower due to the small difference between the contact angles for pure

PTES (~ 75°) and pure APTES (~ 60°). As previously mentioned, this is a result the greater maximum contact angles (θc ≈ 108° vs. 75°) of the respective alkyl silanes due to the difference in aliphatic chain length (n = 8 vs. 5). Due to these facts, OTCS is a favorable

107 candidate over PTES for creating mixed silane surfaces with steeper and more noticeable gradient profiles.

Figure 48. Static contact angles for PTES gradient backfilled with APTES. The black lines represent the contact angles for APTES (- - -) and PTES (– · –) controls, respectively. The line is meant to guide the eye. The error bars show the standard deviations for three measurements taken at each distance. The data in Figure 48 demonstrates how the contact angles for PTES→APTES

(infusion rate of 1 ml/min) decreased almost linearly from the PTES end (xr = 0.0) to the

APTES end (xr = 1.0). The shallowness of the curve resulted from the small difference in maximum θc between PTES and APTES. Similar behavior is demonstrated by

OTCS→APTES mixed SAMs, as seen by the contact angles in Figure 49. Here, the effect of the infusion rate for is revealed by the slope of the curves – as the rate increased from

1.0 to 7.5 ml/min, the slopes became shallower, as validated in Figure 49b where the difference in contact angles (Δθc) at opposite ends of the substrate dramatically leveled off past 2.5 ml/min. Therefore, a suitable infusion rate must be slow enough to allow enough silane molecules to react with the surface but fast enough to create a slope in the profile and inhibit saturation of the infused silane across the entire length of the substrate.

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Figure 49. Static contact angles for OTCS gradients backfilled with APTES: a) contact angles after various rates (ml/min) of OTCS infusion. The black lines represent the contact angles for APTES (- - -) and OTCS (– · –) controls, respectively. The lines are meant to guide the eye. The error bars show standard deviations for three measurements taken at each distance; b) the change in contact angle as a function of infusion rate. In addition to infusion rate, the profile of the gradient can also be affected by the distance (lm) the meniscus is allowed to travel up the substrate before the reaction is terminated (refer to Figure 10). In the previous example, the solution front travels up to the very end of the substrate before it is removed and the reaction is stopped (lm = 1). Figure

50 reveals the effect of lm on the contact angle profile for OTCS→APTES. Infusions at 5.0 and 7.5 ml/min and full distances (lm = 100% of the substrate length, solid lines) exhibit results similar to Figure 49 while the same rates at shorter distances (lm = 70%, dotted lines) produce contact angle profiles that are longer (greater distance before the onset of

109 declination) and steeper (greater Δθc). The steeper slopes of shorter lm result from the reaction cutoffs occurring at shorter times and therefore leaving more of the substrates unmodified. Furthermore, the profiles slope rather than completely drop-off due to the concurrent deposition from the vapor phase above the solution meniscus (refer to Figure

74 in Appendix A). Additional data from more combinations of lm cutoffs and infusion rates are vital to substantiate the aforementioned trends.

Figure 50. Static contact angles for OTCS gradients backfilled with APTES: a) contact angles for infusion rates of 5 and 7.5 ml/min with full (filled symbols) and partial (open symbols) solvent fronts. The lines are meant to guide the eye. The error bars show the standard deviations for three measurements taken at each distance. The black lines represent the contact angles for APTES (- - -) and OTCS (– · –) controls, respectively; b) the change in contact angle as a function of solvent front for rates of 5 and 7.5 ml/min.

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5.2.2.2 Surface Chemistry

X-ray photoelectron spectroscopy was utilized to assess the chemical composition of the gradient organosilane SAMs in the same fashion as described in Section 5.2.1.2.

Peaks for O 1s, N 1s, C 1s and Si 2p photoelectrons were measured and averaged over three different spots at the same distance xr. Like the co-adsorbed mixed-silane SAMs in

Section 5.2.1.2, the Si and O peaks dominate the composition due to the signal of the underlying Si/SiO2 substrate in addition to the head groups of the adsorbed silanes. Again, the end of the substrate with the greater concentration of alkyl silane or amino silane had a larger signal for C 1s or N 1s, respectively. The comparison of these signals (N/C ratio), as well as O 1s and Si 2s, provides some insight on the relative amounts of alkyl- or aminosilane molecules adsorbed to a substrate.

Figure 51 shows XPS data for a PTES→APTES mixed SAM that was infused at a rate of 1 ml/min. In general, the N 1s atomic concentrations increase with xr. The N/C ratio follows the nitrogen concentration profile quite closely, with the exception of the first two data points, which is likely due to deficient carbon signals. Additionally, the third axis displays the calculated surface coverage of adsorbed APTES molecules, σAS. The coverage ranged from about 0.60 – 1.0 silanes/nm2, which appears to be low with respect to the footprint of 0.5 nm2 for alkoxysilanes71 (i.e. 2 silanes/nm2). This low value is not surprising, though, since van der Waals forces are weak among short-chain organosilanes which lead to large tilt angles and sub-optimal packing densities.65 Unfortunately, due to lack of resources, XPS data for OTCS was not obtained, although it would be expected to mirror the contact angle data. In brief, the XPS data helps to corroborate the findings from the

111 contact angle measurements demonstrating an increase in APTES coverage further away from the alkylsilane dominant ends of the gradients.

Figure 51. XPS data for PTES→APTES SAMs: N 1s atomic % and APTES surface coverage (red) and N/C ratio (green). The green regions signify the steepest part of the experimental curves, i.e. the most significant change in composition.

5.3 Effect Surface Chemistry on Nanoparticle Coverage and Structure

After fabrication, the mixed silane substrates mentioned above were decorated with

11 nm Au-Cit NPs by the simple incubation process described in Chapter 3. Images of the particle assemblies were subsequently taken via SEM. ImageJ was used to assess properties of the particles including count, size, position, area and circularity. Particle density

2 (NP/μm ) and area fraction were calculated and plotted against APTES molar fraction (χAS) for co-adsorbed silanes or relative distance (xr) for gradients. Custom Matlab code (see

Appendix B) was used to generate radial distribution functions (RDF) and Voronoi tessellation diagrams to analyze two-dimensional structural information of the particle assemblies.

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5.3.1 Nanoparticle Areal Density

5.3.1.1 Co-adsorbed Mixed Silane Surfaces

The coverages for AuNPs deposited onto PTES + APTES surfaces are presented in

Figure 52 as functions of χAS, with ionic strengths of 0.5 mM (●) vs. 3 mM (♦) (κa = 0.415 and 1.04). NP coverages are described by area density (Γ, NP/μm2) and average

27 interparticle separation (r0, nm), which is calculated by

−2 푟0(nm) = 1⁄√훤(nm ) (5.5)

Both plots demonstrate a monotonic decline in coverage as χAS drops from one to zero with steep declines at reduced χAS. Several main differences exist between the two conditions.

First, the higher ionic strength obviously results in greater particle coverage and closer particle separation. The predicted effective diameter is indicated by the dashed line.

Second, the onsets of rapid decline in particle coverage take place at χAS ≈ 0.0002 and 0.02, respectively, differing by nearly two orders of magnitude. This difference in coverage can be derived from either inconsistencies in the silane coverages between the two data sets or an effect of ionic strength on charged aminosilane molecules. Both sets of surfaces were created with an identical procedure and a consistent environment, so the former cause should have less influence. Also, the AuNPs were deposited at nearly the same pH (5.9 and

6.1, respectively). Therefore, ionic strength does appear to influence the physicochemical properties of the silane surfaces and consequently the manner of which AuNPs bind at certain χAS values. Different behavioral regimes exist for the mixed silane films depending upon the chain length, grafting density, charge fraction and the ionic strength of the AuNP solution.140 Similar to polyelectrolyte brushes, a greater ionic strength decreases the range and strength of the repulsive electrostatic interactions, while simultaneously increasing the

113 number of charged aminosilane molecules within the mixed silane film, which at a given

χAS leads to higher coverage and smaller particle spacings, which is observed for χAS >

0.005. It is possible in this case, that higher ionic strength results in a greater number of free ions available to associate with the protonated amines, thus limiting the number of charged binding sites accessible for incoming AuNPs.121 This concept, though, opposes the fact that the protonation of amines increases with ionic strength.124 To substantiate the observed trends, a more rigorous data set with several more ionic strengths should be examined.

Figure 52. Particle coverage data for Au-Cit NPs adsorbed onto SAMs of APTES mixed with PTES or OTCS as a function of APTES molar fraction (χ ): (left axis) NP density and (right axis) interparticle AS separation (r0). The blue and red curves demonstrate the added effect of ionic strength (● 0.5 mM vs. ♦ 6.7 mM) on the AuNP adsorption, while the blue and green curves demonstrate the effect of alkyl chain length (● 5 vs. ■ 8). The trendlines are meant to guide the eye. The dashed lines represent the effective AuNP diameters at a given ionic strength, i.e. the ideal interparticle spacing. The vertical dotted lines mark the onsets of rapid decline in particle coverage.

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Additionally, the effect of alkyl chain length in mixed monolayers on AuNP adsorption is also shown in Figure 52. The blue and green curves demonstrate the effects of chain length of the alkyl silane mixed with APTES (i.e., ● 5 vs. ■ 8 carbons). For χAS =

1, both curves show about the same density of about 1100 NP/μm2, which correlates to the theoretical r0 ≈ 30.7 nm for I = 0.5 mM. The PTES + APTES sample maintains a steady coverage down to χAS ≈ 0.0002 where is drops off quickly (i.e., the onset point). On the other hand, the coverage for OTCS + APTES steadily decreases with χAS and quickly drops off near χAS = 0.1, nearly three orders of magnitude higher than PTES. As mentioned when comparing PTES + APTES at different ionic strengths, inconsistencies in surface preparation is always a possible factor for describing differences in particle coverage. The great magnitude of the difference in this case, though, is convincing that alkyl silane affects the structure of the mixed silane film as well. This is corroborated by the XPS and contact angle data for the surfaces without AuNPs which show similar trends (refer to Section

5.2.1). Therefore, the resulting particle assemblies greatly reflect the structure and phase behavior of their supporting silane films. Since OTCS is more hydrophobic than PTES, there may be a greater amount of phase separation or even aggregation of the grafted silanes. Alternatively, the SEM images in Figure 53 demonstrate increased NP clustering when χAS < 0.06, which may indicate there are some regions where the aminosilane concentration is sufficient enough to bind AuNPs but low enough to reduce some of the total particle-surface attraction to allow in-plane mobility of the AuNPs, whereas above this threshold, the adsorbed particles are mostly isolated. This notion is also examined for

AuNP assemblies on gradient mixed silane films (see Section 5.3.1.2). To gain better insight of the trends, several more alkyl silanes with shorter and longer alkyl chains should

115 be analyzed. Additionally, the phase behavior and surface energetics should be further assessed via atomic force microscopy (AFM) and/or dynamic contact angle hysteresis.

Figure 53. SEM images of AuCit assemblies on SAMs of APTES mixed with PTES or OTCS: (top) PTES + APTES, I = 0.5 mM; (middle) PTES + APTES, I = 3 mM; (bottom) OTCS + APTES, I = 0.5 mM. 5.3.1.2 Gradient Mixed Silane Surfaces

In an effort to produce a continuous concentration gradient of AuNPs on a single substrate, monolayers of PTES or OTCS were created by CRI and subsequently backfilled by APTES (PTES→APTES and OTCS→APTES, respectively). AuCit NPs were successively adsorbed onto the surfaces (I ≈ 1.6 mM), and the NP densities and interparticle separations as a function of xr are revealed in Figure 54. The blue and green curves demonstrate the effects of chain length of the alkyl silane mixed with APTES (i.e., ● 5 vs.

■ 8 carbons), which in general, are fairly similar. Near xr = 1 (APTES only), both curves show about the same density of around 1300 – 1500 NP/μm2. Both curves decrease gradually with xr, although the PTES→APTES data has a greater slope and is not quite monotonic. As a result, the onset of declination is at a much larger xr than the

116

OTCS→APTES curve (approximately 0.73 vs. 0.38). Although, due to the spread in the

PTES→APTES data, its onset is not very precise, which makes it difficult to infer the cause of the discrepancy. If nothing else, it could simply be an artifact of processing, either with the silane films or from the AuNP solutions. To alleviate these uncertainties, more replications of this dataset along with the inclusion of organosilanes with different chain lengths and/or head groups would be favorable. Lastly, the trends for PTES→APTES and

OTCS→APTES agree well with their respective contact angle data (see Figure 77 in

Appendix A), thus demonstrating consistency between the micro- and nano- scales.

Overall, the data shows that gradients of PTES and OTCS mixed with APTES afford gradient AuNP assemblies that are mostly comparable at a given xr.

Figure 54. Particle coverage data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr): (left axis) NP density and (right axis) interparticle separation (r0). The blue and green curves demonstrate the effect of alkyl chain length (● 5 vs. ■ 8). The trendlines are meant to guide the eye. The dashed lines represent the effective AuNP diameters at a given ionic strength, i.e. the ideal interparticle spacing. The vertical dotted lines mark the onsets of rapid decline in particle coverage.

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In addition, the effects of infusion rate and meniscus advancement (lm) during infusion is revealed in Figure 55. Here, OTCS was infused at 5.0 and 7.5 ml/min while allowing the meniscus to proceed to either the full or partial (70%) length of the wafer. As explained by the contact angle data in Section 5.2.2.1, the faster infusion rate of 7.5 ml/min results in less adsorption of OTCS and allowing for more subsequent adsorption of APTES, thus leading to more immobilized AuNPs, although the differences are subtle. Both rates demonstrate gradually increasing particle density as xr increases, although the steepness of the curves are significantly more pronounced for the partially exposed substrates, particularly between xr = 0.6 – 0.8, i.e. where the infusion was terminated. The slope in this region, though, was still gradual due to successive vapor deposition, which ceased once the substrate was removed from the vessel. It is worth noting that the longer the substrate sits after infusion, the more OTCS vapor that deposits above the solution front and the trend becomes shallower. Therefore, the differences in density between the different rates of the partially exposed substrates could have resulted from slight differences in hold time instead of or in addition to a greater APTES/OTCS surface ratio. Ultimately, this data demonstrates that the extent and the shape of the particle adsorption trends can be tuned by adjusting silane infusion rate and the extent of solution exposure, with the latter seeming to have greater influence.

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Figure 55. Particle coverage data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with OTCS as a function of relative distance (xr): (left axis) NP density and (right axis) interparticle separation (r0). The blue and red curves demonstrate the effect of infusion rate (● 5 vs. ■ 7.5 ml/min) and the solid and dashed curves represent full and partial solution exposure, respectively. The trendlines are meant to guide the eye. The black dashed line represents the effective AuNP diameter at a given ionic strength, i.e. the ideal interparticle spacing. The vertical dotted lines mark the onsets of rapid decline in particle coverage.

5.3.2 Two-dimensional Structure of Nanoparticle Assemblies

As with the AuNP assemblies from Chapter 4, the data produced by radial distribution functions (g(r)) and Voronoi tessellations were calculated and analyzed to assess and quantify the two-dimensional structures of AuNP assemblies on mixed silane surfaces.

5.3.2.1 Co-adsorbed Mixed Silane Surfaces

In Figure 56 below, the 2D structural data for AuNP assemblies on PTES+APTES surfaces are presented as functions of χAS, for ionic strengths of 0.5 mM vs. 3 mM. Three plots for each sample set reveal several pieces of useful structural information. The top and

119 middle plots provide results from the radial distribution functions (g(r)), where r is the average interparticle separation, which was determined for the primary (r1), secondary (r2) and aggregate peaks (raggr). To recall, the primary and secondary peaks are the first and second largest maxima in g(r) for r > 2a, while the aggregate peaks are associated with maxima for r ~ 2a. Additionally, r0 is the interparticle separation calculated from the NP density (see Equation (5.5). Lastly, the aggregation ratio Gaggr = g(raggr)/g(r1) is used as a measure of 2D global aggregation.

The behavior of Au-Cit adsorption onto PTES+APTES surfaces is similar for both ionic strengths, where for χAS > 0.02, values for r1, r2 and Gaggr are nearly the same as those for pure APTES surfaces (dot/dash lines), while above 0.02, each increase notably. On the other hand, several main differences between the two data sets also exist. First, the minimum values for r1 and r2 are approximately 28 nm and 20 nm for 0.5 mM and 60 nm and 45 nm for 3 mM, which is in alignment with DLVO theory. Second, the upward trends for r1, r2 and Gaggr are considerably steeper for 3 mM and the curves appear to be more

“compressed”. Additionally, the Gaggr data shows that higher ionic strengths are more likely to produce aggregates. It is rather interesting, though, that for both ionic strengths, Gaggr peaks below the threshold of χAS ≈ 0.02 and then returns to baseline as χAS continues to decrease. This observation might suggest that at a certain χAS, there are sufficient APTES molecules on the surface to facilitate dense coverage of AuNPs but also few enough to lower the particle-surface attraction and allow in-plane rearrangement of the particles after adsorption. This may be why aggregation is notable at moderate χAS but then decreases as

NP coverage becomes less dense, as supported by the NP density data in Figure 52.

120

Furthermore, results from Voronoi tessellation data at the bottom of Figure 56 provide the fractions of Voronoi cells with six sides (f6) as well as those with five, six and seven sides (f5,6,7). In a highly-ordered structure, f6 would be very high, i.e. hexagonal or

137 crystalline (f6 ≥ 0.98). On the other hand, less-ordered structures, i.e. liquid-like, have a smaller f6 (< 0.75) and larger f5 and f7. At best, the AuNP structures approach the thresholds

36 for a liquid-like RSA arrangement, as indicated by the dashed lines for f6 (0.504) and f5,6,7

(0.964). The structures assembled from 0.5 mM solutions yield fairly constant values of f6 and f5,6,7 while those from 3 mM solutions decrease below χAS ≈ 0.02, indicative of structural degradation. Therefore, although adsorbed particles may gain some mobility below this threshold, other forces are too weak to induce in-plane ordering – most likely a sufficiently high particle volume fraction,38, 42 which is very difficult to achieve with

AuNPs due to limited colloidal stability.

In addition, the effect of substrate chemistry on AuNP structure is displayed in

Figure 57. Here, both PTES+APTES and OTCS+APTES supported assemblies deposited from 0.5 mM Au-Cit NP solutions (the PTES+APTES samples are the same as in Figure

56), and there are some noticeable differences. As previously mentioned, the structural data for PTES+APTES is fairly consistent across all χAS. Only for χAS < 0.02 do r1, r2 and Gaggr increase slightly, which signify some increase in interparticle spacing and a somewhat higher degree of aggregation. Furthermore, the f6 values from the Voronoi data show little change for all χAS, meaning that the local structure remains rather steady as well.

121

Figure 56. Structural data for Au-Cit NPs adsorbed onto PTES + APTES mixed monolayers with respect to APTES molar fraction (xAS) at ionic strengths of 0.5 and 3 mM: (top-left axis) interparticle separation (r), (top-right axis) separation divided by NP radius (r/a); (middle) ratio of g(r) of the aggregate peak to the primary peak and (bottom) fraction of edges (fn) for Voronoi cells. The trendlines are meant to guide the eye. The dashed line (---) represents the AuNP diameter (2a), i.e. the minimal hard-sphere spacing. The dot/dash line (– ⋅ –) represents values for xr = 1 (i.e., APTES only surfaces). The dashed lines in the Voronoi data represent the values from Hinrichsen et al.36 The dotted grey lines depict the onsets of significant structural change.

On the other hand, the g(r) data for OTCS+APTES is much less consistent, with fluctuating values for r1, r2 and Gaggr for χAS < 0.01. After gradually increasing, r1 and r2 begin to drop significantly for χAS < 0.04, which is a result of increased aggregation, as

122 supported by the Gaggr values, as well as decreased NP coverage (Figure 52). These issues are also likely responsible for the significant drop in f6 and f5,6,7 when χAS < 0.04. The reduction in NP coverage clearly stems from an insufficient surface concentration of

APTES molecules to facilitate a full monolayer of AuNPs (as supported by the XPS data in Figure 45). The increased aggregation, though, could either be a result of sufficiently weak particle-surface interaction strength to allow in-plane mobility or localized chemical heterogeneity of the surface, e.g. phase separation between alkyl and amino silanes or small islands of aminosilanes where several AuNPs preferentially adsorb to a confined area.

Chemical heterogeneity is a strong candidate due to the properties of the silanes used. PTES is structurally similar to APTES, thus rendering them quite compatible. The two molecules only differ by their end group: –CH2CH3 vs. –NH2, respectively. On the other hand, OTCS and APTES differ by end group (–CH3 vs. –NH2), alkyl chain length (7 vs. 3) and head group (–SiCl3 vs. –Si(OCH2CH3)3), thus making this mixed silane system more complex. Trichlorosilanes typically have faster rates of condensation than triethoxysilanes due to steric and inductive effects of the substituents,141 so for nearly equivalent concentrations of each in solution, OTCS will adsorb preferentially over

APTES. Therefore, as χAS approaches 0.50, OTCS is expected to dominate the surface composition more so than PTES, which is supported by the XPS data in Figure 44 (i.e. smaller N-1s composition). Alternatively, APTES is anticipated to react faster than PTES due to its slightly shorter alkyl chain, greater hydrophilicity and self-catalyzing nature.46-

48, 70 Hence, adsorbed APTES is still detectable, even at very low χAS.

123

Figure 57. Structural data for Au-Cit NPs adsorbed onto PTES + APTES and OTCS + APTES mixed monolayers with respect to APTES molar fraction (xAS). Ionic strength = 0.5mM for both data sets. 5.3.2.2 Gradient Mixed Silane Surfaces

The data in Figure 58 reveals some disparity in the structures for AuNP assemblies on mixed gradient films. Values for r1, r2 and r0 are similar for PTES→APTES and

OTCS→APTES except for xr = 0.2 – 0.6, inside of which minor increases are seen

PTES→APTES. For xr < 0.2, both gradients show increasing separations, indicative of

APTES concentrations too low to facilitate full monolayers of AuNPs. Furthermore, Gaggr

124 values for PTES→APTES hover mostly around 0.5, which reflect the small amount of aggregation present for all xr, which is also seen in the SEM images. A few instances at low xr (0.1 and 0.3) exhibit rather high amounts of aggregation which are likely due to small silane island formations. Since Gaggr is average for xr above and below these points, they are considered trend outliers. These deviations are not noticeable in the XPS or contact angle data and therefore are likely localized defects and are not consistent with the rest of the gradient. On the other hand, small Gaggr values reveal very little aggregation for

OTCS→APTES.

Moreover, the Voronoi data also confirms better structural order for

OTCS→APTES over PTES→APTES, as suggested by the overall greater f6 and f5,6,7

36 values, although both fall shy of the maximum RSA values (dashed lines). Decreasing f6 and f5,6,7 values suggest structural degradation for PTES→APTES and OTCS→APTES when xr < 0.4 and xr < 0.2, respectively. The difference between these structural thresholds is fairly different from one another, unlike those for co-adsorbed mixed silanes, which are very similar. Although, due to the spread in the PTES→APTES data, a distinct threshold is not completely evident and it is uncertain if the disparity is a consequence of dissimilar silanes interacting, AuNP interactions before immobilization or even an artifact of processing. Replicates of these data would be useful for better verification. Otherwise, the structural differences between the PTES→APTES and OTCS→APTES datasets are somewhat inconclusive.

125

Figure 58. Structural data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr).

126

CHAPTER 6

6. CONCLUSIONS

6.1 Effect of pH and Ionic Strength

In this study, commensurate particle and surface chemistries along with solution pH and electrolyte content were employed to approach AuNP assemblies with various surface coverage and 2D organization. The attractive interactions between AuNPs and

APTES-functionalized silicon were balanced by repulsive particle–particle interactions which resulted in assemblies of strongly bound AuNPs with defined particle spacing and arrangement.

The stability of Au-Cit and Au-MPS NP solutions was assessed by UV-Vis absorbance stability ratios and zeta potentials, which were monitored as pH increased from

3 – 10 for I = 0.1 – 10 mM. The data revealed that Au-Cit NPs were very solution stable within this range due to the rising number of negative charges of the citrate molecules surrounding the AuNPs while Au-MPS NPs were less stable due to comparably lower charge densities. Interestingly, for Au-Cit NPs, zeta potentials exhibited increases in magnitude when ionic strength was raised at a given pH value while the opposite trend occurred for Au-MPS NPs. The difference in these trends was attributed to the manner in which citrate and MPS molecules bind to AuNPs (electrostatic vs. covalent) and consequently how their surface charge densities change with an ionic environment

(dynamic vs. fixed). Additionally, steeper slopes in the UV-vis and zeta potential data at

127 high ionic strengths suggested that NP stability is more sensitive to changes in pH where there is a higher degree of charge screening. The determination of which pH/ionic strength regimes produce high charge densities gave indication to which combinations will afford dense assemblies of isolated AuNPs on positively-charged surfaces.

Assemblies of Au-Cit and Au-MPS NPs on Si/APTES surfaces were deposited at various pH/ionic strength combinations. SEM micrographs revealed that assemblies were densest around pH 3 – 4, although some aggregation was present. The density steadily decreased from pH 3 – 7, after which a sharp decline occurs, correlating to the pKa of

APTES. At higher pH values (> 7), surface coverage of AuNPs declined in correlation with the reduced number of binding sites on the APTES surface. Therefore, uniform assemblies of dense, isolated AuNPs were typically limited to deposition conditions which were mildly acidic (pH ≈ 6) and had low-moderate ionic strengths (I = 0.1 – 5 mM). Also, high ionic strengths screened many of the charges present on AuNPs resulting in assemblies not only higher in density but also contained small to substantial amounts of aggregation. In addition to solution environment, particle coverage and organization also showed a strong dependence upon the surface chemistry of the AuNPs – Au-Cit NPs were more charge- stable than Au-MPS NPs and therefore were more resilient towards variations in pH or ionic strength.

Minimum interparticle separations for AuNP assemblies extracted from maxima in the radial distribution functions were found to decrease with increasing ionic strength, as expected from DLVO theory. At high ionic strengths, interparticle repulsions were significantly reduced, thus resulting in minimal separations (i.e., clustering/aggregation).

Additionally, separations increased concomitantly along with pH, as predicted by the

128 trends in zeta potentials, from around 20 nm to over 30 nm. Interestingly, the calculated separations began to increasingly deviate from theoretical separations depending upon the solution environment; particularly, they were underestimated when I ≤ 5 mM and pH < 7 and overestimated when I ≥ 3 mM and pH > 7. These trends were also noticed when comparing fractional surface coverage to κa. To knowledge, the influence of pH upon these deviations has not been previously mentioned in literature. Furthermore, small secondary peaks in the radial distributions functions, along with lack of peak splitting, confirmed that the AuNP assemblies lacked any long-range order, consistent with RSA assemblies.

Lastly, Voronoi tessellations revealed that the local in-plane order of AuNP assemblies, as characterized by f6 values, generally decreased along with pH, although decreases were also observed at low pH values for high ionic strengths, which were more pronounced for Au-MPS NPs. It was further determined that the pH values for maximal order (highest f6) increased almost linearly with ionic strength for Au-Cit, whereas order leveled off for Au-MPS past I = 1 mM. Thus, order was optimized for AuNPs assembled from mildly acidic solutions with low-moderate ionic strengths. At these aforementioned conditions, the structures were mostly random and liquid-like, in good agreement with predictions for RSA.

Ultimately, a processing regime was laid out that afforded uniform assemblies of isolated AuNPs achieved through alterations of acid/base interactions and electrolyte concentration. In order to bolster the above trends, it is beneficial to replicate the datasets using more ionic strengths, within the thresholds of stability. Furthermore, the particle stabilizing ligands should contain the same terminal functionality (e.g., carboxylate) as to

129 more purely investigate the effects of electrostatically and covalently bound ligands on

AuNP stability.

Thus, it is evident that AuNPs assembled in these processing regimes were strongly bound to the surface and therefore lacked the in-plane mobility necessary for structural rearrangement into higher ordered configurations. To circumvent this issue, the interaction strength between the particles and the surface must be reduced. Outside of solution-based methods, this is achievable by either modifying the surface chemistry where the

AuNP/adsorbate interaction is inherently weaker or by reducing the number of available sites for particle binding.

6.2 Effects of Surface Composition

In this study, the surface chemistry of planar Si/SiO2 substrates was altered to modulate the attractive interactions between positively-charged surfaces and negatively- charged AuNPs. Mixed-silane SAMs of amino- and alkyl-silane molecules were fabricated in an attempt to decrease the overall surface charge density and thereby weaken the particle-surface interactions sufficiently to permit lateral rearrangement of adsorbed

AuNPs into structures of higher order than typical assemblies confined by RSA. Two main approaches for mixed amino- and alkyl-silane surfaces were employed: co-adsorption at varying molar fractions and concentration gradients by controlled-rate infusion sequential adsorption.

The co-adsorbed silane surfaces were made by mixing varying molar fractions of

APTES (χAS) with either PTES or OTCS. As expected, large static contact angles (θc) revealed increasing hydrophobicity (lower surface energy) with decreasing χAS (pure

APTES to pure alkyl silane). The increase in θc with decreasing χAS for APTES+PTES

130 and APTES+OTCS reflected the characteristic θc for the alkyl silanes with respect to the alkyl chain length. Furthermore, the rate of change in θc for APTES+PTES was quite steady for all χAS, while the rate for APTES+OTCS changed significantly between χAS =

0.02 – 0.03. This signifies a more distinct transition of surface character and might hint to a χAS where the adsorption kinetics of the mixture is considerably altered. Nitrogen concentration data from XPS also hinted that OTCS+APTES formed higher quality mixed SAMs due to closer fit to theoretical N/C ratios, despite the chemical similarity between APTES and PTES. Furthermore, APTES enrichment was greater for PTES mixtures and OTCS mixtures, suggesting that OTCS adsorbed more competitively with

APTES than does PTES.

The effects of silane chemistry and ionic strength were assessed for AuNPs assemblies on mixed silanes, and the results typically showed declining coverage at a certain threshold as χAS decreases. Au-Cit NPs assembled onto APTES+PTES and

APTES+OTCS produce similar maximum densities but the onset χAS of rapid coverage decline differed by nearly three orders of magnitude. Despite this, all datasets demonstrated increased NP clustering when χAS < 0.01, again indicating an energetic barrier where the particle-surface attraction is weakened enough to allow in-plane mobility of the AuNPs.

Moreover, aggregation increased and local order degraded more for APTES+OTCS than

APTES+PTES, which could be a result of greater chemical/structural incompatibility. To gain better insight of these trends, several more alkyl silanes with shorter and longer alkyl chains should be analyzed.

The effect of ionic strength was demonstrated by comparing AuNPs assembled on

APTES+PTES surfaces at 0.5 mM and 3 mM. The 3 mM samples produced denser particle

131 coverages which began to decline at a χAS nearly two orders of magnitude higher than for the 0.5 mM samples. This contradicted expectations for increased amine protonation and subsequent AuNP coverage from the higher ionic strength to yield an onset at a similar or lower χAS. It may be possible that the higher ionic strength solution has more free ions available to associate with the protonated amines, thus limiting the number of charged binding sites accessible for incoming AuNPs, although this contradicts the previous notion.

Additionally, higher ionic strength resulted in more aggregation and degraded local order, possibly suggesting that AuNPs gained in-plane mobility or demonstrate localized heterogeneity of the surface composition. To substantiate the observed trends, a more rigorous data set with several more ionic strengths should be examined.

Sequentially adsorbed gradient silane surfaces were made by depositing PTES or

OTCS via controlled-rate infusion and subsequently applying APTES to backfill the remaining surface vacancies. The surface characteristics and AuNP assemblies were analyzed on a single surface at certain distances relative to the beginning of the gradient

(xr). This allowed the silane fractions to be investigated as a continuum rather than a series of discrete concentrations and helped to minimize systematic processing errors. Gradients showed greater hydrophobicity at small xr (higher alkylsilane concentration) which progressed to become more hydrophilic with increasing xr (more aminosilane). Mixed silane gradients were compared by the effects of alkylsilane chain length, infusion rate and meniscus advancement.

First, the longer chain length of OTCS afforded steeper profiles in contact angles and APTES surface coverage with increasing xr than for PTES. The maximum APTES coverage, though, was about half the theoretical value, due to large tilt angles and sub-

132 optimal packing densities characteristic of short-chain organosilanes. Both types of gradients afforded comparable gradient AuNP assemblies whose coverages increased monotonically with xr. They also had similar primary and secondary interparticle separations, but PTES→APTES demonstrated considerably more aggregation than did

OTCS→APTES. Furthermore, better structural order was observed for OTCS→APTES compared to PTES→APTES, as suggested by the overall greater f6 and f5,6,7 values, although both fall shy of maximum theoretical RSA values. The trends in aggregation and order, though, began to decline at larger xr values for PTES→APTES than for

OTCS→APTES, a behavior that was not quite consistent with the results for co-adsorbed

PTES+APTES and OTCS+APTES, and it is uncertain if this disparity was a consequence of dissimilar silanes interacting, AuNP interactions before immobilization or even an artifact of processing.

Second, the rate of infusion affected the steepness of the gradient profile: a rate too fast or too slow resulted in a gradient dominant in either aminosilane or alkylsilane, respectively. Different infusion rates (1 – 7.5 ml/min) for OTCS→APTES yielded increasingly flat profiles in contact angle while AuNP coverage trends differed subtly.

Third, partial infusion (70% length of the substrate) resulted in steeper profiles in contact angle and AuNP coverage than with full infusion, particularly at slower infusion rates.

Thus, the extent and the shape of the particle adsorption trends was tuned by adjusting alkyl chain length, silane infusion rate or the extent of solution exposure, with the latter seeming to have greater influence. To fortify the observed trends and to alleviate uncertainties from processing, more replications of this dataset along with the inclusion of organosilanes with different chain lengths and/or head groups would be favorable.

133

CHAPTER 7

7. FUTURE WORK

The results reported herein have provided key information on the fundamental processes regulating the self-assembly of charged nanoparticles onto functionalized planar substrates.

However, there still remains questions unanswered and parameters unexplored that would improve the understanding of the chemistry and physics behind the particle-particle and particle-surface interactions that drive colloidal self-assembly.

1. To what extent does particle chemistry influence stability and adsorption?

While this question was partially addressed in this study by comparing

stabilizing ligands that were bound electrostatically (citrate) and covalently

(MPS), these molecules have different negatively-charged functionalities

– – (carboxylate (–COO ) vs. sulfonate (–SO3 )). To mitigate the effects of these

slightly different chemistries, it would be more appropriate for both to have the

same terminal functionality, such as carboxylates like citrate (HOC(COO–

– – )(CH2COO )2) and mercaptopropionate (HSCH2CH2COO ). Citrate is

generally used as a stabilizer simply because it is residual from AuNP synthesis.

Although, to make the ligands even more comparable, the molecules could even

have the same number of functional groups as to make the charge density per

molecule the same. Another route is to compare terminal functionalities alone,

where the rest of the molecules are the same (e.g. mercaptopropionate vs.

134

mercaptopropanesulfonate vs. mercaptopropanephosphonate). One last

constriction would be to ensure the lengths of the compared molecules are

nearly the same so that interparticle separation due to sterics plays a minimal

role.

2. What is the effect of particle volume fraction on AuNP assembly and order?

It is known from computer simulations that certain volume fractions of

nanoparticles in solution is required to obtain assemblies with a higher degree

of order than the liquid state, usually ≥ 0.001.38, 42, 45 When the volume fraction

is high enough, particles in solution are compressed to the point of “pre-

ordering” in solution and then deposited almost as a multi-particle entity. For

many AuNP systems, it is very difficult to achieve such volume fractions and

maintain stability. Infact, the volume fractions of AuNPs in this study were only

on the order of 10-5. Therefore, it would be extremely useful to utilize a ligand

and/or method to increase the volume fraction of AuNPs while maintaining

stability and a charged functionality. Consequently, more orderd AuNP

assemblies could be achieved even with strong particle-surface interactions.

Although, due to RSA, the final structure would more likely resemble a

collection of ordered domains. At this point, particle-surface interactions could

be optimized to permit 2D reorganization of particles into even higher-ordered

structures.

3. What is the dispersion of silanes in a mixed silane SAM?

While methods exist for achieving this, they were not performed in this study.

The truest approach would be to map out a sample with XPS or another surface

135

sensitive analysis. This would provide very accurate detail on the chemical

dispersion but would be very costly in time and resources. Another method is

to perform dynamic contact angle goniometry on mono- and bi-functional

surfaces and determine advancing and receding contact angles. This is done by

monitoring a drop of water (or other solvent) onto a surface and continually

adding (advancing) to determine wettability of the surface and then

subsequently withdrawing the water (receding) to determine adhesion between

the liquid and the surface (see Figure 73, Appendix A). The hysteresis is the

difference between the advancing and receding contact angles, and a larger

value is indicative of greater heterogeneity in the surface energetics and

therefore the chemistry as well. Furthermore, atomic force microscopy (AFM)

could also provide information on heterogeneity by comparing the roughness

of SAMs of mixed silanes to those of pure silanes, as well as assessing the

surface morphology for domains (i.e., aggregates and islands) of unmixed

silanes.

4. What is the adhesion force between the AuNPs and modified surface?

By determining the force of adhesion between AuNPs and silane surfaces, an

energetic barrier dividing particle mobility and immobility could be

ascertained. This could be accomplished by using an AFM tip to determine the

force required to move a single AuNP142 and then correlate that to the density

of aminosilanes on the surface. Then, a mixed silane surface could be fabricated

with the appropriate aminosilane density to afford the densest coverage of

136

AuNPs possible while also allowing in-plane particle mobility, which could

result in more highly-ordered AuNP assemblies.

5. What is the true pKa of aminosilane SAMs?

The pKa of a pure aminosilane such as APTES is around 10. But, when attached

to SiO2, it drops to around 7.5. Methods such as chemical force titration (CFM)

and contact angle titration can be employed to obtain an average pKa of a

surface modified with aminosilane93 or a mixture of amino- and alkyl-silane.

For CFM, a gold-coated AFM tip is modified with a hydroxy- or carboxyl-

terminated thiol which will electrostatically interact with aminosilanes.

Depending on the pH of a solution surrounding the modified surface, a fraction

+ of amines will be protonated (–NH3 ) or deprotonated (–NH2). Consequently,

+ the modified AFM tip will adhere to NH3 but not NH2), and the pKa of the

surface can be determined at the pH where the adhesion force is halfway

between that for a fully protonated and a fully deprotonated surface. The same

basis for titration can be employed with contact angles, where aminosilane

surfaces are wetted with drops of increasing pH and contact angles will

consequently increase as a result of deprotonation and loss of adhesion. Thus,

a steep change in contact angles will take place at a pH near the pKa of the pure

or mixed aminosilane SAMs. Therefore, silane surfaces can be fabricated with

a precise amount of particle-surface interaction.

6. What influence of ionic strength on the adsorption of AuNPs on mixed silanes?

As seen from the data in Section 5.3.1.1, the onset of rapid decline in particle

coverage occurred at higher χAS for a higher ionic strength. This is difficult to

137

rationalize since the ionic strength should really only alter the particle density

and spacing. To get a better grasp on this anomaly, it would be beneficial to

repeat the experiment with additional ionic strengths and ensure the consistency

among mixed silane surfaces. Furthermore, it would be enlightening to

investigate multiple ionic strengths on more than one mixed silane system (e.g.,

OTCS in addition to PTES).

7. What is the effect of temperature on nanoparticle adsorption and arrangement?

Increasing temperature of the AuNP solution during adsorption may help to

reduce the interaction energy between particle and surface and lead to in-plane

mobility. The particles along with the stabilizing ligands should be thermally

stable.

138

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APPENDICES

APPENDIX A

A. Additional Figures and Equations

Ionic Strength

Ionic strength is defined as

푛 1 (A.1) 퐼 = ∑ 푐 푧2 2 푖 푖 푖=1

where

ci = concentration of ion i (mol/L) zi = valence of ion i (+/– integer) ni = stoichiometric number of ion i (x or y in formula AxBy) αi = ion specie ratio

The ionic strength of citrate/phosphate buffers (sodium salts) with NaCl is calculated by:

1 2 2 2 (A.2) 퐼 = [(푛 + ∙ 푐 + ∙ 푧 + ) + (훼 − ∙ 푐 − ∙ 푧 −) + (훼 2− ∙ 푐 2− ∙ 푧 2− ) 2 퐻 퐻 퐻 퐻2퐶푖푡 퐻2퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐻퐶푖푡 퐻퐶푖푡

2 2 + (훼퐶푖푡3− ∙ 푐퐶푖푡3− ∙ 푧퐶푖푡3− ) + (푛푁푎+ ∙ 푐푁푎+ ∙ 푧푁푎+ )

2 2 + (훼 − ∙ 푐 − ∙ 푧 − ) + (훼 2− ∙ 푐 2− ∙ 푧 2− ) 퐻2푃푂4 퐻2푃푂4 퐻2푃푂4 퐻푃푂4 퐻푃푂4 퐻푃푂4

2 2 2 + (훼 3− ∙ 푐 3− ∙ 푧 3− ) + (푛 + ∙ 푐 + ∙ 푧 + ) + (푛 − ∙ 푐 − ∙ 푧 − )] 푃푂4 푃푂4 푃푂4 푁푎 푁푎 푁푎 퐶푙 퐶푙 퐶푙

151

1 2 2 2 = [(1 ∙ 푐 + ∙ 1 ) + (훼 − ∙ 푐 − ∙ −1 ) + (훼 2− ∙ 푐 2− ∙ −2 ) 2 퐻 퐻2퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐻퐶푖푡

2 2 2 ( 3− 3− ) ( + ) − − + 훼퐶푖푡 ∙ 푐퐶푖푡 ∙ −3 + 2 ∙ 푐푁푎 ∙ 1 + (훼퐻2푃푂4 ∙ 푐퐻2푃푂4 ∙ −1 )

2 2 2 + (훼 2− ∙ 푐 2− ∙ −2 ) + (훼 3− ∙ 푐 3− ∙ −3 ) + (1 ∙ 푐 + ∙ 1 ) 퐻푃푂4 퐻푃푂4 푃푂4 푃푂4 푁푎

2 + (1 ∙ 푐퐶푙− ∙ −1 )]

1 = [ 푐 + + (훼 − ∙ 푐 − ) + (훼 2− ∙ 4푐 2− ) + (훼 3− ∙ 9푐 3− ) 2 퐻 퐻2퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐻퐶푖푡 퐶푖푡 퐶푖푡

+ (2 ∙ 푐 + ) + (훼 − ∙ 푐 − ) + (훼 2− ∙ 4푐 2− ) 푁푎 퐻2푃푂4 퐻2푃푂4 퐻푃푂4 퐻푃푂4

+ (훼 3− ∙ 9푐 3− ) + 푐 + + 푐 − ] 푃푂4 푃푂4 푁푎 퐶푙

Solve for c + from pH and c from the specie ratios: H H3Cit

푝퐻 = −log (푐퐻+ ) (A.3)

−푝퐻 푐퐻+ = 10

푡표푡푎푙 푐 = 푐 + 푐 − + 푐 2− + 푐 3− (A.4) 퐻3퐶푖푡 퐻3퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐶𝑖푡

푡표푡푎푙 푐 = 푐 (훼 + 훼 − + 훼 2− + 훼 3− ) 퐻3퐶푖푡 퐻3퐶푖푡 퐻3퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐶푖푡

Substitute the above equation into Equation (A.2c and set the first occurrence of c + = c and second c + = c Na Na2HPO4 Na NaCl to obtain the final ionic strength equation:

1 (A.5) = [ 푐 + + 푐 (1 ∙ 훼 − + 4 ∙ 훼 2− + 9 ∙ 훼 3− ) + 푐 (2 + 1 ∙ 훼 − 2 퐻 퐻3퐶푖푡 퐻2퐶푖푡 퐻퐶푖푡 퐶푖푡 푁푎2퐻푃푂4 퐻2푃푂4

+ 4 ∙ 훼 2− + 9 ∙ 훼 3− ) + 2 ∙ 푐 ] 퐻푃푂4 푃푂4 푁푎퐶푙

Ion Speciation

Table 9 provides information on acid-base ion speciation for all ligand, adsorbate and buffer molecules used in our experiments. First, the acid-dissociation equilibria for each ith specie of a molecule with n acidic protons are expressed as

152

퐾 1 + −푖 퐻푛퐴 ⇔= 퐻 + 퐻푛−푖퐴

퐾 −푖 2 + −푖 퐻푛−푖퐴 ⇔ = 퐻 + 퐻푛−푖퐴

⋮

퐾푛 퐻퐴−(푛−1) ⇔ = 퐻+ + 퐴−푛 (A.6) and their respective rate constants (K1–Kn) are

+ − [퐻 ][퐻푛−1퐴 ] 퐾1 = [퐻푛퐴]

+ 2− [퐻 ][퐻푛−2퐴 ] 퐾2 = − [퐻푛−1퐴 ]

⋮

[퐻+][퐴−푛] 퐾 = 푛 [퐻퐴−(푛−1)] (A.7)

For each successive deprotonation, the ith specie loses one proton and decreases in charge by one. Lastly, we can show the sum of the concentrations of all of the species in solution as

− 2− −(푛−1) [퐻푛퐴]0 = [퐻푛퐴] + [퐻푛−1퐴 ] + [퐻푛−2퐴 ] + ⋯ + [퐻퐴 ] (A.8)

+ [퐴−푛]

– 2– As an example, citric acid (H3Cit) has four possible species (H3Cit, H2Cit , HCit and Cit3–) which results in three deprotonation equilibria, whose rate constants are expressed as

[ +][ −] 퐻 퐻2퐶𝑖푡 −4 (A.9) 퐾1 = = 7.41 x 10 [퐻3퐶𝑖푡]

[ +][ 2−] 퐻 퐻퐶𝑖푡 –5 퐾2 = − = 1.74 x 10 (A.10) [퐻2퐶𝑖푡 ]

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[퐻+][퐶𝑖푡3−] 퐾 = = 3.98 x 10–7 3 [퐻퐶𝑖푡2−] (A.11)

The total concentration of citric acid ([H3Cit]0) is equal to the sum of the concentrations of all the species in solution, i.e.

− 2− 3− [퐻3퐶𝑖푡]0 = [퐻3퐶𝑖푡] + [퐻2퐶𝑖푡 ] + [퐻퐶𝑖푡 ] + [퐶𝑖푡 ] (A.12)

Next, using this mass balance and the rate constant expressions above, the equilibria can be rewritten as

퐾 [퐻 퐶𝑖푡] [퐻 퐶𝑖푡−] = 1 3 (A.13) 2 [퐻+]

퐾 [퐻 퐶𝑖푡−] 퐾 퐾 [퐻 퐶𝑖푡] [퐻퐶𝑖푡2−] = 2 2 = 1 2 3 (A.14) [퐻+] [퐻+]2

퐾 [퐻퐶𝑖푡2−] 퐾 퐾 퐾 [퐻 퐶𝑖푡] [퐶𝑖푡3−] = 3 = 1 2 3 3 (A.15) [퐻+] [퐻+]3

By substituting specie concentrations for [H3Cit] and combining expressions, we obtain

퐾 [퐻 퐶𝑖푡] 퐾 퐾 [퐻 퐶𝑖푡] 퐾 퐾 퐾 [퐻 퐶𝑖푡] [퐻 퐶𝑖푡] = [퐻 퐶𝑖푡] + 1 3 + 1 2 3 + 1 2 3 3 3 0 3 [퐻+] [퐻+]2 [퐻+]3

퐾 퐾 퐾 퐾 퐾 퐾 = [퐻 퐶𝑖푡] (1 + 1 + 1 2 + 1 2 3) 3 [퐻+] [퐻+]2 [퐻+]3

[퐻+]3 + 퐾 [퐻+]2 + 퐾 퐾 [퐻+] + 퐾 퐾 퐾 = [퐻 퐶𝑖푡] ( 1 1 2 1 2 3 ) (A.16) 3 [퐻+]3

This new form now allows us to determine the fraction α of [H3Cit] solely as a function of pH (i.e., [H+] = 10–pH) and the rate constants:

+ 3 [퐻3퐶𝑖푡] [퐻 ] (A.17) 훼H3Cit = = + 3 + 2 + [퐻3퐶𝑖푡]0 [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

This process is repeated for each remaining specie, and the following fractions are obtained:

154

− + 2 [퐻2퐶𝑖푡 ] 퐾1[퐻 ] − (A.18) 훼퐻2퐶푖푡 = = + 3 + 2 + [퐻3퐶𝑖푡]0 [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

2− + [퐻퐶𝑖푡 ] 퐾1퐾2[퐻 ] 2− (A.19) 훼퐻퐶푖푡 = = + 3 + 2 + [퐻3퐶𝑖푡]0 [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

3− [퐶𝑖푡 ] 퐾1퐾2퐾3 3− (A.20) 훼퐶푖푡 = = + 3 + 2 + [퐻3퐶𝑖푡]0 [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

The above procedure is applied to all other acidic molecules and the results are summarized in Table 9.

155

Table 9. Acid/base speciation data for ligand, adsorbate and buffer molecules. Specie fractions are relative – to the total concentration of all related species. MPS = S(CH2)3SO3 .

Molecule Specie Ka {ref.} pKa Specie Fraction, α

[퐻+]3 Citrate H Cit {129} 3 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 퐾 [퐻+]2 (K ) H Cit– 7.41 x 10-4 3.13 1 1 2 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 퐾 퐾 [퐻+] (K ) HCit2– 1.74 x 10-5 4.76 1 2 2 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

3– -7 퐾1퐾2퐾3 (K3) Cit 3.98 x 10 6.40 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 [퐻+] MPS Au–MPS-H {130} + [퐻 ] + 퐾1

– -3 퐾1 (K1) Au–MPS 1.26 x 10 2.9 + [퐻 ] + 퐾1 [퐻+] APTES {23, 26, 93} [퐻+] + 퐾 1 퐾 (K ) 3.16 x 10-8 7.5 1 1 [퐻+] + 퐾 1 [퐻+]2 Carbonate H CO {129} 2 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1푘퐾2 퐾 [퐻+] (K ) HCO – 4.50 x 10-7 6.35 1 1 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2

2– -11 퐾1퐾2 (K2) CO3 4.68 x 10 10.33 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2 [퐻+]3 Phosphate H PO {129} 3 4 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 퐾 [퐻+]2 (K ) H PO – 7.08 x 10-3 2.15 1 1 2 4 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3 퐾 퐾 [퐻+] (K ) HPO 2– 6.30 x 10-8 7.20 1 2 2 4 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

3– -13 퐾1퐾2퐾3 (K3) PO4 4.27 x 10 12.37 + 3 + 2 + [퐻 ] + 퐾1[퐻 ] + 퐾1퐾2[퐻 ] + 퐾1퐾2퐾3

156

By plotting the specie fractions for citrate, MPS and APTES, we can determine the pH ranges where negatively-charged Au-Cit and Au-MPS NPs will best interact with positively-charged APTES surfaces. Figure 59 displays the ion speciation diagrams for citrate and MPS ligands as well as grafted APTES (Si/APTES). As pH increases, the fractions of negatively-charged citrate and MPS species increase while the fraction of

+ positively-charged APTES (–NH3 ) decreases. It should be noted that for an increase in ionic strength, the apparent pKa decreases for citrate and MPS and increases for APTES.

However, in the range of ionic strengths used in these experiments, the change in pKa is negligible. In these diagrams, the effect of ionic strength is disregarded. Ideally, optimal charge interaction between APTES and AuNPs would occur at the pH where the fractions

3- + of their highest-charged states intersect. Specifically, specie fractions between Cit /NH3

- + and MPS /NH3 are optimized at pH values around 6.95 and 5.20, respectively. These pH values indicate where the strength of particle-surface interaction would be maximized, but this is not necessarily true for AuNP density which is more dependent on the number of

3- + available attachment points (i.e. 훼 +). This is especially evident in the case for Cit /NH3 푁퐻3 where their mutual maximum fractions are around 0.78, which is a 22% decrease in available attachment points. Thus, to maximize AuNP density, a pH around 5 – 6 would

- be ideal, where Au-Cit is still contains a large fraction charged species (i.e. H2Cit and

2- HCit ) and 훼 + is near maximum. 푁퐻3

157

deprotonation

1.00 H Cit 0.80 3 α - H2Cit 2- 0.60 HCit Cit3- MPS-H Fraction, Fraction, 0.40 MPS- + 0.20 NH3

Species NH2 0.00 0 2 4 6 8 10 12

Figure 59. Ion speciation plots for citrate (blue lines) and MPS ligands (red lines) along with Si/APTES surfaces (green lines). The dotted line represents α = 0.50 which correlates to the pKa values for each equilibrium. The buffering capacity is the ability of a buffer to withstand fluctuation in pH for a given pH value. Figure 60 displays the buffering capacity for the buffering systems used in this study at I = 100 mM. Note that the maxima in the plots correlate to the pKa’s of the respective buffer. The dependence upon ionic strength can be seen in the plot for 20 mM

1 1 citrate. In this case, a /5 reduction in ionic strength correlates to about a /2 reduction in buffering capacity within the buffering region.

Figure 60. Buffer capacity of various buffering systems used in this work. Note that the maxima for each plot correlates to the pKa values.

158

Table 10. Changes in pKa for various ion species with increasing ionic strength and increasing temperature.

Species pKa ΔpKa ΔpKa / °C I (mM) 0 0.1 1 3 5 10 T=10–30°C - H Cit 2 3.13 0.00 -0.02 -0.03 -0.03 -0.04 -0.002 2- HCit 4.76 0.00 -0.05 -0.08 -0.10 -0.13 -0.001 3- Cit 6.40 0.00 -0.08 -0.13 -0.16 -0.22 0.002 - H PO 2 4 2.15 0.00 -0.02 -0.03 -0.03 -0.04 0.005 2- HPO 4 7.20 0.00 -0.05 -0.08 -0.10 -0.13 -0.002 3- PO 4 12.35 0.00 -0.08 -0.13 -0.16 -0.22 -0.010 - HCO 3 6.35 0.00 -0.02 -0.03 -0.03 -0.04 -0.006 2- CO 3 10.33 0.00 -0.05 -0.08 -0.10 -0.13 -0.009 - MPS 2.90 0.00 -0.02 -0.03 -0.03 -0.04 -0.009 + NH3 7.50 0.00 0.02 0.03 0.03 0.04 0.062

Figure 61. Fractional speciation of citric acid (H3Cit) and APTES with respect to solution pH. The vertical line indicates the pH where surface charge and particle charge are optimized and the associated specie fractions are denoted in the legend.

159

Figure 62. Fractional speciation of 3-mercaptopropanesulfonic acid (H–MPS) and APTES with respect to solution pH. The vertical line indicates the pH where surface charge and particle charge are optimized and the associated specie fractions are denoted in the legend.

Figure 63. Fractional speciation of phosphoric acid (H3PO4) with respect to solution pH.

Figure 64. Fractional speciation of carbonic acid (H2CO3) with respect to solution pH.

160

UV-vis Spectra of Gold Nanoparticles

UV-vis spectra of Au-Cit and Au-MPS solutions with pH values ranging from 3 –

10 and ionic strengths of 0.1 – 10 mM are displayed in Figures Figure 65 and Figure 66.

Note that at high ionic strength and low pH, AuNPs become less stable as exemplified by peak broadening. The stability of the AuNP solutions was assessed by the ratio of absorption peaks at 520 nm and 600 nm (Rads = A520 / A600) – the larger value for Rads, the greater the stability.

Figure 65. UV-Vis spectra for Au-Cit NPs at various pH and ionic strengths of 1, 3, 5 and 10 mM.

161

Figure 66. UV-Vis spectra for Au-MPS NPs at various pH and ionic strengths of 0.1, 1, 3 and 5 mM.

Hard-sphere Approximation of aeff

For irreversible particle adsorption, the surface coverage θ is given by

푎 2 휃 = 휃푗푎푚 ( ) (A.21) 푎푒푓푓

where θjam = 0.547 is the RSA jamming limit, a is the particle radius and aeff is the radius of the effective area excluded by a charged particle. The effective radius can be approximated by comparing the screened Coulomb potential u(r) with thermal energy kBT

29 and setting aeff as the solution to the equation (λ/kB T)u(aeff) = 1. A second order iterative solution leads to

162

−1 푎푒푓푓 = (2휅) ln (퐴/ ln 퐴) (A.22) with

2 −2 퐴 = 휆푍 휅퐿퐵 exp(2휅푎) (1 + 휅푎) (A.23)

2 where the fitting parameter λ = 2.8, the Bjerrum length LB = e / kBT (4πϵϵ0) = 0.72 nm in water and Z is the charge saturation value given by

푍 = (푎⁄퐿퐵)(4휅푎 + 6) (A.24)

Plugging Equation (A.22 into Equation (A.21 provides the theoretical surface coverage

-5 θmax for any κa value, and it follows that θmax approaches 0 for κa < 10 and converges to

θjam when κa > 40. For the parameters used in these experiments (a = 5.7 nm and κa = 0.19

– 1.81 (I = 0.1 – 10 mM)), θmax ≈ 0.014 – 0.233.

Hydrodynamic Diameter

The Stokes-Einstein relation calculates hydrodynamic radius of a colloid, which incorporates the distance a particle diffuses within a fluid:

푘푇 (A.25) 푑 = 퐻 3휋휂퐷 where dH is the hydrodynamic diameter, D is the translational diffusion coefficient, k is

Boltzmann’s constant, T is the absolute temperature and η is the viscosity.

Radial Distribution Functions of AuNP Assemblies

The change in structure for AuNP assemblies as a function of pH is assessed by the g(r) plots in Figure 67 and Figure 68. For all assemblies, the primary peaks shift to longer separations with increasing pH as a result of greater interparticle repulsion. Assemblies

163 with low density (high pH or low ionic strength) result in jagged curves as a result of smaller data sets for calculating g(r). In addition, with increasing ionic strength, peak shapes become less defined and aggregation peaks (r ≈ 11 nm) become more pronounced, indicating the loss of local order.

Figure 67. Radial distribution functions g(r) of Au-Cit assemblies at various pH values for I = 1 – 10 mM. Note that peaks around 9 – 11 nm become more profound with increasing ionic strength. The dashed vertical line represents the minimal center-center spacing for 11.4 nm AuNPs.

Figure 69 displays average locations the primary (g1(r)) and secondary peaks (g2(r)) in the radial distribution functions for Au-Cit and Au-MPS assemblies as a function of pH at various ionic strengths.

164

Figure 68. Radial distribution functions of Au-MPS assemblies at various pH values for I = 0.1 – 5 mM.

Figure 69. Average locations the primary (g1(r)) and secondary peaks (g2(r)) in the radial distribution functions for Au-Cit and Au-MPS assemblies as a function of pH at various ionic strengths. Filled symbols signify AuNP solutions made with citrate/phosphate buffers while open symbols denote the use carbonate buffers. The error bars represent the standard deviation in g(r).

165

Figure 70 displays the average surface coverage θ for Au-Cit and Au-MPS assemblies calculated from Equation (A.21 setting aeff = r0/2, where r0 is the position of the primary peak in the radial distribution function g(r), as determined in Figure 35. These

-1 values are compared to the predicted maximum surface coverage θmax where aeff = a + κ .

Values of θ begin to decline when pH increases. It can also be seen that at the highest ionic strength for Au-Cit (10 mM) and Au-MPS (5 mM), the calculated surface coverages are close to predicted values at low pH, but then fall at higher θ when ionic strength decreases.

Figure 70. Average surface coverage for Au-Cit and Au-MPS assemblies calculated from Equation (A.21 using aeff = r0/2, where r0 is the position of the primary peak in the radial distribution function g(r). Filled symbols signify AuNP solutions made with citrate/phosphate buffers while open symbols denote the use carbonate buffers.

166

Figure 71. Plots of interparticle separation (r) vs. pH at different ionic strengths for Au-Cit assemblies. The blue and orange curves denote the primary and secondary peak positions, respectively. The secondary axis normalizes r by the particle radius (a). Closed and open symbols represent assemblies from citrate- phosphate and carbonate buffered solutions, respectively. The dashed line represents the minimum separation for particles in contact (hard spheres).

Figure 72 shows the relationship between the primary peak (r1) and the interparticle separation calculated from NP density (r0) for assemblies of (a) Au-Cit and (b) Au-MPS at various ionic strengths. The dotted line represents r0 = r1. The closer the data is to unity, the better the NP density predicts the actual interparticle separation. For Au-Cit, the actual separations are slightly overestimated (r0 > r1) for I = 1 – 5 mM and underestimated (r0 < r1) for 10 mM, with the disparity increasing as pH rises. The data for Au-MPS shows similar behavior, although the spread is significantly greater. Many of the points, though fall close to r0 = r1. Thus, the true interparticle separations extracted from the primary peaks

167 of the radial distribution functions can be predicted from the NP densities with good accuracy.

Figure 72. Primary peak (r1) vs. interparticle separation from NP density (r0) for assemblies of (a) Au-Cit and (b) Au-MPS at various ionic strengths. The dotted line represents r0 = r1.

Contact Angle

γLV

θC θ θc γSV A θR γSL

(a) (b) (c)

Figure 73. Schematic representation of contact angles between a planar surface and a liquid drop: (a) static (θC), (b) advancing (θA) and (c) receding (θR). The vectors indicate the interfaces between solid, liquid and vapor phases.

168

Figure 74. Controlled-rate infusion setup demonstrating the vapor phase above the solution meniscus.

AuNP Assemblies on Mixed Silanes

Figure 75. AuNP adsorption data for PTES → APTES gradients with respect to relative distance (xr): (left axis) NP density, (right axis) area fraction (θ) and (far right axis) interparticle separation (r0). The trendline is meant to guide the eye. The dashed line represents the effective AuNP diameter, i.e. the ideal interparticle spacing.

169

Figure 76. AuNP adsorption data for PTES → OTCS gradients with respect to relative distance (xr). The following plot demonstrates the agreement in trends of NP density (filled symbols) and static contact angles (x’s) for PTES→APTES and OTCS→APTES gradients.

The trends agree exceptionally well for the latter.

Figure 77. Particle coverage compared to contact angle data for Au-Cit NPs adsorbed onto gradient SAMs of APTES mixed with PTES or OTCS as a function of relative distance (xr). The blue and green curves demonstrate the effect of alkyl chain length (● 5 vs. ■ 8). The trendlines are meant to guide the eye.

170

APPENDIX B

B. MATLAB Code

Radial Distribution Function function [rdf] = rdf_2d(filename,cutoff,step) %% -> Part 1: Open the file and get the atom information % * Load in from the data file * Data = dlmread(filename); % Read in data from txt file NAtoms = length(Data); BoxCoor=zeros(2,2); % Assign a box size based on the atom positions for i=1:2 BoxCoor(i,1)=min(Data(:,1+i)); BoxCoor(i,2)=max(Data(:,1+i)); end BoxL = BoxCoor(:,2) - BoxCoor(:,1); X = Data(:,2) - BoxCoor(1,1); % In range [0,BoxL(1)] Y = Data(:,3) - BoxCoor(2,1); % ' 2 ' %% -> Part 2: Calcualte the RDF %Select all atoms that are farther than 'cutoff' away from the edge cindex=find(min(X,Y)>cutoff & min(BoxL(1)-X,BoxL(2)-Y)>cutoff); % Pre-allocates the RDF bin array NBins=cutoff/step; rdf=zeros(NBins,1); % Get the distance to each atom for k=1:length(cindex) dist=sqrt((X(:)-X(cindex(k))).^2 + ... (Y(:)-Y(cindex(k))).^2); temp=histc(dist,0:step:cutoff); rdf=rdf+temp(2:(NBins+1)); % Tally them RDF style end % Convert tally to RDF rdf=rdf/(length(cindex)*NAtoms); Area=prod(BoxL); for k=1:size(rdf,1) rdf(k)=rdf(k)*Area/(pi*(k^2-(k-1)^2)*step^2); end %% -> Print it out as a histogram fp=fopen('rdf.csv','w'); fprintf(fp,'BinMid,RDF,\n'); for i=1:NBins fprintf(fp,'%.2f,%.3e,\n',i*step-step/2,rdf(i)); end fclose(fp); end

171

Voronoi Analysis function [f, n ] = vorocolor(datafile,xsize,ysize) %This program reads in a data file A containing the 2D coordinates of a % series of points or atoms. Data file A should be in the form % [i x y] or [i x y z] where i is the atom number/type. % %VOROCOLOR 2-D Voronoi diagram with colored cells % VOROCOLOR(A) plots the Voronoi diagram for the points x,y in A and % colors the cells according to its number of edges. To remove % statistical errors due to edge effects 5% of the dimensions is % removed from each edge. %VOROCOLOR(A,xsize,ysize) can be used to set the boundary conditions to % periodic where xsize is the dimension in the x direction and ysize % is the dimension in the y direction. % %VOROCOLOR outputs the distribution of cells with each number of edges % in a matrix such that the first colum is the number of edges, the % second colum is the corresponding number of cells, and the third % column is the corresponding fraction of cells. Note: the % distribution for cells with 9 edges is actually the distribution % for cells with 9+ edges. %VOROCOLOR saves the following in a folder named according to the input file % .eps, .png, & .fig images of the colored Voronoi diagram % .mat MATLAB workspace containing matrix A (x,y points), the distribution % matrix, and the area matrix % .txt MATLAB diary %Jennifer Luna-Singh - May 2013

[path, filename, ext]=fileparts(datafile); Data=load(datafile); A=Data(:,2:3);

[a,b]=size(A); if b~=2 disp('Matrix must have dimension M x 2') return end mkdir([path '/' filename]); diaryname=strcat(filename,'_diary.txt'); diary([path '/' filename '/' diaryname]) if nargin==1 bc=0; else bc=1; end if bc==1; AP=zeros(9*a,2);

for i=1:a AP(i,1)=A(i,1); AP(i,2)=A(i,2); end for i=1:a AP(i+a,1)=xsize+A(i,1); AP(i+a,2)=A(i,2); end for i=1:a AP(i+2*a,1)=2*xsize+A(i,1); AP(i+2*a,2)=A(i,2); end for i=1:a AP(i+3*a,1)=A(i,1);

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AP(i+3*a,2)=ysize+A(i,2); end for i=1:a AP(i+4*a,1)=xsize+A(i,1); AP(i+4*a,2)=ysize+A(i,2); end for i=1:a AP(i+5*a,1)=2*xsize+A(i,1); AP(i+5*a,2)=ysize+A(i,2); end for i=1:a AP(i+6*a,1)=A(i,1); AP(i+6*a,2)=2*ysize+A(i,2); end for i=1:a AP(i+7*a,1)=xsize+A(i,1); AP(i+7*a,2)=2*ysize+A(i,2); end for i=1:a AP(i+8*a,1)=2*xsize+A(i,1); AP(i+8*a,2)=2*ysize+A(i,2); end

A=AP; end clear AP if bc==1 axis_dim=[xsize 2*xsize ysize 2*ysize]; xv=[xsize 2*xsize 2*xsize xsize xsize]; yv=[ysize ysize 2*ysize 2*ysize ysize]; in=inpolygon(A(:,1),A(:,2),xv,yv); a=sum(in)

area_total=xsize*ysize; area_ideal_hex=area_total/a; ideal_side=sqrt((2*area_ideal_hex)/(3*sqrt(3))); ideal_c2c=2*sqrt(area_ideal_hex/(2*sqrt(3))); else xmax=max(A(:,1)); ymax=max(A(:,2)); axis_dim=[.05*xmax .95*xmax .05*ymax .95*ymax]; xv=[.05*xmax .95*xmax .95*xmax .05*xmax .05*xmax]; yv=[.05*ymax .05*ymax .95*ymax .95*ymax .05*ymax]; in=inpolygon(A(:,1),A(:,2),xv,yv); a=sum(in); area_total=xmax*ymax; area_ideal_hex=area_total/length(A); ideal_side=sqrt((2*area_ideal_hex)/(3*sqrt(3))); ideal_c2c=2*sqrt(area_ideal_hex/(2*sqrt(3))); end

[V,C]=voronoin(A); %% disp('Making Vornoi') f1=figure(1);set(f1,'Visible','off'); axis(axis_dim); axis(axis); p=(3:9); n=zeros(1,7); p=(3:9); n=zeros(1,7); for i = 1:length(C) [r(i) c(i)]=size(C{i}); if all(C {i}~=1) if in(i)==1 if c(i)==3 patch(V(C{i},1),V(C{i},2),'r')

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n(1)=n(1)+1; end if c(i)==4 patch(V(C{i},1),V(C{i},2),'c') n(2)=n(2)+1; end if c(i)==5 patch(V(C{i},1),V(C{i},2),'m') n(3)=n(3)+1; end if c(i)==6 patch(V(C{i},1),V(C{i},2),'w') n(4)=n(4)+1; end if c(i)==7 patch(V(C{i},1),V(C{i},2),'g') n(5)=n(5)+1; end if c(i)==8 patch(V(C{i},1),V(C{i},2),'y') n(6)=n(6)+1; end if c(i)>=9 patch(V(C{i},1),V(C{i},2),[1 0.5 0.1]) n(7)=n(7)+1; end end end end total=sum(n); for i = 1:length(n) f(i)=n(i)/total; end distribution=[p' n' f']

B=[ 1 0.5 0.1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0]; colormap(B); hcb = colorbar('YTickLabel',{'9+','8','7','6','5','4','3'}); set(hcb,'YTick',[1/14,3/14,5/14,7/14,9/14,11/14,13/14]); hold all voronoi(A(:,1),A(:,2)); axis off;

%imagename_1=strcat(filename,'_color.fig'); %imagename_2=strcat(filename,'_color.eps'); imagename_3=strcat(filename,'_color.png'); %saveas(f1,[path '/' filename '/' imagename_1],'fig'); %print('-depsc',[path '/' filename '/' imagename_2]); print('-dpng','-r900',[path '/' filename '/' imagename_3]); clf

%% disp('Saving Data') wname=strcat(filename,'_data.mat'); save([path '/' filename '/' wname],'distribution','area','side'); diary off; end

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APPENDIX C

C. Reprint Permissions

Figure 11. Top left: pH variation with variation in χAu (decreases left to right); Top right: relative reactivity of the dominant Au3+ complexes and their associated pH values; Bottom: schematic of two reaction pathways for the synthesis of citrate-reduced AuNPs. (Reprinted with permission; Ji, X.; Song, X.; Li, J.; Bai, Y.; Yang, W.; Peng, X., Size Control of Gold Nanocrystals in Citrate Reduction: The Third Role of Citrate. J. Am. Chem. Soc. 2007, 129, 13939-13948.)

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Figure 12. SPR peak wavelengths of AuNPs as function of the ratio of gold and citrate concentrations. The different symbols mark the gold concentration of the reaction (■ – less than 0.8 mM; ○ – 1 mM; – 1.2 mM). The lines are a guide to the eye. (Reprinted with permission; Kimling, J.; Maier, M.; Okenve, B.; Kotaidis, V.; Ballot, H.; Plech, A., Turkevich Method for Gold Nanoparticle Synthesis Revisited. J. Phys. Chem. B 2006, 110, 15700-15707.)

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Figure 19. Phase diagrams of ordered and disordered surface structures for a volume fraction of 0.01 and a Debye screening parameter κa =1. (Reprinted with permission; Gray, J. J.; Bonnecaze, R. T., Adsorption of Colloidal Particles by Brownian Dynamics Simulation: Kinetics and Surface Structures. J. Chem. Phys. 2001, 114, 1366-1381.)

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