Science, Faculty of
Chemistry, Department of
DSpace
UBCV
Goodman, Diane
Doctor of Philosophy - PhD
University of British Columbia
The interaction forces exerted by latex particles bearing densely grafted polymer layers of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), and poly(N-isopropylacrylamide) (PNIPAM) in aqueous media (good solvent) were investigated by atomic force microscopy (AFM). The molecular weight (Mn), grafting density (σ), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography (GPC) and multi-angle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. The hydrodynamic thicknesses were measured by dynamic light scattering and were comparable to the equilibrium thicknesses measured by AFM. The values were also similar to those predicted by a numerical self-consistent mean field model after scaling the dimensions and flexibility of the lattice chains using experimentally determined parameters. Force profiles of PDMA (0.017 nm-2 ≤ σ ≤0.17 nm-2) and PMEA (σ = 0.054 nm-2) brushes were purely repulsive upon compression, with forces increasing with Mn and σ, as expected, due to excluded volume interactions. At a sufficiently low grafting density (σ = 0.012 nm-2), PDMA exhibited a long-range exponentially increasing attractive force which was attributed to bridging. A bridging force was detected in the PNIPAM brush at σ = 0.037 nm-2; at this density the PDMA brush force profile was purely repulsive. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The Mn and PDI of the polymer brushes were determined by two independent force techniques, the suitability of which depended on the interaction of the polymer with the AFM tip. For non-adsorbing polymers, the distribution of contour lengths measured by stretching individual chains was compared with GPC distributions for surfaces with different grafting densities. The force technique was appropriate for dense brushes in good solvent but underestimated the Mn for surfaces with low σ (mushroom regime). A novel technique was developed for determining the molecular weight distribution of an adsorbing polymer brush based on a purely empirical relationship between the decompression force profile and the cumulative weight fraction obtained by GPC.
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INTERACTIONS OF GRAFTED P O L Y M E R BRUSHES M E A S U R E D B Y ATOMIC FORCE MICROSCOPY by DIANE G O O D M A N B.Sc. (Chemistry) McGil l University, 1997 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Chemistry ) We accept this thesis as conforming To the required standard THE UNIVERSITY OF BRITISH C O L U M B I A July, 2004 © Diane Goodman, 2004 Abstract The interaction forces exerted by latex particles bearing densely grafted polymer layers of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), and poly(N-isopropylacrylamide) (PNIPAM) in aqueous media (good solvent) were investigated by atomic force microscopy (AFM). The molecular weight (M n ), grafting density (a), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography (GPC) and multi-angle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. The hydrodynamic thicknesses were measured by dynamic light scattering and were comparable to the equilibrium thicknesses measured by A F M . The values were also similar to those predicted by a numerical self-consistent mean field model after scaling the dimensions and flexibility of the lattice chains using experimentally determined parameters. Force profiles of P D M A (0.017 nm"2 < a < 0.17 run"2) and P M E A (a = 0.054 nm" ) brushes were purely repulsive upon compression, with forces increasing with M n and o, as expected, due to excluded volume interactions. At a sufficiently low grafting density (a = 0.012 nm" ), P D M A exhibited a long-range exponentially increasing attractive force which was attributed to bridging. A bridging force was detected in the PNIPAM brush at a = 0.037 nm"2; at this density the P D M A brush force profile was purely repulsive. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The M n and PDI of the polymer brushes were determined by two independent force techniques, the suitability of which depended on the interaction of the polymer with the A F M tip. For non-adsorbing polymers, the distribution of contour lengths measured ii by stretching individual chains was compared with GPC distributions for surfaces with different grafting densities. The force technique was appropriate for dense brushes in good solvent but underestimated the M n for surfaces with low a (mushroom regime). A novel technique was developed for determining the molecular weight distribution of an adsorbing polymer brush based on a purely empirical relationship between the decompression force profile and the cumulative weight fraction obtained by GPC. iii Table of Contents Abstract i i Table of Contents iv List of Table Titles x List of Figure Captions xi List of Abbreviations and Symbols xxi Acknowledgements xxvii 1. Introduction l 1.1 Overview 1 1.2 Motivations for this work 3 1.2.1 Advantages of using Spherical Grafting Surface 3 1.2.2 Development of Atomic Force Microscopy Applications 4 1.3 Polymers in Solution 7 1.3.1 Ideal Polymers 7 1.3.2 Real Polymer Solutions 10 1.3.3 Terminally Attached Polymers on Flat Surfaces 13 1.3.4 Polymers at Spherical Interfaces 17 1.4 Atomic Force Microscopy (AFM) 19 iv 1.4.1 General Instrumentation 19 1.4.2 Construction of a Force Curve 22 1.4.3 Geometric Considerations 26 1.4.3.1 Derjaguin Approximation 26 1.4.3.2 Colloid Probe Microscopy 27 1.4.3.3 Standard Silicon Nitride Tip Geometry 28 1.4.4 Different Interaction Forces 29 1.4.4.1 Electrostatics 30 1.4.4.2 van der Waals 33 1.4.4.3 Derjaguin-Landau-Verwey-Overbeek (DLVO) theory 33 1.4.4.4 Steric Forces 34 1.4.4.5 Other Compression Interactions 37 1.4.4.6 Adhesion (Johnson, Kendal, and Roberts (JKR)) 37 1.4.4.7 Polymer Extension 38 Synthesis and Characterization of Functionalized Latex Particles 40 2.1 Introduction 40 2.2 Experimental 41 2.2.1 Synthesis and Characterization of Latex Particles 41 2.2.1.1 Preparation of Polystyrene Seed Latex 41 2.2.1.2 Shell Growth Copolymerization: Synthesis of ATRP Initiator Layer 42 2.2.1.3 Characterization of Latex 42 2.2.2 Atomic Force Microscopy (AFM) 47 2.2.2.1 General Experimental Setup 47 2.2.2.2 A F M Probes 47 2.2.2.3 Force Measurement Procedure 52 2.3 Results and Discussion 57 2.3.1 Elasticity of Shell Latex 57 2.3.2 Electrostatic Interactions 59 2.3.2.1 Silicon nitride tip and flat silicon nitride sample 59 2.3.2.2 Silicon nitride tip and shell latex (diameter D* = 650 nm) 64 2.3.2.3 Sulfate latex particle probe (D* = 9.6 jum) and flat silicon nitride surface 70 2.3.2.4 Comparison of i) silicon nitride tip and sulfate latex particle (D* = 9.6 jum) and ii) sulfate latex particle probe (D* = 9.6 fjm) and flat silicon nitride surface 74 2.3.3 Van der Waals Interactions 75 2.3.4 DLVO Interactions 77 2.3.5 Summary of Interactions 78 2.3.6 Equilibrium Considerations 80 2.3.7 Surface Roughness 81 2.4 Summary 92 vi Compression Forces in Neutral Polymer Brushes Measured by A F M in Good Solvent Conditions 93 3.1 Introduction 93 3.2 Experimental 94 3.2.1 Synthesis of Grafted Polymer by Controlled Atom Transfer Radical Living Polymerization 94 3.2.2 Analysis of Grafted Latex 95 3.2.3 Preparation of Surfaces with Different Grafting Densities 96 3.2.4 X-ray Photoelectron Spectroscopy (XPS) 96 3.2.5 AFM Measurements 97 3.3 Results and Discussion 98 3.3.1 AFM Imaging 98 3.3.2 Force Curve Analysis 109 3.3.2.1 Weakly Adsorbing Chains 109 3.3.2.2 Strongly Adsorbing Chains 128 3.3.2.3 Equilibrium Considerations 136 3.3.2.4 Environmentally Responsive Polymers 3.4 Summary 146 vn 4. Estimation of Molecular Weight and Polydispersity of Polymer Brushes from A F M Decompression Profiles 147 4.1 Introduction 147 4.2 Experimental 149 4.3 Non-Adsorbing Polymers: PDMA 151 4.3.1 Results and Discussion 151 4.3.2 Summary 167 4.4 Adsorbing Polymers: PNIPAM 168 4.4.1 Introduction 169 4.4.2 Summary 184 5. Comparison of Experimental Brush Thicknesses with Self-Consistent Field Model Predictions 186 5.1 Introduction 186 5.2 Self-Consistent Field Model 188 5.3 Scaling Lattice Parameters 189 5.4 Comparison of Experimental and Theoretical Results 195 5.5 Summary 200 6. Concluding Remarks and Future Work 201 viii References 204 Appendix 1 217 Appendix 2 221 Appendix 3 223 Appendix 4 229 Appendix 5 230 ix List of Table Titles Table 1.1. Excluded volume conditions Table 2.1 Young's moduli of materials Table 2.2. Electrostatic Interaction between Symmetrical Silicon Nitride Tip/Sample Table 2.3. Electrostatic Interaction between Silicon Nitride Tip and Shell Latex (D* = 650 nm): Single Exponential Fit Table 2.4. Electrostatic Interaction between Silicon Nitride Tip and Shell Latex (D* = 650 nm): Double Exponential Fit Parameters Table 2.5. Electrostatic Interaction between Sulfate Latex Probe (D* = 9.6 //m) and Silicon Nitride Sample: Single Exponential Fit Parameters Table 3.1. Properties of P D M A Grafted Latex Table 3.2. Properties of P D M A Brushes with M n ~ 30 600 and PDI =1.35 Table 3.3. Properties of PMEA-6-PNIPAM Copolymer Brushes Table 4.1. Characteristics of P D M A Brushes Table 4.2. Effect of Solvency on Molecular Weight Estimation of P D M A Brush Table 5.1. Thickness L of P D M A brush (M„ = 30 600, PDI = 1.33, R = 650 nm) obtained by SCF (athermal conditions), HT and A F M . Table 5.2. Experimental and lattice properties of P D M A brushes Table A5-1. Characteristics of PNIPAM brush List of Figure Captions Figure 1.1. Features of a basic force curve on a hard surface: A) large tip-sample separation B) jump-to-contact C) constant compliance D) adhesion E) tip snaps free of sample. Figure 1.2. Typical force curves obtained upon compression of compliant and non-compliant samples. Figure 1.3. Comparison of A) raw force curve and B) adjusted force curve according to the method of Ducker et al. (1992). Figure 1.4. Typical force profiles and theoretical force laws for a sphere interacting with a flat surface. See text (Section 1.4.4) for description of parameters. Figure 1.5. Schematic of energy versus separation profile for D L V O interaction. Figure 2.1. S E M image of typical batch of monodisperse shell latex Figure 2.2. a) Main components of atomic force microscope: A. A F M "head" containing laser, photodiode, and adjustment knobs. B. Glass fluid cell or "tipholder". C. Sample (1 cm x 1cm glass) fixed on steel puck. D. Piezo scanner, b) Large scale view of fluid cell (facing up) showing groove for O-ring and 3 ports for fluid/atmospheric control. Figure 2.3 a) Silicon nitride substrate holding 4 cantilevers: 1) wide leg 200 jum long, k ~ 0.12 N/m 2) wide leg 100 fjm long, k ~ 0.58 N/m 3) narrow leg 100 jum long, k ~ 0.38 N/m 4) narrow leg 200 jum long, k ~ 0.06 N/m. b) S E M image of square pyramidal shaped tip at apex of cantilever, c) Image of colloid particle probe prepared by attaching polystyrene latex (diameter ~ 10 jum) to apex of silicon nitride cantilever. xi Figure 2.4. Resonance curves showing shift in frequency for loaded (D* = 9.6 jum polystyrene latex) and unloaded silicon nitride cantilever. Figure 2.5. A) Raw and B) adjusted force curves obtained with silicon nitride tip on glass and shell latex samples in 5 M NaCI. Figure 2.6 Compression profiles between silicon nitride tip and silicon nitride sample in NaCI solution, a) Data corresponding to 0.1 m M (*) and 10 m M (o) represent the average of 9 and 2 force profiles, respectively. Solid lines are best fits to a single exponential decay, b) Compression profile in 100 mM NaCI solution. Figure 2.7. Interaction between silicon nitride tip and shell latex (D* = 650 nm) in 10 m M and 100 mM NaCI. The data represents an average of 10 force profiles. Dotted lines are best fits to an exponential decay. Figure 2.8. Interaction between 9.6 //m sulfate latex probe and flat silicon nitride surface as a function of ionic strength. Solid lines show best fit to single exponential decay. Figure 2.9. Effect of ionic strength on measure decay length of force profile between polystyrene particle probe and silicon nitride surface (see Fig. 2.8). Figure 2.10. Interaction between latex particle probe (D* = 9.6 um) and silicon nitride surface in 1 M NaCI. Tip and sample are as the same as in Fig. 2.8. Solid line represents best fit to vdW interaction (Eq. 2.22). Figure 2.11. Comparison of D L V O (solid lines) and purely electrostatic fits (symbols) to interaction between a latex particle probe (9.6 um) and silicon nitride surface as a function of ionic strength. xii Figure 2.12. Reproducibility of compression profiles of shell latex (D* = 650 nm) in 10 m M NaCI at rates ranging between 500 and 2500 nm/s. Figure 2.13. a) Tapping Mode image in air ( 4 x 4 pm ) of shell latex (D* = 650 nm) b) Single scan line obtained by section analysis showing horizontal (LH) and vertical ( L V ) dimensions of latex particle c) High resolution image ( l x l pm ) showing roughness of shell latex. Figure 2.14. Topographical (left) and phase (right) images obtained in Tapping Mode in air of a) polystyrene core latex and b,c) shell latex with varying HEA-C1 initiator 2 7 2 concentrations. HEA-C1 concentrations: b) 2.81 x 10-7 mol/m c) 20.0 x 10" mol/m . Figure 2.15. A F M images a) 5 x 5 jum2 and b) 2 x 2 jum2 of D* = 9.6 /urn shell latex in air. Figure 2.16. a) Schematic of rough latex sphere having radius R + r. b) Spherical cap defined by region of sphere lying above shaded plane. Figure 2.17. Interaction of silicon nitride tip and shell latex (D* = 650 nm) in 10 m M NaCI at 10 different locations on a sample. Figure 3.1. Representation (to scale) of conical A F M tip (35° half angle) compressing spherical brush (diameter = 650 nm). The tip is located at the point of zero separation, i.e. constant compliance region. Dotted line represents a 65 nm thick layer of grafted polymer at equilibrium. Diagram shows tip located at a) uppermost point of particle and b) directly between two particles. The region of contact between the tip and the grafted polymer layer is given by a disc of diameter C. For simplicity, we define the region of xiii contact so that the polymer layer cannot access the tip at a vertical distance greater than the equilibrium thickness. Figure 3.2. Tapping Mode images in of a) shell latex in air b,c) P D M A ( M n = 4 x 106) brush in air d) P D M A brush in water. Figure 3.3. Tapping Mode images ( 2 x 2 um2) in air of a) core latex b) shell latex c) P D M A brush (M„ = 39 600) d) P D M A brush (M„ = 80 400) e) P D M A brush (M„ = 166 000) f) P D M A brush (M„ = 204 000) g) P D M A brush (M„ = 217 000) Figure 3.4. Tapping Mode images ( 2 x 2 um ) in water (100 m M NaCI) of a) core latex b) shell latex c) P D M A brush (M„ = 39 600) d) P D M A brush (M„ = 80 400) Figure 3.5 Tapping Mode images ( 2 x 2 um ) in P D M A brush (Mn = 40 000) showing in situ hydrolysis of chains with time t: a) Before hydrolysis b) t = 5 min c) t = 1.5 hours d) 4.5 hours e) 8 hours f) 8.5 hours Figure 3.6. Compression profiles of shell and grafted latex with varying molecular weight P D M A in 150 mM NaCI solution (a = grafting density). Figure 3.7. Compression profile of P D M A brush ( M n 30 600) grafted to polystyrene latex particles (650 nm diameter) before and after correction for the electrostatic contribution. The purely electrostatic profile of the shell latex is also shown. A F M measurements were performed in 10 m M NaCI. The shell and brush profiles are averages of 10 and 75 curves, respectively. The arrow denotes the separation corresponding to the equilibrium brush thickness, L e . xiv Figure 3.8. Effect of grafting density on compression of P D M A brushes ( M n 30 600) grafted to polystyrene latex particles measured in 10 mM NaCI. Curves have been corrected to remove electrostatic contribution (see text). Each curve represents the average of data from ~ 75 locations on the sample. See text and Table 1 for discussion of uncertainty. Figure 3.9. Effect of grafting density on equilibrium thickness of P D M A brushes measured by A F M ( M n ~ 30 600, PDI = 1.35). Dotted line corresponds to best fit of linear region (0.0171 nm"2 < a < 0.170 nm"2) with slope of 0.45. Figure 3.10. Long-range attraction in P D M A brushes at various grafting densities. Curves represent single force measurements where the infrequent occurrence of bridging was observed. Curves are fit to an increasing exponential. Figure 3.11. Frequency of bridging events (N ~ 75 measurements) observed in P D M A brushes of varying grafting density. Figure 3.12. Effect of monomer type on compression of brushes. Curves show typical single force profiles. PDMA: M n ~ 30 600, D = 5.1 nm; PNIPAM: M n 48 000, D = 5.2 nm. Measurements are inlO m M NaCI, pH 7. Figure 3.13. a) Survey scans of silicon nitride and P M E A samples b) High-resolution C 1 s XPS spectra od silicon nitride, P D M A , P M E A and PNIPAM samples. Figure 3.14. Effect of PNIPAM block length on compression of PMEA-6-PNIPAM copolymer brush. Curves show typical single force profiles. P M E A : M n ~ 32 500, PDI = 1.12, a = 0.054 nm . Measurements performed in 10 mM NaCI, pH 7. xv Figure 3.15. Force profiles obtained by the compression of (o) P M E A ( M n — 32 500; PDI = 1.24; a = 0.045 nm"2), ( A ) PNIPAM ( M n = 47 700; PDI = 1.33; a = 0.036 nm"2), (*) PMEA-6-PNIPAM (MnPMEA = 32 500; M n,p N, P AM = 9 700; PDI = 1.24; a = 0.045 nm"2) and (•) PMEA-6-PNIPAM ( M „ J P M E A = 32 500; M n PNIPAM = 42 500; PDI = 1.24; a = 0.045 nm"2) brushes by A F M latex tip. Figure 3.16. Compression (closed symbol) and decompression (open symbol) of brushes under conditions of equilibrium a) PMEA: M n = 32 500, a = 0.054 nm and non-equilibium b) PNIPAM: (M„ = 48 000, a = 0.037 nm 2. Measurements performed in 10 m M NaCI, pH 7. Curves show typical single force profiles. Figure 3.17. a) Reproducible compression profiles of a PNIPAM brush obtained sequentially at a single sample location at a rate of 1.5 jum/s. The brush properties were M n = 94 900, PDI = 1.35, and a = 0.067 nm"2. b) Effect of scan rate on compression profile of the PNIPAM brush. Curves show typical single profiles. Measurements were performed at the same sample location as in (a). Solid lines are provided to guide the eye. * Figure 3.18. Effect of temperature on compression profile of a PNIPAM brush (D = 650 nm, M n = 48 000, PDI = 1.35, a = 0.037 nm"2). Measurements were performed in 10 m M NaCI with a silicon nitride tip. Figure 3.19. Effect of temperature on compression profile of PNIPAM brush (D* - 10 /urn) with silicon nitride tip in 10 mM NaCI. Note: Zero Separation corresponds to position at 4 nN. xvi Figure 3.20. Compression profile of PNIPAM brush (Mn 48 000) by S i 3 N 4 Tip: Effect of [Na 2S0 4] Figure 3.21. Compression profile of PNIPAM brush (D* = 9.6 fjm) with silicon nitride tip in Na2SO"4. Note: Zero Separation corresponds to position at 10 nN. Figure 3.22. Compression profile of PNIPAM brush (D* = 10 fjm) with silicon nitride tip in NaCI. Note: Zero Separation corresponds to position at 9 nN. Figure 4.1 Decompression profile of a P D M A brush ( M ^ G P C ~ 30 600, P D I G p c = 1-35, a = 0.037 nm"2) in 10 m M NaCI. Solid line represents fit to worm-like chain (WLC) model with persistence length q = 0.41 ± 0.04 nm and extension ratio ?^ = 0.88. Figure 4.2. Typical force profile showing advancing (compression (o)) and receding (stretching (*)) directions of P D M A brush ( M n 30 600, a = 0.17 nm"2). Solid arrows depict rupture events corresponding to L R . Dotted arrow indicates onset of repulsion corresponding to equilibrium thickness L e of polymer layer. Figure 4.3. Comparison of M n and M w determined by rupture separations from A F M and GPC. Figure 4.4. Comparison of contour length distributions obtain by A F M and GPC for high 2 2 (a = 0.171 nm" ) and low (a = 0.0125 nm" ) grafting densities. Distributions are normalized so that 'Lfi AL = 1, where ft is the frequency of A F M rupture event. Figure 4.5. Representation of the most probable interaction of an A F M tip with polymer at A) high and B) low grafting density. The tip approaches the grafted layer (I) with the xvii asterisk denoting the most probable initial point of contact. Upon compression (II), the tip may form additional contacts along a single chain as well as with multiple chains. With sufficient extension (III), the chain ruptures from the tip at the contact point denoted by the asterisk, at a separation L R . Figure 4.6. Effect of rate and contact time on molecular weight measured using A F M rupture separations. Measurements were performed on P D M A brush (a = 0.0125 nm") in 10 m M NaCI using a silicon nitride A F M tip (k ~ 0.06 N/m). Data was collected at 50 locations on the sample for each set of conditions. Figure 4.7. Effect of solvent quality on compression profiles of P D M A brush for a = 0.17 nm"2. Curves are average of data obtained at 75 locations on the sample. Figure 4.8. Distribution of rupture forces for P D M A brushes of two representative grafting densities. Data is normalized so that IlfiAFli = 1. Figure 4.9. Decompression profile of a PNIPAM brush (M n G pc = 47 700, PDIGpc = 1.33, a = 0.037 nm"2) in 10 mM NaCI, pH 7. Dotted line shows non-linear least squares fit to Eq. 4.11 (see text). Figure 4.10. Decompression curves of PNIPAM brushes obtained at various locations on a single sample surface as well as on different samples (same material). Curves are normalized by dividing by the maximum attractive force F m in each measurement. Values are listed in Appendix 5. Material and conditions are as in Fig. 4.9. Figure 4.11 Depiction of maximum accessible distance r for chain of contour length L C and tip of radius R. xviii Figure 4.12. Maximum (left-hand ordinate) and minimum (right-hand ordinate) number of chains 77 with molecular weight that have access to the A F M tip a separation L from the grafting surface. The calculation is based on the number fraction of chains in a PNIPAM brush of MnsGPC = 47 700 and a - 0.037 nm"2. The accessible number of chains is estimated from Eq. 4.8, see text for discussion of assumptions. Figure 4.13. Decompression profile of PNIPAM brush with average contour length L c -106 nm, M n = 47 700, PDI =1.33 (GPC results) showing direct relationship with cumulative weight fraction of grafted chains. Figure 4.14. Comparison of distribution of weight fraction of PNIPAM brush measured by GPC and calculated from analysis of decompression profile (see text). Very low weight fractions obtained at the low molecular weight end have been removed from the GPC distributions. Dashed and solid lines correspond to the log-normal distribution fits to the A F M data (SI and S2 respectively). Brush properties obtained by GPC are for SI: ( M n = 47 700, PDI = 1.33, a = 0.037 nm"2) and for S2: (M„ = 94 900, PDI = 1.35, a = 0.067 nm"2). Figure 5.1. Segment distribution of a single end-grafted chain in the radial (r) (dash-dot line) and normal (z) (solid line) directions. (N = 50; % = 0). Dashed line indicates R r m s . Figure 5.2. Rrms as a function of N L for a single grafted chain. Figure 5.3. Dependence of R g measured by light scattering on molecular weight. Solid lines represent best fits to a power function (see Eq. 1.4). xix Figure 5.4. Comparison of brush thickness L obtained by HT and SCF as a function of N a l / 3 . To correct for the spherical nature of the brushes, the measured L H T values were modified according to Eq. 5.11. Lattice chains were scaled according to the parameters listed in Table 5.2. Calculations were performed in athermal conditions (% = 0). Figure A2.1 Effect of nonlinearities in piezo. Sensitivity (nm/V) of piezo is less at the beginning of a cycle than at the end, for both extension and retraction. Figure A2.2 Nonlinear waveform applied to electrodes to produce linear scanner motion. Triangular waveform is shown for reference. xx List of Abbreviations and Symbols Abbreviations AFM atomic force microscopy ATRP atom transfer radical polymerization DLVO Derjaguin-Landau-Verwey-Overbeek FJC freely jointed chain GPC gel permeation chromatography HT hydrodynamic thickness LCST lower critical solution temperature LS light scattering MALLS multi-angle laser light scattering PDI polydispersity index (= M n / M w ) PDI, A F M PDI determined by A F M technique for adsorbing chains SCF self-consistent mean-field SEM scanning electron microscopy SFA surface force apparatus STM scanning tunneling microscope vdW van der Waals WLC worm-like chain XPS X-ray photoelectron spectroscopy Symbols a parameter determined from light scattering A H Hamaker constant xxi A 0 drive amplitude As surface area of the spherical cap As,R surface area of particle of radius R Asp setpoint amplitude c mass concentration C o o characteristic ratio Ad cantilever deflection D distance between grafting points D' average diffusion coefficient e elementary charge E electric field E Young's modulus f fraction of surface covered by features 1 force per unit area between two flat surfaces f, frequency of AFM rupture event. F force F m maximum attractive force F R rupture force h height of spherical cap AHmix enthalpy of mixing I ionic strength k spring constant kB Boltzmann constant lc length of cantilever I length of a monomer unit h electrical length of chamber XXll IK Kuhn length or statistical segment length 1L lattice length A L tip-sample separation L * distance over which the interaction scales to zero L A separation at which attractive interaction is first detected LAFM brush thickness determined by A F M L C contour length U s contour length of individual chain L E equilibrium thickness L H average horizontal distance L H T brush thickness determined by HT L M separation at maximum attractive force L R rupture separation LSCF brush thickness determined by SCF L V average vertical distance L V * inverse Langevin m parameter depending on geometry of grafting surface rh mass M molecular weight M , mass on tip M peak molecular weight M i molecular weight of an individual chain Mmon molar mass of a monomer M n number average molecular weight M N ,AFM M n determined by A F M technique for adsorbing chains M n , G pc M n measured by GPC M„,R M n calculated from rupture separation xxiii weight average molecular weight M w calculated from rupture separation exponent (Eq. 3.2) ion density number of segments in each radial degree of polymerization number of chains (Eq. 4.4) Avogardo's number number of Kuhn segments number of lattice segments persistence persistence of lattice weight fraction of chains pressure persistence length (q = 3lp) radial (parallel to grafting surface) radius of the tip at any distance z from the surface (Eq. 1.14) radius of hemispherical features radius extension ratio ideal gas constant radius of gyration hydrodynamic radius root-mean-squared distance of segments from the cylinder axis length between two segments standard deviation xxiv S* contact stiffness AS m i x entropy of mixing T temperature M,(z,r) interaction potential of a segment of component i V molar volume V applied voltage W(h) free energy per unit area between two planar surfaces Ax distance moved by piezo z ion valency z layer (normal to grafting surface) Z coordination number y S L work of adhesion of the two surfaces in a liquid T, number fraction of chains (GPC/MALLS) 8 dielectric constant 6 0 vacuum permittivity Ae interaction energy ^ zeta potential TJ viscosity 77,- m a x maximum number of accessible chains K"1 decay length (or inverse Debye length) H electrophoretic mobility Vo, Vi resonance frequencies before and after added mass v Poisson's ratio v average particle velocity xxv V Flory exponent (1/2 for theta solvent; 3/5 for good solvent) Vex excluded volume parameter ( v e x = 1 -2%) cumulative weight distribution n osmotic pressure Po concentration of counterions at surface A concentration of counterions at x away from a surface Pec bulk concentration of counterions a grafting density <yc surface charge density charge density on tip C?c,s charge density on surface V partial specific volume q>s site fraction (lattice parameter) <P (z,r) volume fraction in lattice radial 3C Flory-Huggins parameter potential surface potential CD natural resonance frequency xxvi Acknowledgements: This work would be significantly less coherent without the contribution of select individuals. Firstly, I thank my supervisor Don Brooks for guiding me with the necessary balance of focus and freedom, and whose broad interdisciplinary grasp has been a great admiration. I am also particularly grateful to Dr. Jayachandran Kizhakkedathu, our synthetic polymer guru, for supplying me with materials for investigation and critical analysis. Having had the pleasure of working with Raymond Norris-Jones, to whom I am indebted for the gratuitous psychotherapy he has provided over the years, was a rare experience. I would like to thank all of the remarkable scientists with whom I have overlapped. It is thanks to you that I leave the Brooks lab with a deep appreciation not only for colloids and surface science, but also for mycology, vino, the laborious preparation of biryani, and the complex politics of Transylvania. Much appreciation to Dr. Johan Janzen, Dr. Doina Hritcu, Dr. Aniko Takacs-Cox, Dr. Rajesh Kumar, Yevgenya Lee, Bryan Coad and Peter Easthope for technical assistance and for having enriched my years with your wonderful and unique personalities. I thank the Canadian Institutes of Health Research, Canadian Blood Services, Natural Sciences and Engineering Research Council of Canada and Canada Foundation for Innovation for financial support. I am also indebted to the special friends who have followed the daily challenges of my research with great enthusiasm. I am especially grateful to my family for having instilled in me the discipline, drive, and confidence necessary to complete this work, and for empowering me with an endless supply of love and encouragement. xxvii 1. Introduction 1.1 Overview The goal of this work is to correlate the properties of latex particles bearing densely grafted polymer chains with the interactions measured by directly probing the polymer layer with a solid inorganic surface or colloidal particle using atomic force microscopy (AFM). The results have significance for the field of colloid science as well as for the development of surface analysis techniques. From a colloid perspective, the microscopic interactions among elements of the system are regarded as fundamental to the understanding of the macroscopic behavior of the particles. The ability of grafted polymers to stabilize colloids or to reject protein, for example, has long been attributed to the delicate balance of enthalpic and entropic contributions arising from intra and intermolecular interactions within the polymer layer (Yang et al., 1999; Schroen et al., 1995; Bergstrom et al, 1992; Gombotz et al, 1992; Jeon et al, 1991). With protein binding known to be the first step in the response of the immune and complement systems against foreign materials, surfaces bearing grafted polymers have been used extensively in the medical field due to their improved biocompatibility (Tirell et al, 2002; Peppas and Langmuir, 1994). Such materials have also found widespread application as sensors or chemical gates (Ito et al, 1992), drug delivery vehicles (Woodle and Lasic, 1992), and chromatography media (Brooks et al, 2000; Johansson et al, 1998; Brooks and Muller, 1996; Van Zanten, 1994). Clearly, the rational design of materials tailored to exhibit a particular response to a stimulus is highly desirable. The relationship between the properties of the grafted layer and the ability of the material to effectively exclude macromolecules in a good solvent 1 has been investigated (Xu and Marchant, 2000; Yang et al., 1999). It is now recognized that decreased adsorption is achieved through terminally attaching non-adsorbing flexible polymers having a high grafting density and high molecular weight. Studies have suggested that the grafting density is the main factor that determines adhesion (Xu and Marchant, 2000; Yang et al, 1999). When the distance between grafting points is below the characteristic dimensions of the random coil of the chain (see Section 1.3.3), the grafted layer is called a polymer brush. With the development in recent years of new synthetic routes to surface-initiated polymerization, particularly in the Brooks laboratory (Jayachandran et al, 2002), polymer brushes can be prepared with good control over molecular weights, molecular weight distributions, and grafting densities from a variety of monomers. Variability in the biocompatibility of grafted polymers presented in the literature suggests that the interactions can be quite complex (Xu and Marchant, 2000; Yang et al, 1999; Du et al, 1997). Even the behavior of poly(ethylene glycol) (PEG), one of the most extensively investigated polymers due to its success as an antifouling coating in the biomedical industry, is not fully understood. The polymer, initially believed to be biologically inert, has demonstrated an affinity for proteins in a number of cases (Efremova et al, 2001; Sheth et al, 1997; Golander et al, 1992). Factors such as higher order solvent interactions as well as amphiphilicity of the polymer appear to be responsible for the observed protein binding. A simple, reliable and direct method for systematically measuring such interactions would be highly beneficial. 2 1.2 Motivations for this work 1.2.1 Advantages of using Spherical Grafting Surfaces The investigation of polymers grafted to spherical as opposed to flat surfaces offers one main advantage. The high surface area of the particles allows for a sufficient amount of grafted material to be made available for analysis by conventional methods such as gel permeation chromatography (GPC) and light scattering (LS) techniques, provided that the graft can be released quantitatively. This enables the results from the force measurements to be directly correlated with properties such as molecular weight, molecular weight distribution, and grafting density of the chains. Typically, the amount of polymer available when brushes are prepared on flat surface, such as inorganic substrates used for sensors (Weisenhorn et al, 1993) or polymeric membranes used in filtration and separation applications (Domke and Radmacher, 1998), is insufficient for molecular weight characterization by the standard techniques. The molecular weight of brushes prepared by a "grafting from" method (Zhao and Brittain, 2000), whereby the chains grow from surface initiators by the successive attachment of monomers, is commonly estimated from that of the solution polymers that form in parallel with the grafted species. Such inferences, however, may not always be appropriate given that surface initiated polymerization can be very different from bulk polymerization (Kizhakkedathu et al, 2003). Brushes can also be prepared by the "grafting to" method, whereby fully grown chains of a known molecular weight are attached to the surface, and the molecular weight estimated from that of the initial polymer. If, however, the grafting is affected by the polydispersity of the initial polymer whereby chains of different lengths are not equally reactive with the surface, then the assumption that the molecular weights of the original 3 and grafted chains are equal may not be valid. The grafting density is often not stated or is estimated using the bulk polymer density and the thickness of the dry polymer layer measured by ellipsometry. The brushes used throughout this work have been prepared on latex particles by other members of the Brooks laboratory using surface-initiated atom transfer radical polymerization (Jayachandran et al, 2002). The synthesis is outlined in Sections 2.2 and 3.2. The polymer was cleaved at the point of attachment to the latex by hydrolysis and characterized by GPC coupled to a multi-angle laser light scattering detector (MALLS) . Average grafting densities were estimated from the amount of hydrolyzed polymer per amount of latex and the surface area of the particles. The use of well-characterized particles enabled the measured interactions to be correlated with molecular weight and grafting densities. Due to the good control over properties of the grafted material, latexes could be prepared with similar graft properties but different monomer type or particle size, allowing these factors to be examined independently. 1.2.2 Development of Atomic Force Microscopy Applications Since its invention in 1986 as an imaging technique (Binnig et al, 1986), atomic force microscopy has become an increasingly popular tool for measuring interaction forces on the atomic and molecular levels. Although still a relatively new method, the employment of A F M in the polymer community has become widespread and the pace at which new applications continue to emerge is staggering. A detailed review has been published by Maganov (2000). Single chain configurations of polymers have been visualized through A F M imaging (Kumaki et al, 1996), and the probing of steric forces (Vermette and Meagher, 2002; Kidoaki et al, 2001a; Yamamoto et al, 2000a; Butt, et 4 al, 1999), adhesion interactions (Vansteenkiste et al. 2000; Kidoaki and Matsuda, 1999; McGurk, et al, 1999) and viscoelastic properties (Domke and Radmacher, 1998; Radmacher et al, 1995) in polymeric materials by A F M has become fairly common. Despite the vast number of polymer related papers published on A F M , many do not provide characterization using an independent method and do not relate their findings to other more established techniques. Consequently, the development and employment of new applications for the technique proceed rapidly while their accuracy and reliability is concurrently evaluated. The well-characterized surfaces utilized here have enabled us to compare the results obtained by A F M with those of more established techniques and to set up some criteria for which use of the A F M approach is valid. The molecular weight and molecular weight distributions obtained by an A F M technique are compared with those determined by G P C / M A L L S . The equilibrium thicknesses of the grafted layers measured by A F M are compared with hydrodynamic thicknesses measured by dynamic light scattering, as well as with thicknesses predicted by a self-consistent mean field model. It should be noted that the existing established techniques for characterizing polymers in terms of molecular weight and molecular weight distribution typically require the chains to be in solution, free from the grafting surface. Releasing the polymer from the surface for analysis, which can be done in some cases by chemically cleaving the chains at the point of grafting, while ensuring that any potential labile linkage along the chain remains intact, may not always be feasible. The development of a direct method for characterization of end-grafted polymers by A F M that does not require isolating the chains from the surface would clearly be advantageous. 5 While the cleanliness of the surface is vital in obtaining reproducible force measurements, this factor has been largely ignored in the bulk of the literature (Senden, 2001). Throughout this work, much attention has been given to minimizing surface contamination to ensure that the measured interactions are related to the controlled, systematic changes made to the system. The information obtained from force measurements of a material being probed depends on the direction in which the perturbation is applied. The majority of investigations of grafted polymers have focused on the response of the layer to direct compression. Here, our report on the response of densely grafted polymer chains to a pulling force applied in the direction normal to the surface is among only a handful of similar investigations in the literature (Yamamoto et al, 2000c). The stretching behavior of polymer systems has certainly been examined extensively, however the materials investigated have mainly been restricted to adsorbed polymers and low-density tethers. The lack of attention given to the stretching of chains in a dense polymer brush is presumably due to the complexity of interpreting the contributions from multiple chains as well as multiple segments on a single chain to the overall force profile. The method developed here for analyzing the stretching behavior of densely grafted polymers is novel and extends the scope of materials which can be characterized by A F M to include strongly adsorbing brushes. The remainder of this chapter w i l l be divided into two sections. The first w i l l focus on the interactions of polymers in solution. This w i l l allow for a better understanding of the nature of the forces being probed. The second section w i l l review the technical aspects of atomic force microscopy and discuss some recent trends in the literature. The 6 breadth of these topics is great and the goal is not to give an exhaustive account of the many experimental and theoretical advances in the fields, but to concentrate only on the findings that are of direct relevance to this work. 1.3 Polymers in Solution 1.3.1 Ideal Polymers Polymers are macromolecules that are formed by linking together a large number of small repeating units called monomers. The number of monomers is referred to as the degree of polymerization, N. Due to the typically high degree of polymerization and to rotation of bonds along the backbone, chains can adopt a large number of possible conformations. The conformations are not all equally favorable and rotation can be restricted i f the monomers possess bulky side groups. For flexible polymers, the thermal energy is of the same order of magnitude as the energy barrier associated with rotation about the bonds along the backbone. The structure of such molecules is therefore constantly fluctuating and must be described in terms of an average conformation. Based on a statistical mechanical treatment, the shape of a flexible chain is found to be, on average, that of a random coil (Teraoka, 2002). The trajectory of the random coil is akin to the motion of a particle diffusing under a random force. The simplest way to describe the average conformation of a polymer is to consider an ideal chain consisting of a series of vectors or bonds of length / connecting volumeless points that can freely overlap. Although the ideal chain ignores complex interactions between segments and solvent molecules, this is not unrealistic, as it shall become apparent that under certain conditions, real polymers in solution can behave ideally. 7 The space occupied by a chain has roughly the dimensions of a sphere with radius Rg, known as the radius of gyration. The Rg is defined as the root-mean-squared (rms) distance of the segments from the center of mass and, for an ideal polymer, it is given by (Teraoka, 2002): R2g=\l2N (1.1) where N is the number of randomly oriented bonds of length /. In terms of an actual polymer, N is the degree of polymerization and / is the length of the monomer. The value of Rg is considerably less than that of the contour length, Lc, which is the length of a fully stretched chain given by: LC=IN (1.2) The fixed valence angle of bonds along the backbone is typically accounted for by using the projected bond length as a measure of the monomer size. For vinyl polymers, which have a bond angle fixed to the tetrahedral angle of the sp3 orbitals (109.5°) and a C-C bond length of 0.154 nm, the length of a monomer is about 0.25 nm. Various models have been developed to describe the random walk of an ideal polymer. The most simple and common models are those of the freely jointed chain (FJC) and the freely rotating chain. In the former, the bond angle and dihedral angle are both assumed to be free, while in the latter, the restriction on the bond angle is maintained but free rotation about the dihedral angle is permitted. To account for the stiffness of real chains whose ability to rotate depends on the architecture of the chain, Flory introduced the characteristic ratio, Coo, and modified Eq. 1.1 so that Rl = ^-l2N, s 6 where Coo is, by definition, unity for a freely jointed chain and larger for a more rigid 8 chain (Flory, 1953). The persistence, p, is a dimensionless parameter that has also been C used to describe chain stiffness, and is equal to —— (Fleer et al, 1993). 6 The wormlike chain (WLC) model, which is commonly employed to describe the structure of more rigid, semiflexible polymers, uses the persistence length, q, as a measure of chain stiffness. In this more complicated model, the segments retain a "memory" of chain direction of neighboring segments. The directional correlation, which decays exponentially with s, the length of the chain separating the two segments, can be expressed as (Teraoka, 2002): < cos0(s) > - Qxp(-s/q) (1.3) When two segments are separated by a distance s < q, the directional correlation is still present and < cos#(J) > * 0, whereas when I » q, the segments are no longer correlated. The persistence length roughly describes the maximum length of a chain segment that remains straight. The persistence length of reasonably flexible chains is only somewhat larger than the size of a monomer, whereas for stiff rods, q —> co . The persistence length is also related to the persistence by p = -t-. A segment with length twice the persistence length is considered statistically independent. Kuhn (1934) recognized that it is possible to describe a semiflexible chain with persistence length q and N repeating units of size / as completely flexible, by dividing the chain into a smaller number of segments NK, where the length of a segment lK is somewhat larger than that of a monomer. The length of a statistical segment, or Kuhn length, is related to the persistence length by lK =2q. 9 1.3.2 Real Polymer Solutions The chains considered above consist of non-interacting segments whose trajectory is described as a random walk through space. On a lattice, this is equivalent to allowing a segment to revisit the same site, since the segment has no memory of where it has been. When the interaction of segments and solvent molecules is favorable, the walk through space is no longer random but self-avoiding, resulting in an expanded, swollen chain. The proportionality between the degree of polymerization and the radius of gyration, which was given in Eq. 1.1 for an ideal chain, can be expressed more generally as: Rg=aMv (1.4) where M is the molecular weight of the polymer, a is a parameter determined by light scattering, and v is the Flory exponent (Fleer et al, 1993). The exponent is v =1/2 for ideal chains and v = 3/5 for real chains in a good solvent. The value of a depends on the size of the monomer, stiffness of the chain, and solvent quality. As with small molecules, there is an excluded volume associated with real polymers in good solvent that impedes them from freely overlapping. The interactions of macromolecules in solution are, however, fundamentally different from those of other solutions, and are the basis for their unique physical properties. The finite size of small molecules causes deviations from ideality at high concentrations. To a good approximation, the system behaves ideally when the solution is sufficiently dilute. Due to the connectivity of monomers in a macromolecule and the subsequent intrachain interaction, the finite volume of the molecule is significant even at low concentrations where chains are isolated from other chains. At high concentrations, the interchain interactions dominate the excluded volume effects. 10 The effective excluded volume depends on the quality of the solvent and increases with the preference a segment has for interacting with a solvent molecule over another segment. Both enthalpic and entropic effects contribute to the excluded volume parameter. The well known Flory-Huggins mean-field model of polymers is a widely used lattice theory for treating the excluded volume (Flory, 1953; Huggins, 1942). In the mean-field theory it is assumed that the segments are distributed homogeneously throughout the solution and that all segments experience, on average the same force field. It is valid for a high density of weakly interacting chains. Briefly, the polymer and solvent molecules are arranged on a lattice with each site being occupied by either a segment or solvent of equal volume. The free energy of the system before and after mixing is compared. The expression for the entropy of mixing, AS m j X , comes from the different number of possible arrangements of chains on a lattice when all sites are occupied by polymer (i.e. a melt) and when sites can consist of segment or solvent. The enthalpy of mixing AH m j X is associated with the Flory-Huggins parameter, %, which is the change in interaction energy, As, involved in bringing a solvent molecule immersed in pure solvent and surrounding it by polymer. The % parameter was initially defined as: ZAs kBT where Z is the lattice coordination number, kg is the Boltzmann constant, and T is temperature. A positive % indicates that segment-segment contacts are preferred over segment-solvent contacts whereas a negative x means that segment-solvent contacts are preferred. The excluded volume term appears as the second virial coefficient in the expansion of the osmotic pressure f l in terms of mass concentration c (Teraoka, 2002): 11 n RT c • + M -2-x 2 J c 2+... (1.6) where R is the ideal gas constant, M is the molecular weight, and v is the partial specific volume, V is the molar volume, and subscripts 1 and 2 refer to the solvent and polymer, respectively. When the second virial coefficient is equal to zero (x = 1/2), the solution can be considered approximately ideal. The ability of the solution to behave ideally at high concentrations is unique to polymer systems. As indicated in Eq. 1.5, the % parameter can be adjusted by changing the solvent quality as well as the temperature. The state characterized by % = 1/2 is known as the theta condition, and denotes the ability of polymers to freely overlap. A value of % < 1/2 means that the excluded volume term is positive resulting from a net repulsion between segments. Similarly, the excluded volume term can be negative (x > 1/2) indicating that there is an overall attraction between segments. These conditions are summarized in Table 1.1. Table 1.1. Excluded volume conditions Chi Parameter" 2" Virial Coefficient Solvent Conditions X > lA negative poor X = Vi zero theta (ideal) X < V2 positive good a When x = 0, the solution conditions are athermal and the contact energy between segment and solvent is the same. The good solvent conditions are fully attributed to a favorable increase in entropy. Due to a discrepancy between x values determined from the heat of mixing measured by calorimetry as well as from solvent activities measured as a function of polymer 12 concentration, the definition of the chi parameter was modified to include an entropy term. It is therefore more accurate to view the chi parameter as a measure of free energy rather than simply interaction energy. As described above, chains are attracted to one another when the formation of segment-solvent contacts is unfavorable. The resulting increase in local segment concentration, however, is associated with a reduction in entropy as a result of the lower number of chain configurations in the region of overlap. The effect of the entropic contribution is to increase the excluded volume and favor chain repulsion. Theta conditions are achieved by the balancing of these two opposing forces, which enables the polymers to freely interact. 1.3.3 Terminally Attached Polymers on Flat Surfaces The general principles discussed above are applicable to terminally attached polymers as well as free chains, with the important distinction being an additional reduction in local entropy due to the confinement of one chain end. In addition, the density at which the polymer is grafted controls the local segment concentration and dictates the extent to which interchain interactions are significant. The ability of densely grafted polymers to stabilize colloids and to exclude protein stems from the repulsive force exerted by the layer in response to additional macromolecular crowding. Grafted polymers can be categorized into two distinct regimes, with the fundamental parameter being the average distance between grafting points D relative to Rg (Alexander, 1977). At sufficiently low grafting densities a, a chain in good solvent occupies roughly a half-sphere with radius comparable to the radius of gyration. At high o~, interchain interactions are significant and the chains stretch away from the surface due to excluded volume effects. The formal distinction is made when D > 2Rg, denoting the mushroom 13 regime, and D < 2Rg, which corresponds to the brush regime. In this work, only grafted polymers that are classified as brushes are investigated. Our physical picture of a polymer brush can be attributed to Alexander (1977), who described the free energy W(L) of a chain in a brush as the sum of the chain stretching energy and the excluded volume interactions. An expression for the equilibrium thickness of the brush is derived by minimizing W. An alternate mean-field approach used by Fleer et al. (1993) predicts a different free energy, expressed as: W kBT ( L2 +vex*N2l^ (1.7) 4pNl2 2L where L is the distance of the free chain ends from the grafting surface, p is the persistence (defined in Section 1.3.1), and v e x is the excluded volume parameter, defined here as l - 2 x . The first term, which describes the energy required to stretch an elastic chain, is proportional to the square of the displacement L like a normal Hookian spring. The contribution of the excluded volume to the free energy is given in the second term. Although the above equation overestimates both the stretching and excluded volume contributions, these errors counteract when W is minimized and the expression obtained for the equilibrium thickness Le is the same as that derived by Alexander (1977): Le=N{pvexcrl5)m (1.8) The important result is that the equilibrium thickness of a flat brush in good solvent is linearly dependent on the degree of polymerization and varies as grafting density to the power of 1/3. Experimental tests of the above power law based on the thickness of different brushes using neutron scattering and reflectivity techniques have produced ambiguous results. 14 Some studies have shown brush heights to obey the predicted scaling law (Auroy et al., 1991) while others have produced different values for the exponents. Bijsterbosch et al. (1995) measured the thickness of adsorbed PS-PEO block copolymer layers for various PEO block lengths and found the height to scale as L e ~ N 0 8 o 0 4 1 . The slight difference between the measured and predicted exponents was attributed to the uncertainty in the grafting density of the brushes, which was estimated from fitting a model density profile to the reflectivity curve. Numerical SCF calculations by Currie et al. (1999a), however, have found that the exponent is roughly constant for long chains but may vary for short chains. This leads to erroneous predictions when determining the relationship between L e and a using the data from a range of molecular weights. When the thickness was plotted against a independently of the molecular weight, the fitted power law resulted in an exponent of 0.33 for N = 700 and 0.35 for N = 450, which agrees with theory. The Alexander-de Gennes model is advantageous in that it is conceptually the most simple, however it contains a number of assumptions which are inconsistent with results of more sophisticated models. Their description of a brush assumes a constant concentration profile throughout the brush with all chain ends located at the outer edge of the polymer layer. A different picture of the brush using self-consistent field (SCF) arguments suggests that the polymer concentration decreases monotonically away from the grafting surface and the free chain ends are located throughout the layer (Fleer et al., 1993). Here, no assumptions are made a priori about the volume fraction cp(L), which is determined self-consistently using the interaction potential, which in turn depends on the local volume fraction distribution. In the SCF models, parameters such as solvent quality and polydispersity are found to have large effects on the volume fraction profile and the 15 chain end distribution. Despite the fundamental differences, both models find the brush thickness in good solvent to scale with N and a 1 / 3 according to Eq. 1.8. The brush predicted by SCF, which has a parabolic volume fraction profile, is "softer" than the step-function brush, which abruptly vanishes at the periphery. Consequently, the energy required to compress the parabolic brush is predicted to have a weaker dependence on compression than that of the step-function brush, particularly in the region of low compression. In the region of strong compression, the free energy is dominated by excluded volume interactions and the two models predict the same dependence. The pressure P(L) between a flat brush with equilibrium thickness L e and a planar surface is derived by the Alexander-de Gennes theory (de Gennes, 1987) as: P(L) = k s T Z)3 9/4 f ^3/4 \Le J (1.9) where D is the mean distance between grafting points. The original equation, which was derived for the compression of two identical flat brushes each with equilibrium thickness L e , contained 2L e in place of L e . The interaction between a brush and a flat surface can be described by the same equation after making the appropriate L e substitution, since the original derivation assumes no interpenetration of the brushes as they are compressed. The first term in Eq. 1.9 results from the osmotic pressure, which increases with polymer concentration as the two surfaces are brought together. The second term, which lowers the pressure, represents the decrease in elastic energy as the chains are compressed. The above expression is roughly exponential over the range of 0.2 < L / L e < 0.9 and can be approximated as (Israelachvili, 1992): 16 P(L) = 5°kfexp(-2KLILt) (1.10) The surface force apparatus (SFA) and atomic force microscopy (AFM) techniques have been used to test Eq. 1.10 by fitting the force profiles obtained for compression of a flat brush to an exponential and solving for the parameters D and Le. When using compression data obtained by A F M , Eq. 1.10 must be modified to account for the tip geometry (Butt, et al, 1999; Yamamoto et al, 2000a,b). Refer to the review of brush interactions in Section 1.4.4.4 for a more thorough description of the results in the literature. 1.3.4. Polymers at Spherical Interfaces The investigations of terminally attached polymer chains on a planar surface have been extended to include chains anchored to curved surfaces (Lin and Gast, 1996; Wijmans and Zhulina, 1993; Dan and Tirell, 1992; Ball et al, 1991), which is directly relevant to this work. The description of chains attached to spherical surfaces has practical implications, providing a model for such structures as polymers grafted onto small colloidal particles or the corona of polymer micelles. The effect of curvature is significant, particularly when the surface is highly curved or when the chains are very long, as the volume accessible to the chains increases with distance from the grafting site according to a power law (Zhulina et al, 1991). Due to the additional volume available, chains grafted to a spherical surface are less stretched than chains with similar molecular weight and density grafted to a flat surface. One major difference between the pictures of planar and curved brushes is the prediction of a "dead zone" near the spherical interface where the probability of locating a free chain end vanishes (Wijmans and Zhulina, 1993). A dead zone has not been associated with planar brushes. The size of the dead zone was 17 found to be a complex, nonmonotonic function of the particle radius, and depended on whether the curvature was small, intermediate, or large. Daoud and Cotton (1982) derived an expression for the volume fraction profile of a spherical brush of radius R based on the step-like model of Alexander (1977) and de Gennes (1980): / r, \m(3v - l ) /2v cp(L)=cj^l2v\-±-\ (1.11) where L is the perpendicular distance from the pointing of grafting, v is the Flory exponent which depends on the solvent quality (v = 3/5 for a good solvent and v= 1/2 for a ©-solvent), and m depends on the geometry of the grafting surface (m = 0, 1, and 2 for planar, cylindrical, and spherical surfaces, respectively). In the case of R » L, the volume fraction profile resembles that for a planar brush. The average brush height is approximately given by: Le ~ aN3/(3+m)crV{3+m)(R/a)m,(3+m) (1.12) where a is the characteristic monomer size. As the interface curvature decreases, the equilibrium thickness approaches that of a planar brush. Based on SCF arguments, Dan and Tirell (1992) found the characteristic radius of curvature at which the brush starts to deviate from planar behavior to be within an order of magnitude of the chain dimensions of the planar brush (R / L e < 10). Also using a SCF approach, Wijmans and Zhulina 3/5 (1993) found good agreement with the scaling laws L e ~ N for flat surfaces and L e ~ N for spherical surfaces (star-shaped polymers) when the grafting density was high. Deviations from the power laws were found at low grafting densities. 18 1.4 Atomic Force Microscopy (AFM) The structure and properties of terminally attached polymer layers can be investigated by various experimental techniques. The volume fraction profile has been described using neutron scattering and reflectometry (Bijsterbosch et al, 1995; Cosgrove et al, 1994) and the layer thickness measured by hydrodynamic methods (Cohen and Khorosheva, 2001). The interactions of the grafted layer can also be probed by direct force techniques using the surface force apparatus and the atomic force microscope. In the following section, the major instrumentation issues of the A F M and recent relevant applications are described. 1.4.1 General Instrumentation The A F M measures the force between a sample surface and the apex of a sharp probe that is positioned at the end of a microfabricated cantilever. The surface chemistry of the probe can be modified, enabling the interactions between various materials to be examined. Every A F M has two main components that enable the force law, or the force as a function of separation, to be determined. The first is a mechanism that varies the relative position of the surface in a very precise manner. A typical design has the sample adjacent to a piezoelectric tube, which expands and contracts with applied voltage. The second component includes a force sensing spring and a detection system to monitor changes in deflection caused by interactions between the tip and surface. The cantilever bends toward or away from the surface depending on whether the interaction force is attractive or repulsive. An optical detection system is commonly employed to measure the deflection, whereby a laser beam is reflected off the backside of the cantilever onto a position sensitive photodiode. Deflection of the cantilever by a distance Ad results in 19 deflection of the laser beam by an angle of roughly 2Ad/lc where lc is the length of the cantilever (100-200 pm). Due to the optical lever system, the deflection of the laser at the photodiode is ~ 1,000 times the deflection of the cantilever (Prater et al, 1990). The force is calculated by multiplying the measured deflection by the spring constant k according to Hooke's law. By convention, the deflection of the tip towards the sample is negative (attraction) and away from the sample is positive (repulsion). In many ways, the atomic force microscope is similar to the surface force apparatus. In the case of the SFA, the force between two curved mica surfaces positioned perpendicular to one another is measured. Typically, the radius of curvature of the mica surfaces is roughly 1 cm. In contrast, the typical radius of curvature R of commercially available A F M probes is significantly smaller, ranging between 5 and 40 nm. Due to the small tip radius, A F M offers high spatial resolution and can be used to probe heterogeneous surfaces. With the measured force being directly proportional to the contact radius (Section 1.4.3.1), the high resolution comes at the expense of sensitivity. The forces measured by A F M are typically between 10"9 and 10"'° N . The success of the technique is based on the ability to microfabricate cantilevers with k of the same order as interatomic spring constants. The spring constant of a material is related to the mass m and natural resonance frequency co by k = co m. The vibrational frequencies of atoms 1 ^ in a molecule or crystalline solid are typically > 10 Hz. The spring constant between 25 atoms of m ~ 10" kg is therefore on the order of 10 N/m. By comparison, commercially available cantilevers have spring constants as low as 0.01 N/m. The spring constant of the A F M cantilever should be sufficiently small to be able to sense the force between atoms or molecules. At the same time, a high co is required to minimize sensitivity to external 20 vibrations such as building noise (~ 100 Hz). These conditions are simultaneously achieved through microfabrication of cantilevers. The A F M differs from other force sensing techniques in that it was initially developed as an imaging tool. The development of the A F M by Binnig, Quate and Gerber (1986) was motivated by the desire to image non-conducting surfaces, which was a requirement for the scanning tunneling microscope (STM). Although not as sensitive as the STM, the A F M is much more versatile and has been used to examine a wide range of materials in various atmospheres. With the ability to probe interactions in fluids, A F M is very attractive to investigators interested in biological and polymeric materials. The topography of a sample is mapped by monitoring the deflection of the tip as it is raster scanned across the surface. Particularly for soft samples that are easily deformed, it is desirable to maintain a small scanning force. This is achieved by a feedback loop that adjusts the height of the sample to maintain a small, predetermined cantilever deflection, and therefore a small force. The scanning force can further be reduced by driving the tip to oscillate at high frequency while it is raster scanned over the surface. In this mode of operation, variations in surface topography or composition are detected by measuring changes in the amplitude of oscillation rather than deflection. When first invented, it was a feat to even obtain a decent image of a surface using A F M . Since then, considerable progress has been made. In 1996, the first A F M image of a random coil conformation of a single polymer chain frozen on a substrate was obtained (Kumaki et al, 1996). A thorough review of recent trends in imaging of polymeric materials is given by Maganov (2000). The bulk of this thesis however does not focus on imaging but rather on the 21 measurement of force as a function of tip-sample separation. The following section is therefore concerned with direct force measurements. 1.4.2 Construction of a Force Curve Direct force measurements are obtained by varying the position of the tip in the direction normal to the surface, as opposed to applying a raster motion of the type used in imaging. The features of a force curve depend on the nature of the interaction forces between the tip and sample. The most basic force curve showing the deflection of the tip interacting with a hard surface as a function of relative sample position is presented in Fig. 1.1. The main features are labeled (A) through (E). The tip-sample interaction at each of these points is shown schematically at the left of the figure. The cycle begins with the tip located at a distance sufficiently far from the sample (A) that no interaction is measured (zero deflection). The sample is moved closer to the tip and contact is eventually made at point (B). Here, an attractive van der Waals force causes the tip to deflect toward the sample (negative) in what is often referred to as the 'jump-to-contact'. The cantilever undergoes a mechanical instability during the jump-to-contact as it experiences a change in force with sample position that is larger than the spring constant. The convention in the literature is to remove any data points obtained over this small region. Further movement of a relatively hard sample toward the tip by a distance Ax causes the tip to deflect an equal distance Ad. This region (C) which has a slope of Ad/Ax = 1 (nm/nm) is called the region of constant compliance. In this region, the cantilever is more compliant than the sample and the optical sensitivity (volts/nm) of the detector with respect to the cantilever deflection can be measured. The deflection of the tip can be 22 converted from the measured value, in volts, to units of length (nm) by dividing by the optical sensitivity. The features (A) through (C) arise from bringing the sample and tip closer together. A force curve obtained by moving the sample in this direction is referred to here as a compression profile. When the force on the tip reaches a predetermined value, the motion of the sample is reversed and the decompression profile is obtained. In the curve shown in Fig. 1.1, the force in the reverse direction (C to D) initially follows that of the forward direction (B to C). Such behavior is typically observed on hard surfaces. When probing compliant samples, hysteresis in this region can occur as a result of relaxation effects. This case will be addressed later in more detail. The sample is further retracted from the tip until the cantilever deflection reaches zero. V B i cf 4 ; -— j O CO 5= CD •D sample position (nm) Figure 1.1. Features of a basic force curve on a hard surface: A) large tip-sample separation B) jump-to-contact C) constant compliance D) adhesion E) tip snaps free of sample. 23 In the case where no bonds have formed between the tip and sample upon forced contact, the deflection signal will remain at zero as the sample is retracted even further. In most situations, however, the tip adheres to the sample (D) for some distance past the point where initial contact was made on approach (B). At some critical position, a spring instability occurs again and the deflection abruptly returns to zero (E). The maximum attractive (negative) force measured just prior to zero deflection is the force of adhesion and is commonly referred to as the "pull-off or "rupture" force. The force of adhesion is related to the interfacial energies between the tip and sample surfaces, and the solution. An adhesive force of the type shown in Fig. 1.1 is typically observed between the tip and a hard surface. When a polymer chain bridges the surface and the tip, however, a very distinctive adhesive force that is easily distinguishable from the one depicted is observed. Relatively compliant samples may be indented by the tip, in which case the measured deflection is equal to Ax less the amount of indentation. Force curves obtained on samples that are hard and soft relative to the tip are compared in Fig. 1.2. The shape of the force curve in this region provides information on the elastic properties of deformable bodies such as cell surfaces, thin polymer films, and polymer brushes. To obtain valuable information in this region, the spring constant of the cantilever should be comparable to that of the material being probed. If the cantilever is too stiff, it will not be sensitive to the elastic forces of the sample; if the cantilever is too soft, the force curve will describe the properties of the cantilever rather than the material under investigation. 24 • compliant sample position (nm) Figure 1.2. Typical force curves obtained upon compression of compliant and non-compliant samples. In a typical A F M experiment, tip deflection is recorded as a function of sample/piezo position. Since it is often desirable to fit the experimental data to a theoretical force law, which is expressed in terms of force as a function of surface separation, the sample position must be converted into tip-sample separation. Ducker et al. (1992) were the first to perform this transformation by describing the change in separation AL as the difference between the piezo position Ax and the tip deflection Ad. A raw force curve is compared with an adjusted force curve in Fig. 1.3. In the region of constant compliance where Ax = Ad, the separation does not change. Note that the abscissa in the adjusted force curve in Fig. 1.3 gives the change in separation, AL. Actual values of L are obtained by assigning a position to correspond with L = 0. By convention, this is denoted by the onset of the constant compliance region. One advantage of the SFA over the A F M is that in the former, the absolute distance between the surfaces is measured rather than inferred. 25 In an A F M experiment, the probe must fully compress the sample to obtain the surface separation L = 0 nm as defined above. Application of such high loads may damage some soft surfaces, while in some very compressible samples, it may not even be possible to reach the constant compliance region with a given tip. A B o CD "a x sample position L 0 tip-sample separation AL Figure 1.3. Comparison of A) raw force curve and B) adjusted force curve according to the method of Ducker et al. (1992). 1.4.3 Geometric Considerations 1.4.3.1 Derjaguin Approximation It is often desirable to relate the force measured between two surfaces to a known force law. This poses a challenge when the precise geometry of the A F M tip is not known. A convenient expression for relating the force law between a sphere of radius R and a flat surface to the free energy per unit area W(L) between two planar surfaces is given by the Derjaguin approximation (Derjaguin, 1935): F(L)sphers=2xRW(L)ph (1.13) The above expression also holds for the interaction between two perpendicular cylinders of radius R. This allows the force measured between two crossed cylinders of known 26 radius, as in the case of the SFA, to be related to the force between any two equivalent surfaces of a different radius simply by scaling by R . A similar expression is given for the force between two spheres of radii R i and R2, whereby R in Eq. 1.13 is replaced by 1.4.3.2 Colloid Probe Microscopy The difficulty in modeling the interaction between a flat surface and one with an odd geometry such as that of an A F M tip can be circumvented by attaching a particle of known radius to the end of the cantilever and applying the Derjaguin approximation. This technique, now referred to as colloid probe microcopy, was first performed by Ducker et al. (1992), who measured the forces between a 3.5 um silica particle and a flat silica surface in aqueous solution as a function of ionic strength and pH. The measured force/radius (F/R) agreed with theoretical values obtained by combining the electrostatic and van der Waals interactions of two planar surfaces and applying the Derjaguin approximation. Following the same approach, L i . et al. (1993) measured the interaction forces between two 2 jam polystyrene particles in solution as a function of ionic strength and found good agreement with theoretical predictions. Since then, colloid probe microscopy has been used to investigate the interactions between a flat surface bearing adsorbed or grafted polymer and a probe of known geometry consisting of polystyrene (Courvoisier et al., 1998), silica (Meagher et al., 2002; Braithwaite et al., 1996), zirconia (Biggs, 1995), and alumina (Muir et al., 2001). Typically, the measured force is fit to the expression given by Alexander (1977) for the pressure, or force per unit area between a flat brush and a planar surface. This is done by integrating Eq. 1.10 from Leq to L to 27 obtain the energy per unit area between a brush and a flat surface and applying the Derjaguin approximation to give the force between a flat brush and a spherical surface. 1.4.3.3 Standard Silicon Nitride Tip Geometry The derivation of the Derjaguin approximation assumes that the sphere can be described as a series of very small locally flat concentric rings. Furthermore, Eq. 1.13 is only valid when L « R and L * « R , where L* is the distance over which the interaction scales to zero. The A F M tip is commonly modeled as a parabola with a spherical apex, but the applicability of the Derjaguin approximation to the A F M measurement is questionable due to the very small radius of a standard A F M tip. Force measurements obtained using standard silicon nitride A F M tips have been compared with known force laws by integrating over the whole tip surface. For a rotational symmetric tip, the force is integrated over an area of 2nrdr, where r is the radius of the tip at any distance z from the surface. The force F on the tip is related to the pressure, or force per unit area / between two flat surfaces by (Butt, et al, 1999): dr F = 2n ffrdr = 2TT f°f(z)r — dz (1.14) dz The parabolic shape of the tip can be described by z - L = r 12R , where R is the radius of curvature of the tip. Differentiating r with respect to z gives drldz = R/r, which can then be substituted into the above equation. Butt et al. (1999) described the force between a flat brush and a parabolic tip by integrating Eq. 1.10 over the tip surface, giving: D ^ v L„ 50kBTRLe D3 2nL v Le j (1.15) 28 1.4.4 Different Interaction Forces Standard A F M and colloid probe microscopy have been used to investigate the interactions between a wide range of materials and have been used to test a number of force laws. In Fig. 1.4, various force laws for a sphere interacting with a planar surface are shown, along with the corresponding force profile. Figures 1.4a-c correspond to compression profiles; Figures 1.4d-e correspond to decompression profiles. In the following sections, a description of the individual force laws relevant to this work is given. Since an A F M experiment does not distinguish between different forces, the nature and range of various interactions are described to enable interpretation of the force profiles measured. APPROACH RETRACT A Electrostatic Double-Layer D Adhesion B van der Waals 6 L2 E Polymer Extension (WLC) PL i f . - - r . i 4 C Steric (Brush) Figure 1.4. Typical force profiles and theoretical force laws for a sphere interacting with a flat surface. See text (Section 1.4.4) for description of parameters. 29 1.4.4.1 Electrostatics The concentration of counterions near a charged surface depends on the electrostatic potential y/x at any point x and can be described by a Boltzmann distribution: px=PlBe-*er>/k°T (1.16) where is the bulk concentration, e is the electric charge and z is the ion valency. At the surface (x = 0), the concentration of counterions p0 is calculated according to the above equation where y/ is equal to the surface potential, y/0. The counterion concentration is related to y/by the Poisson equation: zepx=-££a—\ (1.17) dx Combination of Eq. 1.16 and 1.17 yields the nonlinear Poisson-Boltzmann (P-B) equation: ezy/ d w 2ez . , —Y = PooSinh \kBTJ (1.18) The solution to the P-B equation as written above gives the potential at any point x away from a flat surface. Linearization of the sinh function for small potentials (ei///kBT « 1) gives: % 2 ^ r ^ V (1.19) The solution to the linearized P-B equation is the Debye-Huckel equation: Vx =^0exp(-/a) (1.20) The electric double layer is the region over which electroneutrality is achieved. It is characterized by the decay length, or inverse Debye length, K " 1 , given by: 30 K~x = (ss0kBTI2e2z2pJ12 (1.21a) which, for a z:z electolyte (i.e. NaCI) can be written as: K~x =(££0kBT/2e2Navl)]/2 (1.21b) where N a v is Avogardo's number and the ionic strength I = — 2 f N a v At high surface potentials, the exact solution of the non-linearized P-B is: " l + ye-*3 2kBT Vx = log 1 . „ - K T \ —ye ^ML^-™ ( 1.22a) where y = tanh(e^ 0/4kBT) « tanh[^ o(wF)/103] (1.22b) The above treatment, known as the Gouy-Chapman theory, applies to symmetrical 1:1 electrolytes. The Grahame equation may be used to relate the charge density and surface potential in an electrolyte solution. For a symmetrical 1:1 electrolyte such as NaCI, the Grahame equation gives: crc = fiee0kBT [NaClf2s\X)h(ey/0 l2kBT) (1.23a) = 0.117[AfaC/] l / 2sinh(^ o/51.4) (1.23b) where Eq. 1.23b is at 25° C, [NaCI] is in M , y/0 in mV, and a c in C/m 2. The above equations describe the potential and the distribution of counterions away from an isolated charged surface. A repulsive force exists between two equally charged surfaces. The origin of the force is not electrostatic and is attributed solely to the osmotic repulsion of the counterions in the gap (Israelachvili, 1992). The repulsive force increases as the surfaces are brought together and the counterions in the double layers are forced to 31 overlap. The pressure P at any point x between two identically charged flat surfaces separated by a distance L in an electrolyte solution is given by: Px(L) = kBT (1.24) where ^ pmj is the total ionic concentration at the midplane. Assuming the potential at the midpoint is the sum of the potentials from each surface and can be described by the Gouy-Chapman theory, the resulting pressure between two planar surfaces is given by: P(L) = 64kBTPye-*L (1.25) The electric field between two identical parallel planar surfaces vanishes at the midpoint and the only contribution to the overall force is from the osmotic pressure of the counterions. The interaction obtained for the symmetric case is described below. A different expression is derived for the electrostatic interaction between asymmetric surfaces as a result of dissimilar charge densities or geometry (Russel et al., 1989). That case is considered in Section 2.3.2. The interaction free energy per unit area W is obtained by integrating equation (1.25) with respect to L. At low surface potentials, below about 25 mV, the surface charge density a c is directly related to the surface potential and the electrostatic interaction energy between two identical surfaces is given by: W{L) = 2££oKi//02e~KL = 2CTc2e~KL IKES0 (1.26) The above expressions are valid for L > K " 1 . At smaller separations, the exact interaction potential can only be determined by numerical solutions of the Poisson-Boltzmann equation. 32 1.4.4.2 vanderWaals The van der Waals (vdW) force arises from the interactions between either permanent or induced dipoles. The vdW interaction free energy per unit area between two flat surfaces is a function of their inverse separation squared and is given by (Israelachvili, 1992): W(L) = -AH l\2nL2 (1.27) where A H is the Hamaker constant. The Lifshitz theory (Lifshitz, 1956) provides an expression to calculate the Hamaker constant in terms of the macroscopic properties of the media such as the dielectric constants and the refractive indices. The constants for many materials are found in the literature. The van der Waals force between two surfaces in a medium can in theory be attractive or repulsive, but typically appears in the approach curve as a small negative deflection (attraction) just prior to contact. 1.4.4.3 Derjaguin-Landau-Verwey-Overbeek (DLVO) theory The combination of the double-layer and the van der Waals (vdW) interactions is often described as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory (Derjaguin and Landau, 1941; Verwey and Overbeek, 1948). Any additional interactions such as the steric repulsion between grafted polymer layers are referred to as non-DLVO forces. The D L V O theory is commonly used to describe the behavior of colloidal particles and to explain the conditions under which stability is achieved. The relative vdW and double-layer contributions to the overall D L V O interaction profile is demonstrated in Fig. 1.5. Because it is described by a power law, the vdW attraction always exceeds the double layer repulsion at small distances. The interaction energy at contact is known as the primary minimum. Depending on the ionic strength, a secondary minimum at some 33 distance may be observed where attractive vdW forces dominate at larger separations and repulsive double-layer forces dominate at intermediate separations. The thermal energy of large particles may not be sufficient to overcome the repulsive energy barrier on a reasonable timescale and the particles can become trapped in the secondary minimum (Israelachvili, 1992). While the primary minimum is thermodynamically the most stable state, particles trapped in the secondary minimum are said to be kinetically stable. Further increase in ionic strength or decrease in surface charge density lowers the repulsive energy barrier and can result in aggregation. At very high ionic strength or very low charge density, attractive vdW forces dominate at all separations. tr *> ~ c 0 o I .ViBoubfeaye® -U l-X" 1-1** .V*: \ repulsion \ Energy \ barrier v > \ / \ ^ ^ 1 \ v 1 \ ** , / Total \% ^ - « * t W t ^ " 7 1 1 0 1 ^ 2 min Separation L \ / « attraction • — 1 rntn Figure 1.5. Schematic of energy versus separation profile for D L V O interaction. 1.4.4.4 Steric Forces The forces involved in the compression of polymer brushes are often termed steric forces, although it should be recognized that these forces are not a result of a physical 34 barrier as in the conventional meaning of "steric". The forces exerted by polymer brushes are a consequence of excluded volume interactions, as discussed in Section 1.3.3. In the literature, compression profiles of end-grafted polymers in good solvents have exhibited a monotonically increasing repulsive force with decreasing tip-sample separation (Efremova et al, 2001; Kidoaki et al, 2001a; Overney et al, 1996; Sheth et al, 2000; Vermette and Meagher, 2002). The measured force profiles obtained by both SFA and A F M have been compared with the expression derived by Alexander (1977) for a brush interacting with a flat surface (Eq. 1.10). The SFA data obtained by bringing together two mica sheets bearing end-functionalized adsorbed polystyrene in good solvent fit the predicted force law after making the appropriate geometric modifications (Tautonera/., 1990). Yamamoto et al (2000a) examined the force between highly dense (0.4 chains/nm2) brushes of poly(methyl methacrylate) (PMMA) of different molecular weights with a silica particle probe using A F M . They found the repulsive force to increase monotonically as the tip-sample separation decreased. Equilibrium thicknesses increased with molecular weight of the graft. The measured force profiles did not fit the theoretical model of Alexander for compression of a brush. A possible explanation for the poor fit was that the expression was derived for "moderately high" grafting densities and could not be applied to brushes with a as high as that used in the study. O'Shea et al (1993) found that the compression profile of a grafted block copolymer in good solvent could be described by an exponential but the equilibrium thickness obtained by fitting to Eq. 1.10 was too large. There, the surfaces were prepared by the physisorption of poly(ethylene oxide) (PEO) /polystyrene (PS) onto mica. The distance 35 between chains D measured by fitting reflectometry data was ~ 11 nm, and the radius of curvature R of the silicon nitride tip was -100 nm. The tip shape was not considered since R was significantly larger than D, however this approximation might not be entirely reasonable. The discrepancy was attributed to the simplicity of the model, which does not consider the ability of the unanchored PEO segments to move along the mica surface or the PS segments to splay around the A F M tip. Other experimental studies have examined the possibility of chain splaying, which has been predicted by theoretical models (Steels et al, 2000a; Guffond et al., 1997; Murat and Grest, 1996; Subramanian et al, 1996). Kelley et al. (1998) compared the compression profiles obtained by A F M and SFA for a copolymer brush in a good solvent and found that the A F M profiles were less steep than the corresponding SFA profiles in the region of high compression. They attributed this behavior to chains escaping behind the A F M tip. Butt, et al. (1999) measured the steric forces between a silicon nitride A F M tip and polymers grafted on a silicon substrate in good and theta solvents. The force profiles fit an exponential as predicted by Alexander (1977) and the fitted value of D agreed within experimental uncertainty with an estimate based on the polymerization time. One motivation of the study was to test whether an escape transition occurred. It has been predicted that upon compression by a finite size obstacle, a chain will partially escape behind the obstacle at a critical compression to minimize the free energy (Guffond et al., 1997; Murat and Grest, 1996). The data was fit to functions predicted by Guffond et al. which describe the behavior of a confined and escaped chain in a theta solvent. They found that the parameters obtained by these fits were unrealistic and concluded that the 36 data could not be described by these equations. It was proposed that an escape transition might not be observed since the grafting density is relatively high and the space around the tip is already occupied by polymer. 1.4.4.5 Other Compression Interactions One noteworthy phenomenon associated with using an A F M tip modified with a polystyrene latex particle probe is the observation of an attractive "hook" that pulls the particle into contact with the surface (Considine et al, 2001). The attraction is manifested as a "jump-to-contact", but occurs at much longer range (20-400 nm) than would be expected for van der Waals interactions. This behavior has been attributed to the incomplete wetting of the polystyrene and any other hydrophobic material by water, which leads to the coalescence of gas bubbles on the surfaces as they are brought together. The range of attraction varied significantly and was associated with the local roughness of the surfaces. The attractive force diminished when the water was degassed. This type of attractive hook, however, was not observed in the present work. 1.4.4.6 Adhesion (Johnson, Kendal, and Roberts (JKR)) The work of adhesion is the change in free energy per unit area when two surfaces are separated from contact to infinity. The Derjaguin approximation can be used to relate the adhesion force of two rigid spheres to their work of adhesion. Real macroscopic bodies are always to some degree compressible and their contact area depends on the elastic modulus of the materials. The force of adhesion, or "pull-off force between an elastic sphere and a flat surface is described by the Johnson, Kendal and Roberts (JKR; 1971) theory as: F = -3nRySL (1.28) 37 where R is the radius of the sphere and ysL is the work of adhesion of the two surfaces in a liquid. In the force measurements performed here, JKR adhesion was typically observed between a silicon nitride tip and a bare (no graft) polystyrene latex surface or a glass substrate. One assumption of the JKR theory is that surfaces are perfectly smooth, limiting its ability to describe real surfaces. The rupture forces measured between polystyrene particles of various R in water, for example, were typically lower than those predicted by the JKR model (Hodges et al, 2002). This discrepancy was attributed to the roughness of the hard polystyrene surface, which has the effect of reducing the total contact area. In addition, the data was sufficiently scattered so that no trend could be made with varying the particle radius. 1.4.4.7 Polymer Extension Typically, a polymer tethered to a surface that adsorbs onto the tip by the free end will, under moderate tension, exhibit a restoring force that varies nonlinearly with distance. The attractive force increases with chain extension until the gradient eventually exceeds the spring constant of the cantilever, causing a mechanical instability. When the elastic restoring force is greater than the adhesion force of the chain to the tip, the polymer snaps free from the tip and the deflection signal returns to the baseline. The origin of the restoring force is mainly entropic, arising from the reduction in the number of configurations available when the polymer chain is stretched (Rief et al, 1997; Marko and Siggia, 1995). The shape of a typical force profile resulting from stretching a single polymer chain is shown in Fig. 1.4. 38 The elastic restoring force of an ideal chain that is weakly stretched is proportional to the displacement L, i.e. it obeys Hooke's law, and is given by: F { L ) = JJIBLL (1.29) where L c is the contour length or the length of the fully stretched chain. The above equation was derived by taking the derivative of the free energy of an ideal chain determined from the probability distribution of the end-to-end vector at equilibrium. The Gaussian probability distribution is valid for low extensions. The elasticity of a flexible chain can be described at all extensions using the distribution function of the freely jointed chain (FJC) according to (Flory, 1969): F(D=-±fL; (1.30) where L v * is the inverse Langevin function (Z v (x) = coth x -1 / x) . The stretching force measured by A F M for a number of polymers has been shown to fit the FJC model (Oesterhelt, 1999; Wang et al, 2002; Zhang et al., 2000a). The worm like chain model is also commonly used to describe the stretching behavior of polymers. The restoring force is given by: F(L) = -kBT 1-A V Lc J (1.31) where q is the persistence length of the polymer (Section 1.3.1). The W L C model has also fit the stretching force profiles measured by A F M for a number of polymers quite well (Al-Maawali et al, 2001; Yamamoto et al, 2000c; Kellermayer et al, 1997). 39 2. Synthesis and Characterization of Functionalized Latex Particles 2.1 Introduction The advantage of grafting onto particles with high surface area is not without cost. The latex surface introduces a number of considerations that are not present when probing polymer layers grafted onto hard flat substrates. The polystyrene surface beneath the grafted polymer layer is spherical, rough, non-rigid, and charged. The packing of the latex on the glass substrate is not necessarily uniform and the odd shape of the AFM tip introduces additional geometric considerations. A number of the properties of the underlying latex substrate can affect the polymer brush interactions with the AFM tip. The separation range and magnitude of interactions measured on non-grafted latex are examined in order to determine the contribution of the latex substrate to the force profile and distinguish it from that of the grafted layer. In this chapter, the effects of lateral inhomogeneities, which may arise from the surface roughness of the polystyrene, curvature of the latex and the non-uniform packing of particles on the underlying glass substrate are also investigated. These effects are considered individually by examining the variation in data obtained on non-grafted latex at different locations on the sample. Electrostatic interactions measured between well-characterized surfaces are compared with those calculated by the Debye-Huckel equation. Independent estimates of surface charge density allow the theory to be experimentally tested. The effect of tip geometry is considered within the framework of the Derjaguin approximation. The 40 profiles of a surface interacting with i) a standard A F M tip and ii) a modified particle probe are compared and the limitations of the approximation are evaluated. It should be noted that similar experiments have already been performed in the literature (Senden and Drummond, 1995; L i et al, 1993; Ducker et al, 1992; Butt, 1991b). Given that force measurements performed by A F M are highly susceptible to contamination and misinterpretation, a large motivation for the experiments performed in this chapter was to provide confidence to the experimental procedure and results. The reasonable agreement between the measured and predicted interactions suggests that the results are indeed reliable. 2.2 Experimental 2.2.1 Synthesis and Characterization of Latex Particles The synthesis of negatively charged polystyrene latex particles having a copolymer shell of styrene and atom transfer radical polymerization (ATRP) initiator is described briefly in the following sections. The synthesis was kindly performed by Dr. Jayachandran N . Kizhakkedathu in the Brooks laboratory and the procedure is outlined briefly below. A more detailed description can be found in a previously published report (Jayachandran et al, 2002). 2.2.1.1 Preparation of Polystyrene Seed Latex Uniformly dispersed polystyrene (PS) seed latex was synthesized by surfactant-free polymerization of styrene, water, NaCI and potassium persulfate (KPS) at 70 °C for 24 h under an argon atmosphere using a stirring rate of 350 rpm (Jayachandran et al, 2002). The latex suspension was cleaned by dialysis (1 week) against distilled water with daily 41 changes and repeated centrifugation (5 times) and solvent replacement. The solid content of the suspension was determined by freeze-drying. 2.2.1.2 Shell Growth Copolvmerization: Synthesis of ATRP Initiator Layer The synthesis of the ATRP initiator, 2-(methyl 2'-chloropropionato) ethyl acrylate (HEA-C1), is described in an earlier report (Jayachandran et al, 2002). A suspension of PS latex particles was heated to 70 °C with stirring at 350 rpm, degassed and purged with argon. Styrene and HEA-C1 were added successively to the suspension followed by a solution of degassed initiator (KPS in water) and the reaction was allowed to proceed for 6 hours. The latex was cleaned by dialysis against water for one week followed by 5 cycles of centrifugation and resuspension. The solid content was determined by freeze-drying. 2.2.1.3 Characterization of Latex Conductometric Titration The surface initiator concentration was calculated from a conductometric titration of saponified latex according to the following procedure (Jayachandran et al, 2002; Hritcu, 1999). The latex (2 g) was stirred with 1 mL 2 N NaOH for 36 h at room temperature. The suspension was centrifuged and the pellet resuspended in distilled water acidified with 0.1 N HCI. This process was repeated until the pH was 7.0. The total negative charge on the surface was determined from a conductometric titration with 0.04 N NaOH. The total negative charge on the surface arises from the sum of the sulfate surface charge due to KPS shell initiator and the carboxyl groups produced from hydrolysis of the ATRP 42 initiator in the copolymer shell. The surface sulfate charge of the latex was determined from a conductometric titration of the latex before hydrolysis. The difference between the two values gave the surface concentration of the initiator. A typical surface concentration of initiator was 1.72 x 10"5 mol/g or 2.01 x 10"6 mol/m2 (specific area = 8.57 m2/g) of the latex, implying ~ 9 A apparent separation between the initiator sites, assuming a two dimensional square lattice arrangement. For the same sample, the titrated negative surface charge concentration obtained before hydrolysis was 0.275 x 10"5 mol/g or 3.2 x 10"7 mol/m 2 of latex. Electrophoresis The movement of charged particles in an electric field, or the electrophoretic mobility, can be used to estimate the potential near the surface of the particles (Seaman, 1975). The mobility p of the charged particles is related to the zeta potential the potential at the hydrodynamic surface of the particle according to the Smoluchowski equation: M - ^ = ^ (2.1) where V = average particle velocity, V = applied voltage, IE = electrical length of chamber, and rj = viscosity. The zeta potential is commonly used as an estimate for the surface potential y/Q at the plane of charge. The mobility of the particles in the electric field is governed by the electric force, the fluid drag and the electroosmotic retardation. For negatively charged surfaces, the electric force pulls the particles in the direction of the anode while the counterions in the double layer surrounding the particle are pulled toward the negatively charged cathode. 43 The solvated cations and surrounding water molecules move in the direction opposite to the particle, resulting in a retarding force. Cancellation of terms from these opposing forces gives an expression for the mobility that does not depend on the particle diameter, D*, when D* » K " 1 . For all latex samples used in this work, the above condition applies. Electrophoretic mobilities of latex particles were measured in a Rank Mark I apparatus with a cylindrical chamber at 25° C in 10 mM NaCI. The velocities of ten individual particles were recorded manually, alternating the direction of the field after each measurement to obtain an average value v . Mobilities ^//m-cm^ were calculated V-s from the average velocity (//m/s), applied voltage (40 V) and electrical length (/E = 11.86 cm) according to Eq. 2.1. The typical latex diameter used throughout this work was - 650 nm, however in some experiments the use of larger particles (D* - 10 /urn) was required. Due to the small specific surface area of the large particles, insufficient material was available for conductometric titration of the surface charges. Instead, electrophoretic mobility measurements were performed and the zeta potential was determined. Using the zeta potential as an estimate for the potential at the surface, the charge density was calculated according to the Grahame equation (see Eq. 1.23) (Israelachvili, 1992): Gc = ^££okBTNAvl-\000 sinh(ey/a 12kBT) (2.2) where I is the ionic strength and N A v is Avogadro's number. In contrast to the uniform velocity of the smaller sulfate and shell latexes prepared in the laboratory, the 10 /urn sulfate latex particles exhibited a broad distribution of velocities. While latex synthesized in the laboratory was prepared by a surfactant-free 44 method, the commercially prepared (Interfacial Dynamics Corporation, OR) large particles were stabilized by surfactant. The surfactant appeared to give rise to the non-uniform distribution of charge density. To remove the surfactant from the surface, the latex suspension was centrifuged and the supernatant replaced with methanol (repeated 3x). The particles remained uniformly distributed with no aggregation evident upon inspection in an optical microscope. The suspension was again centrifuged and the supernatant replaced with water (repeated 5x). Electrophoretic mobility measurements performed in 10 mM NaCI following the methanol rinse yielded a narrow distribution of particle velocities. Particle Size Measurements Particle size measurements performed by scanning electron microscopy (SEM) and the hydrodynamic diameters obtained from dynamic light scattering had narrow distributions. The sizes measured by the two techniques agreed within the experimental uncertainty. A S E M image of a typical batch of latex is presented in Fig. 2.1. The Brownian motion of dispersed particles described by dynamic light scattering is used to estimate the hydrodynamic size of the particles. The technique, which measures fluctuations in scattered intensity of light at a particular angle, provides a measure of the average diffusion coefficient D', which can be related to the hydrodynamic radius R H of the particles by the Stokes-Einstein equation (Russel et al, 1989): where t] is the viscosity of the bulk medium. The hydrodynamic radius derived from the measured D' is defined as the radius of a hard sphere that diffuses with the same 45 characteristics as the particles being investigated. Although real particles are not perfectly hard or spherical, the hydrodynamic radius is commonly used to describe the apparent size of hydrated latex particles as well as latex bearing adsorbed or grafted polymer. Here, the hydrodynamic thickness (HT) of the copolymer shell was determined by taking the difference between the R H of the shell and seed latexes. Measurements were performed on a Beckman Coulter N4 Plus particle size analyzer. Dispersed particles were allowed to thermally equilibrate for 5 min and measurements were taken at 20 °C. For the batch of latex used most frequently throughout this work, the particle diameter increased from 551 ± 10% nm for the seed latex to 669 ± 10% nm for the shell latex, giving a hydrodynamic thickness value of 59 ± 74% nm for the shell. The large uncertainties associated the hydrodynamic thickness measurements are discussed in Section 3.3.2. Figure 2.1. SEM image of typical batch of monodisperse shell latex 46 2.2.2 Atomic force Microscopy (AFM) 2.2.2.1 General Experimental Setup A F M measurements were performed on a Multimode, Nanoscope Ilia controller (Digital Instruments (DI), Santa Barbara, CA). A schematic of the main components of the A F M is shown in Fig. 2.2a. The cantilever is fixed above the sample in a glass fluid cell or "tip holder" and the piezo scanner is located directly beneath the sample. In this design, the sample moves upon application of a voltage to the piezo while the position of the tip is fixed. In other models the tip moves while the sample is fixed. Only the relative motion of the sample/tip, however, is measured. Prior to performing each experiment, the tipholder and tips were cleaned and the samples were freshly prepared. These steps were fundamental in obtaining successful reproducible measurements. A highly detailed account of the preparation of the individual components is provided in Appendix 1. 2.2.2.2 A F M Probes Silicon Nitride Commercially manufactured silicon nitride (Si3N4) probes were obtained from Digital Instruments (Santa Barbara, CA). A single substrate holds four cantilevers (shown in Fig. 2.3a), each having different dimensions and therefore different spring constants. In the image, the large dark rectangle is the substrate; the V-shaped cantilevers at each end are designated by arrows and numbered 1 to 4. Typically, cantilevers of length 200 jum with spring constant k ~ 0.06 N/m as quoted by the manufacturer were used. In some cases, the spring constant was calibrated more accurately according to the method described in Section 2.2.2.3. 47 Figure 2.2. a) Main components of atomic force microscope: A. A F M "head" containing laser, photodiode, and adjustment knobs. B. Glass fluid cell or "Upholder". C. Sample (1 cm x 1cm glass) fixed on steel puck. D. Piezo scanner, b) Large scale view of fluid cell (facing up) showing groove for O-ring and 3 ports for fluid/atmospheric control. 48 Figure 2.3 a) Silicon nitride substrate holding 4 cantilevers: 1) wide leg 200 fjm long, k ~ 0.12 N/m 2) wide leg 100 pm long, k ~ 0.58 N/m 3) narrow leg 100 /um long, k ~ 0.38 N/m 4) narrow leg 200 fjm long, k ~ 0.06 N/m. b) SEM image of square pyramidal 49 shaped tip at apex of cantilever, c) Image of colloid particle probe prepared by attaching polystyrene latex (diameter ~ 10 jum) to apex of silicon nitride cantilever. An integrated square-pyramidal shaped tip is located at the apex of the V-shaped cantilever, as shown by the high resolution S E M image in Fig. 2.3b. The opening angles are 35° as quoted by the manufacturer. Images obtained by SEM suggest that the tip is spherical at the apex (Drummond and Senden, 1994). The radius quoted by the manufacturer is 5 - 40 nm. The backside of the cantilever is coated with gold to increase the reflectivity required for detection of the laser beam. The silicon nitride surface is prepared by a chemical vapour deposition process on a glass chip followed by masking with a polymer film and etching to create the integrated cantilever and tip. Manufactured in this way, the tip and cantilever have the same surface chemistry. Surface sensitive techniques such as X-ray Photoelectron Spectroscopy (XPS) performed at the center of the cantilever can therefore be used to estimate the properties of the tip. The surface of silicon nitride in air consists of a several nanometer thick layer of silicon dioxide (Senden and Drummond, 1995). The surface nitrogen atoms of native silicon nitride are each bonded to three silicon atoms (S13N). In aqueous solutions, the surface atoms undergo a series of reactions so that the hydrolyzed silicon nitride surface consists of silanol (Si-OH) and silylamine (Si-NI-12) groups. The surface reactions are given by (Senden and Drummond, 1995): S i 3 N + H 2 0 =^>Si2-NH + Si-OH (2.4) S i 2 - N H + H 2 0 => S i -NH 2 + Si-OH (2.5) S i -NH 2 + H 2 0 => N H 3 (aq) +Si-OH (2.6) 50 The relative contribution of each group to the surface composition depends on the extent of hydrolysis. The following equations describe the acid-base dissociation equilibria for the amphoteric silanol and the basic silylamine groups: S i - O H 2 + « S i - O H + H + K\ (2.7) Si-OH o Si-O" + H + K2 (2.8) S i 2 - N H 2 + <=> S i 2 - N H + H + K\ (2.9) S i - N H 3 + ^ S i - N H 2 + H + K2 (2.10) The pKa values estimated from the acid-base equilibrium constants of silica are 1 2 pK& = -0.2 and pKa = 5.8. Based on values for organic amines in water, the pK\, values are expected to be between 10 and 11. The charge density a c of the hydrated, zwitterionic silicon nitride surface is given by: oc =e([Si-OH 2 ] + [ S i 2 - N H 2 ] + [Si-NH 3 +]-[Si-CT]) (2.11) The isoelectric point of colloidal silicon nitride particles in 10 mM NaCI has been shown to vary between pH 4.2 and 7.6 depending on the relative amounts of silanol and silylamine surface groups (Bergstrom and Bostedt, 1990). Colloidal Particle Although silicon nitride probes were typically employed in this work, it was of interest in some cases to examine the interaction of a sample with a latex particle probe. The interest in colloidal interactions as well as the desire to model interactions between materials of known geometry led to the development of colloid probe microscopy (Section 1.4.3.2). Following the procedure of Ducker et al. (1992) who first attached a 51 silica sphere to a microfabricated A F M cantilever, a ~ 10 jum diameter polystyrene latex particle (Interfacial Dynamics Corporation, Portland, OR) was attached to the apex of a tipless V-shaped silicon nitride cantilever using an epoxy resin (Epikote 1004, Shell). The cantilever was placed on a heating stage at a temperature slightly above the melting point (90 °C) of the epoxy and was inspected in an inverted optical microscope. A fine glass capillary was used to transfer a very small amount of molten resin to the apex of the cantilever using a three-dimensional micromanipulator. The area to which the resin was applied was smaller than the diameter of the particle. A clean glass capillary was used to pick up a single particle from a glass slide onto which a dilute suspension of latex had been dried. The adhesion between the capillary and the latex was strong enough to move the particle from the slide and position it on the resin. Care was taken to ensure that the glue did not contact the outer side of the latex particle that would be in contact with the sample during the experiment. The resin hardened upon bringing the cantilever from the heating stage to room temperature. The colloid probes were rinsed with Mil l i -Q water to ensure that the particle was securely fastened to the tip. A sample colloid probe prepared by attaching a latex sphere (D* ~ 10 jum) to an A F M cantilever is shown in Fig. 2.3c. 2.2.2.3 Force Measurement Procedure Piezo Calibration The A F M scanner is made from a piezoelectric material that expands and contracts upon applied voltage, the direction of motion depending on the polarity. The scanner consists of three independently oriented piezo electrodes, two of which (X and Y) provide lateral movement of the sample for imaging and one (Z) which moves the sample 52 in the direction normal to the tip. The Z-piezo maintains the feedback loop during imaging and adjusts the sample position during force measurements. The sensitivity of the Z-piezo, i.e., the ratio of voltage applied to movement of the piezo (V/nm), must be calibrated in order to describe the abscissa of the force curve in terms of piezo/sample position rather than voltage. The sensitivity of the X - and Y-piezos must also be determined for the lateral dimensions of a scanned area to be accurately measured. Details of the calibration procedure are provided in Appendix 2. Optical Lever Calibration As described in Section 1.4.2, a force curve provides a plot of cantilever deflection, Ad, versus piezo movement, Ax. The deflection signal measured from the change in the laser position on the photodiode is in units of volts. In order to obtain a value of Ad in nanometers, which can eventually be converted into units of force using Hooke's law, the measured signal must be divided by the optical sensitivity (V/nm). The optical sensitivity is a measure of the change in the voltage signal produced by a given change in deflection (nm) and depends on the alignment of the laser spot on the edge of the cantilever. The optical sensitivity changes when the cantilever is removed and reinserted into the tip holder as well as when the position of the laser is adjusted and must therefore be recalibrated after each change. Calibration of the optical sensitivity was performed by obtaining a force curve on a hard surface (i.e. glass) and measuring the slope of the linear constant compliance region (photodiode (V) vs. piezo position (nm)) after contact had been made (refer to Section 1.4.2). The laser and cantilever were not adjusted following calibration, allowing the 53 voltage signal measured on the latex sample to be converted into nanometers by dividing by the optical sensitivity. Determination of Zero Separation The constant compliance region on a compressible sample will eventually be reached if sufficient force is applied. The maximum force applied to the sample is known as the trigger force and is input in the A F M software during the measurement. The trigger force determines the point at which the direction of the approaching piezo is reversed, indicating the commencement of the retract portion of the cycle. The trigger force was set high enough so that the constant compliance region was reached, indicated by a slope of unity in the region of high compression. As described in Section 1.4.2, the abscissa of the raw force curve was converted into tip-sample separations (AL) by taking the difference between the piezo position Ax and the tip deflection Ad, where AL = Ax - Ad according to the method of Ducker et al. (1992). Absolute separation values were obtained by defining zero separation as the onset of the constant compliance region beyond which point the slope Ad/Ax was unity. Zero deflection was taken at the baseline when the tip and sample were sufficiently far apart that no interaction was detectable. Spring Constant Determination In some cases, it was desirable to determine the spring constant k more accurately. The spring constant depends on the dimensions of the cantilever and varies with thickness cubed (Senden and Ducker, 1994). The nominal spring constants calculated by 54 the manufacturer are based on an average silicon nitride thickness of 0.6 jum, however the actual thickness can vary between 0.4 and 0.7 jum. The uncertainty associated with the nominal k is estimated to be around 10 % (Senden and Ducker, 1994). The method of Cleveland et al. (1993) was used to measure the spring constant of the cantilever. The method involves measuring the change in resonant frequency of the cantilever after the addition of a small mass M i on the end. The spring constant is calculated according to: k = (2n)2 - — ! (2.12) ( l / v , 2 ) - ( l / v 0 2 ) where vo and v\ are the respective resonance frequencies measured before and after the addition of the mass. The particle is attached to the end of the cantilever using the general method described in Section 2.2.2.3, with the epoxy step omitted. Adhesion of the polystyrene latex to the silicon nitride cantilever was sufficiently strong to enable the measurement of k to be performed with the subsequent removal of the particle, making the method nondestructive. Typical resonance curves obtained using the A F M Nanoscope software for an unloaded and loaded cantilever (Fig. 2.4) show a shift in the resonance frequency from 18.71 kHz to 18.02 kHz following the addition of a 9.6 jum diameter polystyrene latex particle. The mass of the particle obtained from the density of polystyrene (1.03 g/cm3) and the volume of a sphere was found to be 4.86 x 10"13 kg. From the above data, the calculated spring constant for the cantilever in this example was 0.086 N/m. In cases where colloid probes were prepared by fastening the particle to the cantilever with resin, 55 the mass of the epoxy was assumed to contribute a negligible amount to M i , as suggested in the literature (Hodges et al, 2002). unloaded loaded Frequency (kHz) Figure 2.4. Resonance curves showing shift in frequency for loaded (D = 9.6 jam polystyrene latex) and unloaded silicon nitride cantilever. Automation of Data Analysis Due to the large number of force curves required for analysis, a semi-automated procedure was written in Matlab (MathWorks, Inc.) for converting the data in the ascii file generated by the A F M software (Nanoscope V . 512) into a force versus separation curve. The code is attached as Appendix 3 with a detailed description of the parameters. 56 2.3 Results and Discussion 2.3.1 Elasticity of Shell Latex Spring constants given throughout this report can be assumed to be the nominal value quoted by the manufacturer, unless specified otherwise. A more accurate measurement of the spring constant was performed typically when analysis of the force data involved comparison with a theoretical model. The raw and adjusted force data obtained on a sample of shell latex (D* = 650 nm) in the forward direction (compression) using a silicon nitride tip (k ~ 0.06 N/m) are presented in Fig. 2.5. To examine the effects of elasticity independent of electrostatic interactions, the measurement was performed at high salt concentration (5 M NaCI). For comparison, the force data obtained on a clean glass substrate under the same conditions is provided. The unadjusted curves (Fig. 2.5a) consist of i) a baseline region (d = 0 nm) and ii) a constant compliance region (Ad/Az =1). The curves indicate that both the glass and shell latex behave as hard surfaces and there is no measurable elastic deformation by the A F M tip. O Glass • Shell Latex 0 5 10 15 20 25 30 Piezo/Sample Position (nm) B O Glass • Shell Latex -5 0 5 10 15 20 25 30 Separation (nm) Figure 2.5. A) Raw and B) adjusted force curves obtained with silicon nitride tip on glass and shell latex samples in 5 M NaCI. 57 To compare the mechanical resistance of the materials to elongation or compression, the values for the Young's modulus, E, of glass, polystyrene, and silicon nitride are presented in Table 2.1. The relatively large E for silicon nitride suggests that tip deformation here is negligible. Table 2.1 Young's moduli of materials Material Young's Modulus (GPa) Silicon nitride0* 150 Glass"'* 50 Polystyrenec 3 °Vinickier and Semenza, 1998 Weisenhorn et al, 1993 cBrandup and Immergut, 1989. It is evident from the values of E that polystyrene can be more easily deformed than glass, but these two materials are indistinguishable to an A F M probe with a spring constant k ~ 0.06 N/m. To evaluate whether a cantilever with a given spring constant k is sufficiently stiff to indent a sample, the relationship between the contact stiffness S* , i.e. the slope of the unadjusted force curve, and the mechanical properties of the sample is considered (VanLandingham et al, 1997): dF 2rF dx ( 1 - v 2 ) where r is the contact radius and v is Poisson's ratio of the sample. Poisson's ratio is defined as the ratio of the transverse strain (deformation) to the strain along the direction of the applied force. For a polystyrene film with E = 3 GPa and v = 0.3, and a probe 58 producing a contact radius of 20 nm, the estimated contact stiffness S* of the polymer is 131 N/m. Similarly for glass, (E = 50 GPa, v= 0.2, and r = 20 nm), the value of S* during indentation is 2080 N/m. A probe with a spring constant significantly larger (104-105 times) than the one used here (k ~ 0.06 N/m) would therefore be required to elastically deform these two materials to any measurable degree. Here, it is the flexibility of the cantilever rather than the stiffness of the sample that is measured. 2.3.2 Electrostatic Interaction 2.3.2.1 Silicon nitride tip and flat silicon nitride sample The interaction between an A F M silicon nitride tip and a flat silicon nitride surface is first considered. The planar geometry of the sample and the symmetrical tip/sample surface chemistry simplifies this system over that of the silicon nitride tip/shell latex sample. The compression profiles of a silicon nitride sample and tip (k ~ 0.094 N/m, determined by the method of Ducker et al. (1992) in 0.1 mM and 10 mM NaCI are presented in Fig. 2.6a. The data represent the averages of 9 and 2 force profiles respectively. Rates of approach ranged between 500 - 2500 nm/s. There was no noticeable rate dependence in this region, as discussed below (Section 2.3.6). The interaction between the same sample and tip at 100 mM NaCI is shown in Fig. 2.6b. Using a non-linear least squares approach, the data in Fig. 2.6a fit an exponential decay (solid lines) of the form: F = F0+Aflte-L" (2.14) 59 To compare the measured force with theoretical models, which generally apply to separations larger than ~ 1 Debye length (K" 1), only the force data shown, i.e. below 0.06 nN, were included. This corresponds to separations L greater than 7 nm at 0.1 m M NaCI and L greater than 4 nm at 10 m M NaCI. Due to the small number of data points available in the region of interest, separations slightly smaller than K " 1 were included. This issue is considered in more detail below. 1 i i i i • 1 f=H • 1 ^ - i • i - ^ - 1 H 1 1 1 1 1 1 1 1 1 1 1 1 1 1-0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 Separation (nm) Separation (nm) Figure 2.6 Compression profiles between silicon nitride tip and silicon nitride sample in NaCI solution, a) Data corresponding to 0.1 mM (*) and 10 m M (o) represent the average of 9 and 2 force profiles, respectively. Solid lines are best fits to a single exponential decay, b) Compression profile in 100 m M NaCI solution. The fitted decay length t and amplitude Af„ are given in Table 2.2. The decrease in decay length with increasing ionic strength suggests that the origin of the repulsion is electrostatic. Based on measurements of a repulsive interaction between a silicon nitride tip and negatively charged glass surface at low ionic strength (0.1-10 mM NaCI), a negative surface charge is expected for silicon nitride. This is consistent with reports in the literature of silicon nitride having a strong negative charge in pH 6 aqueous 60 electrolyte solutions of 0.1-10 mM NaCI (Senden and Drummond, 1995). The aqueous solutions used here were not buffered but have a pH ~ 6. At both ionic strengths in Fig. 2.6a, the profiles exhibit an increasing repulsive force as the surfaces are brought together. An expression for the electrostatic force between a spherical and flat surface based on the linearized Poisson-Boltzmann equation and application of the Derjaguin approximation was obtained (Israelachvili, 1992): F = 2KRW(L) = 4xRac>saCtte-KL IKSS0 = Acalce-KL (2.15) where a c s and a c t are the surface charge densities of the sample and tip, respectively. This equation is valid for surface potentials below ~ 25 mV and was derived for the symmetrical case of G c s = aC j t. In cases where independent estimates of the surface charge densities were made, A c a i c was calculated and the value compared with A n t . The force described by Eq. 2.15 arises from the excess osmotic pressure of the counterions in the region between the surfaces over the bulk pressure, as discussed in Section 1.4.4.1. The exponentially decaying double-layer interaction has a characteristic decay length that is given by the inverse Debye-Huckel parameter (K" 1). The values of K " 1 , which vary with the inverse square root of the ionic strength according to Eq. 1.21 are listed in Table 2.2. The fitted decay lengths t are also indicated. Table 2.2. Electrostatic Interaction between Symmetrical Silicon Nitride Tip/Sample [NaCI] K"'(nm) t(nm) Afit a c , m i „ f l a c , m a x * (mM) (nN) C/m 2 C/m 2 ~ \ 30 i3~9 0.096 -0.003 -0.005 10 3.0 6.27 0.12 -0.007 -0.01 "Charge density of silicon nitride calculated from A n t , assuming a tip radius of 40 nm. ^Charge density of silicon nitride calculated from Af l t, assuming a tip radius of 15 nm. 61 The symmetrical surface chemistry of the tip and sample enabled the surface charge density a c of silicon nitride to be estimated from the fit parameter Ap according to equations 2.14 and 2.15. Upper and lower bounds values of a C j t based on a tip radius of 15-40 nm are give in Table 2.2. By comparison, the surface charge densities calculated by Zhmud et al. (1998) for silicon nitride in 1 mM univalent background electrolyte were -0.002 C/m 2 and -0.027 C/m 2 at pH 5 and 7, respectively. The authors used a charge-regulation model to calculate the charge density of silicon nitride as a function of surface separation L . The above a c values were calculated at small separation ( K L / 2 = 0.05) and may be taken as lower bound values. The upper bound values (for K L / 2 = 1.00) were a c = -0.008 C/m 2 and -0.04 C/m 2 at pH 5 and 7, respectively. According to literature reports (Senden and Drummond, 1995; Butt, 1992), the charge density of silicon nitride is largely dependent on the pH, as well as the concentration and nature of the background electrolyte. Based on force measurements of a silicon nitride tip interacting with a negatively charged mica surface, silicon nitride was found to be roughly electrically neutral in the absence of background electrolyte at a pH of 6 (Senden and Drummond, 1995). This appears to reflect a roughly equal density of silanol and silylamine groups (see Eq. 2.11). In contrast, the referenced study found the silicon nitride surface to have a net negative charge between pH 6 and 8.5 in the presence of added background electrolyte. The dependence of surface charge density on background electrolyte was attributed to the specific interaction between the counterions and the silylammonium surface groups. The counterion X ~ binding equilibria for the charged sites are given by (Senden and Drummond, 1995): S i - O H 2 + + X S " ^ S i - O H 2 X K\ (2.16) 62 S i - C T + X S " » S i - O X K\ (2.17) S i 2 - N H 2 + + X S ~ < » S i 2 - N H 2 X K\ (2.18) S i - N H 3 + + X S ~ < ^ S i - N H 3 X KAC (2.19) Based on values for silica in NaCI electrolyte, the estimated values of pKc and pKc are -1.2 and 6.8, respectively. Estimates of pK3 andpK^ have not been reported. Complexation of the chloride ions with the silylammonium groups (equations 2.18-2.19) is expected to reduce the density of positively charged sites and result in a net negative surface charge. In the referenced study, the interaction between a silicon nitride tip and both silicon nitride and mica surfaces at pH 6 was measured in 0.1, 1, 10 and 100 mM NaCI. Typically, electrostatic forces are expected to decrease with increasing ionic strength in accordance with the decreasing decay length. In the case of silicon nitride surfaces, however, this trend is complicated by the effect of background electrolyte concentration on surface charge density. The repulsive force between both the silicon nitride and mica samples on the silicon nitride tip increased at any given separation with decreasing background electrolyte for NaCI concentrations of 100, 10, and 1 mM. The repulsive force in 0.1 mM NaCI was, however, smaller than that measured in 1 m M NaCI at any given separation. Presumably, the amount of chloride ions available for binding to the positively charged surface sites is sufficiently low in 0.1 mM NaCI that the net negative charge density is smaller in magnitude than in 1 mM NaCI. The crossover at 0.1 m M NaCI is consistent with the small repulsive force observed in the absence of background electrolyte. 63 The authors also varied the nature of the background electrolyte and found silicon nitride to possess a net negative surface charge at pH 6 in solutions of NaBr, NaCI, and NaOH. Interestingly, the repulsive force at any given separation was largest in NaBr and smallest in NaOH, reflecting the documented trend in the degree of counterion binding of Br" > CI" > OH". Based on the above discussion, Eq. 2.15 may be too simple to describe the electrostatic interaction between two silicon nitride surfaces in electrolytic solutions. This might explain the poor agreement found between the calculated and fit decay length (Table 2.2) for the symmetrical silicon nitride interactions. The silicon nitride o c estimated by fitting the data in Fig. 2.6 to Eq. 2.15 is used in subsequent calculations but it is noted that there may be significant uncertainty associated with the value. 2.3.2.2 Silicon nitride tip and shell latex (D* = 650 nm) The interaction of the same silicon nitride tip (k ~ 0.094 N/m) and a shell latex sample (D* = 650 nm) in 10 mM and 100 mM NaCI is presented in Fig. 2.7. The data represents an average of force profiles obtained at 10 different locations on the sample. The data fit an exponential decay indicated by the dotted lines. Only separations larger than 1 nm were considered in the fitting procedure. The fit parameters t and Ap are given in Table 2.3. 64 Table 2.3. Electrostatic Interaction between Silicon Nitride Tip and Shell Latex (D = 650 nm): Single Exponential Fit [NaCI] K " 1 (nm) t (nm) Aflt(nN) Acalc _ a (mM) (nN) C/m 2 C/m 2 10 3.0 3.1 0.27 0.25 -0.0085 -0.031 100 0.96 0.73 0.8 N / A N / A N / A "Charge density of silicon nitride obtained from average value of a c t !max and a c t min (see Table 2.2) 0.25 0.20 0.15 p 0.10 0.05 4 0.00 4 I V i \ • 10 mM NaCI O 100 mM NaCI <?P3 10 15 20 25 Separation (nm) 30 Figure 2.7. Interaction between silicon nitride tip and shell latex (D* = 650 nm) in 10 mM and 100 mM NaCI. The data represents an average of 10 force profiles. Dotted lines are best fits to an exponential decay. The surface sulfate concentration of the shell latex was 3.2 x 10"7 mol/m 2 of latex as determined by conductometric titration, giving a surface charge density rjC ; S = -0.031 C/m . Upper and lower bounds for Acaic were calculated according to Eq. 2.15 using tip radii of 15 and 40 nm and the appropriate surface charge density a C ; t measured at the 65 given ionic strength. Due to the purely attractive interaction measured between two silicon nitride surfaces at 100 m M NaCI (Fig. 2.6b), the corresponding value of a C j t could not be obtained. The values of Aca/C are listed in Table 2.3. Good agreement between Acaic and Afit is observed for 10 m M NaCI, despite the uncertainty in o~Cjt as well as the various assumptions associated with Eq. 2.15. The limitations of the treatment as well as potential sources of error are considered in the following discussion. Constant Charge Density At small separations, the assumption of constant surface charge density as a function of tip-sample separations breaks down and Eq. 2.15 is no longer valid. Surface charges arise from either the dissociation of surface groups or by the adsorption of ions onto the surface. When the gap between two surfaces is small, the counterion distribution is altered and the surface charge is partially neutralized by an increased number of bound exchangeable ions. The fitting procedure should therefore be performed on data corresponding to separations greater than the Debye length (i.e. L > K " 1 ~ 3 nm in 10 mM NaCI). Due to the small number of data points in the region of interest, however, data from separations as low as 1 nm were included in the fits. Linearization of the Poisson-Boltzmann Equation The electrostatic interaction described by Eq. 2.15 is based on the assumption that the surface potentials are low, where ey/0 « ksT (i.e. y/0 < 25 mV). To obtain an estimate of the surface potentials in the present system using the measured charge density, the Grahame equation (Eq. 1.23) is applied (Israelachvili, 1992). For a surface charge density 66 2 of -0.031 C/m which corresponds to the CTc measured for the shell latex, a value of y/0 = -87 mV in 10 m M NaCI is obtained. The assumptions used to derive Eq. 2.15 are not expected to hold at this high a surface potential. To more accurately treat this data, a full solution of the Poisson-Boltmann equation is required. Such an attempt was not made here, as the primary emphasis of this work is not the electrostatic contribution to the interaction but rather that of the neutral, polymer grafted layer. Indeed, force measurements on the polymer brushes were performed in sufficiently high ionic strength so that the contribution from the charged latex was negligible. Based on comparisons in the literature of the linearized and full numerical solutions of the Poisson-Boltzmann equation, application of Eq. 2.15 may be reasonably appropriate despite the high surface potential. L i et al. (1993) measured the interaction between two polystyrene spheres immersed in electrolyte solutions. The repulsive interaction measured in 1 m M KC1 fit the simple D L V O result derived from the linearized Poisson-Boltzmann equation and the Derjaguin approximation. The D L V O result is the same as Eq. 2.15 with an additional term describing the van der Waals interaction (see Sections 2.3.3 and 2.3.4). The fit yielded a surface potential y/0 = -87 mV which agreed well with the measured zeta potential of -83 mV. A full numerical solution of the Poisson-Boltzmann equation showed that the simple D L V O could be applied in these conditions, despite the high surface potential. 67 Validity of Derjaguin Approximation The relationship in Eq. 2.15 is obtained by employing the Derjaguin approximation, which is valid when L « R and K " 1 « R as described in Section (1.4.3). In a strict sense, the approximation does not accurately describe the present system where the radius of the A F M tip (R = 15^40 nm) is relatively small. To evaluate the conditions under which the treatment could be successfully applied, Drummond and Senden (1994) compared the electrical double layer force (K"1 = 9.8 nm) calculated using i) the exact solution to the Poisson-Boltzmann equation (F P B ) between a spherical and planar surface and ii) the Derjaguin approximation (FD). The exact solution was calculated at conditions of both constant potential and constant charge. The ratio F P B / F D corresponding to a separation of L = 10 nm was evaluated as a function of sphere radius. For surfaces interacting under constant potential, the Derjaguin approximation was found to be accurate to within 10% of the exact calculation for radii > 5 nm. For surfaces interacting under constant charge, the Derjaguin approximation was found to be accurate for radii > 60 nm. Treatment for Asymmetrical Surfaces The expression for the interaction between two charged surfaces (Eq. 2.15) arises solely from the osmotic repulsion of the counterions in the gap. As discussed in Section 1.4.4.1, this treatment is appropriate only for two identical plane parallel surfaces. When the symmetry is removed, either geometrically or as a result of unequal surface charge densities, the electric field at the midplane is no longer zero and an additional stress must be considered (Russel et al., 1989). According to Parsegian and Gingell (1972), the 68 electrostatic force per unit area /between two flat surfaces of charge density aC : t and aC j S separated by a distance L is given by: 2 / = — +°h)e-2KL +°c,s°c,,e-KL\ (2-20) ee0 To estimate the force of a charged flat surface acting on an A F M tip, Butt (1991a) integrated / o n small circular cross-sections of 2nrdr, where r is the horizontal radius of the tip at a given height. Expressions were derived by modeling the tip as a half sphere as well as a cone with a spherical end. For surface potentials below 50 mV, Butt approximated the force on a sphere with radius R as (Butt, 1991b): F = — [ (a 2 , +*l)-e-2KL +2crc^s-e^] (2.21) ££0K The first term in Eq. 2.21 describes the electrostatic contribution and has a decay length of (2K)"1. A n electrostatic interaction exists even when the surface of the tip does not bear free charges, due to polarization charges at the tip/electrolyte interface resulting from the electric field (Butt, 1991a). The second term, which is the same as in Eq. 2.15, describes the osmotic repulsive force of the counterions and has a decay length of K " 1 . When o~ct ~ o~CjS, contribution from the first term is negligible since e_KL > e~2tcL and 2 2 <TCS +<JCT = 2crc S<7CT. The overall force is then accurately described by Eq. 2.15. The first term contributes to the decay only when the two surface charge densities are very different, and then only at small separations. The estimated charge densities of the silicon nitride tip and shell latex surface were sufficiently different to investigate the fits to a bi-exponential of the form: F = F0+A^e-L,t>+Afiiae-U'> (2.21) 69 The fitted decay lengths and Afit values are compared with the values predicted by Eq. 2.15 in Table 2.4. Although the fitted decay lengths are similar to the theoretical values, the parameters obtained for Af l t do not agree with the values of A c a i c . The poor agreement may be attributed to the uncertainty in the determination of aC j t, for which it was assumed that the symmetrical silicon nitride tip/sample force profile can be accurately described by Eq. 2.15. Given the limitations of the Derjaguin approximation, the effect of charge regulation, and the sensitivity of the silicon nitride surface chemistry to pH and ionic strength, the discrepancy between Af l t and A c a i c is not surprising. Table 2.4. Electrostatic Interaction between Silicon Nitride Tip and Shell Latex (D* = 650 nm): Double Exponential Fit Parameters [NaCI] K"V2 ti (nm) ACalc,l Aflt,\ K 1 h (nm) ACalc,2 Aflt>2 (mM) (nm) (nN) (nN) (nm) (nN) (nN) 10 1.5 0.35 0.43 3.7 3 4.2 0.13 0.18 100 0.48 0.55 N/A 0.9 0.96 1.6 N/A 0.09 2.3.2.3 Sulfate latex particle probe (D* = 9.6 fjm) and flat silicon nitride surface A sulfate latex particle probe was prepared according to the method of Ducker et al. (1992). The polystyrene latex (D* = 9.6 pm) was obtained from Interfacial Dynamics Corporation, OR. In contrast to measurements performed with a standard silicon nitride tip, the radius of the particle probe is large relative to the decay length and so the 70 conditions for the Derjaguin approximation apply. The comparison of experimental data with electrostatic theory is therefore more appropriately performed on the present system. The small surface area of the particles precluded the determination of the charge density of the surface sulfate groups by conductometric titration. Instead, electrophoretic mobility measurements were performed on the 9.6 jum latex particles to evaluate the zeta potential. The Gouy-Chapman theory was used to obtain o"c from the estimated surface potential. According to Eq. 2.1, a mobility of // = -3.44 / /mcm/Vs was obtained for particles having V = 11.6 ± 0.5 //m/s, V= 40 V and /E = 11.86 cm. Using the viscosity of 3 2 water at 25° C (n= 1x10" Ns/m ), dielectric constant of water and vacuum permittivity values of £ = 78.5 and ea= 8.85xl0"12 C/Nm 2 , a value of £ = -49.4 mV was obtained for the zeta potential. Assuming that the surface potential y/0 can be approximated from the zeta potential and applying the Gouy-Chapman model (Eq. 2.2), a charge density of o c = -0.0131 C/m 2 was obtained for the sulfate latex in 10 mM NaCI. The interaction between a 9.6 /um diameter sulfate polystyrene latex particle probe and a flat silicon nitride surface measured at different ionic strengths is presented in Fig. 2.8. Each curve fit a single exponential decay, indicated by the solid lines. Only data corresponding to separations larger than the Debye length were included in the fit. The fit parameters are given in Table 2.5. The linear relationship between the fitted decay length and the inverse square root of the ionic strength is demonstrated in Fig. 2.9. For comparison, the inverse Debye-Huckel parameter calculated according to Eq. 1.21 is presented. The fit and calculated decay lengths are in good agreement. The parameters obtained for Am do not agree with the values of A c a | c listed in Table 2.5. The Afit values appear to decrease with increasing decay length however more than 71 three data points may be required to establish a clear trend. According to Eq. 2.15, A c a i c is expected to increase linearly with decay length, and hence with the square root of ionic strength, i f the charge density is constant. Due to the complicated relationship between the surface charge density of silicon nitride and ionic strength, a linear relationship between A c a i c and decay length is not expected here. Given the number of variables, it is not surprising that there is in some cases an order of magnitude difference between Af l t and A c aic. The generally consistent agreement between the fitted and calculated decay lengths, however, suggests that the measurements were performed accurately and the results are meaningful. Separation (nm) Figure 2.8. Interaction between 9.6 jum sulfate latex probe and flat silicon nitride surface as a function of ionic strength. Solid lines show best fit to single exponential decay. 72 30 u-\ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ([NaCI] mM)"1'2 Figure 2.9. Effect of ionic strength on measure decay length of force profile between polystyrene particle probe and silicon nitride surface (see Fig. 2.8). Table 2.5. Electrostatic Interaction between Sulfate Latex Probe (D* = 9.6 //m) and Silicon Nitride Sample: Single Exponential Fit Parameters [NaCI] K " 1 (nm) t (nm) Acaic, _ a Cfc,t (mM) (nN) C/m 2 C/m 2 0.1 30 27 3.3 140 -0.004 -0.0131 1 9.6 8.7 20 31 -0.003 -0.0131 10 3.0 4.4 180 31 -0.009 -0.0131 "Average charge density obtained from aC ; t,max and o~Cit„ 73 2.2.2.4 Comparison of Interaction between i) silicon nitride tip and sulfate latex particle (D* = 9.6 jum) and ii) sulfate latex particle probe (D* = 9.6 /um) and flat silicon nitride surface In the previous section, the interaction between a flat silicon nitride surface and a sulfate latex particle probe was measured. Those results are compared with the interaction measured on the reverse system consisting of a silicon nitride tip and sulfate * latex particle (D = 9.6 jum) sample. The sample was prepared by physisorbing the sulfate latex onto a glass substrate. The large particle diameter relative to the A F M tip suggests that the latex surface can be considered approximately planar. The Derjaguin approximation simplifies the sphere/plane geometry to that of a plane/plane interaction. Given that the surface chemistry in both the standard tip and particle probe experiments was the same, the two systems were expected to give similar plane/plane interactions upon scaling the force by the appropriate radius. The above assumes that application of the Derjaguin approximation to the standard tip system is valid, as was demonstrated by Drummond and Senden (1994). An approach similar to that used in the referenced study for comparing the interactions between a surfactant coated flat surface and a surfactant coated 1) silica particle probe and 2) silicon nitride A F M tip is followed here. There, the effective radius R2 of the tip was estimated by normalizing the force profile ^ ( L ) from the silicon nitride F (L*) * tip system by — , where F\(L*) is the absolute force measured at a given separation ^1 L* using the silica probe system and R\ is the radius of the silica particle. The effective F (L*) radius is given by R2=— R\. The same value for R 2 was obtained when - 1^ ( £ * ) 74 normalization factors corresponding to L* = 10 nm, 15 nm, and 20 nm were used. The radius R.2 is described as a long-range "effective" radius as it may not represent the radius at all separations. Surface roughness, for example, may result in a contact radius that is different from the effective radius at L*. Here, the force profiles obtained with the standard tip (1) and particle probe (2) are fit to an exponential of the form in Eq. 2.14 and compared to the values of Af, t. Only data corresponding to separations greater than K " 1 were included in the fits. Assuming that o"c,tO"c,s is the same in both systems, comparison of equations 2.14 and 2.15 suggests that Ant\ R] — = — . The values of Af^i and Aflt;2 were 0.48 nN and 180 nN respectively. Given Afit,2 R2 the particle radius R2 = 4.8 jum, a tip radius Rj = 13 nm is obtained. This value is very close to the minimum tip radius (15 nm) quoted by the manufacturer. As in the case of the referenced study, the results suggest that despite the ill-defined shape of the tips, the geometry of standard, microfabricated tips can be reasonably approximated as spherical and the Derjaguin approximation applied. 2.3.3 van der Waals Interaction In the preceding analysis, only electrostatic interactions between the A F M probe and sample surface were considered. Although the data presented above fit a purely exponential decay and a power function was not necessary, contribution of the van der Waals attractive interaction must be considered. To interpret the data according to the D L V O theory (Section 1.4.4.3), the van der Waals (vdW) attraction is added to the electrostatic interaction. Application of the Derjaguin approximation to Eq. 1.27 suggests 75 that the vdW force between a sphere of radius R and a planar surface vary with the inverse squared separation, according to (Israelachvili, 1992): Fvdw = —-rj- (2.22) where A H is the Hamaker constant. Due to the limitation of spring-based force measurements, namely that the gradient of the force profile be less than the spring constant, the range over which the van der Waals attractive force can accurately be measured is short. A mechanical instability occurs when the gradient of the force law exceeds the value of spring constant and the surfaces jump into contact. The convention in the literature is to discard data points acquired in this region. Indeed, a stiffer spring could be used to measure the attractive forces; the inevitable drawback however, is the reduction in sensitivity to the repulsive forces. The interaction between the latex particle probe and silicon nitride surface in 1 M NaCI is presented in Fig. 2.10. The same probe and substrate used in the electrostatic measurements were used here. At this high ionic strength the vdW interaction can be examined independently of electrostatics. The data fit a power law of the form: F = K~^ (2.23). L Only data corresponding to separations greater than 9 nm was included in the fitting procedure. The data between 2 < L (nm) < 9 varies linearly with a slope of 0.06 N/m. This corresponds to the region of instability and is not included in the fit. Using a non-linear least squares procedure, a fit parameter of B = 5.5 x 10~27 N m 2 was obtained. Equating the parameter B with the constants in Eq. 2.22 gave a value 0.7 x 10"20 J for the Hamaker constant where R = 4.8 /urn. The literature value of A H for a symmetrical silicon 76 nitride system in water is 6.1 x 10" J (Senden and Drummond, 1995); a value of 0.95 x 20 10" J was reported for two identical polystyrene surfaces interacting in water (Israelachvili, 1992). By comparison, the Hamaker constant obtained here was slightly low. A more accurate value could be determined using a stiffer spring enabling attractive forces over a larger separation range to be measured. Figure 2.10. Interaction between latex particle probe (D* = 9.6 um) and silicon nitride surface in 1 M NaCI. Tip and sample are as the same as in Fig. 2.8. Solid line represents best fit to vdW interaction (Eq. 2.22). 2.3.4 D L V O Interactions The total contribution of electrostatic and van der Waals interaction (DLVO) between a polystyrene sulfate latex probe and silicon nitride flat surface is shown in Fig. 2.11. For comparison, the purely electrostatic contributions are also presented. The symbols (electrostatic) represent the best fits of the data in Fig. 2.8 to a single exponential decay. The solid lines (DLVO) were obtained by summing the best fits of electrostatic and van der Waals interactions. 0.1 n 1 1 1 1 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 30 35 40 45 50 55 60 Separation (nm) T 1 1 1 1 1 r 77 -5 I 0 2 0 4 0 6 0 8 0 Separation (nm) * 0.1 mM NaCI O 1 mM NaCI + 10 mM NaCI 1 0 0 Figure 2.11. Comparison of D L V O (solid lines) and purely electrostatic fits (symbols) to interaction between a latex particle probe (9.6 pm) and silicon nitride surface as a function of ionic strength. The contribution of the vdW forces to the D L V O interaction is negligible at all separations displayed for 0.1 m M NaCI. The vdW contribution is significant at only at low separations (< 5 nm) in 1 m M NaCI and (< 3 nm) in 10 m M NaCI. Based on the curves shown in Fig. 2.11, the purely electrostatic treatment of the data in Fig. 2.8 is reasonable over the region presented. 2.3.5 Summary of interactions The electrostatic interactions between two silicon nitride surfaces (symmetric) and between a silicon nitride and polystyrene latex surface (asymmetric) were examined. In all systems, the force profiles obtained in 0.1 mM, ImM and 10 mM NaCI solutions fit an exponential decay with decay lengths similar to those calculated from the inverse Debye-Huckel parameter. For the symmetrical silicon nitride system, an estimate of the charge density was obtained from the fitted amplitude at various ionic strengths. 78 The asymmetric silicon nitride tip/shell latex (D = 650 nm) sample system was well describe by a purely electrostatic model that accounted only for the repulsive interaction of the counterions. The data was not described well by the bi-exponential model. To justify the use of the Derjaguin approximation, the interactions of two chemically identical systems of silicon nitride and sulfate latex (9.6 fJm) where the nature of the probe was reversed are compared. When scaled by the appropriate radius, the force profiles measured for the two systems were consistent. A l l data obtained at low ionic strength could be described by a purely electrostatic model. At high salt concentration (1 M), the interaction between sulfate latex and silicon nitride fit a power law of the form of the vdW attraction. The Hamaker constant obtained from the best fit was slightly lower than the values reported for symmetrical silicon nitride and polystyrene systems in water. It is instructive to examine these results in the context of those presented in the literature. The interaction between charged surfaces of various natures have been measured by A F M and SFA and the results interpreted within the framework of the D L V O theory. In many systems, good agreement has been reported (Hartley et al., 2002; Hartley et al, 1999; L i et al, 1993; Ducker etal, 1992; Butt, 1991b). Poor agreement with D L V O theory has been attributed to surface roughness (Considine et al, 2001), hairy polymer layers (Woodward et al, 2002), dissolved gas (Considine et al, 1999) and hydration forces (Butt, 1991b). In some cases, D L V O fits could only be obtained when the plane of charge was set to a negative surface separation (Considine et al, 2001; Ducker etal, 1992). 79 The surface potential is often a free parameter obtained from best fits to numerical solutions of the Poisson-Boltzmann equation. This approach requires that the surfaces be symmetric, as it is difficult to decouple the potentials of two dissimilar surfaces in the fitting procedure. A n asymmetric system can be modeled once the potential of one of the surfaces has been evaluated (in a symmetric system). Without estimates of the surface potential based on independent methods such as by measurement of the zeta potential or conductometric titration, uncertainties embedded in the fit parameters may be overlooked. This was noted in a study where the double layer forces measured in an electrochemical surface force apparatus were compared with D L V O predictions (Frechette and Vanderlick, 2001). The measured force profiles were well described by D L V O theory, despite the possible contribution from surface heterogeneity, which was not incorporated into the model. While the results suggest that conventional D L V O theory be applicable to rough surfaces, the effect of surface roughness might be presenting itself in the fitted value of the surface potential. 2.3.6 Equilibrium Considerations The measurements described above were performed at different rates of approach ranging between 500 nm/s and 2500 nm/s. This is not expected to have affected the data, as demonstrated by the reproducibility of the curves in Fig. 2.12. The force profiles in Fig. 2.12 show the interaction between a silicon nitride A F M tip and shell latex (D* = 650 nm) sample in 10 mM NaCI obtained at rates ranging between 500 and 2500 nm/s. The lack of observed rate dependence suggests that the ion concentration around the tip is in equilibrium throughout the measurement. This point was considered by Butt (1991a), who compared typical A F M scan speeds with ionic mobilities and diffusion coefficients 80 for ions in water. With ionic mobilities being ~ 6 x 10" , ions move at a speed of V - s 106 nm/s at a potential difference as low as 1 mV. Similarly, diffusion coefficients for ions in water are ~ 2 x 10- m Is, so that ions diffuse -10 nm in 1 sec. These speeds are significantly faster than those in an A F M experiment, implying that the distribution of ions in water reaches equilibrium much faster than the tip scans the sample during a force measurement. Separation (nm) Figure 2.12. Reproducibility of compression profiles of shell latex (D* = 650 nm) in 10 m M NaCI at rates ranging between 500 and 2500 nm/s. 2.3.7 Surface Roughness In the above sections, the issues of latex rigidity, surface charge, and tip geometry have been addressed. The surface roughness and effects of sample inhomogeneity are the focus of the following section. The general theories used to describe interactions between macroscopic bodies of known geometry assume molecularly smooth surfaces, however real surfaces are generally not smooth and have non-uniform surface properties. This 81 reasoning has been used to account for large (order of magnitude) discrepancies between the measured and predicted behaviour of model particles such as monodisperse polystyrene latex spheres (Sun and Walz, 2001). In addition, oscillatory forces have been observed between rough surfaces in liquid and are believed to have a geometric origin (Israelachvili, 1992). Due to the relatively large surface area associated with the surface force apparatus (SFA), it is limited to ideal surfaces such as arrays of biomolecules anchored to atomically smooth substrates such as mica (Considine et al, 2001). In contrast, the small radius of curvature of the A F M tip enables non-uniform surfaces to be investigated since inhomogeneities are generally large relative to the dimensions of the tip. A F M images of the shell latex were obtained in Tapping Mode, whereby the tip is driven to oscillate at high frequency by a piezoelectric driver while it is raster scanned across the surface. Lateral forces are minimal or nonexistent as the tip intermittently contacts the sample only at the lowest point in the oscillation. Changes in the oscillation amplitude due to variations in topography are used in the feedback signal and the height of the sample is adjusted so that the preset oscillation amplitude (i.e. setpoint amplitude) is re-attained. The ratio of setpoint amplitude A s p to drive amplitude A 0 determines the strength of the tapping force; a small A s p / A 0 corresponds to hard tapping. Brighter spots represent higher regions than darker spots in the topographical images. A F M images of shell latex obtained in Tapping Mode in 10 m M NaCI solution are presented in Fig. 2.13. The 4 x 4 jum topographical image (Fig. 2.13a) shows a roughly hexagonally packed array of latex particle. The A F M Section Analysis software (Digital Instruments, CA) was used to measure the diameters of individual latex particles. The 82 procedure involved drawing a line through the center of a particle to obtain the deflection (nm) as a function of piezo position (in the lateral direction) for a single scan line (Fig. 2.13b). The diameter was taken as the horizontal distance L H between two troughs. The average diameter obtained from 12 particles was 674 ± 3 6 nm. This is in good agreement with the particle diameter measured by dynamic light scattering (650 ± 10 nm). The average vertical distance L V measured from trough to peak was 165 ± 20 nm. The significantly smaller distance measured in the vertical relative to the horizontal direction demonstrates the inability of the tip to trace features with slope greater than the complement of the half angle of the tip. A consistent distance was obtained when measured from the trough on either side of the peak reflecting the symmetry of the tip. The surface roughness of the latex is clearly visible in Fig. 2.13a. The dimensions of the features were measured on a 1 x 1 jum2 image obtained under the same conditions (Fig. 2.13c). The shell latex surface consists of roughly spherical undulations having an average diameter of 102 ± 10 nm. The measured vertical depth of the features, which depends on the geometry of the tip (35° half angle), was 15 ± 4 nm. To investigate the origin of the surface roughness, A F M images of polystyrene core latex as well as shell latex with different HEA-C1 initiator concentrations were obtained (Fig. 2.14). Each scan in Fig. 2.14 consists of a topographical (left) and phase (right) image. The phase images are obtained by monitoring the phase lag of the cantilever oscillation relative to the driven oscillation. This mode of operation is highly sensitive to variations in the viscoelastic properties of a material. While increasing adhesion forces are known to result in a phase lag, interpretation of phase images is not trivial and the relative contrast depends on the tapping force, or the ratio of the set-point amplitude to 83 the drive amplitude. Bar et al. (1997) obtained height and phase images of phase-separated polymer blends and found that as the tapping force was increased from small to large, the images underwent a contrast reversal twice. A controlled study whereby the A s p / A 0 is systematically varied was not performed here, making it difficult to assign features in the phase images to different chemical components. The images are presented however to show enhanced contrast on the heterogeneous surfaces. Figure 2.13. a) Tapping Mode image in air ( 4 x 4 urn2) of shell latex (D* = 650 nm) b) Single scan line obtained by section analysis showing horizontal (L H ) and vertical (Ly) 84 dimensions of latex particle c) High resolution image ( l x l pm2) showing roughness of shell latex. In contrast to the rough surface of the shell in Fig. 2.13, the surface of the polystyrene core latex is quite smooth (Fig. 2.14a). Images of shell latexes having low and high initiator concentration are shown in Figures 2.14 b and c, respectively. The surfaces of shells prepared with relatively low initiator concentration (2.11 x 10"7, 2.81 x 10"7 and 4.47 x 10"7 mol/m2) are structurally similar to the core latex, with a representative image presented in Fig. 2.14b. At high initiator concentration (20.0 x 10"7 mol/m2, Fig. 2.14 c), the surface is considerably rougher with regular spherical features distributed homogeneously over the particles. The origin of the roughness is believed to be phase separation of the copolymer shell, resulting from the increased hydrophilicity of the HEA-C1 over the styrene monomer. The mechanism of the shell copolymerization can be explained in terms of the compatibility of the two monomers and the copolymer in the aqueous and polystyrene phases. While HEA-C1 is more hydrophilic than styrene, both monomers are insoluble in water. Because the initiator for the radical polymerization (potassium persulfate) is water-soluble, initiation begins in the aqueous phase but radicals are immediately captured by the polystyrene latex particles. Copolymerization proceeds inside the polystyrene phase. Diffusion of the copolymer towards the polystyrene/water interface occurs because of the slightly hydrophilic nature of the HEA-C1 component, creating a copolymer shell of significant depth as determined by HT measurements. 85 Figure 2.14. Topographical (left) and phase (right) images obtained in Tapping Mode in air of a) polystyrene core latex and b-c) shell latex with varying HEA-C1 initiator concentrations. HEA-C1 concentrations: b) 2.81 x 10-7 mol/m2; c) 20.0 x 10"7 mol/m2. The separation of two component polymer systems into different phases is well described by the Flory-Huggins model. Only a slightly unfavorable interaction (i.e. x > 0) 86 between segments is required for phase separation to occur, with the critical volume fraction being inversely proportional to the magnitude of the Flory interaction parameter (Flory, 1953; Huggins, 1942). Incompatibility of the copolymer with polystyrene is expected to result in phase separation at a critical concentration of HEA-C1 in the copolymer. This is consistent with the images in Fig. 2.14, which show a smooth surface at low initiator concentration and a rough, phase-separated surface at high initiator concentration. The features in Fig. 2.14c are distributed over a relatively high fraction of the latex surface. Images of a shell latex (diameter = 9.6 pm) prepared with the same ratio of feed initiator concentration to latex surface area as the sample in Fig. 2.14c are shown in Fig. 2.15. The surface features on that sample are also distributed relatively uniformly over the surface but the space between features is larger. The raised features are attributed to regions of copolymer that are slightly enriched with the more hydrophilic HEA-C1 component. Based on the mechanism of shell copolymerization given above, the space between the features is expected to also contain initiator but possibly a slightly lower concentration. Calculations of the density of chains grafted from the surface initiator have assumed a homogenous distribution of initiator over the surface. While regions of high and low initiator concentration may exist when phase separation occurs, the difference is not expected to be large given that a random copolymer is predicted from the reactivity ratios of the monomers. The reactivity ratios of the two monomers are similar, indicating that the rate constant for a reaction of a styrene terminated radical with an HEA-C1 monomer is comparable with that of an HEA-C1 terminated radical with a styrene monmer. Taking 87 the number of moles of styrene and HEA-C1 used in the shell copolymerization (styrene:HEA-Cl feed ratio 3:1), and the reactivity ratios of styrene (0.66) and n-butyl acrylate (0.19), a comonomer structurally related to the initiator at 60 °C (Brandup and Immergut, 1989), the microstructure equation was used to calculate the probable distribution of initiator in the copolymer (Odian, 1991). The calculated diad and triad probabilities of the acrylate are 6.1% and 0.4%, and the diad, triad, and tetrad probabilities of styrene are 33%, 21%, and 1.4% respectively. The distribution of the initiator throughout the copolymer is therefore very likely random. Although phase separation does occur at high initiator concentration, the distribution of features on the surface is fairly regular and the grafting reaction is expected to occur over the entire surface. Further evidence for uniform grafting is given by the consistent force profiles obtained at different locations on a grafted surface in Chapter 3. This is in contrast to the bimodal distribution of force profiles obtained by Kelly et al. (1998) upon compressing regions of high and low chain density on a polymer brush. jr i Figure 2.15. A F M images (a) 5 x 5 //m 2 and (b) 2 x 2 /urn2 of D* = 9.6 jum shell latex in air. 88 The surface area of a sphere having a radius equal to that of the latex particles was used to calculate average grafting densities. For shells with significant roughness, the actual surface area is expected to be larger than the calculated value resulting in an overestimated grafting density. To determine whether the calculated grafting density is significantly affected by the increased surface area of the rough particle, the surface area of a model particle of radius R having hemispherical features of radius r distributed over the surface was estimated. The value of r was taken as the average radius of the surface features measured in Fig. 2.13c. The value of R + r corresponded to the hydrodynamic particle radius of the shell latex measured by dynamic light scattering. In this example, R = 274 nm and r = 51 nm. A schematic of the rough surface is shown in Fig. 2.16a. The fraction/of the particle surface covered by the hemispherical features is given by: Ai R f = (2.25) r disc where As R is the surface area of a particle of radius R, A<n$c is the area of a disc of radius r, and Nr is the number of surface features per particle. The value of Nr was determined by counting the number of surface features per particle in an A F M image. As demonstrated in Fig. 2.13b, the tip does not scan the entire upper hemisphere of the latex particle but rather a spherical cap of height h = Ly. A spherical cap is defined as the region of a sphere of radius R that lies above a given plane, as depicted in Fig. 2.16b, and has a surface area given by: As = InRh (2.26) The average area of a latex particle imaged by A F M (Lv =165 nm) was obtained from 5 2 Eq. 2.26 to be 2.84 x 10 nm . For an average number of features per area of particle 89 imaged of 29, we obtain 1.02 x 10"4 features/nm2 and Nr ~ 96. A fraction / ~ 0.84 is obtained for the ratio of surface area covered by the features to surface area of a latex particle. The surface area of the rough particle Asrough is calculated by summing the area of the smooth particle not covered by surface features, Asgap, and the surface area of Nr hemispherical features ( A s r 12) according to: A, s,r s,rough ^s, gap (2.27) = 4TTRz -NrmA +Nr2nR' In this case, the ratio of Asrough to the surface area of a smooth particle of radius R + r was found to be 1.3, giving an uncertainty in the surface area as well as grafting density of ~ 30 %. The uncertainty in the distance between chains D, calculated from the square root of the area per chain, is ~ 5.5 %. While the uncertainty in D for this case is reasonable, the increased area due to surface roughness could lead to significantly underestimated grafting densities in some cases and should be considered. 2r Figure 2.16. a) Schematic of rough latex sphere having radius R + r. b) Spherical cap defined by region of sphere lying above shaded plane. 90 To determine the effect of surface roughness, curvature, and inhomogeneities in the latex packing, the variation in force profiles obtained at different locations on a sample was examined. The interaction between a silicon nitride tip and shell latex measured at different locations on the sample is presented in Fig. 2.17. The superposition of the curves shows that variation in profiles obtained on a single bead as well as between multiple beads is small. A large effect is expected when the region directly between two adjacent particles is probed, as opposed to the highest point on a particle. However, the frequency of such an occurrence is low. This is discussed in further detail in Chapter 3. - i— i—i—i— i—i—i—i— i—i—i—i— i—i—i—.— i 0 20 40 60 80 Separation (nm) Figure 2.17. Interaction of silicon nitride tip and shell latex (D* = 650 nm) in 10 m M NaCI at 10 different locations on a sample. The negligible effect of roughness shown here is attributed to the contact area of the A F M tip (R ~ 15 to 40 nm), which is small on the scale of the surface roughness. This is in contrast to the significant effect of roughness that is expected when large polystyrene particle probes are employed, which has been used to explain unsuccessful attempts in the literature at fitting the adhesion between polystyrene latex probes and flat surfaces to 91 the JKR theory (Section 1.4.4.6). In general, the effect of roughness is to reduce the effective contact area of a hard surface and result in less adhesion than expected for a particle of known radius (Israelachvili, 1992). When a deformable layer of hydroxypropyl cellulose (HPC) was grafted to a hard polystyrene core, however, the effect of the polymer was to fill the asperities in the polystyrene and increase the effective contact area (Prescott et al, 2002). Given that the bulk of the work in the following sections was performed with a silicon nitride tip, the effects of roughness are not investigated any further. 2.4 Summary The procedure used to obtain the force measurements and perform the data analysis has been validated and the profiles have been described reasonably well by theoretical models. The interactions between silicon nitride and polystyrene latex at various ionic strengths have been examined and the separation range and magnitude of the D L V O forces have been measured. This information is required to decouple the contributions from the shell latex and the grafted layer in the interactions measured on polymer brushes in the following sections. A F M images of the shell latex revealed that some surfaces were significantly rough as a result of phase separation in the copolymer shell. While this may affect the estimated grafting density in some cases, force measurements were reproducible over the shell and did not appear to be affected by the roughness. 92 3. Compression Forces in Neutral Polymer Brushes Measured by A F M in Good Solvent Conditions 3.1 Introduction The interactions between a polymer brush and an opposing surface cannot be described simply by D L V O theory. This is in contrast to the force profiles of non-grafted latex in electrolyte solutions shown in Chapter 3, where the measured decay length agreed with the predicted Debye length. While charged particles bearing grafted polymer layers can, under certain conditions, exhibit exponentially decaying repulsive force profiles, the decay lengths do not match the values calculated for purely electrostatic interactions (Prescott et al, 2002; Vermette and Meagher, 2002). The force profiles measured for some polymer brushes in this work were not monotonically repulsive but exhibited a long-range attraction with repulsion at short range. The shape of the profile depended on the properties of the grafted layer, the solvent quality and the affinity of the polymer for the compressing surface. The focus of this chapter is to examine the response of polymer brushes to normal compression by an A F M tip. Probing the material in this direction provides information on the equilibrium thickness of the layer, the magnitude of steric repulsive forces due to excluded volume effects, and the ability of the polymer to bridge the two surfaces. Force profiles were investigated as a function of chain density and molecular weight of the grafts, monomer nature, tip surface chemistry, solvent quality, temperature and ionic strength. The relationship between the grafting density and the measured equilibrium brush thickness was compared with well-established theoretical predictions. The ability 93 of the Alexander-de Gennes model of surface-brush interactions to fit the force data was evaluated. 3.2 Experimental 3.2.1 Synthesis of Grafted Polymer by Atom Transfer Radical Polymerization from Latex The preparation of grafted polymer layers on latex surfaces by atom transfer radical polymerization (ATRP) was performed by Dr. Jayachandran N . Kizhakkedathu in the Brooks laboratory. The monomers utilized in this work were N,N-dimethylacrylamide (DMA), N-isopropylacrylamide (NIPAM), methoxyethylacrylamide (MEA). The structures are shown in Appendix 4. Detailed descriptions of the graft polymerizations of D M A (Jayachandran et al, 2002), N I P A M (Kizhakkedathu et al, 2004c), and copolymerization of M E A / N I P A M (Kizhakkedathu et al, 2004b) are provided in earlier reports. Briefly, a suspension of the ATRP initiator functionalized latex (Section 2.2.1.2) was degassed for 2.5 h by continuous vacuum and argon cycles and transferred to a glove box. In a typical reaction, the monomer was stirred with CuCI, CuCb, and Cu powder and N,N,N',N',N"-pentamethyldiethylene triamine (PMDETA) for 3 minutes to form a solution. Brij-35 stabilized shell latex was subsequently added and the reaction was allowed to proceed under stirring at room temperature (22 °C) for 12 h. The grafted latex was cleaned by repeated sequential centrifugation and resuspension in water, NaHS03 solution and water to remove adsorbed copper complexes for 8-10 cycles until there was no detectable amount of polymer/monomer/catalyst in the supernatant. 94 3.2.2 Analysis of Grafted Latex The grafted latex was characterized by determining the hydrodynamic size, graft molecular weight, molecular weight distribution and radius of gyration of polymer chains. Particle size measurements were carried out in a temperature controlled Beckman Coulter N4 Plus particle size analyzer by dynamic light scattering. Molecular weights were determined by GPC on a Waters 2690 separation module fitted with a D A W N EOS multi-angle laser light scattering (MALLS) detector from Wyatt Technology Corp. with 18 detectors placed at different angles (laser wavelength A=690 nm) and a refractive index detector from Viscotek Corp operated at A=620 nm. Nuclear Magnetic Resonance (NMR) was performed on a Brucker Avance 300 N M R spectrometer using deuterated solvents with the solvent peak as a reference. Characterization of the grafted polymer chains (molecular weight, molecular weight distribution, mass of the grafted chains per unit area of latex and radius of gyration, R g , was performed by cleaving off the chains by hydrolysis as follows. A known amount of grafted latex (2 g) was stirred with 1 mL of 2 N NaOH (final cone. ~ 0.7 mol/L) until no change in the amount released was detected (two weeks). The supernatant and the washings were collected and analyzed by GPC. The value of dn/dc of the P D M A in the mobile phase calculated at 620 nm was 0.150 mL/g and was used for determining molecular weight parameters. Aliquots of 200 uL of the polymer solution were injected through the two ultrahydrogel columns at 22 °C. The mass of polymer in the cleaved solution was determined using a calibrated RI detector and confirmed by independent absorbance measurements utilizing a P D M A calibration curve at 235 nm (for selected 95 samples). Both approaches agreed to within ± 1.5%, with no systematic differences between the methods. 3.2.3 Preparation of Surfaces with Different Grafting Densities The amount of polymer grafted was determined by quantitative release of the chains at the point of grafting upon hydrolysis of the ester linkage in the initiator. The grafting density was calculated from the surface area of the latex, amount and molecular weight of the polymer grafted as described previously (Jayachandran et al, 2002). The surface area was calculated using the measured latex radius and assuming the particles were perfectly spherical. Brushes with varying graft density and constant M n were prepared by time dependent quantitative hydrolysis of grafted P D M A latex. Grafted latex samples (4g each) were stirred with NaOH (2g, 2N) for different periods of time (up to 96 h) and the hydrolysis was stopped by the addition of HCI (6 N) to the suspension. The supernatant was collected quantitatively by centrifugation of the suspension. The graft densities of these cleaved brushes were determined from the amount of polymer released from different samples at various time intervals. 3.2.4 X-ray Photoelectron Spectroscopy Surface characterization was performed by the Interfacial Analysis & Reactivity Laboratory service at UBC. X-ray Photoelectron Spectroscopy (XPS) analysis was performed using a Leybold Max 200 (Cologne, Germany) equipped with a Mg K a source at a power of 200 W. Elements were identified from survey spectra. High-resolution spectra were also collected at 48 eV pass energy. 96 3.2.5 A F M Force Measurements The general procedures for measurements and data analysis have been provided in Chapter 2. The force between the tip and a clean glass substrate was measured before and after probing each polymer sample to check tip quality. A consistent profile was observed with only a snap-to-contact attraction at very small separations and a primary adhesive force upon retraction, suggesting that the tip remained free of contaminants. By comparison, when the tip is contaminated by adsorbed polymer, the retraction profile of the tip on a clean glass surface exhibits an attractive force that varies non-linearly with extension. This characteristic stretching of polymer chains is described in Chapter 4. Such behavior was not observed during routine tests of tip quality where force profiles on clean glass substrates were obtained. The tips were also inspected under an optical microscope following measurements to ensure that contamination by large particles such as latex had not occurred. Due to the relatively small diameter of the latex (650 nm), force measurements were obtained at random locations and could not specifically be performed on the uppermost point of the particles. The effects on the force curve i f the region directly between two spheres was probed, as opposed to the uppermost point of a particle is considered. A representation (to scale) of an A F M tip (half angle 35°) located at (a) the top of a latex particle (diameter = 650 nm) and (b) directly between two adjacent particles is presented in Fig. 3.1. The representation suggests that the contact area between the tip and the grafted layer when the tip is located between two adjacent particles is significantly higher than when it is at the upper most point of the particle. The compression curves are therefore expected to exhibit larger repulsive forces in (b) than in (a). Indeed, in ~ 1 -4% 97 of the force profiles collected, the repulsive compression forces were of above average magnitude and the data from the corresponding decompression profiles were not included in the analysis. 1303 Figure 3.1. Representation (to scale) of conical A F M tip (35° half angle) compressing spherical brush (diameter = 650 nm). The tip is located at the point of zero separation, i.e. constant compliance region. Dotted line represents a 65 nm thick layer of grafted polymer at equilibrium. Diagram shows tip located at a) uppermost point of particle and b) directly between two particles. The region of contact between the tip and the grafted polymer layer is given by a disc of diameter C. For simplicity, we define the region of contact so that the polymer layer cannot access the tip at a vertical distance greater than the equilibrium thickness. 98 3.3 Results and Discussion 3.3.1 A F M Imaging Tapping Mode A F M images of shell and P D M A grafted latex obtained in air and water are presented in Fig. 3.2. A l l brushes were prepared on latex with diameter ~ 650 nm, unless otherwise noted. The molecular weight of the grafted layer ( M n = 4 x 106) is much higher than that of the typical samples investigated in this report. This sample was chosen to show the distinct difference in particle size of the shell and grafted latex. Figures 3.2a and 3.2b show 20 x 20 fjm topographical scans of shell and grafted latex, respectively, obtained in air. Brighter spots represent higher regions than darker spots. Comparison of the size of the particles in the two images shows that even in air (poor solvent) there is a significant increase in diameter after grafting. The shell latex sample exhibits regions of hexagonally packed arrays. The grafted latex sample is also reasonably ordered but there is significantly more space between the particles (dark regions) which may be occupied by polymer. A higher resolution image ( 5 x 5 fim ) of the brush in air is presented in Fig. 3.2c. The contour of the particles is ill-defined, with the intermediate intensities presumably reflecting the grafted polymer layer. An image of the hydrated brush obtained at the same resolution is presented in Fig. 3.2d. The extended structure adopted by the grafted layer in good solvent is inferred from the reduction in the number of particles packed in a given area. 99 Figure 3.2. Tapping Mode images in of a) shell latex in air b,c) P D M A ( M n = 4 x 106) brush in air d) PDMA brush in water. In Fig. 3.3, a series of Tapping Mode topographical images ( 2 x 2 urn2) in air of non-grafted and P D M A grafted latex showing the effect of graft molecular weight on the surface roughness of the latex are presented. The images in 3.2a and 3.2b are of core polystyrene latex and shell latex, respectively. The increased surface roughness resulting from the addition of the copolymer shell is clearly visible (see Section 2.3.7). The image 100 of the lowest molecular weight brush (Mn = 39 600) in Fig. 3.3c is similar to that of the copolymer shell. This is not unreasonable given that the structure of the grafted polymer is collapsed in air. The increased size of the surface features with increasing molecular weight is demonstrated in Fig. 3.3d through 3.3g. The surface features of the highest molecular weight brush ( M n = 217 000) have significantly enlarged and are not as frequent as on the lower molecular weight brushes. The surface roughness in Fig. 3.3g is similar to that of the core polystyrene latex however the size of the particles has visibly increased. Tapping Mode images ( 2 x 2 jum2) of non-grafted and P D M A grafted latex in aqueous solution (100 m M NaCI) are presented in Fig. 3.4. Left and right scans show topographic and phase images, respectively. Since phase imaging is highly sensitive to variations in the viscoelastic properties of materials, the phase images have been included to show enhanced contrast, particularly in the grafted samples. Again, the shell latex surface is considerably rougher than the core latex surface, as demonstrated by Fig. 3.4a and 3.4b. Images of the hydrated P D M A brushes, M n = 40 000 and 80 000 respectively are shown in Fig. 3.4c and 3.4d. In contrast to the roughly spherical undulations observed on the surface of the shell latex, the grafted surface exhibits elongated features which are more difficult to track with the A F M tip as the M n is increased. Given the thickness of the hydrated layer, the tip may not be free of the polymer even at the highest point in the oscillation. This would likely result in the elongated features observed in Fig. 3.4c and 3.4d. These images are similar to those obtained by Uchida and Ikada(1997) of a grafted polymer layer in poor solvent in Contact Mode. There, the grafted layers formed clusters as a result of the poor solvent quality and exhibited deformation that was not present in 101 air. The deformation was manifested by a tilting of the clusters in the direction of the scan. Figure 3.3a-d Tapping Mode images ( 2 x 2 urn2) in air of a) core latex b) shell latex c) P D M A brush (M„ = 3 9 600) d) P D M A brush (M„ = 80 400) 102 Figure 3.3e-g Tapping Mode images ( 2 x 2 urn2) in air of e) P D M A brush (M„ = 166 000) f) P D M A brush (M„ = 204 000) g) P D M A brush ( M n = 217 000) 103 Figure 3.4. Tapping Mode images ( 2 x 2 um2) in water (100 mM NaCI) of a) core latex b) shell latex c) P D M A brush (M„ = 39 600) d) PDMA brush (M„ = 80 400) 104 To examine the effect of grafting density, the grafted layer was hydrolyzed in situ and the sample was scanned at various time intervals. The idea was to repeatedly scan the same area, but as a result of sample drift the particles in the earlier and later scans are potentially not the same. To perform this experiment, the fluid cell was installed with the O-ring and a solution of 0.1 M NaOH was injected in the inlet port. The sample was allowed to bathe in the solution until immediately prior to imaging, at which point a fresh solution of 100 mM NaCI was flushed through the cell to remove any free polymer. Images were obtained in the NaCI solution. Figure 3.5 shows topographical and phase images of the P D M A brush ( M n = 40 000) at various points during the hydrolysis. An image of the original brush before hydrolysis is shown in Fig. 3.5a. There is no noticeable change in Fig. 3.5b, which was obtained immediately following injection of NaOH solution. After 1.5 h (Fig. 3.5c), there are distinct pits (dark features) around the periphery of the latex in both the topography and phase images. The pits appear to be slightly larger and more numerous after 4.5 h (Fig. 3.5d), resulting in an increase in size of the overall particle contour. These dark features may represent inhomogeneities in the grafting as polymer is gradually released from the surface and the brush layer is more easily penetrated. After 8 h (Fig. 3.5e), the roughness on the surface appears more uniform, perhaps reflecting a more extensively hydrolyzed surface. There is no noticeable change after 8.5 h (Fig. 3.5f). Measurements of the amount of polymer released from the surface with time upon hydrolysis of the chains in suspension (Section 3.2.3) indicated that the grafting density after 1 hour was ~ 50% of the initial value. This is consistent with the most dramatic change in the image occurring between Figures 3.5 b and c after 1.5 h of hydrolysis. 105 After 8 h of hydrolysis in the suspension, only ~ 4% of the remaining chains are released with time. This resulted in a change in the surface that was too small to detect by A F M imaging. This limitation however, could also be due to the lack of mixing during the hydrolysis in the A F M chamber. By contrast, variations in the surfaces were apparent from differences in the force profiles of the surfaces following hydrolysis up to 48 h (see Section 3.3.2.1 below). Figure 3.5a-b Tapping Mode images ( 2 x 2 urn2) in P D M A brush (Mn = 40 000) showing in situ hydrolysis of chains with time t: a) Before hydrolysis b) t = 5 min 106 Figure 3.5c-d c) t = 1.5 hours d) 4.5 hours 107 Figure 3.5e-f e) 8 hours f) 8.5 hours 108 3.3.2 Force Curve Analysis 3.3.2.1 Weakly Adsorbing Chains Effect of Molecular Weight A series of P D M A brushes with increasing molecular weight was prepared according to the method described in Section 3.2.1. The monomer concentration was varied in order to produce brushes with different properties. The reaction conditions and properties of the grafted layer are presented in Table 3.1. Table 3.1. Properties of PDMA Grafted Latex MnxlO-J MJM„ D a(nm) HTb(nm) Le c(nm) 39 600 1.25 3.9 67 95 80 400 1.41 2.2 148 132 166 000 1.53 2.2 296 200 205 000 1.32 2.1 377 207 273 000 1.41 1.5 608 N D 217 000 1.49 1.1 680 N D "Distance between grafting points. Hydrodynamic thickness of grafted layer. cEquilibrium brush thickness measured by A F M . Compression profiles obtained for the series of P D M A brushes with a silicon nitride tip (k ~ 0.58 N/m) in 150 m M NaCI are presented in Fig. 3.6. In each case, the repulsive force increases monotonically as the brush is compressed. The data is truncated in the force dimension to clearly show the onset of repulsion at low compression. The repulsive force in the high compression regime (approaching zero separation) is not displayed, but continues to increase monotonically for all curves. These results are consistent with force profiles of grafted polymer layers presented in the literature obtained by A F M (Prescott 109 et al, 2002; Vermette and Meagher, 2002; Yamamoto et al, 2000a,b; Butt, et al, 1999; Kelley et al, 1998) and S F A (Sheth et al, 2000; Sheth et al, 1997; Tauton et al, 1990) where a monotonically increasing repulsive force that varied roughly exponentially with distance was reported. T 1 1 1 1 —I 1 1 1 1 0 25 50 75 100 125 150 175 200 225 Separat ion (nm) Figure 3.6. Compression profdes of shell and grafted latex with varying molecular weight P D M A in 150 m M NaCI solution (a = grafting density). Tip-sample separations L were calculated according to the method of Ducker et al (1992) with zero separation corresponding to the onset of the constant compliance region. To give some physical meaning to the separations, it was assumed that L = 0 nm corresponds to the point where the tip nearly contacts the latex surface and the brush is fully compressed. It is of course possible that the polymer cannot be further compressed and behaves like a hard surface while a significant, incompressible layer of polymer remains between the tip and the latex. This has been referred to by other authors (Yamamoto et al, 2000c) as an offset distance and is considered in further detail below. 110 Based on the rigidity of polystyrene (compressive modulus = 3000 MPa) (Brandup and Immergut, 1989) and force profiles obtained on non-grafted latex (Section 2.3.1), indentation of the particle is not expected to contribute significantly to the force profiles. Similarly, a significant electrostatic contribution to profiles of brushes having the high M n and a as shown here is not expected. Force measurements on the non-grafted shell latex in Section 2.3.2 showed that at this ionic strength (150 mM NaCI), repulsion occurred over a small separation range and magnitude. The electrostatic contribution is only non-negligible for lower grafting density samples measured at lower ionic strength (10 m M NaCI); that case is considered below. The repulsive forces in Fig. 3.6 are of longer range than those expected by simply considering electrostatics and are attributed to the steric repulsion exerted by the compressed polymer layer. As discussed in Section 1.3.3, a repulsive force arises from the reduction in entropy associated with increasing the local polymer concentration in the region between the grafting and compressing surfaces. The repulsive forces increase with M n and a, reflecting the more extended equilibrium brush structure. The separation at which the repulsive force can first be distinguished from the noise in the baseline (± 0.02 nN) gives the equilibrium thickness, L e ; of the grafted layer. The values of L e correspond to the thickness of the polymer layer between the tip and the latex sample and are listed in Table 3.1. While it is possible that compression of the grafted layer between the polystyrene and glass substrate may result in an overestimated thickness, the motion of this layer is highly restricted and its contribution is assumed to be insignificant. The latex dries on the glass substrate in local hexagonally packed arrays, which are resistant to the 111 large shear forces present during sonication. Based on this, it has been assumed (Kizhakkedathu et al., 2003) that the underlying grafted layer behaves as a rigid body. Also listed in Table 3.1 are the layer thicknesses obtained by HT measurements, which are typically larger than the values of L e obtained by A F M . Two reasons are proposed to explain this discrepancy. The first is associated with the uncertainty in the HT measurements. The hydrodynamic resistance associated with particle diffusion arises from the integrated effects of the drag produced by all of the chains on the surface; it is this resistance that is attributed to that of an equivalent hard sphere whose diameter is provided by the measurement. The resistance is particularly sensitive to the longest chains on the surface (Fleer et al., 1993; Cohen Stuart et al., 1984). In contrast, the A F M tip samples only a small fraction of the total surface area, with a low probability of sampling the very longest chains. While there is this discrepancy in the two sets of measurements, the general trend toward increasing layer thickness with M n is the same in both methods. Alternatively, the discrepancy may be attributed to the uncertainty in L e related to a non-negligible offset distance resulting from a significant, incompressible polymer layer between the tip and the grafting surface. The contribution of an offset distance to the force profile of o = 0.07 nm" brush was examined by Yamamoto et al. (2000c) by scanning across the boundary of the polymer sample and a bare patch of substrate where the polymer was removed. They found an offset distance of 14 nm when measurements were obtained with a silica probe (10 //m diameter) but an offset distance of zero when using a standard V-shaped cantilever of the type used here. They attributed this to the ability of the sharp tip to penetrate the polymer layer and closely approach the substrate. 112 The offset distance here was not measured but was assumed negligible given the use of sharp silicon nitride tips. With the grafting densities in Fig. 3.6 being generally higher than that used in the referenced study, this assumption might not be appropriate. Better agreement between L e and HT was achieved with lower a samples (see below, Table 3.2). For the force profiles presented above, it was possible to compress the chains to a point where the repulsion was like that of the hard, glass surface used as the external calibration standard. Force profiles of higher molecular weight brushes ( M n = 217 000 and 273 000) were obtained (data not shown) but the constant compliance region could not be reached using the same A F M tips (k ~ 0.58 N/m). These brushes could not be fully compressed, even when the largest possible trigger force was applied. It is important to note that the equilibrium thickness measured by A F M is dependent on the spring constant of the probe. Full compression of the higher molecular weight brushes may be achieved using a stiffer tip, but sensitivity to small repulsive forces will be reduced and the equilibrium thickness underestimated. The brush properties in Table 3.1 indicate that it was not possible to investigate the effect of molecular weight independent of grafting density, both of which increased with increasing monomer concentration. The increase in surface chain density and decrease in the amount of solution polymerization with increasing monomer concentration was unexpected. Indeed, a detailed study of the brush properties as a functioned of reaction conditions performed in this laboratory has demonstrated that surface initiated ATRP is quite different from polymerization performed in solution. The focus of this report, however, is not the preparation of the grafted polymers by ATRP, and the reader is 113 referred to a previous publication for a detailed description of the surface model (Kizhakkedathu et al, 2003; Jayachandran et al, 2002). Effect of Grafting Density To examine the effect of grafting density independent of molecular weight, surfaces having the same M n and different a were obtained by hydrolyzing a P D M A brush for various lengths of time and thereby cleaving different number fractions of the chains at their point of grafting. The grafted layer (before hydrolysis) had M n = 30 600, PDI = 1.35, and a = 0.17 nm"2. The brush properties for the series are listed in Table 3.2. A smooth spherical particle was assumed in calculating the tabulated grafting densities, however the actual grafting densities may be significantly lower due to the surface roughness of the latex shell, as discussed in Section 2.3.7. These grafting densities are still considered quite high relative to values reported in the literature, as surface roughness is typically not taken into account. The compression profiles of the non-grafted shell latex and the P D M A brush with the highest grafting density (CT = 0.17 nm"2) in 10 mM NaCI are compared in Fig. 3.7. The curves are averages of 10 and 75 force profiles, respectively. The force from the negatively charged shell latex is electrostatic in origin and arises from the osmotic repulsion of the double-layer counterions. The data corresponding to separations > 1.5 nm fit an exponential with a measured decay length of 3.4 ± 0.1 nm which compares with the Debye length of 3.0 nm (Israelachvili, 1992). The repulsive force from the brush sample can be attributed to the steric interaction from the grafted layer at large separations, and to both steric and electrostatic forces at small separations. The effect of 114 the grafted layer can be examined independent of electrostatics by subtracting the shell profile from the brush profile, indicated by the solid line. As demonstrated by the superposition of the brush profiles before and after shell subtraction at small loads (< 0.35 nN), the force profile of the brush is not significantly affected by the underlying shell latex interactions at long range. The same value for the equilibrium thickness (L e = 65 nm), corresponding to the first detectable repulsive interaction, is obtained when taken from either the non-adjusted or corrected curve in Fig. 3.7. This is true for all samples with a between 0.031 nm"2 and 0.17 nm"2. When the grafting density is lowered to 0.022 nm" , the range of separation and magnitude of the steric force are sufficiently decreased that the electrostatic interactions become significant at smaller loads. In these cases, different values are obtained for the equilibrium thickness when measured before and after the electrostatic correction. Both values are listed in Table 3.2. Separation (nm) Figure 3.7. Compression profile of P D M A brush ( M n 30 600) grafted to polystyrene latex particles (650 nm diameter) before and after correction for the electrostatic contribution. The purely electrostatic profile of the shell latex is also shown. A F M 115 measurements were performed in 10 mM NaCI. The shell and brush profiles are averages of 10 and 75 curves, respectively. The arrow denotes the separation corresponding to the equilibrium brush thickness, L e . Compression profiles of the P D M A brushes of varying a are presented in Fig. 3.8 (Goodman, et al., 2004a). The curves have all been corrected by subtracting the electrostatic contribution from the shell latex. For the following discussion, the attractive profile corresponding to the a = 0.012 nm" sample is ignored and only the brushes with higher a are considered. The low grafting density case will be examined in the following section. The force F as a function of separation L could be fit to a single exponential: F(L) = -aebL (3.1) where a and b are the fitting parameters (Table 3.2). An upper bound curve was calculated from the mean plus one standard deviation of each point and was fit to Eq. 3.1. The uncertainties for a and b given in Table 3.2 are calculated from the difference between the fit parameters obtained for the mean curve and the upper bound curve. 0.04 • a - 0.17 nm"2 • o = 0.081 nm' 1 T 0 = 0.038 nm"2 * o = 0.031 nm' 2 A o = 0.022 nm' 2 + a = 0.017 nm' 2 O » = 0.012 nm"2 Separation (nm) Figure 3.8. Effect of grafting density on compression of P D M A brushes ( M n 30 600) grafted to polystyrene latex particles measured in 10 mM NaCI. Curves have been 116 corrected to remove electrostatic contribution (see text). Each curve represents the average of data from ~ 75 locations on the sample. See text and Table 1 for discussion of uncertainty. Table 3.2. Properties of PDMA Brushes with M„~ 30 600 and PDI = 1.35 Time "(h) a" (nm2) D/Rg c HT " (nm) (nm) (nm) (nm) a * (nN) b (nm"1) R* j (nm) 0 0.17 0.38 58 65 65 68 1.0± 0.3 0.09 ± 0.02 1 1 0.081 0.55 40 48 48 42 0.8 ± 0.2 0.16 ± 0.02 3 5 0.038 0.80 30 34 34 36 0.3 ± 0.5 0.17 ± 0.06 8 7 0.031 0.87 40 32 32 29 0.4 ± 0.4 0.48 ± 0.01 27 15 0.022 1.0 32 25 15 20 0.6 ± 0.5 0.29 ± 0.04 46 24 0.017 1.2 42 15 10 12 0.3 ± 0.4 0.36 ± 0.05 287 48 0.012 1.4 49 - - - - -surface (chains/nm ). cRatio of distance between grafting points to radius of gyration. ^Hydrodynamic thickness measured by particle size analyzer. "Equilibrium thickness measured from force profiles before electrostatic correction. ^Equilibrium thickness measured from force profiles after electrostatic correction. ^Equilibrium thickness measured from fitted decay length ''''Fitting parameters (Eq. 3.1; Fig. 3.8). yTip radius estimated from fits to Eq. 1.15. The separation at which deviation of the repulsive force from the baseline is first observed increases with a. The more extended brush structure associated with larger a is consistent with the stretching of the chains away from the grafting surface in response to 117 2 the increased excluded volume. The equilibrium thickness for the a = 0.012 nm" brush, for which the force profile exhibited a long-range attraction, cannot be determined by this method. As discussed below in Section 3.3.2.3, the attractive bridging interactions depend on the rate of the measurement and are therefore not equilibrium values. The measured equilibrium thickness values are similar to the hydrodynamic thickness measurements obtained by dynamic light scattering as shown in Table 3.2. Based on the small offset distances that were found at similar and higher grafting densities using sharp silicon nitride probes in other reports (Vermette and Meagher, 2002; Yamamoto et al, 2000c), an offset distance in this case is likely negligible except possibly for the highest o" brush. Due to significant scatter in the hydrodynamic thickness HT data, the values cannot be described as increasing with a although the largest HT value is found for the sample with the highest a. The HT values are presented for comparison but it is noted that propagation of the errors associated with the diameter estimates of the grafted and shell latexes gives rise to a large uncertainty for relatively small HT values. For example, a particle diameter increase from 650 nm ± 10% to 710 nm ± 10% results in a HT of 30 n m ± 160%. The dependence of L e on a is demonstrated in Fig. 3.9 and compared with theoretical predictions. Scaling theory predicts that for a moderately dense brush in good solvent, L e varies with cr, and the degree of polymerization, N , according to (Fleer et al, 1993): Le oc No" (3.2) where n = 1/3. The above expression corresponds to the equilibrium thickness measured on a flat brush. A more complicated relationship, which takes into account the effect of curvature, is used to treat the data in Chapter 5. Given the small ratio of L e /R , Eq. 3.2 is 118 used here to approximate the dependence of thickness on grafting density. The exponent has been predicted using different approaches, first by Alexander (1997) and de Gennes (1980) using global energy balance approximations, and then using analytical self-consistent mean-field (SCF) equations (Milner et al, 1988). The linear logarithmic plot obtained in Fig. 3.9 indeed suggests a power-law relationship, however a non-linear least squares fit (R 2 = 0.996) performed on the data for 0.0171 < a < 0.171 gave an exponent n of 0.45, which was higher than the predicted value. This is not unreasonable as theoretical and experimental results in the literature suggest that an exponent > 0.33 may be expected for high-density brushes (Hu and Wu, 2001; Yamamoto et al, 2000b; Lai and Halperin, 1991). This is discussed in more detail in Section 4.3.1. LU 0.01 0.1 Grafting Density a (nm') Figure 3.9. Effect of grafting density on equilibrium thickness of P D M A brushes measured by A F M ( M n ~ 30 600, PDI = 1.35). Dotted line corresponds to best fit of linear region (0.0171 nm - 2 < a < 0.170 nm"z) with slope of 0.45. The exponentially decaying force profiles are in accordance with an expression derived by Alexander and de Gennes (Eq. 1.10) for the force exerted by surfaces bearing polymer 119 brushes in good solvent. The original equation was derived for identical flat brushes, and the result has been divided by two to give the force between a single brush and planar surface. A modified version (Eq. 1.15) was given by Butt et al. (1999) to account for the geometry of the A F M tip-sample system. The theory was tested by comparing Eq. 1.15 with the parameters obtained by fitting the force profiles to an exponential decay (Eq. 3.1). A value for the equilibrium thickness L e jf, t was obtained by multiplying the fit decay length b'1 by 2n. The values of L e jf l t are listed in Table 3.2. The equilibrium thicknesses obtained by the fitting method (Le,fit) and by inspection (L e) are in good agreement. Substitution of the appropriate parameters into Eq. 1.15 and comparison with the fit parameter a allowed the tip radius, R*, to be estimated. The calculated values are listed in Table 3.2. The calculated R* increased from 1 to 287 nm with decreasing o. Given that the expected tip radius quoted by the manufacturer is between 15 and 40 nm, the data cannot be described by this model. The values of R* corresponding to brushes of intermediate grafting density (0.022 < cr < 0.038 nm"2) are within, or close to the expected radius. The unusually low estimates of R* obtained at high grafting density may be the result of chain splaying, which is not accounted for in the model. When the number of chains beneath the tip is sufficiently high, direct compression of the layer is not expected and simulations have shown the chains to bend around the tip. The effect of splaying is to reduce the effective contact area between tip and brush giving rise to a small value of R*. A more reasonable value of R* could be obtained, for instance, by artificially increasing the value of D in the calculation. At low grafting density (a = 0.017 nm"2), the force profile can contain a significant attractive bridging component and is also not adequately described by Eq. 1.15. 120 The ability of the Alexander-de Gennes model to describe repulsive brush interactions has been investigated by a number of authors and an exponentially decaying repulsive force has been typically reported. There have, however, been discrepancies between independent measurements of L e and D and the values obtained from fit parameters. O'shea et al. (1993) used A F M to measure the compression of a planar brush in good solvent prepared by physisorption of the poly(ethylene oxide) block of a PEO-Z>-PS copolymer to mica. The distance between chains, D, obtained by fitting the force curve to Eq. 1.10 agreed reasonably well with independent reflectometry measurements. Unreasonably large L e values, however, were attributed to the simplicity of the model, which does not consider the ability of the unanchored PEO segments to move along the surface or the PS segments to splay around the A F M tip. The use of Eq. 1.10 which describes the interaction between two planar surfaces, rather than a geometrically modified version (Eq. 1.15), was presumably justified by the relatively large tip radius (100 nm), although this is questionable. Butt et al. (1999) measured the interaction between polystyrene grafted to silicon in cyclohexane and an A F M tip. The data was reasonably well described by Eq. 1.15, however a large uncertainty was associated with the spring constant and the grafting density estimate, which was based on the polymerization time. Yamamoto et al. (2000a) measured the force between a silica particle attached to an A F M tip and a flat silicon surface bearing end-grafted poly(methyl methacrylate) chains in toluene (good solvent), prepared by surface-initiated atom transfer radical polymerization (ATRP). The grafting density was 0.4 chains/nm2 , the M n varied between 23 000 and 171 400 and PDI between 1.34 and 1.56 (values based on solution 121 polymerization). The force profiles were repulsive at all separations but did not fit the Alexander-de Gennes model for varying molecular weight. The poor fit was attributed to the high density of the brushes, which exceeded the moderately dense brush regime appropriate for the model. The authors examined the effect of grafting density on the force between a silica probe and P M M A brushes (Yamamoto et al, 2000b) with M n 56 700 and a ranging between 0.07 and 0.7 chain/nm2. The resistance to compression increased with a but the above model could not accurately describe the measured force profiles. To summarize, the Alexander-de Gennes model has described the interaction of polymer brushes of moderate density reasonably well but failed to describe systems of high grafting density. Bridging in Weakly Adsorbing Systems When the grafting density is lowered to a = 0.012 nm"2, which, from D/R g of ~ 1.4 corresponds to a moderately dense brush, long-range attraction is observed at a separation of 70 nm (Fig. 3.8). It is here the tip first contacts the outer layer of the brush and, with repulsion due to segment overlap minimal, an attractive force is detectable. A repulsive force dominates upon further compression as the chains become increasingly confined. The attraction between adsorbed or grafted polymer chains and a surface can be attributed to the ability of the polymer to bridge the two surfaces and pull them together (Ingersent et al, 1986; Luckham and Klein, 1985; Klein and Luckham, 1984; Israelachvili et al, 1984). The response of an elastic chain to the confinement of both ends is to reduce their separation, giving rise to the so-called bridging force (Israelachvili, 122 1992). Attractive segment-surface interactions as well as available adsorption sites on the surface are necessary for bridging to occur, with the optimum condition believed to be moderate surface coverage. At low coverage, the density of bridges will be very low, while at high coverage such as in a brush, the lack of available binding sites on the surface prevents the polymers from forming bridges (Ji et al, 1990). Polymer brushes in the literature have typically exhibited purely repulsive force profiles while bridging is associated with lower density tethers. Although the observation of an attractive force at low grafting density (a = 0.012 nm"2) is consistent with the above discussion, this density is likely higher than that for which bridging is typically reported. This must be inferred since bridging is generally detected when a polymer simultaneously adsorbs onto two surfaces, with the amount of bound polymer typically unspecified. In those cases, bridging trends are correlated only with incubation times (Braithwaite et al, 1996; Biggs, 1995; Klein and Luckham, 1984). Klein and Luckham (1984) measured the interaction between two curved mica surfaces immersed in poly(ethylene oxide) (PEO) in an aqueous medium (good solvent) over time and observed long-range attraction at low coverage (early incubation time). As adsorption of polymer to both surfaces approached saturation with time, a purely repulsive force profile was observed. In systems involving telechelic polymers which have two adsorbing end groups (Eiser and Klein, 1999; Courvoisier et al, 1998), bridging is generally detected at low surface coverage; when only a single end of the polymer is adsorbing, bridging has not been observed even at low coverage (Tauton et al, 1990). The results of those studies confirm that end-grafted non-adsorbing chains can act as stabilizers even at low density, while adsorbing polymers promote flocculation. In this work, bridging 123 between a silicon nitride tip and a relatively high-density polymer brush was observed. This result has significant implications in the areas of colloid stabilization and protein adsorption since the bridging force opposes the entropic repulsion required for effective macromolecular exclusion. One feature that distinguishes these surfaces from those in the literature is the geometry of the grafting surface. The polymer volume fraction at the outer extremity of these spherical brushes is less than would be predicted for a flat surface of similar grafting density, somewhat reducing excluded volume effects so that the attractive bridging force can be observed. As the grafting density is increased (a > 0.022 nm2), the excluded volume becomes significant and the repulsive force dominates. It should be noted that despite the curvature effect, which is more pronounced when the ratio of HT to particle radius is large, these layers are still in the brush regime at all locations away from the grafting surface, with D7R g ranging between 0.45 and 1.39, where D' is the distance between chains calculated at the outer edge. These values are calculated based on the assumption of a smooth spherical shell. Theoretical predictions in the literature indicate that bridging is mainly due to the adsorption of tails. In the case of brushes as opposed to adsorbed polymer, this is equivalent to chain ends. The result is based on self-consistent mean field calculations of the relative amounts of trains, loops, tails and bridges of an adsorbed polymer as a function of surface separation, which have predicted a reduction in tails with increased bridging upon compression, and a roughly constant fraction of trains and loops (Fleer et al, 1993). The detection of bridging by brushes with surface coverages higher than those generally reported may give information about the location of chain ends in the grafted 124 polymer layer. If the free chain ends of the grafted polymer are buried within the random coil and are inaccessible to the penetrating species, entropic repulsion may dominate even at low grafting densities, as was noted in studies on flat surfaces (Tauton et al, 1990). Numerous theoretical models have been developed to predict the distribution of chain-ends in planer grafted polymer layers. In the model of Alexander (1977) and de Gennes (1976), a step-like concentration profile is assumed where all chain ends are found on the outer edge of the brush. More sophisticated approaches, however, predict a roughly parabolic concentration profile with chain ends distributed throughout the layer (Wijmans et al, 1992; Cosgrove et al, 1987; Milner et al, 1988). The total polymer concentration profile, as well as the distribution of chain ends, are functions of solvent quality and polydispersity. An extension of these models to brushes on curved surfaces predicts a more dilute concentration profile, and a so-called "dead zone", or absence of end segments in the region of the grafting surface (Wijmans and Zhulina, 1993; Dan and Tirell, 1992). The spherical brushes examined here having a ratio of R/(R+HT) between 0.92 and 0.97, where R is the radius of curvature of the latex particle, likely have a high fraction of accessible chain ends located away from the grafting surface, which favors the formation of bridges. The profiles in Fig. 3.8 are the average of force curves taken at over 75 different locations on a sample. In examining the individual data, however, bridging was detected even on the high a samples, at a low sampling frequency (~ 3-14 %). The individual profiles in which attraction was observed at various a are presented in Fig. 3.10. The frequency at which these bridging events was observed is shown in Fig. 3.11. Due to the 125 superposition of the curves at long-range before and after the electrostatic correction, the data for the remainder of this report is left uncorrected, as the results presented are not significantly affected. The anomalous bridging at high a could in principle be the result of lateral inhomogeneities in the grafting (i.e., patches of low a), where a decrease in local excluded volume would allow for attractive bridging to be observed. This interpretation seems unlikely, however, given that a random distribution of initiator (HEA-C1) over the surface has been calculated (see Section 2.2.7) (Jayachandran et al, 2002). ••••• o = 0.17 nm'2 a = 0.081 nm'2 a = 0.047 nm'2 - Y - a = 0.038 nm'2 CT = 0.031 nm'2 a = 0.030 nm'2 •••>••• CT = 0.022 nm'2 a = 0.017nm"2 a = 0.012 nm'2 Fit • I 1 1 ' 1 1 1 1 1 • 1 1 1 — 0 20 40 60 80 100 120 140 Separation (nm) Figure 3.10. Long-range attraction in P D M A brushes at various grafting densities. Curves represent single force measurements where the infrequent occurrence of bridging was observed. Curves are fit to an increasing exponential. 126 0.14 0.12 f 0.10 ™ 0.08 o I 0.06-| £ 0.04-j 0.02 0.00 1 I 1 1 w $ i vs. I 2 3 4 5 6 7 8 Distance beween Grafting Points (nm) Figure 3.11. Frequency of bridging events (N ~ 75 measurements) observed in P D M A brushes of varying grafting density. An alternative explanation is that the tip occasionally samples long chains that extend well beyond the average equilibrium thickness into a region where the polymer fraction is low. It is known from G P C / M A L L S that the sample contains a fraction of chains longer than the number average, due to the slight polydispersity (PDI = 1.35) that would be present in all samples. Since the long-range attractive regions for all values of a may be fit to a single curve, the latter interpretation seems more plausible. This reasoning is supported by that of Butt et al., (1999) who proposed that the A F M tip preferentially selects above average length chains. The argument was used to account for the measured polymer contour length that was longer than would be expected from the mean molecular weight of the chains in that study. In Chapter 4, the data obtained by stretching the P D M A chains away from the grafting surface following compression is presented and supports the above conclusion. The length of the stretched bridged chain, based on the separation corresponding to final 127 rupture from the tip, was always larger than the calculated average contour length of 77 nm, which was estimated from the number average degree of polymerization (N=309 based on M n ) and the projected tetrahedral C-C bond length of 0.125 nm. (Two bonds per monomer gives a size of 0.25 nm for repeating units). Final rupture for these anomalous profiles also occurred at separations greater than the average rupture separation measured when bridging was not detected upon compression. This suggests that the long-range attraction observed on compression is the result of bridging of above average length chains. There has been theoretical and experimental research suggesting bridging decays roughly exponentially with distance (Ji et al, 1990; Israelachvili et al, 1984), the dependence being correlated with the exponentially decaying tail of the segment-density distribution near an adsorbing wall. While the volume fraction profde of end-grafted polymer away from a surface differs from that of adsorbed polymer, the data in Fig. 3.10 fits an exponential decay. The decay length was found to be 22 ± 6 nm, which is significantly larger than the value of R g (6.4 nm). 3.3.2.2. Strongly Adsorbing Chains Effect of Monomer Nature The effect of varying the nature of the monomer on the force profiles was investigated by probing polymer brushes prepared with PNIPAM. Experiments were performed in a 10 mM NaCI solution, pH adjusted to 7.0 with dilute sodium bicarbonate solution. Since the structure of PNIPAM is known to be sensitive to salt concentration (Park and Hoffman, 1993), force measurements as a function of ionic strength were performed to confirm that in 10 mM NaCI the polymer was in an extended conformation. These are 128 presented later in Section 3.3.2.4. Samples were allowed to equilibrate for 15 minutes before performing experiments. The force profiles of P D M A and PNIPAM brushes having the same grafting density a = 0.038 nm"2, similar M n (30 600 and 48 000) and D/R g of 0.80 and 0.66 respectively, are compared in Fig. 3.12. The electrostatic contributions have been subtracted. 0.2 0.1 0.0 -0.1 -0.2 -0.3 • PDMA A PNIPAM - i 1 1 1 c 1 1 1 — i 1 1 1 1 1 0 20 40 60 80 100 120 140 Separation (nm) Figure 3.12. Effect of monomer type on compression of brushes. Curves show typical single force profdes. PDMA: M n ~ 30 600, D = 5.1 nm; PNIPAM: M n 48 000, D = 5.2 nm. Measurements are inlO mM NaCI, pH 7. At this grafting density, the P D M A brush is repulsive at all separations whereas the PNIPAM brush exhibits a long range attractive force which is followed by repulsion only at very small separations (~ 5 nm). Based on the measured hydrodynamic thickness of the P D M A (30 nm) and PNIPAM (100 nm) samples, it is inferred that both brushes are in an extended structure due to excluded volume effects. The ability of PNIPAM to bridge the A F M tip at this a may reflect differences in the adsorption of the polymers to silicon nitride, or differences in their excluded volume at a particular a. The results imply that, 129 depending on the monomer, significantly different grafting densities can be required to achieve the same entropic repulsion of brushes in good solvent. X-ray Photoelectron Spectroscopy (XPS) XPS is used to determine the chemical composition of a surface by measuring the kinetic energy of electrons emitted from a sample upon irradiation with X-ray photons. The technique is highly sensitive to the first few atomic layers of a material due to the short path length of the photoelectrons that are excited from the solid. To investigate the relative amounts of adsorption of PNIPAM, P D M A , and poly(methoxyethyl acrylamide) (PMEA) to silicon nitride, silicon nitride substrates were placed in polymer solutions (2% wt/wt) and left overnight. The surfaces were rinsed thoroughly with Mil l i -Q water to remove any free non-adsorbed polymer. The M n of the P D M A and PNIPAM samples were 50 000 and 187 000 respectively. The M n of the P M E A sample was undetermined. XPS analysis was performed on a clean silicon nitride sample as well as on the polymer coated samples. Because the spot size ( 2 x 4 mm2) was smaller than the silicon nitride sample, a gold substrate was placed beneath the sample. Survey scans of the untreated and treated silicon nitride samples in Fig. 3.13a show a C Is peak as well as Si 2s and Si 2p peaks. The C Is peak on the pristine silicon nitride sample is due to the presence of airborne carbon. The Si 2s and Si 2p peaks in the polymer treated samples suggests that at most a thin, i f any, polymer film was present. As a result, the C Is peaks in the polymer treated samples could not be attributed solely to adsorbed polymer, but may result from a combination of airborne and polymer containing carbon. The absolute amounts of adsorbed material could therefore not be determined quantitatively. 130 Survey scan 015 P M E A SPP I I L_ I l_ I I L : L_ 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 binding energy [eV] Figure 13a. X P S survey scans of silicon nitride before (lower) and after (upper) adsorption of P M E A . 131 Binding Energy [eV] Binding Energy [eV] Figure 13b. High Resolution C Is XPS spectra of S i 3 N 4 , P D M A , P M E A , and PNIPAM samples. 132 The high-resolution C Is spectra of the untreated and polymer treated samples are presented in Fig. 3.13b. The intensity of the peak varied as PNIPAM > P D M A ~ P M E A > silicon nitride (pristine), suggesting that the surface exposed to the PNIPAM sample contained the greatest amount of carbon. Since polymer adsorption was allowed to proceed until saturation, the results suggest that the adsorption of PNIPAM to silicon nitride may be greater than that of P D M A and PMEA. This result should not be overemphasized, however, since the higher amount of adsorbed PNIPAM may be the result of the higher molecular weight of the polymer (Fleer et al, 1993). Effect of Molecular Weight The brush properties of the grafted copolymer layers having the first block of P M E A M n ~ 32 500, PDI = 1.24 and a = 0.054 nm 2, and the second block of PNIPAM of variable M n are listed in Table 3.3 (Kizhakkedathu et al, 2004b). The force profiles of the homopolymer P M E A brush and the PMEA-6-PNIPAM copolymer brushes are presented in Fig. 3.14. The inaccuracy of the spring constant quoted by the manufacturer does not allow for direct comparison of results obtained using different tips, therefore a single tip was used to probe the P M E A , PNIPAM, and copolymer samples. The P M E A homopolymer and the copolymer with the shortest PNIPAM block are repulsive at all separations and are indistinguishable. As the PNIPAM block length is increased, the force profiles exhibit a long-range attraction, where the onset of attraction, L A , increases with PNIPAM block length (Table 3.3). The distinctly different profiles obtained before and after addition of the PNIPAM block make the preferential adsorption of PNIPAM to silicon nitride an easy way of confirming the presence of the second block. 133 -0.08 H -u. IU-I— i— i—,—|—i—|—i—|—,—|—,—|—,—|—,—|—,—|—,—| 0 20 40 60 80 100 120 140 160 180 200 Separation (nm) Figure 3.14. Effect of PNIPAM block length on compression of PMEA-6-PNIPAM copolymer brush. Curves show typical single force profiles. P M E A : M n ~ 32 500, PDI = 1.12, <j = 0.054 nm 2. Measurements performed in 10 mM NaCI, pH 7. Although the presence of the shortest PNIPAM block could not be detected under these conditions, a long-range attractive force was detected for even the shortest block length when the silicon nitride tip was replaced with a 10 jum polystyrene latex particle probe (Fig. 3.15) (Kizhakkedathu et ai, 2004b). The larger contact area increased the overall measured force and enabled detection of the weaker bridging interaction of the shortest PNIPAM block. The separations at which the attractive interaction with the A F M probe is first detected, L A , are similar to the independently measured hydrodynamic thickness values and are listed in Table 3.3. As discussed below in Section 3.3.2.3, however, the attractive interactions measured on the PNIPAM samples are rate dependent and L A values do not represent equilibrium measurements. 134 -1.2 / -HK--PMEA-b-PNIPAM(l) -•— PMEA-6-PNIPAM (2) i—'—i—'—I—'—I—'—I—'—i—'—I—'—I—i—I—'—I—•—i—>—i 0 10 20 30 40 SO 60 70 80 90 100 110 Separation (nm) Figure 3.15. Force profiles obtained by the compression of (o) P M E A ( M n = 32 500; PDI = 1.24; a = 0.045 nm"2), ( A ) PNIPAM (M„ = 47 700; PDI = 1.33; a = 0.036 nm"2), (*) PMEA-6-PNIPAM (1) ( M n P M E A = 32 500; M n ! p N i P A M = 9 700; PDI = 1.24; a = 0.045 nm" 2) and (•) PMEA-6-PNIPAM (2) M n , P M E A = 32 500; M n PNIPAM = 42 500; PDI = 1.24; a = 0.045 nm"2) brushes by A F M latex tip. Table 3.3. Properties of PMEA-6-PNIPAM Copolymer Brushes" M n P N I P A M HT(nm) L A " (nm) L A C (nm) 9 700 40 - 41 42 500 72 105 75 93 500 153 142 -a M n , P M E A = 32 500, ex = 0.045 nm"2, PDI = 1.24. *Onset of attraction measured with silicon nitride tip. cOnset of attraction measured with latex tip. The highest M n sample was not measured with the latex tip. 135 3.3.2.3 Equilibrium Considerations The decompression profiles of brushes that have exhibited a long-range attractive force on approach show considerable hysteresis from the compression profiles. In Fig. 3.16a, the results for the P M E A brush obtained in both advancing and receding directions are presented. The absence of hysteresis indicates that at the rate of a compression/decompression cycle applied (500 nm/s), the compressed chains have returned to their equilibrium position at each separation. The measurements were repeated at various rates (100-3000 nm/s) and the purely repulsive force profiles were found to be independent of scan rate. In contrast, the decompression force of the PNIPAM brush in Fig. 3.16b shows significant hysteresis and is much lower than the compression force at any given separation. Slow relaxation of chains relative to experimental decompression rates has been found to be characteristic of bridged polymers (Luckham and Klein, 1987). This gives rise to the hysteresis observed at small separations, in the region that corresponds to the beginning of decompression. For adsorbed polymers, this effect has been attributed to the temporarily higher fraction of polymer on the surface after compression, which reduces the mean concentration of polymer within the gap, resulting in a lower force (Luckham and Klein, 1985). In this case, where the chains are densely grafted onto the polystyrene surface and adsorb only onto the A F M tip, the monomers are slow to desorb from the tip upon decompression and the chain elasticity reduces the force as the chains are stretched. The rate used in this experiment, corresponding to 0.001 s between measured points, was typically faster than the rates used in the referenced studies, which 136 found that relaxation of the adsorbed chains to their equilibrium configurations could take on the order of many minutes or even hours (Luckham and Klein, 1985). • i — . — i — , — i — . — i — . — i — , — , — , — i i—•—i—'—i—•—i—1—i—1—i—'—i—'—i—'—i—i—i 0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 Separation (nm) Separation (nm) Figure 3.16. Compression (closed symbol) and decompression (open symbol) of brushes under conditions of equilibrium a) P M E A : M n = 32 500, a = 0.054 nm 2 and non-equilibium b) PNIPAM: (M„ = 48 000, a = 0.037 nm 2. Measurements performed in 10 m M NaCI, pH 7. Curves show typical single force profiles. That an attractive bridging force could be measured on approach, given the high loading rate that was used here, differs from earlier results. In a study where PEO had been adsorbed onto a glass surface, the lack of a detectable bridging force on compression was attributed to the high rate of approach (25 nm/s, or 0.02 s between sample points) that did not allow sufficient time for bridges to form (Braithwaite et al., 1996). While this rate was much higher than in other experiments where bridging was detectable (10-60 s between sample points) (Luckham and Klein, 1985), it is still considerably lower than that used here. Multiple compression profiles of a PNIPAM brush obtained at a given location on the sample at a rate of 1.5 jum/s were reproducible, as shown by the superposition of curves 137 in Fig. 3.17a. Although the relaxation times for bridged chains to return to their equilibrium structure have been shown to be long relative to the timescale of the A F M experiment, the bridged chains adhere to the tip and stretch well beyond the equilibrium thickness during the decompression cycle. The time required for a stretched chain to return to equilibrium has been calculated to be on the order of milliseconds, which is faster than the timescale of the experiment (Wong et al., 1997; Sheth et al., 1997). Unlike the repulsive steric forces, the non-equilibrium bridging interactions depend on the rate of compression, as demonstrated in Fig. 3.17b. Compression of the PNIPAM brush by the A F M tip in the same location as that in Fig. 3.17a showed a decrease in the magnitude of the attractive force with increasing scan rate. The results did not depend on the order in which the scans were performed. The pronounced attractive bridging force, which decreased with increasing scan rate, returned when the scan rated was reduced. In addition to the hysteresis apparent at small separations characteristic of the slow relaxation of bridged chains, the shape of the decompression curve over the entire separation range is quite different from one in which single chain elasticity is observed (Goodman, et al, 2004b; Yamamoto et al, 2000c; Butt, et al, 1999). The roughly continuous decrease of the adhesion force over a large separation, larger than the contour length of the brush, reflects the polydispersity of the brush and appears to result from the sequential detachment of chains of different lengths from the tip. The steps apparent at large separations represent the inhomogeneities in the chain lengths, particularly in the high molecular weight region where the fraction of chains of a particular length is small. The interpretation of decompression curves such as the one presented in Fig. 3.16b is described in Chapter 4. 138 0.08-0 .06-0 .04-0 .02-0 .00-Z -0 .02-g -0 .04-£ -0 .06--0 .08--0 .10--0 .12--0 .14-(a) 0 20 40 60 — I — ' — I — ' — i — i — i — i — i — ' — i — ' — i — i 80 100 120 140 160 180 200 Separation (nm) -0-14 I i 0 20 40 60 80 100 120 140 160 180 200 Separation (nm) Figure 3.17. a) Reproducible compression profdes of a PNIPAM brush obtained sequentially at a single sample location at a rate of 1.5 jum/s. The brush properties were M n = 94 900, PDI = 1.35, and a = 0.067 nm"2. b) Effect of scan rate on compression profde of the PNIPAM brush. Curves show typical single profdes. Measurements were performed at the same sample location as in (a). Solid lines are provided to guide the eye. 139 3.3.2.4 Environmentally Responsive Polymer Poly(N-isopropylacrylamide) in aqueous solution undergoes a phase transition at its lower critical solution temperature (LCST) of ~ 32 °C (Park and Hoffman, 1993). Below the LCST, the polymer is soluble in water and adopts a random coil structure. Above the LCST, water is a poor solvent and the polymer forms a collapsed, globular structure. The coil-to-globule transition is related to the destruction of hydrogen bonds that stabilize the hydrated coil structure. The conformational change can therefore also be induced by the addition of salts as well as any hydrogen bond breaking agent (Park and Hoffman, 1993). For grafted polymer surfaces prepared with PNIPAM, the ability of the layer to exclude macromolecules can be tuned by adjusting the external stimuli (Kidoaki et al, 2001b). The structural change of PNIPAM layers has been investigated by hydrodynamic thickness in the Brooks laboratory (Kizhakkedathu et al, 2004c). Here, the environmental response of well-characterized PNIPAM brushes is examined by direct compression by an A F M tip. Effect of Temperature A l l measurements on PNIPAM brushes were performed at pH 7 adjusted with dilute sodium bicarbonate. The effect of temperature on the compression profile of a PNIPAM brush (Mn = 48 000, PDI = 1.35 and a = 0.037 nm - 2) is presented in Fig. 3.18. The measurements were performed in 10 mM NaCI with a silicon nitride A F M tip (k ~ 0.06 N/m) at a rate of 1.4 pmls. A heater element equipped with temperature controller and readout (Digital Instruments, CA) was mounted under the sample and the system was allowed to equilibrate for 15 minutes. The temperature corresponds to that of the heater element, which is assumed to be in equilibrium with the fluid. The temperature of the 140 fluid was not measured directly. Force measurements were obtained at successively increasing temperatures between 26 and 32 °C. The samples were fastened to the sample puck holder using an epoxy adhesive (3M, 2216 Scotchweld) that was resistant to temperature change in the region measured. As discussed above, the PNIPAM brush exhibits a long-range attractive force profile at room temperature due to bridging between the grafting surface and the A F M tip. In Fig. 3.18, an attractive interaction is evident at all temperatures with the onset of attraction decreasing with increasing temperature. These results may imply a gradually collapsing structure over the measured temperature range. 0.20 0.15 0.10 -S 0.05 <D <J s if 0.00 -0.05 J -0.10 9* o 26 C x 28 °C A 30 °C o 32 °C — i — 20 40 ~6o" 80 Separation (nm) 100 Figure 3.18. Effect of temperature on compression profde of a PNIPAM brush (D* = 650 nm, M n = 48 000, PDI = 1.35, a = 0.037 nm"2). Measurements were performed in 10 m M NaCI with a silicon nitride tip. Since the attractive interactions are non-equilibrium measurements and have been shown above to be highly variable over the surface, the profde of a PNIPAM brush that 141 exhibited a repulsive force profile at room temperature was investigated. The effect of temperature on the compression profiles of a PNIPAM brush (Mn = 166 000, PDI = 1.53 prepared on a 9.6 /um shell latex particle with a silicon nitride tip (k ~ 0.58 N/m, rate = 1.2 //m/s) is demonstrated in Fig. 3.19. Due to the large particle radius, curvature effects are minimal and the repulsive steric force exerted by this brush is significant. The repulsive forces were very large and the brush could not be compressed to the point of constant compliance upon application of maximum compressive loads using a cantilever of this stiffness. As a result, the zero separation does not correspond to the actual separation between the tip and grafting surface and the layer thickness cannot be evaluated from these profiles. Following a similar approach to that of Hartley et al. (2002), the zero separation was taken as the point corresponding to the maximum deflection of the tip and the abscissa is presented in terms of relative separation. Assigning zero separation to an arbitrary but constant force value enables the force profiles obtained at different temperatures to be compared. The profiles in Fig. 3.19 suggest that the structure of the grafted layer begins to collapse with increasing temperature at around 32 °C, corresponding to the LCST of PNIPAM. The phase transition appears gradually over the range of 30 to 34 °C, however this may be due to the relatively large temperature interval used in that region (°2 C). Theoretical predictions (Zhulina et al., 1991) and experimental evidence (Balamurugan et al., 2003) suggest that the structural collapse with decreasing solvent quality occurs over a broad temperature range for grafted layers, as opposed to the sharp phase transition observed for an isolated chain. The gradual transition has been attributed to interchain interactions in the brushes, which reduce solvent-monomer interaction without 142 inducing chain contraction (Zhulina et al., 1991). The effect is expected to be more pronounced with increasing grafting density and decreasing dimensionality. For curved surfaces, the density of chains and hence interchain interaction decreases with increasing distance from the grafting surface according to a power law. The prediction that the collapse of spherical and cylindrical PNIPAM brushes follows a second order phase transition (Zhulina et al., 1991) is supported by experimental evidence (Habitcht et al., 1999; Auroy and Auvary, 1992). A true thermodynamic phase transition is not predicted for planar brushes. i—.—,—,—,—.—,—,—i—,—,—,—i—,—,—,—, 0 100 200 300 400 Relative Separation (nm) Figure 3.19. Effect of temperature on compression profile of PNIPAM brush (D* = 10 jum) with silicon nitride tip in 10 m M NaCI. Note: Zero Separation corresponds to position at 4 nN. Hydrodynamic thickness measurements performed in the Brooks laboratory (Kizhakkedathu et al., 2004c) on a PNIPAM brush of M n = 796 000, PDI = 1.26 and a = 0.043 nm" and D = 509 nm also indicate a gradual change in particle size over a temperature range of 22 to 36 °C. The smooth transition was attributed to the high-density of the brushes, suggesting that interchain interactions might play a role in the collapse of the chains. Given that the particle diameter of the latex used in Fig. 3.19 is 143 much larger than the brush thickness (i.e. small curvature effect), the gradual collapse over a range of temperatures is consistent with the predicted behavior. It is perhaps surprising that the transition did not occur over a broader temperature range. Effect of Salt Concentration The effect of increasing Na2S04 concentration (pH = 7) from 0 to 400 mM on the force profile of a PNIPAM brush ( M n = 48 000) is demonstrated in Fig. 3.20. The onset of attraction decreases with increasing salt concentration and reaches a minimum at ~ 200 mM. This is consistent with hydrodynamic thickness measurements performed in this laboratory of a PNIPAM brush (Kizhakkedathu et al, 2004c), indicating a structural collapse at 200 mM Na2SO"4. Those results also indicated a gradual collapse occurring over a range of concentrations. The effect of Na2S04 concentration on the structure of a strongly repulsive PNIPAM brush (Mn = 166 000, PDI = 1.53, D* = 9.6 fjm) is demonstrated in Fig. 3.21. The onset of repulsion decreases with increasing salt concentration as the structure of the polymer layer becomes more collapsed. These force profiles also suggest a gradual rather than sharp phase transition. -0.4-1 . , . , . , , , , r -0 20 40 60 80 100 Separation (nm) Figure 3.20. Compression profile of PNIPAM brush (Mn 48 000) by S i 3 N 4 Tip: Effect of [Na 2S0 4] 144 o- ^'^^WSX^ 0 50 100 150 200 250 300 Relative Separation (nm) Figure 3.21. Compression profile of PNIPAM brush (D* = 9.6 jum) with silicon nitride tip in N a 2 S 0 4 . Note: Zero Separation corresponds to position at 10 nN. The effect of NaCI concentration on the force profiles of the same PNIPAM brush is shown in Fig. 3.22. The relatively consistent profiles between 0 and 150 mM NaCI suggest that a higher salt concentration is required to induce a structural change than in Na2S04 . That is consistent with the HT measurements performed in this laboratory showing a transition at ~ 1 M NaCI (Kizhakkedathu et al, 2004c). On the sample used to obtain Fig. 3.22, however, the grafted layer is in a more collapsed structure at 200 m M NaCI. It should be noted that the temperature/salt concentration at which a coil-to-globule transition is induced is expected to vary with grafting density and particle size as a result of different degrees of interchain interactions (Zhulina et al, 1991). The large particle diameter (D* = 9.6 /um) of these brushes allows for higher interchain interaction than the brushes investigated by Kizhakkedathu et al (2004c). The initial collapse of this brush here at ~ 200 mM NaCI is consistent with experimental evidence and theoretical 145 predictions that the transition occurs over a broader range with increased interchain interaction. Unfortunately, force profiles at concentrations greater than 200 mM NaCI were not obtained due to experimental complications. There was insufficient sample remaining to repeat the experiment. 1 [NaCI] 8-|i_ • 1 rnM .* o 100 mM % * 150 mM 6 _ A ^ A 200 mM i > 1 • 1 1 1 ' 1 1 1 1 1 0 50 100 150 200 250 300 Relative Separation (nm) Figure 3.22. Compression profile of PNIPAM brush (D* = 9.6 jum) with silicon nitride tip in NaCI. Note: Zero Separation corresponds to position at 9 nN. 3.4 Summary The effect of grafting density and monomer type on the force exerted by polymer brushes in a good solvent on an A F M tip has been investigated. A long-range attractive bridging force can be observed at a sufficiently low a, in contrast to the monotonically increasing repulsive force seen in the higher a brushes. The density at which the bridging force could be observed was considerably larger for the PNIPAM brushes than for the P D M A or P M E A brushes. The response of PNIPAM brushes to varying environmental stimuli was also examined by A F M and the results compared with those obtained by hydrodynamic methods. 146 4. Estimation of Molecular Weight and Polydispersity of Polymer Brushes from A F M Decompression Profiles 4.1 Introduction The ability to characterize polymer brushes prepared by the "grafting from" method (Zhao and Brittain, 2000) can be a challenge, particularly i f the amount of grafted material is below that which is required for conventional methods of molecular weight determination such as multi-angle light scattering or gel permeation chromatography. This is often the case when the grafting is performed on flat surfaces where the surface area available for grafting is low. When prepared on small spherical particles, which have high surface area, the polymer must still be released from the surface for analysis. This may require chemically cleaving the polymer at the point of grafting while ensuring that any potential labile linkage along the chain remains intact and is not always feasible. Advances in single-molecule atomic force microscopy over the last few years have led to the development of a technique in which the M n and PDI derived from adhesion profiles of end-grafted polymers have been accurately determined (Al-Maawali et al, 2001; Yamamoto et al, 2000c). The measurement involves stretching the polymer, which is adsorbed on the A F M tip at the free chain end, away from the grafting surface, and estimating the contour length L c j of the chain from the separation at which the bond ruptures. The molecular weight Mj of an individual chain is calculated using L c j , and the size and molar mass of the monomer. Collection of a large number of force curves is 147 required to obtain an accurate statistical distribution of the contour lengths so that the average values of M n and PDI can be determined. The stretching of individual polymer tethers (Haupt et al, 2002; Haupt et al, 1999; Bemis et al, 1999; Ortiz and Hadziioannou, 1999; Chatellier et al, 1998) on surfaces of low grafting density a has received more attention than that of chains within a dense brush (Yamamoto et al, 2000c), presumably because of the complexity of analyzing ruptures from multiple chains. When the force curve can be attributed to the extension of a single chain, as is the case with low-density tethers, multiple ruptures represent the detachment of segments from one chain, with the contour length related only to the separation at final rupture. The M n and polydispersity of poly(dimethylsiloxane) tethers on a flat silicon substrate was recently estimated from single-chain force profiles in this way (Al-Maawali et al, 2001). Yamamoto et al. (2000c) were the first to investigate the elastic properties of a grafted chain in a dense polymer brush. They circumvented the difficulty in interpreting a force profile consisting of multiple contacts with multiple chains by studying a copolymer brush that consisted of a long non-adsorbing poly(methyl methacrylate) (PMMA) block and a short adsorbing poly(4-vinylpyridine) (P4VP) block on the free end. Since only contacts from the short P4VP at the free end contributed to the extension profile, the rupture separations could be successfully used to calculate the M n and PDI. In this chapter, the method described above for estimation of molecular weight and polydispersity is evaluated as a function of grafting density for a non-adsorbing polymer brush in good solvent (Goodman, et al, 2004b). The M n and PDI of a series of P D M A brushes of varying a in good solvent were determined by the A F M technique and 148 compared with the values obtained by GPC. Here, there is no adsorbing end block to ensure that rupture separation corresponds to the length of the fully extended chain. It is indeed possible for the force profile to contain contributions from both multiple contact formations along a single chain, as well as contacts from multiple chains. The probability of forming contacts primarily with chain ends, however, is high when the brushes are forced into an extended structure as a result of excluded volume effects. For most of the grafting densities examined, this effect allowed accurate determination of M n from the average contour lengths, with poor results obtained only when a was sufficiently low and a mushroom structure was adopted. A novel technique was also developed to estimate the M„ and PDI of a strongly adsorbing brush (Goodman, et al., 2004c). The shape of the decompression profile of a grafted PNIPAM layer was closely related to the cumulative weight fraction of chains of each length determined by GPC. The separation at maximum attractive force, corresponding to the maximum fraction of adsorbed chains, approximated the average contour length. The weight fraction as a function of molecular weight was obtained from the derivative of the force profile and fit a log-normal distribution, enabling the PDI to be estimated. 4.2 Experimental A F M Measurements Cantilevers were V-shaped silicon nitride with tip radius of 5-40 nm and spring constant of 0.06 N/m as quoted by the manufacturer (DI). The rate of tip-sample approach was typically 500 nm/s for the P D M A samples and 1.5 um/s for the PNIPAM 149 samples. Experiments were performed in 10 mM NaCI solution and analyzed according to the method described in Chapters 2 and 3. The maximum force applied to the sample, known as the trigger force, was set high enough that the region of constant compliance was reached on all samples. Because a greater force is required to compress a brush with higher grafting density as a result of excluded volume effects, the trigger force generally increased with increasing CT. The trigger value was chosen so that the length of constant compliance was roughly constant for all samples, and therefore the time of contact with the tip following full compression remained constant as well. For a = 0.17 nm"2 and 0.032 nm"2, the lengths of constant compliance were 15 ± 6 nm and 20 ± 4 nm respectively. Using a scan rate of 500 nm/s, the estimated time of contact after full compression was between 0.03 and 0.04 seconds. The inaccuracy of the spring constant quoted by the manufacturer does not allow for an accurate estimate of the mean rupture force of a given sample or for direct comparison of the forces of different samples obtained using different tips. The uncertainties associated with the rupture forces in Table 4.1 represent the standard deviation of the forces measured at various locations on a sample and are not a measure of the total error in the force measurement. As demonstrated by the difference between measured and estimated spring constants (Senden and Ducker, 1994), the error in force can be quite high (as large as 100%). Most of the results presented in this work, however, focus on the rupture separations, which are not affected by any variation in spring constant. 150 4.3 Non-Adsorbing Polymers: PDMA 4.3.1 Results and Discussion The decompression profile of a P D M A brush ( M ^ G P C = 30 600, a = 0.037 nm"2) presented in Fig. 4.1 is characteristic of an individual polymer chain physisorbed to the tip (Al-Maawali et al, 2001; Yamamoto et al, 2000c; Ortiz and Hadziioannou, 1999; Haupt et al, 1999; Bemis et al, 1999; Kellermayer et al, 1997). The subscript is used to distinguish M ^ G P C from that measured by the A F M rupture technique, MN,R. The attractive force produced by stretching the tethered chain increases monotonically with moderate tension. At sufficiently high extension, the elastic restoring force exceeds the adhesive force between the polymer and the tip and the chain breaks free from the tip at rupture separation L R . The contour length L C i of the chain segment between the point of grafting and the point of attachment to the tip is related to L R according to: where R , the extension ratio, is a measure of the extent to which the chain is stretched before dissociating from the tip. The extension ratio is typically determined by fitting the force curve to a statistical mechanical ideal chain model, such as the freely-jointed chain (FJC) (Wang et al, 2002; Zhang et al, 2000a; Oesterhelt, 1999) or the worm-like chain (WLC) (Al-Maawali et al, 2001; Yamamoto et al, 2000c; Kellermayer et al, 1997) models. The force profile in Fig. 4.1 fits the W L C model in which the force due to stretching a single chain varies with extension L according to: 'C,l (4.1) F = -kBT 1 1 L q A(\-LILci)2 4 Lci ) (4.2) 151 where q is the persistence length, L c j is the contour length of the portion of the chain being extended, and L R / L C J J is equal to the extension ratio R . From the fitting parameters, values of q = 0.41 ± 0.04 nm and ?^ = 0.88 were obtained. The above model predicts that when L « L C ; j , the force is directly proportional to the extension and the chain behaves as a Hookian spring. The force varies nonlinearly with increased extension and eventually diverges as L C ; j is approached, due to the reduction in entropy associated with fewer possible chain configurations. Many L c j values are averaged to obtain a mean contour length L C . 0.20-, y I 0.15- j 6 0.10- i 0.05- I l 1 ' 1 I 1 ' 1 I 1 1 1 I 1 1 1 I I ' ' ' I ' 0 20 40 60 80 100 120 140 Separation (nm) Figure 4.1 Decompression profile of a P D M A brush ( M ^ G P C = 30 600, P D I ; G P C = 1 35, a = 0.037 nm' ) in 10 m M NaCI. Solid line represents fit to worm-like chain (WLC) model with persistence length q = 0.41 ± 0.04 nm and extension ratio R = 0.88. A typical force curve is presented in Fig. 4.2, showing both the compression and extension of a higher density P D M A brush (o = 0.17 nm" ). The entire range of data including the high compression region is displayed in the inset. In the main figure, the data from the inset is expanded in the region of -0.2 to 0.4 nN. There is no hysteresis 152 observed in the advancing and receding force profdes from 0 to ~ 50 nm separation, suggesting that the brush returns to its equilibrium structure at each data point following initial decompression. Some hysteresis may be observed for samples with lower grafting density, which may suggest chain splaying upon compression. Separation (nm) Figure 4.2. Typical force profile showing advancing (compression (o)) and receding (stretching (*)) directions of P D M A brush (M„ 3 0 600 , a = 0 .17 nm"2). Solid arrows depict rupture events corresponding to L R . Dotted arrow indicates onset of repulsion corresponding to equilibrium thickness L E of polymer layer. Upon further extension, chains adhering to the A F M tip are stretched, until eventually breaking free from the A F M tip at rupture separation L R . In the example, two rupture events occurred with L R (1) = 65 nm and L R (2) = 102 nm. A l l values of L R are taken as the distance from the point of grafting ( L = 0 nm) to the point of detachment from the A F M tip, irrespective of whether additional rupture events are detected at smaller separations. The rupture separation corresponds to the length of the fully stretched chain segment located between the point of grafting from the latex and the point of rupture 153 from the A F M tip. It is not known whether the two rupture events observed in Fig. 4.2 represent the detachment of a single chain at different points along its length, or two chains with different contour lengths. These different scenarios are indistinguishable here and all rupture events from the ~ 75 profiles taken per sample are included in the data set. By comparing the values of L R with the distribution of contour lengths calculated from the GPC data, the probability of measuring bond rupture at the free chain end can be assessed. The following expressions are used to calculate M n and M w from L R (Al-Maawali et al, 2001): M, = Mmon ±± (4.3) M„,„=I^ (4.4) M„,R = (4.5) i PDIR=-f± (4.6) M n , R where M m o n is the molar mass of a dimethylacrylamide monomer (99 g mof 1), / is the length of a monomer unit taken from the projected C-C bond length to be 0.25 nm, and TV is the number of chains. The subscript R denotes molecular weights calculated from the rupture separations, which are to be distinguished from M n and M w measured by GPC. The values are listed in Table 4.1. It should be noted that the contour lengths were assumed to equal the rupture separations, however the true contour length is likely somewhat larger due to the non-unity extension ratio (R = 0.88). 154 Table 4.1. Characteristics of P D M A Brushes" Time* (h) a (nm 2) D / R G C (nm) F R ^ H N ) M„,R M W , R P D I R 0 0.171 0.375 0.84 83.1 0 .14 + 0 .14 33 0 0 0 49 2 0 0 1.49 1 0 .0806 0.546 0.62 80.6 0.27 + 0.21 32 0 0 0 4 9 800 1.56 3 0 .0472 0 .714 0.44 88.3 0.33 ± 0.26 35 000 56 4 0 0 1.61 5 0 .0376 0.800 0.42 74.7 0.35 ± 0.29 2 9 600 48 300 1.63 10 0 .0304 0.89 0.39 90.9 0.32 ± 0.29 36 000 56 700 1.58 15 0 .0220 1.046 0.32 74.6 0.25 + 0.18 2 9 600 49 500 1.68 24 0.0171 1.183 0 .19 83.4 0.22 + 0 .16 33 0 0 0 47 800 1.45 48 0 .0125 1.387 - 49.1 0.50 + 0.35 19 4 0 0 36 800 1.89 96 0 .00590 2 .018 - 24.6 0 .14 + 0.13 9 800 14 700 1.50 °GPC results: M n = 3 0 600, M w = 41 3 0 0 and PDI = 1.35. "Length of time chains were hydrolyzed from grafting surface. cRatio of distance between grafting points to radius of gyration. rfRatio of equilibrium thickness L e measured by A F M to contour length L c calculated from M„,GPC , molar mass (99 g/mol) and size (0.25 nm) D M A monomer. e Average rupture separation (~75 force curves). ^ Average rupture force. The molecular weights estimated from the contour lengths for each sample of different grafting density are plotted in Fig. 4.3 against D/R g , the ratio of the distance between grafting points to radius of gyration. The M 0 J R values obtained here compare well with the M n from GPC (solid line) for D/R g between 0.375 and 1.18. There is less agreement between the two methods as the distance between chains is increased, with the A F M technique underestimating M n . Like M N JR, M w R is roughly constant for samples having a D/Rg less than 1.18, although it is consistently larger than the value determined by GPC. For larger D/R g , the M W J R also decreases. 155 60k A M p r (AFM) ^ ^ M " r ( A F M ) M n (GPC) M"W (GPC) 0.0 0.5 1.0 D/R Figure 4.3. Comparison of M n and M w determined by rupture separations from A F M and The discrepancy between M n R a n d M n at higher D/R g may be explained by comparing the distribution of contour lengths obtained from the two methods in Fig. 4.4, particularly in the region of below average length. For a = 0.171 nm"2, the highest probability of length measured by the A F M technique approximated the average contour length measured by GPC, with only a small contribution from ruptures with L R values below that of the shortest chain observed by GPC. In contrast, the number of short segments contributing to the distribution for a = 0.0125 nm" is significantly larger, suggesting that the probability of a segment detaching from the A F M tip at a point along the chain rather than at the end increases as the grafting density decreases. Indeed, this agrees with advanced brush models (Lai and Binder, 1991; Murat and Grest, 1996; Milner et al., 1988) which predict the ends to be distributed throughout the brush, in contrast to the earlier step-like volume fraction profile of Alexander (1977) and de Gennes (1980) that assumed all chain ends were located at the outer edge of the brush. An explicit expression GPC. 156 for the end density distribution away from the grafting surface for a compressed brush, given by Milner et al. (1988) predicts the end density at the outer layer of the brush to increase with a, supporting the above interpretation. 1 r 0.020 Contour Length L (nm) 0 25 50 75 100 125 150 175 200 225 250 275 300 325 Contour Length L (nm) Figure 4.4. Comparison of contour length distributions obtain by A F M and GPC for high (a = 0.171 nm"2) and low (a = 0.0125 nm"2) grafting densities. Distributions are normalized so that E / A L = 1, where / is the frequency of A F M rupture event. 157 A model for the interaction of the tip with the polymer brush at A) high and B) low grafting density is depicted in Fig. 4.5. The equilibrium brush structure of the polymer layer before contact with the tip is show in (I). The asterisk denotes the most probable initial point of contact, located at the outer edge of the layer. In the high o~ case (A), the asterisk is located at the chain end due to the highly extended equilibrium structure. Upon compression (II), the tip may form additional contacts along a single chain as well as with multiple chains. For clarity, contacts with multiple chains in the low CT representation (B) are not shown. Note that at low a, the tip may never contact the chain end, which is buried within the coil. With sufficient extension (III), the chain ruptures from the tip at a separation L R . It is emphasized that although other contacts may be formed during compression (II), the data in Fig. 4.4 suggest that the asterisk represent the most probable contact at which rupture is measured. The rupture separation measured at high and low grafting densities is related to the contour length L C by A) L R ~ L C and B) L R < L C respectively. This representation differs from a reported model where the tip was thought to slide down the length of the polymer upon extension and rupture at the chain end (Al-Maawali et al, 2001). In the referenced model, contacts could break and form to reduce the tension caused by pulling on the chain. The kinetics in that study were sufficiently slow so that on the time-scale of an A F M experiment, segment-tip contacts were able to overcome the energy barrier for detachment many times. The tension was then transmitted to the nearest monomer as the polymer slid along the tip. When the tension could no longer be reduced by sliding, the chain would stretch and eventually rupture from the tip. The separations at rupture were used as estimates of the contour length. 158 A \ I I I I J W T h B y.tf-X-X-X-X-X-XX-X-X- \ I W1 Lr I n I I I Figure 4.5. Representation of the most probable interaction of an A F M tip with polymer at A ) high and B) low grafting density. The tip approaches the grafted layer (I) with the asterisk denoting the most probable initial point of contact. Upon compression (II), the tip may form additional contacts along a single chain as well as with multiple chains. With sufficient extension (III), the chain ruptures from the tip at the contact point denoted by the asterisk, at a separation L R . 159 It should be noted that the accurate determination of M n in this study could, in part, be due to the spherical nature of the brush. Theoretical models predicting the distribution of chain ends in brush layers have shown different behaviors for chains grafted to flat versus curved surfaces (Wijmans and Zhulina, 1993), with the distribution being dependant on the radius of curvature R. A depletion layer near the grafting surface is predicted for spherical brushes, where the probability of finding chain ends in the region is extremely low. Subsequently, there is a higher probability of locating chain ends away from the grafting surface in spherical than flat brushes. Any effect due to curvature in this system however, is expected to be small, since even the brush with the largest thickness had a relatively low L e / R ratio (0.095). From the ratios of equilibrium thickness to contour length L e / L c in Table 4.1, we see that the thickness of the highest a brush at equilibrium is ~ 84% of its fully extended structure. Perhaps surprisingly, the contribution from short segments only affected the distribution for samples with a = 0.0125 nm"2 and lower. Following the trend in L e / L c , these samples would have thicknesses less than 19% of the fully extended length. The technique, enabling determination of M n over a large range of grafting densities, is therefore not limited to tightly packed brushes where the equilibrium thickness of the brush approaches the contour length. To establish whether the time the tip remained in contact with the fully compressed sample had any affect on the molecular weights measured by this technique, the experiment was repeated on sample a = 0.0125 nm"2 at two different trigger forces. Based on the length of the constant compliance regimes and the compression rate (500 nm/s), the estimated contact times for these measurements were 0.03 (trial #1) and 0.06 s (trial 160 #2). The effect of contact time on the average rupture separation Mn,AFM and M W I A F M is presented in Fig. 4.6. The results suggest that over this range of time there is no detectable effect. Similarly, to establish the effect of rate on the measured molecular weights, the experiment was performed at 500 nm/s (trial #1) and 2000 nm/s (trial #3) and the results presented in Fig. 4.6. The constant molecular weight values suggest that there is no detectable dependence in the range of rates examined. It is noted, however, that the molecular weights are significantly lower than those presented in Fig. 4.3 for sample a = 0.0125 nm" . The data in Fig. 4.6 was obtained using a tip from a different wafer than the one used to obtain the data in Fig. 4.3. Differences in the tip geometry are expected to affect the results, particularly at low grafting density where the distance between chains at the grafting point approaches the tip radius. 65k 60k 55k 50k 45k 40k 35k 30k 25k 20k. 15k> 10k. 5k. 0 M B M n (AFM) WZft IvT (AFM) Trial Conditions: 1. Rate = 500 nm/s; Contact Time = 0.03 s 2. Rate = 500 nm/s; Contact Time = 0.06 s 3. Rate = 2000 nm/s; Contact Time = 0.008 s Figure 4.6. Effect of rate and contact time on molecular weight measured using A F M rupture separations. Measurements were performed on P D M A brush (a = 0.0125 nm"2) in 10 m M NaCI using a silicon nitride A F M tip (k ~ 0.06 N/m). Data was collected at 50 locations on the sample for each set of conditions. 161 To establish the density regime in which the technique could be successfully applied, the dependence of L e on a was compared with theoretical predictions. According to Eq. 3.2, the equilibrium thickness of a moderately dense brush in good solvent is expected to vary with CT", where n = 1/3. As discussed in Section 1.3.3, the power law has been investigated by measuring the thickness of different planar brushes using neutron reflectivity and neutron scattering. While some studies found that brush heights obeyed the predicted scaling law (Auroy et al, 1991), others have reported different values of the exponent n (Richards et al, 1997; Bijsterbosch et al, 1995; Kent et al, 1992). In Fig. 3.9, the equilibrium thickness was plotted as a function of grafting density for 0.0171 < CT < 0.171. The value for the exponent obtained (n = 0.45) was higher than the predicted value. Also, the data could not be fit above and below CT < 0.0171 nm"2 to a single exponent power-law. This transition point corresponds to the same grafting density at which M n R and M n disagreed, presumably due to a reduction in accessible free chain ends. These results are similar to those of Yamamoto et al. (2000b) who measured the equilibrium thickness using A F M of planar poly(methyl methacrylate) brushes, having M n ~ 56 700, in good solvent as a function of grafting density (0.07 < CT (chains/nm" < 0.7). They obtained an exponent n ~ 0.4, which is comparable to the value obtained here despite the slightly lower M n and CT values used here. The discrepancy between the measured and predicted exponent was attributed to higher order virial interactions at high grafting densities (Lai and Halperin, 1991). These are not taken into account in Eq. 3.2 which was derived for moderate grafting densities. The value of their exponent also 162 appeared to increase with a, however this result could not be explicitly established due to an insufficient number of high a data points. The effect of curvature must again be addressed as it has been found that, like the chain end distribution, the height of a spherical brush depends on the radius of curvature R. For spherical geometry, Wijmans and Zhulina (1993) have found the brush height to scale roughly as: H « ( o N 3 R 2 ) 0 2 (4.7) This equation, however, does not describe these results, predicting a lower exponent when curvature effects are significant. Based on the scaling results obtained, the method of M N > R determination from rupture separations is expected to be applicable to a moderate to highly dense brush regime. The rupture technique was less successful at accurately predicting the PDI, giving M W J R values that were consistently overestimated. This is likely due to a bias in the A F M technique towards very long chains. Very long chains have the advantage of reaching and adsorbing to the tip even when they are not being directly compressed, resulting in an over-representation in the retraction force profile compared to their average spatial frequency. From the GPC distribution we see that a small number fraction of chains having a much higher than average molecular weight are present. According to the distribution profiles in Fig. 4.4, the relative contribution to the force profiles from very long chains (> 300 nm) is greater than from intermediate chains, when compared with the actual frequencies obtained by GPC. If the molecular weight is recalculated after having removed the two largest values of L R , which contribute only - 1 % of the total number of 163 rupture events sampled, a M„,R ~ 31 000, M W ; R ~ 41 000 and PDI, R ~ 1.31 is obtained. This PDI is much closer to that measured by GPC (PDI = 1.35). The number of chains being directly compressed by a disc of radius 15 nm can range from 4 to 120 (for 0.0059 < a < 0.171 nm"), assuming a uniform grafting density. While the probability of a chain adhering to the tip is higher for those polymers being directly compressed, nearby chains may adhere anywhere along the surface of the tip. In the study performed by Al-Maawali et al. (2001), a better correlation was found between P D I R determined using the A F M technique and GPC, and it was therefore assumed that uncertainty due to tip shape convolution is minor. The good agreement between the PDI measured by the two methods in the reference system was only found for surfaces prepared by a grafting-to reaction in which the polymer concentration was low. Poor agreement found using high polymer concentrations was attributed to a preferential adsorption and reaction of long chains. Although the a values were not provided, the surfaces prepared in the referenced system were presumably of much lower grafting density than those used here. Polydispersity also affects the distribution of chain ends, with the ends of longer chains located farther from the grafting surface (Currie et al, 1999b). This effect may also alter the distribution of contour lengths in favor of longer chains, so that the separation at rupture more closely approximates their actual contour length than does that for shorter chains. To examine the effect of solvency, force profdes of the highest grafting density brush (a = 0.17 nm"2) were obtained in various alcohols (methanol, ethanol (100%), isopropanol). The alcohols were chosen since they are poorer solvents than water for the 164 grafted P D M A and are also poor solvents for polystyrene. Compression profdes of the non-grafted polystyrene shell latex suggest that the latex behaves as a hard incompressible surface in methanol (similar to in water at high salt concentration). Differences in the data obtained in the various solvents should therefore reflect changes in the structure of the polymer brush layer with negligible contribution from the underlying latex. The M N , A F M and M W ; A F M values calculated from the rupture separations are listed in Table 4.2. The values measured in the alcohols were similar to those in water and did not display a trend upon decreasing the solvent quality for the alcohols tested. According to the above model, decreasing the solvency would have the same effect as decreasing the grafting density (i.e. a more collapsed equilibrium structure would result in a decrease in average rupture separation). To further investigate the structure of the polymer layer, the compression profiles obtained in the different solvents are presented in Fig 4.7. Each profde represents the average profile obtained at ~ 75 different locations on the sample in a given solvent. At large separations (small compression), the force profdes in all solvents are similar. Upon further compression, the brush exerts a smaller repulsive force in the alcohols than in water. In this region the profdes in the different alcohols are remarkably similar to one another but are notably different from that in water. According to the data and model, the most probable point of rupture is that where initial contact between the tip and polymer layer is formed (see Fig. 4.5). The superposition of the compression data at large separations coupled with the agreement of average rupture separations in various solvents supports the above model for tip-polymer interaction. 165 Table 4.2. Effect of Solvency on Molecular Weight Estimation of P D M A Brush* M N A F M M W I A F M Water (10 mM NaCI) 33 000 49 200 Methanol 36 800 50 300 Ethanol(100%) 40 800 59 800 Isopropanol 34 500 44 700 aBrush properties: a = 0.17nm"2, M n j G P C = 30 600, Mw = 41 300. 0-7-1 . • | ; • water o e - | " O methanol 4 ' A ethanol °' " 1 m * isopropanol Z 0.4-c <D 2 0.3-o LL 0.2-0.1 -0.0-0 10 20 30 40 50 60 70 80 Separation (nm) Figure 4.7. Effect of solvent quality on compression profiles of P D M A brush for a = 0.17 nm" . Curves are average of data obtained at 75 locations on the sample. In all samples, the forces at the point of rupture F R were measured and their distribution was examined. The values were averaged for each sample and are listed in Table 4.1. The mean forces ranged between 0.14 and 0.33 nN, and histograms showing the force distribution of two representative samples, a = 0.171 nm" and 0.022 nm" , are presented in Fig. 4.8. Due to the uncertainty in the spring constant and the use of different tips 166 throughout this work, the mean forces of the different samples are not directly compared and the large uncertainty associated with these values is noted. The data is simply presented to illustrate the distribution of forces over the surface. 0.008 -, 0.00 0.12 0.24 0.36 0.48 0.60 0.72 0.84 Force F R ( n N ) Figure 4.8. Distribution of rupture forces for P D M A brushes of two representative grafting densities. Data is normalized so that HfjAFR = 1. 4.3.2 Summary Agreement between the M n values determined by A F M and GPC confirms the validity of the rupture technique over a range of brush densities. The failure of the method to accurately predict M n at low grafting densities provides a lower limit above which the technique could be successfully applied. In addition to the practical implications of the study, a correlation could potentially be made between the distribution of chain ends in polymer and the difference between the rupture separations measured by A F M and the contour lengths measured by GPC. A power-law relationship between the layer thickness estimated by A F M and the grafting density, with an exponent of 0.45, was observed only 167 over the density regime for which the M n could accurately be measured by the rupture method. 4.4 Adsorbing Polymers: PNIPAM 4.4.1 Introduction In the previous section it was shown that even at high grafting densities, the decompression profiles of non-adsorbing polymer brushes are characteristic of single chain stretching. In contrast, a very different decompression profile is obtained when the polymer brush strongly interacts with the A F M tip during compression as is the case with PNIPAM. Discrete bond rupture events are not discerned due to overlapping data from the simultaneous stretching of multiple chains of a nearly continuous range of lengths. The force profile is characterized by a maximum attractive force, which decays to zero with increasing chain extension. Decompression profiles of polymer brushes exhibiting such features have not previously been reported in the literature. The magnitude of the force at any separation is related to the number of chains of a particular contour length adsorbed to the tip. The total number of chains being stretched decreases with increasing extension, as progressively longer chains approach their contour lengths and break free from the tip. Here, the fraction of grafted chains of a given length is determined by analyzing the decaying attractive force. This novel technique allows for estimation of M n and PDI from a single force profile, in contrast to the large number of curves required to obtain a statistical distribution of contour lengths when chains are stretched individually. 168 4.4.2 Results and Discussion The force profile obtained by stretching a PNIPAM brush ( M n G p c = 47 700 and a = 0.037 nm') away from the grafting surface using a silicon nitride tip is presented in Fig. 4.9. The attractive force increases with extension and reaches a maximum value F m at a distance L m of 90 nm. A decaying attractive force is observed upon further extension until a separation of about 300 nm. This is in contrast to the decompression profile of a P D M A brush of the same grafting density (Fig. 4.1) which exhibited an abrupt jump indicating the rupture of a single chain from the tip. While the majority of single chain force profiles presented in the literature has been measured on surfaces bearing lower density tethers (Al-Maawali et al, 2001; Kellermayer et al, 1997; Oesterhelt, 1999) or physisorbed polymers (Wang et al, 2002; Kienberger et al, 2000; Haupt et al, 1999), the constant grafting density used to obtain Figures 4.1 and 4.9 indicates that the atypical profile cannot be solely attributed to the high density of grafted chains. The dramatic difference in the profiles reflects the higher probability for PNIPAM to adsorb to the silicon nitride tip. The profile in Fig. 4.9 is likely due to the simultaneous stretching of a large number of PNIPAM chains adsorbed to the A F M tip following bridging interaction upon compression. 169 l-i 1 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 -50 0 50 100 150 200 250 300 350 Separation (nm) Figure 4 . 9 . Decompression profile of a PNIPAM brush (M n j G p c = 47 700, P D I ; G P C = 1.33, a = 0.037 nm" ) in 10 m M NaCI, pH 7. Dotted line shows non-linear least squares fit to Eq. 4.11 (see text). A similar force profile with a maximum attractive force that decayed with increased extension when stretching PNIPAM chains physisorbed onto glass with a silicon nitride A F M tip in an aqueous medium was observed by Zhang et al. (2000a) The PNIPAM had a weight average molecular weight M w of 2.4 x 106 g/mol and a PDI of 1.3. When the 7 * * polymer was adsorbed onto glass from a dilute solution (6.4 x 10" g/ml), individual chains were stretched and the force profile fit an extended FJC model. When the measurement was initially attempted on a surface to which the polymer had adsorbed from a more concentrated solution (2.5 x 10'4 g/ml), the authors could not obtain a clean force-extension trace. The example presented of such a profile had similar features to those observed here. Interestingly, single chain elongation has been performed on other polymers absorbed onto glass from higher concentrations (Zhang et al, 2000b; L i et al, 170 1999), suggesting that the probability of chains adsorbing to a silicon nitride tip during compression is higher for PNIPAM than for these other polymers studied. The maximum attractive force F m measured was -0.7 ± 0.2 nN for the PNIPAM sample having Mn,GPc = 47 700 and -1.2 ± 0.4 nN for M n,Gpc = 94 900. The individual values are listed in Appendix 5. The uncertainties represent the standard deviation for the average value and reflect the variation in maximum attractive force. Due to the error associated with the nominal spring constant which can be as large as 100% (Senden and Ducker, 1994), the absolute magnitude of the forces are not emphasized. The data is presented only to demonstrate the relative force values measured over the surface. Multiple force measurements obtained at different locations on the sample showed some variation in F m , as did repeated measurements obtained at the same location; their contributions are included in the above uncertainties. The decompression profile is likely sensitive to the number of chains adsorbed to the tip during compression, which is highly dependent on the local structure of the brush. Self-consistent mean-field calculations have predicted the fraction of bridged chains to be strongly dependent on the distribution of free chain ends (Tang and Witten, 1996; Fleer et al, 1993; Johner and Joanny, 1992). If the local brush configuration does not return to equilibrium between successive compression-extension cycles, the fraction of bridged chains will vary resulting in non-reproducible force measurements. The bridging fraction is also sensitive to variations in chain configurations over the grafting surface. The overall shape of the force profile, however, was constant and did not depend on the location of the measurement, the number of cycles, or the rate of compression. The rate dependence of bridging interactions over the range 0.60 to 12 um/s upon compression of 171 the PNIPAM brushes was demonstrated in Section 3.3.2.3. Despite the increase in the attractive bridging force observed with decreasing rate of approach, a rate dependence could not be established for the decompression profdes of the bridged chains over a range of 0.30 to 6.0 pm/s with respect to the location of the attractive minimum, the maximum separation at which interaction was detected, or the frequency of discrete rupture events. The curves were normalized by dividing by the maximum attractive force F m in each profde and plotted in Fig. 4.10. The good superposition suggests that the procedure established for determining the distribution of contour lengths from the decompression profile does not depend on the total number of chains adsorbed to the tip. i—•—i—'—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i - 5 0 0 50 100 150 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 Separation (nm) Figure 4.10. Decompression curves of PNIPAM brushes obtained at various locations on a single sample surface as well as on different samples (same material). Curves are normalized by dividing by the maximum attractive force F m in each measurement. Values are listed in Appendix 5. Material and conditions are as in Fig. 4.9. 172 The separation, L m , corresponding to the point where the attractive force is maximum, is 85 ± 12 nm for the 9 curves presented in Fig. 4.10. This is slightly lower than the average contour length of the brush of 106 nm, obtained by multiplying the number average degree of polymerization (from GPC/MALLS) with the size of a monomer unit (0.25 nm, taken from the projected C-C bond length and assigning two bonds per monomer). The attractive force does not return to the baseline until a separation of about 300 nm, a value well beyond the average contour length. The portion of the curve where L > L m can be interpreted by considering the relationship between the fraction of adsorbed chains and the pulling force. Calculations based on the Milner-Witten-Cates self-consistent mean-field model (Johner and Joanny, 1992) have found that the pulling force obeys a second order polynomial as a function of the fraction of chains in a polymer brush bridged to an adsorbing plate, N, according to -F = a(bN-N2), where a and b are constants containing the reduced adsorption energy. While compression has been shown to favor the formation of bridges, pulling reduces the fraction of bridges and eventually leads to rupture. The pulling force at a given extension should be determined by the fraction of chains adsorbed to the tip at that particular length, assuming rupture occurs at an extension roughly equal to the contour length of the chain. The separation, L m , at which the attractive force is a maximum, should therefore be close to the contour length of the highest fraction of adsorbed chains. If adsorption to the tip following compression occurs independently of chain length, L m should approximate the average contour length determined by GPC. The observation of a decaying attractive force at separations much larger than the average contour length is attributed to the rupture of chains of above average contour 173 length. This is reasonable due to the polydispersity of the sample (PDI = 1.33) which indicates that numerous chains with contour length greater than the mean are present. To establish the extent to which above average length chains contribute to the force profile, the maximum number of chains of molecular weight Mj that can access an A F M tip located at separation L from the surface was calculated. Assuming a hemispherical tip of radius R = 40 nm, the maximum number of accessible chains rjjmax was calculated from the grafting density a and number fraction of chains T( determined from G P C / M A L L S according to: = Y , ™ r " (4-8) where rt is the radius of a disc on the grafted layer defining the maximum area from which chains of contour length L C j can access the tip. It was assumed that fully extended chains located along the circumference of the disc can access the tip from a normal distance equal to L c > i , so that r2 = [{R + LCI)2 -(R + L)2] (Fig. 4.11). » • Figure 4.11 Depiction of maximum accessible distance r for chain of contour length L c and tip of radius R. 174 The number of accessible chains is presented in Fig. 4.12 for a brush of a = 0.037 nm"2 using the T, data obtained by GPC for the PNIPAM brush of M n , G p c = 47 700. The calculation is performed for a tip located at the grafting surface, (L = 0), a distance above the surface roughly equal to L c , (L = 100 nm), and a distance greater than L c (L= 200 nm). The number of accessible chains having Mj > M n is significant for all three tip positions. The calculation likely overestimates the number of accessible chains by assuming that all polymers located at a lateral distance between zero and rj from the center of the tip have equal access when chains located directly beneath the tip are more likely to adsorb. A calculation of the minimum number of accessible chains, r}itm\n, where chains of any Mj located within a disc of radius r = 40 nm were assumed accessible, predicts that a much smaller but still finite number of chains with Mj > M n had access to the tip (Fig. 4.12). Attributing the attractive force detected at large separations to the rupture of long chains from the tip is therefore within reason. 10000 100000 1000000 Molecular Weight M, (g mol"1) Figure 4.12. Maximum (left-hand ordinate) and minimum (right-hand ordinate) number of chains rj with molecular weight that have access to the A F M tip a separation L from 175 the grafting surface. The calculation is based on the number fraction of chains in a PNIPAM brush of Mn,GPC= 47 700 and a = 0.037 nm"2. The accessible number of chains is estimated from Eq. 4.8, see text for discussion of assumptions. The cumulative weight distribution, of chains determined from G P C / M A L L S is found to be approximately parallel to the decaying region of the decompression profde, as demonstrated by the superposition of the two curves in the double Y-axis plot in Fig. 4.13. The contour length along the x-axis is assumed to equal the separation, L, in the A F M trace, and is related to the individual molecular weights Mj determined by GPC according to: < 4 - 9 ) Mnwn I where Mmon is the molar mass of the monomer and / is the size of the monomer, 0.25 nm. The cumulative weight distribution is defined here as a function of individual molecular weight Mj according to: £(M (.) = 2/»(M ( .) (4-10) where Pj is the weight fraction of chains having molecular weight M / and i is counted down from the highest molecular weight chain. This is in contrast to the conventional representation of cumulative weight fraction, £ , where £ = 1 corresponds to the highest molecular weight chain. The two notations are related by £ = 1 - £ . The representation used here enables the fraction of chains adsorbed to the tip to be directly related to the cumulative fraction of chains present in the brush, since the smallest number of chains adsorbed on the tip occurs at high extension. The total number of chains adsorbed to the 176 tip is reduced with increasing extension as the chains become fully stretched and sequentially detach from the tip. -50 0 50 100 150 200 250 300 350 400 450 Contour Length L (nm) Figure 4.13. Decompression profde of PNIPAM brush with average contour length L c = 106 nm, M n = 47 700, PDI = 1.33 (GPC results) showing direct relationship with cumulative weight fraction of grafted chains. The decaying attractive force profde has been found to coincide with the cumulative weight fraction, as opposed to the cumulative number fraction of grafted chains, for high density brushes. This observation likely indicates a slightly biased sampling of higher molecular weight chains by the A F M tip rather than a fundamental relationship between the pulling force and the cumulative weight fraction. As demonstrated in Section 4.3, the M n measured by A F M and GPC agreed but the M w measured by A F M was overestimated. This was attributed to the ability, of very long chains to adsorb onto the tip from locations outside the direct region of compression. The relationship between the force profde and the cumulative weight distribution is purely empirical and is not supported by theoretical calculations, however it enables the 177 distribution of weight fractions to be estimated and the PDI to be determined. The weight fraction distribution, P^(LCI), is obtained from the first derivative of the cumulative distribution, or in this case, the decompression profile. Before taking the derivative, the force profile for L > L m is first fit to a monotonically increasing exponential function of separation L using a least squares procedure: F = c(\-e-k(l-d)) (4.11) where c, d, and k are numerical fitting parameters. The use of Eq. 4.11 to fit the data was based on the empirically observed good fits, as demonstrated in Fig. 4.9. By obtaining Pi (Lc t) from the derivative of the fitted curve rather than the actual force data, little weight was placed on variations between force profiles caused by discrete rupture events, such as the local maximum attractive force occurring at ~ 225 nm in Fig. 4.9 and at ~ 275 nm in Fig. 4.13. These discrete rupture events reflect the inhomogeneity in the lengths of the grafted chains attached to the tip. As can be seen from the superimposed curves in Fig. 4.10, the data in the region between below 225 nm is relatively smooth, depicting a continuous rupturing of chains from the tip over the range of contour lengths. Discrete rupture events are observed predominantly in the high separation region, between 225 and 325 nm, where the fraction of chains is low and the probability of stretching a single chain is higher. The chi squared value for these fits ranged between 0.001 and 0.003, depending on the contribution of discrete rupture events. The weight fractions, P (L , ) , were obtained by taking the derivative of the fitted '. AFM c'' ° force curve for separations L > L m . Only the weight fractions of chains having L c j > Lm were obtained by this method. Weight fraction distributions calculated for the two PNIPAM samples are presented in Fig. 4.14, along with the distributions measured by 178 GPC. The individual weight fractions measured from the GPC data are such that I,P, = 1. The weight fractions calculated from the force profde are normalized so that , i,GPC b the peak value of Pi AFM is equal to that of Pt GPC . The weight fractions distributed as a function of molecular weight fit a log-normal distribution: P = P. + C ( 2 ^ s 2 ) - ' / 2 e x p [ - ( l n M - l n M ) 2 / 2 5 2 ] (4.12) where M is the peak molecular weight on the log scale, s is the standard deviation, and P0 and C are fitting constants. Values for M n , M w , and PDI can be obtained from the fit parameters according to (Teraoka, 2002): M„ = M e x p ( -5 2 / 2 ) (4.13) Mw = Mexp(s212) (4.14) PDI = exp(s2) (4.15) 0.012-, I 1 . 1 — 1 1 1—i i i i . i 10000 100000 1000000 Molecular Weight M (g mol"1) Figure 4.14. Comparison of distribution of weight fraction of PNIPAM brush measured by GPC and calculated from analysis of decompression profile (see text). Very low 179 weight fractions obtained at the low molecular weight end have been removed from the GPC distributions. Dashed and solid lines correspond to the log-normal distribution fits to the A F M data (SI and S2 respectively). Brush properties obtained by GPC are for SI: ( M n = 47 700, PDI = 1.33, CT = 0.037 nm - 2) and for S2: (M„ = 94 900, PDI = 1.35, CT = 0. 067 nm - 2). When both I n M and s were free parameters in the fit, the value obtained for M N ,AFM by Eq. 4.13 was typically lower than MN >GPC- Instead, M ^ A F M was calculated according to Eq. 4.9 by taking the separation L m as an estimate for the average contour length. By setting the value of M 0 , A F M and combining Eq. 4.12 and 4.13, the distribution could be fit with only a single parameter, s. The statistical chi-squared values were on the order of 10" 1 . The PDI,AFM was calculated from each of the fitted force curves according to Eq. 4.15. Values obtained for M n AFM and PDI AFM from individual force curves are tabulated in the Appendix 5. The average P D I , A F M was 1.3 ± 0.1 for both PNIPAM samples, which agreed well with the PDIQPC values of 1.33 and 1.35. The M N ,AFM values for the two samples were (3.8 ± 0.5) x 104 and (9.4 ± 1.4) x 104, which compare to the corresponding values obtained from G P C / M A L L S of 4.77 x 104 and 9.49 x 104. The M W : A F M values for the two samples were (4.9 ± 0.7) x 104 and (12 ± 1.2) x 104 and the respective M W ! G P C values were 6.34 x 104 and 12.8 x 104. The values for the two samples were obtained by averaging over 9 and 12 curves, respectively. The values of M ^ A F M presented are the averages of individual measurements obtained on a given sample and the uncertainties are represented by the standard deviations. In addition, we consider here the contributions to the uncertainty in M P J A F M based on a single estimate of L m . Since the separation L is calculated from the difference between 180 the change in piezo position and the change in deflection signal, the uncertainty in L depends on that of the optical lever sensitivity (± 5%). There is also an inherent error associated with defining L = 0 nm, the constant compliance region on the polymer brush surface, due to the possible presence of an incompressible polymer layer between the tip and the latex. The calculations here have assumed the thickness of this layer to be negligible based on the use of sharp tips and grafting densities, which have been associated with small offset distances (Yamamoto et al, 2000c). In order to associate an error with the definition of zero separation however, a nominal offset distance of 5 nm is used and an upper bound value for L m is calculated where zero separation is L = 0 ± 5 nm. The estimated uncertainties in the L m values in this work were between 2 and 7%, providing values for the relative uncertainties in the individual M N A F M estimates. The individual values are given in Appendix 5. A number of factors contribute to the uncertainty in the P D I , A F M value obtained from a single force profile. The ability of the exponential function in Eq. 4.11 to fit the decompression profile depends on the "jaggedness" of the force data resulting from discrete rupture events. The uncertainty in the PDI ,AFM is also affected by the quality with which the Gaussian distribution fits the weight fraction data. The chi squared values are given above as a measure of evaluating the fits of the data. It is recognized, however, that the good fits are misleading since the difference between the data and the fitted curve clearly does not represent the uncertainty in the PDI ,AFM value. The uncertainty associated with the estimation of P D I A F M is best indicated by the standard deviations obtained from multiple measurements. 181 It should be noted that the lowest molecular weight data used in the fit of Eq. 4.12 was not Mn AFM, but a data point slightly larger than Mn A FM- This is due to the uncertainty associated with relating the decompression profile with the cumulative weight distribution in this region and with the availability of data on only the right side of the log-normal distribution. Typically, the peak in the weight fraction distribution corresponds to an inflection point in the cumulative distribution, as the two curves are related by the first derivative. Because data in the low molecular weight region is not obtained by this technique, the values of P^AFM do not plateau as M approaches MN,AFM (for M > M nAFivi), but steadily increase. The P^AFM in this region were therefore not included in the fits. The data presented in Fig. 4.14 was used to obtain the fitted distributions. Although it has been demonstrated that the probability of detecting chains larger than the average contour length is significant (Fig. 4.12), there is another possible interpretation of the non-zero force at large separations. Spherical brushes that are adsorbed onto a flat substrate for analysis have a grafted layer between the particle and substrate as well as between the tip and particle. Compression of both layers could give rise to an equilibrium thickness twice as large as expected, while the stretching of both layers could result in rupture separations twice as long as the expected contour length. Based on the results in Section 4.3, however, the average contour lengths measured by A F M were found to agree with those estimated from the molecular weights obtained by G P C . It is therefore concluded that contributions from the grafted layer adjacent to the glass substrate were minimal. 182 The maximum attractive force F m measured was -0.7 ± 0.2 nN and -1.2 ± 0.4 nN for the samples having M ^ G P C = 47 700 and 94 900, respectively. Although the magnitude of the force varied between measurements, the values were always well below that required to break a typical C-C bond (-5-6 nN) (Ortiz and Hadziioannou, 1999). The quoted bond strength was calculated using the unperturbed potential well at zero loading rate, by solving for the derivative of the Morse potential V(x) at the separation x m a x where the attractive force is a maximum. The above suggests that the measurements are associated with the dissociation of a collection of chains physisorbed to the tip. Nevertheless, the quality of the tip was repeatedly checked by obtaining force curves on clean glass after exposing the tip to the PNIPAM brush. The force curves on glass did not have any distinguishing features that would suggest contamination of the tip for the results presented. It should be noted that contamination of the tip by the PNIPAM brushes occurred more frequently than when non-adsorbing polymer brushes such as P D M A were probed using the same sample preparation technique, presumably due to the larger attractive forces associated with PNIPAM. Two initial force measurements resulted in tip contamination but a more thorough rinsing procedure and more rigorously clean sample preparation allowed experiments to be successfully repeated without contamination. While reasonable estimates of the M n and the PDI of the two samples were obtained by the method described here, it involves a number of approximations that contribute to uncertainties in the results. Equating the separation at maximum force with the average contour length gave M ^ A F M values that were underestimated as compared with GPC values. The inability of the method to account for chains with molecular weight lower 183 than the average allows for only one side of the distribution of weight fractions to be fit. The fit parameters are therefore based on a symmetrical distribution of chain lengths on a log scale. Given that the weight fractions obtained by GPC are slightly positively skewed even after the logarithmic transformation (Fig. 4.14), this assumption is inaccurate. The direct relationship between the decompression profile and the cumulative weight fraction, however, suggests that some of these sources of error cancel each other out. While high molecular weight chains that have a low probability of occurrence may not always be probed due to the small contact area between the tip and sample, the same chains may access the tip from locations beyond the direct region of compression and be over-represented. 4.4.3 Summary The stretching behavior of a dense PNIPAM brush that strongly adsorbs to a silicon nitride A F M tip has been investigated. The shape of the decompression profile was closely related to the cumulative weight fraction of chains of each length determined by GPC. The separation at maximum attractive force, corresponding to the maximum fraction of adsorbed chains, approximated the average contour length. The weight fraction as a function of molecular weight was obtained from the derivative of the force profile and fit a log-normal distribution, enabling the PDI to be estimated. Characterization of the molecular weight and polydispersity of polymer brushes remains a challenge, particularly when the grafting surface is flat and the amount of grafted material is low. Even when the amount of material is sufficient for analysis by conventional methods such as GPC, cleaving the polymer from the grafting surface is not always possible. The method described here allows the molecular weight and 184 polydispersity of polymer brushes to be estimated provided the adsorption of polymer to A F M tip is favorable. Although only the PNIPAM/silicon nitride system was investigated, the technique should be applicable to different polymers through modification of the tip surface chemistry to obtain the desired polymer-tip interaction. This technique is founded on a purely empirical relationship between the decompression profile and the cumulative weight fraction. The correlation between number average contour length and the separation at maximum attractive force is also empirical. Based on these observations, a practical application has been developed for the decompression profile of an adsorbing brush whereby the molecular weight and polydispersity of the polymer, under the appropriate conditions, can be determined. 185 5. Comparison of Experimental Brush Thicknesses with Self-Consistent Field Model Predictions 5.1 Introduction The purpose of this chapter is to compare the brush thicknesses measured by hydrodynamic and force techniques with those predicted by a self-consistent mean-field (SCF) model. Due to the limitations of the experimental techniques, thicknesses could not be determined for the entire set of brushes with different properties prepared in the Brooks laboratory. Estimation of the hydrodynamic thickness of the grafted layer by measuring the difference in particle size before and after grafting by dynamic light scattering is restricted to particles diameters between ~ 0.003 and 3 pm. To be able to accurately predict the thickness of brushes on large latex particles (> 3 pm) using the SCF model is therefore beneficial. The dynamic range of the force technique is determined by the ability to fully compress the brush by an A F M tip. In cases where constant compliance is not attained or there is a significant offset distance, the equilibrium thickness cannot be determined from the repulsive force profile. The force technique is therefore limited to brushes with low grafting density or low molecular weight. For a given M n and a, the ability to measure equilibrium thickness is further reduced with increasing particle size. This is because the volume available to the polymers away from the surface does not vary as strongly with distance as curvature is decreased, making it more difficult to compress brushes prepared on flat or minimally curved surfaces. 186 A number of theoretical models have been used to predict the thickness of polymer layers grafted on planar surfaces. The approaches are based on describing the segment density as a function of distance away from the grafting surface. As discussed in Section 1.3.3, the early scaling models assumed a constant concentration profile throughout the brush (Alexander, 1977). A different profile was predicted by analytical self-consistent field (SCF) arguments, which found the polymer concentration to decrease parabolically away from the grafting surface (Milner et al, 1988). The mean-field model used here is based on that developed by Scheutjens and Fleer (1979, 1980) to describe the adsorption of polymers on a surface, whereby the properties of the segments in each layer of a Cartesian lattice are averaged. Leermakers et al. (1990) extended that model to include cylindrical coordinates, allowing the segment density to be calculated in two dimensions. The cylindrical lattice model was further developed in the laboratory of Dr. Charles Haynes (Department of Chemical Engineering, UBC) by Steels et al. (2000a,b) to describe the distribution of end-grafted polymer around a particle in the directions normal (z) and radial (r) to the grafting surface. In this work, the Steels/Haynes numerical SCF model was employed to predict the structure of grafted polymer layers. In the SCF model, no assumptions are made a priori about the volume fraction, which is determined self-consistently. A complete description of the calculations is presented in published reports (Steels et al, 2000a,b). There have also been reports in the literature describing end-grafted chains at spherical surfaces by the SCF lattice model (Wijmans and Zhulina, 1993; Dan and Tirell, 1992). In the model used in the present work, the chains are grafted onto a flat surface, however, 187 the experimental thicknesses obtained for brushes prepared on latex particles were analyzed below to account for curvature effects. 5.2 Self-Consistent Field Model In lattice models, the space is divided into discrete regions over which the properties of the segments are averaged. In the cylindrical lattice, layers in the direction normal to the grafting surface and rings in the radial direction are numbered z = 1, ..., Z m a x and r = 1, • Rmax, respectively. The lattice sites in each ring within a given layer are considered indistinguishable and treated by mean-field averaging. The conformation of non-interacting ideal polymer chains can be modeled as a random walk. To describe the more realistic situation of interacting segments, a step-weighted walk is used to account for the preference of a segment in a lattice site located in cylindrical coordinates (z,r) relative to the bulk solution. In this model, steps can be taken within the same layer (z), into a higher/lower layer (z ± 1), within the same radial (r), into inner/outer radials (r + 1), as well as in any combination of a layer/radial step (i.e. in and down). The step probabilities depend on the lattice coordination number. For a hexagonal lattice (12 nearest neighbours), the step probability is 6/12 for remaining in the same layer and 3/12 for stepping into an adjacent layer. The volume fraction of a segment i in a given coordinate, <p{ (z, r), depends on the step -Uj(z,r)i , j weighting factor. Steps are weighted by the appropriate Boltzmann factor, e , where «,(z,r) is the interaction potential of a segment of component / located in radial (z,r). The interaction potential depends on the Flory-Huggins interaction parameter Xy for unlike components (/ and j) as well as on the average volume fraction of j in the 188 corresponding coordinates, ^ ; ( z , r ) | , where the angular brackets represent the layer average. The layer average is needed because each radial (z', r') adjacent to a given radial (z, r) contains a different volume fraction of any component. The layer average is obtained by multiplying q>j(z',r') by the appropriate step probability and summing over all adjacent lattice positions (z',rf) • Because the volume fraction (pt(z,r) depends on the interaction potential via the Boltzmann weighting factor, which in turn depends on the local volume fraction of each component, <pt (z, r) is determined self-consistently and must be solved numerically. The general shape of the brush profiles calculated by the above model is similar to the parabolic density distribution predicted by the analytical SCF model. The numerical model, however, indicates a depletion zone near the grafting surface and an extended "tail" region at the outer edge of the brush where the density decreases less sharply (Steels et al, 2000b). The brush height corresponds to the layer in which the segment density is below an arbitrary critical small value. The brush height can be compared with experimental values by multiplying the height in terms of layer number by the scaled lattice length (see Section 5.3). The height varies directly with chain length and surface segment density to the power of 1/3 according to predictions of the Alexander-de Gennes model (Alexander, 1977). 5.3 Scaling Lattice Parameters The model describes the segment density distribution in the brush as a function of layer location away from the grafting surface. In order to compare predicted and measured brush thicknesses, the lattice unit must be assigned a dimension, i.e. lattice length / L (nm). 189 The lattice length should be chosen so that the properties of the lattice chain having N L number of segments are comparable with those of the real chains. The subscript L distinguishes the number of lattice segments from the degree of polymerization N . To properly scale the lattice parameters, both the length and flexibility of the lattice chain should be comparable to that of the real chains. A general approach for scaling lattice chains is given by Fleer et al. (1993), whereby the contour length as well as radius of gyration of the lattice chains are equated with the corresponding L c and R g of the real chains. Using the expressions for L c and R g derived for an ideal polymer (see Section 1.3.1) they obtained: NLlL=Nl (5.1) Rg=aMl,2=p\'2Nl'2lL (5.2) where the subscript L distinguishes the lattice parameters from those of the real chain, M is the molecular weight of the polymer, N is the degree of polymerization, / is the monomer length (0.25 nm for vinyl monomers), pi is the persistence of the lattice (i.e. measure of chain stiffness as defined in Section 1.3.1) and a is an experimental parameter determined by light scattering. Combination of Eq. 5.1 and 5.2 yields the following expressions: 2 NL=M 1PL 1 I2PL ^ \ a l M m o n J (5.4) where M m o n is the monomer molecular weight. The lattice persistence, as defined by Fleer et al. (1993), is fixed by the lattice geometry and is given by: 190 PL = T (5.5) where Z is the coordination number. For a tetrahedral (Z = 4), cubic (Z = 6), and hexagonal (Z = 12) lattice,^ = 0.277, 0.233, and 0.196, respectively. The idea here is that the lattice chains can be made stiffer by increasing 1L. For the contour length to be properly scaled, N L must then be set accordingly to satisfy Eq. 5.1. Due to the non-linear relationship between R g and N (Eq. 5.2), however, different N L and 1L combinations can be chosen to describe chains with the same contour length but different degrees of stiffness. The above treatment can be used to scale non-interacting ideal chains (i.e. a random walk model). In a good solvent, the excluded volume implies that the walk is no longer random but rather self-avoiding, giving rise to an expanded, less flexible chain. This is expressed by the universal exponent v = 0.59 (~ 3/5) obtained in a good solvent as opposed to 1/2 obtained in a theta solvent (see Eq. 1.4). In the case of a step-weighted walk, it is no longer realistic to describe the stiffness solely in terms of the lattice geometry due to the dependence of the segment density in each radial (z,r) on the interaction potential. In this work, the stiffness of the lattice was determined by measuring the variation in the dimensions of a single lattice chain grafted to a surface as a function of N L under athermal conditions. The chain dimensions are described in terms of R r m s , the root-mean-squared distance of segments from the cylinder axis according to: R rms 2> r 2 ns(r) (5.6) 191 where the number of segments in each radial ns(r) is given by the calculated volume fraction q> (z,r) multiplied by the number of lattice sites in the radial r summed over all layers. The value of Rrms is determined in terms of number of radials from the cylinder axis (i.e the point of grafting). Multiplication of Rrms by lL gives the radius of the lattice chain in units that can be compared with the experimentally determined radius of gyration. The segment density distribution calculated for a single end-grafted chain in the radial (r) (dash-dot line) and normal (z) (solid line) directions with N = 50 is shown in Fig. 5.1. The RrmS calculated according to Eq. 5.6 is indicated by the dashed line. Note that the number of segments in a given radial ns(r) was obtained by summing the volume fraction in the radial over all layers. The distribution of segments in both z and r directions contribute to R r m s and the parameter can therefore be compared with the radius of gyration of a real three dimensional polymer chain. 5 10 Radial (r) or Layer (z) Figure 5.1. Segment distribution of a single end-grafted chain in the radial (r) (dash-dot line) and normal (z) (solid line) directions. (N = 50; % = 0). Dashed line indicates R r m s . 192 The persistence of the lattice was obtained by approximating RrmJi as Rg in Eq. 5.2: Rrms = PL^I (5-7) where the exponent b is obtained by plotting Rmis versus N L and fitting the data to a power law. The R r m s calculated as a function of N L is shown in Fig. 5.2 for N L between L L 25 and 125 for % = 0.5 and % = 0. The data was fit to a function of the form y = p x using a non-linear least-squares approach, giving fit parameters p = 0.81, b = 0.47 for % = 0.5 and p = 0.78, b = 0.50 for % = 0. In both cases the fitted exponent b is similar to the value 0.5 predicted for a theta solvent (Eq. 5.2). The fit parameters gave a lattice persistence pi = 0.81 and 0.78 for % = 0.5 and 0, respectively. The persistence obtained at athermal conditions was used to scale the brushes in this work. The value at theta conditions is provided only for comparison. According to the discussion in Section 1.3.1, the persistence of a chain relates the ratio of statistical segment length to monomer length by 6p = -j-. Recall that for a freely jointed chain, p = — . For a stiffer chain, the length of a segment that can be described as 6 completely flexible (i.e. statistically independent) is greater than the size of a monomer. In terms of a lattice, the value of pL is used to determine the lattice length lL (see Section 5.4 below). The values of lL calculated here ranged between 0.40 and 0.69 nm, corresponding to ~ 1.5 - 3 monomers per lattice site. 193 — I ' 1 1 1 ' 1 ' 1 ' 1 ' 1 20 40 60 80 100 120 140 N, Figure 5.2. Rrms as a function of N L for a single grafted chain. A similar approach to that described by Fleer et al. (1993) was used to scale the lattice chains to the real chains, with a modification to account for the excluded volume in good solvent. Equation 5.2 was replaced by the more general expression Rg = aMv (see Eq. 1.4). This leads to the following expressions for the lattice parameters: a2M M{2v~X) ^ mon1Y1 N, = P,J P,J,M2^ mon a (5.8) (5.9) where v = 3/5 for a good solvent (Fleer et al., 1993) and a was determined experimentally by light scattering. The parameter a depends on the size of the monomer, stiffness of the chain, and solvent quality. The R g measured by light scattering (Teraoka, 2002) as a function of molecular weight M w for P D M A is presented in Fig. 5.3. The data in Fig. 5.3 was fit to a power 1 9 4 function of the form y according to E q . 1.4. = ax3'5 (solid line) giving a fit parameter of a = 0.011 nm 60 n o or | 304 20 A 40 ^ 50 104 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Molecular Weight M (x 10"5) Figure 5.3. Dependence of R g measured by light scattering on molecular weight. Solid line represents best fits to a power function (see E q . 1.4). 5.4 Comparison of Experimental and Theoretical Results In Chapter 3, the thicknesses of P D M A brushes (Mn = 30 600, PDI = 1.33) having different grafting densities measured by A F M and HT measurement were presented. Here, the lattice length and number of segments for a brush with the same properties were determined according to E q . 5.8 and 5.9 to be //. = 0.47 nm and NL = 166, respectively. These values indicate that the size of a lattice segment is between 1 and 2 monomers. The degree of grafting on the lattice is specified in terms of the fraction of a surface site occupied by polymer cps (chains/surface site). This was calculated using the 195 experimentally measured grafting density CT (chains/area) and the size of a monomer / (0.25 nm) according to: <Ps=^f- (5-10) The surface site fractions are listed with experimental grafting densities in Table 5.1. The grafting densities have been corrected (lowered) to account for the surface roughness of the particles (see Eq. 2.27). The calculated thickness of the brushes LSCF are listed along with the thicknesses L H T and L A F M , measured by hydrodynamic and force methods, respectively. Table 5.1. Thickness L of P D M A brush ( M „ = 3 0 600, PDI = 1.33, R = 6 5 0 nm) obtained by SCF (athermal conditions), HT and A F M . a ( n m 2 ) a q>s* LSCF (nm) L H T (nm) L A F M ( 0.13 0.053 N / A 58 65 0 .062 0.025 24 40 48 0 .029 0 .012 19 3 0 34 0 .024 0.0096 18 4 0 3 2 0 .017 0 .0068 17 3 2 25 0 .013 0.0053 16 42 15 a Experimental grafting densities. * Surface site fraction (lattice parameter). The thickness for the highest grafting density sample (CT = 0.13 nm"2) could not be calculated by the SCF model. This limitation is related to the mean-field model, in which the properties of a layer are expressed in local concentrations and individual chain conformations are not considered (Fleer et al, 1993). There are constraints in the 196 numerical procedure associated with calculating changes in concentration when the local concentration gets very high. For a chain of N L = 166 (Table 5.1), for example, the concentration profde and layer thickness could not be calculated for a surface site fraction greater than 4.7%. The hydrodynamic thicknesses of P D M A brushes having different M„, a, and particle radius, R , are listed in Table 5.2. Lattice chains were scaled to model brushes having these properties using the above approach; the calculated thicknesses LSCF are listed in Table 5.2. Table 5.2. Experimental and lattice properties of P D M A brushes M „ N PDI a R h N L <Ps LSCF L H T (nm2) (nm) (nm) (nm) (nm) 15 000 152 1.48 0.051 339 0.40 94 0.013 11 28 53 440 540 1.74 0.025 339 0.52 259 0.014 33 106 88 500 894 1.31 0.0031 358 0.58 388 0.0023 31 38 186 100 1880 1.46 0.0031 358 0.67 703 0.0037 69 43 213 100 2153 1.59 0.0023 289 0.69 784 0.0030 73 70 An expression relating the thickness L s p h e re of a spherical brush of radius R to that of an equivalent flat brush L f | a t (i.e.same N and a) is given by Komura and Safran (2001): -flat - ~R v5/3 ^sphere R + 1 -1 (5.11) 197 The above equation was used to correct for the spherical nature of the brush in order to compare the measured hydrodynamic thickness values with those predicted by SCF for a planar brush. Using the values of L H T and R, the equivalent thickness Lfiat on a flat surface was calculated. The corrected LHT values and the corresponding LSCF values are plotted as a function of NCT in Fig. 5.3. Data from both Tables 5.1 and 5.2 are included. 120 100 I 80 $ 60 ^ 4 0 4 20-I 0 o °o o — I — 5 0 o H T • S C F > • o 100 — I ' 1— 150 200 Na 2 5 0 300 Figure 5.4. Comparison of brush thickness L obtained by HT and SCF as a function of NCT . To correct for the spherical nature of the brushes, the measured LHT values were modified according to Eq. 5.11. Lattice chains were scaled according to the parameters listed in Table 5.2. Calculations were performed in athermal conditions (x = 0). The data in Fig. 5.4 suggests that when properly scaled, the brush thicknesses predicted by the SCF model compare reasonably well with experimentally measured HT values, however the LSCF values were generally lower than L H T - The low LSCF values could be attributed to a poor choice of interaction parameter. Modeling the brush in a better solvent, for instance, is expected to give slightly larger values of LSCF- The 198 software, however, was unable to evaluate segment density distributions for the lattice parameters listed in Table 5.1 and 5.2 at better than athermal solvent conditions and the program consistently crashed. The higher LHT values may be the result of HT being particularly sensitive to long chains (Fleer et al, 1993; Cohen Stuart et al. 1984). Experimental HT values are often much larger than the layer thicknesses measured by ellipsometry (Takahashi et al, 1984) and by neutron scattering (Barnett et al, 1981). This effect is also demonstrated by Cohen Stuart et al. (1984) who evaluated the hydrodynamic thicknesses of adsorbed polymer layers using segment density profiles calculated with the Scheutjens and Fleer (1980) adsorption theory. They found that the solvent flow at the periphery of the adsorbed layer is significantly affected by the distribution of tails. The inability of the model to account for the polydispersity of the chains also gives LSCF values that are lower than would be expected i f PDI were considered. While a range of chain distributions could not be modeled here, the segment density distribution could be obtained for a bimodal polymer consisting of short and long chains. It was found that at a given grafting density, the long chains are more extended in the bimodal brushes than in the monodisperse brushes at the same grafting density. This is consistent with the SCF predictions of Currie et al. (1999b) where the effect of varying the mixing fraction and length of the shorter chains in a bimodal brush was investigated. In addition to predicting the layer thickness, the SCF model employed here can be used to describe the segment density distribution for a particle positioned within the brush layer. It would be indeed interesting to compare the model predictions with the compression profiles obtained in an A F M experiment. Given the difficulty in evaluating 199 the segment density distribution using moderately high surface site fractions in a non-compressed brush, however, the software invariably crashed upon introduction of a particle into the grafted layer, as the local concentration became too high. 5.5 S u m m a r y The thicknessess of P D M A brushes determined by hydrodynamic and A F M methods were compared with those calculated by the numerical SCF model. The lattice was scaled in order to describe the length and stiffness of real P D M A chains in good solvent. The dependence of the RMS radius of a single tethered chain on the chain length was used to determine the stiffness of the lattice. The excluded volume of the real chains was accounted for by modifying the scaling equations to include the experimental parameters obtained by light scattering. An expression correcting for the spherical nature of the brush was employed to directly compare the experimentally determined brush thicknesses with those predicted for a planar surface. The predicted brush thicknesses were typically slightly lower than the experimentally measured hydrodynamic thicknesses after making the appropriate geometric correction. The approach does not account for the polydispersity of the brush, which might explain the lower predicted thicknesses. 200 6. C o n c l u d i n g R e m a r k s a n d Future W o r k In this work, the interactions between an A F M probe and neutral, end-grafted polymer layers of varying molecular weight, grafting density and monomer nature were investigated by direct force measurements. The polymer brushes were characterized by gel permeation chromatography and dynamic light scattering to determine the molecular weight distribution and thickness of the grafted layer. The equilibrium thicknesses measured by A F M were comparable to hydrodynamic thickness values. The values were also similar to the brush thicknesses predicted by a numerical SCF model after scaling the length and flexibility of the lattice chains against those of real chains using experimentally determined parameters. Force measurements on non-grafted and grafted latex showed that brush thicknesses were larger than the length of the electric double layer, indicating that electrostatics do not contribute significantly to interactions at the outer layer of the brush. Techniques were developed to estimate the molecular weight and molecular weight distribution of the polymer brushes utilizing two distinct force techniques, the suitability of which depended on the strength of interaction between the chains and the A F M probe. Employment of these techniques is particularly advantageous when characterizing brushes prepared on flat surfaces where the amount of grafted material available for analysis is low. The methods are also highly versatile, as they do not require the polymer to be released from the grafting surface. A F M imaging revealed that the surface roughness of the shell latex depended on the concentration of initiator in the copolymer and suggested a possible phase separation. The relatively consistent repulsive force profiles obtained laterally over the surface, 201 combined with the predictions of a random copolymer based on reactivity ratios of the monomers, suggest that the distribution of chains over the surface is likely uniform. Depending on the degree of phase separation, however, grafting densities can be overestimated when surface roughness is not taken into account. Maximum grafting densities may therefore be achieved using an optimum initiator concentration that maximizes the number of grafting points while minimizing surface roughness. The compression profiles of polymer brushes obtained as a function of grafting density and monomer nature indicated that the overall interaction depends on a delicate balance between excluded volume and bridging forces. Unlike previous reports in the literature where bridging has been associated with adsorbed polymer and low-density tethers, these high-density brushes exhibited strong attractive interactions under the appropriate conditions. These unexpected results were attributed to chain molecular weight distribution and the spherical nature of the brush, as the volume available to the chains increases as a function of distance from the point of grafting on curved surfaces. Future Extensions to this Work The above findings emphasize the contributions of grafting density, molecular weight, molecular weight distribution, monomer nature, surface geometry, and surface roughness to the interactions of polymer brushes. Further investigation into the interactions of these surfaces with proteins using A F M might be of interest. Preliminary studies involving protein coated latex probes interacting with spherical P N I P A M brushes suggested that force profiles can be used to test for selectivity of protein rejection. The profiles of a P N I P A M brush interacting with H S A and IgG coated latex probes exhibited a long-range 202 attractive force. The attractive force was of shorter range and magnitude than that exerted on a shell latex probe with no adsorbed protein. In contrast, the same brush exerted a strong repulsive steric force on a fibrinogen-coated probe at all separations. 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The latex film was rinsed thoroughly and sonicated in Milli-Q water to remove any latex which had not strongly physisorbed onto the glass. Significant shear was induced on the samples to ensure that the films would remain intact during measurements. This proved to be extremely important in preventing the AFM probe from being contaminated by free latex during the measurements. This step was repeated until inspection of the film under an optical microscope showed that no free latex could be detected following the addition of a drop of water to the film. The glass substrate was glued onto a steel puck using double-sided adhesive tape and the sample was positioned in the AFM. To avoid expansion of the glue during force measurements, placement of the substrate on the puck was performed gently with minimal pressure applied. To minimize lateral motion during the force measurements, the goal was to prepare a closely packed monolayer of latex. Inspection under an optical microscope suggested that regions of monolayer coverage were present. An optical viewing system located above the AFM enabled us to position the tip and obtain force measurements in these regions. In some experiments, it was of interest to examine the interaction between an AFM tip and a flat silicon nitride surface. These samples were prepared by fastening a clean 217 silicon nitride substrate (see Fig. 2.3a) onto a clean glass slide. As described in Section 2.2.2.2, each rectangular silicon nitride substrate (~4 mm x 2 mm) holds 4 V-shaped cantilevers with integrated tip. Since the substrate, cantilever and tip all have the same surface chemistry, force measurements were performed with the AFM probe located roughly above the center of the silicon nitride substrate. A water-insoluble resin (Epikote 1004, Shell) was used to fasten the silicon nitride to the glass rather than the standard double-sided adhesive tape. This modification was required since the small dimensions of the silicon nitride substrate necessitated that both silicon nitride and glass surfaces be immersed in the fluid, causing the adhesive to come in contact with the water. //. Tip holder (fluid cell) The tip holder is equipped with an inlet and outlet port for fluid applications and a groove in which an O-ring may be placed (see Fig. 2.2). Alternatively, fluid may be added without the O-ring and the drop is held to the sample by surface tension. The latter approach was typically used here as the O-ring introduced an unnecessary source of contamination to the setup. The glass tip holder was cleaned by sonication in Milli-Q water before each experiment, dried with Argon, and wiped free of prints with lens paper. The tip holder was rinsed with Milli-Q water immediately after each use to prevent contamination from salts or adsorbed polymer. 218 iii. Probes The probes used in this work were either commercially available silicon nitride tips or colloidal particle probes prepared in the laboratory. The term "tip" is used to describe the irregularly shaped protrusion from the microfabricated silicon nitride cantilevers; modified cantilevers onto which a spherical latex particle is fastened are referred to as "particle probes". A detailed description of the geometry and surface chemistry of the silicon nitride tip is described in Section 2.2.2.2. Also described is the procedure for preparation of the particle probes. Tips were rinsed with Milli-Q water and inspected for damage under a light microscope immediately prior to use. Dust particles were commonly found on the commercially available tips upon arrival, but were easily blown off with a stream of argon or rinsed off with water. iv. Fluid Aqueous solutions of NaCI were most frequently used in this work. Solutions were filtered through a 0.22 jum filter before placing a drop (~ 30 /uL) on the sample. Inspection under a light microscope ensured that air bubbles were not present in the fluid cell. Hydrophobic polystyrene particle probes were soaked in fluid (~ 5 min) immediately prior to being positioned in the tip holder to prevent the formation of air bubbles on the particle surface. Once all AFM components were in position, the tip-sample system was allowed to equilibrate in the fluid medium for 5-10 min before commencing measurements. Evaporation was continuously monitored and the fluid was replaced when necessary, 219 which was typically every ~ 20 min. Significant evaporation disrupts the deflection of the laser and is detectable by an unusually unstable baseline. In experiments where the precise concentration of the solution must be maintained, more frequent replacement of the fluid may be necessary. In the experiments performed on polymer brushes, salt was typically added to the solutions in order to minimize electrostatic interactions so that interactions due to the grafted layer could be examined independently. Changes in ionic strength caused by slight evaporation did not appear to significantly affect those results. In some cases it was desirable to examine interactions in a given tip-sample system in different fluid environments. Care was taken to minimize concentration errors upon fluid replacement, which can be significant given the small amount of fluid involved. Ideally, fluid is replaced by flushing the fresh liquid through the sealed chamber using the inlet and outlet ports of the fluid cell. This, however, could not be done due to the elimination of the O-ring. To avoid changing the optical lever sensitivity, the tip could not be removed from the tip holder to be rinsed between measurements. The fluid was replaced by lifting the AFM "head" (see Fig. 2.2a), removing the liquid from the sample surface with a syringe, adding a fresh drop, and repositioning the AFM head so that the tip was immersed in the new solution. A drop of fluid typically remained on the cantilever when the AFM head was lifted. Concentration errors were reduced by repeating the cycle (~ 10 times) so that both tip and sample were thoroughly rinsed with the new solution. Reproducible force measurements of a silicon nitride tip on glass in performed 10 mM NaCI before and after dilution suggested that the technique was effective. 220 Appendix 2 Piezo Calibration The sensitivity of the three piezos was measured by scanning a silicon calibration reference having a regular series of 200 ± 6 nm deep pits spaced 10 pm apart and determining the voltage required to move the piezo a known distance. The relationship between the applied voltage and the motion of the piezo is nonlinear, which complicates the calibration. The curve showing the change in piezo position with applied voltage in Fig. A2.1 is less steep at the beginning of the cycle than at the end for both extension and retraction. Because the piezo sensitivity (nm/V) is higher at the end of a scan line than at the beginning, there is a hysteresis between the extending and retracting directions. To correct for the nonlinear response of the piezo, a nonlinear voltage is applied in real-time, which produces a linear response by the piezo (Fig. A2.2). Following the procedure outlined in the AFM MultiMode Instruction manual (Digital Instruments, 1996), the X-and Y- piezos were calibrated by scanning the silicon sample at a particular rate and measuring the dimensions of the features at the beginning and end of the scan. Because the features on the calibration standard are of constant dimensions at any point, differences measured in the size at different times along the scan indicate nonlinearities in the piezo. The measured feature dimensions were input into the AFM calibration software and the voltage as a function of time was adjusted to compensate for the nonlinear motion of the scanner. The procedure was repeated until the size of the features measured at all points along the scan cycle was accurate. Similarly, the Z-piezo was calibrated by comparing the measured depth of the features with the known value. 221 Nonlinearities in the Z-piezo were corrected for by scanning the calibration sample near the top, bottom, and middle of the piezo voltage range. Because the sensitivity of the scanner decreases with age, the piezo was recalibrated every six months, as recommended by the manufacturer. O D_ O N Q) Voltage Figure A2.1 Effect of nonlinearities in piezo. Sensitivity (nm/V) of piezo is less at the beginning of a cycle than at the end, for both extension and retraction. Triangular Waveform Corrected, Nonlinear Waveform Figure A2.2 Nonlinear waveform applied to electrodes to produce linear scanner motion. Triangular waveform is shown for reference. 222 Appendix 3 Automation of Data Analysis in Matlab The file 'V512_app.m' (or 'V512_ret.m') converts the raw deflection data (bits) measured in the direction of sample-tip approach (or retract) into units of nanometers. The optical sensitivity must be calibrated and input during the experiment in order to obtain the correct deflection values. The deflection data is automatically adjusted so that the deflection at the largest separation in the baseline is equal to zero. The user must manually confirm that that the slope of the force curve generated by running V512_app.m is equal to 1 nm/nm in the region of large compression. If the maximum slope is below one, the measurement must be repeated using a larger trigger force (see above). The piezo position corresponding to the onset of the constant compliance region is determined manually and is used as an input parameter for the file 'sepa.m'. This file converts the piezo position in the abscissa into tip-sample separation. The spring constant of the cantilever is also input and the ordinate is converted from units of deflection to units of force. The program also corrects for drift by accounting for the slope in the large separation region where the tip and sample do not interact and subtracting off the baseline force. The range of data corresponding to the baseline varies with each measurement and must be defined manually by the user. In some cases, a mean force curve was generated by averaging the force versus separation data from a large number of curves. The file 'mean_force.m' interpolates the data of the specified force curves over a particular range and calculates the mean force at each separation. 223 Appendix 3a. Creating raw force curve (deflection (nm) versus piezo position (nm) from ASCII fde. % File: "v512_app.m" %INPUT PARAMETER: afmfile %afmfile = fdename.asc (NOTE: fdename must be 8 characters). %The ascii data file generated by the Digital Instruments force curve software consists of 1) a header containing experimental parameters and 2) deflection data. The data is in 2 columns and 512 rows. Rows 1-256 correspond to approach (compression) data; rows 257-512 correspond to retract (decompression) data. Each force curve (approach and retract) consists of 512 data points. Column 1 gives the odd numbered data points; column 2 gives the even numbered data points. The data is in units of bits and must be converted into units of deflection using the optical sensitivity parameters in the file header according to: deflection (nm) = deflection (bits)*(2.5 V/65536 bits)*optical sensitivity (nm/V) The photodiode voltage range is 2.5 V; a 16 bit D-A converter corresponds to 2 1 6 = 65536 bits. The optical sensitivity must be determined before measurement by calibration on a hard sample such as glass. If calibration is done after the measurement, the value of the detector (optical) sensitivity in the heading will be incorrect. The correct value will need to be entered manually. The piezo positions corresponding to the 512 data points are calculated using the size of the scan ("ramp size") and piezo sensitivity in the header according to: position (nm) = ramp size (V)* piezo sensitivity (nm/V) / 511 The piezo sensitivity is a constant for a given piezo scanner and is determined during the general calibration routine. % OPEN AFM FILE HEADER AND ASCII DATA fid=fopen(afmfile,'r'); %GET RAMP SIZE (V) AND CONVERT TO (nm) USING SENS. Zscan (i.e. piezo sensitivity) %Get Sens. Zscan (nm/V) (i.e. piezo sensitivity nm/V) 224 for header=l:58 sens_zscan = fgetl(fid); end piezosens 1 =(sens_zscan); piezo_sens2=findstr(piezo_sensl,' nm/V'); piezo_sens3=piezo_sens 1(18 :piezo_sens2-1); piezo_sens=str2num(piezo_sens3); %Get Ramp Size (V): fid=fopen(afmfile,'r'); for header=l:356 ramp_sizea = fgetl(fid); end ramp_sizeb=findstr(ramp_sizea,'V/LSB)'); ramp_sizec=ramp_sizea(ramp_sizeb+7:end-2); ramp_sizee=str2num(rampsizec); %Convert Ramp Size from V to nm: ramp_size=ramp_sizee*piezo_sens; % CREATE ARRAY OF 512 VALUES OVER RAMP SIZE RANGE: x(l)=0; for i=2:512 x(i)=x(i-1 )+ramp_size/511; end % SEPARATE x (nm) VALUES INTO 2 COLUMNS i.e. xl=(L3.5...255) and x2=(2A6..256) xl=linspace(x(l),x(511),256); x2=linspace(x(2),x(512),256); % GET DETECTOR SENSITIVITY (nm/V) fid=fopen(afmfile,'r'); for header=l: 186 detsensl = fgetl(fid); 225 end detsens2=detsens 1 (23 :end-5); detsens=str2num(detsens2); % GET ASCII DATA fid=fopen(afmfde, 'r'); for header= 1:408 y = fgetl(fid); end for i=l:256 y = fgetl(fid); yl=strtok(y); y2=str2num(yl); column l(i)=y 2; y(l:8)="; y3=str2num(y); column2(i)=y3; end % CONVERT DEFLECTION DATA FROM BITS TO nm defll=(columnl*2.5)/(65536)*detsens; defl2=(column2*2.5)/(65536)*detsens; %COMBINE COLUMNS INTO SINGLE DATA SET n=linspace(l ,256,256); odd=2*n-l; even=2*n; for i=l:256 xrange(odd(i))=x 1 (i); xrange(even(i))=x2 (i); drange(odd(i))=defl 1 (i); drange(even(i))=defl2(i); end % PLOT RAW DATA (DEFLECTION (nm) VS. POSITION (nm)) figure plot(xrange,drange,'r.') yaxis=axis; axis([0 200 yaxis(3) yaxis(4)]) 226 xlabel('Position (nm)') ylabel(Tip Deflection (nm)') title('Raw AFM Data') Appendix 3b. Creating adjusted force profile (force (nN) versus separation (nm)) from "raw" force curve. % File "sep_a.m" %INPUT PARAMETERS: springconst; xstart % spring_const = spring constant (N/m) % xstart = point # corresponding to constant compliance region % Tip/sample separations (nm) are obtained by subtracting the change in deflection from the change in piezo position and defining zero separation. The input parameter "xstart" orresponds to zero separation and is determined from the onset of constant compliance in the raw deflection curve. Force values are obtained by converting the deflection data (nm) into force data (nN) using the spring constant according to Hooke's law. % CORRECT FOR BASELINE DRIFT coeff=polyfit(xrange(length(xrange)-350:length(xrange)-100),drange(length(drange)-350:length(drange)-100),l); base_fit = coeff(l)*xrange+coeff(2); defl=drange-base_fit; % SEPARATION DATA-sep=zeros(l,512-xstart+l); sep(l)=0; for i=2:512-xstart+l sep(i)=(xrange(xstart+i-1 )-xrange(xstart))+(defl(xstart+i-1 )-defl(xstart)); end sep_plot=sep(l :length(sep)); % FORCE DATA force_plot=spring_const*defl(xstart:length(defl)); 227 % PLOTTING FORCE (nN) VERSUS SEPARATION (nm) figure plot(sep(l:length(sep)),spring_const*defl(xstart:length(d^ xlabel('Separation (nm)'); ylabel('Force (nN)*); Appendix 3c. Obtaining average of multiple force curves. Separation values for each curve are not necessarily the same. This program interpolates the data for common separations and averages the data at each point. %File "mean_force.m" % INPUT PARAMETERS: num; filename; spring_const; xstart_str % Note: Filenames ("afmfile") of curves being averaged must be of the form - "*****_##" where ***** is common for all files and ## is any number > 10. % filename = *****. % num = array containing ## % For example, to obtain the average of 3 curves with filenames (afmfile = ) "glass-10.asc", "glass ll.asc", and "glass-12.asc': % filename = "glass-" %num= [10 11 12] % spring_const = spring constant (N/m) % xstartstr is array of numbers corresponding to xstart for each of the files being averaged (i.e. in the same order as used to define "num") sep_interpolate=linspace(0,1000,1000); force_matrix=zeros(length(num), 1000); mean_force 1 =zeros( 1,1000); xstart=zeros( 1 ,length(num)); for q=l :length(num) filestring= [filename int2str(num(q)) '.asc']; afmfile=filestring; v512_app_mod; xstart=xstart_str(q); sep_a_mod; force_matrix(q,:)=interpl(sep_plot,force_plot,sep_interpolate,'spline'); end mean_force_app=mean(force_matrix); 228 Appendix 4 H 2C=GH-C-N(CH 3) 2 O N,N-Dimethylacrylamide (DMA) II II 2 C-CI I-C-N-CI l(Cl I3), O N-Isopropylacrylamide (NIPAM) H H 2 C=CH-C-N-CH 2 CH 2 -OCH 3 O Methoxyethylacrylamide (MEA) 229 Appendix 5 Table A5-1 Characteristics of PNIPAM brush (M n,GpC = 47 700, PDI G P C = 1.33, a = 0.037 nm"2) determined from individual decompression profdes. Sample L m (nm) a M" M n , A F M ° sd PDI A F M 6 F J r max Rateg (104 Da) (104 Da) (nN) (fim/s) 1 92 ± 5 4.7 4.2 ± 0.2 0.49 1.28 -1 1.5 2 68 ± 5 3.7 3.1 ±0.2 0.60 1.43 -0.9 1.5 3 90 ± 5 4.6 4.1 ±0.2 0.51 1.29 -0.6 2.25 4 70 ± 5 3.8 3.2 ±0.2 0.62 1.47 -0.6 1.5 5 81 ± 5 4.3 3.7 ±0.2 0.55 1.35 -0.8 1.5 6 106 ± 5 5.4 4.8 ±0.2 0.47 1.25 -0.7 1.5 7 86 ± 5 4.5 3.9 ±0.2 0.54 1.33 -0.6 1.5 8 78 ± 5 3.9 3.5 ±0.2 0.47 1.25 -0.6 0.3 9 90 ± 5 4.6 4.1 ±0.2 0.51 1.29 -0.6 4.65 average 85 ± 1 2 4.4 ± 0.5 3.8 ± 0.5 0.53 1.3 ±0.1 -0.7 ± 0.2 "Separation in decompression profde corresponding to maximum attractive force. Individual uncertainties are based on a nominal ± 5 nm error in defining zero separation. See text for discussion. Uncertainty in average separation is based on standard deviation from multiple measurements. 6Peak molecular weight in Fig. 4.14. c Average molecular weight calculated from L m using equation (4.9) assuming L c ~ L m . Uncertainties are as defined in a. Standard deviation of log-normal distribution (Eq. 4.12). ePolydispersity index obtained from standard deviation of log-normal distribution according to Eq. 4.15. ^Maximum attractive force used to normalize curves in Fig. 4.10. R^ate of compression/decompression. 230 Table A5-2. Characteristics of PNIPAM brush (M n G pc = 94 900, PDI ; G P C = 1.35, a = 0.067 nm"2) determined from individual decompression profiles. Sample L m (nm)" (± 5 nm) Mb (104 Da) (104 Da) srf PDI,AFM e F f 1 max (nN) Rateg (//m/s) 1 179 9.3 8.1+0.7 0.54 1.34 -1.2 0.60 2 177 9.4 8.0 + 0.7 0.57 1.38 -1.0 1.5 3 202 10 9.1+0.9 0.52 1.31 -1.0 1.5 4 220 11 9.9 ± 1.1 0.53 1.33 -1.2 6.0 5 238 12 11 ± 1.3 0.54 1.34 -2.5 6.0 6 248 13 11 ± 1.4 0.53 1.32 -1.4 1.5 7 192 10 8.7 ±0.8 0.58 1.39 -1.1 1.5 8 277 13 13 ± 1.7 0.35 1.13 -1.3 6.0 9 181 9.8 8.2 ±0.7 0.60 1.44 -1.2 6.0 10 196 10 8.9 ±0.9 0.54 1.34 -1.1 6.0 11 199 10 9.0 ± 0.9 0.54 1.35 -1.2 6.0 12 ' 180 9.4 8.1 ±0.7 0.54 1.33 -1.0 1.5 average 207 ± 32 11 ± 1 9.4 ± 1.4 0.53 1.3 ±0.1 -1.3 ±0.4 Reparation in decompression profile corresponding to maximum attractive force. Individual uncertainties are based on a nominal ± 5 nm error in defining zero separation. See text for discussion. Uncertainty in average separation is based on standard deviation from multiple measurements. *Peak molecular weight in Fig. 4.14. c Average molecular weight calculated from L m using equation (4.9) assuming L c ~ L m . Uncertainties are as defined in a. Standard deviation of log-normal distribution (equation (4.12)). ^Polydispersity index obtained from standard deviation of log-normal distribution according to equation (4.15). ^Maximum attractive force used to normalize curves in Fig. 4.10. gRate of compression/decompression. 231
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Chemistry
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Interactions of grafted polymer brushes measured by atomic force microscopy
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