Open 2017 05 23 Asthagarg Phdthesis Final.Pdf

Home , Sedimentation potential, Zeta potential

The Pennsylvania State University

The Graduate School

Department of Chemical Engineering

ZETA POTENTIALS AND MINERAL REPLACEMENT AT SURFACES IN

SATURATED SALT SOLUTIONS

A Dissertation in

Chemical Engineering

Astha Garg

 2017 Astha Garg

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2017 ii

The dissertation of Astha Garg was reviewed and approved* by the following:

Darrell Velegol Distinguished Professor of Chemical Engineering Dissertation Advisor Chair of Committee

Ali Borhan Professor of Chemical Engineering

Manish Kumar Assistant Professor of Chemical Engineering

Ayusman Sen Distinguished Professor of Chemistry

James H. Adair Professor of Materials Science and Engineering, Biomedical Engineering and Pharmacology

Janna Maranas Professor of Chemical Engineering and Materials Science and Engineering Graduate Program Coordinator of Chemical Engineering

*Signatures are on file in the Graduate School

iii

ABSTRACT

Surfaces, fixed or mobile, exposed to salt solutions interact with the solution and with other surfaces through physical interactions, chemical reactions and transport. Understanding these phenomena is key to discerning the system behavior and subsequently manipulating it. A good handle on saturated salt systems can be of immense benefit to modern science and industry. However, their behavior is not adequately understood, especially from a colloidal and surface chemistry perspective. The complexity of interactions under saturated salt conditions and experimental difficulties in carrying out certain measurements have contributed to our limited understanding in this regard. The subject of this thesis is to characterize and transform the nature of surfaces exposed to saturated salt solutions through an in-depth understanding of the surface charge, fluid transport and dissolution- precipitation phenomena in these systems.

The work presented here is conceptually focused on two subjects – zeta potential and mineral replacement. First, I describe careful measurements and interpretation of zeta potential which is a measure of electrical potential at the surface-solution interface. Second, I characterize mineral dissolution-precipitation reactions in terms of fluid flow, the rate and extent of mineral replacement and porosity, under a variety of controlled conditions. These experiments offer insights into the behavior of systems at saturated salt and provide quantitative measurements of key parameters that can be used to evaluate and manipulate the system behavior.

iv TABLE OF CONTENTS

List of Figures ...... x

List of Tables ...... xix

Acknowledgements ...... xx

Chapter 1 Motivation and Research Goals ...... 1

1.1 Motivation ...... 1 1.2 Research Goals ...... 6 1.2.1 Zeta potential at high salt and saturated salt conditions ...... 7 1.2.2 Mineral replacement in the KBr-KCl system ...... 10 1.2.3 Chemical micro-fracking of calcite through mineral replacement ...... 14 1.3 Organization of the thesis...... 16 1.4 References ...... 17

Chapter 2 Theoretical background on Electrokinetics ...... 20

2.1 Definition of zeta potential and the electrical double layer ...... 20 2.1.1 Examples and estimates ...... 21 2.2 Applications of zeta potential...... 22 2.3 Classical theory of the EDL ...... 23 2.3.1 Spatial distribution of charge – the Poisson-Boltzmann equation ...... 23 2.3.2 Relationship between charge density and surface potential – the Gouy- Chapman model ...... 24 2.4 Methods of zeta potential measurement ...... 25 2.4.1 Electrophoresis based techniques ...... 25 2.4.2 Streaming potential ...... 26 2.4.3 Electroacoustics ...... 26 2.5 Colloidal stability ...... 27 2.5.1 DLVO theory...... 28 2.5.2 Rapid aggregation ...... 29 2.6 Electrokinetics ...... 30 2.6.1 Electrophoresis and electro-osmosis ...... 30 2.6.2 Diffusiophoresis and diffusioosmosis ...... 32 2.7 References ...... 33

v Chapter 3 Particle Zeta Potentials Remain Finite in Saturated Salt Solutions ...... 36

3.1 Abstract ...... 36 3.2 Introduction ...... 37 3.3 Methods and Materials: ...... 41 3.3.1 Measuring Zeta Potentials ...... 41 3.3.2 Experimental Details ...... 42 3.3.3 Particle tracking and analysis ...... 46 3.3.4 Method Validation ...... 49 3.3.5 Monte Carlo Simulations of the EDL...... 52 3.4 Results & Discussion ...... 53

3.4.1 Particle Motions at Frequency 20 ...... 53 3.4.2 Zeta potential measurements of sPSL and aPSL ...... 57 3.4.3 Stout and Khair zeta potential ...... 61 3.4.4 Monte Carlo simulation of the EDL ...... 62 3.5 Summary and Conclusions ...... 68 3.6 Author Contributions ...... 69 3.7 Copyright Notice ...... 69 3.8 Acknowledgements ...... 69 3.9 References ...... 70

Chapter 4 Relative Roles of Kinetics, Transport and Thermodynamics in Pseudomorphic Mineral Replacement ...... 77

4.1 Abstract ...... 77 4.2 Introduction ...... 78 4.3 Background ...... 80 4.3.1 Steps in the replacement process ...... 80 4.3.2 Thermodynamics - Lippmann Diagrams ...... 82 4.3.3 Porosity generation ...... 85 4.4 Questions ...... 86 4.4.1 Passivation ...... 86 4.4.2 Solution to solid ratios ...... 87 4.4.3 Porosity ...... 87 4.4.4 Fluid transport ...... 87 4.4.5 Interfacial concentration ...... 88

vi 4.5 Methods and Materials ...... 88 4.5.1 Replacement experiments ...... 88 4.5.2 Fluorescence optical microscopy ...... 89 4.5.3 Electron Microscopy ...... 90 4.5.4 Elemental analysis ...... 90 4.6 Results and Discussion ...... 91 4.6.1 Replacement rate of KCl vs KBr ...... 91 4.6.2 Varying solution to solid ratios ...... 93 4.6.3 Effect of external transport ...... 98 4.6.4 Replaced layer composition for replaced KCl...... 98 4.6.5 Replaced layer composition for KBr ...... 102 4.6.6 Accuracy of the EDS composition measurements ...... 104 4.6.7 Solution composition as a function of distance ...... 107 4.7 Conclusions ...... 109 4.7.1 Passivation ...... 109 4.7.2 Solution to solid ratios ...... 110 4.7.3 Porosity ...... 111 4.7.4 Fluid transport ...... 112 4.7.5 Interfacial concentration ...... 113 4.8 Contributions ...... 114 4.9 Acknowledgements ...... 114 4.10 References ...... 115

Chapter 5 Chemical microfracking - Enhancing calcite porosity through pseudomorphic mineral replacement ...... 118

5.1 Abstract ...... 118 5.2 Objectives...... 119 5.3 Background ...... 121 5.3.1 pMRR of calcium carbonate...... 121 5.3.2 Porosity measurement ...... 122 5.4 Methods and Materials ...... 123 5.4.1 Crystals ...... 123 5.4.2 Buffer solutions ...... 124 5.4.3 Replacement experiments ...... 125

vii 5.4.4 Electron Microscopy and Elemental Mapping ...... 128 5.4.5 Image processing for rim width measurement ...... 128 5.4.6 Mercury porosimetry ...... 129 5.4.7 Dye penetration using confocal microscopy ...... 130 5.4.8 Calculations using VMinteq ...... 130 5.5 Results and discussion ...... 131 5.5.1 Effect of temperature on replacement at pH 8.11, 200 C vs. 50 C ...... 131 5.5.2 Effect of pH on observed replacement ...... 132 5.5.3 Replacement at pH 5 at 50 C ...... 138 5.5.4 Replacement with time ...... 139 5.5.5 Effect of external transport ...... 140 5.5.6 Effect of Phosphate concentration ...... 143 5.5.7 Effect of Ca+2 addition...... 144 5.5.8 Mercury porosimetry at 6 days...... 145 5.5.9 Confocal at 6 days and 12 days. For nicely cut vs. hammered...... 146 5.6 Conclusions ...... 148 5.7 Future work and improvements to experimental setup ...... 149 5.8 Acknowledgements ...... 150 5.9 References ...... 151

Chapter 6 Future Work and Broader Impact ...... 154

6.1 Zeta potential at high and saturated salt ...... 154 6.1.1 Scientific advance ...... 154 6.1.2 Implications for saturated salt systems ...... 155 6.1.3 Broader applicability of technique to biological systems...... 155 6.1.4 Future directions ...... 156 6.2 Pseudomorphic mineral replacement reactions ...... 157 6.2.1 Scientific advance ...... 157 6.2.2 Application to enhanced oil recovery ...... 157 6.2.3 Applicability to synthesis of templated or doped materials ...... 158 6.2.4 Future research directions ...... 159 6.3 References ...... 159

Appendix A Supplemental Information for Zeta at High Salt ...... 160

viii A.1 Lattice Model of the Electric Double Layer ...... 160 A.2 Continuum Model of the Electric Double Layer ...... 164 A.3 Summary of zeta potential measurements ...... 167 A.4 Contributions ...... 169 A.5 Copyright Notice ...... 169 A.6 References ...... 169

Appendix B Boundaries can steer active Janus spheres...... 170

B.1 Abstract ...... 170 B.2 Introduction ...... 171 B.3 Results and Discussion ...... 172 B.3.1 Experimental Characterization of the Orientational Quenching ...... 172 B.3.2 Steering the Active Colloid ...... 175 B.3.3 Theoretical description of the catalytic colloid near a surface ...... 178 B.3.4 Electrostatic colloidal forces...... 179 B.3.5 Phenomenology...... 183 B.4 Conclusion ...... 193 B.5 Discussion: exploring the limits for boundary steering phenomena ...... 194 B.6 Methods ...... 197 B.6.1 Janus Particle Preparation ...... 197 B.6.2 Sample Preparation and Gravitaxis of Janus Colloids ...... 197 B.6.3 Microscopy and Image Analysis ...... 199 B.6.4 Colloid settling and diffusion ...... 200 B.6.5 Electrophoresis/Rotational Electrophoresis ...... 201 B.6.6 Lithographic Manufacture of Rectangular Channels ...... 205 B.7 Acknowledgements ...... 207 B.8 Contributions ...... 208 B.9 References ...... 208

Appendix C Origins of concentration gradients for diffusiophoresis ...... 214

C.1 Abstract ...... 214 C.2 Introduction ...... 215 C.3 Essential Theory of Diffusiophoresis ...... 218 C.4 Origins of Concentration Gradients ...... 225

ix C.4.1 Molecular Exclusion ...... 225 C.4.2 Chemical Reaction ...... 231 C.4.3 Diffusive mixing ...... 233 C.4.4 Externally-imposed ...... 237 C.4.5 Salt or crystal dissolution ...... 241 C.4.6 Molecular Crystallization ...... 244 C.4.7 Sedimentation and screening ...... 247 C.4.8 Evaporation and condensation ...... 248 C.5 Conclusions ...... 250 C.6 Acknowledgments ...... 251 C.7 Contributions ...... 251 C.8 Copyright Notice ...... 252 C.9 References ...... 252

x LIST OF FIGURES

Figure 1-1: Zeta potential, dissolution and precipitation in a geological reservoir. A simplified view of a geological reservoir that has charged colloids suspended in a saturated salt solution. The calcite surface and NaCl crystals participate in dissolution – precipitation equilibria...... 2

Figure 1-2: Charged surfaces in salt concentration gradients can cause flows in dead-end pores through diffusiophoresis...... 3

Figure 1-3: Our hypothesis of chemical-mechanical fracking. pMRR at the fractured surfaces would create additional porosity, opening up more volume for fluid flow...... 5

Figure 1-4: Zeta potential and electrical double layer for a negatively charged particle in water ...... 8

Figure 1-5: Electrophoresis of a particle with positive zeta potential. Particle velocity, u is directly proportional to the electric fields and zeta potential on the particle’s surface. ... 9

Figure 1-7: Camera and electron microscopy images of replacement in the KBr-KCl system. KBr crystal in saturated KCl solution shows replacement of ~ 2 mm over 24 hours, while the KCl crystal shows replacement of ~ 0.2 mm over the same time...... 12

Figure 2-1: Zeta potential and electrical double layer for a negatively charged particle in water ...... 21

Figure 2-2: A sample DLVO plot. The parameters are :  potential = 100 mV, Debye length = 1 nm, particle diameter 2 µm, Hamaker constant = 1.4 x 10-19 J...... 29

Figure 2-3: Fluid and particle velocity when an electric field is applied on fluid in a closed capillary...... 31

Figure 3-1: (a) Schematic illustration of the experimental setup showing polystyrene latex (PSL) particle in a glass capillary subject to an oscillating electric field. The electrolyte solution is characterized by its viscosity (), conductivity (ke), permittivity (), and salt concentration (n0). (b) The Debye length (-−1) decreases as a function of NaCl concentration becoming smaller than the Bjerrum length () at 0.3 M and the ions themselves (ca. 0.3 nm) above 2 M. (c) An illustration of the EDL at two different salt concentrations highlighting the relevant length scales such as ion size, Debye length (shown on left and right edges for low and high salt, respectively), ion-ion spacing, and surface charge spacing (red semi-circles)...... 40

xi through a labview interface. The high speed camera was synchronized with the function generator through an external trigger port...... 46

Figure 3-3: Data analysis and filtering. (a)Fourier transform of the current data i(!) shows a peak only at the applied frequency. This observation suggests that particle motions at frequency 2!0 cannot be attributed to effects that depend linearly on the current. (b) Raw position vs. time for sPSL, showing that 0f0 velocity is so high that all other information is hidden due to it. (c) The filtered position, obtained by subtracting cubic splines fitted to the data split into 24 adjacent sections. This removes information only at low frequencies, f ≤ 24 Hz. The filtered position was used to calculate the fourier transforms shown in Figure 3-5 c,d. All data are for sPSL in 1 M NaCl, f0 = 300Hz and E = 829 V/m...... 47

Figure 3-5: Filtered position x(t) vs. time for a 2.9 m sPSL particle in (a) 10 mM NaCl for E = 1120 V/m and (b) 5.4 M NaCl for E = 733 V/m. Magnitude of the Fourier components for particle velocity |X()| as a function of frequency for (c) 10 mM and (d) 5.4 M NaCl, respectively. The red dot highlights the peak at the applied frequency f0 = 300 Hz. At high salt concentrations, an additional peak is seen at 600 Hz and attributed to field-induced thermal convection (section 3.4.1)...... 50

Figure 3-6: Phase of Fourier transform of position at f0 for (a) sulfated and (b) amidine- functionalized polystyrene latex particles. A phase of 0 implies ζ < 0 and a phase of ±π implies ζ > 0. For situations where the phase was neither of ±π or 0, the measurement was considered as noise...... 50

Figure 3-7: If the frequency of electric field is low (∼ 1 Hz), the ζ measured would be a function of the frequency22 due to electro-osmotic flow (EOF) from the capillary walls being transmitted to the center. (a) We show here that the measured ζ potential of sulfated PSL particles does not depend on frequency for f0 ≥ 300 Hz. Lower frequencies were not applied because electrode degradation led to strong flows. (b) The particle velocity at the applied frequency is linear with E (i.e., mobility does not depend on electric field). This validates that we are operating in the linear response regime...... 51

Figure 3-8: (a) and (b) X(20) plotted against electrical power for sPSL and aPSL for the salt concentrations where the non-linear effect was statistically significant (1-5 M). 2 The X(20) peaks are roughly linear with power (E ). (c) and (d) X(20) plotted against the velocity at zero frequency for sPSL and aPSL in NaCl for the same concentrations, showing that the two are correlated as can be expected from an E2 effect. (e) Phase for each peak at 20 showing that X(20) is in phase with the applied electric field, which is also a sine wave...... 56

Figure 3-9: (a) Zeta potentials of 2.9 m sPSL particles vs. concentration in five different monovalent salts. (b) Zeta potentials of 3.3 m aPSL particles vs. concentration in

xii

four different monovalent salts. Only data for high salt concentrations  100 mM are shown; see Figure 3-10 for a larger salt concentration range. The error bars represent 90% confidence intervals. The green curves show the prediction of the GC model assuming different surface charge densities. The solid curves are fits obtained for data in NaCl...... 58

Figure 3-10 ζ potential plotted against NaCl salt concentration on a logarithmic scale, for each of the 3 particles tested (circles) along with chi-squared fits for each particle (solid lines). The number below each particle name is the best fit value of σ...... 60 figure 3-11: (a) schematic illustration of the lattice model of a charged surface in a symmetric electrolyte. (b) electric potential within the simulation cell averaged over the 1 and 2-directions. the solid markers represent the average of 12 independent monte carlo simulations; the solid curves are predictions of the gc model; the x markers denote the zeta potentials. the simulation parameters are charge density, 휎 = 0.0625푒/ℓ2 and bjerrum length, 휆 = 2ℓ within a cell of dimensions 퐿1 = 퐿2 = 8ℓ and 퐿3 = 32ℓ; the salt concentrations are 푛푐 = 0.005ℓ − 3 (low salt) and 푛푐 = 0.32ℓ − 3 (high salt). (c) zeta potential vs. concentration for different three different  corresponding to conditions similar to experiments on spsl. the markers are results of the mc simulations; solid curves are the gc predictions of equation (3). simulation parameters are the same as in (b) unless stated otherwise...... 63

Figure 3-12: (a) Electric potential near a highly charged surface averaged over the 1 and 2- directions. The solid markers represent the average of 12 independent Monte Carlo simulations; the solid curves are predictions of the GC model; the x markers denote the zeta potential. The simulation parameters are 휎 = 0.0188푒/ℓ2, 휆 = 4ℓ, and 푛푐 = 0.32ℓ − 3 within a cell of dimensions 퐿1 = 퐿2 = 8ℓ and 퐿3 = 32ℓ . (b) Electric potential in the plane 푥3 = ℓ for a particular realization of the surface charge distribution; other parameters correspond to those in (a). (c) Effective zeta potentials 2 vs. concentration for three different  corresponding to conditions similar to experiments on aPSL. The markers are results of the MC simulations; solid curves are the GC predictions of equation (3). Simulation parameters are the same as in (a) unless stated otherwise...... 65

Figure 4-1: Lippmann diagram for the KCl-KBr system.The y axis is the sum of activity products of KBr and KCl and the x-axis shows both xKBr (mole fraction of KBr in solid) - and Br,aq (aqueous activity fraction of Br ). The plot consists of data generated by using a mathematical formulation of the thermodynamics as explained by Pollok et al15(p 217-220). Mathematica was used to calculate the curves...... 83

Figure 4-2: Solubility phase diagram for the KBr-KCl system. The top curve represents solid concentrations and the bottom cure, corresponding solution concentrations, connected by horizontal tie-lines. The curves were calculated using the mathematical formulation of the thermodynamics as explained by Pollok et al15 (p 217-220)...... 85

Figure 4-3: Electron microscopy images of partially replaced cross sections of (left) KCl crystal in saturated KBr solution for 푛퐵푟( 푎푞)푛퐾퐶푙(푠) = 50 and (right) KBr crystal in saturated KCl solution for 푛퐵푟( 푎푞)푛퐾퐶푙(푠) = 150, both at t = 30 mins. The scale bars are both 100 m...... 92

xiii Figure 4-4: Rim width vs. solution to solid ratio. Fluorescence optical microscopy images of dried cross-sections of partially replaced KBr (top row) and KCl (bottom row) crystals, at times 30 mins and 5 hours respectively, for varying solution to solid ratio shown at the bottom left corner for each image...... 93

Figure 4-6: Replaced rim thickness for KCl crystals in saturated KBr solution for various times and solution to solid ratios. Note that the 1.75 mm rim thickness point corresponds to the maximum rim thickness possible since it corresponds to complete replacement. Note that the first time-point corresponds to 30 mins...... 96

Figure 4-7: Effect of exposed surface area on KCl replacement, while keeping the volume of crystal constant...... 97

Figure 4-8: Top and middle: Secondary electrons (SE) images of the cross section of a replaced KCl crystal before (top) and after (middle) it was smoothed using ultra- microtomy. The squares in the middle image represent areas from which the spectrum was averaged to obtain each of the plotted points. Bottom: Solid composition of the rim of a partially replaced KCl crystal obtained through quantitative EDS measurements. The dark area to the right is the unreplaced KCl crystal. Solid lines are guide to the eye...... 99

Figure 4-9: Electron images of blade-cut cross-sections of partly replaced KCl crystals at various solution to solid ratios and times...... 102

Figure 4-10: (Top) SE2 image of the cross section of a replaced KBr crystal smoothed using ultra-microtomy. Bottom: Solid composition of the rim of a partially replaced KBr crystal obtained through quantitative EDS measurements. The non-porous area to the very right is the unreplaced crystal. The white boxes show regions from which spectral data was averaged to get each point on the plot...... 103

Figure 4-11: A zoomed in section of the crystal shown in Figure 4-9 The crystal is oriented perpendicularly to that in Figure 4-9 so that the squares numbered 36-38 lie at the same distance from the replacement front. EDS data was acquired from the regions marked Map Data 36, 37 and 38...... 106

Figure 5-1: Schematic showing how an enhanced porosity from mineral replacement could increase gas yields. Higher the surface area exposed to the replacing fluid, greater the additional porosity generated through replacement...... 119

xiv Figure 5-2: Iceland spar calcite crystal (left), calcite crystals after hammering, sieving and washing (middle), sample S01 (see Table 5-3) calcite crystals after replacement for 6 days (right)...... 124

Figure 5-4: Parr High P and T cell we used for calcite replacement. The vessel can fill upto 50 mL and can go upto 5000 psi and 350 0C. The reactor was pressurized with air...... 127

Figure 5-5: FESEM images of calcite crystals soaked in 2 M phosphate (buffer P1, pH 8.11) for 6 days at (a) 50 C and (b) 200 C ...... 131

Figure 5-6: Rim width vs. pH at 50 and 80 C. FESEM images of cross-sections of calcite crystals after replacement for 3 days in various buffers described in Table 1...... 133

Figure 5-7: Mean and maximum rim thickness observed for calcite crystals as a function of pH, in 3 days...... 134

Figure 5-9: Speciation diagram of phosphate plotted by doing a pH sweep in Visual Minteq with 2 M phosphate at 50 C. The plot at 80 C (not shown here) shifts by less than half a pH point...... 137

Figure 5-10: EDS map of sample S03 (buffer P2, pH 5). (a) Electron image and (b), (c) elemental maps of phosphorous and carbon respectively overlaid on the electron image, for a cleaved calcite crystal from S03 removed at 6 days...... 139

Figure 5-11: Plot of rim thickness with time for S3 – calcite in pH 5 at 50 C, with and without mixing. The error bars are standard deviations calculated based on the variations in thickness from a single image...... 140

Figure 5-13: S90, Runaway reaction with mixing at pH 5. Left : Crystals in one of the 3 bags suspended in the reaction were transformed from separate crystals to one big white mass, taking shape of the bag. (b) The solution had a gelatinous precipitate of white nanoparticles which did not settle in 2 weeks...... 143

xv Figure 5-14: FESEM images of outside surfaces of replaced crystals. At 2.2 M (image a), the outer surface has roughness on a much smaller length-scale than at 0.5 M (image b) without mixing. In the presence of mixing, the outer surface at 2.2 M does not change much (image not shown) but at 0.5 M, the outer surface has much finer roughness due to mixing (image c). These images correspond to the rim cross-sections shown in Figure 5-12...... 144

Figure 5-15: Replacement along a fracture. FESEM image and EDS maps (carbon and phosphorous respectively) of the cross-section of a crystal from the experiment with buffer P2 with 1 mM Ca+2 added...... 145

Figure 5-16: (Left)Cumulative mercury intrusion pore volume as a function of pressure for various partly replaced crystals (S03, S07, S10) and untreated calcite crystals.(Right) Differential intrusion volume against equivalent pore diameter on a logarithmic scale. The area under the curve corresponds to total intrusion...... 146

Figure 5-17: Z-projections of maximum fluorescence from confocal microscopy. Crystals (a)-(c) were soaked in dye without pre-cutting, while (d) was cut before soaking. Crystals in (e) were saw-cut crystals rather than fractured crystals, replaced in buffer B15 (acetate) instead of P2 (HCl) used for (a)-(d) for 12 days...... 147

Figure A-1: Schematic illustration of the lattice model...... 161

Figure A-2: Average potential φ (scaled by e=4π퓵) as a function of position x3 (scaled by 퓵) as computed by the lattice model (black circles). Here, the simulation cell is L1 = L2 = 8퓵 by L3 = 32퓵 and contains M = 4 surface charges and N = 20 ion pairs; the inverse temperature is β = 1. The error bars represent 95% confidence intervals based on ten independent simulations. The open circles represent the average ζ- potential, which is assumed equal to the electric potential at x3 = 0.5퓵. The solid curve shows the solution to the nonlinear Poisson-Boltzmann equation for the same conditions...... 164

Figure B-1: Brownian rotational quenching and alignment near a planar surface (a) Left: Selection of frames from fluorescent microscopy videos (15 µm x 15 µm field of view) for fluorescent platinum-polystyrene (PS) Janus spheres of varying radii, the PS side of the colloid appears bright (a), near to a planar interface in de-ionized (DI) water, and in 10 % aqueous H2O2 solutions. Right: Polar angle, ϴ(t) for typical Janus particles determined from fluorescent microscopy videos (Note the a=2.4 µm particle in water shows strong gravitational alignment constraining ϴ close to 0° ). (b, c) Schematic 3D orientation and experimental trajectories (45 seconds duration, red line) for Pt-PS Janus particle with radius a = 1 µm in (b) DI water settled under gravity against a planar glass substrate and (c) 10 % H2O2 solution at either the top (+g) or bottom (-g) planar surface of a rectangular glass cuvette. (d) Polar Mean Square Angular Displacement (MSAD) as a function of time for three differently-sized Janus spheres. In each graph, the black “Water” line represents the MSAD for Janus particle settled at a planar interface under gravity in water (n>20). The additional curves represent the MSAD for Janus particles with speeds in the defined ranges, at both the top (n>20) and bottom (n>20) planar surfaces of a rectangular cuvette...... 174

xvi Figure B-2: Particles moving along geometric boundaries, at speeds of up to 10 µm/s. (a- b) schematics of Janus particles encountering multi-planar geometries. Red axis indicates forbidden rotations due to proximity to a plane, green axis indicates unquenched axis of rotation: (a) Janus particle encountering a planar edge while moving along a 2D surface, expected to result in Brownian rotational quenching about two orthogonal axes. (b) Janus particle confined within a square groove; parallel vertical walls confine the rotational diffusion about one axis; however, if the particle descends to the base of the groove, it is confined about two orthogonal axes. (c-f) Overlaid still frames from fluorescence microscopy videos with equal time gaps: yellow line shows complete trajectory, green line shows location of vertical cuvette walls, red arrows indication direction of motion: (c) a = 1.55 µm Janus particle (10 % H2O2) moving at the bottom of a rectangular glass cuvette a long way away from the edges. (d) a = 1.55 µm Janus colloid (10 % H2O2) moving along the curved edge of a glass cuvette – inset shows a colloid reaching the cuvette boundary. (e) a = 2.4 µm Janus colloid (10 % H2O2) moving along the straight edge of a glass cuvette- left hand inset shows a magnified region, right hand inset shows a “stuck” aligned agglomerate formed at the cuvette boundary. (f) a = 2.4 µm Janus colloid (10 % H2O2) moving within a rectangular section groove (width = 8.75 µm). (g) SEM image of a section of the rectangular grooves (widths 7-9 µm) used in (f)...... 177

Figure B-3: Electrophoretic behaviour for Janus colloids. (a) Schematic representation of the rotational electrophoresis experiment. Left hand side shows the relevant physical quantities, a Janus sphere with hemispheres with two different zeta potentials (Pt and PS), giving a dipole vector 풆. The dipole vector rotates in an electric field, and the right hand side 3D schematics depict the effect of switching the direction of E. 1. Represents the initial misaligned dipole and applied field orientation immediately after the E field direction is switched, stages 2-5 show two possible rotations to re- align the dipole with the applied field: on the left hand side about an out of plane axis, with constant polar angle, ϴ, and on the right about an axis parallel to the plane where polar angle changes; at position 5 풆 reaches the steady state. The black arrows show the direction of translational motion, which is always aligned with the applied field (see b). (b) Typical position vs. time curves obtained by tracking a Janus particle (a = 2.4 µm) above a glass interface with E = 2.5 V/cm in 1 mM NaCl. E pointed in the negative x direction first and then switched every second. The red circles are times when E changed directions. (c) Typical  vs. time curve for rotation of a Janus colloid (2.5 V/cm, 5 % H2O2, 1 mM NaCl). We changed the direction of E after the particle aligned with the applied field. (d) f() vs. t for (b), from equation 21 (see Methods). (e, f) show still frames from a fluorescence microscopy video for a Pt-PS Janus particle rotating about an out of plane axis (e) and about an axis parallel to the plane (f) from the point at which the applied E-field polarity was reversed to the depicted direction (red arrow). (g) Measured zeta potentials for both Pt (blue markers) and PS (red markers) at two time points following sample preparation, each with and without hydrogen peroxide...... 180

Figure B-4: Schematics of the colloidal swimmer near a substrate, showing the geometry (a) and the surface slip velocity flow field (b) indicates the direction of propulsion...... 183

Figure B-5: MSAD data re-scaled to allow comparison with theory, together with fits to equation 16 with estimated values for B (see equation 10)...... 187

xvii Figure B-6: Schematics of the colloidal swimmer near a substrate, showing the field lines created by the image distribution and 퐄퐢퐦퐚퐠퐞 at the location of the Janus sphere (a), and the real electric field lines (b)...... 190

Figure B-7: Calibration of cell for electrophoretic measurements. (a) Markers represent experimentally measured velocities of sPSL particles as a function of height from the centre. The solid line represents the best fit parabola using spsl and wall as parameters in Bowen’s equation. (b) Shows the spsl and wall calculated from the fit in fig a for 2 independent trials, C1 and C2. The last row shows the spsl measured using Malvern Zetasizer...... 204

Figure B-8: Relationship between particle size, fuel concentration and velocity. Average propulsion velocity versus fuel concentration. Supplementary Figure 1 shows the mean velocity as a function of hydrogen peroxide (H2O2) concentration for all of the Pt-PS (Platinum-Polystyrene) Janus particles investigated in section 1. “Top” refers to particles swimming at the top surface of the cuvette, and “Bottom” to particles sediment at the bottom of the cuvette...... 207

Figure C-2: Essential mechanism of electrolyte diffusiophoresis. The mechanism consists of two parallel additive phenomena: electrophoresis caused by an in-situ electric field (E) generated by a concentration gradient (or more precisely, a chemical potential μ gradient) of NaCl, and chemiphoresis caused by a gradient of NaCl concentration, and therefore a gradient of pressure in the EDL, tangential to the particle surface. This pressure gradient drives fluid flow along the particle surface inside the EDL. For a β negative salt like NaCl, both mechanisms transport the negatively-charged particle towards higher ionic concentration...... 220

Figure C-3: Diffusiophoretic velocity increases and dominates over convective velocity with reduction in porosity. 20 mM NaCl is rejected by an ideal semipermeable membrane with water flux of 23 LMH. Porosity change is time dependent, and also depends on the type of salt (훃) and particle zeta potential 퐩. With higher values of 훃 and 퐩 the diffusiophoretic velocity increases further...... 228

Figure C-4: Generating gradients by diffusive mixing in the laboratory. (a) 2 cm long and 0.15 m thick glass capillaries were filled with different concentrations of a solute and placed in a petri dish that contained no solute91. At the mouth of the capillary, two solutions of different concentrations meet, creating a concentration gradient. (b) A capillary was filled with salt solution and one end was sealed off. The other end was dipped into a bigger capillary that served as a reservoir containing only DI water14. Again, two salt concentrations were placed adjacent, giving a gradient...... 234

xviii Figure C-5: Boundary Layer Diffusiophoresis (BLDP). (a) A transverse salt gradient is created due to the concentration boundary layer as the DI water from outer reservoir flows diffusioosmotically on the inner capillary that contains 10 mM NaCl or KCl. This causes tracer particles to deflect towards the walls due to BLDP as they enter the capillary102. (b) & (c) Tracks of tracer particles as they enter from the outer capillary containing DI water into the inner capillary containing 10 mM NaCl in (b) and 10 mM KCl in (c). The deflection towards the wall is attributed to BLDP. The deflection is small in this case since KCl has a much lower  value14...... 237

Figure C-8: A schematic of diffusiophoresis in crystallization: A small seed crystal of size r0 is spontaneously formed, with density,, radius r0 and >0 (say). Its formation depletes salt of -value, over a length scale R so that the salt concentration goes from saturation, Cs to that of the supersaturated bulk, Cb. The d\Debye length in bulk is - 1. The salt gradient gives rise to a spontaneous electric field and the particle moves towards higher salt concentration as indicated by the direction of udp...... 246

xix LIST OF TABLES

Table 3-1: Zeta potentials of sPSL particles averaged over 1 M to 5.5 M for each salt. The uncertainties are calculated as root mean square of the 90% confidence intervals for the measurement for each salt concentration, for each salt...... 60

Table 5-2: Buffer compositions used for replacement experiments. * mono refers to ammonium phosphate monobasic as the source of phosphate...... 124

Table 5-3: Conditions for experiments reported. All experiments were carried out with fractured crystals...... 125

Table 5-4: Conditions for additional mixing experiments...... 142

Table A-1: Summary of zeta potential measurements ...... 167

Table B-1: Measured values of zeta potential of the Janus particle, platinum and polystyrene halves of the Janus particle in water and 5% H2O2 at time 10 mins and 60 mins. This table shows the actual values of the zeta potential measured for each particle and the averages for each trial, referenced in Figure 3g of the manuscript. The averages indicate very good consistency within a batch and the intra-batch variability is similar for trials with and without H2O2. Thus it is clear that the method of subtracting velocities of tracer particles in the presence of bubbles is effective in removing the effect of complex convective flows around a bubble...... 182

Table B-2: Diffusion coefficients parallel to a wall (D||) and the corresponding gap heights (h) of a suspension of Janus colloids in both water and KNO3 solution at 21oC. Values in brackets are the standard deviation of the mean values...... 200

Table C-1: Categories of concentration gradient origins. Some of the systems “known” to involve diffusiophoresis (DP) are recent discoveries (e.g., diffusive mixing). Also, for some of the categories, the authors are not aware of any known examples in the literature...... 216

Table C-3: Chemical reactions given in the literature that produce diffusiophoretic transport...... 232

Table C-4: Summary of the effects of externally induced diffusiophoresis...... 240

xx ACKNOWLEDGEMENTS

This Dissertation resulted from an almost 5 years long journey through successes and failures, thrills and disappointments, fear and excitement of the unknown. And for this journey, I want to thank my fellow travelers, mentors, guides, friends and rest-houses on the way.

I want to thank my advisor and the greatest teacher ever - Darrell Velegol who guided me through this journey, just as Krishna guided Arjuna in the Geeta. Time spent learning from him not just about colloids, but also about life and about generally staying afloat in a world that’s always running have contributed a great deal in making me a ‘doctor of philosophy’ in the real sense of the word.

Next I want to thank my mom and dad for standing by me in this hopeless labor of love. I want to thank them for believing that if I pursued this love for research, it will certainly take me somewhere, even if they – or I – didn’t know where this ‘somewhere’ was when the journey began. I want to thank them for raising me up to dream big things and to ignore the crowd, and I only follow their examples in what I do.

Coming to my partner in crime and in life, my husband Siddhartha, I am not sure if I should thank him for the dissertation or the dissertation for him. We met on our first journey to Penn State and he has been a witness and the greatest fellow traveler ever on this journey right from day 0. I want to thank him for his beautiful company along the way, his very useful advise that served as a balancing act against my own nature, and for our favorite leisure together – food.

I would also like to thank my in-laws for standing by me in the ups and downs of graduate school, offering me wisdom, strength and patience in times when I absolutely needed it. I want to thank my sister and brother-in-law, who were my go to place for every vacation. Apart from offering a

xxi vacation home, they have brought to life my nephew Saharsh – a 1 year old little bundle of joy. His each little triumph on the journey of ‘growing up’ is an inspiration to me to keep fighting.

I want to also thank my lab-mate Rajarshi Guha for his help, ideas and advice, Sruti who was my first collaborator at Penn State and who taught me the first things around the lab, Abhishek for his inspiring ideas some of which led me to the questions in my thesis and Farzad for long-winded discussions about science, behavior, culture, sexism and food. I want to thank Charles Cartier and

Sambeeta Das who I much enjoyed working with and learning from. I am thankful to undergraduate student Ibrahim who lent a helping hand in my pursuits in the lab, and Alex for his tenacity and good questions.

I am grateful to the many professors who taught me, collaborated with me or mentored me at Penn

State through research, courses and offering valuable feedback being on my thesis committee. I very much enjoyed and learnt immensely from collaborating with Prof. Kyle Bishop, Prof.

Ayusman Sen, Prof. Manish Kumar and Prof. Christopher Gorski at Penn State. Courses taught by

Prof. Kyle Bishop, Prof. Ali Borhan, Prof. Scott Milner, Prof. Kristen Fichthorn, Prof. Christine

Keating, Prof. Kwadwo Osseo Asare and Prof. Jim Adair all shaped my knowledge and thought process that have helped me write this dissertation. Money isn’t everything but certainly, my research would not have been possible without it. I am grateful to Dow Chemicals, NSF MRSEC,

NSF CBET and Halliburton that provided funding for my research.

This work would also not have been possible without my friends Fish, Peng, Animesh, Soumalya,

Sreemoyee, Sravani Di, Sambeeta and Wenjie who always seemed to appear each time I needed company and always willing to share food that I very much enjoyed cooking for them. Last but not the least, I must acknowledge the contribution of tea, coffee and the various cafes in State College where I wrote my thesis - Café Lemont, Webster’s and Barranquero café, Lila Yoga Studio, my

xxii go-to place for keeping my sanity and audible for the greatest source of knowledge and endless entertainment to recharge me for more writing.

Chapter 1

Motivation and Research Goals

1.1 Motivation

The objective of this thesis is to answer questions about the behavior of saturated salt systems from the perspective of surface charge, fluid flows and dissolution-precipitation reactions. Saturated salt solutions exposed to colloidal particles or surfaces are encountered in a broad range of scientific, industrial and medical problems – in the natural processes that transform rocks1 and degrade building materials2, in methods of enhanced oil recovery3,4 and carbon dioxide capture5, in the synthesis of simple6 or designer inorganic particles7 and even in finding a cure for kidney stones8.

In each of these systems, colloidal particles or surfaces interact with each other and with the saturated salt solution. However, our understanding of these systems is often empirical, rather than fundamental. Creating simpler models of these complex systems based on an understanding of the fundamentals is essential to be able to scientifically control, improve, or tailor them to specific applications. This thesis addresses the gap in our knowledge from primarily two perspectives that each involve fixed or mobile surfaces in saturated salt solutions – (i) zeta potential and electrokinetics, and (ii) mineral replacement caused by dissolution – precipitation reactions.

Aqueous saturated salt solutions – solutions saturated with respect to a particular salt crystal – abound in nature, and by definition, contain a surface in chemical equilibrium with the solution.

Consider for example, a simple picture of a geological reservoir that contains limestone walls and sodium chloride deposits in equilibrium with the surrounding water – a salt solution saturated with

2 respect to CaCO3 and NaCl (Figure 1-1). The reservoir also contains droplets of oil and other colloidal particles such as clay particles. The interactions of each of these interfaces - the walls, the oil droplets, and the clay particles - with each other and with the solution lead to changes in the system over time. A key problem in our systems of interest is predicting and controlling such changes in the system namely, material transport, adhesion, chemical composition and material properties. These changes ultimately depend upon the physical and chemical interactions such as those arising due to surface charge or chemical reactions such as dissolution and precipitation. The phenomena of surface charge, and dissolution-precipitation form the subject of this dissertation, as discussed below.

A measure of charge at the interface is provided by the zeta potential, which is a key property involved in adhesion and electric field driven transport of fluid and particles. A starting point for my work on zeta potential was an important discovery that increased oil yields - the discovery that pumping low salinity fresh-water instead of high salinity sea-water gives rise to enhanced oil

3 recovery from geological reservoirs9. The mechanism of this behavior is still a subject of debate, but two possible explanations hinge on the existence of a zeta potential on exposed surfaces in the system. First, Tang and Morrow showed that the salinity dependent yield was contingent upon the presence of colloidal particles10. They further proposed that repulsive or attractive electrostatic interactions could have a role to play since these are salt concentration dependent colloidal interactions10. Secondly, Kar et al11 showed that salt concentration gradients could drive fluid flow and the transport of oil droplets suspended in water provided that surfaces and particles had a finite zeta potential. This was based on the phenomenon of electrolyte diffusiophoresis12, the transport of fluid at a charged surface or of charged particles in the presence of a salt concentration gradient

(Figure 1-2). Thus, two possible explanations of enhanced oil recovery with low salinity brines each relied on the presence of a finite charge on colloidal particles or oil droplets under reservoir conditions – typically high salt and saturated.

Figure 1-2: Charged surfaces in salt concentration gradients can cause flows in dead-end pores through diffusiophoresis. However, the presence of a finite zeta potential under high and saturated salt conditions (for eg. 5.3

M NaCl) is neither known nor easy to test. The primary difficulty is that at high salt concentrations the existing theory is not applicable and existing experimental measurement methods do not work.

The first key contribution of this dissertation is an electrophoretic technique to measure zeta

4 potential of model polystyrene latex particles at high salt conditions (5.3 M NaCl). Our measurements reveal a finite zeta potential up to saturation which continue to follow the theory developed for low salt concentration for some particles even after major assumptions of the classical theory break down.

The second set of contributions in this dissertation focus on pseudomorphic mineral replacement reactions (pMRRs). pMRRs, also called coupled-dissolution-reprecipitation (CDR) reactions are reactions where the space occupied by a parent mineral comes to be occupied by a guest mineral, such that the external morphology of the parent mineral is preserved and porosity is created in the guest phase13–15. These fluid-mediated reactions cause changes in the chemical composition as well as material properties such as porosity and hardness. We hypothesized that these reactions when carried out controllably in a geological reservoir could enhance oil recoveries by creating additional porosity when used in conjunction with conventional mechanical fracking used by oil companies

(Figure 1-3). In modern fracking operations commercialized in 1949 in a patent16 licensed to

Halliburton, fluid is pumped at high pressure to mechanically rupture the rocks, thereby creating fluid pathways for the oil to flow out. We aimed to find the solution composition that would cause pMRR of a reactive reservoir rock such as calcite to create additional porosity in the fracking process, creating chemical-mechanical-fracking.

Figure 1-3: Our hypothesis of chemical-mechanical fracking. pMRR at the fractured surfaces would create additional porosity, opening up more volume for fluid flow. Carrying out and controlling this reaction under reservoir conditions requires sound knowledge of the mechanism. However, the mechanism of these reactions is poorly understood, especially the inter-relationships and relative contributions of thermodynamics, kinetics and fluid transport. In the second part of my thesis, I have tried to build a better theoretical understanding of the replacement process by studying the model replacement system KBr-KCl. An overarching question in this investigation was coming up with general principles to better predict and control mineral replacement reactions, such that these principles are applicable to both high and low solubility systems. I have questioned some of the assumptions that have prevented a better understanding of this system so far. I have contributed to understanding the mechanism of replacement and reconciling many existing results by performing well-controlled experiments to measure the rates of replacement and composition of fluid under a variety of conditions.

Building on a better understanding of the replacement process, I studied the far more complicated and much less understood replacement system – calcite in phosphate solutions, for application to increasing porosity in calcitic geo-reservoirs. In this work, I mapped the replacement process under

6 conditions that were relevant to our intended application but have never been traced before.

Through my systematic investigations, I have contributed not only the conditions necessary for chemically generating micro-porosity in calcite, but also a deeper understanding of the replacement process.

1.2 Research Goals

In this dissertation, I sought to answer questions about the behavior of saturated salt systems from the perspective of surface charge, fluid flows and dissolution-precipitation reactions. Below is a brief look at the three problems I worked on. The description below provides the specific questions investigated, the approach and the key results obtained.

1. Zeta potential at high and saturated salt conditions

What is the zeta potential on model polystyrene latex particles under high and

saturated salt conditions (eg. 5 M NaCl)? How does the zeta potential depend upon

the surface functionalization or salt type?

2. Mineral replacement in the KBr-KCl system

(a) How does the rate of replacement of KCl (or KBr) crystals in saturated KBr (or

KCl) solutions vary with solution to solid ratios and fluid mixing?

(b) What is the composition of the replaced layer for each of the above systems as a

function of position in the crystal? How do these composition differences relate to

the thermodynamics and fluid transport rate?

3. Chemical micro-fracking of calcite through mineral replacement

7 (a) What is the dependence of rate of calcite replacement in 2 M phosphate solutions

on the pH in the range 4-8, at 50 and 80 C? Does the rate of replacement correlate

with the pH dependent rate of calcite dissolution?

(b) What is the increase in porosity generated by pMRR in comparison to bare crystals,

and how deep does it penetrate into the crystal?

1.2.1 Zeta potential at high salt and saturated salt conditions

What is the zeta potential on model polystyrene latex particles under high and saturated salt conditions (eg. 5 M NaCl)? How does the zeta potential depend upon the surface functionalization or salt type?

Most interfaces attain a surface charge in water such as solid-liquid (particles), gas-liquid (bubbles) or liquid-liquid (emulsion droplet) interfaces17. The charge may be a result of ionization of surface groups or due to adsorption of ions from solution. This surface charge is characterized by an electrical potential which is equal to the zeta potential () at the slipping plane. The surface charge attracts counter-ions which form the electrical double layer (EDL) (Figure 1-4). The classical theory of electrokinetics – the Gouy-chapman theory – predicts that the zeta potential is directly proportional to the surface charge density () and is inversely proportional to the square root of salt concentration17. Under the usual assumption of a constant surface charge, the theory predicts that the zeta potential becomes very small at high salt concentrations. However this theory is not expected to work at salt concentrations greater than about 140 mM where its assumptions of no ion-ion correlations and point-sized ions breaks down18.

Figure 1-4: Zeta potential and electrical double layer for a negatively charged particle in water

For particles in salty media, one might therefore anticipate that the structure of the EDL and the corresponding zeta potentials will differ significantly and qualitatively from expectations built largely on the study of dilute electrolytes. It is critical to identify and understand these differences in order to predict the behaviors of colloids in salty environments such as human blood

(≈150 mM), seawater (≈600 mM), wastewater (≈2 M during reverse osmosis), and geological reservoirs (≈5 M). The standard methods used to determine zeta potentials of particles at low ionic strengths are often inapplicable at high salt concentrations, and therefore, few studies reliably report zeta potentials for colloidal particles at high ionic strength. We are especially interested in zeta potential at saturated salt conditions, where the assumptions of classical theory break down most dramatically.

This led me to my questions – What is the zeta potential on model polystyrene latex particles under high and saturated salt conditions (eg. 5 M NaCl)? How does the zeta potential depend upon the

9 surface functionalization or salt type? In this work I have investigated these questions for model polystyrene latex particles which are commercially available, have been well characterized and studied extensively by other researchers at low salt concentrations. However, the measurement technique is applicable to any colloids large enough to be seen by optical microscopy and with density close to that of the medium such as oil droplets and bacterial cells suspended in water.

In this dissertation, I describe an electrophoresis based technique using sinusoidal electric fields and high speed microscopy that we developed to carry out these measurements. Electrophoresis is the motion of charged particles when subjected to an electric field with a velocity proportional to the applied electric field and to the particle’s zeta potential12 (Figure 1-5). The displacement of the particles at high salt was small and noisy, but the use of Fourier transforms enabled the resolution of the velocity at the applied frequency. This was used to calculate the zeta potential.

Figure 1-5: Electrophoresis of a particle with positive zeta potential. Particle velocity, u is directly proportional to the electric fields and zeta potential on the particle’s surface. My measurements show that not only is the zeta potential finite and measurable up to saturation, it is also in accordance with the classical Gouy- Chapman theory for sulfated polystyrene latex particles even after critical assumptions of the theory are violated. While the zeta potential is too small to stabilize these particles electrostatically against aggregation, it is high enough to cause a

10 measurable electrokinetic transport under the influence of applied electric fields (3 – 10 V/cm) or spontaneous electric fields created by salt concentration gradients (diffusiophoresis). Additionally, for amidine functionalized polystyrene latex particles, I find a reversal in zeta potential between

0.5 – 1 M salt, most prominently for KBr among the salts we tested. This is the first observation of charge reversal for particles in simple monovalent salts. Lastly, I also present Monte-Carlo simulations of a simple lattice model of the electrical double layer that support the experimental results.

The development of a simple, reliable technique to carry out zeta potential measurements at high salt is a major advance in this field. This is especially so since commercial instruments often fail to give reliable measurements at high salt, and are effectively black-boxes that contribute further to a lack of reliability. While we focused on saturated salt concentrations here, I anticipate that this technique would be of much use in biological sciences where bodily fluids – urine and blood have high salt concentrations, at the borderline of the range of applicability commercial instruments.

Scientifically, the finding of a finite charge at high salt that follows the classical theory is an important first step in developing the electrokinetic theory for saline aqueous solutions and for the emerging field of ionic liquids.

1.2.2 Mineral replacement in the KBr-KCl system pMRRs, also called coupled-dissolution-reprecipitation (CDR) reactions are fluid mediated mineral replacement reactions where the space occupied by a parent mineral comes to be occupied by a guest mineral such that the external morphology of the parent mineral is preserved and porosity is created in the guest phase13–15. These reactions proceed by dissolution of the parent phase into the fluid that subsequently gets saturated with respect to the guest phase and results in precipitation

11 (Figure 1-6). For pMRR to proceed, the replaced phase must contain porosity so that internal surface can get exposed to the fluid that mediates the reaction.

Figure 1-6: Schematic of mineral replacement of parent AB by a porous layer of the guest AC, mediated by a solution of AC. For replacement to proceed, the interfacial fluid contacting the phase AB should be saturated. pMRRs can be observed in high solubility systems such as KBr crystal in saturated KCl solution, and low solubility minerals such as the replacement of calcium carbonate to hydroxyapatite when exposed to phosphate solutions. Recently, these reactions have found application in new material synthesis and in this thesis I have tried to use it to enhance the porosity in geological reservoirs.

The reactions are also widespread in nature, yet poorly understood owing to a complex inter- dependence between the three primary factors – thermodynamics, kinetics and transport. In order to use it for industrial applications, it is desirable to understand the mechanism of these reactions clearly. With the objective of getting closer to creating a mathematical model of the replacement process, I studied pMRR in the KBr-KCl system. This high salt system has been used previously by researchers as a model system where replacement proceeds within the time-frame of a few hours,

12 and the thermodynamics of the system are well-known19–21. An interesting property of this system is that replacement of KBr in saturated KCl proceeds much faster than that of KCl in saturated KBr.

My questions below try to find the causes and consequences for this difference.

The complete replacement of a 3 mm KBr crystal in saturated KCl solution happens within 2 hours, resulting in a porous KCl crystal. But the reverse reaction – KCl crystal in saturated KBr solution was reported to stop within a few minutes (Figure 1-7). The difference between the two cases has been attributed to the fact that KBr has a larger lattice size and higher solubility than KCl. This, according to previous researchers are the two factors that control porosity in the replaced phase, and a higher porosity leads to a higher replacement rate as more surface area is exposed. However, we hypothesized that solid to solution ratio, as well as fluid transport must also play a role in the replacement process, and could potentially change the outcome, speed and extent of replacement.

(or KBr) crystals in saturated KBr (or KCl) solutions vary with solution to solid ratios and fluid mixing? I hypothesized that I might be able to control the reaction through solution to solid ratios and transport rate. The solution to solid ratios are known to affect the end point of the reaction for

13 KBr in KCl system, but its effect on the rate of pMRR has not been studied. Additionally, the effect of transport has been completely left out of previous studies even though the dissolution of highly soluble salts is generally transport controlled. In my experiments, I found that for solution to solid molar ratios in the range 1-50, KCl replacement in KBr depends on the ratio such that if the ratio is 1, replacement stops in 2 hours but when the ratio is 50, an entire 3 mm crystal can be replaced in 18 hours. On the contrary, KBr crystals are completely replaced for all the ratios tested within 1 hour.

Next, I asked the question - What is the composition of the replaced layer for each of the above systems as a function of position in the crystal? How do these composition differences relate to the thermodynamics and fluid transport rate? To answer this question, I carried out replacement experiments of KCl and KBr, and then measured the composition over an internal cross-section of the replaced crystal using quantitative Electron Dispersive Spectroscopy (EDS or EDX). These measurements showed the presence of gradients in Br:Cl ratio in the rim, as a function of position within the crystal. The solid composition could be related directly to solution composition within the crystal through a mixed solid-solution equilibrium relationship. Through this, I concluded that the solution found in the pore space of the replacement rim in a KCl crystal has a far steeper concentration gradient than the solution in the rim of KBr crystals. This behavior correlates directly with the reduced porosity, slower internal transport rate and subsequently a lower rate of replacement of KCl than KBr.

My study of these reactions helps show that the KBr-KCl reaction can proceed both ways, and that internal transport is the rate limiting factor in KCl replacement. Additionally, it provides many insights into the mechanism that are essential in the formulation of a mathematical model for this system that can eventually help us design replacement reactions for various industrial applications.

14 1.2.3 Chemical micro-fracking of calcite through mineral replacement pMRR of calcite could be used as a way to generate porosity in calcite-rich oil and gas reservoirs, which could result in significant economic benefit. The literature reports replacement of calcite in ammonium hydroxy phosphate (NH4)2HPO4 solutions and in sodium fluoride NaF. Of these, I have considered the use of phosphate rather than fluoride since pumping fluoride in large quantities under the earth might be hazardous for ground water resources. For application to geological reservoirs, we are interested in T between 50-80C. However, previous studies of calcite replacement in 2 M phosphate report replacement at high T (120C ≤ T ≤ 200C) and no replacement for T ≤ 80C. Previous studies have also hypothesized that dissolution is the rate limiting step for this replacement. Since the kinetics slow down at low temperatures, we hypothesized that lowering the pH might allow us to increase the rate of replacement at lower temperatures.

This led me to my first question – What is the dependence of rate of calcite replacement in 2 M phosphate solutions on the pH in the range 4-8, at 50 and 80 C? Does the rate of replacement correlate with the pH dependent rate of dissolution? To answer this question, I performed replacement experiments of calcite in buffers at various pHs in the range 4-8, containing 2 M phosphate and measured the replacement rim width at 3 days through electron microscopy images.

At 50 C, I found that the replacement width was roughly monotonic with pH and followed the expected dissolution rate – the highest replacement was at the lowest pH. But at 80 C, the replacement width was non-monotonic, unlike the dissolution rate. The highest replacement at 80

C was obtained at pH 7, clearly suggesting that the dissolution rate alone isn’t controlling the rate of replacement, and that the more complex precipitation rate may need to be accounted for.

15 Having obtained some replacement, we are interested in getting a high porosity on a controllable and observable time scale of days, preferably with low concentrations of added salts. This brought me to my second question - What is the increase in porosity generated by pMRR in comparison to bare crystals, and how deep does it penetrate into the crystal? For porosity measurements, I used mercury intrusion porosimetry of replaced crystals and found a 10-fold increase in the porosity of calcite replaced for 6 days at 50 or 80 C compared to untreated calcite. To measure the depth of penetration, I soaked replaced crystals in a fluorescent dye for a day and then used confocal microscopy to see how far into the crystal the dye had penetrated. Through these experiments, I found that the dye can penetrate into the crystal at a mm scale even though the rim width is <100

m. This deep penetration is only found in crystals with internal fractures, showing that it is due either to ‘opening up’ access to pre-existing fractures, or due to replacement proceeding much faster at internal fractures.

These reactions have previously been studied from a geological and synthesis perspective for several decades but I have for the first time investigated pMRR from the perspective of enhanced oil recovery, mapping the replacement behavior in regimes that were never tested before – a range of pH, medium temperatures and fairly long times (up to 12 days). While this work focused on calcite, further work might permit the use of pMRR to generate porosity in sandstone or clays.

Previous studies of calcite replacement focused on high temperatures ( T >= 120 C) and failed to find any replacement at lower temperatures. A key contribution of this work is the finding that replacement can be achieved at these low temperatures by setting the right pH of the phosphate solution. Another key contribution is quantifying the total porosity as well as it’s quality – the depth of pores using dye penetration confocal microscopy.

16 1.3 Organization of the thesis

Chapter 2 sets up a theoretical background on the definition, significance and measurement techniques for zeta potential. Chapters 3,4 and 5 form the main body of new findings during the course of my dissertation, and each of these is structured as a stand-alone project. Chapter 3 discusses the zeta potential work, chapter 4 discusses the work on pMRR in the KBr-KCl system, and chapter 5 describes the work on pMRR of calcite. Chapter 6 concludes this work by discussing the scientific significant of this work, applications and possible paths for future work.

Appendices 1-3 continue the discussion on electrokinetics and colloids after Chapters 2 and 3.

Appendix 1 presents details of the theoretical model for Monte Carlo simulations of the electrical double layer at high salt concentrations, done in collaboration with prof. Kyle Bishop. Appendix 2 is derived from a manuscript I co-authored on the steering of active Janus particles close to boundaries. Appendix 3 is derived directly from a review paper on diffusiophoresis written in collaboration with Prof. Darrell Velegol, Rajarshi Guha, Dr. Abhishek Kar and Prof. Manish

Kumar. As a whole, the present work presents techniques to probe the physics and visualize the fluid flows in saturated salt solutions.

All the work presented here has major individual contribution from me, but was done collaboratively. Each of the chapters 3-5 and the appendices A-C has a section each on contributions and acknowledgements to credit these people who were collaborators, mentors or staff without whose assistance this dissertation would not have been possible. The work in Chapter

3, and appendices A-C consists of work already published in the academic literature. The credits for this work have been given appropriately in a footnote one the first page of each of those chapters.

17 1.4 References

(1) Putnis, A. Mineral Replacement Reactions. Rev. Mineral. Geochemistry 2009, 70, 87–124.

(2) Flatt, R. J. Salt Damage in Porous Materials: How High Supersaturations Are Generated. J.

Cryst. Growth 2002, 242, 435–454.

(3) Austad, T.; Shariatpanahi, S. F.; Strand, S.; Black, C. J. J.; Webb, K. J. Conditions for a

Low-Salinity Enhanced Oil Recovery (EOR) Effect in Carbonate Oil Reservoirs. Energy

and Fuels 2012, 26, 569–575.

(4) Alvarado, V.; Manrique, E. Enhanced Oil Recovery: An Update Review. Energies, 2010, 3,

1529–1575.

(5) Pruess, K.; Müller, N. Formation Dry-out from CO2 Injection into Saline Aquifers: 1.

Effects of Solids Precipitation and Their Mitigation. Water Resour. Res. 2009, 45.

(6) Gupta, A. K.; Gupta, M. Synthesis and Surface Engineering of Iron Oxide Nanoparticles

for Biomedical Applications. Biomaterials 2005, 26, 3995–4021.

(7) Guo, Y.; Zhou, Y.; Jia, D.; Tang, H. Fabrication and Characterization of Hydroxycarbonate

Apatite with Mesoporous Structure. Microporous Mesoporous Mater. 2009, 118, 480–488.

(8) Adair, J. .; Aylmore, L. a. .; Brockis, J. .; Bowyer, R. . An Electrophoretic Mobility Study

of Uric Acid with Special Reference to Kidney Stone Formation. J. Colloid Interface Sci.

1988, 124, 1–13.

(9) Morrow, N.; Buckley, J. Improved Oil Recovery by Low-Salinity Waterflooding. J. Pet.

Technol. 2011, 63, 106–112.

(10) Tang, G. Q.; Morrow, N. R. Influence of Brine Composition and Fines Migration on Crude

Oil/brine/rock Interactions and Oil Recovery. J. Pet. Sci. Eng. 1999, 24, 99–111.

18 (11) Kar, A.; Chiang, T.-Y.; Ortiz Rivera, I.; Sen, A.; Velegol, D. Enhanced Transport into and

out of Dead-End Pores. ACS Nano 2015, 9, 746–753.

(12) Anderson, J. Colloid Transport By Interfacial Forces. Annu. Rev. Fluid Mech. 1989, 21, 61–

99.

(13) Putnis, A. Mineral Replacement Reactions: From Macroscopic Observations to

Microscopic Mechanisms. Mineral. Mag. 2002, 66, 689–708.

(14) Altree-Williams, A.; Pring, A.; Ngothai, Y.; Brugger, J. Textural and Compositional

Complexities Resulting from Coupled Dissolution–reprecipitation Reactions in

Geomaterials. Earth-Science Rev. 2015, 150, 628–651.

(15) Pedrosa, E. T.; Putnis, C. V.; Renard, F.; Burgos-Cara, A.; Laurich, B.; Putnis, A. Porosity

Generated during the Fluid-Mediated Replacement of Calcite by Fluorite. CrystEngComm

2016, 18, 6867–6874.

(16) Reistle Jr Carl E. Method of Treating Earth Formations. US 2547778 A, 1949.

(17) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic

Press, 1981.

(18) Storey, B. D.; Bazant, M. Z. Effects of Electrostatic Correlations on Electrokinetic

Phenomena. 2012, 56303, 1–11.

(19) Putnis, C. V.; Mezger, K. A Mechanism of Mineral Replacement: Isotope Tracing in the

Model System KCl-KBr-H2O. Geochim. Cosmochim. Acta 2004, 68, 2839–2848.

(20) Pollok, K.; Putnis, C. V.; Putnis, a. Mineral Replacement Reactions in Solid Solution-

Aqueous Solution Systems: Volume Changes, Reactions Paths and End-Points Using the

Example of Model Salt Systems. Am. J. Sci. 2011, 311, 211–236.

19 (21) Kar, A.; Mceldrew, M.; Stout, R. F.; Mays, B. E.; Khair, A.; Velegol, D.; Gorski, C. A. Self-

Generated Electrokinetic Fluid Flows during Pseudomorphic Mineral Replacement

Reactions. Langmuir 2016.

Chapter 2

Theoretical background on Electrokinetics

In this chapter, I introduce the major concepts that form the basis of the work on zeta potential and electrokinetic transport in this dissertation. The zeta potential () is a key parameter that is a measure of the surface charge on a particle or surface. In what follows below, I discuss the definition, applications, classical theories and measurement techniques for  potential. Next I provide a background on colloidal forces which will enable us to appreciate the challenges in colloidal formulation, especially at high salt concentration.

Lastly, I discuss two electrokinetic phenomena – electrophoresis and diffusiophoresis which depend on the

 potential. This is intended to set a theoretical background that will help understand the motivation, questions, techniques and applications of my work on zeta potential.

2.1 Definition of zeta potential and the electrical double layer

Most particles attain a surface charge in water which may be due to several reasons such as ionization of surface groups as in the case of sulfate groups or silica groups, or due to adsorption of ions on the surface.

This surface charge is characterized by a potential called the surface potential, 휓0 on the particle surface.

The surface charge attracts counter-ions from the solution which form the electrical double layer (EDL). In a fairly simple picture of the double layer, it is thought to consist of a fixed layer of counter-ions held firmly close to the surface, called the Stern layer, and a diffuse layer where the counter-ions are more loosely attached, called the Gouy Chapman (GC) layer. While the Stern layer consists mostly of counter-ions, the diffuse layer consists of both counter-ions and co-ions, with a deficit of co-ions. Over the diffuse layer, the potential drops to zero as we go from the Stern layer to the neutral bulk of the solution.

Since the Stern layer is fixed on the surface of the particle, it forms a slip plane1. The potential at the slip plane is defined as the zeta potential,  which can usually be estimated using measurements of electrokinetic parameters. Since under most situations 휓0 is not directly measurable, it is approximated to be the zeta () potential.

Figure 2-1: Zeta potential and electrical double layer for a negatively charged particle in water

2.1.1 Examples and estimates

 potential of most particles and surfaces in water is negative, typically in the range -15 mV to -150 mV at

1 mM NaCl. Examples of surfaces with negative zeta potential at close to neutral pH include oil droplets2, dust particles3, sulfated4 or caboxylated5 polystyrene latex particles, glass or silica surfaces6 and platinum particles7. Some of these surfaces may become positively charged upon lowering the pH, such as silica or carboxyl surfaces. Positively charged surfaces are less common in nature, but adsorption of positively charged species such as multivalent cations8, eg. Ca+2, proteins9 and surfactants10 can make surfaces positively charged. Synthetic positively charged particles such as amidine-functionalized polystyrene

22 latex11 particles are made positive by functionalization with amidine groups or other positively charged groups. Within the approximation of a thin Debye layer (a >> 1), the  potential reduces in magnitude with salt concentration.

2.2 Applications of zeta potential

The sign of the  potential – positive or negative – can be easily obtained based on experimental measurements, and usually its magnitude can also be estimated based on electrokinetic models. This ability to probe a fundamental surface property by experimental means makes it powerful in understanding many things about the system. Here are some applications of the zeta potential:

1. Surface charge density: By applying theories of zeta potential, an estimate of the surface

charge density can be made. Another independent estimate of surface charge density can be

obtained by other means such as titration. Comparing these two estimates provides us insights

into the solid-solution interface, into the charging of surface groups, arrangement of ions

around the charged surface and adsorption of ions from solution.

2. Electrostatic forces: Zeta potential is one of the key parameters in estimating the electrostatic

forces between particles and/or surfaces. Electrostatic forces play an important role in

stabilizing colloidal suspensions against aggregation, or in adhesion of colloids (such as

particles or bacteria) to surfaces.

3. Electrophoresis: The zeta potential is directly proportional to the speed with which a charged

particle moves in an electric field. Electrophoresis is used to separate proteins on the basis of

their charge. Electrophoresis is also responsible for the motion of charged particles in a salt

concentration gradient where an electric field is generated internally, through a phenomenon

called diffusiophoresis. It is present in many natural situations or can be designed into the

system to our advantage. Another example where an internally generated electric field causes

electrophoresis is the autonomous motion of Pt-Au catalytic nanomotors.

4. Electro-osmosis: Fluid near a fixed, charged surface also moves under the application of an

electric field (electro-osmosis). Electro-osmosis is used as a mechanism to drive fluid flow or

mixing in microfluidic channels since it offers better control and mixing compared to pressure

driven flows.

5. Adsorption: When a surfactant, protein, polymer molecule or organic matter is adsorbed to a

surface, the zeta potential of the substrate can change in both magnitude and sign. The zeta

potential changes only up to the point of complete coverage. Therefore, zeta potential

measurements are often used to determine the extent of adsorption of a molecule on to a

substrate.

2.3 Classical theory of the EDL

2.3.1 Spatial distribution of charge – the Poisson-Boltzmann equation

The classical electrokinetic theory includes a description of the spatial distribution of potential or in other words, a description of the electrical double layer. The Poisson-Boltzmann (PB) equation gives the spatial distribution of the surface potential, 0. For a Z:Z electrolyte, it is written as :

푍푒 푍푒 2 ( 0) = 2 sinh 0 (1) 푘푇 푘푇

The Debye-Hückel parameter,  is a constant in this equation and depends mainly on the solution concentration, C∞. This is a very important parameter that we will come across repeatedly in this dissertation.

The inverse of  is the Debye length, 휅−1, which is the length scale over which the potential decays in the electrical double layer. For a Z:Z electrolyte, it is given as :

2 푍2푒2퐶 휅2 = ∞ (2) 휀푘푇

-19 -10 Where, e = charge on an electron = 1.602 x 10 C,  = dielectric permittivity of the medium = 6.9 x 10

C2/Nm2 for water at 298 K, k = Boltzmann constant, 1.38 x 10-23 J/K and T = temperature.

As can be seen from equation 2, the Debye length is proportional to the square root of concentration. Typical values of the Debye length span from ~ 100 nm in de-ionized water to 9.65 nm in 1 mM KCl, to 0.965 nm in 100 mM KCl.

2.3.2 Relationship between charge density and surface potential – the Gouy-Chapman model

In addition to a description of the spatial distribution of potential, the classical electrokinetic theory also describes the relationship between the surface charge density and surface potential. An approximate form of this relationship is obtained by using an approximate form of the PB theory - the linearized Poisson-

Boltzmann equation (the Debye- Hückel model) :

 = 0 (3)

푘푇 where  = surface charge density (C/m2). This approximation is only valid for small  , i. e.  ~ = 0 0 푒

25 푚푉. For large 0, solving the full PB equation gives the Gouy Chapman (GC) model of the EDL :

 푘푇 푍푒 4 푍푒  = 0  [2 sinh ( 0) + 푡푎푛ℎ ( 0)] (4) 푍푒 2푘푇 푎 4푘푇

In using these equations with experimental data, the surface potential, 0 is often approximated as the  potential which is a parameter more relatable to the experiments.

2.4 Methods of zeta potential measurement

 potential is usually measured using either microelectrophoresis, streaming potential or electroacoustics.

While the definition of  potential itself is ambiguous because the Stern layer cannot be located experimentally, these 3 techniques measure the same potential12.

2.4.1 Electrophoresis based techniques

Electrophoresis is the translation of charged particles when subjected to an electric field, with a velocity directly proportional to the  potential (see section 2.6.1). Micro-electrophoresis is used to measure the zeta potential of particles by measuring the electrophoretic velocity of individual particles using optical microscopy. This was accomplished using the Rank Brother’s instrument13 popular 2 decades ago and by its modern counterparts available commercially. The more popular modern measurement method uses light scattering instead of optical microscopy to observe the velocity of millions of particles in a few minutes, using Dynamic Light Scattering (DLS) found in instruments manufactured by Malvern and Brookhaven.

Usually a known electric field is applied across an electrophoretic cell and the  potential is calculated using

Eq 5 or the more detailed model of O’ Brien and White14. While DLS offers quick measurements for even nano-sized particles, electrophoresis using microscopy offers the ability to directly observe the particle in motion, allowing easy and unambiguous identification of erroneous behavior such as low stability, or changes in the particles appearance with time. Moreover, DLS requires knowledge of the scattering intensity of the surface and poses a problem when a single particle consists of 2 broadly different scattering intensities, as is the case with metal/polystyrene Janus particles discussed in chapter 3.

2.4.2 Streaming potential

When a known pressure gradient is applied across 2 ends of a fixed surface exposed to water, the pressure driven flow carries with it ions which leads to the generation of an electric current, called the streaming current. Measurement of this current by short circuiting the 2 ends of the surface externally allows estimation of the  potential.

2.4.3 Electroacoustics

When a sound wave in the MHz range is applied to a concentrated suspension, it sets the particles and fluid into motion. But since the particles are denser than the fluid, there is relative motion between particles and the fluid. This causes a charge separation because the Stern layer moves with the particles whereas the diffuse layer moves with the fluid. As these dipoles oscillate with the same frequency as the sound wave, an alternating current called the Colloid Vibration Current (CVI) is generated which is measured by externally short circuiting the two ends of the suspension. The magnitude of CVI is directly proportional to

 potential15. In this technique, the signal is enhanced by higher solids concentration and higher density difference between particles and the suspension. Thus, this technique is ideal for concentrated dispersions of high density contrast particles such as mineral particles, but very difficult to use for polymer latex particles or dilute suspensions.

Today, with the availability of much better video microscopy techniques and particle tracking algorithms, microelectrophoresis using microscopy is the answer to many challenging systems and this is the technique which will be used primarily in this work. There are several reasons for choosing this technique over the other two methods mentioned above. While the streaming potential technique is very popular for measurements on rock surfaces, it suffers from 2 distinct disadvantages – (1) the measurement relies heavily on accurate knowledge of the geometry of the surface which is not always possible or easily controlled, and

(2) its application for particles is not straightforward. The electroacoustic technique is not suited for dilute

27 systems which limits its use for active materials such as Janus motors which usually suffer from very low yields. Moreover, electroacoustic measurements are hard to interpret for polydisperse or heterogeneous systems. For example, water from shale gas reserves contains a variety of minerals such as silica, alumina, calcium carbonate, etc. which may also be of different sizes and densities. Under such conditions, only an average value may be obtained using electroacoustics which is usually not enough to predict the system stability.

2.5 Colloidal stability

Formulating stable colloidal suspensions is a classical problem in colloid and interface science. By stable suspension, we mean a suspension where the particles do not aggregate with each other because if they did, the settling rate would increase and the particles will fall out of suspension. Usually, this is not desirable.

For example, acrylic paints are concentrated colloidal suspensions and stability is necessary for a long shelf life of the paint. Other examples where making a stable formulation is an important industrial problem is in drug formulation, food, and cosmetics.

In some other cases, aggregation is desirable. For example, in order to separate milk into curd and whey, an acid such as lime or vinegar is added to a milk (a stable colloidal suspension) causing the suspended proteins to aggregate (or coagulate) and fall out of solution. Another example is the Salting-Quenching-

Fusion (SQF)16 technique of assembling colloidal doublets, developed in the Velegol lab.

The question then is why are particles attracted or repelled by each other, and how can we control this behavior? The answer lies in an understanding of the colloidal forces and energy. The sign, magnitude and spatial range of each of the colloidal forces controls the overall interaction of particles with each other or with other surfaces. In this section, I will introduce the DLVO theory of colloidal stability and the forces included in its description – electrostatic and van der Waals forces. A detailed description of the forces can be found in the classic book by Israelachvili17 or in the pedagogic book by Velegol.

2.5.1 DLVO theory

The DLVO theory of colloidal stability introduced by Derjaguin and Landau (1941) and Verwey and

Overbeek (1948) says that the total interaction between any two surfaces is given by the sum of van der

Waals forces (always attractive) and electrostatic forces (repulsive between surfaces with like charge). The total energy can be plotted as a function of distance between the particles in a DLVO plot, an example of which is shown in Figure 2-2. A positive energy on this plot indicates repulsive interaction and a negative energy represents attraction. The plot shows the sum of electrostatic and van der Waals energies as the solid blue line. In the example shown, the total energy is non-monotonic, going through a secondary minimum, a maximum and a primary minimum at negative infinity. The reason for such behavior lies in the different length scales over each the repulsive electrostatic and attractive van der Waals forces act.

The van der Waals forces between two surfaces are always attractive and relatively long range – the energy scales as 1/ for colloidal particles where  is the separation between particles (<< particle diameter. Also note this is unlike the behavior of van der Waals energy between atoms which scales at 1/6). The range of the electrostatic forces however, depends on the Debye length and acts up to about 3 Debye lengths away from the particle’s surface. Thus, the total interaction varies as a function of distance between the particles.

Figure 2-2: A sample DLVO plot. The parameters are :  potential = 100 mV, Debye length = 1 nm, particle diameter 2 µm, Hamaker constant = 1.4 x 10-19 J.

2.5.2 Rapid aggregation

When the DLVO plot looks like the one shown above, particles can aggregate into a secondary minimum if they come close enough. In this state, the particles can be separated by putting some energy into the system such as sonication for a few minutes. Thermodynamically, they would like to aggregate at the primary minimum where the energy is lowest, but the energy barrier, max (the height of the maxima) may be too high for them to do so in a practical time-frame. If the particles cannot attain the primary minimum, the suspension remains kinetically stable.

Particles do have the ability to overcome small energy barriers due to their thermal energy, given by kT.

So, if max~ kT, the particles can in fact overcome the barrier and go to the primary minimum within some

finite time-frame. When max  3kT, particles aggregate each time they collide and this is called the regime of rapid aggregation. For a suspension with particles of radius a and volume fraction , the rapid aggregation time scale is given by

푎3  = (5) 2푘푇

Thus, even for a suspension where there is no repulsive energy barrier, the volume fraction controls how long it takes to aggregate.

2.6 Electrokinetics

The study of the transport of particles or of fluid under the influence of an electric field is termed electrokinetics. A brief description of 2 electrokinetic phenomena – electrophoresis and diffusiophoresis is presented below. As we will see below, the electric field could be either externally applied or be generated internally.

2.6.1 Electrophoresis and electro-osmosis

2.6.1.1 Electrophoresis

When a particle with a  potential, p is subjected to an electric field, E it moves with an electrophoretic velocity given by the Smoluchowski equation18:

 퐸 푢 = 푝 (6) 푒푝 

Where u = electrophoretic velocity, and  = viscosity of the fluid. This equation is valid if the  potential is ~ kT/e = 25 mV and a >> 1. While this equation was derived for a spherical particle, it was shown by

Morisson19 that it is valid for a particle of arbitrary shape. For higher values of  potential, O’Brien &

White20 showed that the particle double layer undergoes polarization, lowering the electrophoretic velocity.

Thus, the electrophoretic velocity actually undergoes a maxima as  increases rather than the monotonic velocity increase with  as predicted by Eq 2.

2.6.1.2 Electroosmosis

When a fixed surface is exposed to a high dielectric constant protic solvent such as water, it similarly attains a  potential, w which leads to the formation of the EDL. In this case, the application of an electric field causes the motion of ions in the double layer called electroosmosis or electroosmotic flow (EOF), given by18

 퐸 푢 = − 푤 (7) 푒표 

2.6.1.3 Electrophoresis in a closed capillary

When an electric field is applied to a suspension in a closed capillary, the EOF from the glass surface causes a back-pressure at the closed end of the capillary which returns as parabolic back flow (Figure 2-3).

Figure 2-3: Fluid and particle velocity when an electric field is applied on fluid in a closed capillary.

Bowen21 has calculated the expression for velocity of a particle in a rectangular capillary as a function of height, z when the view is centered on the width of the capillary

32 cos(휋푧⁄2푏) 1 cos(휋푧⁄2푏) 푏2 [1 − ( − + ⋯ )] − 푧2 (8) −휀퐸 3 휋3 cosh(휋푎⁄2푏) 33 cos(휋푎⁄2푏) 푢(0, 푧) = [(1 − { })  −  ] 2 192푏 휋푎 1 3휋푎 푤 푝 휂 2푏 1 − (tanh + tanh + ⋯ ) 휋5푎 2푏 35 2푏

Where a = half width of the capillary, and b = half height of the capillary

Eq 4 is linear in p and w. When the u vs. z profile is measured experimentally, it can be used to obtain unique best-fit values of p and w. Another way often used to measure p is to simply measure the velocity at the stationary plane, also called Komagata plane where the fluid velocity is 0 in the cell. The velocity at this plane is entirely due to the particle’s motion. Though simpler in calculation, the accuracy of zeta potential determined by this method depends on the accurate location of the Komagata plane, and slight errors in locating the plane can result in large errors in the measured zeta potential.

2.6.2 Diffusiophoresis and diffusioosmosis

Diffusiophoresis is the chemically-driven transport of colloidal particles driven by a concentration gradient of solute, without the application of any outside force.22 There are two general types of diffusiophoresis: electrolyte and non-electrolyte. Electrolyte diffusiophoresis causes particle transport by generating spontaneous electric fields (electrophoresis)23 and pressure fields in the Debye layer (chemiphoresis)24,25.

Non-electrolyte diffusiophoresis (NEDP) also works by creating a pressure gradient across the particle due to particle-solute interactions, such as repulsive steric exclusion26,27 or attractive van der Waals interactions28,29, and this also is a type of chemiphoresis. Diffusiophoresis has been discussed in detail in this thesis in Appendix 3 which is based on a review article I co-authored.

2.7 References

(1) Lyklema, J. Water at Interfaces: A Colloid-Chemical Approach. J. Colloid Interface Sci. 1977, 58,

242–250.

(2) Kar, A.; Chiang, T.-Y.; Ortiz Rivera, I.; Sen, A.; Velegol, D. Enhanced Transport into and out of

Dead-End Pores. ACS Nano 2015, 9, 746–753.

(3) Roger, K.; Cabane, B. Why Are Hydrophobic/water Interfaces Negatively Charged? Angew. Chemie

- Int. Ed. 2012, 51, 5625–5628.

(4) Garg, A.; Cartier, C. A.; Bishop, K. J. M.; Velegol, D. Particle Zeta Potentials Remain Finite in

Saturated Salt Solutions. Langmuir 2016, acs.langmuir.6b02824.

(5) Behrens, S. H.; Christl, D. I.; Emmerzael, R.; Schurtenberger, P.; Borkovec, M. Charging and

Aggregation Properties of Carboxyl Latex Particles : Experiments versus DLVO Theory. 2000,

2566–2575.

(6) Evenhuis, C. J.; Guijt, R. M.; Macka, M.; Marriott, P. J.; Haddad, P. R. Variation of Zeta-Potential

with Temperature in Fused-Silica Capillaries Used for Capillary Electrophoresis. Electrophoresis

2006, 27, 672–676.

(7) Das, S.; Garg, A.; Campbell, A. I.; Howse, J.; Sen, A.; Velegol, D.; Golestanian, R.; Ebbens, S. J.

Boundaries Can Steer Active Janus Spheres. Nat. Commun. 2015.

(8) Oncsik, T.; Trefalt, G.; Csendes, Z.; Szilagyi, I.; Borkovec, M. Aggregation of Negatively Charged

Colloidal Particles in the Presence of Multivalent Cations. Langmuir 2014, 30, 733–741.

(9) Reynolds, E. C.; Wong, A. Effect of Adsorbed Protein on Hydroxyapatite Zeta Potential and

Streptococcus Mutans Adherence. Infect. Immun. 1983, 39, 1285–1290.

(10) Meyer, E. E.; Lin, Q.; Hassenkam, T.; Oroudjev, E.; Israelachvili, J. N. Origin of the Long-Range

Attraction between Surfactant-Coated Surfaces. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 6839–

6842.

(11) Borkovec, M.; Behrens, S. H.; Semmler, M. Observation of the Mobility Maximum Predicted by

Standard Electrokinetic Model for Highly Charged Amidine Latex Particles. Langmuir 2000, 16,

5209–5212.

(12) Delgado, a. V.; González-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. Measurement and

Interpretation of Electrokinetic Phenomena (IUPAC Technical Report). Pure Appl. Chem. 2005, 77.

(13) Bangham, A. D.; Flemans, R.; Heard, D. H.; Seaman, G. V. F. An Apparatus for

Microelectrophoresis of Small Particles. Nature 1958, 182, 642–644.

(14) O’Brien, R. W.; White, L. R. Electrophoretic Mobility of a Spherical Colloidal Particle. J. Chem.

Soc. Faraday Trans. 2 1978, 74, 1607.

(15) Dukhin, A. S.; Goetz, P. J. Characterization of Liquids, Nano- and Microparticulates, and Porous

Bodies Using Ultrasound; Elsevier, 2002.

(16) Yake, A. M.; Panella, R. a; Snyder, C. E.; Velegol, D. Fabrication of Colloidal Doublets by a Salting

out-Quenching-Fusing Technique. Langmuir 2006, 22, 9135–9141.

(17) Israelachvili, J. N. Intermolecular and Surface Forces: Third Edition; Academic Press, 2011.

(18) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press, 1981.

(19) Morrison, F. . Electrophoresis of a Particle of Arbitrary Shape. J. Colloid Interface Sci. 1970, 34,

210–214.

(20) O’Brien, R. W.; White, L. R. Electrophoretic Mobility of a Spherical Colloidal Particle. J. Chem.

Soc. Faraday Trans. 2 1978, 74, 1607.

(21) Bowen, B. D. Effect of a Finite Half-Width on Combined Electroosmosis - Electrophoresis

Measurements in a Rectangular Cell. J. Colloid Interface Sci. 1981, 82, 574–576.

(22) Anderson, J. Colloid Transport By Interfacial Forces. Annu. Rev. Fluid Mech. 1989, 21, 61–99.

(23) Lin, M. M.-J.; Prieve, D. C. Electromigration of Latex Induced by a Salt Gradient. J. Colloid

Interface Sci. 1983, 95, 327–339.

(24) Lechnick, W. J.; Shaeiwitz, J. A. Measurement of Diffusiophoresis in Liquids. J. Colloid Interface

Sci. 1984, 102, 71–87.

(25) Lechnick, W. J.; Shaeiwitz, J. A. Electrolyte Concentration Dependence of Diffusiophoresis in

Liquids. J. Colloid Interface Sci. 1985, 104, 456–470.

(26) Staffeld, P. O.; Quinn, J. A. Diffusion-Induced Banding of Colloid Particles via Diffusiophoresis: 1.

Electrolytes. J. Colloid Interface Sci. 1989, 130, 69–87.

(27) Staffeld, P. O.; Quinn, J. A. Diffusion-Induced Banding of Colloid Particles via Diffusiophoresis 1.

Electrolytes. J. Colloid Interface Sci. 1989, 130, 69–87.

(28) Sharifi-Mood, N.; Koplik, J.; Maldarelli, C. Molecular Dynamics Simulation of the Motion of

Colloidal Nanoparticles in a Solute Concentration Gradient and a Comparison to the Continuum

Limit. Phys. Rev. Lett. 2013, 111, 184501.

(29) Sharifi-Mood, N.; Koplik, J.; Maldarelli, C. Diffusiophoretic Self-Propulsion of Colloids Driven by

a Surface Reaction: The Sub-Micron Particle Regime for Exponential and van Der Waals

Interactions. Phys. Fluids 2013, 25, 12001.

Chapter 3

Particle Zeta Potentials Remain Finite in Saturated Salt Solutions1

3.1 Abstract

The zeta potential of a particle characterizes its motion in an electric field and is often thought to be negligible at high ionic strength (several moles per liter) due to thinning of the electrical double layer (EDL). Here, we describe zeta potential measurements on polystyrene latex (PSL) particles at monovalent salt concentrations up to saturation (~ 5 M NaCl) using electrophoresis in sinusoidal electric fields and high-speed video microscopy. Our measurements reveal that the zeta potential remains finite at even the highest salt concentrations. Moreover, we find that the zeta potentials of sulfated PSL particles continue to obey the classical Gouy-Chapman model up to saturation despite significant violations in the model’s underlying assumptions. By contrast, amidine-functionalized

PSL particles exhibit qualitatively different behaviors such as zero zeta potentials at high concentrations of NaCl and KCl and even charge inversion in KBr solutions. The experimental results are reproduced and explained by Monte Carlo simulations of a simple lattice model of the

EDL that accounts for effects due to ion size and ion-ion correlations. At high salt conditions, the model suggests that quantitative changes in the magnitude of surface charge can result in qualitative

1 This chapter has been adapted and reprinted with permission from A. Garg, C. Cartier, K. Bishop, D. Velegol, Particle Zeta Potentials Remain Finite in Saturated Salt Solutions. Langmuir, 32, 11837. Copyright 2016 American Chemical Society.

37 changes in the zeta potential – most notably, charge inversion of highly charged surfaces. These findings have important implications for electrokinetic phenomena such as diffusiophoresis within salty environments such as oceans, geological reservoirs, and living organisms.

3.2 Introduction

The zeta potential () of a colloidal particle determines the particle’s stability in solution and its motion in an electric field. Physically, this potential difference derives from the separation of charge bound to the particle’s surface (physically or chemically) from that of mobile counter-ions in solution. Charge separation over a finite length scale is driven by thermal fluctuations and gives rise to the so-called electric double layer (EDL). In the classical Gouy-Chapman (GC) model, this

−1 2 1/2 length scale is identified as the Debye screening length,  = (푘퐵푇/2푒 푛0) , which depends on the dielectric permittivity (  ), thermal energy ( 푘퐵푇 ), elementary charge ( 푒 ), and salt concentration (푛0) (here assuming a 1:1 electrolyte). Despite their widespread application and effectiveness, the GC model and its derivatives make a variety of assumptions that break down at high salt concentrations1 that approach saturation. Notably, these continuum descriptions neglect the finite size of ions and molecules2–4, which are actually larger than the predicted screening length in concentrated electrolytes (Figure 3-1b,c). Furthermore, the mean-field approximations used to describe electrostatic interactions fail to account for ion-ion correlations4–6 that ultimately guide crystallization from saturated solutions. At high salt concentrations, the predicted screening length

2 becomes smaller than the Bjerrum length,  = 푒 /4푘퐵푇, over which ion-ion correlations are significant7 (Figure 3-1b). For particles in salty media, one might therefore anticipate that the structure of the EDL and the corresponding zeta potentials will differ significantly and qualitatively from expectations built largely on the study of dilute electrolytes. It is critical to identify and understand these differences in order to predict the behaviors of colloids in salty environments such

38 as human blood ( 150 mM), seawater ( 600 mM), wastewater ( 2M during reverse osmosis), and geological reservoirs ( 5 M).

The standard methods used to determine zeta potentials of particles at low ionic strengths are often inapplicable at high salt concentrations. Methods based on electrophoresis measure the velocity of particles in an applied electric field. Application of such fields within concentrated electrolytes results in large electric currents that polarize electrodes and rapidly heat the sample. The resulting temperature variations can induce significant convective flows and complicate the estimation of fluid properties needed to infer particle zeta potentials (e.g., dielectric constant and viscosity). Due to such challenges, few studies reliably report zeta potentials for colloidal particles at high ionic strength. Dilute latex particle dispersions have been examined by phase angle light scattering

(PALS) for salt concentrations up to 3 M8,9 and by a combination of optical tweezers and high- speed microscopy up to 1 M10. Concentrated inorganic mineral particle systems have been examined using the electroacoustic method11–14 at salt concentrations as high as 3 M. These studies found finite zeta potentials for particles in 1-3 M monovalent salt solutions as well as concentration- dependent shifts in the isoelectric point12,14. However, we know of no reports that investigate particle zeta potentials at salt concentrations at or near saturation (5.4 M for NaCl) where finite size effects and ion-ion correlations are most pronounced. In strongly interacting charged systems (e.g., multivalent electrolytes), ion-ion correlations are known to drive counterintuitive phenomena such as charge inversion (also called charge reversal), whereby an excess of counter-ions binds to a charged surface to reverse its polarity15. Similar effects have been hypothesized for monovalent electrolytes near saturation. Additionally, it has been suggested that the EDL can never be thinner than the finite size of the counter-ions, leading to the failure of GC predictions at high ionic strength16. Within such thin double layers, changes in the structure of interfacial water may also contribute to charge separation and the associated zeta potential – even for uncharged surfaces13.

39 Investigating these and other interesting hypotheses requires experimental data on particle zeta potentials at saturated salt conditions.

Here, we describe a method for measuring particle mobilities up to saturated salt conditions and present data for polystyrene latex particles in several monovalent salt solutions (KCl, KBr, and

NaCl). We use electrophoresis with a sinusoidal electric field (300 Hz) to drive oscillatory particle motions, which are captured and quantified using high-speed video microscopy. An apparent zeta potential is then inferred from the measured mobility using the Smoluchowski equation. For negatively charged, sulfated polystyrene latex particles (sPSL), we find finite zeta potentials of

  − 20 mV at saturated salt conditions. Moreover, the measured zeta potentials and their dependence on salt concentration are found to be consistent – within experimental uncertainty – with predictions of the GC model despite violating many of its foundational assumptions. By contrast, positively charged, amidine-functionalized PSL (aPSL) exhibit more complex behaviors including charge reversal in KBr, LiCl and NaCl solutions. To guide the interpretation of our experimental results, we investigate a lattice model of the EDL that incorporates effects due to finite ion size and ion-ion correlations. By comparing the results of this model to those of the standard GC model, we explain how the latter can make successful predictions at even the highest salt concentrations for weak ion-ion coupling but breaks down when such coupling is strengthened.

Moreover, we show that breakdown of the GC model is accompanied by charge inversion, in qualitative agreement with experimental observations for aPSL. Our results indicate that electrokinetic phenomena – particularly diffusiophoresis17–20 – are present even in saturated salt solutions and may therefore contribute to the many transport processes occurring in oceans, geological reservoirs, and living organisms. 

41 3.3 Methods and Materials:

3.3.1 Measuring Zeta Potentials

We used the sinusoidal response of particles subject to a sinusoidal electric field to measure the electrophoretic mobility and thereby infer the zeta potential. In a typical experiment (see Figure

3-1a), a dilute suspension of polystyrene latex microparticles (diameter 푎  3 μm) in an aqueous electrolyte was flowed into a glass capillary. The particles were subject to an oscillating electric field of magnitude 퐸0 and frequency 푓0 = 휔0/2휋 directed along the length of a capillary, 퐸(푡) =

퐸0 sin(휔0푡). The motion of a single particle was captured using high-speed video microscopy, and its dynamic trajectory 푥(푡) was reconstructed using particle tracking algorithms (see below). For particles much larger than the screening length (휅푎 ≫ 1), the electrophoretic particle velocity 푢 is related to the applied field by the Smoluchowski equation21

 푢 = 휇퐸 = 푠푚 퐸, (1) 

where 휇 is the electrophoretic mobility, 휂 is the fluid viscosity, and 푠푚 is the Smoluchowski zeta potential. Integrating this equation, we obtain the following expression for the anticipated particle trajectory

푠푚 푥(푡) = − 퐸0 cos(휔0푡). (2) 휔0

The reported zeta potentials were obtained by linear regression of particle trajectories using equation (2).

42 3.3.2 Experimental Details

We collected data on three different types of surfactant-free, polystyrene latex particles (density,

 = 1055 kg/m3): sulfated PSL (radius, a =2.9 m; surface charge density,  = −9.7 C/cm2), carboxylated PSL(a = 3.2 m;  = −11.9 C/cm2), and amidine functionalized PSL (a = 3.3 m;

 = 34.9 C/cm2) henceforth denoted sPSL, cPSL, and aPSL, respectively. The particles were suspended at low volume fractions (10-5) into freshly prepared, aqueous solutions of ACS grade

NaCl, KCl, KBr, LiCl and CsCl. Salt solutions were freshly prepared and their conductivity was measured using a Hach H170 pH and conductivity meter. Conductivity measurements are shown in Figure 3-4 d. The measured current i, conductivity ke, and cross-sectional area of the cell A were used to determine the applied electric field as E = i/keA.

The suspension was drawn into an RCA-1 cleaned 1 x 1 x 50 mm glass capillary (Vitrocom) positioned on a glass slide and gold electrodes (ca. 1 cm of 16 strands of 0.003 inch diameter wire,

A M Systems) were inserted at each end. The capillary was sealed using Bondic UV glue and was immediately relocated to the microscope (Zeiss Axio Imager A1m upright microscope) stage for imaging. A 50x long working distance objective was used to focus in the central plane of the capillary (scale of 0.25 µm per pixel). A sinusoidal voltage was applied using a function generator

(Keithley Model 3390) and a voltage amplifier (Trek Model 2205); current through the circuit was monitored (Keithley 2612 A) using a LabVIEW interface (schematic in Figure 3-2).

The sinusoidal voltage had a frequency 푓0 = 300 Hz (Figure 3-2) and was applied for for 0.5 – 2 s. The measured current i, conductivity ke, and cross-sectional area of the cell A were used to determine the applied electric field as E = i/keA (E = 300 – 1000 V/m). Simultaneous to applying the voltage, the motion of a single particle was observed with a microscope using a 50x objective focused near the center of the capillary (scale of 0.25 μm per pixel). A high-speed camera (Phantom

43 v310) synchronized with the voltage source recorded the particle’s motion at 6000 frames per second. Gravitational forces induced particle motions perpendicular to the applied field; however, the particles remained in focus for at least 1 s – even in the densest electrolyte (4 M CsCl,  = 1498 kg/m3).

Our experimental setup was designed to mitigate a variety of challenges that arise when measuring zeta potentials at high salts. The use of AC fields was essential to avoid the rapid polarization of the electrodes at high salt concentrations, at which the electric current density can exceed 30 mA/mm2. To prevent oscillatory electroosmotic flows in the center of the channel, the applied frequency was chosen to be much faster than the rate of momentum diffusion over the width 푊 of the capillary – that is, 휔 ≫ 휈/푊2~1 s−1 where 휈 is the kinematic viscosity22. At the same time, the frequency was chosen to be small enough that field-induced particle displacements were clearly distinguishable from those due to Brownian motion. The cell was not thermostated; however, the temperature increase was mitigated by applying the voltage for short times to reduce heat generation and by using a narrow capillary to increase the rate of heat transfer to the surroundings.

At the highest power input of 1.3 W, the measured current and hence the conductivity increased by

3.9% in 2 s, which corresponds to a temperature increase of 1.9°C using a typical coefficient of conductivity variation23. Further details of the experimental set-up and problems encountered are discussed below.

44 3.3.2.1 Heat generation and convective flows

The cell was not thermostated; however, heat generation was minimized by applying the voltage for short times of 0.5-2 s and by using a cell with high surface to volume ratio. During a 2 s time period, we measured a change in current and hence conductivity of 3.87% for the highest electrical power of 1.3W. This corresponds to a temperature change of 1.9 ◦C using a typical coefficient of conductivity variation = 2 %/◦C.

Alternatively, we could estimate the temperature increase assuming that all heat dissipated

 by the ionic current contributes to heating the electrolyte in the cell: ∆T = iEtexp=ρcp = 12.2 C, where i is the measured current density (29.9 mA/mm2), E is the applied electric field (978 V/m),

3  texp is the measurement duration (2s), ρ is the density (1133 Kg/m ), and cp (4186 J/Kg/ C) is the specific heat. This gives a much higher value since it ignores the heat dissipated to the surroundings through the capillary walls. Even for short experiments and small temperature increases, natural convection cannot be avoided at the highest salt concentrations. As discussed in Section 2.4 of the

SI, thermally driven flows are responsible for steady particle motions and for those at two times the driving frequency. We emphasize that these effects do not impact electrophoretic particle motions at the driving frequency.

3.3.2.2 Gravity

We should emphasize that the electric field is horizontal while settling is vertical. Thus, our measurements are affected by gravity only to the extent that it causes the particles to go out of focus.

The polystyrene latex particles used have a density of 1055 kg/m3. Even for the densest suspension we used (4 M CsCl, ρ =1598 kg/m3), the particles rose at a rate of 2.3 µm/s, which kept them in focus for 1 s (with a numerical aperture of 0.55, the depth of field was 2.5 µm).

45 3.3.2.3 Electroosmotic flows

By contrast to thermal flows, electroosmotic flows are potentially problematic as they occur at the frequency of the applied voltage and could therefore interfere with measurements of electrophoretic particle motions. We prevented electroosmotic flows in the center of the channel by operating at sufficiently high frequencies. Oscillatory flows originating at the walls of the channel decay over a length (ν/)1/2, which is much smaller than the width of the channel. Thus, while EOFs are likely present near the channel walls, they are not present in the center of the channel where particle motion is measured. This reasoning is further supported by the agreement between particle zeta potentials measured at low salt conditions using our method and a commercial instrument.

3.3.2.4 Electrode polarization

The large flow of electrons produced for the high conductivity solutions used here can cause electrode polarization that can further lead to formation of bubbles. This is avoided by using a relatively high frequency alternating field (300 Hz). Also electrode surface area is increased by using bundles of 16 strands of gold wire as electrodes. We used bundled electrodes over blackened

Pt electrodes to increase surface area because this was a lot quicker than blackening, that requires an overnight operation.

Figure 3-2: Electronics and instrumentation. A function generator generated a sine wave that was amplified by the amplifier. The voltage from the amplifier was connected across the sample cell, and a Keithley source-measure-unit recorded the current through a labview interface. The high speed camera was synchronized with the function generator through an external trigger port.

3.3.3 Particle tracking and analysis

Dynamic particle trajectories x(t) along the length of the capillary were reconstructed from the recorded images at 10 nm resolution using the Trackmate plugin in Fiji24. Low frequency translational motions were removed by subtracting a smoothing spline fit to the noisy trajectory

(Figure 3-3).

𝑖푡 ∑ 푋()푒 , and examined the (complex) Fourier components 푋() to confirm the validity of equation (2) (see below). The mobility was obtained by performing a least squares fit of the filtered position data directly to equation (2) (Figure 3-4 a). In deriving the zeta potential from the electrophoretic mobility, it is important to recognize that the viscosity and the dielectric constant of concentrated electrolytes differ significantly from that of pure water. For example, the viscosity of saturated NaCl is 70% higher than that of water while the relative permittivity (휀푟 = 휀/휀0 where

휀0 is the permittivity of free space) is 50% lower. Failure to account for these changes leads to errors in the predicted zeta potential of more than 300%. We used literature data for the

48 concentration-dependent viscosity and dielectric constant for monovalent electrolytes summarized below (Figure 3-4 b,c) to best approximate the Smoluchoswski zeta potential from the measured mobilities (Figure 3-4 a).

Figure 3-4: (a) Mobility (u/E) vs. salt concentration for sulfated PSL in various salts. Error bars are obtained from 90% confidence intervals. (b), (c) data compiled for (b) viscosity25–27] and (c) relative permittivitys28–32; at T = 25 ◦C. (d) Measured conductivity for each of the salt solutions at T = 25 ◦C. For each condition (i.e., particle surface chemistry, salt, and concentration), the reported zeta potentials were obtained by averaging at least six measurements taken on different particles. The

90% confidence intervals reported in Figure 3-9 represent the larger of two errors: that obtained

49 from linear regression on each particle and that derived from the distribution of zeta potentials measured for various particles. Variations in the zeta potential from particle to particle were typically smaller than the 90% confidence interval for each particle, indicating good repeatability.

3.3.4 Method Validation

To confirm the validity of equation (2), we examined the Fourier components 푋() to assess their dependence on the applied frequency and field strength. Equation (2) implies that 푋() should be finite and real only at the driving frequency, corresponding to a pure cosine component at 0. At low salt concentrations (10 mM NaCl), the trajectories appear roughly sinusoidal, and the dominant

Fourier component was indeed that of the driving frequency 푓0 = 300 Hz (Figure 3-5 a,c). By contrast, at high salt concentrations (5 M NaCl), the sinusoidal motion of the particle is hardly visible above the noise; however, the Fourier component at the driving frequency can still be clearly resolved (Figure 3-5 b,d). We further confirmed (i) that the phase of 푋(0) was near 0 or ±π

(Figure 3-6), (ii) that the particle velocity 0푋(0) was linearly proportional to the field strength

(Figure 3-7), and (iii) that the inferred zeta potential was independent of the driving frequency

(Figure 3-7).

Interestingly, an additional component at two times the driving frequency 2푓0 was observed at high salt concentrations. The magnitude of this component increased linearly with the electric power supplied, indicating a second order dependence on the applied field (Figure 3-8 a,b). As detailed in the results section 3.4.1, we attribute these observations to thermally-induced convective flows, which depend on the rate of Joule heating within the capillary. Importantly, these effects are second order in the field and do not contribute to the first order, electrophoretic motions of interest here

(nonlinear electrophoretic effects are third order in the field as required by symmetry33).

Finally, we performed an independent validation of our measurement technique by comparing its predictions to those of a commercial PALS-based instrument (Malvern Zetasizer Nano ZS90) at lower salt concentrations. For 2.9 m sPSL particles in 1 mM NaCl, our setup gave a zeta potential of −110 ± 2.4 mV compared with −107 ± 4.8 mV from the commercial instrument.

52 3.3.5 Monte Carlo Simulations of the EDL

We performed Monte Carlo simulations of the EDL at high salt concentrations using the lattice restricted primitive model, which accounts for effects due to ion size and ion-ion correlations

(figure 3-11 a). In the model, ions are represented by point charges (±푒) positioned within a uniform dielectric medium onto discrete lattice sites separated by a distance, ℓ. Physically, the lattice spacing mimics effects due to ion size, and the parameter ℓ can be interpreted as the diameter of a solvated ion (typically, 0.2-0.5 nm). Initially, M surface charges, M counterions, and N ion pairs are distributed onto a rectangular simulation cell of dimensions 퐿1×퐿2× 퐿3. The surface charges are distributed at random within the 푥3 = 0 plane (figure 3-11 a) to create an average surface charge density of 휎 = 푒 푀/2퐿1퐿2 (the factor of two corrects for the fact that the surface is bounded by the electrolyte on two sides and not just one, as in experiment). Similarly, the 2푁 +

푀 ions are distributed at random onto bulk lattice sites (푥3 ≠ 0) to give a nominal salt concentration of 푛푐 = 푁/퐿1 퐿2 (퐿3 − ℓ) within the cell.

The positions of the ions are equilibrated using the Metropolis Monte Carlo algorithm34; those of the surface charges are fixed throughout the simulation. During each Monte Carlo move, two sites are selected at random and their contents swapped. If the move lowers the electrostatic energy of the system, it is accepted unconditionally. If it raises the energy of the system, it is accepted with probability p(Accept) = exp(−훥푈/푘푇) where 푘푇 is the thermal energy, and 훥푈 is the energy increase accompanying the change in ion configuration. For lower salt concentrations, several such lattice swaps are conducted during each Monte Carlo move to achieve an acceptance frequency of around 50%. During each simulation, the system is equilibrated for 5×105 attempted moves; the resulting distribution is then sampled over the course of an additional 5×105 moves. Each condition is simulated twelve times using different realizations of the surface charge distribution;

53 the final results are obtained by averaging over these realizations. The electrostatic energy 푈 is computed using the Ewald method34, which is described in detail in Appendix 1

The behavior of this model is fully specified by three dimensionless parameters: (i) the salt

−3 concentration within the periodic cell 푛푐 (scaled by ℓ ), (ii) the surface charge density 휎 (scaled

2 2 by 푒/ℓ ), and (iii) the Bjerrum length, 휆 = 푒 /4휋휀푘퐵푇 (scaled by ℓ), which characterizes the strength of ionic interactions. At room temperature (25 oC),  ranges from 0.71 nm in pure water to ~1.3 nm in 5 M NaCl, which is ca. 1 to 4 times the characteristic ion diameter (ℓ = 0.4 nm).

3.4 Results & Discussion

3.4.1 Particle Motions at Frequency 20

At high salt conditions (salt concentration ≥ 500 mM), we observe a second peak in the power spectrum at two times the driving frequency - that is, at 20 (Figure 3-5). We note that this peak is not seen in the current data (Figure 3-3). We hypothesize that this effect is due to convective flows that arise from electrically induced thermal gradients within the cell. Here, we present an analysis of these flows and provide additional experimental data that supports our hypothesis. We approximate the experimental cell as a long channel between two parallel boundaries separated by a distance 2H (Figure 3-1 a). Application of an electric field E(t) = E0 cos(0t) down the length of the channel results in a steady current density j(t) = keE(t), where ke is the constant conductivity.

Joule heating due to the electric current induces thermal gradients within the cell as described by the following equation for thermal transport

(3)

54 where ρ, cp, and k are the constant density, specific heat, and thermal conductivity of the electrolyte, and v is the convective velocity. The boundaries of the channel are modeled as

(4) where h is a heat transfer coefficient. Assuming there are no fluid flows (v = 0), this differential equation can be solved analytically to obtain the transient temperature distribution within the cell

(5) where Bi = hH/k is the dimensionless Biot number. Note that there are two contributions: one steady due to the time averaged heating within the cell; the other oscillatory with frequency 20. Both contributions have a characteristic temperature gradients of order , which increases with increasing electric field and with increasing conductivity (salt concentration). This temperature gradient can induce buoyancy-driven convection as captured by the so-called Boussinesq approximation35

(6) where ρ0 is the fluid density at some reference temperature T0, P is the dynamic pressure, g is the acceleration due to gravity, β is the thermal expansion coefficient, and ν is the kinematic viscosity.

In particular, we consider the case in which gravity acts in the z-direction (parallel to the channel but perpendicular to the field). The characteristic flow velocity can then be approximated by balancing buoyant and viscous forces (last two terms) to obtain

(7)

-6 2 -4 For 500 mM NaCl in water (ν = 1.0 × 10 m /s, β = 2.1 × 10 1/K, ke = 4.2 S/m) in an H = 500 µm

55 channel and subject to an E0 = 400 V/m field, this approximation predicts flow velocities of order

10 µm/s. As the flow velocity depends linearly on the temperature gradient, we anticipate both steady flows and oscillatory flows at frequency 20. Importantly, as these effects are second order in the applied field, they do not contribute to our measurement of the ζ potential, which is first order in the field. Finally, we note that the buoyancy-driven flows are not expected to impact the temperature gradients within the cell; convective transport with velocity v over the channel width

-2 H is slow compared to thermal conduction, vHρcp/k ∼ 10 << 1. This observation justifies our neglect of convection in equation 3 above.

Our putative explanation for particle motions based on field-induced, buoyancy-driven flows is further supported by experimental observations. First, the motion observed at 20 goes linearly with the square of electric field, or electrical power (Figure 3-8 a,b). Second, these effects are only observed at high salt concentrations where the electrical conductivity is large such that Joule heating becomes significant. This observation rules out explanations based on second-order electrokinetic effects such as induced-charge electrophoresis, which should also be present at lower salt concentrations. Third, oscillatory particle velocities at frequency 20 are of the order of magnitude suggested by the above analysis and correlate with steady particle velocities at 00

(Figure 3-8 c,d). This observation suggests that motions at 00 and 20 derive from a common origin - namely, a second-order effect whereby velocities depend on the square of the applied field.

Finally, we note that particle motions at 20 are quite variable from particle to particle, which likely reflects the spatial heterogeneity of flows within the cell.

Figure 3-8: (a) and (b) X(20) plotted against electrical power for sPSL and aPSL for the salt concentrations where the 2 non-linear effect was statistically significant (1-5 M). The X(20) peaks are roughly linear with power (E ). (c) and (d)

X(20) plotted against the velocity at zero frequency for sPSL and aPSL in NaCl for the same concentrations, showing that the two are correlated as can be expected from an E2 effect. (e) Phase for each peak at 20 showing that X(20) is in phase with the applied electric field, which is also a sine wave.

57 3.4.2 Zeta potential measurements of sPSL and aPSL

Our experimental zeta potential measurements are summarized in Figure 3-9 for negatively charged, sPSL particles (Figure 3-9 a) and for positively charged, aPSL particles (Figure 3-9 b) dispersed in a series of monolavent electrolytes. The measured zeta potentials of sPSL particles are negative at all salt concentrations and remain finite up to saturated NaCl concentration of 5.4 M (Figure 3-9 a).

Apart from fluctuations due to experimental uncertainty, the zeta potentials are roughly constant for each salt beyond 1 M (Table 1), ranging from ca. −20 mV for KCl to −40 mV for LiCl and comparable to the thermal potential of 푘퐵푇/푒 = 25 mV. The maximum salt concentration of 5.4

M represents the solubility of NaCl but is considerably lower than that of LiCl (13 M). We attempted measurements in saturated LiCl; however, the signal was overwhelmed by noise due to the ca. 13-fold decrease in the ratio / and thereby the particle mobility. A tabulated summary of all of our zeta potential measurements can be found in Appendix 1.

Figure 3-9: (a) Zeta potentials of 2.9 m sPSL particles vs. concentration in five different monovalent salts. (b) Zeta potentials of 3.3 m aPSL particles vs. concentration in four different monovalent salts. Only data for high salt concentrations  100 mM are shown; see Figure 3-10 for a larger salt concentration range. The error bars represent 90% confidence intervals. The green curves show the prediction of the GC model assuming different surface charge densities. The solid curves are fits obtained for data in NaCl.

59 For comparison, Figure 3-9 a also shows the zeta potentials predicted by the standard GC model, which relates the zeta potential to the surface charge density 휎 as

휎 2푘푇 푒 = sinh ( ) ≈  , (8) 휀 푒 2푘퐵푇

21 where the approximate equality is appropriate for small zeta potentials ( < 푘퐵푇/푒) . The charge density is estimated to be σ = −9.7 C/cm2 based on independent conductometric titrations36; however, this method is known to overestimate σ as it neglects ion conduction in the Stern layer37,38.

Therefore, we derived an additional estimate of σ = −5.1  0.16 C/cm2 for NaCl by fitting the GC model to the experimental data using nonlinear least squares regression. Only zeta potentials obtained at salt concentrations larger than 10 mM were used in the fitting process, as the assumption of constant surface charge is known to fail at lower concentrations for “hairy” particles39 such as

PSL. Even at 5 M salt concentrations, at which the predicted Debye length −1 = 0.12 nm is smaller than the ions themselves (e.g., 0.37 nm for Na), the continuum GC model provides a reasonable description of the experimental data. GC model fits for aPSL, sPSL and cPSL particles over a larger range of salt concentrations can be found below (Figure 3-10).

Salt KCl KBr CsCl NaCl LiCl

avg (mV) −18.8  7.0 −29.5  7.4 −28.9  7.6 −30.4  8.0 −40.1  7.4

By contrast to sPSL, zeta potentials of positively charged, aPSL particles exhibit qualitatively different behaviors at high salt concentrations (Figure 3-9 b). For each of the salts investigated

(KCl, KBr, NaCl and LiCl), the zeta potentials decrease to zero at high concentrations despite following closely the predictions of the classic electrokinetic model at low salt concentrations38.

Additionally, for KBr, LiCl, and NaCl, the zeta potentials change sign to become negative at concentrations above ~1M. Comparing the different salts, charge inversion is significantly more pronounced for KBr than KCl, suggesting that Br− counter-ions have higher affinity for the aPSL surface that Cl−. This trend is consistent with the Hofmeister series, which orders ions based on their ability to precipitate proteins40 and correlates with the extent of ion hydration41. Interestingly,

61 the co-ions also appear to influence the degree of charge inversion, with the magnitude of the effect increasing as Li+ > Na+ > K+. These observations indicate that the detailed structure of the EDL at high salt depends on the chemical identity of all ions present in the electrolyte. By contrast, the zeta potentials at low salt depend only on the ionic strength (independent of chemical identity) and perhaps the identity of some potential determining ions21 (e.g., hydroxide).

We do not think that the salt-specific effects could be explained by pH of the salts. The solutions are expected to have pH in the range 5-7 and the amidine group is a strong base (pka ~ 10-11) so that pH changes in the range 5-7 are not expected to vary the ionization state of these groups.

3.4.3 Stout and Khair zeta potential

Our reported zeta potentials are based on the Smoluchowski equation; however, we also considered the more rigorous treatment of Stout and Khair2 that accounts for ion steric effects3 and ion-ion correlations42 since we are in a regime where the Debye length (κ-1) is on order of the Bjerrum length (λB). This treatment accounts for ion steric effects and ion-ion electrostatic correlations. The relevant results from their work are presented in Figure 2 of their paper where the dimensionless mobility, M̃ e = 3ηMe/2ζSK is plotted on the y axis, against κR on the x axis, for different values of the dimensionless correlation length δc = κℓc. Here ζSK is the zeta potential calculated from the Stout and Khair treatment, ℓc is the correlation length, and R is the particle radius.

For our conditions, κR falls between 1578 (100 mM) to 15000 (4 M). For these values of κR, M̃ e has already reached an asymptote and does not depend on κR. The value of δc depends on the choice of ℓc which is bounded such that ℓi ≤ ℓc ≤ λB. Here ℓi is the size of an ion. Through κ and through changes in viscosity and dielectric constant, δc also depends on the salt concentration.

From these relationships, we find that at 100 mM, 0:3 ≤ δc ≤ 0:75, and at 4 M, 0:25 ≤ δc ≤ 1. For these values, we find that at 100 mM, 1:1 ≤ ζSK/ζsm ≤ 1:5, and at 4 M, 1:1 ≤ ζSK/ζsm ≤ 2.0.

Using the above analysis we find that the Stout and Khair zeta potential (SK) is consistently larger than the Smoluchowski zeta potential (sm). For example, in 4M NaCl, SK can be up to two times larger than sm depending on the choice of the correlation length. Importantly, we are operating in a regime where the Stout and Khair model predicts a significant mobility correction but no mobility reversal as observed in experiment. We chose to present our results in terms of the Smoluchowski zeta potential rather than SK or the raw mobilities for several reasons. First, the Smoluchowski equation normalizes the mobilities by a concentration-dependent factor / that provides numbers of comparable magnitude for a broad range of salt concentrations. Second, sm is considerable simpler than the Stout and Khair zeta potential and involves no unknown quantities such as the correlation length. Finally, the surface charge density implied by the zeta potential (equation 8) can be compared to that obtained by titration to provide additional information on the arrangement of ions in the EDL. Those readers who prefer to consider the measured mobilities directly can do so

(Figure 3-4).

3.4.4 Monte Carlo simulation of the EDL

figure 3-11: (a) schematic illustration of the lattice model of a charged surface in a symmetric electrolyte. (b) electric potential within the simulation cell averaged over the 1 and 2-directions. the solid markers represent the average of 12 independent monte carlo simulations; the solid curves are predictions of the gc model; the x markers denote the zeta potentials. the simulation parameters are charge density, 휎 = 0.0625푒/ℓ2 and bjerrum length, 휆 = 2ℓ within a cell of −3 −3 dimensions 퐿1 = 퐿2 = 8ℓ and 퐿3 = 32ℓ; the salt concentrations are 푛푐 = 0.005ℓ (low salt) and 푛푐 = 0.32ℓ (high salt). (c) zeta potential vs. concentration for different three different  corresponding to conditions similar to experiments on spsl. the markers are results of the mc simulations; solid curves are the gc predictions of equation (3). simulation parameters are the same as in (b) unless stated otherwise. To better interpret our experimental findings, we performed Monte Carlo simulations of the EDL at high salt concentrations using the lattice restricted primitive model (see Methods and figure 3-11 a). Despite its simplicity, this model offers insights as to how the continuum GC model breaks down (or not) at high salt concentrations due to finite ion size and ion-ion correlations. We first consider the case of small surface charge densities (휎 < 4휀푘퐵푇/푒ℓ) characteristic of sPSL particles

64 (figure 3-11 b,c). At low salt concentrations, when the Debye screening length is greater than the ionic radius (휅−1 > ℓ/2), the electric potentials predicted by the lattice model agree well with those of the continuum GC model (figure 3-11 b, low salt). At high salt, however, the lattice model presents a qualitatively different picture of the EDL, whereby an excess of counter-ions accumulates at the surface resulting in damped oscillations in the potential (figure 3-11 b, high salt).

Nevertheless, the zeta potentials predicted by the two models are remarkably similar. Here, the zeta potential is defined – somewhat arbitrarily – as the electric potential at 푥3 = 0.5ℓ, the plane separating the surface charge from the first layer of counter-ions. figure 3-11 c shows these zeta potentials as a function of salt concentration for three different values of the Bjerrum length  spanning the range found in experiment. Notably, there is strong agreement between the predictions of the MC simulations and the continuum GC model – even at concentrations above the critical value where 휅−1 = ℓ/2 (black x’s). Intuitively, one might guess that the zeta potential could never fall below  = 휎ℓ/2휀, which corresponds to all counter-ions located in the single layer closest to the surface. In fact, the over-adsorption of counter-ions in this layer leads to an even smaller zeta potential – one more closely in line with predictions of the GC model,  = 휅휎/휀.

These simulation results provide one possible explanation for the surprising success of the GC model in describing the experimental findings for sPSL particles.

For highly charged surfaces (휎 > 4휀푘푇/푒ℓ) such as that of aPSL particles, the zeta potentials predicted by the lattice model at high salt concentrations are significantly greater than the thermal potential (Figure 3-12 a). Moreover, the electric potential within the plane of the first counter-ion layer shows significant heterogeneity, with peaks and valleys separated by many times the thermal potential (Figure 3-12 b). Consequently, it is reasonable to expect that the ions in this layer will not move freely in the direction parallel to the surface upon application of an external field. These ions may instead form a tightly bound Stern layer that does not contribute to electrophoretic motion.

Figure 3-12: (a) Electric potential near a highly charged surface averaged over the 1 and 2-directions. The solid markers represent the average of 12 independent Monte Carlo simulations; the solid curves are predictions of the GC model; the 2 −3 x markers denote the zeta potential. The simulation parameters are 휎 = 0.0188푒/ℓ , 휆 = 4ℓ, and 푛푐 = 0.32ℓ within a cell of dimensions 퐿1 = 퐿2 = 8ℓ and 퐿3 = 32ℓ. (b) Electric potential in the plane 푥3 = ℓ for a particular realization of the surface charge distribution; other parameters correspond to those in (a). (c) Effective zeta potentials 2 vs. concentration for three different  corresponding to conditions similar to experiments on aPSL. The markers are results of the MC simulations; solid curves are the GC predictions of equation (3). Simulation parameters are the same as in (a) unless stated otherwise.

To approximate this scenario, we introduce a second potential denoted 2 and defined as the electric potential at 푥3 = 1.5ℓ, the plane separating the first and second ion layers. In qualitative agreement with experiments on aPSL particles, 2 is comparable to the thermal potential and changes sign upon increasing the salt concentration (Figure 3-12 c). This effect is more pronounced for larger Bjerrum lengths, which corresponds to stronger electrostatic interactions and stronger ion-ion correlations. These results suggest that electrostatic effects alone – neglecting

66 contributions due to solvation and dispersion interactions – can provide a suitable mechanism for the inversion of highly charged surfaces at high salt concentrations. At the same time, this simple model cannot explain differences among specific salts (except indirectly via the characteristic ion size, ℓ and the permittivity, 휀).

As noted above, the specific salt effects observed in experiment are largely consistent with expectations based on the Hofmeister series. Poorly hydrated counter-ions are expected to interact more strongly with hydrophobic surfaces such as PSL15,40 thereby reducing the magnitude of the zeta potential. Consequently, the zeta potentials of sPSL particles increase in magnitude as LiCl >

NaCl > KCl at high salt concentrations – in order of increasing ion hydration. Notably, the results for CsCl deviate from this trend. A similar argument can be made to explain the behavior of aPSL particles at high salt. The adsorption of an excess of counter-ions (Cl− or Br−) results in a negatively charged surface to which poorly hydrated co-ions adsorb more strongly (K+ > Na+ > Li+).

Furthermore, we note that charge inversion of positively charged, hydrophobic particles has been observed previously at lower salt concentrations for polyanions43 and for monovalent anions such as ClO4− and SCN−15. The salt concentrations required to induce charge reversal increases as SCN

− 9,15 (200 mM), ClO4− 15 (400 mM), and Br− (1 M, this study) – again consistent with the Hofmeister series.

Given the extreme thinness of the double layer at high salt concentrations, it is remarkable that continuum approximations to the dielectric permittivity and the liquid viscosity are so effective. In both the GC model and the lattice model, it is assumed that the dielectric constant in the EDL is same as that in the bulk, despite inevitable changes in water structure near the solid surface.

Nevertheless, we note that the characteristic electric field within the double layer is too small to induce significant alignment of water molecules therein.44 In relating the electrophoretic slip velocity and the zeta potential, it is assumed that the continuum equations of hydrodynamics are

67 applicable with a constant viscosity equal to that of the bulk liquid. This assumption is supported by previous experiments that reveal that the viscosity of a fluid approaches its bulk value over molecular dimensions45. The continuum hydrodynamic treatment also assumes the validity of the no slip boundary condition at the particle surface despite some evidence to the contrary46. One fortunate consequence of the thin double layer is that theories developed for flat plates – such as the present lattice model – provide an excellent approximation for the relatively large spherical particles studied here. Thus, the Smoluchowski equation should provide results very close to that of the model proposed by O’Brien and White that includes double layer polarization47.

Our observation of negative zeta potentials for positive aPSL particles at high salt can be explained by a combination of two effects: (1) the over-adsorption of counterions at the charged surface, (2) the displacement of the shear plane to enclose some of these counterions. Based on the MC simulations, the first effect is attributed to ion-ion correlations, which are increasingly significant at high salt concentrations. We attribute the second effect to the high surface charge of aPSL particles, which reduces the mobility of the most closely bound counterions. However, differences in the behavior of sPSL and aPSL particles may also result from differences in their “hairiness”39 due to dangling polyelectrolytes at the particle surface. For hairy particles, the shear plane encloses counterion charge even at lower salt concentrations resulting in a discrepancy between surface charge estimates from titration and from zeta potential measurements37,48–50. In our experiments, these discrepancies are more significant for aPSL particles than for sPSL particles. Consequently, the over-adsorption of counterions “behind” the shear plane at high salt concentrations could result in zeta potentials of opposite sign for aPSL (more “hairy”) but not for sPSL (less “hairy”). The

Ohshima model51 describes the electrokinetics of soft (i.e., hairy) particles; however, there are two key difficulties in applying this model to explain our experiments. First, we do not have a way to independently measure the frictional coefficient  of the polyelectrolyte layer, which is necessary

68 for a quantitative comparison. Second, the model relies on a mean-field treatment of electrostatics that does not allow for charge reversal as observed in our experiments for aPSL particles.

3.5 Summary and Conclusions

We have measured finite electrophoretic mobilities of negatively charged, sulfated PSL and positively charged, amdine-functionalized PSL particles up to saturation in NaCl, KCl and KBr.

Our measurements were made by applying sinusoidal electric fields in a disposable cell using high- speed microscopy to capture the particle motion. As a simple way for normalization of the mobilities, we have presented our results in terms of Smoluchowski zeta potentials. Equipped with zeta potential measurements, we attempted to test the validity of the classical mean field continuum

GC model at high salt concentration, approaching saturation.

At the outset we hypothesized that the continuum picture might break down as the electrostatic screening length, -1 becomes smaller than the hydrated ion size and the Bjerrum length, .

However, experiments indicated that the classical picture – no change in sign of zeta potentials - is still qualitatively valid for sPSL particles. MC simulations reproduced these experimental trends for surfaces with relatively low surface charge density. Interestingly, over-adsorption of counter- ions within the EDL allows the effective screening length to be smaller than the ionic size in agreement with the continuum model.

Experiments also indicate that the more strongly charged aPSL particles undergo charge inversion in KBr, LiCl and NaCl at salt concentrations ~ 1 M. In this case, the MC simulations show that the potential in the first layer of counter-ions is large and heterogenous, suggesting that the layer is likely immobile. By shifting of the plane of shear to enclose the first layer of counter-ions, the model reproduces the inversion of the zeta potential at high salt concentrations.

Our experiments indicate that these zeta potentials, while too low to stabilize dispersions (~kBT/e), are large enough to cause electrokinetic transport even in high ionic strength systems, notably geological reservoirs, sea water, and blood. In these systems, spontaneous electric fields may result from salt concentration gradients, which cause diffusiophoresis at charged surfaces17,52. Thus, diffusiophoresis might yet be a useful tool to affect transport in otherwise unreachable places, as long as a concentration gradient exists or can be created.

3.6 Author Contributions

I along with Dr. Darrell Velegol came up with the question and a way to do the measurement. I collaborated with Dr. Charles A. Cartier to create the set up for measurements. I carried out the measurements and analysis. Dr. K. J. M. Bishop designed and carried out the simulations. The manuscript was written through contributions of all authors.

3.7 Copyright Notice

Reprinted (adapted) with permission from (Garg, Astha, et al. "Particle Zeta Potentials Remain

Finite in Saturated Salt Solutions." Langmuir 32.45 (2016): 11837-11844. Copyright (2016)

American Chemical Society.

3.8 Acknowledgements

This work was funded in part by Penn State Materials Research Science and Engineering Centers under National Science Foundation grant DMR-1420620. D.V. would like to acknowledge support from NSF CBET 1603716. C.A.C. acknowledges support from the National Science

70 Foundation under Award CBET-1351704. K.J.M.B. acknowledges support from the Center for

Bioinspired Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award DE-SC0000989.

ABBREVIATIONS sPSL, aPSL and cPSL – sulfated, amidine-functionalized and carboxylated Polystyrene Latex respectively, EDL - Electrical Double Layer, GC model - Gouy-Chapman model, PALS – Phase

Angle Light Scattering

3.9 References

(1) Carnie, S. L.; Torrie, G. M. The Statistical Mechanics of the Electrical Double Layer. Adv.

Chem. Phys. 1984, 546, 141–253.

(2) Stout, R. F.; Khair, A. S. A Continuum Approach to Predicting Electrophoretic Mobility

Reversals. J. Fluid Mech. 2014, 752, R1.

(3) Bikerman, J. J. Structure and Capacity of Electrical Double Layer. Philos. Mag. 1942, 33,

384–397.

(4) Storey, B. D.; Bazant, M. Z. Effects of Electrostatic Correlations on Electrokinetic

Phenomena. Phys. Rev. E 2012, 86, 56303.

(5) Quesada-Pérez, M.; González-Tovar, E.; Martín-Molina, A.; Lozada-Cassou, M.; Hidalgo-

Álvarez, R. Overcharging in Colloids: Beyond the Poisson-Boltzmann Approach.

ChemPhysChem 2003, 4, 234–248.

71 (6) Bazant, M.; Kilic, M.; Storey, B.; Ajdari, A. Towards an Understanding of Induced-Charge

Electrokinetics at Large Applied Voltages in Concentrated Solutions. Adv. Colloid Interface

Sci. 2009, 152, 48–88.

(7) Israelachvili, J. N. Intermolecular and Surface Forces: Third Edition; Academic Press,

2011.

(8) Quesada-Pérez, M.; Martín-Molina, A.; Galisteo-González, F.; Hidalgo-Álvarez, R.

Electrophoretic Mobility of Model Colloids and Overcharging: Theory and Experiment.

Mol. Phys. 2002, 100, 3029–3039.

(9) Oncsik, T.; Trefalt, G.; Borkovec, M.; Szilágyi, I. Specific Ion Effects on Particle

Aggregation Induced by Monovalent Salts within the Hofmeister Series. Langmuir 2015,

31, 3799–3807.

(10) Semenov, I.; Raafatnia, S.; Sega, M.; Lobaskin, V.; Holm, C.; Kremer, F. Electrophoretic

Mobility and Charge Inversion of a Colloidal Particle Studied by Single-Colloid

Electrophoresis and Molecular Dynamics Simulations. Phys. Rev. E 2013, 87, 22302.

(11) Rowlands, W. N.; O’Brien, R. W.; Hunter, R. J.; Patrick, V. Surface Properties of

Aluminum Hydroxide at High Salt Concentration. J. Colloid Interface Sci. 1997, 188, 325–

335.

(12) Kosmulski, M.; Dahlsten, P. High Ionic Strength Electrokinetics of Clay Minerals. Colloids

Surfaces A Physicochem. Eng. Asp. 2006, 291, 212–218.

(13) Dukhin, A.; Dukhin, S.; Goetz, P. Electrokinetics at High Ionic Strength and Hypothesis of

the Double Layer with Zero Surface Charge. Langmuir 2005, 21, 9990–9997.

72 (14) Kosmulski, M.; Rosenholm, J. B. High Ionic Strength Electrokinetics. Adv. Colloid

Interface Sci. 2004, 112, 93–107.

(15) Calero, C.; Faraudo, J.; Bastos-Gonzalez, D. Interaction of Monovalent Ions with

Hydrophobic and Hydrophilic Colloids : Charge Inversion and Ionic Specificity. J. Am.

Chem. Soc. 2011, 133, 15025–15035.

(16) Vinogradov, J.; Jaafar, M. Z.; Jackson, M. D. Measurement of Streaming Potential Coupling

Coefficient in Sandstones Saturated with Natural and Artificial Brines at High Salinity. J.

Geophys. Res. 2010, 115, B12204.

(17) Velegol, D.; Garg, A.; Guha, R.; Kar, A.; Kumar, M. Origins of Concentration Gradients

for Diffusiophoresis. Soft Matter 2016, 12, 4686–4703.

(18) Guha, R.; Shang, X.; Zydney, A. L.; Velegol, D.; Kumar, M. Diffusiophoresis Contributes

Significantly to Colloidal Fouling in Low Salinity Reverse Osmosis Systems. J. Memb. Sci.

2015, 479, 67–76.

(19) Kar, A.; Mceldrew, M.; Stout, R. F.; Mays, B. E.; Khair, A.; Velegol, D.; Gorski, C. A. Self-

Generated Electrokinetic Fluid Flows during Pseudomorphic Mineral Replacement

Reactions. Langmuir 2016, 32, 5233–5240.

(20) Staffeld, P. O.; Quinn, J. A. Diffusion-Induced Banding of Colloid Particles via

Diffusiophoresis 1. Electrolytes. J. Colloid Interface Sci. 1989, 130, 69–87.

(21) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic

Press, 1981.

73 (22) Minor, M.; van der Linde, A. J.; van Leeuwen, H. P.; Lyklema, J. Dynamic Aspects of

Electrophoresis and Electroosmosis : A New Fast Method for Measuring Particle Mobilities.

J. Colloid Interface Sci. 1997, 189, 370–375.

(23) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Academic Press, 1959.

(24) Jaqaman, K.; Loerke, D.; Mettlen, M.; Kuwata, H.; Grinstein, S.; Schmid, S. L.; Danuser,

G. Robust Single-Particle Tracking in Live-Cell Time-Lapse Sequences. Nat. Methods 2008,

5, 695–702.

(25) Mao, S.; Duan, Z. The Viscosity of Aqueous Alkali-Chloride Solutions up to 623 K, 1,000

Bar, and High Ionic Strength. Int. J. Thermophys. 2009, 30, 1510–1523.

(26) Isono, T. Density, Viscosity, and Electrolytic Conductivity of Concentrated Aqueous

Electrolyte Solutions at Several Temperatures. J. Chem. Eng. Data 1984, 29, 45–52.

(27) Ozbek, H.; Fair, J. A.; Phillips, S. L. Viscosity of Aqueous Sodium Chloride Solutions from

0-150C. In Americal Chemical Society 29th Sountheast Regional Meeting; Tampa, FL, 1977.

(28) Chen, T.; Hefter, G.; Buchner, R. Dielectric Spectroscopy of Aqueous Solutions of KCl and

CsCl Dielectric Spectroscopy of Aqueous Solutions of KCl and CsCl. J. Phys. Chem. A

2003, 107, 4025–4031.

(29) Chandra, A. Static Dielectric Constant of Aqueous Electrolyte Solutions: Is There Any

Dynamic Contribution? J. Chem. Phys. 2000, 113, 903–905.

(30) Wei, Y.-Z.; Sridhar, S. Dielectric Spectroscopy up to 20 GHz of LiCl/H2O Solutions. J.

Chem. Phys. 1990, 92, 923–928.

74 (31) Wei, Y.-Z.; Chiang, P.; Sridhar, S. Ion Size Effects on the Dynamic and Static Dielectric

Properties of Aqueous Alkali Solutions. J. Chem. Phys. 1992, 96, 4569–4573.

(32) Hasted, J. B.; Ritson, D. M.; Collie, C. H. Dielectric Properties of Aqueous Ionic Solutions.

Parts I and II. J. Chem. Phys. 1948, 16, 1–21.

(33) Dukhin, A. S.; Dukhin, S. S. Aperiodic Capillary Electrophoresis Method Using an

Alternating Current Electric Field for Separation of Macromolecules. Electrophoresis 2005,

26, 2149–2153.

(34) Frenkel, D.; Smit, B. Understanding Molecular Simulation : From Algorithms to

Applications; 2nd ed.; Academic Press: San Diego, 2002.

(35) Deen, W. M. (William M. Analysis of Transport Phenomena; Oxford University Press, 2012.

(36) S37495 Certificate of Analysis for Lot 1129648, 2013.

(37) Zukoski IV, C. F.; Saville, D. A. The Interpretation of Electrokinetic Measurements Using

a Dynamic Model of the Stern Layer. II. Comparisons between Theory and Experiment. J.

Colloid Interface Sci. 1986, 114, 45–53.

(38) Borkovec, M.; Behrens, S. H.; Semmler, M. Observation of the Mobility Maximum

Predicted by Standard Electrokinetic Model for Highly Charged Amidine Latex Particles.

Langmuir 2000, 16, 5209–5212.

(39) Seebergh, J. E.; Berg, J. C. Evidence of a Hairy Layer at the Surface of Polystyrene Latex

Particles. Colloids Surfaces A Physicochem. Eng. Asp. 1995, 100, 139–153.

(40) Parsons, D.; Boström, M.; Lo Nostro, P.; Ninham, B. Hofmeister Effects: Interplay of

75 Hydration, Nonelectrostatic Potentials, and Ion Size. Phys. Chem. Chem. Phys. 2011, 13,

12352–12367.

(41) Kunz, W. Specific Ion Effects in Colloidal and Biological Systems. Curr. Opin. Colloid

Interface Sci. 2010, 15, 34–39.

(42) Bazant, M.; Storey, B.; Kornyshev, A. Double Layer in Ionic Liquids: Overscreening versus

Crowding. Phys. Rev. Lett. 2011.

(43) Gillies, G.; Lin, W.; Borkovec, M. Charging and Aggregation of Positively Charged Latex

Particles in the Presence of Anionic Polyelectrolytes. J. Phys. Chem. B 2007, 111, 8626–

8633.

(44) Yeh, I.-C.; Berkowitz, M. L. Dielectric Constant of Water at High Electric Fields: Molecular

Dynamics Study. J. Chem. Phys. 1999, 110, 7935–7942.

(45) Israelachvili, J. N. Measurement of the Viscosity of Liquids in Very Thin Films. J. Colloid

Interface Sci. 1986, 110, 263–271.

(46) Joly, L.; Ybert, C.; Trizac, E.; Bocquet, L. Hydrodynamics within the Electric Double Layer

on Slipping Surfaces. Phys. Rev. Lett. 2004, 93, 257805.

(47) O’Brien, R. W.; White, L. R. Electrophoretic Mobility of a Spherical Colloidal Particle. J.

Chem. Soc. Faraday Trans. 2 1978, 74, 1607–1626.

(48) Zukoski, C. F. I. Studies of Electrokinetic Phenomena in Suspensions, PhD Thesis,

Princeton University. Princeton, New Jersey, 1984.

(49) Zukoski IV, C. F. An Experimental Test of Electrokinetic Theory Using Measurements of

76 Electrophoretic Mobility and Electrical Conductivity. J. Colloid Interface Sci. 1985, 107,

322–333.

(50) Zukoski IV, C. F.; Saville, D. A. The Interpretation of Electrokinetic Measurements Using

a Dynamic Model of the Stern Layer: I. The Dynamic Model. J. Colloid Interface Sci. 1986,

114, 32–44.

(51) Ohshima, H. Electrophoresis of Soft Particles. Adv. Colloid Interface Sci. 1995, 62, 189–

235.

(52) Anderson, J. L. Colloid Transport by Interfacial Forces. Annu. Rev. Fluid Mech. 1989, 21,

61–99.

Chapter 4

Relative Roles of Kinetics, Transport and Thermodynamics in Pseudomorphic Mineral Replacement

4.1 Abstract

Pseudomorphic mineral replacement of KBr crystals in saturated KCl has been studied before extensively, but the reverse reaction has been barely studied. He we report the rate, extent and composition of the replaced layer for the reverse reaction – replacement of KCl crystal in saturated

KBr. We find that full replacement of the crystal can be achieved provided the solution to solid mole ratio is >= 0.2 , contrary to previous reports of the replacement stopping after an hour. This shows that kinetic and transport effects can lead to complete replacement in spite of ‘positive relative volume change’ predicted based on thermodynamic equilibria. By comparing the composition of the replaced solid for KBr in KCl and KCl in KBr, we find that the gradient for KBr in KCl is far gentler than for KCl in KBr, indicating that internal transport is far slower for the latter. Thus, we find that the much slower rate of replacement of the latter than the former may be explained simply by the internal transport limitation. Lastly, we find that mixing does not increase the rate of replacement of KCl in KBr in spite of the transport limitation, because it is the internal and not external transport that is limiting in this case, and because external mixing is not expected to create any additional fluid flow internally over and above fluid diffusion. These findings provide insights into the relative roles of fluid transport, kinetics and thermodynamics of the replacement reaction, moving us one step closer to making a theoretical model for this and other more complicated replacement systems.

78 4.2 Introduction

Pseudomorphic mineral replacement reactions (pMRRs) are mineral replacement reactions where the space occupied by the parent mineral comes to be occupied by a guest material, but the macroscopic shape is preserved. pMRRs have been observed broadly in nature in a variety of low and high solubility systems1,2 ranging from carbonates to chloride. The time scale for these transformations is often several orders of magnitude lower than possible by solid-state diffusion alone. Therefore, the presence of a fluid phase and porosity in the guest phase are considered to be pre-requisites for these reactions. The most widely accepted mechanism for this reaction is that pMRR proceeds through dissolution and precipitation reactions, coupled through the concentration at the fluid-solid interface3. The porosity, created during the process of replacement due to a difference in the volume of material dissolved and precipitated, provides a pathway for the fluid to keep penetrating deeper into the crystal. pMRRs are of interest because they occur in geological processes1,4, have been used as a route to synthesize templated, porous materials5–7, play a role in corrosion processes, and can be used to create porosity in geological reservoirs for enhanced oil recovery. In order to interpret natural pMRRs or to use them for technological advancements, it is desirable to accurately model the complex interplay of thermodynamics, kinetics and fluid transport that lead to pMRRs. In this light, replacement in the KBr-KCl system has been studied extensively as a model system to understand the mechanism of replacement because it happens at a reasonable time-scale (minutes to hours) and the thermodynamics of the system are well-known. However, even though thermodynamic implications have been explored in-depth for pMRR in this model system, much about the role of fluid transport and kinetics remains either unexplored or misunderstood. The objective of this work is to gain insights into the role of internal and external fluid transport, reaction kinetics and thermodynamics by experimentally determining the fluid concentration in the crystal

79 and the rate of replacement under various conditions. This would help us upgrade our understanding of the mechanism of pMRR and take us one step closer to making a quantitative model for this system, and eventually for more complicated systems. It will also help us reconcile sometimes contradictory experimental observations as well as the existing theoretical understanding of dissolution, precipitation and transport.

Here we show that full replacement of the crystal can be achieved with either configuration - KBr crystals in KCl solution, or vice versa in spite of ‘positive relative volume change’ predicted based on thermodynamic equilibria in the latter case. The rate and extent of replacement depends on the molar ratio of KBr to KCl, but not on external mixing.

A typical experiment with the KBr-KCl system is observing a small, transparent KBr crystal in a saturated KCl solution. It is observed that the crystal turns white on the outside, and when the crystal is removed and sectioned, a white rim is observed around a transparent inner core. This replacement reaction proceeds the other way as well – KCl crystal in saturated KBr solution – but

~10 times slower than the former8. Though the former reaction has been studied extensively through a variety of innovative techniques including interferometry9, isotope tracing10 and in-situ optical microscopy11, the latter reaction has been largely ignored. The slow progress of the replacement of KCl crystals in KBr solution has been interpreted as ‘stopping’8 of the reaction after an initial period of fast exchange. This has been attributed to a positive relative volume change (i.e. lack of porosity) calculated based on the assumption that the entire system is in thermodynamic equilibrium. A key theme of this work is that for understanding experiments at realistic time- scales of hours, we must recognize the fact that the system may not be in overall equilibrium, even as local equilibria exist. Therefore, the porosity must be determined by not only thermodynamic factors - the lattice size and amount of the appropriate solid phase that precipitates

- but also the interfacial fluid concentration and threshold supersaturation, that depend on fluid

80 transport and reaction kinetics. Here we gain insights into both the reactions by making quantitative measurements of the solid composition through EDS (Electron Dispersive

Spectroscopy). These are supplemented by measurements of the rate of replacement for various times and solid/solution ratios, along with qualitative information from electron- microscopy images.

4.3 Background

4.3.1 Steps in the replacement process

The preservation of parent shape as well as features at various length scales ranging from nanometers to meters suggests that there must be a robust and broadly applicable mechanism for pMRR reactions. One of the earliest hypothesis was that these reactions occur through a solid- diffusion mechanism, but this hypothesis has been discarded as the rates are much higher than could be obtained through solid dissolution, and because it has been observed that the presence of fluid is essential to the replacement reaction1. The most widely accepted theory now is that the crystallographic information is conveyed through the synchronization of dissolution and precipitation reactions that are coupled through the concentration at the fluid-solid interface3.

Another more complicated hypothesis given by Merino12 et al says that crystallographic information is transferred mechano-chemically through pressure solution and force of crystallization, however this has been contradicted recently by some researchers13.

Let’s take a look at the steps in the replacement of KBr crystal in a saturated KCl solution.

81 1. Dissolution: When a KBr crystal is exposed to a saturated KCl solution, KBr begins to

dissolve at the interface. This is because the saturated KCl solution is not in equilibrium

with solid KBr, meaning that it is under-saturated with respect to KBr14.

2. Precipitation and porosity generation: As soon as dissolution happens, the solution

becomes supersaturated with respect to a mixed KBr,Cl solid which precipitates out on the

surface. It precipitates onto the surface and not else-where because nucleation is easier on

the surface, and because supersaturation is highest close to the surface where dissolution

happens. The precipitate however does not occupy the entire space cleared up by

dissolution. This has been confirmed through experiments and can be understood by

considering that KBr crystal has a lattice size of 6.598 Å while KCl has a lattice constant

of 6.292 Å. Moreover, 1 mol of dissolved KBr may not lead to 1 mol of precipitated KCl,Br.

Rather, this would depend on the fluid composition on the Lippmann diagram (section

4.3.2).

3. Fluid transport: The regions not filled by the precipitate act as pores to hold the fluid and

to further cause replacement mediated by the fluid. However, during the process of

dissolution-precipitation, KBr concentration in the fluid increases due to dissolution and

KCl concentration reduces due to precipitation. Diffusion of Br- and Cl- into and from the

bulk solution tries to counter these concentration gradients. Thus, the interface fluid

concentration is a function of the diffusion rate that depends on the existing fluid path as

well as time and position in the crystal.

If one wanted to model this system, one would be faced with the problem of concentration boundary conditions at the fluid-solid interface within the pores. Since high solubility systems have fast kinetics, the usual practice in such a case is to assume a solution saturated with respect to the solid. But because we have solid KCl and a saturated KBr solution, we can never get to

82 ‘equilibrium’ – a saturated KCl solution, which would require getting rid of all KBr from the

solution. Therefore, the interfacial fluid concentration at the dissolution front will be

somewhere between saturated KCl and saturated KBr on the Lippman curve (explained in the

next section) which shows the concentrations of all solutions that are saturated, with respect to

a certain mixed solid composed only of KBr and KCl. The interfacial concentration would

depend on the kinetics, the geometry of the pore (transport) and on threshold supersaturation,

where the onset of crystallization happens. It would effectively depend on the thickness of the

layer of solid that participates in the equilibrium, as elucidated further by Pollok et al15. Since

the kinetics and extent of supersaturation are not known exactly for these mixed solutions,

we would like to measure the interfacial fluid concentration experimentally.

4.3.2 Thermodynamics - Lippmann Diagrams

KBr and KCl can undergo complete solid solution, meaning that a whole range of solids can precipitate from a saturated solution, spanning from pure KBr to pure KCl. The actual composition of the precipitated solid depends on the solution concentration. The solid-solution equilibria for this system can be represented using a Lippmann diagram16,17 as shown below (Figure 4-1). The y- axis shows the sum of solubility products  = [K+]([Br-] + [Cl-]) where the quantities in square brackets are activities.

Figure 4-1: Lippmann diagram for the KCl-KBr system.The y axis is the sum of activity products of KBr and KCl and - the x-axis shows both xKBr (mole fraction of KBr in solid) and Br,aq (aqueous activity fraction of Br ). The plot consists of data generated by using a mathematical formulation of the thermodynamics as explained by Pollok et al15(p 217-220). Mathematica was used to calculate the curves.

- The x-axis indicates both the activity fraction of Br in the aqueous phase (Br,aq) and the mole fraction of KBr in the solid phase (xKBr). The solidus curve corresponds to xKBr and the solutus curve corresponds to the Br,aq. Saturated KCl solution lies on the left on this plot and saturated KBr solution lies at the rightmost point. These are also the points where the solidus and solutus curves meet, indicating that the precipitating solid has the same concentration as the solution at these points, i.e. the pure end members. However, there is another such point called the alyotropic point, analogous to an azeotrope in 2-component vapor liquid equilibria18.

When the  for a solution at a given Br,aq falls below both the curves, the solution is under- saturated and no precipitation takes place. On the other hand, if the solution lies above both the curves, the solution is super-saturated and precipitation of a solid will take place. An important point here is that the solution may be supersaturated with respect to a range of solid compositions

84 on the solidus curve. The thermodynamics, as represented by the Lippmann diagram could be used to determine the solid composition with the highest thermodynamic driving force for precipitation using the concept of ‘maximum supersaturation’14,19. The actual composition of the precipitating solid may be decided not just by the thermodynamics but also the kinetics, often resulting in precipitation of a less stable but kinetically favorable precipitate. However, for a system with fast kinetics as is typical of systems with a high solubility, we might expect the precipitating solid to be the thermodynamically stable one.

In order to actually use the Lippmann diagram to interpret experimental results or predict outcomes, it is convenient to consider the solubility phase diagram developed by Pollok et al15,20 where the experimental solubility data has been used to go from solution activity fraction to solution mole fraction on the x-axis, and from the sum of activity products to the sum of concentrations of Br-

(aq) and Cl- (aq) on the y-axis. This is shown in the figure below (Figure 4-2). The solid and solution concentrations in equilibrium are connected by horizontal tie-lines.

4.3.3 Porosity generation

A key feature of the mineral replacement reaction is that a porosity is observed in the replaced phase. In fact, it has been found that the presence of porosity is essential to the progress of mineral replacement1. Porosity in the precipitated phase must result from the difference in the volume of the material dissolved vs. the material precipitated. This difference depends on two factors – the molar volume of the precipitating phase, and the moles of material precipitated. Each in-turn depends on the fluid concentration at the interface, and the process thermodynamics and kinetics.

For the case of KCl and KBr, we can use the Lippmann diagram to predict the precipitating phase for a given interfacial fluid concentration. Going a step further, Pollok et al calculated the porosity

86 of the precipitating phase for various molar ratios of KBr to KCl by assuming either an overall system equilibrium, or a strictly local equilibrium only. Their calculations predict that KCl cannot be replaced in KBr solutions due to no porosity, contrary to our finding that even mm scale crystals can be fully replaced. Therefore, we sought to observe the crystal porosity qualitatively using

FESEM under various conditions.

4.4 Questions

Below is a list of the existing assumptions of the replacement process, our questions to delve further into them, and our hypotheses. We will come back to this list towards to end to reconcile what we found. Our goal here was to question to the assumptions that have kept us from gaining a deeper understanding of the replacement process.

4.4.1 Passivation

Existing picture: KCl replacement stops after a period of initial growth due to

‘passivation’ at the surface.

Question: Does a KCl crystal in KBr solution form a passivation layer and stop

replacement always, never, or only under certain conditions? Does the rate and extent

of replacement depend on the molar ratio of KCl in the solid phase to KBr in the

solution phase (solid to solution molar ratio)? If so, what is this dependence?

87 4.4.2 Solution to solid ratios

Existing picture: KCl and KBr replacement extents depend on the solution to solid

ratio. The rate of replacement may depend on this ratio as well.

Question: What is the dependence of rate and extent of replacement on the molar ratio

n n of KCl (KBr) in the solid phase to KBr (KCl) in the solution phase ( Br( aq) or Cl( aq) nKCl(s) nKBr(s)

or simply solution to solid molar ratio)?

4.4.3 Porosity

Existing picture: KCl replacement in KBr is accompanied by a positive relative

volume change, due to which there is no porosity in the parent phase. KBr in KCl is

accompanied by a negative relative volume change due to which there is porosity and

replacement proceeds all the way. Relative volume changes, based on the assumption

of overall system equilibrium can be used to predict actual porosity.

Question: What is the porosity of the rim of replaced KCl crystals vs. the rim of

replaced KBr crystals? Does the porosity of the rim vary with distance from the outside

of the crystal? What does the porosity look like qualitatively?

4.4.4 Fluid transport

Existing picture: If mixing changes the rate of replacement, the reaction is transport

limited. Otherwise the reaction is not transport limited. Since KCl and KBr have a high

solubility, their replacement reactions must be limited by fluid transport.

88 Question: Does the rate of KCl replacement in KBr depend on external mixing? Does

the internal fluid have concentration gradients in the absence of mixing, indicating

limitations on internal fluid transport? Do these internal fluid concentration gradients

persist even in the presence of mixing?

4.4.5 Interfacial concentration

Existing picture: An unknown amount of the solid is dissolved into an unknown amount of solution. The ratio of these amounts results in the precipitation of a certain concentration and amount of solid. The knowledge of these amounts can help us infer the reaction kinetics and transport.

Question: What is the solid composition as a function of position within the crystal? How do these change over time? What can these tell us about the ratio of thickness dissolved to diffusion thickness?

4.5 Methods and Materials

4.5.1 Replacement experiments

Optical grade KBr and KCl crystals (International Crystals) were cut to roughly 3x3x6 mm size

using a blade and a 3D printed tool for sizing. The crystals were then soaked in hexane for 5

minutes to remove organic contaminants and dried using Kim wipes. Saturated solutions of

KBr and KCl were prepared by dissolving excess ACS grade powders (Sigma Aldrich), heating

up the solution to about 50 C with stirring, and then letting it cool back to 25 C. Experiments

were carried out in a water bath on top of a thermostated multi-position stir plate (Ika RT 5)

maintained at 26 C. A temperature sensor dipped in the bath indicated that the temperature

was maintained at 25.2  1.2 C. The solutions were equilibrated in the bath for at least 12

hours before an experiment was started. 0.1 g of Sulfo-Rhodamine B sodium salt (SRB) (Sigma

Aldrich) dye powder was added per 100 mL of solution in order to observe the porosity using

confocal microscopy. The replacement was carried out by dropping a crystal into the

equilibrated solution in a 20 mL glass vial for low solid to solution ratios or a 1.7 mL centrifuge

tube for high solid to solution ratios. After the experiment, the crystal was pulled out using a

tweezer and patted dry immediately using kim wipes. The sample was left to dry in air at room

temperature overnight.

푛 For the purpose of solution to solid ratio calculation ( 퐵푟 (푎푞) = moles of Br (aq) divided by 푛퐶푙 (푠)

푛 moles of Cl(s) for KCl in KBr experiments, or 퐶푙 (푎푞) for KBr in KCl experiments), the crystal 푛퐵푟 (푠)

size was assumed to be exactly 3x3x6 mm. It was found that the rim width for KCl in KBr

experiments varied substantially in different trials (~20%), probably due to the slow dynamics

of temperature changes. Therefore, all experiments corresponding to the data points reported

on a single plot were all obtained in a single trial.

4.5.2 Fluorescence optical microscopy

The dried crystals were cut using a razor blade perpendicular to the long end on two sides such

that we obtained a cross-section with a transparent center (unreplaced crystal) and a white outer

replaced layer. This was placed on a glass slide on the stage of a Nikon TE 300 inverted

microscope in fluorescence mode with green light from a mercury lamp corresponding to SRB

(excitation/emission maxima 565/586). The dye penetrated the replaced layer along with the

90 fluid and only the rim appeared bright. Grayscale images of the crystal observed with a 4x

objective were taken using a QImaging CCD camera at a resolution of 1392x1040 pixels which

resulted in a calibration of 1.73 m/pixel. The images were analyzed using Fiji ImageJ to obtain

rim widths. The side with the greatest width was chosen for analysis of each crystal, since there

were non-uniformities resulting from low mass transfer at the side facing the bottom. The

averages and standard deviations reported are all results from a single side for each crystal.

4.5.3 Electron Microscopy

Cross-sections cut above using a razor blade were stuck onto carbon tape and mounted on an

aluminium stub. The samples were sputter-coated with iridium (Emitec) to prevent charging.

There were observed using a Zeiss Sigma Field-Emission Scanning Electron Microscope (Zeiss

SIGMA VP-FESEM) at 5-10 kV with the secondary electrons (SE2) detector at magnifications

of 50x – 250x.

4.5.4 Elemental analysis

Blade-cut crystals were further smoothed using a Leica UC6 ultramicrotome. Smoothed crystals were sputter coated with iridium to prevent charging. An EDS detector was used to capture composition data along with FESEM images on the Zeiss SIGMA VP-FESEM. A working distance of 7.5 mm was maintained for EDS measurements, 15 kV accelerating voltage and 60 mm aperture was used for each measurement which resulted in a dead-time of 30-50%. The data acquisition and processing was handled by Aztec (Oxford) software.

The beam was calibrated thrice before the start of each session by collecting data from a piece of copper tape. K, Br and Cl were standardized using unreplaced optical grade KBr and KCl crystals

91 used for replacement. This was done by collecting spectrum from a smooth surface of pure KBr and KCl. The software also identified up to 10% of C and O but this was specified to be not present in the sample. The standardization data was saved into a calibration file which was used to calculate compositions for the replaced samples.

A count rate of at least 1 million per area selection was obtained for each spectrum reported. EDS spectral data was collected from rectangular selections in smooth regions, avoiding the porosity.

Distance from the edge for each spectrum was calculated as the center of mass for each rectangular region. Image analysis for this was done using ImageJ.

4.6 Results and Discussion

4.6.1 Replacement rate of KCl vs KBr

We carried out a typical replacement experiment starting with both end-members for the same molar ratio of solid to solution, for 30 minutes. FESEM images of replaced cross-sections from this experiment are shown in Figure 4-3. The inner, relatively smooth region in each case shows the unreplaced crystal core while the porous rims show the replaced layers. The overall crystal shape was preserved in each case. As previously reported, the replacement front for KCl is much sharper than for KBr. We measured the rim widths to be 0.15 mm for replacement in KCl and 0.54 mm for replacement in KBr. The measured rim width for KBr is 3.6 times that for KCl, much less than 10 times, as reported previously15.

Also, there appear to be obvious qualitative differences in the texture and porosity of the replaced layer in each case. The replaced layer in KCl appears to be composed of two distinct parts – the outer one is a continuous, porous layer while the inner one looks similar to a column of pebbles

92 thrown in together, with porosity in between individual pebbles. The replaced layer in KBr on the other hand is always continuous with a gradient of porosity, and the pores always grow inward, perpendicular to the crystal boundaries.

Figure 4-3: Electron microscopy images of partially replaced cross sections of (left) KCl crystal in saturated KBr 푛 푛 1 solution for 퐵푟( 푎푞) = 50 and (right) KBr crystal in saturated KCl solution for 퐵푟( 푎푞) = , both at t = 30 mins. The 푛퐾퐶푙(푠) 푛퐾퐶푙(푠) 50 scale bars are both 100 m. We wanted to see if the replacement of KCl was simply slow, or had it actually stopped? Upon letting the reactions run for long times in excess solution (ratio of solution moles to solid moles =

50), we found that a 3x3x6 mm crystal of KCl was replaced completely in less than 18 hours

(between 5 hrs to 18 hrs) while a KBr crystal of the same size was replaced completely in about 1 hour. Hence, contrary to previous work with this system, we found that under favorable conditions

(excess solution) and long times, KCl could indeed be replaced at a mm scale. Since porosity is a pre-requisite for these reactions to proceed, we can conclude that no passivating layer had formed due to re-precipitation of KCl that might prevent fluid access of the internal crystal surface.

93 4.6.2 Varying solution to solid ratios

We hypothesized that our results were different from those of previous researchers due to differences in the solid to solution ratios. While our experiments so far were done under an excess solution condition, previously reported experiments may have been done with solution to solid molar ratio of close to 1, though the conditions have not been reported15. We tested the replacement of both KBr and KCl for different solution to solid ratios. A dye dissolved in the solution during replacement penetrated the crystal and illuminating the rim under fluorescent light. The results from these experiments are summarized in Figure 4-4. Note that we chose 30 mins for KBr crystals and

5 hours for KCl crystals in order to see incomplete replacement in each case. We find that KBr replacement does not depend on the solution to solid ratios for the range tested, but KCl replacement depends strongly on it. KCl replacement reduces drastically with decreasing amount of solution in the system. This observation helps us reconcile our results with those of previous researchers.

Figure 4-4: Rim width vs. solution to solid ratio. Fluorescence optical microscopy images of dried cross-sections of partially replaced KBr (top row) and KCl (bottom row) crystals, at times 30 mins and 5 hours respectively, for varying solution to solid ratio shown at the bottom left corner for each image.

94 Figure 4-5 below shows the modified Lippmann diagram given by Pollok et al – a solubility phase diagram - annotated with the overall mole fraction of Br (XBr,total ) for each of the experiments tried.

The green lines correspond to experiments with KBr crystal in KCl solution ranging from 0.02 

XBr,total  0.5 and the red lines correspond to experiments with KCl crystals in saturated KBr solution ranging from 0.5 XBr,total  0.98. We would like to point out that the same ratio of moles in solution to solid can lead to different outcomes for the KBr and KCl starting crystals (in satd. KCl and KBr solutions respectively) owing to asymmetry of the Lippmann diagram16 (section 4.3.2 ). The most striking example is the case of XBr,total = 0.5 which was testing starting with both end members and obviously leads to different results. We hypothesize that if we carried out a KBr in KCl experiment at an even higher fraction of XBr,total, we might see a dependence on the solution to solid ratios as thermodynamic limitations kick-in.

Figure 4-5: Solubility phase diagram for KBr-KCl annotated with the solution to solid ratios teted in experiments. The green lines correspond to KBr crystal in KCl experiments, and red lines to KCl crystal in KBr. n Our next question was – for KCl replacement in low solution to solid ratio ( Br( aq) = 1, bottom nKCl(s) rightmost image in Figure 4-4) – is the replacement just proceeding slowly, or has it actually stopped? We sought to answer this question by measuring the replacement rim width at 0.5 hrs, 2 hrs, 5 hrs, 18 hrs and 30 hrs for high to low solution to solid molar ratios. This data is shown in

Figure 4-6.

n seems to be lower for the lower ratio ( Br( aq) = 1). This difference does not show at 30 mins, but nKCl(s) shows for all subsequent points. Since the rim width doesn’t change much between 2 hours and 30 hours, it appears that an overall thermodynamic equilibrium has been attained. The case for a thermodynamic equilibrium is also supported by KCl replacement experiments for varying exposed surface areas, keeping the total crystal volume and solution to solid ratios constant (Figure 4-7).

The experiment shows that for a high solution to solid ratio, higher surface area leads to higher mass replaced as the rim width remains constant – this points to a diffusion limited reaction that keeps the length penetrated constant. But for the low solution to solid case, we see that a higher surface area leads to lower rim width in order to keep the mass constant. This suggests that there is a thermodynamic limitation in this case. The equilibrium point can be estimated from Lippmann diagrams following the methodology of Pollok et al15, and can be confirmed through XRD

97 measurements that are out of the scope of this work. However, there still remains the question of whether the replacement is slow because of a ‘closing off’ of the crystal. We will address this question later in this chapter, when we look at FESEM images of internal cross-sections of replaced crystals.

Figure 4-7: Effect of exposed surface area on KCl replacement, while keeping the volume of crystal constant.

n The replacement rate of KCl in KBr depends only weakly on the Br( aq) ratio for values from 5 to nKCl(s)

50. One way this might happen is that for each case, we get the same porosity meaning that we get the same solution concentration (at least approximately). The rate of replacement does depend on time for each case, potentially due to a diffusion limitation. We can estimate a diffusion time based on the rim width L and ion diffusivity, D (t ~ L2/D) which comes out to about 19 minutes - about

100 times the actual time taken for replacement! This suggests either that the reaction has kinetic limitations as well, or the diffusion length is ~10 times higher than the rim width, on account of the tortuosity. Such a high tortuosity, if that is the case, points to a very low porosity medium.

98 4.6.3 Effect of external transport

We also carried out one set of KCl replacement experiments with mixing for the solution excess

n case ( Br( aq) = 50). While we recovered and measured crystals for 0.5, 2 and 5 hours, we could not nKCl(s) recover crystals at 18 hours and 30 hours. The crystals were suspended on a nylon string initially and the crystal fell down either because it was weak, or due to dissolution. For the 3 points measured,

n the rim thicknesses lie between those marked for Br( aq) = 50 and 12.5 in Figure 4-6. Thus, external nKCl(s) mixing does not substantially alter the rate of replacement, at least for the first 5 hours. This is somewhat surprising because dissolution in high solubility systems is generally transport limited.

But the observation is well justified because in this case, it must be the internal transport and not external transport that must be rate limiting. We expect that external mixing will not cause mixing within the internal fluid because of the small length scales. It also provides us a pointer if we need to speed up a replacement reaction that is transport limited – a mixing method that could function even at small length scales, such as electrokinetic fluid flow. Our result seems to be in contradiction with Kar et al21 who showed that KBr replacement in saturated KCl solution increased when the solution was flowed rather than stagnant, but since adding the flow also effectively increased the amount of solution present, their effects may be attributed entirely to a higher solution to solid ratio.

4.6.4 Replaced layer composition for replaced KCl

Previous researchers have hypothesized that the KCl replacement stops when the evolving solution composition going from saturated KBr to more KCl rich reaches a point on the solubility phase diagram where there’s a positive relative volume change. For KCl in saturated KBr solution, Pollok et al calculated this transition from negative to positive relative volume change to be at XBr = 0.4

99 (solid composition). We sought to see if this was indeed that case – had replacement stopped when

XBr reached a value of 0.4 in the replaced layer?

100 the spectrum was averaged to obtain each of the plotted points. Bottom: Solid composition of the rim of a partially replaced KCl crystal obtained through quantitative EDS measurements. The dark area to the right is the unreplaced KCl crystal. Solid lines are guide to the eye. In order to test this hypothesis, we performed quantitative EDS measurements on a cross-section of a partly replaced KCl crystal in saturated KBr solution under excess solution conditions (t = 5

n hours, Br( aq) = 50) following the procedure described in section 4.5.4 above (see Methods section). nKCl(s)

Figure 4-8 shows the electron image and corresponding EDS compositions calculated by taking spectra at various positions. The darker area to the right is the unreplaced KCl surface and the EDS data shows no Br here. Also, we get 50% K for each region, as expected from a solid composed entirely of KBr and KCl. Looking close to the crystal edge (left-most points in Figure 4-8), we find that the precipitate is very Br-rich. This makes sense, since a small amount of crystal equilibrates with a large amount of KBr solution outside. However, as we go within the crystal, we see a steep reduction in the Br content for the first 100 m, followed by a region of almost constant composition for the next 300 m. Then the last 100 or so microns again see a steep reduction in Br concentration until we get to pure KCl. We would like to point out that the composition measurements from this analysis suffer from some additional uncertainty due to the drying process

– replacing crystals are simply removed from solution and patted with kim wipes, which might not remove all the fluid within the crystal pore space. The drying of this solution will affect the measured composition from dried crystals.

Comparing the top and middle images in Figure 4-8, we find that the blade-cut crystal before smoothing (top image) reveals additional texture compared to the middle image obtained after smoothing, providing hints as to the way material precipitated within the crystal. The top figure clearly shows the presence of 4 zones from left to right in the partially replaced crystal

1. the leftmost, smooth, continuous zone corresponding to almost pure KBr from the EDS

data,

101 2. then an abrupt change-over to haphazardly arranged smaller crystals creating porosity

among individual crystals that corresponds to the region with very gentle concentration

change seen in the EDS data,

3. then a rough, low porosity region corresponding to the steep concentration gradient in

the EDS data, and

4. lastly, the rightmost smooth, unreplaced KCl crystal.

This visual correspondence to the zones seen in the EDS data is helpful in getting an idea of replaced layer compositions for KCl crystals replaced under a variety of conditions without actually doing quantitative EDS measurements each time. We can use this idea to analyze the images of partly replaced KCl crystals under low and high solution to solid ratios, and with mixing, at 3 different times shown in Figure 4-9.

All the images shown in Figure 4-9 show each of the four zones enumerated above, except the bottom right image. But we often see that the smooth KBr layer often separates out from the replaced crystal during sample preparation, so it is likely that the first layer may have just fallen off in this case during mixing. The presence of all these zones at all times shows that the surface is both texturally and compositionally re-equilibrated as time progresses. Thus, it may be justified to assume that the solution is in equilibrium with the solid at this point, and this information can be used along-with the phase solubility diagram to determine the solution concentration in the crystal at each point, as we do in the next section.

Secondly, it also suggests that during the growth of the rim, it is primarily the middle section that becomes broader, with the innermost and outermost concentrations staying fixed. This is important information for determining the boundary conditions on the solution concentration – the innermost concentration is decided by the excess unreacted KCl solid, while the outermost concentration is set by the excess solution outside the crystal. Also, coming back to a question we

102 had raised in section 4.6.2 while looking at replacement under conditions of low solution to solid ratios – is the replacement slow because of a ‘closing off’ of the crystal? The first column of images in Figure 4-9 clearly show that the first zone is just as porous as in other cases even at 15 hours, So the reaction may have slowed down because of low thermodynamic driving force and not because of closing off of the crystal due to a passivating layer. Moreover, this smooth zone 1 is not the last layer to form, rather it is perhaps the first layer to form.

Figure 4-9: Electron images of blade-cut cross-sections of partly replaced KCl crystals at various solution to solid ratios and times.

4.6.5 Replaced layer composition for KBr

We carried out a quantitative EDS analysis similar to the above for partly replaced KBr crystals as

n well (t = .5 hours, Br( aq) = 50). In sharp contrast to observations for a KCl crystal, we see that the nKCl(s) replaced layer concentration varies smoothly throughout the rim. The gentle slope in solid

103 concentration is accompanied by a continuous reduction in the porosity of the rim. The last point corresponds to unreplaced KBr and that comes abruptly because the replacement front is sharp, as reported previously.

104 4.6.6 Accuracy of the EDS composition measurements

Conventional quantitative EDS analysis on a flat, homogeneous and polished surface can provide accuracies as good as 1-2%22. However, given the compositionally heterogeneous and porous nature of the replaced samples on which the EDS analysis was performed, the measurements inherently suffer from certain inaccuracies. In our samples care was taken to smoothen the surface to a roughness of 1 m or lesser using ultra-microtomy, but the sample is porous rendering the x- rays from lower lying regions susceptible to absorption at elevated regions in the sample. Secondly, the sample likely has variation in composition and porosity in all 3 dimensions, though we expect the composition variation to be continuous rather than abrupt owing to the smoothing effects of solid-solution equilibria and fluid diffusion. While we avoided large pores in selecting surface areas for EDS sampling, the possibility of pores within the interaction volume under the surface is not ruled out.

The region sampled by the electron beam is a 3D interaction volume that depends on the beam energy as well as the atomic weight of the material being probed which can be estimated using

Monte Carlo simulations23. A simpler way of describing the volume is a length scale called the electron range that is the radius of the hemisphere centered at the surface that encompasses 90% of the interaction volume22. An expression for the electron range R is given by22

0.0276 퐴 푅 (푚) = 퐸1.67, 푍0.89 0

3 where A is the atomic weight (g/mol), Z is the atomic number,  is the density (g/cm ), E0 is the beam energy (keV), and R is calculated in micrometers. Using the average values of Z and A for

KCl and KBr along with the respective densities and 15 keV energy we obtain electron ranges of

3.6 m and 2.9 m for KCl and KBr respectively. Thus, this is roughly the penetration depth of the x-rays used for EDS analysis.

105 To get meaningful data in the presence of various sources of error, we obtained each spectrum by averaging the x-rays collected from an area that is approximately 35 m x 50 m and presumably is up to 4 m deep based on the analysis above. This was done in order to get an average value from the area as opposed to sampling a tiny area that may or may not represent the compositional average for that area.

To further verify the consistency of our results, we zoomed in on an area (500 x instead of the usual

250 x magnification) and acquired EDS spectra from three 16x16 m square regions spaced 100

m apart (Figure 4-11). All the squares were approximately the same distance from the edge and were centered on a line parallel to the edge, hence expected to have approximately the same composition. The compositions from the 3 squares yielded 49.4%  0.5% K, 14.9%  0.8% Cl and

35.7%  0.3% Br where the uncertainties noted are standard deviations from the 3 square regions.

The low uncertainties ascertain that the measurements are consistent over the large area chosen for each spectrum, and each measurement is likely a good approximation of the average composition in that region. Additionally, the composition data shown in Figure 4-8 and Figure 4-10 is reasonable in that the composition varies monotonically from high percentage of the guest (KBr for Figure 4-8) at the edge to a low percentage of the guest at the replacement front.

106

107 4.6.7 Solution composition as a function of distance

Figure 4-12: Circles represent bromide mole fractions in solid phases (considering only Br and Cl, excluding K) as a function of distance from the edge of crystal for replaced KCl and KBr crystals shown in Error! Reference source not found. and Figure 4-9 respectively, and marked as KCl, solid and KBr, solid respectively. Squares represent corresponding solution concentrations calculated using solubility phase diagram by assuming solid-solution local equilibria. All lines are guides to the eye. As discussed above in Section 4.6.4 above, images in Figure 4-9 show that re-equilibration of the replaced layer takes place over time. The replacement is mediated through solution, so its only fair to assume that solution concentrations cause this re-equlibration, and that the solution is in equilibrium with the solid. Therefore, making use of the EDS data above and the solubility phase diagram shown in Figure 4-2, we calculated the corresponding equilibrium solution compositions

108 for both the KCl crystal and KBr crystals. These are shown along with the solid compositions in

Figure 4-12. Note that we do not show corresponding solution compositions for the last solid compositions in each case, because these correspond to pure (or almost pure) crystals not in contact with any solution.

The KCl curves, shown in red show that the solid and solution compositions are close together as in the solubility diagram in Figure 4-2. The KBr curves, shown in blue on the other hand are farther apart, again tracing back to similar behavior on the solubility diagram. Both solutions show the presence of concentration gradients but the gradient is far steeper in the KCl crystal than in the KBr crystal – pointing to the lower porosity and correspondingly lower diffusivity in the KCl crystal.

Also, it is worth noting that close to the outside edge, the KBr crystal has solution that has equal amounts of Cl and Br, while for the KCl crystal, this solution contains almost no KCl. This shows how severe the internal transport limitation is for the KCl crystal, compared to KBr crystal. The absence of KCl near the edge of the KCl crystal provides another reason why mixing does not change the replacement – mixing can only increase the Br content of that solution but is it already at the maximum possible Br. However, for KBr in KCl, we might expect mixing to change the composition of the solid precipitate as it might make the solution concentration close to the edge more Cl rich, and slow down the gradient even further. This would in-turn reduce the porosity gradient and keep the porosity high, making the replacement go even faster for KBr.

The high KBr content in the KCl replacement rim also provides a reason for why KCl rim thickness is so low for low solution to solid ratios, even as the rim width of KBr crystal seems not to be affected by it. Due to high KBr precipitation in the case of KCl, relatively high amounts of KBr are lost during the initial replacement causing it to replace only to a small extent.

Lastly, the abrupt change-over from zone 1 (continuous KBr layer) to zone 2 (haphazard mixed crystals) as enumerated in section 4.6.4 in the rim of replaced KCl crystals suggests that zone 1 has

109 relatively high porosity compared to zone 2 and 3, in direct contradiction to previous works that identify this layer as a low porosity ‘passivating layer’, perhaps due to its closed appearance.

4.7 Conclusions

Above, we have performed many new experiments to better understand the role of fluid transport, thermodynamics and kinetics in the pseudomorphic mineral replacement in the KBr-KCl system.

Data on the rates of replacement with varying solution to solid ratios and mixing, the rim composition from quantitative EDS measurements and qualitative data from electron-microscopy images help us consolidate past knowledge as well as gain a much better understanding of this system. The key conclusions are that KCl crystals can be replaced even on a mm scale in saturated

KBr solutions albeit about an order of magnitude lower than KBr crystals in saturated KCl solutions.

The replacement rate is much slower for KCl due to lower internal porosity but it does not stop due to closing of the porosity, as previously thought. Lastly, both these replacement processes are limited by transport – KCl replacement is limited mainly by internal transport, and KBr replacement is limited by both internal and external transport. Conclusions in more detail on each of the questions listed previously are summarized below.

4.7.1 Passivation

Existing picture: KCl replacement stops after a period of initial growth due to

‘passivation’ at the surface.

Question: Does a KCl crystal in KBr solution form a passivation layer and stop

replacement always, never, or only under certain conditions? Does the rate and extent

110 of replacement depend on the molar ratio of KCl in the solid phase to KBr in the

solution phase (solid to solution molar ratio)? If so, what is this dependence?

New knowledge: What looks like a passivating layer is in-fact a continuous, porous

KBr rich layer that is not responsible for stopping replacement. Previous observations

of stopped KCl replacement may be attributed to low solution to solid ratios.

4.7.2 Solution to solid ratios

Existing picture: KCl and KBr replacement extents depend on the solution to solid

ratio. The rate of replacement may depend on this ratio as well.

Question: What is the dependence of rate and extent of replacement on the molar ratio

n n of KCl (KBr) in the solid phase to KBr (KCl) in the solution phase ( Br( aq) or Cl( aq) nKCl(s) nKBr(s)

or simply solution to solid molar ratio)?

New knowledge: The rate of KCl replacement has a weak dependence on solution to

solid ratios for ratios between 5 to 50, observed for 30 hours. But the extent and

consequently, rate is lower for the ratio = 1. The extent (and presumably rate) of KBr

replacement is invariant with the solution to solid ratio between 1-50. Based on EDS

solid composition data, we think that the extent of KCl replacement is lowered for low

solution amounts (but not so for KBr) because the KCl rim has a high KBr content (but

the KBr rim has relatively lower KCl content). Thus, we think it is a thermodynamic,

not kinetic effect.

111 4.7.3 Porosity