The effect of adsorbed poly (vinyl alcohol) on the properties of model silica suspensions

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Title:
The effect of adsorbed poly (vinyl alcohol) on the properties of model silica suspensions
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xxiii, 436 leaves : ill. ; 28 cm.
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English
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Khadilkar, Chandra, 1959-
Publication Date:

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Subjects / Keywords:
Polyvinyl alcohol   ( lcsh )
Silica   ( lcsh )
Suspensions (Chemistry)   ( lcsh )
Rheology   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
Statement of Responsibility:
by Chandra Khadilkar.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001130257
notis - AFM7515
oclc - 20188692
sobekcm - AA00004812_00001
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AA00004812:00001

Full Text












THE EFFECT OF ADSORBED POLY (VINYL ALCOHOL)
ON THE PROPERTIES OF MODEL SILICA
SUSPENSIONS













BY

CHANDRA KHADILKAR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1988

OF F LIBRARIES












ACKNOWLEDGEMENTS


I would like to express my sincere gratitude to Dr. M.D. Sacks for

his invaluable guidance and financial support during the course of this

study. I would like to thank him for allowing me to work in the area of

colloid science and for demonstrating the importance of reproducibility

and hard work in scientific research.

I am also grateful to Dr. C.D. Batich, Dr. L.L. Hench,

Dr. D.O. Shah, and Dr. E.D. Whitney, members of supervisory committee,

for their helpful suggestions.

I would like to thank Mr. H.W. Lee, Mr. O.E. Rojas, Mr. G.W.

Scheiffele, Mr. S.D. Vora, and Mr. T.S. Yeh for their help during the

course of this work. Thanks are also due to Professor B. Moudgil for

allowing me to use spectrophotometer and Gel Permeation Chromagraphy

apparatus. I would like to thank Ms. Hazel Feagle for typing, editing,

and compilation of this dissertation.

I also wish to convey my sincere gratitude to my parents and to my

wife for their encouragement and support during the course of this work.















TABLE OF CONTENTS


Page

ACKNOWLEDGENTS . . ii

LIST OF TABLES ................. ....... viii

LIST OF FIGURES. . . .. ix

ABSTRACT .................. ......... xxii

CHAPTERS

I. GENERAL INTRODUCTION AND AIM OF THE STUDY . 1

II. ADSORPTION OF POLYMERS AT SOLID/LIQUID INTERFACE. 5

Introduction. . . .. 5
Description of Adsorbed Polymer . 9
Adsorbed Amount of Polymer (A) . 9
Bound Fraction (p). . ... 11
Direct Surface Coverage (0) ....... 11
Segment Density Distribution 0(X,Y,Z) .. .. 11
Theoretical Models. . ...... ..12
Adsorption Energy Parameter (xs). .. 13
Segment-Solvent Interaction Parameter (X) ..... 14
Polymer Adsorption Theories: General Framework .. .15
Results of Polymer Adsorption Theories. ........ .18
Effect of Adsorption Energy Parameter ... .19
Effect of Solvent-Segment Interaction
Parameter ................. .... 19
Effect of Polymer Concentration and Molecular
Weight. . .. ...... 19
Experimental Techniques .. .. 21
Adsorbed Amount of Polymer . ... 21
Trains, Bound Fraction, and Direct Surface
Coverage. ............. ... 22
Thickness of Adsorbed Layer . .. 23
Segment Density Distribution .... 26
Adsorption Energy Parameter . ... 27
Adsorption of Polydisperse Polymers ... 27
Experimental Results for PVA-Water System ... .29
Properties of Poly (Vinyl Alcohol), PVA ...... .29
PVA Characterization. ...... . 31
Adsorbed Amount of Polymer. . .... 33
The Nature of Solid . ... 33


iii












The Effect of Acetate Content . .
The Effect of Molecular Weight of PVA .
The Effect of Solvency . .
Adsorbed Layer Properties and Adsorbed
Amounts .... ... .. .... .. .. .. .
The Segment Density Distribution ....
The Effect of Particle Radius . .
PVA Adsorption on Silica . .
Summary . . . .

III. ELECTROSTATIC INTERACTIONS BETWEEN COLLOIDAL PARTICLES.

Introduction . . .
Development of Charge at Solid-Liquid Interface .


Dissociation of Surface Groups .
Adsorption of Potential Determining Ions. .
Adsorption of Ionized Surfactants .
Isomorphic Substitution . .
Electrical Double Layer . .
Double Layer Interactions . .
Interaction Between Two Flat Plates .
Interaction Between Two Spherical
Particles . . .
Van der Waal's Interaction . .
Microscopic or Van der Waal's Method .
Flat Plates . . .
Spherical Particles . .
Retardation Effect . .


Effect of Medium on the Van der Waal's Attraction .
Macroscopic Approach . .....
Hamaker Constants . . ....
The Effect of Polymer Layer on Van der Waal's
Attraction . . ...
Potential Energy Curves and the DLVO Theory .
The Effect of Hamaker Constant . ...
The Effect of Surface Potential . .
The Effect of Electrolyte Concentration .. ....
The Effect of Particle Radius .......
The Stability-Instability Approach ......
Kinetics of Coagulation .. ... ......
Summary . . ....

IV. EFFECT OF ADSORBED POLYMER ON DISPERSION STABILITY. .


Introduction . . ...
Factors Influencing Steric Stabilization .
The Adsorbed Amount of Polymer .
The Solvent-Segment Interaction Parameter .
The Effective Hamaker Constant and the Size
of Particles . .


Applications and Advantages of Steric Stabilization .
Thermodynamic Basis of Steric Stabilization .


* *












Polymer Solution Thermodynamics .. 90
The Entropy of Mixing . .. 90
The Enthalpy of Mixing. ... 92
The X Parameter ............... ..... 93
The Theta Point ...... ................... 95
Classification of Steric Stabilization. ... .. 98
Quantitative Theories of Steric Stabilization .. 99
The Three Domains of Close Approach .. 101
The Interpenetration Domain . .. 103
Interpenetration Without Mixing ... 107
The Potential Energy Diagrams . .... 111
Time Scale of Approach of the Second Interface. 111
The Potential Energy of Interaction ... 113
Thermodynamically Limited Stability ... 115
Non-thermodynamically Limited Stability .. 119
Bridging Flocculation . .... .122
Kinetic Aspects of Bridging Flocculation. ... 127
Kinetics of Flocculation. ... . 130
The Potential Energy Diagrams for Bridging
Interparticle Interactions. . ... 133

V. STRUCTURE OF SUSPENSIONS. .. . .... .. .. 140

Introduction. . . 140
Fractal Geometry. . . ... 141
Models of Aggregate Formation . .... 143
Eden Growth .................. ... 143
Diffusion Limited Aggregation (DLA) .. 145
Cluster-Cluster Aggregation (CCA) . .. 146
Hierarchial Model . . .. 148
Kinetics of Aggregation . 148
Smoluchowski's Equation . .. 150
Equilibrium Properties of Suspensions .. 153
The Order-Disorder Transition . ... 154

VI. RHEOLOGICAL BEHAVIOR OF COLLOIDAL DISPERSIONS 160

Introduction. . . .. 160
Viscosity Definition. . ... 161
Classification of Rheological Behavior of Colloidal
Dispersions . . .. 163
Newtonian Dispersions . .. 165
Pseudo-plastic Dispersions. . ... 165
Dilatant and Shear Thickening Dispersions .. 167
Bingham Plastic Dispersions . .. 167
Thixotropic Dispersions . .. 167
Factors Affecting Rheological Behavior of Colloid
Dispersion . . .. 170
Interparticle Interactions. ... 170
Brownian Motion ......... 170
Hydrodynamic Interactions ......... 171
Rheological Behavior of Stable Systems ... 171















The Effect of Adsorbed Layer . .
Stable Dispersions with Soft Interactions .
Rheological Behavior of Flocculated Dispersions .
Structure of Flocculated Dispersions .
Flow Behavior of Flocculated Dispersions. .
Flocculated Dispersions Showing No Time Dependence
Elastic Floc Model . .


. 175
S. 180
. 181
S. 181
S. 186
S. 187
. 190


VII. MATERIALS PROPERTIES AND CHARACTERIZATION/
EXPERIMENTAL PROCEDURES . . .


Introduction . . .
Silica as a Model Material . .
Silica Preparation and Characterization .
Silica Washing Procedure . .
Silica Calcination Treatment .
Effect of Calcination Treatment on the Nature
the Silica Surface . .
Silica Size and Size Distribution .
Silica Surface Area . .
Silica True Density . .
Poly Vinyl Alcohol . .
Synthesis and Properties . .
Solubility, Solution Behavior and Interfacial


Activity . .
Fractionation of As-received PVA. .
Acetate Content of Polymer .
Molecular Weight and Molecular Weight
Distribution . .
Viscometry . .
Gel Permeation Chromatography .
Conformation and Solution Parameters.
PVA Configuration Parameters .
The X Parameter . .
Adsorption Measurements . .
Suspension Preparation Procedure .
Suspension Characterization .
Electrophoresis . .
Rheological Measurements .
Consolidation and Green Microstructure
Summary . . .


196
196
199
203
204

204
210
215
217
219
219

219
221
222

223
223
226
239
239
242
246
247
251
251
253
254
256


VIII. RESULTS AND DISCUSSION . .


Electrostatically Stabilized Dispersions..
Effect of Adsorbed PVA on the Properties of
Silica Dispersions . .
Effect of Amount Adsorbed . .
Effect of Silica Calcination Treatment. .
Effect of PVA Molecular Weight .
Fractional Surface Coverage .
Effect of Suspension pH . .


. .
Model
* .
* .
. .
. .
. .
. .


. .. 257

. .. 257

. .. 272
. .. 272
. .. 284
. 318
. 318
. .. 334



rr
rrr
rr
r
r
r~
rrr
rr~r
rr
r~r
rr
rr












Effect of pH and Molecular Eight with the Plateau
Adsorbed Amount of Polymer. .... . 346
Selection of Optimum Molecular Weight ....... 367
Effect of Adsorbed Layer Thickness on the Maximum
Solids Loading in Suspension. .... . 372
Effect of Silica Particle Size. ...... .. 375
Effect of PVA Degree of Hydrolysis on Adsorption
Behavior. . .. ... 388
Effect of Solvent Quality on the Rheological
Behavior. . . 400


IX. SUMMARY AND SUGGESTIONS FOR FUTURE WORK ... ..

Summary ............. ......... ..
Suggestions for Future Work ... .......

LIST OF REFERENCES .... ............ ...

BIOGRAPHICAL SKETCH. . .. ............


414

414
417

420

436
















LIST OF TABLES


Table Page

3.1 Effect of Ionic Strength and Valency on the Electrical
Double Layer Thickness. .... . 51

3.2 Compilation of Hamaker Constants for Silica-Water-PVA
System. . . .. . 67

4.1 Classification of Steric Stabilization. . ... 100

6.1 Classification of Flow Behavior . ... 164

7.1 Geometric Mean and Specific Surface Area of Various Silica
Lots Used . . ... ..... .216

7.2 Viscometric Molecular Weight and Acetate Content of PVA
Fractions . . .. 225

7.3 Molecular Characteristics and Elution Volume of PEO
Calibration Standards ... . 228

7.4 Gel Permeation Chromatography Data for Unfractioned PVA
Samples . . . 229

7.5 Effect of Molecular Weight Elution Volume Calibration
Curve on the GPC Results. . .. 235

7.6 Comparison of Viscometric Molecular Weight and GPC Results
for Various PVA Fractions. . ... 238

7.7 PVA Dimensions in Solution. . ... 243

8.1 Properties of Silica and PVA Used to Investigate the Effect
of Adsorbed Amount of PVA on the Suspension Properties. 274

8.2 Properties of Silica and PVA Used to Investigate the Effect
of Silica Calcination Temperature on the Suspension
Properties . . ... 286

8.3 Molecular Weight and Degree of Hydroxylation of PVA Samples
to Study the Effect of Degree of Hydroxylation on the
Suspension Properties. . . 390


viii















LIST OF FIGURES


Figure Description Page

2.1 Schematic representation of an adsorbed polymer
molecule. . . .. 8

2.2 Conformations of adsorbed polymer molecules (a) single
point attachment, (b) train-loop-tail adsorption,
(c) flat multiple site attachment, (d) random coil,
(e) nonuniform segment distribution, and
(f) multilayer. . . .. 10

2.3 Plots of (a) degree of occupancy, 8, and (b) the
effective layer thickness, 6, as a function of the
adsorbed amount of PVA on AgI.. .... .. 37

2.4 Plot of segment density as a function of distance from
a surface for adsorbed PVA on PS-latex. .. .39

3.1 Fraction of double layer potential versus distance from
a surface: (a) curves for 1:1 electrolyte at three
concentrations and (b) curves for 0.001 M symmetrical
electrolytes of three different valance types.. 52

3.2 Schematic illustration of the variation of potential as
a function of distance from a charged surface in the
presence of a stern layer, subscripts o at wall, 6 at
stern surface, d in diffuse layer.. .... 52

3.3 Schematic illustration of the effect of adsorbed
polymer layer on Van der Waal's attraction. ... .68

3.4 Total potential energy of interaction V(d)total = VR(d)
+ VA(d) where VR(d) is the potential energy of
repulsion due to double-layer interactions and VA(d) is
attractive potential due to Van der Waal's
interactions. . ... ....... 71

3.5 The effect of the Hamaker constant on the total
interaction energy curves.. .... ...... 73

3.6 The effect of zeta potential on the total interaction
energy curves.. . .. 75












3.7 The effect of concentration of 1:1 electrolyte on the
potential energy curves.. . .. 76

3.8 The effect of particle radius on the total interaction
energy curves.. . . .... 78

3.9 Theoretical dependence of stability ratio on
electrolyte concentration.. . ... 81

4.1 The three domains of close approach of sterically
stabilized flat plates, (i) Noninterpenetration (d >
2L); (ii) Interpenetration (L < d < 2L);
(iii) Interpenetration plus compression (d < L).. .. 102

4.2 The distance dependence of the steric interaction
energy for two equal spheres of radius a, stabilized
by polymer layers with different segment density
distribution functions. (1) exponential; (2) constant;
(3) Gaussian; (4) radial Gaussian. d is the minimum
distance between surfaces of the spheres, 8 is the
barrier thickness, and AGS is the interaction energy.

4.3 The free energy of interaction between particles
covered by equal tails (f) and equal loops (a). For
particles covered by equal tails, (b) gives the volume
restriction effect and (c) the osmotic repulsion; (f)
is the resultant of adding (b), (c), and (e). ... 116

4.4 Schematic illustration of the effect of segment-solvent
interaction parameter, x, on the potential energy
diagram (A) poor solvent, x > 0.5, (B) theta solvent, X
0.5, and (C) good solvent, X < 0.5. ... 118

4.5 The free energy of interaction of polystyrene latex
particles stabilized by poly (vinyl alcohol) according
to Hesselink, Vrij, and Overbeek (1971); stabilizer
molecular weight 1, 8,000; 2, 17,000; 3, 28,000; 4,
43,000 .. .. .. ..... 120

4.6 Plots showing the effect of particle size and adsorbed
amount on the depth of the minima in the total
potential energy of interaction.. .. 120

4.7 Schematic illustration of bridging flocculation with
adsorbed polymer. . . 123

4.8 The effect of thickness of the electrical double layer
on bridging flocculation. . ... 125

4.9 Schematic diagram showing mixing, adsorption, and
flocculation upon addition of polymeric flocculent. 128











4.10 The effect of solids loading 0 and 8/a on collisions
Zf/Zo . . .132

4.11 Schematic representation of the approach of a second
(uncovered) particle to a covered one. It was assumed
that, at large interparticle distance H the number of
segments which adsorb on the (originally) bare particle
per unit area is equal to the number of segments per
unit area which would lie beyond Hi in the absence of
the second particle (i.e., shaded area).. .. 134

4.12 Schematic representation of the bridging process.
(a) At large distances, a loop of i segments has its
unpurturbed configuration. (b) After adsorption of the
first segment, two bridges of i/2 segments each are
formed. (c) At shorter distances, two bridges of iH
segments and a train of KH segments adsorbed on the
second surface. . . ... 136

4.13 The total free energy of interaction between coated and
uncoated plates as a function of distance of
separation. . . 137

5.1 Eden cluster produced by monomer-cluster growth.. 144

5.2 An aggregate grown by the DLA process.. .. 144

5.3 An aggregate grown by the CCA process.. .. 147

5.4 Schematic plot of phase diagram for monosized spherical
particles. The volume fraction of solids as a function
of ionic concentration is plotted. Solid lines are
theoretical phase boundaries. . .. 156

5.5 Schematic illustration showing (a) "hard" and (b)
"soft" interactions between particles. The potential
energy of interaction as a function of distance of
separation is plotted.. . .... 158

6.1 Schematic illustration of the concept of viscosity
under laminar flow conditions.. . .. 162

6.2 Schematic plots of (a) shear stress versus shear rate
and (b) viscosity versus shear rate for various types
of flow behaviors.. . .. 166

6.3 Schematic representation of thixotropic flow behavior,
(a) shear stress versus shear rate, and (b) viscosity
versus shear rate plots... . 169

6.4 Schematic plot of dependence of relative viscosity on
the volume fraction solid in suspension.. .. 173













6.5 Plot of relative viscosity versus volume fraction latex
particles of different sizes. Data was fitted using
Krieger equation. . . 176

6.6 Plot of relative viscosity versus dimensionless shear
rate, ir, for monodisperse suspensions of polystyrene
spheres at 0 0.50 in different fluids.. .. 178

6.7 Schematic illustration of the effect of shear on the
stability of suspensions. . ... 185

6.8 Schematic illustration of flow curve parameters for
pseudoplastic flow behavior.. . .. 188

7.1 Schematic representation of various types of surface
groups present on the silica surface. .. 206

7.2 The diffuse reflectance Fourier transform infrared
spectra of silica powders calcined at various
temperatures . .. .. 207

7.3 Concentration of surface silanol groups as a function
of the temperature of calcination.. .... 209

7.4 Scanning electron micrograph of silica powder.. ... 212

7.5 A histogram (number of particles in a given diameter
class versus particle diameter) of a typical silica
batch.. . . 213

7.6 Plot of particle size distribution for silica
determined by x-ray sedimentation.. .. 214

7.7 Gas pycnometer density versus calcination temperature
for Si02 powders. .... .. 218

7.8 Molecular weight calibration curves for PEO standards
and commercial PVA88. Log M is plotted as a function
of elution volume.. . .. 231

7.9 GPC chromatograms, showing refractive index detector
response, h, as a function of elution volume for
several unfractioned PVA samples. . ... 233

7.10 GPC chromatograms, showing the effect of acetone
fractionation of Vinol 540 and Vinol 203 polymer
samples on distribution widths. . ... 237

7.11 Stockmayer-Fixman plot for PVA88. . ... 240













7.12 Plot of absorbance versus PVA concentration in solution
for various molecular weight polymers.. .. 248

8.1 Plot of zeta potential versus suspensions pH for 20
vol.% SiO2 at ionic strength of 1 x 10-2 moles/liter
NaC . . .. 258

8.2 The effect of zeta potential on (a) shear stress versus
shear rate and (b) viscosity versus shear rate plots.

8.3 Schematic illustration showing the structural breakdown
of a floc due to applied shear. . .. 261

8.4 DLVO plots of potential energy of interaction versus
distance of separation at indicated C potentials. 263

8.5 Plot of relative viscosity versus zeta potential for 20
vol.% SiO2 suspensions. . ... .265

8.6 Plot of (a) CFP versus zeta potential and (b) CFP
versus zeta potential square for 20 vol.% Si02
suspensions.. . .. .. 266

8.7 Plot of (a) extrapolated yield stress versus zeta
potential and (b) extrapolated yield stress versus zeta
potential square for 20 vol.% SiO2 suspensions. 269

8.8 Plots of specific volume frequency versus pore radius
obtained by mercury porosimetry for sedimented samples
with indicated pH values. . ... 271

8.9 Adsorption isotherm for 20 vol.% Si02 suspensions
prepared with varying concentration of PVA with
molecular weight = 24,000 at pH 3.7.. .. 273

8.10 Plots of relative viscosity versus shear rate for 20
vol.% SiO2 suspensions prepared at pH 3.7 with varying
PVA concentrations and pH 7.3 (-60 mV zeta potential)
with no PVA.. . . .. 277

8.11 Plot of yield stress versus adsorbed amount of PVA with
molecular weight = 24,000 at pH 3.7.. .. 279

8.12 Plot of relative viscosity versus adsorbed amount of
PVA for 20 vol.% SiO2 suspensions prepared with varying
PVA concentration.. . .... 280

8.13 Plot of hysteresis area versus adsorbed amount of PVA
of 20 wt.% SiO2 suspensions.. . .. 281

8.14 Plot of (a) sediment density versus fraction plateau
coverage and (b) median pore radius versus fraction


xiii












plateau coverage for compacts prepared from 20 vol.%
SiO2 suspensions with varying PVA concentrations at pH
3.7 and pH 7.3 with no polymer. . .. 283

8.15 Adsorption isotherms for silicas calcined at various
temperatures with PVA molecular weight = 215,000 at pH
3.7.. .. ... . ... 285

8.16 Plot of plateau adsorbed amount versus silica
calcination temperature.. ... .. 288

8.17 Plots of plateau adsorbed amount versus silica
calcination temperature for (a) PEO adsorption on Cab-
O-Sil and (b) PVA adsorption on Cab-O-Sil.. .... 290

8.18 Plot of relative viscosity versus shear rate for 20
vol.% suspensions prepared with uncalcined silica and
with silica powder calcined at 5000C and 7000C. 292

8.19 Plot of yield stress versus calcination temperature for
20 vol.% silica suspensions at pH 3.7 prepared with
silica particles calcined at various temperatures. PVA
concentration in solution was sufficient to achieve
plateau coverage of the silica particles. .. 293

8.20 Plot of relative viscosity versus calcination
temperature for 20 vol.% silica suspensions at pH 3.7
prepared with silica particles calcined at various
temperatures. PVA concentration in solution was
sufficient to achieve plateau coverage of the silica
particles.. ..... 294

8.21 Plot of hysteresis area versus calcination temperature
for 20 vol.% silica suspensions at pH 3.7 prepared with
silica particles calcined at various temperatures. PVA
concentration in solution was sufficient to achieve
plateau coverage of the silica particles. .... 295

8.22 Schematic plot of the total interaction energy versus
distance of separation between two polymer-coated
particles with varying adsorbed amounts.. 297

8.23 Schematic illustration (a) showing silica surface
covered with only enough PVA to make particles
hydrophobic and (b) excess of PVA adsorption prevents
cocervation.. . 299

8.24 Schematic plot of (a) disjoining pressure as a function
of distance of separation for two parallel water films
stabilized with PVA film and (b) disjoining curve for
homopolymer. The specific attractive component in the


xiv












case of PVA derives from the hydrophobic interactions
between acetate groups. . ... 301

8.25 Plot of (a) relative density for slip cast samples
versus silica calcination temperature and (b) median
pore radius versus silica calcination temperature.. 303

8.26 Plot of mercury porosimetry data for slip cast samples
prepared from uncalcined and 7000C calcined silica
powders. Samples were prepared from 20 vol.% silica
suspensions at pH 3.7 with the plateau coverage of Si02
particles with PVA of molecular weight = 215,000. 304

8.27 Plot of (a) relative viscosity versus adsorbed amount
and (b) relative viscosity versus fractioned plateau
coverage for 20 vol.% SiO2 suspensions prepared with
uncalcined and 7000C calcined powders.. ....... 306

8.28 Schematic illustration of floc structures formed with (a)
uncalcined and (b) 7000C calcined silica particles at low
surface coverages with adsorbed polymer.. .. 307

8.29 The depth of the free energy minimum as a function of
the total amount of polymer between the surfaces at
various solvency conditions for two molecular weights
of polymer. Ot is the total amount of polymer between
the plates expressed as the number of equivalent
monolayers, Afmin is the interaction energy, and r is
the number of segments per chain ......... 309

8.30 Plots of (a) yield stress versus adsorbed amount and
(b) yield stress versus fractioned plateau coverage for
20 vol.% silica suspensions prepared with 7000C
calcined and uncalcined silicas with varying PVA
concentration in solution.. . .... 311

8.31 Schematic illustration shows the total number of
bridges, n total formed between two spherical particles
total
of radius a separated by distance 2h. .. 312

8.32 Plots of (a) relative density of gravity cast samples
versus fraction plateau coverage and (b) median pore
radius versus fraction plateau coverage for compacts
prepared from 20 vol.% Si02 suspensions of uncalcined
and 700C calcined silicas with varying PVA
concentrations. ................ 315

8.33 Plots of (a) hysteresis area versus adsorbed amount and
(b) hysteresis area versus fraction plateau coverage
for 20 vol.% Si02 suspensions prepared with uncalcined
and 7000C calcined silicas with varying PVA
concentrations. . . 316













8.34 Plots of adsorption isotherms for two PVA samples with
different molecular weights (i.e., 24,000 and 215,000
g/mole) determined using 20 vol.% SiO2 suspensions at
pH 3.7 . . 319

8.35 Plots of (a) relative viscosity versus adsorbed amount
and (b) relative viscosity versus fraction plateau
coverage for two PVA samples with different molecular
weights... . .. 321

8.36 Plots of relative viscosity versus shear rate for 20
vol.% SiO2 suspensions prepared using indicated
molecular weight PVA samples at fixed PVA concentration
in solution. Adsorbed amount was the same (0.15 mg
PVA/m2 SiO2) for all suspensions. . 322

8.37 Plot of relative viscosity versus PVA molecular weight
(log scale) at fixed adsorbed amount of polymer.. 323

8.38 Plots of (a) yield stress versus adsorbed amount and
(b) yield stress versus fraction plateau coverage for
20 vol.% silica suspensions prepared with two PVA
samples with different molecular weights. 325

8.39 Plot of yield stress versus PVA molecular weight (log
scale) at fixed adsorbed amount.. .. 326

8.40 Plots of (a) hysteresis area versus adsorbed amount and
(b) hysteresis area versus fraction plateau coverage
for 20 vol.% SiO2 suspensions prepared with two PVA
samples of different molecular weights. .. 328

8.41 Plot of hysteresis area versus PVA molecular weight
(log scale) at fixed adsorbed amount of polymer.. 329

8.42 Plots of (a) relative density of sedimented samples
versus fraction plateau coverage and (b) median pore
radius versus fraction plateau coverages for compacts
prepared using two PVA samples of different molecular
weights... . . .. 330

8.43 Plot of relative density of compacts prepared using
gravity casting and slip casting versus PVA molecular
weight at fixed adsorbed amount of polymer. 332

8.44 Plots of relative density versus CFP (= 0F/Op) for two
PVA samples with different molecular weights. Results
for compacts prepared at pH 3.7 and pH 7.6 with no
added PVA are also shown. . .... 333













8.45 Adsorption isotherm of PVA with molecular weight =
24,000 at two different suspensions pH's 335

8.46 Plot of plateau adsorbed amount of PVA with molecular
weight = 200,000 as a function of suspensions pH. 336

8.47 Plots of (a) relative viscosity of 20 vol.% suspensions
versus adsorbed amount of PVA with molecular weight =
24,000 and (b) relative viscosity versus fraction
plateau coverage for suspensions prepared at pH values
3.7 and 7.6 with varying PVA concentration. ... 338

8.48 Plots of (a) yield stress versus adsorbed amount of
polymer and (b) yield stress versus fraction plateau
coverage for suspensions prepared at pH values 3.7 and
7.6.. . ..... . .340

8.49 Schematic illustration shows the prevention of bridging
flocculation due to diffuse electrical double layer.. 341

8.50 Plots of (a) sediment density versus fraction plateau
coverage and (b) median pore radius versus fraction
plateau coverage for compacts prepared from 20 vol.%
Si02 suspensions with varying amounts of PVA
concentrations at indicated suspension pH values. 342

8.51 Plot of zeta potential versus adsorbed amount of PVA
with molecular weight 24,000 at suspensions pH 7.6. 344

8.52 Schematic plots of effective adsorbed layer thickness,
6, as a function of measured zeta potential at
indicated ionic strengths. The zeta potential with no
adsorbed polymer is = -65 mV. . 345

8.53 Plots of plateau adsorbed amounts of polymer versus PVA
molecular weight (log scale) at suspensions pHs 3.7 and
7.8. Suspensions were prepared using 20 vol.% Si02
with sufficient concentration of PVA in solution with
varying PVA molecular weights at indicated pH values. 347

8.54 Plots of relative viscosity versus shear rate for 20
vol.% SiO2 suspensions at pH 7.8 with plateau adsorbed
amounts of PVAs having indicated molecular weights.. 348

8.55 Plots of relative viscosity versus shear rate for 20
vol.% Si02 suspensions at pH 3.7 with plateau adsorbed
amounts of PVAs having indicated molecular weights. 349

8.56 Plots of relative viscosity versus PVA molecular weight
(log scale) for 20 vol.% Si02 suspensions with plateau
adsorbed amounts of polymer at indicated pH values. 351


xvii













8.57 Plots of hysteresis area versus PVA molecular weight
(log scale) for 20 vol.% SiO2 suspensions at pH 3.7
with plateau adsorbed amounts of polymers.. ... 354

8.58 Plots of yield stress versus PVA molecular weight (log
scale) for 20 vol.% Si02 suspensions with plateau
adsorbed amounts of polymers at indicated pH values.. 355

8.59 Plots of (a) relative density of gravity cast samples
versus PVA molecular weight and (b) median pore radius
versus PVA molecular weight for compacts prepared using
20 vol.% SiO2 suspensions with plateau adsorbed amounts
of polymers with different molecular weights at
indicated pH values.. . . 357

8.60 Plots of (a) relative density of slip cast samples
versus PVA molecular weight and (b) median pore radius
versus molecular weight for compacts prepared using 20
vol.% Si02 suspensions with plateau adsorbed amounts of
PVAs with different molecular weights at indicated pH
values. . . 358

8.61 Schematic plots of relative viscosity versus volume
fraction of solids in suspensions for particles with
the indicated thicknesses of adsorbed polymer. This
thickness, 6, is indicated as a fraction of the
particle radius... . 360

8.62 Plot of (a) relative viscosity versus volume fraction
silica in suspensions prepared at pH 7.6 and (b)
relative viscosity versus volume fraction of latex
particles as reported by Krieger. . 361

8.63 Plot of relative density of gravity cast samples versus
volume fraction silica at pH 7.6. . ... 362

8.64 Plots of the adsorbed layer thickness, 6, versus PVA
molecular weight determined from the relative viscosity
values of 20 vol.% suspensions prepared at pH 7.8.
Also shown are the radius (Rg) and diameter (2 x R.) of
gyration of the polymers in solution as determined by
intrinsic viscosity measurements. . 364

8.65 Plots of adsorbed PVA layer thickness, 6, on SiO2
particles versus square root of PVA molecular weight.
Adsorbed layer thicknesses of PVA onto PS latex
particles is also shown.. . .. 368

8.66 Schematic plots of minimum molecular weight (log scale)
required to stabilize suspensions as a function of
particle radius with different values of Af /VA
ratios. The solid lines separates stable an unstable


xviii












regions of suspensions prepared with spherical
particles of fixed size with varying molecular weight
or suspensions prepared with fixed molecular weight and
varying particle radius... . 370

8.67 Schematic plots of maximum true solids loading, 0 ,
achievable in suspensions prepared with spherical
monosized particles of varying size using indicated
molecular weights of polymer. . 374

8.68 Adsorption isotherms for PVA with molecular weight =
215,000 for 20 vol.% SiO2 suspensions prepared using
0.4 uin and 0.7 um size particles with varying PVA
concentrations. . . ... .376

8.69 Plots of (a) relative viscosity versus adsorbed amounts
of PVA and (b) relative viscosity versus fraction
plateau coverage for 20 vol.% SiO2 suspensions prepared
using 0.4 Um and 0.7 mu size particles. .. 378

8.70 Schematic illustration showing the effect of adsorbed
layer thickness, 8, on the hydrodynamic volume of two
different size particles. . 379

8.71 Plots of (a) yield stress versus adsorbed amount of PVA
and (b) yield stress versus fraction plateau coverage
for 0.4 um and 0.7 um size particles. ... 381

8.72 Schematic illustration showing (a) concentration
profile, 0(Z), of adsorbed layer consisting of three
regions (i) proximal (very sensitive to the details of
the interactions), (ii) central (self-similar), and
(iii) distal (controlled by a few loops and tails) and
(b) "self-similar grid" presentation of an adsorbed
polymer layer.. . ..... 382

8.73 Plots of hysteresis area versus fraction plateau
coverage for 0.4 um and 0.7 um size particles.. 384

8.74 Plots of (a) relative density of sedimented samples
versus fraction plateau coverage and (b) median pore
radius versus fraction plateau coverage for 0.4 um and
0.7 um size particles.. .. . 386

8.75 Plots of normalized median pore radius (i.e., median
pore radius/particle radius) versus fraction plateau
coverage for 0.4 um and 0.7 pm size particles.. ... 387

8.76 Adsorption isotherms for PVAs with similar molecular
weights but varying degree of hydroxylation of 20 vol.%
SiO2 suspensions. . . 389


xix












8.77 Plots of relative viscosity versus shear rate of 20
vol.% silica suspensions prepared with different PVAs
with indicated degree of hydroxylation. The
suspensions are prepared at pH 3.7 with the plateau
adsorbed amounts of PVAs . 393

8.78 Plots of specific volume frequency versus pore radius
for gravity cast samples prepared from 20 vol.% SiO2
suspensions with plateau adsorbed amounts of PVAs with
indicated degree of hydroxylation.. . 394

8.79 Plots of (a) relative viscosity versus adsorbed amounts
and (b) relative viscosity versus fraction plateau
coverage for 20 vol.% SiO2 suspensions prepared using
varying PVA concentrations in solution. The degree of
hydroxylation of different PVAs used is shown in the
figure. . .... .. ... 396

8.80 Plots of hysteresis area versus fraction plateau
coverage for 20 vol.% siO2 suspensions prepared using
PVAs with indicated degree of hydroxylation.. .. 397

8.81 Plots of (a) yield stress versus adsorbed amount and
(b) yield stress versus fraction plateau coverage for
20 vol.% Si02 suspensions prepared using PVAs with
indicated degree of hydroxylation.. .. 398

8.82 Plots of (a) relative density of gravity cast sample
versus fraction plateau coverage and (b) median pore
radius versus fraction plateau coverage of compacts
prepared from 20 vol.% Si02 suspensions with varying
PVA concentration in solution. The degree of
hydroxylation for various polymers is indicated in the
figure . 399

8.83 Plots of (a) relative viscosity versus Na2SO4
concentration and (b) yield stress versus Na2SO4
concentration for 20 vol.% Si02 suspensions with
plateau coverages of particles with adsorbed polymer. 402

8.84 Plots of relative viscosity versus shear rate for 20
vol.% SiO2 suspensions with varying Na2SO4
concentration.. . 403

8.85 Plot of hysteresis area versus Na2SO4 concentration in
solution suspensions were prepared at pH 7.8 with the
plateau adsorbed amount of PVA with molecular weight =
200,000.. . . 405

8.86 Plots of (a) relative density of gravity cast samples
versus Na2SO4 concentration and (b) median pore radius
versus Na2SO4 concentration.. . .. 406














8.87 Plots of (a) relative density of slip cast samples
versus Na2SO4 concentration and (b) median pore radius
versus Na2SO4 concentration in solution.. .. .... 407

8.88 Plots of Na2SO4 concentration versus PVA concentration
in solution. Solid line separates single phase region
(i.e., true polymer solution) from the two phase region
(i.e., precipitated polymer and solvent). .. 410

8.89 Plots of relative viscosity versus Na2SO4 concentration
for suspensions of polymer coated particles and
suspensions prepared with no added polymer at pH 7.8. 411

8.90 Plots of (a) relative density of gravity cast samples
versus Na2SO4 concentration and (b) median pore radius
versus Na2SO4 concentration of compacts prepared from
suspensions of polymer coated particles and suspensions
with no added polymer at pH 7.8.. ... ..... .412


xxi
















Abstract of a Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



THE EFFECT OF POLY (VINYL ALCOHOL) ON THE
PROPERTIES OF MODEL SILICA SUSPENSIONS

By

Chandra S. Khadilkar

December 1988




Chairman: Dr. Michael D. Sacks
Major Department: Materials Science and Engineering



The effect of interparticle interactions on the properties of model

suspensions of monosized, spherical silica particles was investigated.

The electrostatic interactions between particles were controlled by

changing suspension pH. The effect of adsorbed polymer was investigated

using water soluble poly (vinyl alcohol), PVA. The adsorption was

dependent on a variety of factors including the overall polymer

concentration in suspension, PVA molecular weight, PVA degree of

hydroxylation, silica surface hydroxylation, and suspension pH. The

adsorption characteristics were correlated with the state of particulate

dispersion in suspension using theological measurements. Suspension and

green compact properties were highly dependent upon the fraction of

silica surface covered by the adsorbed polymer and the thickness of the

adsorbed polymer layer. Suggestions are made for selecting polymer


xxii












molecular weight to prepare stable suspensions with higher solids

loading.


xxiii














CHAPTER I
GENERAL INTRODUCTION AND AIM OF THE STUDY


Particle/liquid suspensions are prepared in various ceramic

processing operations such as mixing, milling, spray granulation of

powders, slip casting, tape casting, extrusion, etc. The control of

theological behavior of suspensions is important to maximize the

processing efficiency and also to obtain the desired properties of the

final products. The theological behavior of particle/liquid suspensions

can be modified by changing (1) particle characteristics (e.g., size and

shape distribution), (2) liquid characteristics (e.g., viscosity), (3)

particle concentration (solids loading of the suspensions), (4)

interparticle forces in suspension, and (5) additives like dispersants,

polymers, etc.

The interparticle interactions in suspensions can be broadly

classified into two categories: (1) electrostatic interactions and (2)

interactions due to adsorbed polymer. The electrostatic interactions

arise due to development of charge at the solid/liquid interface. The

electrically-charged interface leads to the formation of diffuse

"electrical double layer" surrounding each particle. The overlap of two

electrical double layers during Brownian encounter gives rise to

repulsive forces between the particles which can overcome the Van der

Waal's attraction. The effects of surface potentials (or charge) and

ionic concentrations on the stability of dispersions can be

quantitatively described using the "DLVO" theory (Chapter III).












Organic polymers are extensively used as processing aids in ceramic

forming operations. In addition to acting as binders and plasticizers,

polymers are often used to control the theological properties of

dispersions. The interactions between particles with added polymer are

highly dependent on the adsorption behavior of polymer on particle

surfaces. Generally, at low polymer concentrations in solution,

suspensions can be destabilized (i.e., particles are aggregated) due to

"bridging flocculation" where a polymer molecule can adsorb

simultaneously onto two or more particles. At sufficiently high polymer

concentrations in solution, under certain conditions, stable suspensions

(i.e., in which primary particles are well separated) can be prepared.

Two important factors controlling the interactions between the particles

are (1) the fractional coverage of the particle by adsorbed polymer

(which affects the bridging flocculation) and (2) the thickness of the

adsorbed layer (which governs the stability at complete coverage in a

good solvent).

A model ceramic powder (i.e., well-characterized, agglomerate-free,

spherical, narrow-sized silica) was used in this investigation. The

electrostatic interactions between particles were modified by varying the

suspension pH and ionic strength. The effect of surface potentials on

the flow curve parameters (i.e., extrapolated yield stress, relative

plastic viscosity, etc.) were analyzed using the "elastic floc" model.

Water soluble poly (vinyl alcohol), PVA, was used to investigate

the effect of adsorbed polymer on the suspension properties. PVA being a

neutral polymer, the effects of electrostatic interactions and the

effects of adsorbed polymer on the dispersion stability can be studied












less ambiguously. The concentration of PVA in solution can be readily

determined; hence, the adsorbed amounts of PVA could be determined

easily. The polymer adsorption behavior and theological properties on

the same system are rarely reported in literature. The adsorption

experiments are generally carried out using dilute suspensions of high

surface area, agglomerated powders, whereas theological measurements are

conducted on concentrated suspension where adsorption behavior and

interparticle interactions are not very well defined. In this study,

most of the theological measurements and adsorption experiments were

carried out at the same solids loading (= 20 vol. %). The adsorption of

PVA onto the silica surface was dependent on a variety of factors

including the overall solution concentration, polymer characteristics

(PVA molecular weight and degree of hydroxylation), silica surface

nature, suspension pH, etc. The adsorption characteristics were

correlated with the state of particulates in suspension using theological

measurements. Suspension theological properties and green compact

properties (e.g., relative density, median pore radius, etc.) were highly

dependent on the fraction of silica covered by the adsorbed polymer and

the thickness of the adsorbed layer.

A floc structure (i.e., floc compactness, strength, etc.) consistent

with the theological behavior and green compact characteristics is

proposed. (Experimental techniques to obtain this information are not

yet readily available). Finally, some suggestions regarding selection of

polymers to achieve stable suspensions with high solids loading are made.

In the first part of thesis, we deal with general and theoretical

concepts related to this work. In Chapter II, we describe the polymer












adsorption behavior at solid/liquid interface. Chapter III deals with

the electrostatic interactions between colloidal particles, and Chapter

IV deals with the effect of adsorbed polymer on dispersion stability.

The effect of interparticle interactions on the state of particulate

dispersion in suspension is described in Chapter V. The correlation

between suspension structure and theological behavior is discussed in

Chapter VI. The silica preparation and characterization is described in

Chapter VII. PVA fractionation and characterization is also described in

Chapter VII. In Chapter VIII, we discussed experimental results obtained

in this study. First, we describe the effect of electrostatic

interactions on the theological behavior of 20 vol.% silica suspensions.

Subsequently, PVA adsorption behavior on silica particles is correlated

with the theological properties of suspensions and green compact

characteristics.

















CHAPTER II
ADSORPTION OF POLYMER AT SOLID/LIQUID INTERFACE


Introduction

Adsorbed polymer at solid/liquid interface has a profound effect on

the stability behavior of suspensions. Typically, at low polymer

dosages, flocculation of particles in the suspension can occur, while at

the high polymer concentration, stable suspensions can be prepared.

Polymer adsorption behavior has been extensively studied because of the

present and the potential applications in industry, technology, and

medicine. The polymer adsorption behavior is important in various

processes (tape casting, slip casting, extrusion of ceramic parts,

adhesion, separation of polymers, soil improvement, etc.) and various

products (paints, cosmetics, magnetic tapes, pharmaceuticals, dyes,

foods, lubricants, etc.). Theoretical interests in the polymer

adsorption process stems from the fact that insight can be gained into

the nature of the forces acting between polymer segments and surfaces and

between particles coated with the adsorbed polymer. From the ceramic

processing point of view, by the optimization of the adsorption process,

one can control both the suspension properties as well as consolidated

microstructures obtained from these suspensions.

The adsorption behavior of the polymer is different from the

adsorption behavior of the small molecules (e.g., gas adsorption at

solid/gas interface, surfactant adsorption, etc.). This difference












arises because polymers have a large number of internal degrees of

freedom (i.e., flexibility).

Polymer molecules have a random coil type of arrangement in the

solution. A full description of the shape of a molecule requires the

description of the relative positions of each atom of the molecule (the

configuration, see Flory 69). It is common to assume that a polymer

chain consists of a number of connected chain segments for the

theoretical treatments. Then, the conformation of the adsorbed polymer

is described by specifying the relative positions of the endpoints of

these segments (Kuhn 34). To understand the adsorption behavior of

polymers, one needs to consider both the energetic and kinetics of the

adsorption process. Polymer molecules experience short-range attractive

forces near the adsorbing interfaces. For each polymer segment adsorbed

on the surface, there is a decrease in the free energy of the system. At

the same time, upon adsorption, the random coil structure of the polymer

molecule in the solution will be distorted, which will lead to a decrease

in the number of conformations of the adsorbed polymer. This entropic

factor will oppose the adsorption process. Final conformation of the

adsorbed polymer depends on this subtle balance between the entropic and

the enthalpic terms. Also, though there is a small energy decrease due

to adsorption process per segment of the polymer molecule, large number

of segments per molecule can be adsorbed, and the total energy decrease

per molecule can be quite large. Actual bonding mechanism between the

polymer segment and the surface may involve various interactions such as

electrostatic interactions, Van der Waal's interactions, hydrogen bonding

or hydrophobic bonding.










7


The actual conformation of the adsorbed polymer near solid-liquid

interface depends upon various factors such as solid-liquid, polymer-

liquid and polymer-solid interactions, flexibility of the polymer

molecule, concentration of the polymer in the solution, etc.

Experimentally, it has been found that the adsorption isotherm

(i.e., adsorbed amount of polymer as a function of equilibrium

concentration of polymer in solution at fixed temperature and pressure)

of high molecular weight polymers display high affinity type of

character, i.e., a steep initial part of the adsorption isotherm followed

by a pseudo-plateau region. Adsorbed amounts at the plateau region are

typically on the order of approximately one to four mg/m2. This amount

is much more than that can be accommodated in a close-packed monolayer of

the polymer segments. This led early investigators to propose the

conformation of the adsorbed polymer as shown in Figure 2.1 (Jenkel and

Rumbach, 51). From Figure 2.1, it is clear that not all of the segments

of the adsorbed polymer are in direct contact with the surface. This

type of conformation is commonly called as "train-loop-tail"

conformation. "Train" is defined as a sequence of consecutive segments

in direct contact with the surface. "Loop" is defined as a sequence of

segments with the end segments in direct contact with the surface, and

remaining segments are in contact with the solution. "Tail" is defined

as the portion of the chain with end segments in contact with the

surface. From this type of conformation, it is clear that there is a

significant change in the polymer conformation upon adsorption compared

to the random coil arrangement in the solution and that the adsorbed

polymer has sufficient extension in the solution. Actual details of the






Train-Loop-Tail
Polymer


conformation


of Adsorbed


Tail


Liquid

Train ,1 I_


Loop




S\\


Solid


Schematic representation of an adsorbed polymer molecule.


Figure 2.1













conformation are dependent on the various factors mentioned previously.

Some other types of conformations of the isolated adsorbed polymer

molecules are shown in Figure 2.2 (Sato and Ruch 80).



Description of Adsorbed Polymer

The adsorption behavior of the polymers at the solid/liquid

interface is commonly characterized using the following parameters.

Adsorbed Amount of Polymer (A)

This is the most commonly measured parameter in any adsorption

experiment and is usually obtained by "solution depletion" techniques.

Adsorbed amounts are commonly expressed in the units of mg of polymer

adsorbed per unit area of the solid surface. It is also common to define

the dimensionless adsorbed amount or adsorbance, y, as the number of

segments adsorbed per surface site or the number of (equivalent) complete

monolayers than can be formed from the adsorbed amounts (Cohen Stuart

80a). This means that y is the ratio between the adsorbed weight per

unit area and the weight adsorbed per unit area in a complete monolayer,

A
mon.
y A/A (2.1)
mon

As we have seen earlier, there is a conformational change upon the

adsorption of the polymer. Hence, for a complete description of polymer

adsorption, it is not sufficient to measure only the adsorbed amount of

polymer, as similar adsorbed amounts could be obtained for the thick

adsorbed layer of polymer with low segment concentrations or thin

adsorbed layer with high segment concentration.














(a) (b) (c)


(d)


(e)


(f )


Figure 2.2


Conformations of adsorbed polymer molecules (a) single
point attachment, (b) train-loop-tail adsorption,
(c) flat multiple site attachment, (d) random coil,
(e) nonuniform segment distribution, and (f) multilayer
(Sato and Ruch, 1980).


-jvb4i


j k-












Bound Fraction (p)

This is defined as the fraction of adsorbed amount of polymer in

direct contact with the surface, i.e.,

p Atr/A (2.2)

where Atr is the amount of polymer adsorbed per unit area in trains. The

bound fraction measures the change in the conformation upon adsorption.

The p close to one indicates the polymer lies flat on the surface having

two-dimensional structure; on the other hand, p close to 0 indicates

polymer has essentially random coil shape with no significant change in

conformation (Figure 2.c).

Direct Surface Coverage (8)

This is defined as the fraction of the available surface sites

occupied by polymer segments.

0 = Atr/A
Smon (2.3)

where Atr and A as defined previously and from the definition of 8
mon

and p, it follows that

y 0/p (2.4)

Segment Density Distribution p (X. Y, Z)

Segment density is the time-averaged volume fraction of segments per

unit volume in the vicinity of the polymer molecule. In solution, many

polymers adopt random coil conformation. For such a random coil, the

segment density averaged on all conformations is usually Gaussian in any

direction passing through the center of the molecule. (More accurately,

the distribution is better represented by a prolate ellipsoid of

revolution, see Flory 53.) Upon adsorption, there is a significant

change in the conformation of the polymer molecules. At low adsorption












density (i.e., isolated polymer molecules) the segment density

distribution will be dependent upon Z (i.e., distance from the adsorbing

surface) and also on X, Y (ie., position parallel to the surface). At

higher adsorption densities, there will be a significant lateral

interpenetration of the molecules (since the volume percent occupied by

the segments is approximately ten percent at typical segment densities,

i.e., there is enough empty space in a given polymer molecule) and the

segment density distribution will be dependent on Z only. This segment

density distribution is the most important feature of the adsorbed

polymer in the theory of steric stabilization. Various types of segment

density distributions have been proposed for the adsorbed polymer and

will be reviewed later (Napper 83). The segment density distribution

determines the extension of the adsorbed polymers into the solution

phase. This extension of the adsorbed polymer layer can be expressed in

terms of a thickness parameter such as the root mean square layer

thickness 6, which is defined as follows:


82 Z2 p (Z) dZ/ f p (Z) dZ (2.5)
o o

Theoretical Models

The adsorption behavior (and hence, conformation) of polymers at

solid-liquid interface is governed by various factors including polymer

segment-surface, surface-solvent, and segment-solvent interactions. The

driving force for the adsorption is the reduction in the net free energy

due to bonding of a polymer segment to the surface. This binding process

involves the removal of the solvent molecule from the surface and

replacement with the polymer segment. Energy change associated with this












process is denoted by the dimensionless adsorption energy parameter, Xs.

This polymer adsorption process is opposed by the entropy changes

associated with the changes in conformation upon adsorption. Polymer

molecules have three-dimensional random coil structure in solution, and

upon adsorption, some of the segments (i.e., train) are restricted to two

dimensions.

This process is associated with considerable loss of entropy per

molecule, and the magnitude depends on the chain length and flexibility.

At equilibrium, the distribution of polymer molecules between the surface

and the solution is essentially determined by the following five

independent parameters: concentration of the polymer in solution, chain

length (molecular weight), flexibility, adsorption energy parameter, and

polymer-solvent interaction parameter. Variables, such as temperature,

time (kinetics), and polydispersity, may also play an important role.

Below, we will define some of these variables and discuss the effect of

these independent variables on the adsorption.



Adsorption Energy Parameter (x,)

As mentioned earlier, the bonding between the surface and the

segment is the driving force for adsorption. A precise definition of Xs

is due to Silberberg (Silberberg 68). The energy change (i.e., net

enthalpy change) associated with the transfer of a polymer segment in a

pure polymer from a bulk site to a surface site, minus the corresponding

energy change for a solvent molecule in pure solvent, is denoted by

-XskT. By choosing proper reference states (i.e., pure polymer and pure

solvent), Xs is made independent of solvent-segment interactions and













depends only on the nature of the surface. It is clear from the

definition that for Xs > 0 indicates segments are preferred over the

solvent by the surface. Due to adsorption, polymer loses part of its

conformational entropy and will oppose the adsorption. Hence, a certain

minimum adsorption energy, denoted by Xsc, is required for the adsorption

to take place.



Segment-Solvent Interaction Parameter (x)

Linear, flexible polymer molecules have a random coil shape in the

solution. For an "ideal" chain (i.e., polymer molecule represented as

chain consisting of volumeless, non-interacting statistical units), this

random coil conformation can be described by random walk in three

dimensions. For an ideal chain, it can be shown that the radius of

gyration is proportional to the molecular weight of the polymer and can

be represented by the following equation:

1/2 w05 (2.6)

where is the root mean square radius of gyration and Mw is the

molecular weight of the polymer (Flory 53). However, real chain segments

have volume and interact with each other, and this effect is usually

represented by the excluded volume effect, which can be defined in terms

of either segment-segment interaction energy or in the framework of the

Flory-Huggins theory of polymer solutions as the segment-solvent

interaction parameter, x. The parameter x represents the quality of the

solvent. Theoretically, X < 0 for a very good solvent, X = 0 for an

athermal solvent, and x 1/2 for an ideally poor or a 8 solvent. X

represents an exchange process (and in such a way that), xkT represents












the difference in energy of a solvent molecule immersed in a pure polymer

compared with one surrounded by pure solvent molecules. For x > 0, the

solvent is poor and segment-segment contacts are preferred over segment-

solvent contacts. The adsorption of polymer at the solid-liquid

interface leads to an increase in the concentration of the segments near

the surface, and the segment-segment or the segment-solvent interaction

parameter has a profound effect on the adsorption. In poor solvents,

adsorbed amounts of polymer are larger due to the fact that segments

prefer other segments over solvent molecules. The x parameter is one of

the basic parameters of the polymer solution thermodynamics, and hence,

plays an important role not only in the polymer adsorption behavior but

also in the theories of steric stabilization.



Polymer Adsorption Theories: General Framework

The aim of polymer adsorption theories is to try to relate the

conformations of the adsorbed polymer molecules to independent variables

(such as adsorption energy parameter, Xs, solvent-segment interactions,

X, molecular weight of the polymer, M, its concentration in solution,

etc.). Various investigators have paid a lot of attention to the

theoretical development of these models (for e.g., see Eirich 77;

Hoeve 65,66,70,71; Silberberg 62,67,68; Scheutjeans and Fleer 79,80;

deGennes 80,82,87). Since a large number of polymer molecules are

involved, a statistical thermodynamic approach is usually employed.

Contributions of the entropy and the energy of many chains in a given

concentration gradient near the surface are evaluated. To evaluate these

contributions, the thermodynamic theory of polymer solutions, as









16

developed by Flory and Huggins, is often employed (Flory 53). More

recently, scaling concepts have been applied to the polymer adsorption

(deGennes 87).

To describe polymer adsorption behavior, according to the methods of

statistical mechanics, the partition function of the system is set up

(see, Cohen Stuart 80a).

Q E Q e-U/kT (2.7)
where Q is the degeneracy, i.e., the number of different ways of

arranging systems having energy, U.

To evaluate Q and U, appropriate reference states are chosen

(usually unmixed pure components). To evaluate Q, all possible energy

states of the system are considered. To determine the equilibrium state

of the system, Q is maximized. For example, Q is related to the free

energy of the system by

G = -kT Ln Q (2.8)

and hence, G should be at minimal for equilibrium. To evaluate and

maximize Q, one needs to make certain assumptions, and the quality of

these assumptions leads to differences between various theories.

The earlier polymer adsorption theories (for e.g., Hoeve, Roe,

Silberberg, etc.) were formulated to describe the conformations of

isolated polymer chains. In these theories, train-loop-tail type of

polymer conformation was assumed. The chain conformation statistics,

such as average train, loop sizes, and tail, loop size distributions were

computed (but, tails were ignored). The segment-surface interaction was

taken into account using the adsorption energy parameter, Xs, (i.e.,

first layer interactions), but the solvent-segment interaction was

ignored. Since these early theories ignored solvent-segment interactions












and formulated for isolated chains (i.e., non-interacting with other

adsorbed polymer molecules), their usefulness is limited.

Later theories employed Flory-Huggins polymer solution model to

account for segment-segment and segment-solvent interactions (Hoeve,

Silberberg, Roe, Scheutjeans and Fleer). The theories of Hoeve and

Silberberg start with the train-loop model of the adsorbed polymer (i.e.,

tails were neglected) and the conformation probabilities of the adsorbed

chains were computed. To evaluate U, assumptions were made regarding the

shape of the segment density profile. Hoeve assumed the exponential

profile for the evaluation of U (i.e., segment-segment, segment-solvent

interactions) while Silberberg assumed step function for the segment

density profile (Silberberg 68). This assumption regarding segment

density profile to evaluate U has been avoided in the recently developed

theories of Roe, Scheutjeans and Fleer (Roe 74, Scheutjeans and Fleer

79,80). These theories do not assume a model for the mode of polymer

adsorption of an individual molecule. They derive the partition function

for the mixture of free and adsorbed polymer chains and solvent

molecules; a number of ways of arranging polymer chains and solvent

molecules in a given (arbitrary, but fixed) concentration gradient near

the surface was determined. Maximization of the partition function gives

the equilibrium concentration profile (Scheutjeans and Fleer 79,80). To

evaluate U, segment-segment and segment-solvent interactions were

calculated using Flory-Huggins theory. Roe neglected the tails in

evaluation of the energy term and his model predicts overall segment

density profile. Later theory (SF) gives the complete distribution of

polymer conformation near the surface and gives information about train,












loop, and tail distributions. The important difference between the Roe

and the SF theory is the contribution of the long dangling tails to the

overall segment density profile at relatively large distances from the

interface, and these long tails can play an important role in the

flocculation and stabilization of the system. Unfortunately, no simple

analytical expressions are available with these theories and substantial

computational time is required to calculate the conformation of the

adsorbed polymer.

The scaling relation applicable to semi-dilute polymer solutions has

been extended for the polymer adsorption problem by deGennes (see,

deGennes 87). This theory is limited to athermal solvent (good solvent

with x 0) with moderate adsorption energies. Though this theory is

analytical, the results are in the form of power-laws without exact

coefficients.

In the next section, some of the predictions of these polymer

adsorption theories will be discussed. These theories are mostly

applicable for mono-dispersed homopolymers polymer on a homogeneous

substrate. Other complications arising due to inhomogeneous surface

structure and charge at the interface are not taken into account.



Results of the Polymer Adsorption Theories

In this section, the dependence of properties of the adsorbed

polymer layer (such as total surface coverage (i.e., the adsorbed amounts

A), direct surface coverage (i.e., occupancy in the first layer 8), bound

fraction (p), root mean square layer thickness (6), segment density

distribution) on various independent variables (such as solution











concentration, chain length, X and Xs) will be reported. Only general

trends will be reported. For detailed comparison between various

theories, recent reviews are recommended (Fleer 87, Fleer and Lyklema

83).

Effect of Adsorption Energy Parameter (Xc)

All theories predict that the adsorption energy parameter should

exceed a certain critical (non-zero) adsorption energy, i.e., Xs > Xsc

for the adsorption of polymer to take place. This critical adsorption

energy parameter Xsc corresponds to the minimum energy necessary to

compensate the unfavorable entropy loss of the segment, upon adsorption,

compared to segment in solution. If the Xs > Xsc, then the surface

coverage increases sharply with increasing Xs. At high Xs values, the

surface becomes saturated and the total surface coverage 8, becomes

independent of Xs. For lattice theories, the critical value of Xsc is

related to the lattice type employed (Scheutjeans and Fleer 79,80).

Effect of Solvent-Segment Interaction Energy Parameter (x)

The effect of solvent on adsorption behavior is pronounced. The

adsorbed amount of polymer increases while bound fraction p decreases

with decreasing quality of the solvent (i.e., as the solvent becomes

poorer). (Though the adsorbed amount and the direct surface coverage are

increased, the ratio, the bound fraction p is decreased.) Average loop

and tail size are increased with decreasing the quality of solvent

(Scheutjeans and Fleer 79,80).

Effect of Polymer Concentration and Molecular Weight

Adsorption isotherms for high molecular weight polymers are the high

affinity type. Adsorbed amounts are high for higher molecular weight












polymer. For a good solvent, adsorbed amounts tend to reach a limiting

value for high molecular weights, but from a poor solvent, various

theories predict different trends. The increased amounts of adsorbed

polymer with increasing molecular weight (and concentration in solution)

are accommodated by increases in the average size of the loop and tails.

This leads to an increase in the thickness of the adsorbed layer with

increasing polymer concentration and molecular weight. For a low polymer

concentration (typically, 0p < .01, where 0p is the volume fraction of

polymer in the solution), the adsorbed amount in a 8-solvent increases

linearly with log Mw. This dependence, as predicted by SF theory, is

different from the empirical power law relations, i.e., A a MV, where A

is the plateau adsorbed amount of polymer (mg/m2) and a is an empirically

determined constant. For dilute concentration, the bound fraction

decreases with increasing molecular weight. Root mean square thickness

also increases with the molecular weight and the concentration.

The effect of tails, ignored in the earlier theories, is important

at finite polymer concentrations. (At extremely low polymer

concentrations, the adsorbed polymer lies in relatively flat

configuration). These tails will affect the average layer thickness and

the segment density profile at the outer region of the adsorbed layer,

and hence, will be very important for colloidal stability.

The segment density distributions predicted by various theories are

very important in various theories of steric stabilization. As mentioned

earlier, Hoeve assumed an exponential segment density distribution (Hoeve

65) whereas Silberberg assumed it to be step function (Silberberg 68).

Roe and SF theory can calculate segment density distributions without any









21



assumptions (Roe 74; Scheutjeans and Fleer 79,80). Both theories predict

an approximately exponential segment density distribution near the

surface. At larger distances, S.F. theory predicts a high density

compared to Roe's theory. This higher density is due to long dangling

tails. These long tails can dominate interparticle interactions and the

hydrodynamics of coated particles. The tail length increases with

increase in the molecular weight almost linearly for high molecular

weight polymer (Cohen Stuart 80a). Hence, molecular weight of the

polymer is among the most important variables for controlling theological

and other properties of the dispersion. In the next section, various

experimental techniques used to characterize polymer adsorption will be

briefly described.



Experimental Techniques

An excellent review is available for the details of various

techniques (Cohen Stuart, et al. 86a). Adsorbed amount A, direct surface

coverage 8, bond fraction p, layer thickness 6, and segment density

distribution (Z), can be characterized experimentally.

The Adsorbed Amount of Polymer

Generally, a "solution depletion" technique is used to determine the

adsorbed amount of polymer. In this method, from the equilibrium and

initial known concentrations of polymer in solution, the adsorbed amount

of polymer is determined. Centrifugation is commonly used to separate

particles from the suspension, and the supernatant is analyzed. Various

analytical techniques are used to determine the solution such as

gravimetric, complex formation to give species which adsorb in the UV or












visible part of the electromagnetic spectrum (Zwick 65), etc. In certain

cases, direct determination of the adsorbed amount is possible (e.g., IR,

ellipsometry).

Trains, Bound Fraction, Direct Surface Coverage

Techniques to determine these parameters are broadly classified into

spectroscopic methods, electrochemical methods, and calorimetric methods.

(1) Spectroscopic Techniques: Spectroscopic techniques include infrared

(IR), electron spin resonance (ESR), and nuclear magnetic resonance

(NMR). Due to specific interactions between polymer segments and solid

surface, shifts in a characteristic band, either for the adsorbate (e.g.,

the carbonyl or benzene group in a polymer) or the adsorbent (e.g., the

hydroyl group on an oxide) is utilized to determine the bound fraction

using IR spectroscopy (for e.g., see Killmann 76; Takahashi et al. 80;

Fontana et al. 61,63,66; Korn et al. 80a,80b, etc.). ESR can only be

used for spin labeled polymers (Robb and Smith 74). Mobility criteria

are used to distinguish between adsorbed and non-adsorbed segments.

Segments having different mobility will give different magnetic

relaxation times and hence mobility. NMR technique is also based on the

mobility criterion to estimate p.

(2) Electrochemical Methods: Adsorbed neutral polymer affects the

electrical double layer properties (such as change in the double layer

capacitance and shift in the point of zero iLarge, PZC). These

properties can be utilized to determine the fraction of surface area

occupied by segments, 8 (Koopal 78).

(3) Microcalorimetric Approach: In this metkod, the heat of immersion

of adsorbent is measured at various adsorbed amounts of polymer.













Calibration can be achieved from the heat offimmersion of a monomeric

analog compound of the adsorbed group (Korn et al. 80a,80b; Cohen Stuart

et al. 82; Killmann et al. 71; Hair 77).

There are several problems associated with these techniques, such as

distinguishing between contributions due to adsorbed and non-adsorbed

polymer, differentiation between train and loop segments, etc.

Thickness of the Adsorbed Layer

Methods to determine the thickness of the adsorbed polymer layer can

be divided into two broad categories: (1) ellipsometry and

(2) hydrodynamic methods.

(1) Ellipsometry: In this method, change in the properties of the

elliptically polarized light upon reflection, due to the adsorbed

polymer, is measured. From the measured phase shift and the amplitude of

the reflected light, under the assumption of homogeneous polymer layer,

the ellipsometric thickness and the refractive index of the film can be

calculated (e.g., see Killmann 76,77). Clearly, the assumption of

homogeneous segment density distribution leads to ambiguity in the

measured thickness. Also, this method is suitable for flat surfaces with

good reflectivity, and hence, limited mostly to bulk metal substrates and

some oxide films.

(2) Hydrodynamic Methods: These methods measure the extent of outward

shift of the slip plane due to the adsorbed polymer layer. Essentially,

they measure the drainage characteristics of the adsorbed layer, and

since the drainage characteristics of the adsorbed polymer layer (i.e.,

consisting of loops and tails) are not known, an exact definition of the

hydrodynamic thickness is not possible. Also, if the adsorbed polymer












layer is not homogeneous (e.g., at low adsorption densities), this method

may over estimate the thickness. To measure the hydrodynamic thickness,

several techniques have been employed.

(i) Capillarity: In this method, the inside wall of the fine capillary

is coated with the adsorbed polymer layer, and the decrease in the flow

rate due to adsorbed layer is measured (i.e., the effective decrease in

the diameter of the capillary is determined). In this method,

homogeneous coating of the capillary is critical (e.g., see Rowland and

Eirich 66; Priel and Silberberg, 78).

(ii) Viscometry: In this method, the increase in the viscosity of the

suspension of dispersed particles due to adsorbed polymer layer is

measured. Due to the adsorbed polymer layer, there is an increase in the

effective radius of the particle, hence, higher effective volume fraction

solids in the suspension. For dilute dispersions, the intrinsic

viscosity, [C], is measured (Barsted et al. 71; Dawkins and Taylor 80)

while, for the concentrated suspensions, the high shear viscosity is

determined (Dobroszkowski and Lambourne 66). To get information about

the adsorbed layer, other parameters affecting the viscosity must be

taken into account. Factors such as electroviscous effects, aggregation

of particles, effect of shear on the thickness of the adsorbed layer,

polymer degradation, etc. can complicate the interpretation. In this

study, the adsorbed polymer thicknesses are determined from the high

shear rate viscosities. The effect of PVA molecular weight on the

adsorbed layer thickness will be reported later.

(iii) Photon Correlation Spectroscopy: In this method, the diffusion

coefficients of the particles with and without adsorbed polymer are










25

measured using "Doppler" broadening of an incident laser line (for e.g.,

see van den Boomgaard et al. 78; Kato et al. 81; Garvey et al. 76;

Killmann et al. 85,86,88, etc.). From the measured diffusion

coefficients, the particle radius, and hence, the adsorbed layer

thickness, is calculated using the Stokes-Einstein equation:

D kT/6rioRh (2.9)

where Rh = hydrodynamic radius of the particle, no = viscosity of the

suspension medium, T absolute temperature, and k = Boltzmann constant.

This method is limited to monosized, spherical particles.

To obtain accurate values of the adsorbed layer thickness, diffusion

coefficients are determined at various solid concentrations and the plot

of diffusion coefficient vs. solid concentration is extrapolated to zero

solids concentration. This procedure then eliminates the effects of

interparticle interactions on the diffusion coefficient. As the adsorbed

polymer layer is usually a small fraction of the particle radius, it is

essential to obtain accurate values of particle radii with and without

polymer.

(iv) Electrokinetics: In this method, the decrease in the electrokinetic

potential (Zeta potential) of the charged particles, due to adsorption of

neutral polymer, is measured to estimate the hydrodynamic thickness.

Essentially, this method measures the outward displacement of the slip

plane due to adsorbed polymer. Again, several complications are present

in interpreting this data and the measured thickness is very sensitive to

the ionic strength of the solution (Koopal 78; Cohen Stuart et al.

84a,84b,85).













(v) Other Methods: Sedimentation rate (i.e., change in the

sedimentation coefficient due to the adsorbed polymer layer), (Garvey et

al. 74) direct force-distance measurements (i.e., half the distance at

which a certain minimum force is observed between two approaching

surfaces, coated with the adsorbed polymer), etc., have been used to

measure the thickness of the adsorbed layer (Sonntag et al. 82; Lubetkin

88; Gotze and Sonntag 87,88).

From the above discussion, it is clear that there are several

techniques available to measure the layer thickness, but due to

uncertainty about the effect of the tail-loop conformation of the

adsorbed polymer on the properties of measured layer thickness, each

technique gives some kind of average property of the adsorbed layer.

Recently, it has been shown that the hydrodynamic thickness is

essentially determined by the tails and that the loop contribution is

negligible (Cohen Stuart 86a).

Segment Density Distribution

Small angle neutron scattering (SANS) has been used to obtain the

segment density distribution for the adsorbed polymer. In this

technique, the ability of neutron to distinguish between hydrogen and

deuterium atoms, due to different coherent scattering cross sections, is

utilized. By using a suitable mixture of H20/D20, particles can be

contrast matched, and by measuring scattering intensity at various

angles, information about the adsorbed polymer can be obtained.

Unfortunately, the method is not sensitive enough yet to detect small

concentrations of the tail segments at larger distances (Barnett et al.

82).













Adsorption Energy Parameter

As mentioned earlier, Xs represents the energy change associated

with the exchange process of replacing solvent molecule from the surface

with the polymer segment. Cohen Stuart has proposed a method to measure

this parameter (Cohen Stuart 80a). In this method, a second solvent

having strong affinity for the surface is added to the solution. With

increasing concentration of the solvent displacedr), eventually polymer

can be desorbed completely from the surface, and from this critical

displacer concentration, Xs can be determined.



Adsorption of Polydisperse Polymers

Polymers used in practical application are mostly polydisperse,

and polydispersity has an important effect on the adsorption behavior.

This effect arises due to the difference in the adsorption behavior of

long and short molecules. Long molecules are preferentially adsorbed

over short molecules. As discussed earlier, the adsorption process is

controlled by the various free energy changes related to adsorption

process. The energy decrease due to adsorption of polymer segments is

opposed by the entropy loss. The decrease in entropy arises from two

contributions: (1) the loss of configurational entropy due to the

unmixing of polymer molecules and solvent molecules and (2) the decrease

in conformation entropy due to the decrease in number of different

possible arrangements of the polymer as a result of the attachment of

segments to the solid surface. In dilute solutions, which is of

practical interest in most adsorption studies, the conformational entropy

losses for one large chain compared to two shorter chains, each half the











length of the loner chain length, are similar. However, the decrease in

configurational entropy for the two short chains is twice that of the

longer chain. Hence, adsorption of the long chain.is preferred over the

two short chains. Also, the long chain can displace the short chains

from the surface. Theory based on the above principles has been

developed, and it is successful in explaining various effects arising due

to the polydispersity of polymers (Cohen Stuart 80a,80b,84a; Koopal 81).

(1) Rounding of the adsorption isotherms: All polymer theories and

experiments using monodispersed polymers exhibit sharp adsorption

isotherms, whereas polydisperse samples lead to more rounded isotherms.

(2) Irreversibility: The observed irreversibility of adsorption

isotherms can be explained from the above theory.

(3) The effect of amount of adsorbent on the amount adsorbed and

the shape of the adsorption isotherm: Experimentally, it has been found

that the adsorption isotherms are sharper and the plateau adsorbed

amounts larger if the adsorption isotherms were determined using dilute

dispersions (i.e., small surface area/volume of the solution ratio)

(Koopal 81).

Preferential adsorption of the high molecular weight polymer over

the low molecular weight leads the fractionation of the polymer. The

molecular weight distribution in the adsorbed layer is shifted to higher

molecular weight as compared to that in the solution (Furusawa et al.

82). Also, from the practical processing point of view, the

preferentially adsorbed high molecular weight fraction may dominate the

properties of the dispersions, such as the rheology and the consolidation

behavior.












Additional factors, such as the charge on the solid surface and the

effect of the solid surface structure, will be discussed in the

experimental section.



Experimental Results for PVA-Water System

Properties of Poly (Vinyl Alcohol), PVA

PVA is a commonly used polymer as a steric stabilizer in aqueous

media. PVA is prepared by alcoholysis of poly (vinyl acetate), PVAc, and

is generally not hydrolysed fully. (Often the degree of hydrolyses is on

the order of 88 mole percent or greater). It is, therefore, a copolymer

of PVAc and PVA. This can be represented as follows:

CH2 CHOAc Polymerization > -CH2-CH-CH2-CH-CH2-
I I
vinyl acetate OAc
OAc OAc
poly (vinyl acetate)
> -CH2-CH-CH2-CH-CH2-CH-
I I I
OH OAc OAc

poly (vinyl alcohol) containing acetate groups.

where symbol OAc represents acetate groups, -COOH. Copolymers have been

shown to be the best steric stabilizer for the following reasons:

Usually, they consist of two types of segments having contrasting

solubilities in a given aqueous or non-polar dispersion media. Less

soluble segments of the copolymer will preferentially attach themselves

to the solid surface, and thus, the polymer is firmly anchored to the

surface. Thus, such a copolymer then consists of two types of segments,

anchoring moieties and stabilizing moieties. Strong attachment of the

polymer with the surface will prevent desorption of polymer or lateral

movement of the polymer on the surface when two particles coated with












with adsorbed polymer will be encountered during Brownian collisions. In

good solvents, the stabilizing moieties will offer repulsion, due to

overlap of segments (i.e., due to osmostic effects).

This copolymeric nature of PVA makes direct comparison between

experimental results and theoretical predictions difficult and only

qualitative trends will be discussed. Also, the previously discussed

theories were mainly developed for the monosized, homopolymers, while

commercial polymers are usually polydispersed. In this section,

available literature on the PVA adsorption behavior on various substances

will be reviewed.

Two types of PVA's, i.e., partially hydrolysed, PVA88,

(approximately 88 percent hydrolysed) and completely hydrolysed, PVA98,

(greater than 98 percent hydrolysed) have been employed in various

experimental investigations. Boomgaard et al. fractionated as-received

polymer by sequential addition of acetone (i.e., a non-solvent) to

approximately five wt.% PVA solution (van den Boomgaard et al. 78).

Garvey et al. used preparative scale Gel Permeation Chromatography (GPC)

to obtain narrow molecular weight fractions (Garvey et al. 74). These

investigators did not measure the polymer molecular weight distribution

or the polydispersity index Mw/Mn, where Mn is number average molecular

weight and Mw is the weight average molecular weight. Acetone fractions

gave fractions of varying molecular weights, but the degree of hydrolysis

was also different for different fractions. (The degree of the

hydrolysis decreased from the approximately ninety to approximately

eighty mole percent with the decrease in the molecular weight) (van den

Boomgaard et al. 78). Other studies used as-received commercial polymer.












PVA Characterization

From IR and UV spectra, Koopal concluded that the commercial samples

used in his study were atactic and contained no or very little impurities

(impurities, such as 1,2 glycol units and one or two conjugated groups if

present are present as the end groups) (Koopal 78). The acetate group

distribution is "blocky" for the PVA88, and acetate groups were

distributed more or less "randomly" for the PVA98. Dunn (Dunn 80) and

Barnett et al. (Barnett et al. 82) assumed that for the PVA88, the

average block consists of three acetate groups. They assumed that the

average acetate block size increases and the width of the acetate block

size distribution increases with increasing PVA molecular weight.

The Mark-Houwink-Sakurada (MHS) equation was generally used to

determine the viscometric average molecular weight, My of the polymer.

[n] kMya (MHS) (2.10)

where [n] is the intrinsic viscosity and k and a are MHS empirical

constants. The values of the constants k and a used by various

investigators are different. This can lead to different values of My for

the same polymer (i.e., same En]). The values of k and a are dependent

on the temperature, the acetate content, and the polydispersity of the

sample. The value of constant a was in the range of 0.64 to 0.60 for

PVA98 and was in the range of 0.71 to 0.63 for PVA88 (e.g., see Koopal

78). The PVA solution properties (i.e., the segment-solvent interaction

parameter x) and polymer molecule dimensions in solution (i.e., radius of

gyration, end to end distance, etc.) were determined from the measured

intrinsic viscosity and molecular weight for a series of samples with

varying molecular weights. If these two quantities are not independently












available, then the MHS equation (Equaiton 2.9) was used to determine Mv

from the measured intrinsic viscosity. Hence, the values of solution

properties and polymer molecule dimensions were influenced by the values

of constants k and a used. For this reason, these values (i.e., X, 2,

etc.) should be compared with caution since different values of constants

k and a are employed by various investigators.

(1) The Segement-Solvent Interaction Parameter: X

Detailed comparison of the available values of x parameter has been

made by Koopal (Koopal 78). At 250C in aqueous solutions, the x values

were in the range of 0.462 to 0.488 for PVA88 and in the range of 0.475

to 0.499 for PVA98. Thus, the degree of hydrolysis does not have

significant effect on the solvent quality for typical PVA polymers. It

should be noted that the aforementioned values of the x parameter

indicate that water is a relatively poor solvent for PVA. This also

suggests that intersegmental interactions occur in the polymer chain

(Koopal 78). van den Boomgaard et al. have determined the effect of

temperature on the x parameter (van den Boomgaard et al. 78). With

increase in the temperature from 250C to 50C, the x value changed from

0.464 to 0.485, indicating worsening of the solvency for PVA. Tadros and

Vincent and Barker and Garvey have determined the effect of type and

electrolyte concentration on the solvency (Tadros and Vincent 79; Barker

and Garvey 80). With increase in the electrolyte concentration, the

solvency decreases. They also found that Na2SO4 has greater effect on

solvency compared to NaC1, i.e., lower concentration can change solvent

quality.












(2) The Xs Parameter:

One needs to measure the adsorption energy parameter for both

acetate and alcohol groups since the PVA adsorption mechanism may involve

adsorption of these two groups. Heat of adsorption of low molecular

weight analogues may be useful with this respect, but Xs values are not

available for the various systems investigated. Typically, values in the

range 1 2 kT have been assumed for Xs (Barnett et al. 82).



The Adsorbed Amount of Polymer

The Nature of Solid

PVA adsorption behavior has been studied on AgI solid particles (Fleer

71), AgI particles and sol (Koopal 78), silicas of various types (e.g.,

precipitated, Cab-o-sil, Ludox, Tadros 78), polystyrene latex particles

(made by emulsion and dispersion stabilization, Garvey, et al. 74,76),

montmorillenite clays (Greenland 62, Heath and Tadros 83). Due to

differences in the chemical nature and surface heterogeneities (e.g.,

silica powder calcined at various temperature leads to various types of

surface groups and the concentration of each group is dependent on the

thermal history; polystyrene latex particles made by dispersion

polymerization technique have more hydrophobic surface, etc.), it is not

possible to compare adsorption data on the same basis. Also, other

variables, such as solid concentration, aging time, polydispersity of the

polymer samples, and the method of sample preparation, etc., can have an

important effect. The detailed comparison with the literature results

will be made in the results and discussion section. Here, we will

briefly describe the important results.













The Effect of Acetate Content

The plateau adsorbed amounts (i.e., "saturation adsorbed amount" or

adsorbed amounts at "complete" surface coverage) are generally more for

PVA88 (i.e., partially hydrolysed PVA) than PVA98 (i.e., fully hydrolysed

PVA) of similar molecular weights. This effect have been found on

various substrates (e.g., AgI, Koopal 78; silica, Tadros 78; PS latex,

Barnett, et al. 82). The larger adsorbed amount for PVA88 can be due to

(i) increase in the adsorbed amount in the first layer (i.e., A ) or
mono


due to (ii) the formation of larger loops and tails. The adsorbed amount

differences in the monolayer between these two polymers cannot account

for this difference, hence, the contribution of the first layer to this

difference is small (Koopal 78). The increase in adsorption with

increasing acetate content has been attributed to greater adsorption in

loops and tails. As explained earlier, X (PVA98) and X (PVA88) are only

slightly different, and the difference in adsorption behavior cannot be

explained by the solvency effect. The preferential adsorption of acetate

groups onto AgI particles has been determined by Koopal from the

electrochemical method (i.e., from the shift in the point of zero change)

(Koopal 78). The preferential adsorption of acetate groups leads to

accumulation of acetate groups in the first layer and gives an important

contribution to the gain in the free energy of adsorption (i.e., Xsl, the

adsorption energy parameter for acetate groups is expected to be larger

than the adsorption energy parameter for alcohol groups, Xs2). The

differences in flexibility of these two polymers (i.e., it can be assumed

that the flexibility of PVA88 is relatively lower due to bulky acetate

groups) will have effect on the size of the trains and loops. The train














size is limited by the length of the acetate blocks and lower flexibility

of PVA88 can set constraints on the minimum loop size (i.e., the average

loop size is expected to be larger for PVA 88). The preferential

adsorption of acetate groups has been confirmed by NMR studies on PS

latex particles (Barnett, et al. 82).

The Effect of Molecular Weight of PVA

As expected from the theoretical results, increased plateau adsorption

with increasing molecular weight of PVA has been observed. Generally,

this effect is represented by the following power law relation:

A KM(a (2.11)

where A is the plateau adsorbed amount of polymer and K and a are

empirical constants. (Please note that the Equation 2.11 is empirical in

nature. Modern adsorption theories (for e.g., SF, Roe) predict A a log

M. which is an entirely different type of functional relation). For the

adsorption of PVA98 on the PS latex (made by dispersion polymerization),

a 0.5 has been reported (Garvey et al. 74). Weak molecular weight

dependence has been observed for adsorption on AgI particles, a 0.1 for

PVA98 and a 0.2 for PVA88 (Koopal 78). The hydrodynamic thickness of

the adsorbed polymer layer increases with the molecular weight (Garvey et

al 74; Killmann et al 88). The hydrodynamic thickness has been measured

using various techniques (Electrophoresis, Viscometry, PCS, ultra

centrifugation, slow speed centrifugation, direct force measurements,

etc.). Again, the relation between the hydrodynamic thickness and

molecular weight is represented by a power law. Generally, the measured

hydrodynamic thicknesses were comparable to the random coil dimensions in

solution.












The Effect of Solvency

Increases in temperature (van den Boomgaard et al. 78) and additions of

electrolyte (Tadros and Vincent 79; Barker and Garvey 80) increased the

plateau adsorbed amounts. This has been related to the worsening of

solvent quality with temperature and electrolyte. Decreases in the

measured hydrodynamic thickness with increasing temperature and

electrolyte concentration were observed.

Adsorbed Layer Properties and Adsorbed Amounts

It has been suggested from theoretical results (e.g., see Fleer 87)

that, although adsorbed layer properties such as 0, p, adsorbed layer

thickness, etc. are dependent on Mw and solution concentration, it is

still possible to express the adsorbed layer properties as a function of

the adsorbed amount only (i.e., the properties of the adsorbed layer are

the same for the high molecular weight polymer at low concentrations and

for the low molecular weight polymer at high concentrations provided the

adsorbed amount is the same). Based on the above hypothesis, Koopal

plotted adsorbed layer properties, such as the first layer occupancy 0,

and effective layer thickness 6 (measured experimentally), as a function

of adsorbed amount (Koopal 78). His results are shown in Figure 2.3. As

expected from the theoretical and other experimental results, the root

mean square thickness increased with increasing adsorbed amounts. The

results for PVA98 and PVA88 are plotted on the same graph since no

significant difference was found in X (PVA98) and X (PVA88) values. From

the above results, he concluded that the acetate content and molecular

weight influenced the adsorbed layer properties through adsorbed amounts

only.






























0 .5 1 1.5 2
ADSORBED AMOUNT (mg PVA/m2 )


.5 1 1.5 2

ADSORBED AMOUNT (mg PVA/m2)


Figure 2.3


Plots of (a) degree of occupancy, 9, and the effective
layer thickness, 6, as a function of the adsorbed amount
of PVA on AgI and (b) the fraction of segments adsorbed
in trains as a function of the total adsorbed amount
(Koopal, 1978).












The Segment Density Distribution

The segment density distributions have been determined (Figure 2.4)

using SANS for adsorbed PVA on PS latex particles (Barnett et al. 82).

Typically, an exponential segment density distribution was observed near

the surface. (This would be expected by the polymer adsorption theory of

Hesselink in which the conformation consists of loops and trains, but no

tails--Hesselink 71a.) However, higher segment density at the

intermediate distances were related to longer "slightly folded" tails

(Barnett et al. 82). This type of segment density distribution was

different from the homopolymer PEO adsorbed on PS latex, where more or

less exponential decay in the segment density was observed. In the study

of PVA adsorbed on PS, the root mean square thickness calculated from the

segment density distribution was smaller than results obtained by PCS.

It was concluded that the SANS results were not sensitive enough to

detect tails (which are present in low concentration) and the tails are

responsible for the higher measured hydrodynamic thickness determined by

PCS (Barnett et al. 82).

The Effect of Particle Radius

The effect of particle radius on adsorption behavior and the

hydrodynamic thickness has been studied by Garvey et al. (Garvey et al.

76) and Ahmed et al. (Ahmed et al. 84). The former investigators related

the increasing hydrodynamic thickness with decreasing particle radius to

a geometric factor (Garvey et al. 76). Other groups correlated this

observation to change in the conformation of the adsorbed polymer due to

the change in the particle radius (Ahmed et al. 84).






















0
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0 G








4j


4V ,
2 c:

u 0


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04
-4










(i-u) ,LISNa(I (I~ ZIwI ION
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PVA Adsorption on Silica

Tadros has investigated the PVA adsorption behavior on various types

of silicas (Tadros 78). Here, we will state the results from his

investigation. A detailed comparison of his results and the results in

this study are made in Chapter VIII.

(1) The Effect of Silica Calcination Treatment:

It was observed that the plateau adsorbed amount is a strong

function of silica surface characteristics. The maximum in the plateau

adsorbed amounts was observed for approximately 700*C calcined silica.

This observation was correlated with the optimum density of isolated

silanol groups on 700*C calcined silica.

(2) The Effect of Surface Charge:

The maximum adsorption occurs at the point of zero change, p.z.c.,

of the oxide and progressive decrease in the adsorption was observed

above p.z.c (Tadros 78). (This effect was not observed for AgI particles

and sol--Koopal 78, Fleer 71).



Summary

From the above discussion, following general trends have been

established regarding adsorption behavior of PVA.

Water is a relatively poor solvent for PVA (X is close to 0.5).

Partially hydrolysed PVA is blocky, while for fully hydrolysed PVA,

acetate groups are randomly distributed.

Partially hydrolysed polymer adsorbs more than fully hydrolysed PVA.

Adsorption density increases with increase in the molecular weight.













- NMR and electrochemical methods suggest that the acetate segments are

preferentially adsorbed.

- Adsorbed layer properties such as bound fraction (p) and effective

thickness are functions of amount adsorbed only for PVA adsorption on

AgI.

- Segment density distribution is exponential near the surface and

relatively higher density (compared to an exponential distrituion)

observed at the intermediate distances is related to the presence of

slightly folded tails for PVA adsorption on PS.

- Hydrodynamic layer thickness is substantial (five to fifty nm) and, it

is primarily the tails which are responsible for these large measured

thicknesses.

Calcination temperature and pH are among the most important variables

controlling PVA adsorption behavior onto silica.

In the next Chapter, we will review the electrostatic interactions

between colloidal particles.
















CHAPTER III
ELECTROSTATIC INTERACTIONS BETWEEN COLLOIDAL PARTICLES


Introduction

Properties of the colloidal dispersion are directly influenced by

the interparticle interactions. A colloidal dispersion is a two-phase

mixture consisting of dispersed particles (solid) in a continuous

dispersion medium (liquid). Particles are said to be colloidal in

character if at least one of its dimensions is in the size range 1 nm to

104 nm (1 um). In this size range, specific surface area is large

(usually few m2/gram up to 1000 m2/gram), and hence, the interparticle

interactions are dominated by the solid-liquid interface characteristics.

Also, in this particle size range, the gravitational force is not

important, and particles are moving randomly in the dispersion media due

to thermal energy, i.e., Brownian motion. Particle encounters due to

Brownian motion either leads to either formation of doublets (or higher

order multiplates) or particles remain as individual units depending on

the interparticle interactions. In the absence of any repulsive

interactions, these random collisions lead to permanent contacts between

particles and this reduces the free energy of the system. (The free

energy is lowest when the particles are all clumped together). The

origin of attractive interactions between particles is in the Van der

Waal's attraction between the atoms of the colloidal particles. The

characteristics of the aggregates formed also depend on the interparticle












forces. To prevent such aggregation of particles during collisions,

there are two mechanisms available to overcome attraction.

(1) Electrostatic Interactions: If the colloidal particles can be given

an electric charge (either positive or negative) and if all particles

have the same sign of charge, particles will repel one another during

approach.

(2) Interactions of Adsorbed Polymer: Under certain conditions (i.e.,

depending on the coverage of particle surfaces with adsorbed polymer,

thickness of the coating, solvency for polymer, etc.), adsorbed polymer

layer can prevent close approach of the particles.

These two repulsive interactions impart stability to the colloidal

dispersion. The dispersion is said to be stable if the dispersed phase

(colloidal particles) remains essentially as distinct single particles on

a long time scale (e.g., days, months, years). Such a dispersion may be

stable either due to kinetic (e.g., in the case of electrostatic

interactions) or thermodynamic reasons (e.g., stabilization with adsorbed

polymer). It is clear from the above definition that the stability

criteria is essentially based on the state of particulates in the

dispersion. The time scale is employed as a reference because, in the

absence of repulsive interactions, the number of particles (kinetic

units) in moderately concentrated suspensions can be reduced to half in a

matter of seconds due to encounters arising from Brownian motion (von

Smoluchowski 16a,16b,17).

The stability criterion based on the time scale (for e.g., time it

takes to reduce the particle concentration to half, etc.) may not be

useful to evaluate the stability of ceramic dispersions. The reasons are












two fold: (i) typically particles in the size range of 0.05 um to 5-10 um

are often employed in various ceramic processing operations, and hence,

suspensions are not strictly colloidal in nature. Also, the density of

particles is usually greater than the density of suspending media leading

to sedimentation of particles although particles are well dispersed.

(ii) the particle concentration is also quite high, and usually, it is

not possible to determine the change in particle concentration. Other

techniques, such as theological behavior, sedimentation behavior,

properties of the sediment (porosity, average pore size, etc.) can be

used to evaluate the stability of these dispersions.

Although interatomic attractive interactions are short range (a r-6

where r is the distance between the atoms), their summation over

colloidal particle sizes leads to long range attraction. To overcome

this attraction, the repulsion must also be long range.

In this chapter, we will review two components of interactions

(1) Van der Waal's attraction between colloidal particles, and

(2) electrostatic interactions.

Summation of these two components, under the assumption of

additivity, leads to well known theory developed by Deryagin and London

and independently by Verwey and Overbeek (commonly known as "DLVO"

theory) to explain the stability behavior of the electrostatically

stabilized dispersions (e.g., see Verwey and Overbeek 48). Excellent

monographs are available to discuss various aspects of this theory, hence

only the basic principles will be outlined here (e.g., see, Hiemenz 77,

Hunter 87, Overbeek 82a,82b, Lyklema 68, etc.).












Development of Charge at Solid-liquid Interface

There are basically four different methods by which the charge can

be developed at the solid/liquid interface (Hunter 87).

Dissociation of Surface Groups

This method is the charge determination mechanism for several oxides

(e.g., alumina, silica, etc.). The surface of these oxides is

hydroxylated to various extents. (For example, for precipitated silica

used in this investigation, the surface is almost completely

hydroxylated, i.e., the surface is nearly fully covered with silanol

groups, Si-OH). Dissociation of surface silanol groups leads to surface

charge development, as described by the following reactions:


-SiOH + H+ > SiOH 2
(-S surface) + (liquid) > i 2(surface) (3.1)

-SiOH(surface) + OH (liquid) -io (surface) + H20(liquid)


From the above reactions, it is clear that the silica surface can develop

a positive or a negative surface charge.

A zero point of charge, (p.z.c.), is defined as a pH at which the

surface charge is zero. Another important characteristic of the oxide

material is its isoelectric point, i.e.p., which is defined as the pH at

which the electrophoretic mobility is zero. H+ and OH- ions are called

the potential determining ions. In the absence of specific adsorption of

ions, the p.z.c. and the i.e.p. are the same. Below the i.e.p., the

silica surface is positively charged, and above the i.e.p., negative

charge is developed and its magnitude can be increased by increasing pH

of the solution.












Adsorption of Potential Determining Ions

A familiar example is silver iodide particle/water suspensions in

which the particles can preferentially adsorb an Ag+ or I- ions,

rendering them positive or negative charge, respectively.

Adsorption of Ionized Surfactants

In this case, the charge is produced by the preferential adsorption

of the ionic surfactants on the surface, for example, the preferential

adsorption of C12H25SO4- ions from sodium dodecyl sulfate, C12H25SO4-Na+

surfactant.

Isomorphic Substitution

This charge development mechanism is important in the case of clay

minerals (e.g., sodium montmorillenite). Inside the solid lattice, lower

valent ions may replace higher valent ions (e.g., Al+3 replaced a Si+4

ion in the "tetrahedral silica layer," resulting in a deficit positive

charge on the particle surface.

For the present investigation, dissociation of surface silanol

groups on the silica particles is the important mechanism of charge

development. The silica used in this study has an i.e.p. near pH = 3.7.

Hence, at high pH's, the silica surface develops negative surface charge,

and at pH near 3.7, no net charge is present on the silica particles.

(Hence, there is no net electrostatic repulsion between two approaching

particles at pH = 3.7.)



Electrical Double Layer

The development of surface charge is not yet a sufficient condition

for stability because electroneutrality requires that the particle and










47


its immediate surroundings should have no net charge. In other words,

the surface charge must be balanced by an equal but opposite counter

charge in the solution. The rigid alignment of counter ions in the

solution is implausible because of thermal agitation, which causes the

counter ions to diffuse throughout the solution. To understand the

stability, it is of crucial importance to understand the distribution of

counter ions in the solution.

The stability of the charged particles can be understood

qualitatively as follows: If the counter charge is very diffusely

distributed and extends far from the particle surface, then when two

particles having the same sign of charge (and hence, same sign of the

counter ions in the diffuse layer) start approaching each other due to

Brownian motion (or due to an applied shear field), the diffuse layer

starts to overlap (even though the particles are far apart), thus giving

rise to an electrostatic repulsive force. On the other hand, when the

double layer is compressed (i.e., the counter ions are crowded close to

the particle surface), particles can approach closer before they feel the

electrostatic repulsion, and at that distance, the strong Van der Waal's

attraction leads to flocculation of the particles.

To explain the stability behavior quantitatively, a description of

the potential (or charge) distribution around the colloidal particles is

required. To describe the variation of the potential with the distance

from the charged surface, the Poisson equation is used as shown below:

V2 -P (3.2)
E E
o r

where T is the potential, V2 is the Laplace operator, Er is the relative

permittivity, Eo is the permittivity of the free space, and p is the












local charge density (i.e., number of charges per unit volume). To solve

this equation, one needs to know the charge density as a function of

potential.

The work required to bring an ion to a position where the potential

T is given by ZieY. The probability of finding an ion at that position

is given by the Boltzmann factor:

n. -Z.eW
exp ( k (3.3)
n. kT
10

where T is the temperature, k is the Boltzmann constant, ni is the number

of ions of type i per unit volume, and nio is the concentration far from

the surface (i.e., the bulk concentration). The valance number Zi is

either a positive or negative integer and e is the charge on the

electron. The charge density is related to the ion concentrations, as

follows:

Z.eW
p E n. e Z. E Z. e n. exp ( (3.4)
i 1 1 o kT

Substituting for the charge density, one obtains the Poisson-Boltzmann

equation, as follows:

-Z.eW
V2 E n. Z.e exp ( ) (3.5)
2 lo i kT
or i

The following assumptions were made in solving the above equation:

(1) The surface charge on the particle and the space charge in the

solution are considered as smeared out. (2) The ions are considered as a

point charges, their distribution in the solution being determined by

their valancy and not by their volume, shape or polarizability. This

assumption makes the theory non-specific (e.g., the difference between












Li+ and Na+ ions cannot be distinguished). (3) The solvent is considered

as homogeneous and continuous, and the solvent affects the charge

distribution through its dielectric constant Er.

It is clear from the above equation that the potential distribution

depends in a complex way on the ionic composition of the solution. This

equation does not have an explicit general solution and has been solved

for certain limiting cases (e.g., low surface potentials) and for simple

geometries (i.e., flat plate, spherical particle, etc.).

At room temperature, the exponent ZieT/kT = ZiY/25.4 if T is

expressed in millivolts.

Debye-Huckel solved the above equation for flat plate geometry and

for low surface potentials, (i.e., Zij < 25.4 mV). Under these

conditions, they showed that the potential decays exponentially (Hunter

87):

'V = Vo exp (-xx) (3.6)


where x is the distance from the interface and the X, the Debye-Huckel

parameter, is defined as follows:

e2 E. .2 1/2
e En. Z.
10( 1) (3.7)
E E kT
ro

x has the units of reciprocal length, i.e., x-1 has the units of length.

The exponential rate of the potential decay is controlled by H (Equation

3.6). If the double layer thickness is defined as the distance over

which the potential drops to (1/e) of its value at the surface, then x -

becomes the measure of the "double layer thickness." At 250C in water,

the value of x is given by:

x = 3.288 4 I (nm-1) (3.8)










50

where I is the ionic strength (= 1/2 E CiZi2 where Ci is the ionic

concentration in mole/liter). Table 3.1 shows calculated values of

X-1 (i.e., the double layer thickness) for several different electrolyte

concentrations and valences for aqueous solutions at 250C.

From the table, it is clear that the valency of the counter ions and

the electrolyte concentration are important parameters to the control

double layer thickness, and hence, the electrostatic interactions between

colloidal particles.

Figure 3.1 shows the variation of the potential with the distance

from the surface. The drop is dramatic for the higher electrolyte

concentrations or valances.

The Poisson-Boltzmann equation has been solved for flat plates

without the Debye Huckel approximation (i.e., ZiY < 25 mV) by Gouy-

Chapman. The results are applicable only to symmetrical electrolyte,

i.e., Z+ = Z-. According to the Gouy-Chapman, the variation of potential

within the double layer can be described by the following equations

(Hunter 87):

Y = Yo exp (-Kx) (3.9)

where y is defined by the relationship

S= exp (ZeW/2kT) 1 (3.10)
exp (ZeW/2kT) + 1

and yo is calculated from the above equation when Y = Yo. From Equations

3.9 and 3.10, it is clear that it is the complex ratio y that varies

exponentially with x in the Gouy-Chapman theory. For the low potentials,

as expected, the above equation reduces to the Debye-Huckel approximation

(i.e., Equation 3.6).

















TABLE 3.1

Effect of Ionic Strength and Valency on the
Electrical Double Layer Thickness, x-1


Symmetrical
-1
Ionic Strength Electrolyte w1
(moles/liter) Z+ : Z. (nm)



1 x 10-4 1:1 30.41

2:2 7.60

3:3 3.36



1 x 10-3 1:1 9.61


1 x 10-2 1:1 3.04


1 x 10-1 1:1 0.96

















Figure 3.1


Fraction of double
layer potential
versus distance
from a surface:
(a) curves for 1:1
electrolyte at
three concentra-
tions and (b)
curves for 0.001 M
symmetrical
electrolytes of
three different
valance types.


Figure 3.2


II I


-I
S Oiffuse layer
2 1
o yp
M


Distance from wall


Schematic
illustration of
the variation of
potential as a
function of
distance from a
charged surface in
the presence of a
stern layer,
subscripts o at
wall, 6 at stern
surface, d in
diffuse layer.


* '


Potential


J4


I
. s'--- ----


I












To describe the potential variation as a function of distance from

the interface for spherical particles, the Poisson-Boltzmann equation

should be solved in spherical coordinates. For the case of low surface

potentials, analytical solution is available and given by the following

equation:

S() a (a-r) (3.11)
9 (r) = ---- e
o r

where V (r) is the potential at a distance r from the particle center and

a is the particle radius.

In the theoretical development of the above equations, Debye-Huckel

and Gouy-Chapman treated ions as point charges, i.e., the effect of ion

size was ignored. To account for the finite volume of the ions, Stern

divided the aqueous part of the double layer by a hypothetical boundary

known as the Stern surface (Hunter 87). The Stern surface is situated at

a distance 6 from the actual surface as shown in Figure 3.2.

The Stern theory is difficult to apply quantitatively because it

introduces several parameters into the picture of double layer which

cannot be evaluated experimentally. There are several other models

available to describe the charge and the potential variation at the

charged interface, but they suffer the same problem as the Stern's model

(Hunter 87).

It is important to note that the existence of the Stern layer does

not invalidate the expressions for the diffuse part of the double layer,

but one needs to use a potential at the Stern layer, 86. This Stern

layer potential is usually equated with the zeta potential, which is the

potential measured using an electrokinetic method. The exact location of












at which the zeta potential is determined is not known, but it is assumed

to be close to the Stern layer.

In summary, in this section, we looked at the various charge

development mechanisms at the solid-liquid interface. The charge on the

solid surface leads to the distribution of the counter ions in the

solution. This model of the charged interface is often called the

electrical double layer model. The potential variation as a function of

distance from the interface can be obtained by solving the Poisson-

Boltzmann equation. Under the assumptions of low potentials (Debye-

Huckel approximation) and simple geometries, analytical solutions can be

obtained. The parameter of great importance is X (the Debye-Huckel

parameter), which can be used to describe the effect of the concentration

and valence of the counter ions on the potential distribution near the

charged surface. To describe the stability behavior of the

electrostatically stabilized dispersions, calculations are often made of

the interaction energy as a function of distance of separation between

particles. In the next section, expressions for the interaction energy

due to overlap of the electrical double layers will be developed.



Double Layer Interactions

When two particles approach each other, overlap of the double layer

occurs. The rate of approach of the two particles compared with the

relaxation time of the diffuse double layer to adjust to the new

situation is an important parameter. But, generally, two cases can be

distinguished. They are denoted as the "constant potential" and the

"constant charge" interactions.












In the first case, it is assumed that during the encounter of two

colloidal particles, the surface potential Wo remains constant. Under

these conditions, analysis shows that, to keep the surface potential

constant, the surface charge density, oo, should decrease. In the second

case, it is assumed that during the encounter the surface charge density

remains constant, and in this case, the overlap of the diffuse double

layer leads to an increase in Vo. The condition in which both To and oo

are not constant is also possible and has been called a charge regulation

(Hunter 87).

The repulsive interactions due to the overlap of the double layer

can be analyzed using two approaches (Lyklema 68).

(a) the free energy change involved when the overlap occurs, or

(b) the increase in the osmotic pressure due to accumulation of the ions

between the particles.

Following the free energy change approach, there is an increase in

the free energy of the double layer upon interaction, hence, work must be

performed to bring the particles closer. In other words, the overlap of

the double layer leads to repulsion between particles.

The repulsion energy VR(d) represents the work necessary to bring

the particle surfaces from infinity to a distance d. To calculate VR(d),

the free energy of the system as a function of the distance of separation

should be known. It is clear that VR can be represented by the following

equation:

VR(d) = 2 [G(d) G(m)] (3.12)

where G(d) represents the free energy at the distance d and G(a)

represents the free energy at the infinite separation, i.e., for the












isolated double layer. The factor 2 results from the fact that two

double layers are involved. On the basis of the above scheme, DLVO

theory formulates the repulsive interaction energy. The exact solution

is available only for simple shapes (e.g., flat plate) and under certain

approximations (e.g., low potentials). For two flat plates, VR as a

function of distance d has been tabulated by Overbeek for any given value

of the surface potential To and concentration of ions in solution

(Overbeek 52).

The following approximate analytical equations are often used to

represent VR.

Interaction Between the Two Flat Plates

Under the assumption of the linear superposition1 principle, and

under the condition of the constant surface potential during the double

layer overlap, the potential energy is given by the following equation

64n kTy2
VR(d) 4exp (-xd) (3.13)
R exp (-Xd)

where VR is the repulsive interaction energy per unit area (J/m2) and no

is the ion concentration (total number of ions/m3), and the other symbols

have been previously defined.

The above expression is also valid for the constant charge case.

Comparison of the above expression with the exact results (Overbeek 52)

show that over a considerable range of overlap, the above equation is a





1 The assumption is that the potential between two interacting
particles is equal to the sum of potentials of individual double layers
at the same distances from the surface. This is valid in the case of low
surface potentials, i.e., for d > 1/n, the diffuse layer thickness, x-1.












good approximation, though the approximation tends to overestimate the

value of VR (Hunter 87).

A more elaborate expression, valid for higher surface potentials

under the conditions of the constant charge, is also available (Gregory

73).



Interaction Between Two Spherical Particles

This case is more important in the case of colloidal dispersions.

(1) For large values of xa: Large values of xa means that the particle

radius, a, is relatively large compared to the thickness of the diffuse

layer, x-1. Under the conditions of low potentials and thin diffuse

double layer, the repulsion energy can be calculated by Deryaguin

procedure (see Hunter 87). Following this procedure, it is possible to

calculate the interaction energy between two spherical particles if the

interaction energy as a function of distance of separation is available

for the flat plate case under similar conditions. For the case of two

identical spherical particles, the energy of interaction can be

calculated from the following equation:


V (d) (sphere) na VR(d) (flat plate) dD (3.14)
d

where a is the radius of the particle.

Substituting for VR (flat plate), the approximation valid for low

potentials is given by:

V (d) (sphere) 2nE E2aT In ( 1 + exp (-wH) )(3.15)
R r o o

Note that Equation 3.15 gives the total repulsive energy between two

spherical particles (in Joules) whereas flat plate expression (Equation












3.13) gives the energy per unit surface area (in Joules/m2). For the

case of somewhat higher surface potential, the interaction energy is

given by the following equation:

64nan kTy
VR(d) (sphere) = 2 0 exp (-nd) (3.16)
K

For the spherical particles at high potentials, no analytical formula is

available, but a graphical solution is available (Overbeek 52).

(2) For the case of low ma, i.e., when the thickness of the diffuse

layer, x-1, is large compared to particle radius, a, the interaction

energy is given by the following equation:

4nE E aW 2
VR r2ad 0 exp (-d) (3.17)


where 8 is a factor which allows for the loss of spherical symmetry in

the double layer and has been defined by Verwey and Overbeek (Overbeek

52).

From the above equations, it is clear that the repulsion is

determined by the ionic strength (through Debye-Huckel parameter x) and

the surface potential, Vo. For the case of spherical particles, the size

of the particle (i.e., radius a) is also important.

In the above equations, the finite size of counter ions (i.e.,

presence of the Stern layer) was ignored, and hence, these expressions

are not valid for the distances comparable to atomic dimensions.

Additional interactions due to solvation and hydration of ions and

hydrophobic interactions have been reported (Israelachvili and Pashley

82,83; Pashley and Quirk 84; Pashley et al. 82). Theses short range













interactions have been related to repeptization phenomenon (Overbeek

82b).

As mentioned earlier, the other term in DLVO calculations is the

attraction energy term arising due to the Van der Waal's interaction

between the colloidal particles leading to the flocculation of particles.

This attraction energy term will be discussed in the next section.



Van der Waal's Interactions

The Van der Waal's interactions between neutral molecules may

originate from three possible sources: permanent dipole-permanent dipole

(Keesom), permanent dipole-induced dipole (Debye), or induced dipole-

induced dipole (London) interactions. The distance dependence of these

interactions can be represented as a power law, i.e., potential energy of

interaction a r-x where x 6 and all interactions lead to attraction

between molecules. In the case of non-polar molecules as the dipole

moment is zero, Debye and Keesom interactions are absent. On the other

hand, London interactions, also known as dispersion forces, are always

present. The London dispersion force is attributed to correlated

electronic motion in the atoms under consideration. This correlated

motion of electrons leads to a decrease in the potential energy of the

system (i.e., attraction). This attraction energy is short range since

it is inversely proportional to the sixth power of the separation, but

the total interaction energy between two colloidal particles (i.e., a

collection of a large number of atoms) is quite large and of long-range

order and comparable to electrostatic repulsion energy under certain

conditions. The contributions to total interaction energy from the Debye












and Keesom interaction is usually small since dipolar contributions tend

to average out when large number of atoms are considered.

There are two methods of calculating the magnitude of Van der Waal's

attraction energy between two colloidal particles, (i) microscopic and

(ii) macroscopic procedure.



Microscopic or Van der Waal's Method

The classical procedure adopted by Hamaker was based on two

principles

(1) the additivity of London dispersion forces: The total interaction

energy between two colloidal particles was calculated using summation of

pairwise interactions between all the atoms or molecules of the two

macroscopic bodies.

(2) The summation of these interaction energies between atoms or

molecules can be replaced by an integration provided that the distance

between the particle surface is large compared with the atomic distances.

Under these assumptions, the Van der Waal's attraction energy between the

two colloidal particles can be represented as follows:

VA A(A) H(G) (3.18)

Hence, A(A) is a function of so-called Hamaker-Van der Waal's constant of

the material and H(G) is determined by the geometry of the system. For

example,

Flat Plates

For two flat plates of substance 1, the Van der Waal's attraction

energy is given by (Hamaker 37):

11
V (3.19)
A 12nd2












where A11 is the Hamaker constant for the substance 1, d is the distance

between two flat plates, and the negative sign indicates that the energy

is attractive. The Hamaker constant A11 for substance 1 is defined by

A n q2 (3.20)


where ql is the density of atoms in the colloidal particle and 011 is the

constant in the London equation:


V -11- (3.21)
11 6
r

describing interaction energy V11 between atoms or molecules. 11 is

proportional to the polarizability of the atoms, and hence, increases

with the size of the atom. From the above equation, it is clear that the

Van der Waal's attraction energy VA increases with square of the density

of the substance and the interaction is of long range. (Note VA a d-2

for "bulk" materials, compared to V11 a r-6 for molecular interactions.)

Spherical Particles

For two unequal spheres of radius al and a2 separated by a distance

d in vacuum (d is the distance between two surfaces), the Van der Waal's

attraction energy is given by the following equation (Hamaker 37):

-A 2
VA herer) 12 2 2 2
x +xy+x x +xy+x+y x +xy+x+y


where x d/2al and y d/2a2

For two spherical particles, having same radius a, it can be shown

that for large separations, VA decreases with the sixth power of d as in

the London expression, but for short distances (i.e., d << a) VA

decreases slowly with the distance:












-A1
S -A 1 a (3.23)
A -12 d

This distance dependence of the attractive (as well as the repulsive)

energy of interaction is of great importance. As it will be shown later,

at short and at long distances, the Van der Waal's attraction energy

dominates the total interaction energy while at the intermediate

distances of separation, electrostatic repulsion, which decay

exponentially with the distance, may dominate the total energy of

interaction. The above equation indicates that, for a small distance, VA

tends to assume very large negative value. However, the above equations

are no longer valid for very short distances (i.e., dimensions comparable

to the atomic dimensions) because strong Born repulsive interactions

(usually represented as VBorn a d-12), which arise from the overlap of

electronic orbitals of approaching molecules, are operative.



Retardation Effect

The equations given above for VA were derived under the assumption

of the additivity of interactions between atoms. The origin of the

London-Van der Waal's interaction is the electromagnetic interactions

between atoms and molecules. The above equations for VA do not allow for

the finite time of propagation of electromagnetic waves from one atom to

the other, and the induced-dipole becomes retarded against the inducing

one when the distance between the atoms becomes comparable to the wave

length of the London frequency. This leads to reduction in the London

dispersion force between atoms. Casimir and Polder have shown that due

to retardation the inverse sixth power law [Equation (3.21)] gradually

changes into an inverse seventh power law with increasing distance












(Casimir and Polder 48, Gregory 69, and Visser 72). The retardation

correction is negligible when the distances between the atoms are

comparable to the atomic dimensions. However, for the interactions

between the colloidal particles at the distances of the order of ten to

one hundred nmn, the retardation effect can be significant. Equations are

available to correct for the retardation effect for the flat plates and

for the spherical particles (Gregory 67). The retardation effect leads

to reduction in the attraction energy and makes the dispersion force much

longer range.



Effect of Medium on the Van der Waal's Attraction

The equations derived above for the Van der Waal's attraction energy

can be used for the case of two colloidal particles interacting in

vacuum.

In most practical cases, colloidal particles are embedded in a

medium (e.g., water). To get the interaction energy VA in this case, the

Hamaker content All is replaced by the effective Hamaker constant. The

effective Hamaker constant, A131, now depends not only on All (particle-

particle attraction) but also on A13 (particle-medium attraction) and A33

(medium-medium attraction) where subscript 1 refers to particle and 3

refers to medium. The effective Hamaker constant is defined as:

A131 A A11 33 2A13 (3.24)


where All nq B1 A33 n3 33 and A13 = nqlq3 13, and it is generally

1/2
assumed that 013 = (B11033) 2, and hence,


A131 (A111/2 A331/2)2 (3.25)












Thus, to account for the medium, All should be replaced by A131 in all

the previous equations for VA. From the above equation, it is clear that

the effective Hamaker constant is always positive (i.e., there is always

net attraction between two particles) and the magnitude of the Van der

Waal's attraction is reduced due to the presence of the medium (i.e., the

medium imparts a certain measure of stability to the dispersed

particles). By choosing A33 close to A11, the Van der Waal's attraction

can be substantially reduced and at All A33, there is no net attraction

between particles. Thus, to evaluate Van der Waal's attraction energy,

the Hamaker constants should be available for the materials under

consideration.



Macroscopic Approach

One of the main drawbacks of the microscopic or the Hamaker theory

is the assumption regarding additivity of interactions. The Van der

Waal's attraction VA has been calculated using a different approach by

Lifshitz and collaborators using the macroscopicc" approach. In this

theory, the interacting bodies are treated macroscopically, i.e.,

interacting bodies are considered as two semi-infinite phases separated

by the distance d. The bodies are characterized by their complex

dielectric constant. The interaction is evaluated using fluctuation

theory. The spontaneous electromagnetic fluctuation in one body induces

a fluctuation polarization in the other body. The correlation between

the fluctuating fields in the two objects decreases the free energy of

the system, and hence, leads to attraction. The Lifshitz theory has some

advantages over the classical microscopic theory. The assumption












regarding additivity is avoided and contributions of bonding between the

atoms and the molecules to the interactions are taken into account. The

Lifshitz approach is more accurate to calculate VA, but mathematics

involved is quite complicated and requires dielectric constant data over

a wide frequency range of the materials of interest. Due to these

difficulties, the Hamaker microscopic approach is generally used in

practice.



Hamaker Constants

To calculate the Van der Waal's attraction energy for practical

systems, the values of the Hamaker constants should be available. In

principle, there are two ways to estimate the Hamaker constants (see for

e.g., Visser 72, Gregory 69, Lyklema 68):

(1) Direct Calculations: In this case, the Hamaker constant can be

calculated by the microscopic approach (e.g., see equation 3.20) using

molecular properties such as polarizability or by the macroscopic

approach using dielectric constant data.

(2) Indirect Evaluation From the Experimental Data on Colloidal

Stability: In this method, the Hamaker constant will depend on the

experimental tool used to determine stability and the stability criteria

used. The Hamaker constant can be experimentally determined from various

techniques such as (i) flocculation experiments on dispersion of

colloidal particles, (ii) from the measurements of direct force of

interactions between crossed wires, (iii) from equilibrium film thickness

measurements, (iv) surface tension measurements, and (v) from theological

data, etc. (Visser 72).









66

Table 3.2 shows the list Hamaker constants for the present system

under investigation (i.e., silica-water-PVA). Data for other materials

can be found in the above references.

The effective Hamaker constant will be also influenced by the

electrolyte concentration, surface contamination, and adsorbed polymer

layers. The effect of the adsorbed polymer layer will be discussed next.



The Effect of Adsorbed Polymer Layer on Van der Waal's Attraction

The effect of adsorbed polymer layer of thickness 6 on the

attractive force can be compared at (i) constant center-to-center

distance of spheres, h (see Figure 3.3) or (ii) at constant separation of

outer surfaces, d.

If one makes comparison at the constant center-to-cetner distance,

then the adsorbed layer usually leads to an increase in attraction

between particles. This is due to an effective increase in the particle

size and decrease in the distance of separation between particles. If

comparison is made at the constant distance of separation d, the adsorbed

layer usually reduces the attraction between particles. In this case,

the original spheres are separated by a greater distance and generally

the adsorbed material has lower Hamaker constant. The attraction energy

between two equal spheres of radius a, separated by distance d with the

adsorbed layer thickness 8, is given by the following equation:

1 1/2 1/22 1/2 1/2 2
V (d) [H (A 12- A12 ) + H (A22 A )3 +
A 2 11 11 22 22 22 33
(3.26)
SH (1/2 .1/22 (1/2 1/2,
2 H (A A ) (A A )(3.26)
12 11 22 22 33
















TABLE 3.2

Compilation of Hamaker Constants for Silica-Water-PVA System



Hamaker Constant
Material x 10-20 J Technique Reference


Silica 6.6 Macroscopic Hunter 87

(A11) 14.8 Visser 72

50.0 Microscopic

16.4 Surface Tension


Water 3.7 Macroscopic Hunter 87

(A33) 4.4 Lifshits Visser 72

3.3-6.4 Microscopic "

3.0-6.1 Macroscopic "

4.8-3.0 Colloid Chemistry "

5.5-6.4 Surface Tension "


PVA 6.8-8.8 Microscopic Visser 72
(A22)


Hamaker Constant
Material in Water x 10-20 J Technique Reference


Silica 0.85 Macroscopic Hunter 87

(A131)


PVA 0.50 Microscopic Visser 72
(A232)





















































Figure 3.3


Schematic illustration of the effect of adsorbed polymer
layer on Van der Waal's attraction.












where All, A22, A33 are Hamaker constants in vacuum for solid, polymer

and liquid, respectively and H11, etc. are geometric functions defined

as:


H(xy) + 2 Y + 2 in ( ++x ) (3.27)
x +xy+x x +xy+x+y x +xy+x+y


where for H11, x (d+26)/2a and y 1, for H22, x d/2(a+6) and y =1,

and for H12, x (d+6)/2a and y = (a+6)/a. It can be shown from

Equations 3.26 and 3.27 that if the adsorbed layer is sufficiently thick

and when A22 A33, the attraction between particles virtually

disappears. To evaluate the Hamaker constant A22 for the adsorbed layer,

two additional features need to be considered: (i) the adsorbed layer

will be a composite, i.e., it will consist of polymer segments plus

solvent molecules and (ii) the segment density will not be uniform. Both

of these effects on the attraction energy have been discussed by Vincent

(Vincent 74).



Potential Energy Curves and the DLVO Theory

Since the electrostatic repulsion and the Van der Waal's attraction

are assumed to operate independently and since both are being scalar

quantities, they can be added to give the total interaction energy,

Total This is the basis of DLVO theory. The total interaction energy

can be represented as:

V(d) total= VR(d) + VA(d) (3.28)

where VR is the electrostatic repulsion energy and VA is the Van der

Waal's attraction energy term. Substituting for VR and VA from the

previously developed equations, the total interaction energy as a












function of distance of separation between the particles can be plotted.

In this type of plot, the attraction energy term is represented as a

negative term and the repulsive energy by a positive term. Figure 3.4

shows schematically the total interaction energy as a function of the

distance of separation between two surfaces. The shape of the total

interaction energy curve is important in determining the stability of

colloidal dispersions and can be used pictorially to show the influence

of various relevant parameters on the stability. The type of curve shown

in Figure 3.4 results because of the different distance dependence of

the interaction energy terms VR and VA. The Van der Waal's attraction

energy term is important at close approach since at close approach VA a

1/d and also at large distances when VA a d-7 due to the retardation

effect. At the intermediate distance of separation, the electrostatic

repulsion (which decreases exponentially with the distance) is more

important. The summation of these two interaction energy terms having

different distance dependence leads to a total attraction energy curve

having a maxima in a potential energy separating two minimas. The

primary minima results from the strong Van der Waal's attraction at the

short distances and the Born repulsion due to overlap of electron clouds.

At such close distances of approach, recent experiments indicate that an

additional energy term, VS, arising due to solvent structural effects,

should be included (e.g., see Israelachvili and Pashley 82,83). Due to

these additional complications, the exact location and depth of the

primary minima cannot be determined quantitatively. The secondary minima

results from the long-range Van der Waal's attraction and the rapid decay

of the electrostatic repulsion. The depth of the secondary minima is























\ VR


total potential
Energy


- -


secondary
minimum


between
surfaces


, primary minimum
I
I


Figure 3.4


Total potential energy of interaction V(d) = VR(d) +
VA(d) where VR(d) is the potential energy t repulsion
due to double-layer interactions and VA(d) is attractive
potential due to Van der Waal's interactions (Overbeek,
1952).


>1

0




0
C-
4,



a.


,'VA












usually not significant compared to the thermal energy of the particles.

Hence, flocculation of particles in the secondary minima tends be weak.

The other important characteristic of the total interaction energy curve

is the presence of the potential energy maxima. If the height of the

potential barrier, V is greater than the thermal energy of the
max

particles (i.e., V >> kT) then the potential barrier can prevent
max

flocculation of the colloidal particles and the dispersion is stable in a

colloid chemical sense. The fraction of particles that can surmount such

a potential barrier is given by Boltzmann's law. The fraction decreases

exponentially with increasing height of the potential barrier. Vmax of

the order of 5-15 kT has been considered sufficient to achieve long-term

stability (Overbeek 82b). It should be noted that, in the case of flat

plates, the potential energy per unit area is plotted. In these cases,

the total interaction energy is obtained by multiplying by the

appropriate cross sectional area of the particles. In the case of

spherical particles, the net interaction energy is plotted. To

understand the stability behavior, factors influencing the repulsion

energy term VR, and the attraction energy term VA should be considered.

The Effect of Hamaker Constant

The range of values of Hamaker constant for substances (ignoring

retardation effects) immersed in water can be given as follows (Hunter

87):

A 131 30 10 for metal particles

3 1 for oxides and halides, and

= 0.3 x 10-20 J for hydrocarbons.

















































4 8 12 16

DISTANCE OF SEPARATION (nm)


Figure 3.5


The effect of the Hamaker constant on the total
interaction energy curves.


50 kT







25 kT







0 hT







-25 kT












As discussed earlier, this difference essentially arises due to

differences in the polarizability of these materials. Figure 3.5 shows

the effect of the Hamaker constant on the total interaction energy curve.

All other factors (i.e., the surface potential Yo and the Debye-Huckel

parameter x) were kept constant. As expected with increasing values of

A121, the height of the potential barrier decreases and the depth of the

secondary minima increases.

The Effect of Surface Potential, V

The electrical double layer repulsion term VR is usually dominated

by two parameters (a) the near surface potential To and (b) the thickness

of the double layer, 1/x. Figure 3.6 shows that the height of the

potential barrier increases as To increases. (For oxide materials, such

as silica, To can be adjusted by varying the pH of the solution.) The

exact value of To is difficult to determine experimentally due to

complications, such as specific ion adsorption and presence of the Stern

layer, etc., so usually the near-surface potential, i.e., the zeta

potential, C is used. This experimentally determined zeta potential does

establish a lower limit of T,.

The Effect of Electrolyte Concentration

The Debye-Huckel parameter, K, which represents the thickness of the

electrical double layer, depends on both the concentration and the

valance of the indifferent electrolyte (See Equation 3.7). Figure 3.7

shows the effect of concentration of a 1:1 electrolyte on the total

potential energy curve. The potential energy barrier decreases with

increasing electrolyte concentration, and above a certain concentration,

the barrier vanishes. Thus, the addition of an indifferent electrolyte

























3


5
0
2
U





0 1


w




0

-1





Figure 3.6


75 kT


A131=0.85 10-20 (J)
IS = 1 102 (moles/liter)
Sa= 0.2 (pm) 50 kT
\ = 50 (mV)


40
25 kT

30
25

0 kT

10

0
r- -25 kT
4 8 12 16 20

DISTANCE OF SEPARATION (nm)

The effect of zeta potential on the total interaction
energy curves.
















































4 8 12 16

DISTANCE OF SEPARATION (nm)


Figure 3.7


100 kT



-75 kT



-50 kT



25 kT



0 kT



- -25 kT
20


The effect of concentration of 1:1 electrolyte on the
potential energy curves.












can cause a hydrophobic colloid to undergo flocculation. For a given

salt, the critical concentration needed to induce aggregation can be

predicted quantitatively by DLVO theory.

Effect of Particle Radius

The total interaction energy is influenced by the particle radius as

follows. The Van der Waal's attraction energy is proportional to radius,

a, and the electrical double layer repulsion is proportional to a2

hence, the potential energy barrier increases with a. Thus, the bigger

particles are more likely to be stabilized by the electrostatic repulsion

(Figure 3.8).

In summary, for preparing electrostatically stabilized dispersions,

one should operate under the conditions of high zeta potentials and low

ionic strengths. We will examine the effect of electrolyte concentration

in more detail as it proves the validity of the DLVO theory.



The Stability Instability Approach

From the above discussion, it is clear that the form of the total

potential energy curve gives an explanation for the stability behavior of

lyophobic dispersions. When the potential energy barrier has a large

positive value (usually greater than = 10kT), the system is kinetically

stable due to large activation energy opposing transition from the

secondary minima to the primary minima. With decreasing height of the

potential barrier, V the transition from stable to unstable

dispersion is facilitated. Theoretically, the onset of instability can

be defined by the following condition (Overbeek 52):


V(d)total = 0 and dV(d) total/dd = 0
total total


(3.29)