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The electrokinetic properties of calcium oxalate monohydrate

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Title:
The electrokinetic properties of calcium oxalate monohydrate
Creator:
Curreri, Peter Angelo, 1952-
Copyright Date:
1979
Language:
English
Physical Description:
ix, 207 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Adsorption ( jstor )
Aggregation ( jstor )
Calcium ( jstor )
Citrates ( jstor )
Diphosphates ( jstor )
Ions ( jstor )
Macromolecules ( jstor )
Oxalates ( jstor )
pH ( jstor )
Urine ( jstor )
Calcium oxalate ( lcsh )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph. D
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 198-206.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Peter Angelo Curreri.

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University of Florida
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University of Florida
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Copyright Peter Angelo Curreri. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000095684 ( alephbibnum )
06337170 ( oclc )
AAL1115 ( notis )

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THE ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE









By

PETER ANGELO CURRERI









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







UNIVERSITY OF FLORIDA 1979

































Copyright 1979

by

Peter Angelo Curreri



































To Dad
















ACKNOWLEDGEMENTS


Sincere appreciation is extended to the faculty members of the Department of Materials Science and Engineering and in particular to my graduate supervisory committee for their support.

Special thanks to Professor George Onoda and

Professor Birdwell Finlayson for the enthusiastic contribution of their thoughts and expertise during this work.

I also wish to thank Mr. Brian McKibben,

Mr. Doug Deason, and Mr. Mike Stoufer for assistance in some of the experimental measurements; Dr. Marjorie H. Malagodi and Dr. W. C. Thomas, Jr., for clinical samples; Mr. Bernard Burton, Mr. Art Smith, and Ms. Lindreth Du Bois for technical assistance; and my wife Linda for help in figure preparation.

This work was supported by National Institutes of Health grant AM20586-01 and by National Institutes of General Medical Sciences grant GM21056-02.











iv

















TABLE OF CONTENTS

Page
ACKNOWLEDGEMENTS ..........................................vi

ABSTRACT .............................................. vii

CHAPTER
I INTRODUCTION.................................... 1

II AN ELECTROPHORETIC STUDY OF CALCIUM OXALATE NIONOHIYDRATE ............................. 5
Introduction................................. 5
Materials and Methods. ........................ 10
Results.......................................... 12
Discussion................................... 37
Summary ...................................... 49

III ELECTROPHORETIC BEHAVIOR OF CALCIUM OXALATE MONOHYDRATE IN SOLUTIONS WITH NATURALLY
OCCURRING MACROMOLECULES ....................... 50
Introduction.....................................
Materials and Methods ........................ 55
Results and Discussion ....................... 56
Conclusions.................................... 87

IV AGGREGATION MECHANISMS OF SUPER-MICRON
CALCIUM OXALATE MONOHYDRATE.................... 89
Introduction ............ ...................... 89
Materials and Methods ........................ 91
Results and Discussion....................... 97
Conclusions.................................. 111

V THE ELECTROKINETIC PROPERTIES OF CALCIUM
OXALATE MONOHYDRATE IN NATURAL AND
ARTIFICIAL URINES.............................. 112
Introduction................................. 112
Materials and Methods ................. ...... 115
Results and Discussion ....................... 117
Conclusions.................................. 151







V














TABLE OF CONTENTS - continued.



Page
CHAPTER
VI THE NERNST-GOUY-STERN MODEL: ITS VALIDITY AND LIMITATIONS FOR THE CALCIUM OXALATE
MONOHYDRATE DOUBLE LAYER....................... 155
Introduction................................. 155
Results and Discussion ....................... 159
Conclusions.................................. 190

APPENDIX
APL COMPUTER PROGRAMS USED IN CHAPTERS II,
III, AND VI FOR MAKING NGS MODEL DOUBLE
LAYER CALCULATIONS............................. 193

BIBLIOGRAPHY.......................................... 198

BIOGRAPHICAL SKETCH................................... 207





























vi














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



ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE By

PETER ANGELO CURRERI

August 1979

Chairman: George Y. Onoda, Jr. Major Department: Materials Science and Engineering

The electrophoretic properties of monohydrate calcium oxalate in aqueous solutions involving the addition of single electrolytes were found to be consistent with the Nernst-Gouy-Stern (NGS) model of the electrical double layer. For five multivalent salts studied, evidence for specific adsorption was given. The specific adsorption potentials found were approximately proportional to the valence of the adsorbing species. The proteins and the mucopolysaccharides studied also showed evidence of specific adsorption.

Physical crowding of protein adsorbate was indicated by calculations using experimentally determined Langmuir adsorption parameters. When this occurred, there was no longer a mobility sign reversal. This indicated that further protein adsorption was completely



vii













electrostatically driven because it could not bond directly to the surface.

Aggregation of super-micron calcium oxalate was shown to occur in nonsupersaturated solutions if the particle collision rate was increased by application of a fluid velocity gradient. Large polymeric molecules were shown to be capable of flocculating calcium oxalate. It was shown that calcium oxalate can have a finite electrophoretic mobility in urine. The small ions in urine alone could not account for the effect of urine on the mobility of calcium oxalate; however, when the mucopolysaccharides in urine were accounted for, the electrophoretic behavior of calcium oxalate in the artificial solution was similar to that in real urine. Addition of citrate or mucopolysaccharide to concentrated artificial urine gave a measurable negative mobility and decreased the size of aggregates as measured by the Coulter Counter.

The range of validity of the NGS model for calcium oxalate was examined using solutions with known solution chemistry. At low concentrations of a multiple ion solution (an artificial urine solution with eight salts added), it was found that the NGS model accurately predicted the electrophoretic data. However, at higher



viii














concentrations the deviation between experiment and theory increased. The theoretical and experimental values for the adsorption densities and electrophoretic mobilities were compared for calcium oxalate in solutions containing citrate or pyrophosphate. A unique solution set of the two constant parameters, the maximum numbers of adsorption sites and the specific adsorption potential, was found to exist for each system in which both the adsorption and the electrophoretic data existed. Over a wide range of adsorbate concentrations, the results were consistent with the NGS model.




























ix
















CHAPTER I
INTRODUCTION


The electrokinetic properties of a solid particle in an aqueous suspension can give important information about the electrical double layer on the particle. The double layer properties of particles are directly related to the adsorption of species onto the surface of the particles and to the aggregation tendency of the particles. Adsorption and aggregation are critical aspects of many hypotheses of renal stone formation. The most common mineral constituent of renal stones in the United States is calcium oxalate. To date, there has been no previous systematic study of the electrophoretic properties of calcium oxalate. Double layer structure of other salts which are sparingly soluble - notably AgI -- has been studied extensively. The theory of the double layer that has been developed from these studies is critical to our understanding of the stability of suspensions to aggregation. In some cases the properties of the double layer can be critical to the adsorption behavior of species from solutions. Calcium oxalate monohydrate, because of the apparently well behaved nature




1






2






of its solid solution interface and its well studied solution chemistry, promises to be a model solid by which to test some of the basic aspects of double layer theory. Consequently both the electrokinetic properties and adsorption behavior of calcium oxalate systems for all adsorbate concentrations possibly could be quantitatively described by an appropriate double layer model.

In this work we studied the electrophoretic

properties of calcium oxalate in solutions ranging in complexity from those with a single salt added to those solutions as complex as urine. Electrophoretic measurements along with sufficient solution chemical information and some knowledge of the nature of the solid's double layer can allow the direct determination of the occurrence of adsorption. It can also give information as to whether the mode of adsorption is primarily specific or electrostatic. Adsorption can be detected for systems where it would be difficult or impossible to determine its occurrence with direct experimental adsorption methods such as solution depletion. Further, insight can be gained into the most significant adsorbing species in complex solutions like urine. We thus studied the electrophoretic behavior of calcium oxalate in these systems to gain an understanding of the character of calcium







3






oxalate's double layer and to provide a basis for a better understanding of the mechanisms of formation of renal calculi.

The main areas we investigated were the following.

1) Using simple systems with only a single salt

added, we determined if the double layer properties

of calcium oxalate are like those of a classical

sparingly soluble salt, and if not what the anomalies

are.

2) We studied the effect of some natural macromolecules to see if they affect the electrokinetic

properties of calcium oxalate differently than

smaller ions (we in particular wanted to see if

macromolecules that were strong inhibitors of crystal

growth would also strongly affect calcium oxalate's

mobility).

3) We studied the modes of aggregation of supermicron calcium oxalate to see if aggregation would

occur in high ionic strength solutions and to see

if the adsorption of macromolecules could induce

aggregation.

4) Mobilities of calcium oxalate in artificial

and natural urines were studied to see if significant







4






electrokinetic potentials on calcium oxalate can

exist in urine, or if the high ionic strength would

bring the potential to zero (if a finite mobility can exist for calcium oxalate in urine, we wanted

to identify which molecular components were controlling the electrokinetic properties).

5) We combined adsorption and electrophoretic

data for the same systems to see if adsorption and

electrokinetic properties of calcium oxalate can

be consistently modeled by double layer theory.

The most significant results of this study are that calcium oxalate's double layer in many acts like that of a classical sparingly soluble salt. It can have a significant mobility in urine-like solutions. The electrophoretic and adsorption properties, as far as can be determined, can be quantitatively predicted by the Nernst-Gouy-Stern (NGS) model of the double layer if it is assumed that a unique set of the two adjustable parameters of the Stern equation exists for every specifically adsorbing ion.

















CHAPTER II
AN ELECTROPHORETTC STUDY OF CALCIUM OXALATE MONOHYDRATE Introduction

The Nernst-Gouv-Stern (NGS) model (1-4) of the double layer at solid-water interfaces has long been of interest because of its analytic simplicity. The first serious attempts to test the NGS model or the Nernst-Gouy-SternGrahame (NGSG) model for solid systems used silver iodide (5-10). Several qualitative and semiquantitative aspects were in agreement with these theories. However, the fact that the capacity of the Stern layer (assuming the NGS model), in the absence of specific adsorption, depended heavily on surface charge (11) created additional analytical complexities. In the presence of specific adsorption, the Stern theory was acceptable only if specific adsorption potentials were assumed to vary with adsorption density. The latter assumption has been predicted (12,13) on the basis of an analysis of a discreteness-of-charge effect that takes into account the self-atmosphere potential of counter-ions adsorbed in an inner Helmholtz plane (i.h.p.). It has also been suggested that there is a diffuse layer of charge in the




5






6






solid phase (14-17). For silver halides, the charged species are lattice defects (vacancies and interstitials). The space charge in the solid can give rise to behavior that might appear to be due to a Stern layer with variable properties.

For oxides, the theoretical concept is further complicated by the inapplicability of the Nernst equation in describing the surface potential (to) (18-20). Modifications (21-23) of the Nernst equation that take into account the variable chemical potential of the hydrogen ions at the surface have had rather complicated forms and have not been tested fully by experiment. Another complication with some oxides is the presence of gel-like structures at the surface, which give rise to higher adsorption densities (24-30).

The importance of complex ions in solution has been stressed, particularly by Matijevic (31,32) in relation to specific adsorption (reversal of charge). Any quantitative test of double layer theory requires an identification of species that adsorb and of the concentration of the species in solution. For example, the adsorption of aluminum ions (33-35) on various solids, as a function of pH, could not be understood until the complex ion chemistry of hydrated aluminum species was appreciated.






7






On the basis of these considerations, the likelihood that a particular solid might more closely approach a behavior predicted by the NGS or NGSG model is greater by having the following characteristics. The solid must be ionic and sparingly soluble, be thermodynamically stable in water, attain equilibrium rapidly, have no hydroxylated surface groups that can undergo acid-base reactions, have no gel-like surface structure, form easily characterized particles, and have no significant solidstate conduction processes that can give rise to a solid phase diffuse layer. In addition, if the solid is to be analyzed adequately, the chemistry of the solutions in its presence must be well understood, particularly in relation to complex ions.

A remaining difficulty, even if a solid has all

those characteristics, is the discrete ion effects associated with the inner Helmholtz plane. Specific adsorption potentials may still vary with adsorption density. A conceivable situation where this effect may not be nearly as important is that in which the specifically adsorbing ions are large or remain hydrated toward the surface. Such ions may have a locus of center of charge outside the i.h.p., and may instead lie nearer the outer Helmholtz plane (or o.h.p., the closest approach







8






of hydrated counter-ions of the diffuse layer). In this case, the simpler Stern model, with only one layer, might suffice.

The adsorption of complex (hydrated) ions onto solid surfaces is not totally understood. However, the studies by James and Healy (36) strongly suggest that hydrolyzable metal ions can adsorb onto oxides without losing their primary hydration sheath. They presented a model for adsorption based on competition between the free-energy changes favorable to adsorption (coulombic and chemical) and those unfavorable to adsorption (solvation energy).

During the course of studying the electrokinetic

behavior of calcium oxalate monohydrate (CaC202'H20), it occurred to us that this material may have many of the characteristics that might favor the applicability of simple double layer models. This material is present in small amounts of human urine (37), with particle sizes around 5 pm. It is also the major mineral constituent in urinary stones in the United States (38). Surface chemistry in general is being studied because of its possible relation to the stability, coagulation, and flocculation of particles in urine. In the present work, therefore, we have concentrated on chemical species normally present in urine. One of the important






9






hypotheses of stone formation is that coagulation or flocculation is a major step in the overall mechanism (39).

An analysis of calcium oxalate in terms of the NGS double layer model was tempting because, as far as can be ascertained from published reports, it appears to nearly satisfy the criteria felt to be most favorable for this expectation. It is sparingly soluble, is stable in water, equilibrates rapidly, does not form gels, has no hydroxylated surface groups, forms well-defined particles, and gives no evidence of solid-state conduction processes at or near room temperature. Furthermore, its solution chemistry has been investigated extensively because of the importance of crystallization phenomena in renal lithiasis.

This work analyzes the electrophoretic behavior of calcium oxalate with respect to variations in solution chemistry. Adsorption of potential-determining ions was not measured directly because of experimental difficulties associated with the measurement of oxalate at low concentrations and because of the low surface areas (n3.0 m2/g) of our powder. We expect to overcome these problems, in part by using finer powders; the adsorption isotherms will provide a more complete picture of the phenomena we are






10






investigating. In the meantime, we have been able to analyze the electrophoretic data in a way that we believe to be sufficiently valid for testing some aspects of double layer theory. We have learned which types of ions (including complex ions) will specifically adsorb and have obtained considerable insight into the mechanisms of adsorption. The results and analysis indicate that the electrophoretic behavior of calcium oxalate is not inconsistent with the simple NGS theory.


Materials and Methods

Calcium oxalate monohydrate was precipitated by mixing equimolar concentrated solutions of calcium chloride (CaC12) and sodium oxalate (Na2C204); analyticgrade chemicals were used, and the water was deionized and then distilled in a borosilicate glass still and had
-6 -I
a conductivity of less than 1.5 x 10 (cm) -1 The precipitate was washed with the purified water until sodium could no longer be detected by atomic adsorption spectroscopy in the wash. X-ray analysis of dry precipitate confirmed the whewellite form of CaC204H20. The particles were around 5 pm in diameter, as ascertained by scanning electron microscopy and Coulter Counter measurements.













Suspensions of CaC204*H20 in water were prepared by

ultrasonic dispersion at a concentration of 0.35 g/L. The purified water used for the dispersions and solutions showed no evidence of particle contamination by inspection through the electrophoresis microscope. The prepared suspensions were equilibrated for at least 12 h. Final suspensions were made by adding various electrolyte solutions to the dispersion at a ratio of nine parts suspension to one part solution. These solutions were prepared from analytic-grade reagents and were passed through 0.22 pm filters to remove undissolved particles. The final suspensions were equilibrated for at least 12 h. The p1H values of the various suspensions were measured with glass electrodes.

Electrophoretic measurements were carried out on a commercial instrument. Except for the electronic components, the electrophoretic apparatus was housed in a constant-temperature chamber, held at 370C � 1oC, with glove ports and windows through which the eyepieces of the microscope extended outward. In a preliminary study of the possible effect of suspension concentration on


*Zeta Meter, Inc., 1720 First Avenue, New York, New York 10028.






12






mobility, it was found that mobility did not change over a concentration range of 0.1 - 1.0 g/L; the 0.35-g/L concentration was therefore adopted.

The activities and concentrations of various ions in solution, in the presence of calcium oxalate, were calculated for each experimental condition for which the overall composition was known. An established computer program (40) (EQUILS) uses the Davies modification of the Debye-Huckel theory (41,42) for activity coefficients, the equilibrium constants (43-55) listed in Table I, and the principles of mass conservation. No corrections were needed for adsorption effects (which are not accounted for in the mass balance), because it was estimated to be negligible, owing to the low surface area of the powder and the low solid:liquid ratio of the suspensions.



Results

Calcium and Oxalate Ions

Ions common to the solid and aqueous phases are Ca2+
2
and C204 . The activities of these two species are related through the solubility constant. The variations in mobility with (Ca2+) were investigated ; CaC 2 and


ST) = activity (on the molar scale) , when applied to ionic species.






13





Table I
Stability Constants Used in Ion Equilibrium Calculationsa Stability
Constant,
Reaction (M-I) Reference Ca 2+ + C2042- CaC204 0.274 x 104 43

2+ 22 2
Ca + CaC204 NaC204 - 0.134 x 102 43 Ca 2+ + CaC2 0 CC 204 0.714 x 102 43 H + C2042- HC204 0.215 x 10 44 Ca2+ + OH- CaOH+ 0.295 x 102 45 K+ 2- 2 K + C204 KC204 0.134 x 102 46

NH4 + C204 NH4C204 0.130 x 10 46 Ca2+ + HP042- CaHPO4 0.319 x 102 47
2+ 2

Ca2+ + H2PO4 CaH2P04 0.319 x 102 47 H + HPO42- H2PO4 0.152 x 108 48 Na HPO42- NaHPO4 0.129 x 102 49 H+ 3- 2- 13 H + PO4 HPO4 0.152 x 10 50 Ca2+ 3-04 47
PO4 + CaPO4 0.346 x 107

H + H2P04 H PO4 0.164 x 103 48 Mg2+ + C2042- MgC204 0.402 x 104 46 Mg2+ + MgC204 2C204+ 0.475 x 101 42 continued






14






Table I - continued.



Stability
Constant,
Reaction (M-1) Reference Mg2+ + OH- MgOH+ 0.380 x 103 45 Mg

Ca2+ + SO4 2 CaSO4 0.200 x 103 51 Na+ + SO42- NaSO4 0.525 x 101 52 H + + SO 2- 3
S4 HSO4 0.100 x 103 53

Ca2+ + 3- CaC 6H507 0.600 x 105 46 H + C6H507 3- HC6 115072 0.272 x 107 54 Ca + HC6H507 2- CaHC6H507 0.505 x 10 46 H+ 2- 6
H + HC6H507 2 H2C6H507 0.561 x 10 54 H + H2C6H507 H3C6H507 0.127 x 104 54 Ca2+ + H2C6H507 ' CaH2C6H507 0.125 x 102 55 S+ P 207- HP20 7 0.615 x 101 46 + 3- 2- 7 S+ HP207 H2207 2- 0.615 x 10 45

H + H207 H3P 07 0.190 x 102 45 Ca + P2074 CaP 2 0 7 0.562 x 10 45 Ca2+ P74- CaHP0 0.550 x 10 45 CaH+ + P20 4- CaOHP 03- 0.269 x 108 45 aThe complex CaC204 has a concentration in solution at 380C of (6.16 � 0.38) x 10-6 M (43).





















Figure 1. Electrokinetic properties with CaC12 and Na2C204 additions, as function of
calcium ion activity. Range of pH resulting from addition of electrolyte to
system was 6.3-7.0.











E 0

E 2C20-04
+2
-+20

+ - experimental +10
o 0+10
O O o 0

-I - --10
4
0-20
1 I I I I I I 20 a -7 -6 -5 -4 -3 -2 -1

Log Ca2+ Activity






17






Na2C204 solutions were used to alter the activity. The (Ca2+) was calculated from the EQUILS program for the known additions. The results are given in Fig. 1. It should be noted that the ionic strengths varied with the electrolyte added; as shown later, however, this posed no serious problem in analysis, because the EQUILS program characterizes these changes, and they can be taken into account in the analysis of the double layer theory.

The condition of zero mobility at 370C is found (by interpolation in Fig. 1) to be pCa = 5.2, which also corresponds to pC204 = 3.45 (because pK = 8.65). In the only other known attempt (56) to measure the point-ofzero charge of CaC204-H20, the suspension effect was used; the results were a pzc at 250C of pC204 = 2.5 and pCa = 5.11 (where pK = 8.1). Considering the differences in temperature (370C vs. 250C), the results agree reasonably well.



The variations in mobility with pH, resulting from the addition of HCl and NaOH solutions, are shown in


*Mobility is read from left legend; data points and smooth lines drawn through them represent experimental values. Broken lines, curves, and right legend are referred to later in discussion. This is also true for Figs. 2 (top), 3, 4, 5 (top), 6 (top), and 7 (top).






18






Fig. 2 (top). In the intermediate pH range of 5 to 10, the mobility remains approximately constant. This would not be expected if H+ ions were reacting with the surface (e.g., by hypothesized surface hydroxyl, OH, groups), as in the case of oxides. This supports our original inference that ionizable surface OH groups are not present on calcium oxalate surfaces.

The variations in mobility at low and high pH and the constant values at intermediate pH appear to relate to variations in (Ca2+) with pH. In Fig. 2 (bottom), the activities of the various species present in solution (calculated from EQUILS) are plotted. The shape of the (Ca2+)-pH curve is similar to the shape of the mobility-pH curve. To a first approximation, the variation in mobility with pH could have been predicted by combining the information in Fig. 1 with that in Fig. 2 (bottom). This correspondence could not be exact, however, because ionic strengths are not comparable. In the analysis of double layer theory, corrections are made for ionic strength to obtain better comparisons. Electrolytes

The variations in mobility with the addition of

nine electrolytes were investigated; the results are shown





























Figure 2. Effect of pH on (top) electrokinetic properties
and (bottom) activity of ionic species.








Log Ion1 Activity Mobility (um s-Vollt Cm-')








03
D

(D

I-) I I I



0'






e P
0 0

Stern Potential (mV)






21






in Figs. 3 and 4. The data are presented as mobility vs. the total concentration of the salt added. Actual activities for the various species at equilibrium resulting from these additions are discussed and presented separately.

The 1:1 electrolytes caused a gradual reduction in mobility with increasing concentration, as expected for indifferent ions. The (Ca2+) remained nearly constant during these additions (from EQUILS), as shown in Table II.

The addition of sodium sulfate (Na2SO4) reduced the mobility to zero at about 4 x 10-3 M and appeared to reverse the sign at higher concentrations, although the data are less reliable at these high ionic strengths. The calcium activity was lowered slightly by the addition of Na2SO4 (Table II), but not enough to account for more than a small fraction of the change in mobility due to the Na2SO4 addition. The decrease in mobility with concentration was too fast to be accounted for by the ionic strength when compared with the monovalent electrolyte at comparable ionic strength or as determined by the method described later. Therefore, it suggests that
2
SO4 2-, which is the dominant ionic form of the sulfate (by many orders of magnitude) in the solution, specifically adsorbs to the surface.









Table II
Calculated pCa for Experimental Data in Figures 3-7 Fig. 3:
NaH2PO4(M) 10-5 10-4 10-3 6x10-3 8x10-2 10-2 pCa 4.31 4.32 4.33 4.36 4.39 4.35

Na2SO4 (M) 10-5 10-4 10-3 2x10-3 4x10-3 pCa 4.32 4.32 4.34 4.34 4.35

NaC1(M) 2x10-5 2x104 4x10-4 2x10-3 6x10-3 8x10-3 2x10-2 pCa 4.32 4.32 4.32 4.32 4.36 4.39 4.29

KCI(M) 1.5x10-4 10-3 2x10-2 3x10-2 4x10-2 5x10-2 pCa 4.32 4.32 4.29 4.28 4.28 4.27

-4 -3 -2 -2 -2
NH4C1 (M) 1.5x10-4 10 10 2x10 4x10 pCa 4.32 4.32 4.31 4.29 4.27

Fig. 4: -5 -4 -3 -2 MgC12(M) 4x10 4x10 4x10 4x10 pCa 4.30 4.16 4.15 3.63

MgC12(M), in 10-2 M Na2C204 4x10-5 4x10-4 4x10-3 4x10-2 pCa 6.31 6.30 6.11 4.90

Na4P207(M) 10-5 10-4 10-3 pCa 4.33 4.40 4.60 continued










Table II - continued.



Na3C6H507(M) 10 10-4 10 10 pCa 4.35 4.51 4.87 5.09 Fig. 5:
-4
10 M Na3C6H507, pH= 4.4 5.6 6.6 7.3 8.25 pCa 4.23 4.39 4.50 4.52 4.55
-3
0 -3 M Na3C6H507, pH= 4.5 5.75 6.6 7.4 7.75 pCa 4.28 4.69 4.88 4.93 4.93
-2
10- M Na4C6H57, pH= 5.0 6.0 7.25 8.1 8.25 pCa 4.66 5.00 5.09 5.10 5.10

Fig. 6:
-4
5x10 M Na4P207, pH= 4.0 4.75 6.9 7.5
pCa 4.10 4.18 4.43 4.48

Fig. 7:
10-2 M NaH2PO4, pH= 5.0 6.4 7.25 8.25 pCa 4.35 4.40 4.52 4.69




















Figure 3. Electrokinetic properties vs. logarithm of concentration of electrolyte added.
Resulting pH ranges were as follows: NaH2PO4, 5.9-5.0; Na2SO4, 6.0-6.3; NaC1,
5.9-6.1; KCI, 6.2-6.4; NH4C1, 6.6-7.3. Solid lines omitted for monovalent
electrolytes for clarity.











> -+20

I+ -+ 10

0 IO C
2 Experimental Theoretical
- - [ NaH2PO4 -10 A Na2SO4 . ,0 -2 NaCI -20 f
__ KCI -- ---. 0 NH4CI

-5 -4 -3 -2
j Log [Concentration Added] (M)




















Figure 4. Electrokinetic properties vs. logarithm of concentration of electrolyte added.
Data points with solid lines are experimental; broken lines are calculated
from theory. Resulting pH ranges were as follows: MgC12, 6.2-6.0; MgC12 in
0.01 M Na2C204, 7.0-6.3; Na3C6HI507, 6.6 (adjusted with HC1); Na4P207, 7.1-7.7.








MgC 12

0- I I I O
-2- co

I

I,



." --- \- NaC -20 Eo -3- -- 3
5 -4 -3 -2 -I0



LlJ
Log [Concentration Added] (M)







28






When trisodium citrate (Na3C6H507) was added, a

reversal in the sign of the mobility occurred at 4 x 105 M (Fig. 4). In this experiment, the pH was adjusted with HC1 titrant to maintain a p1 of 6.6. The program EQUILS revealed that (Ca 2+) changed from 4.5 x 10-5 M to

8.6 x 10-6 M when the trisodium citrate concentration varied from 10-5 M to 10-2 M. This change in (Ca2+) could account, by the use of data in Fig. 1, for a reduction of C to near zero, but could not account for the larger negative values of 4 obtained. Therefore, it appears likely that specific adsorption is occurring. The principal ionic citrate species in the system were C6H5073- and HC6H507 2-. Figure 5 (bottom) shows that the calculated activities of these two ionic species underwent large changes in opposite directions in adjusted solutions ranging in pH after equilibration from 4 to 8. In this pH range, for calcium oxalate without Na3C6H507, the mobility remains relatively constant as was shown in Fig. 2. Therefore, the direction in which the mobility varied with pH, with constant concentration of citrate salt, indicated which of these anions was affecting the mobility. As shown in Fig. 5 (top), the mobility became more negative with increasing pH (for the three total concentrations of electrolyte). This can be explained by





























Figure 5. Effect of pH with 10-2, 10-3, 10-4 M Na3C6H507
additions. Top, electrokinetic properties; data points with solid lines are experimental; broken
lines calculated from theory. Bottom, activity
of HC6H5072- and C6H5073-






30






.o . I - E o
_> --10

- -2 -o :-3 10o


S ....... ...2 -.-.3 0
r4

00

oo
-C



-3- 10 - 10-2

-0 3010
4 - 4
S10-4/ - 10-4 o H C, H5 O 6 73

4 6 8 10 12

pH






31






the increasing (C6H50 3-) shown in Fig. 5 (bottom), and not by the decreasing (HC6C 5072 ). We conclude, therefore, 3
that the specific adsorption of the C6H507 species was occurring.

Sodium pyrophosphate (Na4P207) additions caused a

reversal in sign of the mobility at around 1.5 x 10-5 M, as shown in Fig. 4. In this case also, the changes in (Ca2+) were not sufficient to expect a charge reversal on this basis alone. The effects of pH variations on mobility, at a constant electrolyte concentration of

5 x 10-4 M, are shown in Fig. 6 (top). The corresponding activities of ionic species are shown in Fig. 6 (bottom). The more negative mobilities with increasing pH cannot 2
be attributed to the species H2P207 , in that its activity decreased with increasing pH. The activities of HP2073-, CaP2072-, and P2074- increased with pH, so the adsorption of one or a combination of these species can explain the change in mobility. From these data, no single species is readily identifiable as the specific adsorbing one.

The effects of additions of sodium phosphate monobasic (NalH2PO4) on mobility (Fig. 3) are interesting because of its weak tendency to reduce the mobility. It did not reverse the charge at concentrations as high as





























Figure 6. Effect of p1l with 5 x 10-4 M Na4P207 addition.
Top, electrokinetic properties. Bottom, activity
of multivalent pyrophosphate species.






33



I - -+0 >

>0 0

-I --!0 c E theoretical 40
0
->2 -20 .0- experimental 1 o -30
~-3h

I


-4 H2207

-





o -7 CV


I I

2 4 6 8 10 12 pH






34






10-2 M. This behavior can be better understood by considering the complex ions formed. Under the conditions of this experiment, most of the electrolyte was in the
2
H2PO4 form. The (HPO4 ) was only a few percent of the 3
(H2PO4 ). The (P04 3-) was lower by nearly 8 orders of magnitude. Consequently, the dominant species was the monovalent species, which was probably functioning as an indifferent counter-ion, whereas only a small amount of HPO42- was available to contribute to lowering the mobility by specific adsorption. The effect of pH on mobility, with a constant total electrolyte concentration of 10-2 M, is shown in Fig. 7 (top). Above a pH of around 7, the solution became supersaturated. It is not known whether the precipitation of phosphate occurred under those conditions. If we assume that it did not precipitate, the activities of H2PO4 , HP042-, and P0432
were as shown in Fig. 7 (bottom); the (HPO4 ) increased with pH, with a corresponding decrease in the mobility.
2
This indicates the specific adsorbing role of HPO4 (or
3
possibly P04 3-) and the absence of specific adsorption by H2 PO4 If precipitation of phosphate occurred, however, this interpretation is not valid.

Magnesium chloride (MgC12) additions caused a small increase in the mobility (Fig. 4). This suggests that






























Figure 7. Effect of pH with 10-2 M NaH2PO4 addition. Top,
electrokinetic properties. Bottom, activities of
phosphate species.





36

+2 +-20 > E2 E S+1 -+10
experimental
0 I '- I I 0 O E o I -iO
1 CL .= theoretical



HP04
-3 -

-4

> -5

-6

7

-8


2 4 6 8 10 12 pH






37






Mg2+ (the dominant cation) was specifically adsorbing. To accentuate this effect, the oxalate activity was adjusted to 0.01 M, to create a negative mobility. Later addition of MgC12 caused an increase in mobility, reversing the sign to positive at 5 x 10-3 M, as shown in Fig. 4. For these changes, little variation in (Ca2+)
-2
was calculated (Table II) to occur until 4 x 10-2 M MgC addition. These results indicate the specific adsorption role of Mg+



Discussion

"Experimental" Stern Potential

The calculation of zeta potential, C, from electrophoretic mobility is often not straightforward. The Smoluchowski equation (57) is valid only for some restricted conditions. Analyses by Hickel (58), Henry (59,60), Overbeek (61), Booth (62), and Wiersema et al. (63) have shown that deviations from the Smoluchowski equation due to retardation and relaxation effects are reduced with smaller ( (<<25 mV) or larger Ka (>>1), where K is the reciprocal of the thickness of the double layer and a is the particle radius. In our experiments, the smallest K was calculated to be
5 - at the lowest ionic strengths). Because
2 x 10 cm (at the lowest ionic strengths). Because






38





-4
a = 4 x 10- cm, the lowest value of Ka is 80. In most cases Ka is over 100 so the retardation and relaxation effects should produce little error. In addition, the influence of particle shape becomes unimportant at high Ka as long as the anisotropy is not too great. Although other effects, such as surface conductance, may give rise to error, they are harder to evaluate. With these justifications (and reservations), we use the Smoluchowski equation to calculate zeta potential from mobility: S47T U,


where n is the viscosity, U is the electrophoretic mobility, and E is the absolute permittivity of the aqueous phase.

To relate ( to double layer theory, we further

assume that c = $6. The validity of this assumption has been debated; Lyklema (64) has recently provided some strong arguments for justifying it. The y6 calculated by setting & = 6 and using the Smoluchowski equation will be called the "experimental" Stern potential, in contrast with the "theoretical" Stern potential calculated from theoretical double layer equations. The experimental 96 calculated for the various mobilities can be read from the data in Figs. 1, 2 (top), 3, 4, 5 (top), 6 (top), and 7 (top) by the right-hand legend.







39






The Nernst-Gouy-Stern Model

The Ca2+ and C2042- ions are common to both phases (solid and liquid) and therefore would be expected to be potential determining ions for this system if equilibrium is established. This is supported by the observations that the ( - (Ca2+) curve remains linear for over three orders of magnitude (Fig. 1) and that the pH alters ( (Fig. 2) only according to what would be expected by its
2'
effect on (Ca2+). Admittedly, while the potential determining role of Ca2+ and C2042- is not proven conclusively, the evidence is sufficient to warrant making this assumption so that a double layer analysis could be carried out.

The Nernst equation is

k = in (Ca 2+)
o ze (Ca 2+)

2+
where (Ca zc is the activity at the thermodynamic condition 9o = 0, io is the surface potential, z is the valence of the potential determining ion, and k, T, and e are the Boltzmann constant, absolute temperature, and electronic charge, respectively.

The Gouy equation, expressed in its most general form [following Grahame (S)], is






40






DD kT
D 2 kT n (exp - zieG - 1), [2]
1 i

where oD is the charge in the diffuse layer, D is the
-12
dielectric constant, D is equal to 1.112 x 10 coul
-1 -1
volt cm , ni and zi are the number of ions per cubic centimeter and the valence of species i, and iP is the potential at the Stern layer. The sign taken in front of the square root is opposite that of $6"

One of the Stern equations is (1) D'D
= 0 [3] where a is the total surface-charge density, 6 is the thickness of the Stern layer, and D' is the dielectric constant of the Stern layer.

In the absence of specific adsorption (1),

a + oD = 0 [4] Without specific adsorption, the dependent variables are a, aD' o0, and ,6' which can be determined from Eqs. [14], assuming that the independent variables are the activities and concentrations of species in solution, and a value is assigned to D'/6.

With specific adsorption, an assumption must be made as to the location of the plane where it occurs. Analytically, the simplest case is to assume that the






41






specific adsorption plane and the plane of closest approach for counter-ions in the diffuse layer coincide. This assumption is clearly incorrect for the double layer on mercury (5) and is probably also invalid for silver iodide. However, for calcium oxalate, it is conceivable that hydrated ions may specifically adsorb (e.g., possibly through hydrogen bonding with the carboxyl groups). Therefore, it is worthwhile to examine this possibility. For this case, the other Stern equation is (1)

= � ( 1 N NlZje
Os .e z e ( - ) '[5
1 + exp T
nm kT

where as is the charge density in the Stern plane, N1 is the number of adsorption sites per square centimeter of surface, N is Avogadro's number, M is the molecular weight of the solvent, n. and z. are the number of ions per cubic centimeter and the valence (including sign) of a specifically adsorbing species j, and pj is the specific adsorption potential of species j. Also, Eq. [4] must be modified to give

a + a + D = 0. [6] The five dependent variables - a, as, aD, ~o, and can be determined from Eqs. [1], [2], [3], [5], and [6], assuming values for .i and NI. A computer method of







42






numerical analysis was used to solve the two combinations of simultaneous equations (i.e., with and without specific adsorption).


Analysis of Conditions Involving Potential-Determining Ions and Indifferent Electrolytes

In the NGS model with no specific adsorption, these values were used for the constants: (Ca2+ pzc = 6.31 x 10-6; D = 8.21 x 10-11 F/cm; D' = 6.5; and 6 = 5 x 10 cm. The EQUILS program provided the necessary activity and concentration values for each condition; these were used as the independent variables.

Theoretical calculations for conditions simulating those in Fig. 1 are given (as a broken line) in the figure, with the experimental values. A surprisingly excellent agreement was found near the pzc, and for

3 x 10-6 < (Ca2+) < 10. Significant deviations occurred above and below this calcium activity range. For (Ca2+) > 10- , the theoretical i6 drops with increasing (Ca2+) because of the increasing ionic strength. The experimental 9 does not exhibit this change, but rather continues to increase (although more slowly) at higher (Ca2+). At low values of (Ca2+), below 3 x 10-6 the theoretical curve tends to flatten out faster than the experimental curve, where the ionic strength is also increasing, owing to the addition of sodium oxalate.






43






Because of the discrepancies at low and high (Ca2+), possible explanations were examined. It was doubtful that deviations from the Smoluchowski equation were occurring at these higher ionic strengths inasmuch as Ka is much larger and surface conductance error is expected to be smaller with increasing ionic strength. Increasing the value of D'/6 in Eq. [3], which increases the capacitance of the Stern layer, raises the theoretical values of $6 at low and high (Ca2+), but it also increases

6 throughout the intermediate range in such a way that the theoretical 4 -(Ca2+) slope becomes greater than the corresponding experimental slope. Furthermore, a maximum in the theoretical curve remains. One possible way of rationalizing these results is to assume that the Stern capacitance increases as (Ca2+) departs significantly from (Ca2+)pzc. However, this is contrary to what was found (or assumed) for silver iodide (6), where the capacitance increased with more negative 9o values.

Another possible explanation for the discrepancy 2+ 2
is the specific adsorption of Ca2+ and C204 . At first thought, this proposal may seem invalid, because by definition the potential-determining ions should adsorb with unit thermodynamic activity. But these ions conceivably adsorb in two forms - a dehydrated form and a







44






hydrated form. The dehydrated form enters lattice positions in the crystal. The hydrated form is bonded to the surface and in this form is distinct from the species entering the lattice. The adsorption of the hydrated ions could be expected to follow the Stern isotherm relationship in that its activity varies with changing adsorption density.

Assuming the possibility of the specific adsorption
2+ 2
of hydrated Ca2+ and C204 species, the NGS theory with specific adsorption can be applied, with the j ions 2+ 02(for Eq. [5]) being Ca2+ and C204 . A value of

4.1 x 1013 cm-2 for N1 was used in the calculations on the basis of estimates of average lattice spacings. The two adjustable parameters are QCa2+ and QC2042-. These were varied to give the best overall fit of theory to data. The best-fitting values were 4Ca2+ = 130 mV and (C2042- = -100 mV, and the resulting curve is plotted in Fig. 1. The fit can be made quite close, as shown.

As suggested by comparing Figs. 1 and 2, the effect of pH on mobility appears to be due to the calcium and oxalate ion activities. To test this, we used the data in Fig. 2 to calculate theoretical 9 -pH curves, using the same double layer parameters as above. The calculated curve is given as the dashed line in Fig. 2. Essentially







45






the same curve is obtained regardless of whether or not
2+ 2
we assume that Ca2+ and C204 are specifically adsorbed. The reason for this similarity is that the activities of these ions remain in a range which gives a 9 value between 0 and 20 mV where specific adsorption effects are not yet important. That is, the (Ca2+) and (C2042-) are small enough so as to minimize their specific adsorption contribution to 9. The agreement between the calculated and experimental curves is not exact, but is reasonably close and shows common trends.

With our present data, it is not possible to exclude either of the two hypotheses -- varying Stern capacitance

(Cs) and specific adsorption of Ca2+ and C2042-. However, we tend to favor the second. Double layer studies on silver iodide (AgI) (6) and mercury (5) have indicated that Cs decreases with increasing negative 0o, whereas we have found the opposite and cannot visualize any logical reason for this difference. Concerning the second hypothesis, the question arises as to why the specific adsorption of potential-determining ions in other systems, such as AgI, have not been observed. The difference may be in the greater solubility of CaC204 (pK = 8.65) than of AgI (pK = 16). In titration with potential-determining ions, the activities of Ca2+ and






46






C2042- become greater than 10-3 within a few pCa2+ units. For Ag and I- studies, the (Ag+) is usually below 10-3, whereas the (I-) remains below 10-5 throughout the titration range. In other words, the concentrations of Ag+ and I are much lower than those of Ca2+ and C2042-, and any weak specific adsorption effects would not be noticed for the former even if they occurred.


Specific Adsorption of Counter-Ions
2- 3- 2The specific adsorption of S04 2-, C6H507 , HPO4 and Mg2+, inferred above, was analyzed with respect to the Stern model for specific adsorption. We assumed that all multivalent pyrophosphate species were specifically adsorbing for purposes of this calculation. Again, we assumed that the ions were hydrated or large enough to be situated at the o.h.p. The concentrations of these ions, for our experimental conditions, were calculated with EQUILS. For each species, a value of 4j was determined by finding the best fit between theory and experiment for the q -concentration curves. Values obtained 2
for qj in this way were -93 mV for SO42-, -107 mV for C 6H 0 -110 mV for HPO 2-, -113 mV for the multivalent
6 507 , 4
pyrophosphate species, and 112 mV for Mg2+. The resulting theoretical curves are compared with the data in Figs. 1,






47






2 (top), 3, 4, 5 (top), 6 (top), and 7 (top). Although the data could not be reproduced perfectly, the similarity is sufficient to provide reasonable confidence that the theory is not inadequate for this purpose. On the Bonding Mechanism for Specific Adsorption

The original Stern theory has given a reasonably consistent and nearly quantitative description for our experimental data. This supports but does not prove the suggestion that the specifically adsorbing ions remain as hydrated species or are, themselves, large enough to have a center of charge near the o.h.p. It should be stated that a different model (e.g., the NGSG model) might also give consistent results if the calculations were possible. If so, quite different values of Ij I might result, and the interpretations of bonding mechanisms which follow would not necessarily be valid. If we assume this to be true, the question remains as to how these species bond to the surface. Two reasonable possibilities are that the water molecules of the hydration sphere of these ions form hydrogen bonds to the surface, possibly to the carboxyl groups of the oxalate ion, and that the hydrated ions form ionic bonds with the surface ions.






48






For all the specifically adsorbing ions studied

(including Ca2+ and C2042-), |j* ranges between 93 and 130 mV, with an average of 109 mV and a standard deviation of � 12 mV. Considering the wide range of 4j expected for various types of bonds, the experimental values of 4j for the seven species might be considered to be essentially identical.

It should be noted, however, that Eq. [5] is the

form for the Stern equation, where, following Grahame (5), the work, w, is expressed as ze(46 + ), in contrast with the convention used by Overbeek (61), where w is expressed as zeq6 + 4. Grahame's convention normalizes the specific adsorption potential to unit valence; Overbeek's convention does not. Having used the former, we conclude that the normalized specific adsorption potential is approximately the same for all the ions considered. Therefore, the total chemical work term, zet, is proportional to the valence.

Ionic bonding depends on the valence of the adsorbing ion. However, the specific adsorption energies, zep, are equivalent to 2-5 kcal/mole. Usual ionic bonds with simple cations and anions involve energies about one order of magnitude greater. However, with hydration molecules intact, or with large anions, the distance of separation






49






between charge centers is greater, thereby weakening the ionic bond. This bond must be specific with some surface sites; that is, some form of discrete ion-pair interaction must be assumed.

The alternative, the hydrogen bond mechanism, is

attractive because the energies, 2-5 kcal/mole, are what might be expected. However, the importance of valence that has been inferred does not seem to be explained by this approach.



Summary

Our experimental results are consistent with the

hypothesis that the electrophoretic behavior of calcium oxalate monohydrate follows the NGS double layer theory. From our limited data it appears sufficient to consider specific adsorption as occurring at or near the outer LHelmholtz plane. The specific adsorption potentials of seven different species, assuming the NGS theory, were found to be nearly identical when normalized to unit valence. This supports an ionic bonding mechanism involving hydrated ions, rather than a hydrogen bonding mechanism. Whether the calcium oxalate monohydrate system more broadly fits the NGS model needs still to be explored by adsorption measurements involving the potential-determining ions.
















CIIAPTER III
ELECTROPHORETIC BEHAVIOR OF CALCIUM OXALATE MONOHYDRATE
IN SOLUTIONS WITH NATURALLY OCCURRING MACROMOLECULES


Introduction

The adsorption of macromolecules at solid-liquid interfaces has been the subject of much interest in physical chemistry; however, much is still not understood about the mechanisms of adsorption. Direct measurements of macromolecular adsorption have shown that it usually appears to follow the Langmuir monolayer adsorption model. Langmuir adsorption for macromolecules was first reported for the adsorption of the albumin and gelatin proteins on collodian membranes (66); since then, it has been found for numerous systems. These systems include: albumin in quartz (67); bovine serum proteins on quartz (68); lysozyme on kaolin clay (69); y-globumin, serum albumin, and fibrinogin on charged and uncharged polyethylene (70,71); and polyacrylamides on calcium phosphate (72). Solution depletion adsorption studies (73) on calcium oxalate monohydrate with several proteins and two mucopolysaccharides have also shown that adsorption follows the Langmuir model.

The Langmuir adsorption parameters can be influenced by both the charge on the macromolecule and by the charge


so50







51





on the surface. Because of the amphoteric nature of proteins, their charge can usually be altered with solution pH. For the lysozyme-kaolin system (69) it was found that in the pH region where the macromolecule and surface were oppositely charged, adsorption was stronger. The same relation between adsorption and pH has also been shown for protein adsorbing upon silica (74). For surfaces whose potential determining ions are not hydrogen and hydroxyl ions, the effects of surface charge and macromolecule charge can be investigated independently. This type of study has been done with silver iodide (75). For calcium oxalate it has been shown (73) that the adsorption of negative macromolecules increases with increasing pCa while that of positive macromolecules decreases. Macromolecular adsorption can also be influenced by the presence of adsorbing small molecules like phosphate, calcium, and citrate competing for the surface; however, the details of this interaction are not well understood (68,69,71). The electrical double layer of the surface has also been shown to influence the adsorption of macromolecules on a variety of surfaces (76) due to its influence upon the adsorbate concentration near the surface (77).

The mechanisms of bonding of macromolecules to surfaces is the subject of much debate. Electrophoretic






52





studies of the adsorption of cationic synthetic polymer on silica have shown evidence for specific adsorption (78). For the adsorption of non-ionic polymer on silica, hydrogen bonding has been proposed (79). Another proposed bonding mechanism is the tendency to lower the free energy of the system by reducing the interaction between nonpolar groups on the adsorbate and water molecules during adsorption (64). It is clear that there are at least two mechanisms of bonding, one with a heat of adsorption in the range expected for chemical bonding and another whose heat of adsorption is much lower or even negative. Urease adsorbed on montmorillonite could be partially removed by cationic displacement; however, more complete removal resulted from increasing the pH (80). This was interpreted by the authors as suggesting at least two mechanisms of binding. Protein has been shown to adsorb on hydrophobic silica with much less sensitivity to electrostatic forces than protein adsorbed onto hydrophilic silica (64). Analysis of the characteristics of adsorption of protein on silica has suggested that the adsorption occurs on two distinct types of independent sites simultaneously and that the resulting adsorption is consistent with the Langmuir model (71).

The adsorption of macromolecules onto calcium oxalate is of practical interest because of its possible







53





importance in renal stone disease. Calcium oxalate is the major mineral constituent of renal stones in the United States and macromolecular matrix is almost always present throughout the stone (81). The role of the matrix in stone formation is not understood, but it is known that it usually consists of 2.5% of the dry weight of the stone (82). This is made up mainly of mucoprotein - possibly with chemically bound mucopolysaccharides -- and with serum albumin, alpha-globulin, and sometimes gammaglobulin present (83,84). Urinary protein in general (85) and urinary lysozyme in particular (86) are generally higher than normal in concentration in stone formers' urine.

The adsorption of macromolecules could be critical to the following processes that may cause the initiation or the prevention of stone disease: flocculation of crystals in urine by macromolecular bridging (Chapter IV); inhibition of the growth of crystals in urine (87,88); alteration of the interfacial electrical double layer which affects the tendency of crystals to aggregate (89, Chapter II); and attachment of calcium oxalate crystals to macromolecules comprising the walls of the renal system which can lead to fixed stone disease (90).

For the above reasons, we were interested in firstly understanding the mechanisms of adsorption of







54





macromolecules. For this purpose, the mobilities of calcium oxalate in solutions with macromolecules present were chosen for investigation to determine whether their adsorption was specific or electrostatic by observing how it affected the charge on the particles. How the macromolecules affect the mobility could also be compared with the effect of small ions (Chapter II) to gain inferences on the influence of the adsorbate size. Two well studied globular proteins, one whose isoelectric point was acidic, the other with a basic isoelectric point, as well as two mucopolysaccharides were selected for these experiments. We studied the effect of macromolecular concentration (adsorption density), the concentration of a small, strongly adsorbing ion (competition), pH (adsorbate charge), and pCa (surface potential). We then interpreted the results using electrokinetic theory and adsorption parameters estimated from previous work. The most significant findings of this study are that macromolecules can adsorb to calcium oxalate in two ways, specifically and electrostatically, and that when the macromolecules are prevented from approaching close to the surface the adsorption proceeds completely electrostatically.






55






Materials and Methods

Natural polymers obtained commercially were serum albumin bovine (4X crystallized), lysozyme (murmidase), sodium heparin, and chondroitin sulfate. Serum albumin and lysozyme are globular proteins with isoelectric points at pH 4.9 and pH 11, respectively. Sodium heparin and chondroitin sulfate are mucopolysaccharides with random coil structures. Other chemicals were analytical reagent grade. Stock solutions were passed through a

0.22 pm filter to remove undissolved impurities. Calcium oxalate monohydrate powder was prepared as described previously in Chapter II. The pH was adjusted with volumetric titrants of HC1 or NaOH. Water was deionized and then distilled in a borosilicate glass still; the conductivity was less than 1.5 x 10-6 (Qcm)-1 Working suspensions were made by adding macromolecule solutions of varying concentration to suspensions of calcium oxalate that had been equilibrated at least 12 hours after the desired addition of HC1, NaOH, CaC12, Na2C204, or Na3C6H507. The final calcium oxalate present in the systems was 0.315 g/L.

Solutions after the final modifications were equilibrated at least 2 hours at 370C before making electrophoretic measurements. The electrophoresis was carried






56





out using a commercial instrument in a constant temperature chamber at 370C (Chapter II). The equilibration and the electrophoretic measurements were completed within a total of 6 hours. The solution pH was determined with a glass electrode after electrophoresis. Some solutions were then passed through a 0.22 pm filter and analyzed for protein concentration with solution transmission spectroscopy at a wavelength of 280 nm.



Results and Discussion

Figure 8 gives the electrophoretic mobilities of

calcium oxalate in systems with increasing concentrations of the four macromolecules. The concentrations given in the abscissa of Fig. 8 are actually calculated on the basis of the amount of water. However, in the present study, initial concentrations (CI ) are virtually the same as the final concentrations (CE) which exist after adsorption because of the very low total surface area of the particulates present.

In an earlier study, using concentration suspensions having high surface areas, adsorption isotherms were determined by solution depletion methods (73) for three of the macromolecules that we are investigating (serum albumin, sodium heparin, and chondroitin sulfate). The


























Figure 8. Electrophoretic mobility of 0.32 g/L calcium oxalate monohydrate versus
macromolecule concentration. The numbers near the data points are solution
pH.










5.4
+ 7.2 5.3

5 .5 0 5.5 o O > 7.2 i 5.5 5.5

E 7.1
-2- O Lysozyme 7.
V Serum albumin
A Chondroitin sulfate 6.o
.. -3- 7.2
o 0 Sodium heparin

S-4 -6.4


- -5 -4 -3 -2 -1
0

Log [Concentration Added] (g/l) LJ







59






adsorption was found to obey the form of the Langmuir adsorption isotherm. In fact, from this data it could be confirmed that in our present experiments the solution depletion should be negligible (Table III).

We have shown in Chapter II that calcium oxalate in water over the pH range from 3 - 10 has a positive charge with an electrophoretic mobility of about 1.7 mobility units (vm s- /Volts cm- ). Referring back to Fig. 1, the presence of positively charged lysozyme in concentrations as high as 0.1 g/L had little effect on the mobility of calcium oxalate, while the negative polymers made the mobility less positive as their concentrations were increased. Each of the three negative macromolecules reversed the sign of calcium oxalate's mobility. The reversals in mobility may be due to adsorption of the macromolecules or by other induced changes such as the alteration of the calcium and oxalate activity or the precipitation of a second solid phase.

To detect the possible precipitation of a second

solid phase we used the following methods. The protein solutions in equilibrium with calcium oxalate in our various experiments were filtered after electrophoresis, and the filtrates were examined with transmission spectrophotometry at 280 nm for solution depletion of protein









Table III
Solution Depletion, AC, Calculated by Using Experimentally Determined Langmuir Parameters

CI (g/L)
Macromolecule 10-1 -2 2 10-3 10-4 10serum albumin, pH = 7.3 A = 0.027 g/L, ACm = 1.55 x 10-2g/L 2.5 x 10-3 8.0 x 10-4 1.0 x 10-4 1.1 x 10-5

alpha - globulin, pH = 6.0 A = 0.024 g/L, ACm = 1.55 x 10-2g/L 1.2 x 10-2 3.3 x 10-3 3.8 x 10-4 3.9 x 10-5

chondroitin sulfate, plH = 7.3 A = 0.421 g/L, AC = 1.79 x 10-2g/L 3.3 x 10-3 3.9 x 10-4 4.0 x 10-5 4.0 x 10-6 4.0 x 10-7

sodium heparin, pH = 7.3 A = 0.120 g/L, ACm = 1.13 x 10-2g/L 4.9 x 10 3 8.0 x 10-4 8.6 x 10 5 8.7 x 10 6 8.7 x 10
n = ~iz g/, am







61





against standard solutions. Since the solids concentration used in these experiments is too small to detect significant solution depletion due to adsorption, any depletion noted could be attributed to precipitation. The remaining solutions were prepared to nine-tenths final volume and then were observed after one-half hour for precipitation before the slurry was added. Finally, a second solid phase can be recognized by the presence of particles of two distinct mobilities during electrophoretic measurement. No evidence of precipitation was found in any of the systems presented in this paper.

If calcium is removed from solution through complexing with, or binding to, the macromolecule, an increase in oxalate concentration in solution will result because the calcium and oxalate ion activities are related to each other through the solubility constant. In Chapter II, the change in calcium oxalate's mobility with the addition of calcium chloride or sodium oxalate was given. Since it requires about 10-2 M of sodium oxalate to bring the mobility of calcium oxalate from its value of +1.7 in water to -1.7, and that the total oxalate in the system is limited to 2.2 x 10-3 N by the solids content of our suspensions, the mobility change due to the presence of the mucopolysaccharides cannot be explained






62





by increased oxalate ion activity alone. The mobility changes due to the proteins were less dramatic, but the amount of calcium binding that could possibly be expected can be estimated from values obtained empirically in prior calcium binding experiments. Total serum calcium is about 10 mg/100 cc; the 4.5 g/100 cc of total serum protein at pH 7.4 typically binds about 5 mg of this (91). For a concentration of 0.1 g/L protein, this indicates about 2.7 x 10-6 M of calcium would be bound. Typical values of molar binding ratio for calcium to serum albumin at pH 7.4 (92) have been found to be about 2. For 0.1 g/L serum albumin this gives a concentration of bound
-6
calcium of 2.7 x 10 M. The effect of a change in solution calcium of the magnitude indicated by these values upon mobility in the systems of this study would be negligible.

Since precipitation or binding of calcium or oxalate does not appear to be important, we are left with the conclusion that large changes in mobility with increasing concentrations of macromolecules are due to adsorption. The result that the negatively charged macromolecules have shown evidence of specific adsorption, but the positively charged protein, lysozyme, had little effect upon mobility suggests the alternate possibilities that either lysozyme







63





would adsorb more strongly as the calcium oxalate surface becomes more negative or that these macromolecules could only specifically adsorb to the positive surface sites. To eliminate one of these possibilities we added lysozyme at concentrations up to 0.1 g/L to calcium oxalate suspensions equilibrated (after pH adjustment to 6.5) at three Na2C204 concentrations. Initial mobilities of one slightly positive and two increasingly negative values were obtained. The results given in Fig. 9 show that with increasing lysozyme concentration there was a marginal increase in mobility for the positive suspensions and there was a decrease in mobility from -1.4 to zero in the suspensions with 10-2 M oxalate added. In the suspensions with the intermediate oxalate concentration, however, as lysozyme concentration increased, the sign of the mobility reversed from minus to plus which strongly indicated specific adsorption.

To determine if adsorption onto calcium oxalate caused large alteration of the solution macromolecule interface, we studied the mobility of calcium oxalate in the presence of macromolecule with varying p1l. Adsorbed proteins can sometimes maintain their integrity and cause a covered particle to obtain surface properties similar to the protein (93); conversely, adsorption could

























Figure 9. Electrophoretic mobility of 3.2 g/L calcium oxalate monohydrate versus
lysozyme concentration for different sodium oxalate concentrations. The numbers near the data points are solution pH. The left most data points
are mobilities without lysozyme.










E
0 +2
4 2xO-4M Na204

6.1 6.1
E! __66.2

6.3 6.5 . 6.3


6.5
o -2- 6.5 6.5
o 10-2M NaC204



o O -3 -2 -1
-+
O Log [Lysozyme Concentration Addedl (g/1)






66





possibly alter the charge of the protein. Since the mobility of calcium oxalate in water is fairly constant with the pH range from 4 - 10, the variation in mobility with pH in the presence of adsorbed macromolecules will be due primarily to the effect of pH on the charge of the adsorbed macromolecule. If the macromolecule charge was not altered greatly by adsorption and if the amount of surface coverage is high, then the pH of zero mobility should be close to the isoelectric point of the protein. Figure 10 shows the resulting mobility of calcium oxalate in the presence of 0.1 g/L of macromolecule over a range of solution pH. The mobility of calcium oxalate with adsorbed serum albumin varied from positive to negative as the pH increased. It reversed the sign at about pH 5 which is close to the isoelectric point of serum albumin. Similarly in the presence of lysozyme, the mobility decreased with increasing pH approaching zero at approximately pH 11, which is the same is the isoelectric point of lysozyme. The experiment was not extended to high pl1's to attempt a sign reversal for lysozyme because above pH 11.7 the base alters lysozyme's structure dramatically (69). The result that the mobility of calcium oxalate is sensitive to pH in the presence of







67





positively charged lysozyme shows that a surface potential of opposite charge to the protein is not necessary for adsorption. This suggests that the increase in concentration of the potential determining ion, oxalate (Fig. 9), is providing more negative surface sites for lysozyme specific adsorption. Figure 10 also illustrates that the mobility of calcium oxalate remains highly negative throughout this pH range in the presence of the mucopolysaccharides. This is consistent with findings (94) that show that their surface sulfate groups remain almost completely ionized above pH 3. The moderate increase in mobility with increasing pH is as would be expected from the ionization of their surface carboxyl groups. Thus, the observed mobility of calcium oxalate as a function of pH in the presence of any of these macromolecules does not support a model that depicts large alteration of the macromolecule's solution interface with adsorption.

Since the natural macromolecules presented in this study, as well as some small molecules studied previously (Chapter II), have shown evidence for specific adsorption onto calcium oxalate we tried to determine how they compete with each other for the surface. If a macromolecule and small molecule were competing for the


































Figure 10. Electrophoretic mobility of 0.32 g/L calcium
oxalate monohydrate with 0.1 g/L of macromolecule as a function of solution pH. The
solid curve without data points represents the
mobility versus pH without macromolecule
present.





69




O" Lysozyme +3 V Serum albumin
E A Chondroitin sulfate
+2- O Sodium heparin \ +1 E 0 .4 -I

o

0

-2
0o -4w -5

2 4 6 8 10 12 pH







70





same sites, and if enough sites were available, both species could adsorb, possibly causing an additive effect upon mobility. If the concentration of one species became large enough that it occupied practically all the available sites, the effect upon the mobility of the other species becomes zero. If, however, the species were adsorbing upon different sites the additive effect upon mobility would stay relatively constant. The mobilities of calcium oxalate were measured in suspensions with various concentrations of sodium citrate to which

0.1 g/L of lysozyme or serum albumin was added. Citrate was chosen because it is a relatively small molecule which specifically adsorbs strongly to calcium oxalate (Chapter II, 95) and because it can be added in high concentrations. In Fig. 11 it can be seen that the mobilities of calcium oxalate with lysozyme are substantially less negative than those without lysozyme for
-2
all citrate concentrations. Since at 10-2 M citrate the number of citrate molecules is over a factor of a thousand greater than the number of protein molecules, these data indicate that the lysozyme and citrate are adsorbing upon different surface sites. This is as might be expected since in the pH range indicated lysozyme would be positively charged, while citrate ions would be

























Figure 11. Electrophoretic mobility of 3.2 g/L calcium oxalate monohydrate with 0.1 g/L
macromolecule versus citrate concentration. The solid line without data
points corresponds to the mobility without macromolecule present. The
numbers near the data points are solution pH. The left most data points
are for zero citrate concentrations.









16.6 I I I

-6- 0.1 9/1 Lysozyme




E 6.6
6.6
-2 -No protein

0.8
o . 8.1
-4 -0.1 9/1 Serum albumin
-4
0
0C
o 0 -4 -3 -2
- Log [NaCHO Concentrtion Added]M)
Log [NG3C6H507 Concentration Added] (M)
3 65J






73





negative. With the negative protein serum albumin present, however, there is an additive effect at low citrate concentrations between the two species on mobility, since it is more negative than would be expected from the citrate or serum albumin alone. This effect decreases with increasing citrate concentration until
-2
at 10-2 M the mobility is about what would be expected for either the citrate or the serum albumin alone. This may occur either because the increased citrate concentration has become so large relative to that of serum albumin that effectively all the available sites are being occupied by citrate or the citrate has raised the charge on the surface to the point where adsorption of serum albumin has been electrostatically inhibited. These results indicate that, in the presence of a relatively high concentration of a specifically adsorbing small molecule, adsorption will be limited in the presence of a polymer of the same sign, while if the polymer is opposite in sign adsorption of both species will continue.

Calculations based upon the results of solution depletion experiments (73) indicate that there may be considerable crowding of the molecules as the calcium concentration is increased if we can assume that serum albumin retains its shape upon adsorption and that its






74






adsorption is limited to a monolayer. Adsorption of serum albumin on calcium oxalate at various calcium activities was found (73) to be described reasonably well by the Langmuir adsorption isotherm, CE CE A
- + [7]
AC ACm AC

where A is the macromolecule equilibrium concentration at which half of the surface is covered with adsorbate. It is a measure of the affinity of the polymer to the surface. The term ACm is the change in macromolecule concentration occurring at maximum surface coverage. A least squares fit of the experimentally determined CE/AC versus CE is used to obtain values for A and ACm. In Fig. 12, linear Langmuir plots are given for the macromolecule concentrations used in our experiments utilizing the values of ACm and A determined in the study cited. The AC values have been normalized by weight to our
m
experimental conditions. This figure shows that for serum albumin at a given CE the value of AC increases greatly with increasing calcium activity. The least squares fit of the data to the Langmuir isotherm shows that this is due almost entirely to increasing ACm. Log ACm was found to vary fairly linearly with the log of the calcium concentration for the adsorption of negative proteins (including that of serum albumin).
























Figure 12. Linia Langmuir plots for the concentration range of this study utilizing
parameters determined in a previous study normalized by weight to our
experimental conditions. The solution p1I for alpha-globulin was 6.0, all
others were 7.3. The CE/AC values for serum albumin with 10 mM sodium
oxalate (not shown) are about ten times greater than those for serum albumin alone. Adsorption for 20 mM sodium oxalate was undetectable.







40


30 Se Om:,
Chondroitin Sulfate 020


10 Sodium heparin

Serum albumin,10mM Ca Cla
Serum albumin,20mMCaCI
0.02

.08
CE (960






77






We can obtain values for the percent coverage by estimating the projected area of adsorbed serum albumin at various calcium concentrations and then comparing this to the total calcium oxalate surface area available. We did this in the following manner. Values for ACm for a series of calcium concentrations were obtained from Fig. 13 (some values were estimated using the line drawn through the data points). The value of 0.027 g/L was used for A; values for AC were calculated from Eq. [7]. The surface area of the calcium oxalate used in these experiments as measured by nitrogen gas adsorption is about 3.0 m2/g. The molecular weight and density used for serum albumin were 69,000 g/M and 0.73 g/cm3 respectively. Serum albumin was assumed to be spherical in shape. This yields a projected cross-sectional area for adsorbed protein on the surface, Ap, of about

2.3 x 103 A2/g. The effective area covered by serum albumin for each solution in Angstroms squared per liter is

A = AC x Ap [8]



*This value for surface area gives a more conservative estimate of crowding than the lower surface area which was estimated for the powder in the adsorption study using the optical microscope.


































Figure 13. Concentration of serum albumin adsorbed at
maximum surface coverage versus calcium concentration. Values obtained from a previous
study normalized by weight to our experimental
conditions.






79







-2
















E
-4






L. I

0
_J


-7 -6 -5 -4 -3 -2 Log ECalcium Concentration] ( M )






80






The total surface area for 0.315 g/L calcium oxalate is 6.3 x 1018 2/L. The estimated percent of the total area covered by protein is given in Table IV. These calculations are admittedly somewhat rough, but since even 60% coverage is probably unrealistic (96), the results indicate that above 10-3 M calcium there is likely to be considerable physical crowding of adsorbed molecules.

This analysis of solution depletion data raises a question of how the physical crowding of adsorbed molecules affect their adsorption mechanism. One possibility is multilayer adsorption; however, since the solution depletion data fits the Langmuir model, the explanation that protein is adsorbing on protein is not satisfactory. Consistency with the Langmuir model at the adsorption densities indicated can be explained by the following two mechanisms: The protein distorts its shape with increased calcium activity to allow continued specific adsorption; the protein remains globular and eventually physical crowding prevents further proteins from getting close enough to the surface to specifically adsorb, so then adsorption can only occur electrostatically. Although solution depletion adsorption experiments cannot differentiate between these two mechanisms, we








Table IV
Physical Crowding for Serum Albumin with Increased ACm
[A = 0.027 g/L, CI = 0.1 g/L (Ca) obtained by calculation]

% 'otal
Addition (M) (Ca) (M) ACm (g/L) Ap (2/L) Artea
io-1 -1 -2 -2 120
10 CaCa2 1.0 x 10 1.9 x 102 1.4 x 10 2.8 x 10 299
-22
10 CaCI2 1.0 x 10-2 1.0 x 102 7.0 x 10-3 1.4 x 1020 150

-3-3 -3 -3 19
10 CaC12 1.0 x 10 4.4 x 103 3.0 x 10- 6.0 x 109 64

-4 -4 -3 -3 10
10 CaC12 1.2 x 104 2.1 x 10- 1.6 x 10- 9.2 x 1010 34

10-4 C204 2.2 x 10-5 1.2 x 10-3 9.4 x 10-4 1.9 x 1019 20

i0- C204 3.7 x 106 6.3 x 10-4 5.0 x 10-4 1.0 x 1019 11

10-2 204 9.3 x 10-7 3.2 x 10-4 2.7 x 10-4 5.5 x 1018 6






82






could be able to eliminate one possibility by the effect the adsorption has on calcium oxalate's mobility. To see how the mobility should react to continued specific adsorption (as would occur in the first mechanism stated above), we estimated the charged surface sites per adsorbed molecule over a range of calcium concentration. The total surface charge, before protein adsorption, was calculated using the Nernst-Gouy-Stern model of the double layer and solution equilibria in a manner that has been described in detail (Chapter 11) previously. The total charge was divided by the charge on the electron to give the corresponding number of monovalent surface sites per unit area. The number of molecules per unit area was calculated from the adsorption data given in Table IV. The ratio of these two values gives the number of molecules per apparent monovalent site. The values calculated are listed for positively charged surfaces in Table V. This calculation shows that over this range of calcium activity the number of molecules adsorbed per monovalent site is within 35% of one. Thus, with continued specific adsorption, as the calcium activity is increased, the mobility is likely to remain negative. If, however, crowding of adsorbed molecules occurs (as in the second mechanism), the mobility will be brought to zero but a sign reversal will not occur.






83






Table V
Langmuir Adsorption Density Per Unit Surface Charge for Various Solution Calcium Activities

+1 sites Molecules
(Ca) A(M) 2 +1 site

1.0 x 10-1 4.1 x 10-4 5.0 x 10-4 1.25 1.0 x 10-2 3.0 x 10-4 2.6 x 10-4 0.87 1.0 x 10-3 1.7 x 10-4 1.1 x 10-4 0.65

-4 -5 -5
1.2 x 10 6.7 x 10 6.0 x 10 0.75 2.2 x 10-5 3.9 x 10- 2.8 x 10-5 0.72







84






We measured the electrophoretic mobilities of

calcium oxalate suspensions equilibrated in solution with pCa from 6.4 to 1.2 and with lysozyme or serum albumin added to possibly eliminate one of the above mechanisms. The amount of 0.1 g/L of macromolecule was added to calcium oxalate suspensions equilibrated with various concentrations of sodium oxalate or calcium chloride added. The resulting electrophoretic mobilities with and without polymer are shown in Fig. 14. The presence of serum albumin has an increasing effect on the mobility as the calcium concentration increases. Comparing the curve for the mobility without macromolecule to that with 0.1 g/L serum albumin, we can see that the serum albumin reversed the sign of the mobility from plus to minus at 10-4 N sodium oxalate and at 104 Mi CaC12; however, at higher calcium concentrations the mobility was brought to zero by serum albumin but sign reversal did not occur. Lysozyme appears to have behaved in a similar manner, except the mobility had been approaching zero as the oxalate concentration was increased. One conceivable explanation for this is that the protein may be more sensitive than calcium oxalate to ionic strength. Thus, as the coverage of the surface with macromolecule increases the ionic strength reduces the

























Figure 14. Electrophoretic mobility 0.32 g/L calcium oxalate with 0.1 g/L macromolecule
for various calcium chloride or sodium oxalate additions. The numbers near the data points are solution pH. The solid line without data points is the
mobility of calcium oxalate without macromolecule present.












Electrophoretic Mobility (um s'/ Volt Cm-')


I I + + + + N - 0 N (A -o 4

0 N Co





r--
O














II












98
o

r




- i






87






mobility to zero. This argument is not valid, however, since serum albumin at pH 6.0 and an ionic strength of

5 x 10-2 M has a mobility of about -1.7 (97). These results, combined with the physical crowding inferred from solution depletion data, strongly indicate that when the molecules are prevented from approaching closely enough to specifically adsorb, adsorption continues electrostatically until the difference in charge between the macromolecule and surface is brought to zero.


Conclusions

Proteins and mucopolysaccharides specifically adsorb to the calcium oxalate surface. A surface of opposite charge to the macromolecule is not necessarily needed for adsorption; however, the amount of adsorption appears to be dependent upon calcium activity. A model consistent with the effect of citrate upon the mobility of calcium oxalate in solution with positively or negatively charged protein is one where there is competition for surface sites between the adsorbing small molecule and a like charged macromolecule but one that the adsorption is relatively independent when the molecules are oppositely charged. When specific adsorption is physically prevented by high macromolecular adsorption density at extremes of






88






pCa, the adsorption continues completely electrostatically. Thus, the results of this study indicate that the two simultaneous mechanisms of adsorption for proteins that have been alluded to in the literature are: 1) a specific adsorption mechanism that competes with like charged small molecules for surface sites and 2) a mechanism that is completely electrostatic when physical crowding occurs.
















CHAPTER IV
AGGREGATION MECHANISMS OF SUPER-MICRON
CALCIUM OXALATE MONOHYDRATE


Introduction

The aggregation of super-micron calcium oxalate is

the object of much recent interest because it is perceived as a principal step in the initiation of renal lithiasis (98). Aggregation is defined by Fleisch (98, p. 361) as "the process of crystals binding one to another, resulting in the formation of larger clusters." The combined effect of growth and aggregation of supermicron calcium oxalate in supersaturated solution has received a modest amount of study (99-102). However, no work to date has been published on the aggregation of calcium oxalate in systems where growth is a negligible factor. Since the particle density of crystalluria is too low for a significant collision rate due to Brownian motion, there is doubt as to whether aggregation could be important in urolithiasis (103). The experimental systems used to measure calcium oxalate growth and aggregation (100,102) also have particle densities insufficient for perikinetic aggregation. However, for super-micron particle suspensions the collision rate can



89







90





be substantially increased by a liquid velocity gradient (104-106). The dependence of the aggregation of super-micron calcium oxalate upon a liquid velocity gradient has previously been ignored. Another interesting possibility is that the aggregation of calcium oxalate could be enhanced by the presence of macromolecules, since precipitated calcium oxalate in urine probably is extensively covered by macromolecules (73). Depending upon the extent of their coverage of the particle surface, proteins and other macromolecules can either accelerate aggregation or prevent it (78,107,108).

We therefore chose to study the significance of

various possible aggregation mechanisms for super-micron calcium oxalate as a preliminary investigation for the determination of the role of aggregation in stone formation. In this work a comparison is made of the coarsening calcium oxalate suspensions in saturated and supersaturated systems. High particle density and high electrolyte concentration are used in a nonturbulent apparatus to examine the possibility of perikinetic aggregation. A controlled fluid velocity gradient is employed to study aggregation in suspensions with an increased particulate collision rate. The tendency is examined of calcium oxalate to flocculate in the presence






91






of polymeric macromolecules. We thus monitored particle size information on calcium oxalate in various potentially coagulating systems. The suspension coarsening referred to as growth and aggregation in previous studies may be almost entirely growth related phenomena. However, the most significant result of this study is that supermicron calcium oxalate suspensions can aggregate in a sufficiently large fluid velocity gradient or in the presence of particle bridging macromolecules.


Materials and Methods

Calcium oxalate monohydrate crystals were prepared as previously described in Chapter II. Water was deionized and glass distilled. Calcium oxalate suspensions were dispersed ultrasonically at a concentration of

3.47 g/L and then allowed to equilibrate for 24 hours before use. All chemicals were analytical reagent grade. Stock solutions were passed through a 0.22 um filter to remove undissolved particles. Polyacrylamide and polyethylene oxide, high molecular weight polymeric flocculants, were obtained commercially. The solution pH's


*Nonionic polyethylene oxide (Polyox coagulant, 5 million MW), Union Carbide Corp., New York 10017. Nonionic and




Full Text

PAGE 1

THE ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE By PETER ANGELO CURRERI A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1979

PAGE 2

Copyright 1979 by Peter Angelo Curreri

PAGE 3

To Dad

PAGE 4

ACKNOWLEDGEMENTS Sincere appreciation is extended to the faculty members of the Department of Materials Science and Engineering and in particular to my graduate supervisory committee for their support. Special thanks to Professor George Onoda and Professor Birdwell Finlayson for the enthusiastic contribution of their thoughts and expertise during this work. I also wish to thank Mr. Brian McKibben, Mr. Doug Deason, and Mr. Mike Stoufer for assistance in some of the experimental measurements; Dr. Mariorie H. Malagodi and Dr. W. C. Thomas, Jr., for clinical samples; Mr. Bernard Burton, Mr. Art Smith, and Ms. Lindreth Du Bois for technical assistance; and my wife Linda for help in figure preparation. This work was supported by National Institutes of Health grant AM20586-01 and by National Institutes of General Medical Sciences grant GM21056-02.

PAGE 5

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS vi ABSTRACT vii CHAPTER I INTRODUCTION 1 II AN ELECTROPHORETIC STUDY OF CALCIUM OXALATE MONOHYDRATE 5 Introduction 5 Materials and Methods 10 Results 12 Discussion 37 Summary 49 III ELECTROPHORETIC BEHAVIOR OF CALCIUM OXALATE MONOHYDRATE IN SOLUTIONS WITH NATURALLY OCCURRING MACROMOLECULES 50 Introduction 50 Materials and Methods 55 Results and Discussion 56 Conclusions 87 IV AGGREGATION MECHANISMS OF SUPER-MICRON CALCIUM OXALATE MONOHYDRATE 89 Introduction 89 Materials and Methods 91 Results and Discussion 97 Conclusions Ill V THE ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE IN NATURAL AND ARTIFICIAL URINES 112 Introduction 112 Materials and Methods 115 Results and Discussion 117 Conclusions 151

PAGE 6

TABLE OF CONTENTS continued Page CHAPTER VI THE NERNST-GOUY-STERN MODEL: ITS VALIDITY AND LIMITATIONS FOR THE CALCIUM OXALATE MONOHYDRATE DOUBLE LAYER 155 Introduction 155 Results and Discussion 159 Conclusions 190 APPENDIX APL COMPUTER PROGRAMS USED IN CHAPTERS II, III, AND VI FOR MAKING NGS MODEL DOUBLE LAYER CALCULATIONS 19 3 BIBLIOGRAPHY 198 BIOGRAPHICAL SKETCH 207 VI

PAGE 7

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE By PETER ANGELO CURRERI August 1979 Chairman: George Y. Onoda, Jr. Major Department: Materials Science and Engineering The electrophoretic properties of monohydrate calcium oxalate in aqueous solutions involving the addition of single electrolytes were found to be consistent with the Nernst-Gouy-Stern (NGS) model of the electrical double layer. For five multivalent salts studied, evidence for specific adsorption was given. The specific adsorption potentials found were approximately proportional to the valence of the adsorbing species. The proteins and the mucopolysaccharides studied also showed evidence of specific adsorption. Physical crowding of protein adsorbate was indicated by calculations using experimentally determined Langmuir adsorption parameters. When this occurred, there was no longer a mobility sign reversal. This indicated that further protein adsorption was completely

PAGE 8

electrostatically driven because it could not bond directly to the surface. Aggregation of super-micron calcium oxalate was shown to occur in nonsupersaturated solutions if the particle collision rate was increased by application of a fluid velocity gradient. Large polymeric molecules were shown to be capable of flocculating calcium oxalate. It was shown that calcium oxalate can have a finite electrophoretic mobility in urine. The small ions in urine alone could not account for the effect of urine on the mobility of calcium oxalate; however, when the mucopolysaccharides in urine were accounted for, the electrophoretic behavior of calcium oxalate in the artificial solution was similar to that in real urine. Addition of citrate or mucopolysaccharide to concentrated artificial urine gave a measurable negative mobility and decreased the size of aggregates as measured by the Coulter Counter. The range of validity of the NGS model for calcium oxalate was examined using solutions with known solution chemistry. At low concentrations of a multiple ion solution (an artificial urine solution with eight salts added) , it was found that the NGS model accurately predicted the electrophoretic data. However, at higher vm

PAGE 9

concentrations the deviation between experiment and theory increased. The theoretical and experimental values for the adsorption densities and electrophoretic mobilities were compared for calcium oxalate in solutions containing citrate or pyrophosphate. A unique solution set of the two constant parameters, the maximum numbers of adsorption sites and the specific adsorption potential, was found to exist for each system in which both the adsorption and the electrophoretic data existed. Over a wide range of adsorbate concentrations, the results were consistent with the NGS model.

PAGE 10

CHAPTER I INTRODUCTION The electrokinetic properties of a solid particle in an aqueous suspension can give important information about the electrical double layer on the particle. The double layer properties of particles are directly related to the adsorption of species onto the surface of the particles and to the aggregation tendency of the particles. Adsorption and aggregation are critical aspects of many hypotheses of renal stone formation. The most common mineral constituent of renal stones in the United States is calcium oxalate. To date, there has been no previous systematic study of the electrophoretic properties of calcium oxalate. Double layer structure of other salts which are sparingly soluble — notably Agl — has been studied extensively. The theory of the double layer that has been developed from these studies is critical to our understanding of the stability of suspensions to aggregation. In some cases the properties of the double layer can be critical to the adsorption behavior of species from solutions. Calcium oxalate monohydrate, because of the apparently well behaved nature

PAGE 11

of its solid solution interface and its well studied solution chemistry, promises to be a model solid by which to test some of the basic aspects of double layer theory. Consequently both the electrokinetic properties and adsorption behavior of calcium oxalate systems for all adsorbate concentrations possibly could be quantitatively described by an appropriate double layer model. In this work we studied the electrophoretic properties of calcium oxalate in solutions ranging in complexity from those with a single salt added to those solutions as complex as urine. Electrophoretic measurements along with sufficient solution chemical information and some knowledge of the nature of the solid's double layer can allow the direct determination of the occurrence of adsorption. It can also give information as to whether the mode of adsorption is primarily specific or electrostatic. Adsorption can be detected for systems where it would be difficult or impossible to determine its occurrence with direct experimental adsorption methods such as solution depletion. Further, insight can be gained into the most significant adsorbing species in complex solutions like urine. We thus studied the electrophoretic behavior of calcium oxalate in these systems to sain an understanding of the character of calcium

PAGE 12

oxalate's double layer and to provide a basis for a better understanding of the mechanisms of formation of renal calculi . The main areas we investigated were the following . 1) Using simple systems with only a single salt added, we determined if the double layer properties of calcium oxalate are like those of a classical sparingly soluble salt, and if not what the anomalies are . 2) We studied the effect of some natural macromolecules to see if they affect the electrokinetic properties of calcium oxalate differently than smaller ions (we in particular wanted to see if macromolecules that were strong inhibitors of crystal growth would also strongly affect calcium oxalate's mobility) . 3) We studied the modes of aggregation of supermicron calcium oxalate to see if aggregation would occur in high ionic strength solutions and to see if the adsorption of macromolecules could induce aggregation . 4) Mobilities of calcium oxalate in artificial and natural urines were studied to see if significant

PAGE 13

electrokinetic potentials on calcium oxalate can exist in urine, or if the high ionic strength would bring the potential to zero (if a finite mobility can exist for calcium oxalate in urine, we wanted to identify which molecular components were controlling the electrokinetic properties). 5) We combined adsorption and electrophoretic data for the same systems to see if adsorption and electrokinetic properties of calcium oxalate can be consistently modeled by double layer theory. The most significant results of this study are that calcium oxalate's double layer in many acts like that of a classical sparingly soluble salt. It can have a significant mobility in urine-like solutions. The electrophoretic and adsorption properties, as far as can be determined, can be quantitatively predicted by the Nernst-Gouy-Stern (NGS) model of the double layer if it is assumed that a unique set of the two adjustable parameters of the Stern equation exists for every specifically adsorbing ion.

PAGE 14

CHAPTER II AN ELECTROPHORETIC STUDY OF CALCIUM OXALATE MONOHYDRATE Introduction The Nernst-Gouy-Stern (NGS) model (1-4) of the double layer at solid-water interfaces has long been of interest because of its analytic simplicity. The first serious attempts to test the NGS model or the Nerns t-GouySternGrahame (NGSG) model for solid systems used silver iodide (5-10). Several qualitative and semiquantitative aspects were in agreement with these theories. However, the fact that the capacity of the Stern layer (assuming the NGS model), in the absence of specific adsorption, depended heavily on surface charge (11) created additional analytical complexities. In the presence of specific adsorption, the Stern theory was acceptable only if specific adsorption potentials were assumed to vary with adsorption density. The latter assumption has been predicted (12,13) on the basis of an analysis of a discreteness of charge effect that takes into account the self atmosphere potential of counter-ions adsorbed in an inner Helmholtz plane (i.h.p.). It has also been suggested that there is a diffuse laver of charge in the

PAGE 15

solid phase (14-17). For silver halides, the charged species are lattice defects (vacancies and intersti tials) . The space charge in the solid can give rise to behavior that might appear to be due to a Stern layer with variable properties . For oxides, the theoretical concept is further complicated by the inapplicability of the Nernst equation in describing the surface potential [\\> ) (18-20). Modifications (21-25) of the Nernst equation that take into account the variable chemical potential of the hydrogen ions at the surface have had rather complicated forms and have not been tested fully by experiment. Another complication with some oxides is the presence of gel-like structures at the surface, which give rise to higher adsorption densities (24-30). The importance of complex ions in solution has been stressed, particularly by Matijevic (31,32) in relation to specific adsorption (reversal of charge). Any quantitative test of double layer theory requires an identification of species that adsorb and of the concentration of the species in solution. For example, the adsorption of aluminum ions (33-35) on various solids, as a function of pH, could not be understood until the complex ion chemistry of hydrated aluminum species was appreciated.

PAGE 16

On the basis of these considerations, the likelihood that a particular solid might more closely approach a behavior predicted by the NGS or NGSG model is greater by having the following characteristics. The solid must be ionic and sparingly soluble, be thermodynamically stable in water, attain equilibrium rapidly, have no hydroxylated surface groups that can undergo acid-base reactions, have no gel-like surface structure, form easily characterized particles, and have no significant solidstate conduction processes that can give rise to a solid phase diffuse layer. In addition, if the solid is to be analyzed adequately, the chemistry of the solutions in its presence must be well understood, particularly in relation to complex ions. A remaining difficulty, even if a solid has all those characteristics, is the discrete ion effects associated with the inner Helmholtz plane. Specific adsorption potentials may still vary with adsorption density. A conceivable situation where this effect may not be nearly as important is that in which the specifically adsorbing ions are large or remain hydrated toward the surface. Such ions may have a locus of center of charge outside the i.h.p., and may instead lie nearer the outer Helmholtz plane (or o.h.p., the closest approach

PAGE 17

of hydrated counter-ions of the diffuse layer). In this case, the simpler Stern model, with only one layer, might suffice . The adsorption of complex (hydrated) ions onto solid surfaces is not totally understood. However, the studies by James and Healy (36) strongly suggest that hydrolyzable metal ions can adsorb onto oxides without losing their primary hydration sheath. They presented a model for adsorption based on competition between the free-energy changes favorable to adsorption (coulombic and chemical) and those unfavorable to adsorption (solvation energy). During the course of studying the electrokinetic behavior of calcium oxalate monohydrate (CaC ? 2 *H~0) , it occurred to us that this material may have many of the characteristics that might favor the applicability of simple double layer models. This material is present in small amounts of human urine (37) , with particle sizes around 5 um. It is also the major mineral constituent in urinary stones in the United States (38) . Surface chemistry in general is being studied because of its possible relation to the stability, coagulation, and flocculation of particles in urine. In the present work, therefore, we have concentrated on chemical species normally present in urine. One of the important

PAGE 18

hypotheses of stone formation is that coagulation or flocculation is a major step in the overall mechanism (39) . An analysis of calcium oxalate in terms of the NGS double layer model was tempting because, as far as can be ascertained from published reports, it appears to nearly satisfy the criteria felt to be most favorable for this expectation. It is sparingly soluble, is stable in water, equilibrates rapidly, does not form gels, has no hydroxylated surface groups, forms well-defined particles, and gives no evidence of solid-state conduction processes at or near room temperature. Furthermore, its solution chemistry has been investigated extensively because of the importance of crystallization phenomena in renal lithiasis. This work analyzes the electrophoretic behavior of calcium oxalate with respect to variations in solution chemistry. Adsorption of potential -determining ions was not measured directly because of experimental difficulties associated with the measurement of oxalate at low concen2 trations and because of the low surface areas (^3.0 m /g) of our powder. We expect to overcome these problems, in part by using finer powders; the adsorption isotherms will provide a more complete picture of the phenomena we are

PAGE 19

10 investigating. In the meantime, we have been able to analyze the electrophoretic data in a way that we believe to be sufficiently valid for testing some aspects of double layer theory. We have learned which types of ions (including complex ions) will specifically adsorb and have obtained considerable insight into the mechanisms of adsorption. The results and analysis indicate that the electrophoretic behavior of calcium oxalate is not inconsistent with the simple NGS theory. Materials and Methods Calcium oxalate monohydrate was precipitated by mixing equimolar concentrated solutions of calcium chloride (CaCl^) and sodium oxalate (Na-C^CO ; analyticgrade chemicals were used, and the water was deionized and then distilled in a borosilicate glass still and had a conductivity of less than 1.5 x 10 (Qcm) . The precipitate was washed with the purified water until sodium could no longer be detected by atomic adsorption spectroscopy in the wash. X-ray analysis of dry precipitate confirmed the whewellite form of CaC^O^-H^O. The particles were around 5 urn in diameter, as ascertained by scanning electron microscopy and Coulter Counter measurements .

PAGE 20

11 Suspensions of CaC ? 4 *H~0 in water were prepared by ultrasonic dispersion at a concentration of 0.35 g/L. The purified water used for the dispersions and solutions showed no evidence of particle contamination by inspection through the electrophoresis microscope. The prepared suspensions were equilibrated for at least 12 h. Final suspensions were made by adding various electrolyte solutions to the dispersion at a ratio of nine parts suspension to one part solution. These solutions were prepared from analytic-grade reagents and were passed through 0.22 ym filters to remove undissolved particles. The final suspensions were equilibrated for at least 12 h. The pH values of the various suspensions were measured with glass electrodes. Electrophoretic measurements were carried out on a commercial instrument. Except for the electronic components, the electrophoretic apparatus was housed in a constanttemperature chamber, held at 37°C ± 1°C, with glove ports and windows through which the eyepieces of the microscope extended outward. In a preliminary study of the possible effect of suspension concentration on *Zeta Meter, Inc., 1720 First Avenue, New York, New York 10028.

PAGE 21

12 mobility, it was found that mobility did not change over a concentration range of 0.1 1.0 g/L; the 0.35-g/L concentration was therefore adopted. The activities and concentrations of various ions in solution, in the presence of calcium oxalate, were calculated for each experimental condition for which the overall composition was known. An established computer program (40) (EQUILS) uses the Davies modification of the Debye-Hiickel theory (41,42) for activity coefficients, the equilibrium constants (43-55) listed in Table I, and the principles of mass conservation. No corrections were needed for adsorption effects (which are not accounted for in the mass balance), because it was estimated to be negligible, owing to the low surface area of the powder and the low solid : liquid ratio of the suspensions. Results Calcium and Oxalate Ions Ions common to the solid and aqueous phases are Ca 2and C20^ . The activities of these two species are related through the solubility constant. The variations in mobility with (Ca ) were investigated ; CaCl 2 and T ) = activity (on the molar scale), when applied to ionic species.

PAGE 22

15 Table I Stability Constants Used in Ion Equilibrium Calculations a

PAGE 23

14 Table I continued, Stability Constant , Reaction (M ) Reference Mg 2+ + OH" t MgOH + 0.380 x 10 3 45 Ca 2+ + S0 4 2 " t CaS0 4 0.200 x 10 3 51 Na + + S0 4 2 " t NaS0 4 " 0.525 x 10 1 52 H + + S0 4 2 " t HS0 4 " 0.100 x 10 3 53 Ca 2+ + C 6 H 5 7 3 " t CaC 6 H 5°7 _ 0.600 x 10 5 46 H + + C 6 H 5 ? 3 " t HC 6 H 5 ? 2 " 0.272 x 10 7 54 Ca 2+ + HC 6 H 5 7 2 " t CaHC 6 H 5 7 0.505 x 10 3 46 H + + HC 6 H 5 ? 2 " t H 2 C 6 H 5 O y " 0.561 x 10 6 54 H + + H 2 C 6 H 5 ? " t H 3 C <5 H 5°7 0.127 x 10 4 54 Ca 2+ + H 2 C 6 H 5 O y " t CaH 2 C 6 H 5 O y + 0.125 x 10 2 55 H + + P 2 ? 4 " t HP 2 ? 3 " 0.615 x 10 10 46 H + + HP 2 7 3 " t H 2 P 2 7 2 " 0.615 x 10 7 45 H + + H 2 P 2 ? " t H 3 P 2°7 _ 0.190 x 10 2 45 Ca 2+ + P 2 ? 4 " t CaP 2 7 2 ~ 0.562 x 10 5 45 Ca 2+ + P.O 4 ~ t CaHP-,0 ~ 0.550 x 10 3 45 2 W 7 * ai "2 w 7 CaOK + + P 2 ° 7 4 " t CaOHP 2 7 J " 0.269 x 10 ! 45 The complex CaC204 has a concentration in solution at 38°C of (6.16 ± 0.38) x 10"6 M (43).

PAGE 24

<+^

PAGE 25

16 2 o 2 + I o

PAGE 26

17 Na-C-O. solutions were used to alter the activity. The (Ca + ) was calculated from the EQUILS program for the known additions. The results are given in Fig. 1. It should be noted that the ionic strengths varied with the electrolyte added; as shown later, however, this posed no serious problem in analysis, because the EQUILS program characterizes these changes, and they can be taken into account in the analysis of the double layer theory. The condition of zero mobility at 37°C is found (by interpolation in Fig. 1) to be pCa = 5.2, which also corresponds to pC ? 0. = 3.45 (because pK = 8.65). In the only other known attempt (56) to measure the point-ofzero charge of CaC ? 0.'H ? 0, the suspension effect was used; the results were a pzc at 25°C of pC 9 0. =2.5 and pCa = 5.11 (where pK = 8.1). Considering the differences in temperature (37°C vs. 25°C) , the results agree reasonably well. pH The variations in mobility with pH, resulting from the addition of HC1 and NaOH solutions, are shown in ^.Mobility is read from left legend; data points and smooth lines drawn through them represent experimental values. Broken lines, curves, and right legend are referred to later in discussion. This is also true for Figs. 2 (top), 3, 4, 5 (top), 6 (top), and 7 (top).

PAGE 27

Fig. 2 (top). In the intermediate pH range of 5 to 10, the mobility remains approximately constant. This would not be expected if H ions were reacting with the surface (e.g., by hypothesized surface hydroxyl, OH, groups), as in the case of oxides. This supports our original inference that ionizable surface OH groups are not present on calcium oxalate surfaces . The variations in mobility at low and high pH and the constant values at intermediate pH appear to relate to variations in (Ca ) with pH. In Fig. 2 (bottom), the activities of the various species present in solution (calculated from EQUILS) are plotted. The shape of the (Ca )-pH curve is similar to the shape of the mobility-pH curve. To a first approximation, the variation in mobility with pH could have been predicted by combining the information in Fig. 1 with that in Fig. 2 (bottom). This correspondence could not be exact, however, because ionic strengths are not comparable. In the analysis of double layer theory, corrections are made for ionic strength to obtain better comparisons. Electrolytes The variations in mobility with the addition of nine electrolytes were investigated; the results are shown

PAGE 28

Figure 2. Effect of pH on (top) electrokinetic properties and (bottom) activity of ionic species.

PAGE 29

20 £ _ o 3 £ CO E 3 >^ la o experimenta I 1 1 L1 L pH

PAGE 30

21 in Figs. 3 and 4. The data are presented as mobility vs. the total concentration of the salt added. Actual activities for the various species at equilibrium resulting from these additions are discussed and presented separately . The 1:1 electrolytes caused a gradual reduction in mobility with increasing concentration, as expected for indifferent ions. The (Ca ) remained nearly constant during these additions (from EQUILS) , as shown in Table II. The addition of sodium sulfate (Na~SO.) reduced the _ 3 mobility to zero at about 4 x 10 M and appeared to reverse the sign at higher concentrations, although the data are less reliable at these high ionic strengths. The calcium activity was lowered slightly by the addition of Na 2 S0 4 (Table II), but not enough to account for more than a small fraction of the change in mobility due to the Na~S0, addition. The decrease in mobility with concentration was too fast to be accounted for by the ionic strength when compared with the monovalent electrolyte at comparable ionic strength or as determined by the method described later. Therefore, it suggests that 2SO. , which is the dominant ionic form of the sulfate (by many orders of magnitude) in the solution, specifically adsorbs to the surface.

PAGE 31

22 i— i o3 h-i +-> -H 6 ,Q.H cd f-. ft w c cti u Pn 0> O Ph cm o3 X, U PL, o CM c_3 rt pv, 2 O O)

PAGE 32

23 C • H +J o u X2 u a. LO

PAGE 33

H3

PAGE 34

25 (AW) |D!|U9j0d UJ91S o CM + o + o y. o I o CVI i + I i i LO (D -a < c o c CD o c o CJ en O (,_ujq ||Oy\/,_s turf) Xunqo^.j oi|8Joqdoj|09|3

PAGE 35

T3 T3

PAGE 36

27 (AW) |DI|U9j0cJ UJ8JS O TO -a < o c:
PAGE 37

28 Wh en trisodium citrate (Na-,C,Hr0 7 ) was added, a -5 reversal in the sign of the mobility occurred at 4 x 10 M (Fig. 4). In this experiment, the pH was adjusted with HC1 titrant to maintain a pH of 6.6. The program EQUILS revealed that (Ca ) changed from 4.5 x 10 M to 8.6 x 10 M when the trisodium citrate concentration 5 2 7 + varied from 10 M to 10 M. This change in (Ca ) could account, by the use of data in Fig. 1, for a reduction of X, to near zero, but could not account for the larger negative values of c obtained. Therefore, it appears likely that specific adsorption is occurring. The principal ionic citrate species in the system were C.H^ 3 " and HC.HrO 2 '. Figure 5 (bottom) shows that the calculated activities of these two ionic species underwent large changes in opposite directions in adjusted solutions ranging in pH after equilibration from 4 to 8 . In this pH range, for calcium oxalate without Na^C.HrO-,, the mobility remains relatively constant as was shown in Fig. 2. Therefore, the direction in which the mobility varied with pH, with constant concentration of citrate salt, indicated which of these anions was affecting the mobility. As shown in Fig. 5 (top), the mobility became more negative with increasing pH (for the three total concentrations of electrolyte). This can be explained by

PAGE 38

Figure 5. Effect of pH with 10-2, 10-3, iq-4 m Na3C 6 H 5 7 additions. Top, electrokinetic properties; data points with solid lines are experimental; broken lines calculated from theory. Bottom, activity of HC6H5O72and C 6 H 5 07 3 -.

PAGE 39

30 o £ E 3 o > E --20 --30 o o a. c CO o < O CD O •3

PAGE 40

31 th e increasing (C fi H,-0 7 ) shown in Fig. 5 (bottom), and not by the decreasing (IIC.C 0). We conclude, therefore, 3. that the specific adsorption of the C,Fu0 7 species was occurring. Sodium pyrophosphate (Na.PoOy) additions caused a reversal in sign of the mobility at around 1.5 x 10 M, as shown in Fig. 4. In this case also, the changes in (Ca ) were not sufficient to expect a charge reversal on this basis alone. The effects of pK variations on mobility, at a constant electrolyte concentration of 5 x 10 M, are shown in Fig. 6 (top). The corresponding activities of ionic species are shown in Fig. 6 (bottom). The more negative mobilities with increasing pH cannot 2be attributed to the species H~P~0 7 , in that its activity decreased with increasing pH. The activities 324of HP ? 7 , CaP ? 7 , and p^CU increased with pH, so the adsorption of one or a combination of these species can explain the change in mobility. From these data, no single species is readily identifiable as the specific adsorbing one. The effects of additions of sodium phosphate monobasic (NaH-PO.) on mobility (Fig. 3) are interesting because of its weak tendency to reduce the mobility. It did not reverse the charge at concentrations as high as

PAGE 41

Figure 6. Effect of pH with 5 x 10" 4 M Na 4 P 2 7 addition. Top, electrokinetic properties. Bottom, activity of multivalent pyrophosphate species.

PAGE 42

53 5S o en E-l ir-2 2 ZL I i i i r experimenta \ ^-theoretica: J ! ! L 4 6 8 pH HO

PAGE 43

54 10 M. This behavior can be better understood by considering the complex ions formed. Under the conditions of this experiment, most of the electrolyte was in the H 2 P0~ form. The (HP0 4 ") was only a few percent of the (H-PO. ). The (P0 4 ) was lower by nearly 8 orders of magnitude. Consequently, the dominant species was the monovalent species, which was probably functioning as an indifferent counter-ion, whereas only a small amount of 9 _ HPO,^ was available to contribute to lowering the mobility by specific adsorption. The effect of pH on mobility, with a constant total electrolyte concentration of 10" 2 M, is shown in Fig. 7 (top). Above a pH of around 7, the solution became supersaturated. It is not known whether the precipitation of phosphate occurred under those conditions. If we assume that it did not 23precipitate, the activities of H 7 PC> 4 , HPC> 4 , and P0 4 2were as shown in Fig. 7 (bottom); the (HP0 4 ~ ) increased with pH, with a corresponding decrease in the mobility. 2This indicates the specific adsorbing role of HP0 4 (or z _ possibly PO. ) and the absence of specific adsorption by H ? P0 ~ . If precipitation of phosphate occurred, however, this interpretation is not valid. Magnesium chloride (MgCl 2 ) additions caused a small increase in the mobility (Fig. 4). This suggests that

PAGE 44

Figure 7. Effect of pH with 10" 2 M NaH 2 P0 4 addition. Top, electrokinetic properties. Bottom, activities of phosphate species.

PAGE 45

3o V2

PAGE 46

57 Mg (the dominant cation) was specifically adsorbing. To accentuate this effect, the oxalate activity was adjusted to 0.01 M, to create a negative mobility. Later addition of MgCl~ caused an increase in mobility, 3 reversing the sign to positive at 5 x 10 M, as shown in Fig. 4. For these changes, little variation in (Ca ) 2 was calculated (Table II) to occur until 4 x 10 M MgCl addition. These results indicate the specific adsorption role ol Mg Discuss ion "Experimental" Stern Potential The calculation of zeta potential, z, , from electrophoretic mobility is often not straightforward. The Smoluchowski equation (57) is valid only for some restricted conditions. Analyses by Hiickel (58), Kenry (59,60), Overbeek (61), Booth (62), and Wiersema et al . (63) have shown that deviations from the Smoluchowski equation due to retardation and relaxation effects are reduced with smaller Z, (<<25 mV) or larger Ka (>>1) , where < is the reciprocal of the thickness of the double layer and a is the particle radius. In our experiments, the smallest k was calculated to be 2 x 10 cm (at the lowest ionic strengths). Because

PAGE 47

5S 4 a 4 x 10 cm, the lowest value of Ka is 80. In most cases Ka is over 100 so the retardation and relaxation effects should produce little error. In addition, the influence of particle shape becomes unimportant at high Ka as long as the anisotropy is not too great. Although other effects, such as surface conductance, may give rise to error, they are harder to evaluate. With these justifications (and reservations), we use the Smoluchowski equation to calculate zeta potential from mobility: 4uri 5 U, where n is the viscosity, U is the electrophoretic mobility, and e is the absolute permittivity of the aqueous phase. To relate z, to double layer theory, we further assume that r, = ip «. The validity of this assumption has been debated; Lyklema (64) has recently provided some strong arguments for justifying it. The ip. calculated by setting C = tK and using the Smoluchowski equation will be called the "experimental" Stern potential, in contrast with the "theoretical" Stern potential calculated from theoretical double layer equations. The experimental ij/j. calculated for the various mobilities can be read from the data in Figs. 1, 2 (top), 3, 4, 5 (top), 6 (top), and 7 (top) by the right-hand legend.

PAGE 48

39 The Nernst-Gouy-Stern Model 2 + 2The Ca and C ? 0. ions are common to both phases (solid and liquid) and therefore would be expected to be potential determining ions for this system if equilibrium is established. This is supported by the observations that the r, (Ca ) curve remains linear for over three orders of magnitude (Fig. 1) and that the pH alters z, (Fig. 2) only according to what would be expected by its effect on (Ca ). Admittedly, while the potential deter2+ 2mining role of Ca and C ? 0. is not proven conclusively, the evidence is sufficient to warrant making this assumption so that a double layer analysis could be carried out . The Nernst equation is kT . (Ca 2 + ) ,, , ^o = TE ln " 2+ ' [1] ze (Ca Z ) p zc where (Ca ) is the activity at the thermodynamic v J pzc J condition \p = , i|) is the surface potential, z is the valence of the potential determining ion, and k, T, and e are the Boltzmann constant, absolute temperature, and electronic charge, respectively. The Gouy equation, expressed in its most general form [following Grahame (5)], is

PAGE 49

40 a D = ± DD kT 1 l where a n is the charge in the diffuse layer, D is the 'D 12 dielectric constant, D is equal to 1.112 x 10 coul ' o ' volt cm , n and zare the number of ions per cubic 'o-i r l centimeter and the valence of species i, and iK is the potential at the Stern layer. The sign taken in front of the square root is opposite that of iK . One of the Stern equations is (1) D'D 4m O * 6 ), [3] where a is the total surface-charge density, 6 is the thickness of the Stern layer, and D' is the dielectric constant of the Stern layer. In the absence of specific adsorption (1) , a + a D = 4] Without specific adsorption, the dependent variables are a, Oy., i> , and iK , which can be determined from Eqs . [14], assuming that the independent variables are the activities and concentrations of species in solution, and a value is assigned to D'/<5. With specific adsorption, an assumption must be made as to the location of the plane where it occurs. Analytically, the simplest case is to assume that the

PAGE 50

41 specific adsorption plane and the plane of closest approach for counter-ions in the diffuse layer coincide. This assumption is clearly incorrect for the double layer on mercury (5) and is probably also invalid for silver iodide. However, for calcium oxalate, it is conceivable that hydrated ions may specifically adsorb (e.g., possibly through hydrogen bonding with the carboxyl groups) . Therefore, it is worthwhile to examine this possibility. For this case, the other Stern equation is (1) [5] where o is the charge density in the Stern plane, N, is the number of adsorption sites per square centimeter of surface, N is Avogadro's number, M is the molecular weight of the solvent, n. and zare the number of ions per cubic centimeter and the valence (including sign) of a specifically adsorbing species j , and $ . is the specific adsorption potential of species j. Also, Eq . [4] must be modified to give a + a + a D = 0. [6] The five dependent variables — a, a , a^, if) , and i> . — can be determined from Eqs . [1], [2], [3], [5], and [6], assuming values for tf> . and N, . A computer method of

PAGE 51

42 numerical analysis was used to solve the two combinations of simultaneous equations (i.e., with and without specific adsorption). Analysis of Conditions Involving Potential-Determining Ions and Indifferent Electrolytes In the NGS model with no specific adsorption, these values were used for the constants: (Ca" ) DZC = 6.31 x 10" 6 ; D = 8.21 x 10" 11 F/cm; D' = 6.5; and 6 = 5 x 10" 8 cm. The EQUILS program provided the necessary activity and concentration values for each condition; these were used as the independent variables. Theoretical calculations for conditions simulating those in Fig. 1 are given (as a broken line) in the figure, with the experimental values. A surprisingly excellent agreement was found near the pzc, and for 3 x 10~ 6 < (Ca 2+ ) < 10" 3 . Significant deviations occurred above and below this calcium activity range. For (Ca ) > 10 , the theoretical drops with increasing (Ca ) because of the increasing ionic strength. The experimental iK does not exhibit this change, but rather continues to increase (although more slowly) at higher (Ca" ). At low values of (Ca" ), below 3 x 10 , the theoretical curve tends to flatten out faster than the experimental curve, where the ionic strength is also increasing, owing to the addition of sodium oxalate.

PAGE 52

4 5 Because of the discrepancies at low and high (Ca ) , possible explanations were examined. It was doubtful that deviations from the Smoluchowski equation were occurring at these higher ionic strengths inasmuch as Ka is much larger and surface conductance error is expected to be smaller with increasing ionic strength. Increasing the value of D'/<5 in Eq. [3], which increases the capacitance of the Stern layer, raises the theoretical values of tK at low and high (Ca ) , but it also increases i/j throughout the intermediate range in such a way that the theoretical iK(Ca + ) slope becomes greater than the corresponding experimental slope. Furthermore, a maximum in the theoretical curve remains. One possible way of rationalizing these results is to assume that the Stern capacitance increases as (Ca ) departs significantly from (Ca ) v . However, this is contrary to what was p zc found (or assumed) for silver iodide (6) , where the capacitance increased with more negative i|j values. Another possible explanation for the discrepancy 2 + 7 is the specific adsorption of Ca and C 2 C> 4 . At first thought, this proposal may seem invalid, because by definition the potential-determining ions should adsorb with unit thermodynamic activity. But these ions conceivably adsorb in two forms — a dehydrated form and a

PAGE 53

44 hydrated form. The dehydrated form enters lattice positions in the crystal. The hydrated form is bonded to the surface and in this form is distinct from the species entering the lattice. The adsorption of the hydrated ions could be expected to follow the Stern isotherm relationship in that its activity varies with changing adsorption density. Assuming the possibility of the specific adsorption of hydrated Ca + and C^O, species, the NGS theory with specific adsorption can be applied, with the j ions (for Eq. [5]) being Ca 2+ and C 2 4 ". A value of 17 -9 4.1 x 10 cm for N, was used in the calculations on the basis of estimates of average lattice spacings. The two adjustable parameters are 4>r a 2 + and ~ q 2-. These were varied to give the best overall fit of theory to data. The best-fitting values were * Ca 2 + = 13 ° mV and
PAGE 54

4 5 the same curve is obtained regardless of whether or not 2 + 2we assume that Ca and C^O. are specifically adsorbed. The reason for this similarity is that the activities of these ions remain in a range which gives a iK value between and 20 mV where specific adsorption effects 2+ 2are not yet important. That is, the (Ca ) and (C^O. ) are small enough so as to minimize their specific adsorption contribution to
PAGE 55

4 6 C ? 0. " become greater than 10 J within a few pCa units. For Ag + and i" studies, the (Ag ) is usually •7 _ _ 5 below 10 , whereas the (I ) remains below 10 throughout the titration range. In other words, the concentrations of Ag and I" are much lower than those of Ca and CoO. , and any weak specific adsorption effects would not be noticed for the former even if they occurred. Specific Adsorption of Counter-Ions 232The specific adsorption of SO. , CgH,-0 7 , HPO^ , and Mg , inferred above, was analyzed with respect to the Stern model for specific adsorption. We assumed that all multivalent pyrophosphate species were specifically adsorbing for purposes of this calculation. Again, we assumed that the ions were hydrated or large enough to be situated at the o.h.p. The concentrations of these ions, for our experimental conditions, were calculated with EQUILS. For each species, a value of . was determined by finding the best fit between theory and experiment for the ty .-concentration curves. Values obtained 2 for 4 , -107 mV for C,H.CU 3 " -110 mV for HPO. 2 ", -113 mV for the multivalent pyrophosphate species, and 112 mV for Mg" . The resulting theoretical curves are compared with the data in Figs. 1,

PAGE 56

47 2 (top), 3, 4, 5 (top), 6 (top), and 7 (top). Although the data could not be reproduced perfectly, the similarity is sufficient to provide reasonable confidence that the theory is not inadequate for this purpose. On the Bonding Mechanism for Specific Adsorption The original Stern theory has given a reasonably consistent and nearly quantitative description for our experimental data. This supports but does not prove the suggestion that the specifically adsorbing ions remain as hydrated species or are, themselves, large enough to have a center of charge near the o.h.p. It should be stated that a different model (e.g., the NGSG model) might also give consistent results if the calculations were possible. If so, quite different values of |
PAGE 57

48 For all the specifically adsorbing ions studied 2+ 2-i (including Ca" and C^O. ), \ $ \ ranges between 93 and 130 mV, with an average of 109 mV and a standard deviation of ± 12 mV. Considering the wide range of . expected for various types of bonds, the experimental values of ), in contrast with the convention used by Overbeek (61) , where w is expressed as zeiK + , is proportional to the valence. Ionic bonding depends on the valence of the adsorbing ion. However, the specific adsorption energies, ze , are equivalent to 2-5 kcal/mole. Usual ionic bonds with simple cations and anions involve energies about one order of magnitude greater. However, with hydration molecules intact, or with large anions, the distance of separation

PAGE 58

49 between charge centers is greater, thereby weakening the ionic bond. This bond must be specific with some surface sites; that is, some form of discrete ion-pair interaction must be assumed. The alternative, the hydrogen bond mechanism, is attractive because the energies, 2-5 kcal/mole, are what might be expected. However, the importance of valence that has been inferred does not seem to be explained by this approach. Summary Our experimental results are consistent with the hypothesis that the electrophoretic behavior of calcium oxalate monohydrate follows the NGS double layer theory. From our limited data it appears sufficient to consider specific adsorption as occurring at or near the outer Helmholtz plane. The specific adsorption potentials of seven different species, assuming the NGS theory, were found to be nearly identical when normalized to unit valence. This supports an ionic bonding mechanism involving hydrated ions, rather than a hydrogen bonding mechanism. Whether the calcium oxalate monohydrate system more broadly fits the NGS model needs still to be explored by adsorption measurements involving the potential-determining ions.

PAGE 59

CHAPTER III ELECTROPHORETIC BEHAVIOR OF CALCIUM OXALATE MONOHYDRATE IN SOLUTIONS WITH NATURALLY OCCURRING MACROMOLECULES Introduction The adsorption of macromolecules at solid-liquid interfaces has been the subject of much interest in physical chemistry; however, much is still not understood about the mechanisms of adsorption. Direct measurements of macromolecular adsorption have shown that it usually appears to follow the Langmuir monolayer adsorption model. Langmuir adsorption for macromolecules was first reported for the adsorption of the albumin and gelatin proteins on collodian membranes (66); since then, it has been found for numerous systems. These systems include: albumin in quartz (67); bovine serum proteins on quartz (68); lysozyme on kaolin clay (69); y-globumin, serum albumin, and fibrinogin on charged and uncharged polyethylene (70,71); and polyacrylamides on calcium phosphate (72). Solution depletion adsorption studies (73) on calcium oxalate monohydrate with several proteins and two mucopolysaccharides have also shown that adsorption follows the Langmuir model. The Langmuir adsorption parameters can be influenced by both the charge on the macromolecule and by the charge 50

PAGE 60

51 on the surface. Because of the amphoteric nature of proteins, their charge can usually be altered with solution pH . For the lysozyme -kaolin system (69) it was found that in the pH region where the macromolecule and surface were oppositely charged, adsorption was stronger. The same relation between adsorption and pH has also been shown for protein adsorbing upon silica (74) . For surfaces whose potential determining ions are not hydrogen and hydroxy 1 ions, the effects of surface charge and macromolecule charge can be investigated independently. This type of study has been done with silver iodide (75) . For calcium oxalate it has been shown (73) that the adsorption of negative macromolecules increases with increasing pCa while that of positive macromolecules decreases. Macromolecular adsorption can also be influenced by the presence of adsorbing small molecules like phosphate, calcium, and citrate competing for the surface; however, the details of this interaction are not well understood (68,69,71). The electrical double layer of the surface has also been shown to influence the adsorption of macromolecules on a variety of surfaces (76) due to its influence upon the adsorbate concentration near the surface (77) . The mechanisms of bonding of macromolecules to surfaces is the subject of much debate. Electrophoretic

PAGE 61

52 studies of the adsorption of cationic synthetic polymer on silica have shown evidence for specific adsorption (78). For the adsorption of non-ionic polymer on silica, hydrogen bonding has been proposed (79). Another proposed bonding mechanism is the tendency to lower the free energy of the system by reducing the interaction between nonpolar groups on the adsorbate and water molecules during adsorption (64) . It is clear that there are at least two mechanisms of bonding, one with a heat of adsorption in the range expected for chemical bonding and another whose heat of adsorption is much lower or even negative. Urease adsorbed on montmorillonite could be partially removed by cationic displacement; however, more complete removal resulted from increasing the pH (80). This was interpreted by the authors as suggesting at least two mechanisms of binding. Protein has been shown to adsorb on hydrophobic silica with much less sensitivity to electrostatic forces than protein adsorbed onto hydrophilic silica (64). Analysis of the characteristics of adsorption of protein on silica has suggested that the adsorption occurs on two distinct types of independent sites simultaneously and that the resulting adsorption is consistent with the Langmuir model (71) . The adsorption of macromolecules onto calcium oxalate is of practical interest because of its possible

PAGE 62

53 importance in renal stone disease. Calcium oxalate is the major mineral constituent of renal stones in the United States and macromolecular matrix is almost always present throughout the stone (81) . The role of the matrix in stone formation is not understood, but it is known that it usually consists of 2.51 of the dry weight of the stone (82). This is made up mainly of mucoprotein — possibly with chemically bound mucopolysaccharides — and with serum albumin, alpha-globulin, and sometimes gammaglobulin present (85,84). Urinary protein in general (85) and urinary lysozyme in particular (86) are generally higher than normal in concentration in stone formers' urine . The adsorption of macromolecules could be critical to the following processes that may cause the initiation or the prevention of stone disease: flocculation of crystals in urine by macromolecular bridging (Chapter IV); inhibition of the growth of crystals in urine (87,88); alteration of the interfacial electrical double layer which affects the tendency of crystals to aggregate (89, Chapter II); and attachment of calcium oxalate crystals to macromolecules comprising the walls of the renal system which can lead to fixed stone disease (90) . For the above reasons, we were interested in firstly understanding the mechanisms of adsorption of

PAGE 63

54 ma cromolecules . For this purpose, the mobilities of calcium oxalate in solutions with macromolecules present were chosen for investigation to determine whether their adsorption was specific or electrostatic by observing how it affected the charge on the particles. How the macromolecules affect the mobility could also be compared with the effect of small ions (Chapter II) to gain inferences on the influence of the adsorbate size. Two well studied globular proteins, one whose isoelectric point was acidic, the other with a basic isoelectric point, as well as two mucopolysaccharides were selected for these experiments. We studied the effect of macromolecular concentration (adsorption density), the concentration of a small, strongly adsorbing ion (competition) , pH (adsorbate charge) , and pCa (surface potential) . We then interpreted the results using electrokinetic theory and adsorption parameters estimated from previous work. The most significant findings of this study are that macromolecules can adsorb to calcium oxalate in two ways, specifically and electrostatically, and that when the macromolecules are prevented from approaching close to the surface the adsorption proceeds completely electrostatically.

PAGE 64

55 Materials and Methods rum Natural polymers obtained commercially were sen albumin bovine (4X crystallized), lysozyme (murmidase) , sodium heparin, and chondroitin sulfate. Serum albumin and lysozyme are globular proteins with isoelectric points at pH 4.9 and pH 11, respectively. Sodium heparin and chondroitin sulfate are mucopolysaccharides with random coil structures. Other chemicals were analytical reagent grade. Stock solutions were passed through a 0.22 ym filter to remove undissolved impurities. Calcium oxalate monohydrate powder was prepared as described previously in Chapter II. The pH was adjusted with volumetric titrants of HC1 or NaOH. Water was deionized and then distilled in a borosilicate glass still; the conductivity was less than 1.5 x 10 (ftcm) . Working suspensions were made by adding macromolecule solutions of varying concentration to suspensions of calcium oxalate that had been equilibrated at least 12 hours after the desired addition of HC1, NaOH, CaCl 2 , Na 2 C 2 4 , or Na 7 C,H c 0^. The final calcium oxalate present in the 3 u 5 / systems was 0.315 g/L. Solutions after the final modifications were equilibrated at least 2 hours at 37°C before making electrophoretic measurements. The electrophoresis was carried

PAGE 65

56 out using a commercial instrument in a constant temperature chamber at 37°C (Chapter II). The equilibration and the electrophoretic measurements were completed within a total of 6 hours. The solution pH was determined with a glass electrode after electrophoresis. Some solutions were then passed through a 0.22 ym filter and analyzed for protein concentration with solution transmission spectroscopy at a wavelength of 280 nm. Results and Discussion Figure 8 gives the electrophoretic mobilities of calcium oxalate in systems with increasing concentrations of the four macromolecules . The concentrations given in the abscissa of Fig. 8 are actually calculated on the basis of the amount of water. However, in the present study, initial concentrations (C T ) are virtually the same as the final concentrations (CV) which exist after adsorption because of the very low total surface area of the particulates present. In an earlier study, using concentration suspensions having high surface areas, adsorption isotherms were determined by solution depletion methods (73) for three of the macromolecules that we are investigating (serum albumin, sodium heparin, and chondroitin sulfate). The

PAGE 66

m

PAGE 67

58 Electrophoretic Mobility (urn s '/Volt Cm" 1 ) r~ o o O ZJ O CD 3 O 13 > CL CL CD iQ

PAGE 68

59 adsorption was found to obey the form of the Langmuir adsorption isotherm. In fact, from this data it could be confirmed that in our present experiments the solution depletion should be negligible (Table III) . We have shown in Chapter II that calcium oxalate in water over the pH range from 3-10 has a positive charge with an electrophoretic mobility of about 1.7 mobility units (um s /Volts cm ). Referring back to Fig. 1, the presence of positively charged lysozyme in concentrations as high as 0.1 g/L had little effect on the mobility of calcium oxalate, while the negative polymers made the mobility less positive as their concentrations were increased. Each of the three negative macromolecules reversed the sign of calcium oxalate's mobility. The reversals in mobility may be due to adsorption of the macromolecules or by other induced changes such as the alteration of the calcium and oxalate activity or the precipitation of a second solid phase. To detect the possible precipitation of a second solid phase we used the following methods. The protein solutions in equilibrium with calcium oxalate in our various experiments were filtered after electrophoresis, and the filtrates were examined with transmission spectrophotometry at 280 nm for solution depletion of protein

PAGE 69

6 DO ^

PAGE 70

61 against standard solutions. Since the solids concentration used in these experiments is too small to detect significant solution depletion due to adsorption, any depletion noted could be attributed to precipitation. The remaining solutions were prepared to nine-tenths final volume and then were observed after one-half hour for precipitation before the slurry was added. Finally, a second solid phase can be recognized by the presence of particles of two distinct mobilities during electrophoretic measurement. No evidence of precipitation was found in any of the systems presented in this paper. If calcium is removed from solution through complexing with, or binding to, the macromolecule , an increase in oxalate concentration in solution will result because the calcium and oxalate ion activities are related to each other through the solubility constant. In Chapter II, the change in calcium oxalate's mobility with the addition of calcium chloride or sodium oxalate was given. Since it requires about 10 ^ M of sodium oxalate to bring the mobility of calcium oxalate from its value of +1.7 in water to -1.7, and that the total oxalate in _ 3 the system is limited to 2.2 x 10 M by the solids content of our suspensions, the mobility change due to the presence of the mucopolysaccharides cannot be explained

PAGE 71

62 by increased oxalate ion activity alone. The mobility changes due to the proteins were less dramatic, but the amount of calcium binding that could possibly be expected can be estimated from values obtained empirically in prior calcium binding experiments. Total serum calcium is about 10 mg/100 cc; the 4.5 g/100 cc of total serum protein at pH 7.4 typically binds about 5 mg of this (91). For a concentration of 0.1 g/L protein, this indicates about 2.7 x 10 M of calcium would be bound. Typical values of molar binding ratio for calcium to serum albumin at pH 7.4 (92) have been found to be about 2. For 0.1 g/L serum albumin this gives a concentration of bound calcium of 2.7 x 10 M. The effect of a change in solution calcium of the magnitude indicated by these values upon mobility in the systems of this study would be negligible. Since precipitation or binding of calcium or oxalate does not appear to be important, we are left with the conclusion that large changes in mobility with increasing concentrations of macromolecules are due to adsorption. The result that the negatively charged macromolecules have shown evidence of specific adsorption, but the positively charged protein , lysozyme , had little effect upon mobility suggests the alternate possibilities that either lysozyme

PAGE 72

65 would adsorb more strongly as the calcium oxalate surface becomes more negative or that these macromolecules could only specifically adsorb to the positive surface sites. To eliminate one of these possibilities we added lysozyme at concentrations up to 0.1 g/L to calcium oxalate suspensions equilibrated (after pH adjustment to 6.5) at three Na ? C^O. concentrations. Initial mobilities of one slightly positive and two increasingly negative values were obtained. The results given in Fig. 9 show that with increasing lysozyme concentration there was a marginal increase in mobility for the positive suspensions and there was a decrease in mobility from -1.4 to zero in -2 the suspensions with 10 M oxalate added. In the suspensions with the intermediate oxalate concentration, however, as lysozyme concentration increased, the sign of the mobility reversed from minus to plus which strongly indicated specific adsorption. To determine if adsorption onto calcium oxalate caused large alteration of the solution macromolecule interface, we studied the mobility of calcium oxalate in the presence of macromolecule with varying pH . Adsorbed proteins can sometimes maintain their integrity and cause a covered particle to obtain surface properties similar to the protein (95); conversely, adsorption could

PAGE 74

65 Electrophoretic Mobility (urn s '/Volt Cm ') o c/) O N CD o O 13 O CD 13 o ZJ > Q. CDCD ,Q-, iQ

PAGE 75

6 6 possibly alter the charge of the protein. Since the mobility of calcium oxalate in water is fairly constant with the pH range from 4-10, the variation in mobility with pH in the presence of adsorbed macromolecules will be due primarily to the effect of pH on the charge of the adsorbed macromolecule . If the macromolecule charge was not altered greatly by adsorption and if the amount of surface coverage is high, then the pH of zero mobility should be close to the isoelectric point of the protein. Figure 10 shows the resulting mobility of calcium oxalate in the presence of 0.1 g/L of macromolecule over a range of solution pH. The mobility of calcium oxalate with adsorbed serum albumin varied from positive to negative as the pH increased. It reversed the sign at about pH 5 which is close to the isoelectric point of serum albumin. Similarly in the presence of lysozyme, the mobility decreased with increasing pH approaching zero at approximately pH 11, which is the same is the isoelectric point of lysozyme. The experiment was not extended to high pH's to attempt a sign reversal for lysozyme because above pH 11.7 the base alters lysozyme' s structure dramatically (69). The result that the mobility of calcium oxalate is sensitive to pH in the presence of

PAGE 76

67 positively charged lysozyme shows that a surface potential of opposite charge to the protein is not necessary for adsorption. This suggests that the increase in concentration of the potential determining ion, oxalate (Fig. 9), is providing more negative surface sites for lysozyme specific adsorption. Figure 10 also illustrates that the mobility of calcium oxalate remains highly negative throughout this pH range in the presence of the mucopolysaccharides. This is consistent with findings (94) that show that their surface sulfate groups remain almost completely ionized above pH 3. The moderate increase in mobility with increasing pH is as would be expected from the ionization of their surface carboxyl groups. Thus, the observed mobility of calcium oxalate as a function of pH in the presence of any of these macromolecules does not support a model that depicts large alteration of the macromolecule's solution interface with adsorption . Since the natural macromolecules presented in this study, as well as some small molecules studied previously (Chapter II), have shown evidence for specific adsorption onto calcium oxalate we tried to determine how they compete with each other for the surface. If a macromolecule and small molecule were competing for the

PAGE 77

Figure 10. Electrophoretic mobility of 0.32 g/L calcium oxalate monohydrate with 0.1 g/L of macromolecule as a function of solution pH. The solid curve without data points represents the mobility versus pH without macromolecule present .

PAGE 78

6 9

PAGE 79

70 same sites, and if enough sites were available, both species could adsorb, possibly causing an additive effect upon mobility. If the concentration of one species became large enough that it occupied practically all the available sites, the effect upon the mobility of the other species becomes zero. If, however, the species were adsorbing upon different sites the additive effect upon mobility would stay relatively constant. The mobilities of calcium oxalate were measured in suspensions with various concentrations of sodium citrate to which 0.1 g/L of lysozyme or serum albumin was added. Citrate was chosen because it is a relatively small molecule which specifically adsorbs strongly to calcium oxalate (Chapter II, 95) and because it can be added in high concentrations. In Fig. 11 it can be seen that the mobilities of calcium oxalate with lysozyme are substantially less negative than those without lysozyme for 2 all citrate concentrations. Since at 10 M citrate the number of citrate molecules is over a factor of a thousand greater than the number of protein molecules, these data indicate that the lysozyme and citrate are adsorbing upon different surface sites. This is as might be expected since in the pH range indicated lysozyme would be positively charged, while citrate ions would be

PAGE 80

o Pn CO +-> +-> a as CD 'O co CD P P to i-h co • P O CTj CD ,C EP P •H 3 3 o • rC P -H CO 3 P nj cd . ^fl ftO rC -H 6 OHO PJ rH P O 13 3 "+H £ -H U CD <— t CD rH CD O rH P ifl o o co E X rH CD O H CO jZ P X H -,P .P P -H P H (J rH O • H in P P CD o 6 CD 'H P P cO CO P CO P p a C CD H U O P P. O u CO co co t3 co o P T3 CD P! > o Ph CD CO CD P P -H P CJ p CD i— I CD P C p P p CO P O U P CD CD rd CD O C Ph-h o o p e P o U P CD U i— I CO W £ U CO P CO P O P CD 4-1 P rQ h £ CD O 3 P Ph P! co

PAGE 81

72 O < o c CD O c o O I s O 10 X iD (J ro O en O (i WQ uoa/.$ ujtt) Ajjiiqow oueJoqdojp9|3

PAGE 82

75 negative. With the negative protein serum albumin present, however, there is an additive effect at low citrate concentrations between the two species on mobility, since it is more negative than would be expected from the citrate or serum albumin alone. This effect decreases with increasing citrate concentration until 2 at 10 M the mobility is about what would be expected for either the citrate or the serum albumin alone. This may occur either because the increased citrate concentration has become so large relative to that of serum albumin that effectively all the available sites are being occupied by citrate or the citrate has raised the charge on the surface to the point where adsorption of serum albumin has been electrostatically inhibited. These results indicate that, in the presence of a relatively high concentration of a specifically adsorbing small molecule, adsorption will be limited in the presence of a polymer of the same sign, while if the polymer is opposite in sign adsorption of both species will continue. Calculations based upon the results of solution depletion experiments (73) indicate that there may be considerable crowding of the molecules as the calcium concentration is increased if we can assume that serum albumin retains its shape upon adsorption and that its

PAGE 83

74 adsorption is limited to a monolayer. Adsorption of serum albumin on calcium oxalate at various calcium activities was found (73) to be described reasonably well by the Langmuir adsorption isotherm, C C -I = -£+ -A[7] AC AC AC [/J m m where A is the macromolecule equilibrium concentration at which half of the surface is covered with adsorbate. It is a measure of the affinity of the polymer to the surface. The term AC is the chanee in macromolecule m ° concentration occurring at maximum surface coverage. A least squares fit of the experimentally determined C^/AC versus C^ is used to obtain values for A and AC . In b m Fig. 12, linear Langmuir plots are given for the macromolecule concentrations used in our experiments utilizing the values of AC and A determined in the study cited, m The AC values have been normalized by weight to our m experimental conditions. This figure shows that for serum albumin at a given C p the value of AC increases greatly with increasing calcium activity. The least squares fit of the data to the Langmuir isotherm shows that this is due almost entirely to increasing AC . Log AC was found to vary fairly linearly with the log of the calcium concentration for the adsorption of negative proteins (including that of serum albumin) .

PAGE 84

cO E P. •> 3 3 O -H O • T3 O 6 £ e nd ,3 3 DO 3 O m CD P -H -H rH T3 (/) V) CD rH D C |2 3 X t/> 3 (fl ,£2 P O •H >, O -H ^ if) rC X> <-* £ P Ctf +-> bfl S <+-! ^H CD DO-H • H TJ O-, in T3 P 3 wo CO P 3 rH CD tfl rn (/) o o £ +J .H Mh -H S 3 tfl +j

PAGE 85

76

PAGE 86

77 We can obtain values for the percent coverage by estimating the projected area of adsorbed serum albumin at various calcium concentrations and then comparing this to the total calcium oxalate surface area available. We did this in the following manner. Values for AC for a series of calcium concentrations were obtained from Fig. 13 (some values were estimated using the line drawn through the data points). The value of 0.027 g/L was used for A; values for AC were calculated from Eq. [7]. The surface area of the calcium oxalate used in these experiments as measured by nitrogen gas adsorption is about 3.0 m"/g. The molecular weight and density used for serum albumin were 69,000 g/M and 0.73 g/cm respectively. Serum albumin was assumed to be spherical in shape. This yields a projected cross -sectional area for adsorbed protein on the surface, Ap , of about 2.3 x 10 A /g. The effective area covered by serum albumin for each solution in Angstroms squared per liter is A = AC x Ap [8 *This value for surface area gives a more conservative estimate of crowding than the lower surface area which was estimated for the powder in the adsorption study using the optical microscope.

PAGE 87

Figure 13. Concentration of serum albumin adsorbed at maximum surface coverage versus calcium concentration. Values obtained from a previous study normalized by weight to our experimental conditions .

PAGE 88

7 9 U> < E Z5 E v01 o -7 -6 -5 -4 -3 -2 Log [Calcium Concentration j ( M )

PAGE 89

so The total surface area for 0.315 g/L calcium oxalate is 6.3 x 10 A /L. The estimated percent of the total area covered by protein is given in Table IV. These calculations are admittedly somewhat rough, but since even 601 coverage is probably unrealistic (96), the _ 3 results indicate that above 10 M calcium there is likely to be considerable physical crowding of adsorbed molecules . This analysis of solution depletion data raises a question of how the physical crowding of adsorbed molecules affect their adsorption mechanism. One possibility is multilayer adsorption; however, since the solution depletion data fits the Langmuir model, the explanation that protein is adsorbing on protein is not satisfactory. Consistency with the Langmuir model at the adsorption densities indicated can be explained by the following two mechanisms: The protein distorts its shape with increased calcium activity to allow continued specific adsorption; the protein remains globular and eventually physical crowding prevents further proteins from getting close enough to the surface to specifically adsorb, so then adsorption can only occur electrostatically. Although solution depletion adsorption experiments cannot differentiate between these two mechanisms, we

PAGE 90

EO

PAGE 91

82 could be able to eliminate one possibility by the effect the adsorption has on calcium oxalate's mobility. To see how the mobility should react to continued specific adsorption (as would occur in the first mechanism stated above), we estimated the charged surface sites per adsorbed molecule over a range of calcium concentration. The total surface charge, before protein adsorption, was calculated using the Nernst-Gouy-Stern model of the double layer and solution equilibria in a manner that has been described in detail (Chapter II) previously. The total charge was divided by the charge on the electron to give the corresponding number of monovalent surface sites per unit area. The number of molecules per unit area was calculated from the adsorption data given in Table IV. The ratio of these two values gives the number of molecules per apparent monovalent site. The values calculated are listed for positively charged surfaces in Table V. This calculation shows that over this range of calcium activity the number of molecules adsorbed per monovalent site is within 35% of one. Thus, with continued specific adsorption, as the calcium activity is increased, the mobility is likely to remain negative. If, however, crowding of adsorbed molecules occurs (as in the second mechanism) , the mobility will be brought to zero but a sign reversal will not occur.

PAGE 92

83 Table V Langmuir Adsorption Density Per Unit Surface Charge for Various Solution Calcium Activities +1 sites Molecules CCa) (MJ Molecules +1 site 1.0 x 10" 1 4.1 x 10" 4 5.0 x 10" 4 1.0 x 10" 2 3.0 x 10" 4 2.6 x 10" 4 1.0 x 10" 3 1. 7 x 10" 4 1.1 x 10" 4 1.2 x 1 " 4 6.7 x 1 " 5 6.0.x 10" 5 2.2 x 10" 5 3.9 x 10" 5 2.8 x 10" 5 1.25 0.87 0.65 0.75 0. 72

PAGE 93

84 We measured the electrophoretic mobilities of calcium oxalate suspensions equilibrated in solution with pCa from 6.4 to 1.2 and with lysozyme or serum albumin added to possibly eliminate one of the above mechanisms. The amount of 0.1 g/L of macromolecule was added to calcium oxalate suspensions equilibrated with various concentrations of sodium oxalate or calcium chloride added. The resulting electrophoretic mobilities with and without polymer are shown in Fig. 14. The presence of serum albumin has an increasing effect on the mobility as the calcium concentration increases. Comparing the curve for the mobility without macromolecule to that with 0.1 g/L serum albumin, we can see that the serum albumin reversed the sign of the mobility from plus to -4 , -4 minus at 10 M sodium oxalate and at 10 M CaCl ? ; however, at higher calcium concentrations the mobility was brought to zero by serum albumin but sign reversal did not occur. Lysozyme appears to have behaved in a similar manner, except the mobility had been approaching zero as the oxalate concentration was increased. One conceivable explanation for this is that the protein may be more sensitive than calcium oxalate to ionic strength. Thus, as the coverage of the surface with macromolecule increases the ionic strength reduces the

PAGE 94

r-i c t/5 -H tf O vH rt C 3 t— I rH CD X ri rH OHT) O CO -H E E X t-H O 3 O O J•H t/1 U U J V) M H o O • X fVH c o 0) >s O 3 .-l +J i— i i— i rt •h X O X i— I (J (/) o ,£> E +-> u c O 4-1 PU O 0> r* O X o P.-H Oj X O hf f rH Cti 05 -H P >TlH O -H 0) h Dfl rH O X O

PAGE 95

86 ( uuo 41 o A /. _ s urn) AiujqoiAJ QjjoJOijdcupaG

PAGE 96

87 mobility to zero. This argument is not valid, however, since serum albumin at pH 6.0 and an ionic strength of 5 x 10"" M has a mobility of about -1.7 (97). These results, combined with the physical crowding inferred from solution depletion data, strongly indicate that when the molecules are prevented from approaching closely enough to specifically adsorb, adsorption continues electrostatically until the difference in charge between the macromolecule and surface is brought to zero. Conclu s ions Proteins and mucopolysaccharides specifically adsorb to the calcium oxalate surface. A surface of opposite charge to the macromolecule is not necessarily needed for adsorption; however, the amount of adsorption appears to be dependent upon calcium activity. A model consistent with the effect of citrate upon the mobility of calcium oxalate in solution with positively or negatively charged protein is one where there is competition for surface sites between the adsorbing small molecule and a like charged macromolecule but one that the adsorption is relatively independent when the molecules are oppositely charged. When specific adsorption is physically prevented by high macromolecular adsorption density at extremes of

PAGE 97

pCa, the adsorption continues completely electrostatically. Thus, the results of this study indicate that the two simultaneous mechanisms of adsorption for proteins that have been alluded to in the literature are: 1) a specific adsorption mechanism that competes with like charged small molecules for surface sites and 2) a mechanism that is completely electrostatic when physical crowding occurs.

PAGE 98

CHAPTER IV AGGREGATION MECHANISMS OF SUPER-MICRON CALCIUM OXALATE MONOHYDRATE Introduction The aggregation of super-micron calcium oxalate is the object of much recent interest because it is perceived as a principal step in the initiation of renal lithiasis (98). Aggregation is defined by Fleisch (98, p. 361) as "the process of crystals binding one to another, resulting in the formation of larger clusters." The combined effect of growth and aggregation of supermicron calcium oxalate in supersaturated solution has received a modest amount of study (99-102). However, no work to date has been published on the aggregation of calcium oxalate in systems xvhere growth is a negligible factor. Since the particle density of crystalluria is too low for a significant collision rate due to Brownian motion, there is doubt as to whether aggregation could be important in urolithiasis (103). The experimental systems used to measure calcium oxalate growth and aggregation (100,102) also have particle densities insufficient for perikinetic aggregation. However, for super-micron particle suspensions the collision rate can 8 9

PAGE 99

9 be substantially increased by a liquid velocity gradient (104-106). The dependence of the aggregation of super-micron calcium oxalate upon a liquid velocity gradient has previously been ignored. Another interesting possibility is that the aggregation of calcium oxalate could be enhanced by the presence of macromolecules , since precipitated calcium oxalate in urine probably is extensively covered by macromolecules (73). Depending upon the extent of their coverage of the particle surface, proteins and other macromolecules can either accelerate aggregation or prevent it (78,107,108). We therefore chose to study the significance of various possible aggregation mechanisms for super-micron calcium oxalate as a preliminary investigation for the determination of the role of aggregation in stone formation. In this work a comparison is made of the coarsening calcium oxalate suspensions in saturated and supersaturated systems. High particle density and high electrolyte concentration are used in a nonturbulent apparatus to examine the possibility of perikinetic aggregation. A controlled fluid velocity gradient is employed to study aggregation in suspensions with an increased particulate collision rate. The tendency is examined of calcium oxalate to flocculate in the presence

PAGE 100

91 of polymeric macromolecules . We thus monitored particle size information on calcium oxalate in various potentially coagulating systems. The suspension coarsening referred to as growth and aggregation in previous studies may be almost entirely growth related phenomena. However, the most significant result of this study is that supermicron calcium oxalate suspensions can aggregate in a sufficiently large fluid velocity gradient or in the presence of particle bridging macromolecules. Materials and Methods Calcium oxalate monohydrate crystals were prepared as previously described in Chapter II. Water was deionized and glass distilled. Calcium oxalate suspensions were dispersed ul trasonically at a concentration of 3.47 g/L and then allowed to equilibrate for 24 hours before use. All chemicals were analytical reagent grade. Stock solutions were passed through a 0.22 ym filter to remove undissolved particles. Polyacrylamide and polyethylene oxide, high molecular weight polymeric flocculants, were obtained commercially. The solution pH's *Nonionic polyethylene oxide (Polyox coagulant, 5 million MW) , Union Carbide Corp., New York 10017. Nonionic and

PAGE 101

92 in these experiments as determined by glass electrode ranged from 5.1 to 6.9. Procedure for Determining the Effect of Supersaturation A 250 ml solution of supersaturated calcium oxalate containing 1.5 x 10 _1 M NaCl, 1 x 10~ 3 MCaCl 2 , and 2 x 10" M Na 9 C 9 0» was prepared by mixing stock solutions. A 250 ml saturated solution of calcium oxalate was pre_ 2 pared by ultrasonically dispersing 8.75 x 10 g of calcium oxalate crystals in 1.5 x 10 M NaCl, equilibrating for 12 hours, and then passing the solution through a 0.22 urn filter. After addition of suspension each solution was placed on a magnetic stirrer set for the same stirring speed. The volume and number of particles in size intervals through the range of 5 to 40 ym were determined for increasing stirring time using a Coulter Counter . Sedimentation Experimental Procedures The suspensions for sedimentation were prepared by adding 0.15 g of calcium oxalate to 1.25 ml of water in cationic polyacrilamides (Percol 351 and 455 respectively) , Allied Colloids, Inc., Ridgewood, New Jersey 07540, Anionic polyacrilamide (Separin MG 700) , Dow Chemical Co., Midland, Michigan 48640. *Coulter Counter Model TAII (with population accessory), Coulter Electronics, Inc., 590 West Twentieth Street, Hialeah. Florida 33010.

PAGE 102

9 3 in a test tube and suspending them ultrasonically . To these suspensions either 3.75 ml of 4 M KC1 or 3.75 ml of water was added. The suspensions were allowed to age 12 hours before use. Sedimentation fluids saturated in calcium oxalate were prepared by suspending 0.35 g/L calcium oxalate either in 3 M KC1 or in water, allowing it to equilibrate for 24 hours, and then passing the solution through 0.22 ym filters to remove undissolved particles. A sedimentation electrobalance was then calibrated before each run with the sedimentation fluid in place. Into the sedimentation fluid was stirred the corresponding 5 ml of suspension, and the cumulative sedimentation weight versus elapse time was recorded. The sedimentation in water of glass beads of a known sieve size range was studied as a control using the above procedure . The calculations used to obtain a plot of the cumulative weight percent versus the Stokes diameter from this data were as follows: R v. t > tne weight I of the particles that are greater than Stokes spherical diameter, d, ., equals the accumulated weight on the *Cahn Model RG Electrobalance with Model 2800 Particle Sedimentation accessory, Cahn, Ventron Instruments, Corp., 7500 Jefferson Street, Paramount, California 90723.

PAGE 103

95 Procedure for Determining the Effect of a Shear Gradient To 100 ml of 1.1 M KC1, 10 ml of 3.47 g/L calcium oxalate suspension was added and the resulting solution was equilibrated at 38°C for 1.5 hours. The solution was then resuspended by gentle shaking and 20 ml of it was placed into the sample cup of a vertical-shaft concentric cylinder viscometer. The viscometer had an outside diameter of 28 millimeters with an annular gap of 3 millimeters. This design has been shown (109) to provide laminar flow, and for an angular velocity of 12 revolutions per minute and provide a mean shear gradient at the annular gap of about 1.8 s . The viscometer and the sample stand of the Coulter Counter were kept at 38°C in a thermostated air box. An equilibrated suspension of 0.32 g/L calcium oxalate in 1 M KC1 was passed through a 0.22 ym filter and used as electrolyte for particle size analysis. At 15 minute stirring intervals the suspension was removed from the viscometer and resuspended by gentle shaking. A . 5 ml sample was then removed and the particle number and and volume fraction was analyzed for size intervals spanning the range 1.4 to 40 ym. *Brookf ield Model LV SynchroLectric Viscometer with Model U.L. adapter, Engineering Laboratories, Inc., Stoughton, Massachusetts 02072.

PAGE 104

96 Procedure for Determination of the Effect of Polymeric Flocculants Polymeric flocculants were dissolved in water with a magnetic stirrer. To 5 ml of 3.46 g/L calcium oxalate suspension 0.5 ml of polymer solution with the desired polymer concentration was added. The test tube containing this solution was then rocked gently 10 times and observed visually for f locculation . Light transmission was measured in an optical cuvet using a transmission spectrophotometer. The cuvet was rocked 10 times before measurement. The transmission was recorded at 15 second intervals for 90 seconds, and from these data an extrapolated value was obtained for the transmission at zero time. Transmissions measured immediately and at 24 hours after mixing were essentially the same. Light of wavelength 430 and 650 nm gave transmission curves that were qualitatively the same so only the data for 430 nm are reported here. The most concentrated flocculant solutions used gave transmission values within 2 % of water. Therefore, water was used as the standard for 100% transmission for all solutions. Turbidity was calculated from transmission using the following relation: T = -\ In (T) [12]

PAGE 105

97 where t equals turbidity (cm ) , L equals the optical path length through the solution (cm) , and T equals the fraction of the light transmitted. Aggregation of particles larger than A will cause a decrease in turbidity (110). Results and Discussion Coarsening of super-micron calcium oxalate monohydrate suspensions, reported by Robertson et al . (100) and Felix et al . (102) to occur in vitro for supersaturated solutions, has been thought to be due to "growth and aggregation." We were interested in how much of this coarsening could be due to aggregation. It is possible that both growth and aggregation contribute significantly; however, since these systems are supersaturated and have low particle density, the coarsening may be almost completely due to growth and Oswald ripening of the particles. To better distinguish aggregation from growth we added calcium oxalate suspensions to two solutions; one with the same supersaturation and salt concentration as Robertson's system, and another which was the same as the first except that calcium oxalate was only saturated. Figure 15 gives particle size versus percent total volume

PAGE 106

p

PAGE 107

99 o

PAGE 108

100 histograms for calcium oxalate after being added to these solutions and with zero or ninety minutes stirring. In the supersaturated solution the size at which the particle volume peaked increased from about 7 to 9 ym during stirring. However, in the saturated solution there was no detectable coarsening. The difference between the particle size distributions of calcium oxalate in the saturated and in the supersaturated solutions is consistent with a particle growth and ripening mechanism but not with a classical aggregation mechanism for the following version. Kith increasing supersaturation the rate of growth will increase (111) and the critical radius for Oswald ripening (the particle radius above which the particles will coarsen and below which they will dissolve) decreases (112). However, classical aggregation (113) would not be expected to increase in the supersaturated system since the ionic strength is not increased significantly and since the excess calcium activity would tend to increase, rather than decrease, the repulsive Stern potential (Chapter II). An aggregation mechanism that possibly could explain these results is one which relies upon liquid phase sintering (114) for binding. Thus at least for these experimental systems unless liquid

PAGE 109

101 phase sintering is significant the coarsening of the supersaturated solutions appears to be almost completely due to growth related phenomena. It was of interest to know if aggregation could have been prevented by the technique used in the above experiment. The low particle density and the concentration range of electrolyte required by the apparatus might have limited aggregation. To obtain particle size information while minimizing these possible limitations, we equilibrated a more concentrated calcium oxalate suspension and determined the resulting Stokes size distribution using the sedimentation electrobalance . This technique was chosen because it allows the testing of a complete sample of relatively dense suspension, it minimizes turbulent forces on the particles, and it allows measurement in a wide range of electrolyte concentrations. The technique, however, is limited to qualitative comparisons of aggregation; for without adequate knowledge of the aggregate shape, the friction coefficient opposing the particle sedimentation cannot be determined. Another limitation is that the density of an aggregate is less than a solid sphere; consequently, the Stokes equation will underestimate the diameter. This should not prevent a qualitative determination of

PAGE 110

102 aggregation, however, since it has been shown (115) that even if a large aggregate is 99% water the sedimentation rate should increase drastically over that of deaggregated particles. Figure 16 shows the particles ranged from 4 to 15 ym with a mean of about 10 urn. Considering the difference in analysis used for the two techniques, the agreement between this and the previous data is probably reasonable. The particle density during ageing of the suspension for this experiment, assuming a 10 urn particle o diameter, was about 1.3 x 10 particles per ml. If we assume rapid coagulation according to Smoluchowski (113) the half life for aggregation of the particles can be estimated from this density to be about one-half hour. If this estimate is reasonably accurate then rapid coagulation should result for a given Stern potential when the salt concentration in the solution is above a minimum critical value for the system. To see if aggregation would occur at a reasonably high salt concentration we repeated the above experiment in 3 M KC1. There was no detectable difference, as is shown in Fig. 16, between the particle size distribution in 3 M KC1 from that in water. This result indicates that either the criteria for detectable aggregation has still not been met, or that calcium oxalate may have resistance to aggregation.

PAGE 111

CD 03 i o3 O X o >, to |H O P. • MH (3 Ifl Jh Pi 03 +-> > ,Q 0) E W) to •H O •n if) to < O • p. +J u CO o ^ cni X i P +-> to to ,-H W tO CJ CO > 2 0) £ Td to cu o Mao 03 ^tp tO rd 4-1 U) 03 •H |2 CU H a3 4-> •H OXl +-) T3 c3 CT) t— I 3 Cu Pi 3 3 CO U to +->

PAGE 112

104 £ ->CD E o Q CD O o o o -C CL
PAGE 113

105 If calcium oxalate could aggregate in the classical manner then it is likely that either the salt concentration used in the previous experiments was not high enough or the collision rate was too low. Collisions due to Brownian motion have been shown (104-106) to decrease in frequency as particle size increases over the micron level while for the same sized particles the collisions due to a fluid velocity gradient are increasing in frequency. We therefore applied a uniform shear gradient across a suspension of calcium oxalate in 1 M KC1 and monitored its particle size distribution as a function of time with a Coulter Counter. In Fig. 17, it can be seen that the % total volume peaked at larger particle sizes as shear time increased. Particle population data showed that this increase was due to a decrease in the number of particles less than 5 ym and a corresponding increase in the number of particles in the 5 to 10 urn range. These results indicate (since growth related phenomena should be minimized by the lack of supersaturation) that given an adequate collision rate super-micron calcium oxalate can aggregate. We next investigated whether the aggregation of super-micron calcium oxalate can be expedited by the presence of large macromolecules . Large macromolecules

PAGE 114

u

PAGE 115

107 o

PAGE 116

108 may either combine rapidly many calcium oxalate particles by particle-particle bridging (usually referred to as f locculation) or they may make calcium oxalate surface more resistant to f locculation . To test these alternatives, we added to calcium oxalate suspensions high molecular weight synthetic polymers which ha\ r e been found (116) to effectively flocculate other systems. We then monitored the suspensions visually and by light scattering for f locculation . Figure 18 gives the weight fraction solids of macromolecule added versus the resulting turbidities. No detectable flocculation of calcium oxalate was found upon the addition of polyethylene oxide; however, nonionic, cationic, and anionic polyachrylimides caused a minimum in the turbidity curve that corresponded to visible flocculation of the suspension. The increase in turbidity at macromolecule concentrations above those that caused flocculation indicates "stabilization" of the suspension at high adsorption density (117,118). The maximum in flocculation as a function of concentration observed in this study is consistent with the flocculation behavior of other systems (72,78,107,108) and is thought to be indicative of a particle bridging aggregation mechanism.

PAGE 117

M

PAGE 118

110 1

PAGE 119

Ill Con clus ions Aggregation due to Brownian collisions was not detectable by sedimentation balance even at high particulate and salt concentrations. Aggregation of supermicron calcium oxalate was detectable by Coulter Counter when the particle collision rate was enhanced by a controlled velocity gradient. Calcium oxalate can be flocculated in the presence of macromolecules , presumably by a particle bridging mechanism.

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CHAPTER V THE ELECTROKINETIC PROPERTIES OF CALCIUM OXALATE MONOHYDRATE IN NATURAL AND ARTIFICIAL URINES Introduction Normal urine is believed by many to have constituents in it that adsorb on the surfaces of calcium oxalate crystals present in urine. The adsorption of certain species is somehow critical to the prevention of stone formation or growth. Possible processes affected are: precipitation by nucleation and growth (119-121) ; growth of existing crystals (87,122,123); and coarsening of particles by combinations of aggregation and growth (99102). The adsorbed species may inhibit some of the above processes. Inhibition has been studied by numerous investigators. Citrate, pyrophosphate, and magnesium have been shown (100,122,124) to inhibit calcium oxalate's crystal growth. The mucopolysaccharides heparin and chondroitin sulfate have been shown (124) to inhibit suspension coarsening. A previously unknown urinary peptide was postulated (125) as an inhibitor of calcium oxalate growth but this was later refuted (126). The inhibition of crystallization of calcium oxalate by urine has been 112

PAGE 121

115 shown (127) to be explainable by interactions between known urinary components. Further evidence has been given (128) for the importance of urinary peptides as calcium oxalate growth inhibitors; however, it has also been shown (129) that nucleation and growth inhibition for calcium oxalate by urine can be accounted for by the small ions and mucopolysaccharides present. The adsorption of citrate and pyrophosphate (5) as well as some mucopolysaccharides and proteins (73) on the calcium oxalate surface has been shown to occur in simple solutions. Since the amount of adsorbed molecule necessary for inhibition of calcium oxalate's growth is often much less than a monolayer, it has been suggested (98) that these molecules adsorb to specific growth sites. In Chapters II and III, electrokinetic experiments in simple solutions indicated that many of the multivalent small ions in urine as well as proteins and mucopolysaccharides can adsorb on specific surface sites . The adsorption that occurs in simple solutions does not necessarily occur the same way in urine because of competitive processes (130). Artificial urine-like solutions of controlled composition have been used to test solubility data of calcium oxalate in normal and

PAGE 122

114 stone formers' urines (131); and they also have been used to determine if unknown substances were needed to explain inhibition by urine of calcification (127) and crystallization (119,129). We therefore have decided to study the microelectrophoretic properties of calcium oxalate particles in natural and artificial urines to better understand urine's influence upon the calcium oxalate surface . In this chapter, the mobility of calcium oxalate in urine and urine-like solutions was investigated. The mobilities of calcium oxalate in some natural urines and in artificial solutions of known composition are compared. The effect of artificial solutions containing small ions is analyzed using ion equilibrium information. The effect of the addition of mucopolysaccharides and of proteins to these solutions is also investigated. The possibility of the deaggregation of calcium oxalate suspensions by surface active ions added to urine-like solutions is also investigated. Perhaps the most significant finding of this study is that a combination of small ions and mucopolysaccharides normally present in urine can, by specific adsorption, give calcium oxalate mobilities comparable to those observed in real urine. Also, surface active species appear to be able to deaggregate calcium oxalate in urine-like solutions.

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115 Materials and Methods Water was deionized and then glass distilled. Chondroitin sulfate, sodium heparin, lysozyme muramidase (3x crystallized), and serum albumin bovine (4x crystallized) were obtained from commercial sources. All other chemicals were analytical reagent grade. Stock solutions were filtered through a 0.22 ym filter to remove any undissolved particles. The pH was determined by a glass electrode. Whewellite (calcium oxalate monohydrate) crystals were prepared as described previously (Chapter II) . Electrophoretic measurements were made using a commercial instrument with its sample cell in a thermostated air box (Chapter II). The pH was measured after electrophoresis. Slurries of calcium oxalate in water with a solids content of 0.87 g per 250 ml were suspended ultrasonically . The slurry was equilibrated for at least 12 hours before use. Artificial urine was prepared by mixing stock solutions. The pH was adjusted with HC1 or NaOH just prior to final dilution. Before electrophoresis 10 ml of calcium oxalate slurry was added to 100 ml of solution (for a final solids content 0.32 g/L) , and equilibrated at 38°C for 4 hours. Twentyfour hour urine samples from seven recurrent calcium

PAGE 124

116 oxalate stone formers and five non-calculous control subjects were obtained from the Clinical Research Center. Methods of chemical analysis, treatment of subjects, urine collection and storage procedures were as reported (132) previously. Fresh urine samples were collected from three subjects, who did not have history of stone disease, during the first void of the morning and were used immediately. Real urines were treated the same as the artificial solutions with the following exceptions. When frozen, real urine was kept at about -20°C and thawed in a constant temperature shaker at 38°C for up to 2 hours. If a precipitate persisted in the thawed urine it was decanted before a calcium oxalate slurry was added. As estimated by the electrophoresis microscope this resulted in particulate contamination of 1 5 ? of the final slurry concentration. The real urines were equilibrated for 1 hour after slurry addition. The specific conductance of suspensions was measured with the electrophoretic apparatus in a cell with known cell constant. The computer programs for calculating ion equilibria and *Clinical Research Center, Veterans Administration Hospital, Gainesville, Florida.

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117 electrical double layer parameters have been described (Chapter II, 40) in previous publications. Particle size distributions were determined using a Coulter Counter with the sample stand in a thermostated air box. To 500 ml of urine ion solution with the desired additive and pH, 50 ml of 3.466 g/L calcium oxalate slurry were added. The resulting suspensions were equilibrated for in a thermostated air box for 2 hours. After resuspension about 400 ml was passed through a 0.22 ym filter. The filtrate was then used as electrolyte for calibration and particle size analysis. Of the remaining slurry, 0.5 ml was placed into about 200 ml of filtrate in the counting vessel. The number of and total volume of particles for given size intervals in about 2 ml of sample that passed through the 100 ym aperture of the apparatus was determined. The remaining unfiltered slurry was used as needed for electrophoretic mobility measurement . Results and Discussion Electrophoretic Mobilities in Urine Calcium oxalate crystals in a series of urines were studied to see how the urine would modify the mobility from that found in plain water. Many of the molecular

PAGE 126

118 species in urine have been shown to influence the calcium oxalate surface in simple solutions (Chapter II). Species in urine might either adsorb by simple electrostatic double layer forces or by chemical bonds (specific adsorption). Calcium or oxalate ions in solution could be bound in significant amounts by other small ions or by macromolecules and could influence the magnitude and sign of the surface potential of calcium oxalate (Chapter I); by this means, they could affect the adsorption parameters (95). It is also possible that the ionic strength of urine may be important. Analysis of the electrophoretic behavior of calcium oxalate in urine could eliminate, at least in particular instances, the possible occurrence of some of these mechanisms. Electrophoretic mobilities of calcium oxalate added to urine samples from 15 subjects were measured. Samples of a 24 hour urine collection from five normals and seven stone formers were studied to see if calcium oxalate's mobilities in urines from the two groups were chronically different. The chemical analyses of these urines are given in Table VI. The mobilities in fresh urines from three other normal subjects were also studied. Since the 24 hour urines had been stored frozen, we also froze the fresh samples for up to seven months and

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119 Table VI Chemical Analysis of 24 Hour Urine Samples a (lO'5 M/L) (xlO" 2 ) Sample „ xt ir so -i 2 " HC ft H q°7 2 " hc ?°a 2 " Number Ca Mg P Na K 4 6 5 7 2_4 — 1 1.02 0.71 4.10 1.09 0.28 3.28 0.33 8.16 2 1.14 2.174 12.89 1.59 0.60 9.76 0.56 0.31 3 4.56 3.294 14.36 3.52 0.57 7.87 1.42 0.30 4 2.97 1.907 13.88 1.36 0.86 9.87 0.23 0.21 5 3.35 2.524 14.71 1.26 0.83 11.36 1.68 0.27 6 4.68 2.75 20.66 1.99 0.78 14.29 1.37 0.31 7 2.58 1.67 15.33 1.44 0.09 10.55 1.41 0.36 8 1.74 3.33 19.88 2.58 1.08 20.63 1.73 0.23 9 1.53 3.79 21.37 3.56 1.48 14.43 2.65 0.34 10 1.42 3.40 18.71 4.83 1.43 21.19 1.74 0.31 11 2.05 1.78 9.86 4.20 0.43 11.50 1.48 0.28 12 4.27 5.14 34.06 7.40 1.97 26.00 4.92 0.36 a Samples numbered 1 7 were from stone formers, and samples numbered 8 12 were from normals.

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120 repeated the mobility experiments to see if a major difference existed between the mobilities when the urines were fresh and after they were thawed. The differences in seven trials were found to vary from essentially zero to a maximum of only 0.32 with an average variation of 0.15. It was found that the mobility of all urines for which the mobility could be measured was similar (the combination of high solution conductivity and low mobility prevented the measurement of the mobility in two of the normal 24 hour samples) . Negative values between -0.67 and -1.47 mobility units were found, which are of opposite sign, from the +1.7 mobility units (um s /Volt cm ) in distilled water. For the 24 hour urine of seven stone formers, the mobilities ranged from -0.67 to -1.47 with a mean of -1.12. The 24 hour urine samples from the three normals had mobilities from -1.09 to -1.32 with a mean of -1.24. The mobilities in fresh samples from three normals ranged from -0.91 to -1.39 with a mean of -1.13. The variations in these means, therefore, are small. Some inferences on how the calcium oxalate is affected by urine are suggested by these results. Since all of the urines reversed the sign of calcium oxalate's

PAGE 129

121 mobility, it is apparent that urine of both normal and stone forming people can strongly modify the calcium oxalate surface. Electrostatic adsorption alone is eliminated as a possibility since it could only bring the mobility to zero, but cannot reverse the sign. Ionic strength, at least for the measurable urines, was not high enough to negate the other surface effects by compression of the double layer and bringing the mobility to zero. Thus, the results of these experiments indicate that one or more species in urine is modifying the calcium oxalate surface by either specific adsorption or by increasing the solution oxalate ion concentration. Mobility as Affected by the Small Molecules in Urine We next considered the question as to which molecules in urine influence the observed mobility variations. Small ions in the urine (as those listed in Table VI) and macromolecules in the urine could both cause the mobility sign reversal either alone or together. We measured the mobility of calcium oxalate in an artificial urine solution consisting of the small ions present in the largest concentrations in urine to see if combinations of these ions modify the mobility. The concentrations of chemicals used are given in Table VII. We will henceforth refer

PAGE 130

122 Table VII Artificial Urine Ion Solution Composition Concentration Chemical Compound

PAGE 131

123 to this as the urine ion solution. The composition of the urine ion solution was selected to best match the average concentrations of each species in normals' urine, as determined by various studies (133). Figure 19 (top) gives the mobilities of calcium oxalate in mixtures of urine ion solution and water in different proportions. Mobilities in urine ion solution concentrations of 651 and higher could not be determined because of experimental difficulties associated with low mobility and high solution conductivity. Increasing concentrations of the urine ion solution reversed the sign of the mobility at concentrations as low as 10%. This indicates that there is a significant modification of the calcium oxalate surface by the smaller ions present in urine . The controlled composition and known solution chemistry (40) of the urine ion solution could be utilized to determine if the sign reversal is caused by increased oxalate ion activity or by specific adsorption. In Fig. 19 (bottom), the calculated activities of the species with valence of two or greater are given for calcium oxalate in urine ion solutions of increasing concentration. It can be seen that as the concentration increased, the activity of all ionic species increased

PAGE 132

X u u •H -H +-> c 0> O fn -H O o rt u > a> .h iH +-> o Uh +-> o >> D u u o o £ •H aj "3 6 U 0\

PAGE 133

125 1 +

PAGE 134

126 except the activity of the oxalate ion, which decreased. Thus, the possibility that increased oxalate ion activity caused the mobility to reverse sign can be eliminated. This strongly indicates that the small ions in urine modify the calcium oxalate surface by specific adsorption. This led to asking which of the ionic species in the urine ion solution caused the mobility sign reversal. It could be one, or a combination of some, or all of the negative species having a valence of two or higher. It could also be caused almost entirely by a strongly adsorbing species (Chapter II) like trivalent citrate. By varying the pH of the urine ion solution, we could (as was indicated by equilibrium calculations) selectively vary the activities of the ionic species present. We measured the mobilities of calcium oxalate in 501 urine ion solution at pH values from 4 to 7. Figure 20 (top) shows that as the pH decreased the mobility decreased until at pH 5 the sign changed from negative to positive. Figure 20 (bottom) shows that there was only a small change in the activities of the positive and negative multivalent ions except for trivalent citrate which with increasing pH had an increased activity of almost two orders of magnitude. These results indicate that most of the effect of the urine ion solution upon the mobility

PAGE 135

^ X

PAGE 136

128 MmqoiAj y^jAjpv &°1

PAGE 137

129 of calcium oxalate was caused by trivalent citrate. To further test this dependence we measured the mobility of calcium oxalate in solutions with 10 M trisodium citrate added to 501 urine ion solution, for pH's from 4 through 7. The resulting mobilities varied from zero at pH 4 to -2.5 at pH 8. As in a previous experiment, relatively small changes were calculated for the activities of the positive and negative multivalent ions except for trivalent citrate which increased about two orders of magnitude with increasing pH. Figure 21 shows the combined mobility data of these two experiments plotted versus the calculated trivalent citrate activity. On the same plot are similarly obtained data that have been given previously (Chapter II) for calcium oxalate at various pH values with only sodium citrate added to water. It can be seen in Fig. 21 that the data in simple and urine-like solutions coincide. The dependence of mobility on trivalent citrate activity in urine-like solutions is therefore shown to be strong. The Influence of Natural Macromolecules Upon Mobility in Urine-like Solution The mobility of calcium oxalate in urine ion solutions can now be compared to that of real urine to see if constituents other than the simple ions in urine are

PAGE 138

4-> T3 R cl

PAGE 139

131 I ro O if) X CO O o < o ( luq jjOA/.s urn) A4.i|iqoiAl 0!49JoqdoJ4oa|3

PAGE 140

132 needed to explain the magnitudes of the mobility in real urine. Figure 22 shows the mobilities of calcium oxalate in real urines and in the urine ion solution plotted versus the specific conductances. The points that are connected by lines show mobility in solutions obtained by dilution with water. The specific conductance depends upon the charge, mobility, and concentration of the ionic species (65) and provides a qualitative means to compare the relative concentrations of the urines. It can be seen that the mobilities of calcium oxalate in real urine differ in several ways from that in the urine ion solution. The mobilities in the real urines tended to have higher negative values throughout the range of dilutions. The mobilities in real urine tended to become more rapidly negative when small amounts of solution were mixed with water. Some of these differences between the urine and the urine ion solutions may have been partially due to differing ionic strength and trivalent citrate activity; however, the differences in mobility between the real urines and the urine ion solution were consistent enough to suggest that besides the molecular species represented in the urine ion solution there might be other substances acting on the calcium oxalate surface in the real urines other than the simple

PAGE 141

u o CD O E W
PAGE 142

134
PAGE 143

135 For the above reason, we studied how natural macromolecules interact with the calcium oxalate surface in urine-like solutions. In aqueous solutions where no other electrolytes were intentionally added, we had found previously that certain macromolecules adsorbed strongly. However, there is the possibility that such adsorption could be inhibited by the presence of other electrolytes. To see how natural macromolecules adsorb in urine-like solutions, we measured the mobility of calcium oxalate in 50a urine ion solutions with 0.1 g/L of one of the following four macromolecules: the positive and negative proteins, lysozyme and serum albumin respectively, and the two mucopolysaccharides, sodium heparin and chrondroitin sulfate. In addition to the macromolecules, we studied the adsorption of sodium pyrophosphate since it has been shown to adsorb to calcium oxalate (95, Chapter II) and in sufficient concentrations give it a high negative mobility (Chapter II). We measured the mobilities of calcium oxalate in solutions with 10" 3 M pyrophosphate in 20°o urine ion solution since 50% solution caused precipitation to occur. All of these additions made the mobility somewhat more negative as is shown in Table VIII. These results indicate that pyrophosphate and natural macromolecules (especially heparin)

PAGE 144

136 Table VIII Electrophoretic Mobilities of Calcium Oxalate at 37°C in Urine Ion Solution with Other Additions Solution 50% Urine Ion Solution (UIS) 50% UIS + 10" 1 g/L Sodium Heparin 50% UIS + 10" 1 g/L Chrondoitin Sulfate 50$ UIS + 10 _1 g/L Serum Albumin 50% UIS + 10" 1 g/L Lysozyme 20% UIS 20% UIS + 10"5 M Na 4 P 2 ? El (ym

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137 can significantly effect the mobility in urine-like solutions. If the mucopolysaccharides can specifically adsorb to the calcium oxalate surface in urine-like solutions as is indicated above, then since they normally remain highly ionized in the pH range from 4 to 8 , their influence upon mobility should remain relatively constant with decreasing pH while the effect upon mobility of the urine ion solution decreases. Figure 23 shows that when 0.1 g/L of sodium heparin or chrondroitin sulfate are added in 50% artificial urine at pH values from 4 through 8 the mobility of calcium oxalate remained at a fairly constant negative value. This further supports the hypothesis that these mucopolysaccharides can specifically adsorb in urine-like solutions, since the mobility in this range in 5 % urine ion solution without the mucopolysaccharides present would ordinarily reverse the sign. If we conclude that some small and large molecules adsorb strongly onto calcium oxalate in urine-like solutions, then how is adsorption of these substances affected by the urine-like electrolytes? If their adsorption is as prediced by Nernst-GouyStern double layer theory [as was found for the case in simple solutions (Chapter II)], the mobility of calcium oxalate in the

PAGE 146

id TO M C u +H

PAGE 147

139 CO CD LO Q. Sf __ q — cJ ro ( uuq [\o/\/ s urn) A*!i!qo|/\] 0U9ioqdojp9|3

PAGE 148

140 presence of these strongly adsorbing molecules should be affected by the addition of urine electrolyte through competition for surface sites and by increased ionic strength. The results given in Fig. 24 show that for increasing concentration of urine ion solution the 2 mobility of calcium oxalate in 10 M sodium citrate decreased gradually from -2.67 at 1% concentration to -1.41 at full concentration. Double layer calculations, using a theoretical model and parameters that were discussed previously (Chapter II), indicate that when the increased competition for surface sites and the increased ionic strength are accounted for, the change in mobility due to the increased urine ion solution concentrations is as would be expected. The effect upon the mobility of calcium oxalate, with 0.1 g/L of either mucopolysaccharide present with increasing concentrations of urine ion -2 solution was similar to that obtained with 10 M citrate present. Although sufficient thermodynamic information on the mucopolysaccharides does not exist to allow their analysis by double layer theory, the similarity of the behavior of mobility in their presence to that with citrate present when urine electrolyte was added suggests that both mechanisms of adsorption are similar .

PAGE 149

c u m 4-1 o PI o • H 0) u c o u 4-1 o o +J u TO 4-1 C o 4-1

PAGE 150

142 O ^ C r" °= x |e| c E ^o ° 01 ^ \ 2E v. _ O _ odd t>D< C\J — O •f + o c o -— O 00 c _o c o o Ll. c o 'a o — CJ ( uuo4|OA/,s urn) Aijjjqoi^ 0j|9J0Ljdojp9|3

PAGE 151

143 The specific adsorption that can occur in urinelike solutions raises the question as to whether the addition of these surface active substances to urine ion solutions (in Table VII) in concentrations similar to those found in real urine could produce mobilities comparable to those produced in real urine. Or alternatively is the addition of still other substances needed to accomplish this? To answer this question we measured mobilities in solutions with sodium heparin, chrondroitin sulfate, and pyrophosphate added to the urine ion solution in the approximate concentrations that they are normally found in real urine. The mobility of calcium oxalate in this solution was compared to its mobility in two real urines, after each of a series of dilutions. One real urine selected had a high mobility at full concentration. The other urine had a relatively low mobility at full concentration (more similar to that found for the urine ion solution) . There is approximately 4 x 10"" g/L mucopolysaccharide in normal urine; about 60% of this is chrondroitin sulfate, 25% nonsulfated chrondroitin, and 8% heparin (134,135). Thus, 2.4 x 10" 2 g/L chrondroitin sulfate and 3.2 x 10 g/L sodium heparin were added to the urine ion solution. We also added 10" 5 M/L sodium pyrophosphate (136). The

PAGE 152

144 resulting mobilities are given in Fig. 29. The mobilities in the urine ion solution (Fig. 19) are replotted for comparison. Figure 29 shows that the magnitude of the mobility in the urine ion solution with the additives was large enough to be measurable at full concentration. It was more than adequate to account for the magnitude of negative mobility measured in the real urines. Like the real urines, the urine ion solution with the mucopolysaccharides and pyrophosphate reverses the sign at less than 1% of full concentration. Thus, the behavior of calcium oxalate's mobility in the urine ion solution with the mucopolysaccharides and pyrophosphate added was quite similar to that found in the real urines. The Influence of Adsorption Upon the Deaggregation of Calcium Oxalate in Urine-like Solution Since calcium oxalate can have measurable mobilities in urine, can adsorption of these substances influence the size of calcium oxalate aggregates in urine? The magnitudes of the mobilities of calcium oxalate measured in urine may indicate that the Stern potential, and consequently the electrostatic repulsive energy between particles, is high enough to cause deaggregation of particles in urine [as had been reported in the literature (137) for simple solutions]. On the other hand, since

PAGE 153

ft M a c c 03 +J nj o Sm O +-> u Mh o o +-> u
PAGE 154

146 1

PAGE 155

147 the electrostatic repulsive energy is inversely related to ionic strength, deaggregation in urine-like solutions may not be possible. To see if we could detect deaggregation in urine-like solutions at full strength, we added strongly adsorbing natural substances, in quantities that gave relatively high negative mobilities. We let these solutions equilibrate and then counted the volume and number of particles for each of a series of size ranges and compared them to that measured in the urine ion solution without other additions. Figure 26 shows the resulting histograms of percent of total volume plotted against the mean channel size of particles. It can be seen that the volume histogram for calcium oxalate in the urine ion solution peaked at about 4.5 um. This histogram was essentially the same as that, with similar experimental conditions, for calcium oxalate in . 5 M sodium chloride. It therefore does not indicate that there was deaggregation caused by the urine ion solution alone. However, with addition of chrondroitin sulfate or sodium citrate the histograms shifted their peak to about 3.5 um. With heparin present the histogram has shifted further to peak at less than 3 um. To determine if this shift was due to deaggregation or to some other phenomena (as precipitation), we compared these data to the

PAGE 156

bO 6 •H O T3 -r-1 O -M •h rt rC

PAGE 157

149 — O)

PAGE 158

150 total number of particles counted in each channel. In all cases as the peak shifted to smaller particle sizes the number of particles in each channel less than 4 ym increased while the number of particles in each channel between 4 and 9 ym decreased. This indicates that the shift in the volume histograms to smaller particle sizes was due to the breakup of particles that would have been in the 4 to 9 ym channels. These results strongly indicate that calcium oxalate aggregates can be deaggregated by sufficient concentrations of some surface active substances in urine-like solutions. To see how the deaggregation depends upon concentration of repeptizer and the mobility, we added chrondroitin sulfate and sodium heparin to calcium oxalate in 501 concentration urine ion solution and measured the mobility and particle size histograms for each suspension. If the adsorption on all the particle surfaces is homogeneous, and if deaggregation is occurring at some minimum coverage or Stern potential, it would be expected that total aggregation would occur after some minimum concentration of the repeptizer. On the other hand, if the adsorption was heterogeneous, or if the aggregates were held together by varying forces, then the deaggregation would be expected to occur gradually with

PAGE 159

151 concentration. Figure 27 shows that the percent of total volume of particles with sizes of 4 ym and less increased gradually with increased concentration of repeptizer. Thus, the data favor a mechanism by which the amount of deaggregation is a function of the concentration of the repeptizer added. Conclus ions Calcium oxalate can have finite electrophoretic mobilities in urine. Thus, it could be possible that electrostatic repulsive forces are a significant factor in preventing the aggregation of calcium oxalate in urine. The trivalent citrate species can have a significant effect upon mobility by specifically adsorbing onto calcium oxalate's surface in urine-like solutions. The electrophoretic behavior of calcium oxalate in urine, however, does not appear to be explainable by the small ions alone. Mucopolysaccharides, especially heparin, had the greatest effect of the macromolecules tested (at pH 6.5) upon the mobility of calcium oxalate in urine-like solution. The electrophoretic mobility behavior of calcium oxalate in an artificial solution consisting of small ions and mucopolysaccharides that are present in urine was much like that observed for calcium oxalate in

PAGE 160

^ m J2 p "=* s c c

PAGE 161

153 CO

PAGE 162

154 real urines. Thus, within the sensitivity of these measurements no unknown substances are needed to explain calcium oxalate's mobility in the real urines studied. Particle size data indicated that it is possible for the addition of surface active substances like citiate and mucopolysaccharides to decrease the size of aggregates of calcium oxalate in urine-like solutions.

PAGE 163

CHAPTER VI THE NERNST-GOUYSTERN MODEL: ITS VALIDITY AND LIMITATIONS FOR THE CALCIUM OXALATE MONOHYDRATE DOUBLE LAYER Introduction The Nernst-Gouy-Stern (NGS) model (1) is the foundation upon which modern double layer theory has developed. It contains the minimum necessary theoretical elements from which a consistent picture of the electrical double layer can be given by the classical theory. Yet obtaining a basic understanding of this fundamental model has been limited from the start (138) by experimental systems which contain proposed and empirically determined anomalies to the NGS model. The first systematic experimental tests of the NGS model utilized the reversible electrode materials mercury and silver iodide. For the mercury system it soon became apparent (5) that in order for the experimental data to be consistent with the model the Stern layer had to be broken into the inner and outer Helmholtz planes (NGSG model). However, since no explicit relationship between the potentials at the outer and inner Helmholtz planes was apparent (5,138), experimental tests of the double layer model had to be 155

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156 restricted mainly to cases where there was an absence of specific adsorption. The behavior of the capacities of silver iodide and mercury as a function of salt concentration, however, necessitated the postulation of specific adsorption of monovalent anions (5,6). The apparent variation of specific adsorption potential with surface charge in the mercury system (5) led to the incorporation of discreteness-of -charge effects into the model (12), but often the increase in parameters this necessitated could not be compensated for with new or more accurate experimental information. Thus, comparison of the fit of experimental data to the NGSG theory with and without the discreteness -of -charge addition could often be ambiguous (139). Uncertainty about the structure of water at the interface and thus the location of the liquid shear plane discouraged the use of electrokinetic experiments as a test for the double layer models; consequently, it was over 30 years before work was published (64) showing that electrokinetic data on silver iodine that had been in the literature since the 1940 ' s were consistent with the NGSG double layer model. This result combined with coagulation and viscosity data was shown to strongly indicate that the long postulated structured interfacial water layer was probably nonexistent for silver iodide.

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157 The double layer properties of oxide materials have also been found inconsistent with the NGSG mode]. It was first thought (6,140) that this inconsistency was due to a variation as a function of electrolyte concentration of the slip plane thickness. Further study (19) revealed that while the effect of divalent ion adsorption upon oxides could be accounted for by the NGSG model the effect of monovalent species could not, and by exhaustive variation of parameters (22) it was determined that the only way the theory could explain these effects was to abandon the Nernst equation. A model postulating a gel layer with ion exchange was developed (26,141) to replace the Nernst equation, and with this adjustment to the model electrokinetic and potentiometric titration data for a number of oxides were found to be explainable by the resulting model (27). A subsequent attempt was made (142) to explain the electrophoretic properties of kaolin clay by considering the unknown edge surface as a mixture of oxides. However, probably due to the lack of understanding of the clay surface's asymmetrical charge distribution and also perhaps the presence of a gel layer, the experimental mobility data could not be reconciled with the NGSG model. The electrophoretic behavior of calcium oxalate monohydrate has been shown in Chapter II to fit the basic

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158 NGS theory without modification. This is probably due to the apparent absence in calcium oxalate of characteristics that would conflict with the assumptions of the model; and the apparent retaining by ions, as has been noted in other systems (18,36,142), of a hydration sphere after adsorption causes the inner and outer Helmholtz planes to approximately coincide. Another advantage is the relatively well established solution chemistry of many complex calcium oxalate systems (Chapter II). Investigation of the calcium oxalate double layer properties with respect to those predicted by the NGS model could therefore give insight into the basic concepts of double layer theory. Discrepancies between experimental results and those predicted by the NGS model could uncover fundamental flaws in the model. Further, since calcium oxalate is the major mineral constituent of kidney stones in the United States (38) , better understanding of calcium oxalate's electrostatic and adsorption properties, especially in complex systems, could be valuable in understanding the genesis of renal stones . In this chapter we attempt to improve the understanding of the components of the NGS model by testing the model's prediction of electrokinetic behavior of

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159 calcium oxalate in solutions with multiple adsorbing species and by testing predictions of adsorption and electrophoretic behavior simultaneously. Adsorption parameters for two calcium oxalate systems obtained by the NGS analysis are compared to those obtained from a less elaborate Langmuir model. To do these analyses NGS model calculations are preformed using ion equilibria information for the various systems, and the results are compared to electrophoretic and adsorption data obtained in previous studies. A significant result of this study is that with appropriate selection of two system constants (the maximum number of adsorption sites and the specific adsorption potential), both electrophoretic and adsorption data could be made consistent with the basic NGS double layer model. Results and Discussion The NGS Mo del for Calcium Oxalate in Solutions with Many Ads orbing Species' The Nernst-Gouy-Stern (NGS) model of the electrical double layer has been shown in Chapter II to adequately describe the electrophoretic behavior of calcium oxalate in solutions with the addition of any one of at least ten soluble salts. A critical question regarding the limits

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160 of the applicability of this model is whether it can predict the electrophoretic behavior of calcium oxalate in solutions with many salts present simultaneously. Electrophoretic measurements on calcium oxalate suspensions have been made (Chapter II) in various concentrations of a solution containing eight soluble salts. The concentrations of the salts present in this multiple ion solution are reprinted for convenience in Table IX. This system was studied because of its relevance to renal lithiasis. Sufficient thermodynamic data for this system are available (40) to apply the NGS model. We thus compared theoretical Stern potentials (calculated using the NGS model) to experimental Stern potentials (calculated from electrophoretic mobility data) in the same way that we have described in Chapter II for simpler solutions . The specific adsorption potential, • , used for each ionic species was that which gave the best fit between the experimental and theoretical curves for the simple solutions in the earlier study. Table X gives cj>, for the different ionic species and some sample activities. The calculated Stern potentials plotted versus the multiple ion solution concentrations (ratio of the original multiple ion solution to the final solution

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161 Table IX Multiple Ion Solution Composition* 1 _. . , Concentration ph^m-iral Concentration Chemical 7 Lnemicai _ ? Compound 10 M/L Na 2 H 2 P0 4

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16: o s s ex lo O ^H tfl c

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163 after dilution with water) are given in Fig. 28. For concentrations up to 101 the experimental and theoretical Stern potentials agree within 2 mV, but for the higher concentrations (from 101 to 50 ? o), the deviations are somewhat greater, up to 6 mV. These results show that the NGS model accurately describes the Stern potentials of calcium oxalate in dilute solutions with many adsorbing species present, but as the concentration of the solution increases the model becomes less valid. The increase in deviation between the experimental and theoretical Stern potentials as the concentration of the multiple ion solution is increased was next considered. Several possible reasons for this apparent discrepancy can be offered. One possibility is that the ion equilibrium calculations are not adequately accounting for new multivalent complexes that are formed in the complicated multiple ion solution. Another possibility is that we have not arrived at the proper values of Nj, and (J>. (the Stern equation parameters) for each of the ions present. We have assumed, for example, that N is the same for all species when in fact this may not be the case. A third possibility is that the Stern parameters are affected by the total ionic strengths of the system. This might be expected if the indifferent ions somehow compete for adsorption sites.

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rt

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165 O o CO c o Q. O a c o Q o (Auj) |D|iue|Od uj8|S

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166 To study if ionic strength was a factor in giving the described discrepancy, we carried out experiments which alter the equilibrium conditions without substantially affecting the ionic strength. This is possible by changing the pH. The experimental and theoretical Stern potentials for 5 0% concentration of the multiple ion solution for pH's from 4 through 7 are given in Fig. 29. This pH change has been shown in Chapter I to provide about a 20 mV change in experimental Stern potential with a very small (relative to the previous experiment) change in ionic strength. The results given in Fig. 29 show that there was agreement within 2 mV between the experimental and theoretical Stern potentials for pH values of 5 and below, but the two curves differed up to 7 mV at the higher pH's. This analysis shows the disagreement between experiment and theory is not due to ionic strength. The concentration of citrate ions in the multiple ion solutions is what changes mainly with pH and this accounts for the variations in mobility. To test whether the citrate ion parameters of N. and A. are wrong (to explain the discrepancy), we ran another set of experiments where additional citrate is added. With the _ o addition of 10 M sodium citrate, the results shown in

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X m

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168 X CL o

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169 the bottom of Fig. 18 were found. It can be seen that through the range of multiple ion solution concentration with the excess of trisodium citrate present the experimental and theoretical Stern potentials agreed within about 2 mV. Thus, the resulting Stern potentials for calcium oxalate in these high citrate solutions were accurately predicted by the NGS model and cannot account for the previous discrepancy. As a result of the above experiments, we are left with the final alternative, namely that N. and <)>.. are both different for every ionic species. This possibility is examined in the next paragraphs. Analysis of the Stern Equation The above results suggest that the NGS model as applied may be inaccurately describing the competition between the adsorbing molecules if N, is assumed to be the same for all species. According to the form of the Stern equation employed, the charge density in the Stern layer is given by (N, z . e l — n V ", *? ) • [51 1 + HTrT ex P ET / J where N. is the number of adsorption sites per square centimeter of surface, N is Avogadro's number, M is the

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170 molecular weight of the solvent, k, T, and e are the Boltzmann constant, absolute temperature, and electronic charge, respectively, n. and z. are the number of ions per cubic centimeter and the valence (including sign) of the specifically adsorbing species j respectively, and . is the specific adsorption potential of species j. The adsorption density is J J j j where a • is the charge in the Stern layer due to species ^ J j, and r. is the adsorption density of species j. The determination of adsorption densities as a function of solution concentrations provides an independent set of data that allows closer analysis of the Stern equation. Solution depletion adsorption data for calcium oxalate exist (95) for two of the salts whose effects upon the electrophoretic properties were included in our study — sodium citrate and sodium pyrophosphate. We thus compared the experimental adsorption densities for the calcium citrate system with the theoretical adsorption densities calculated for the same experimental conditions. The results, given in Fig. 30, show that the calculated adsorption densities from the electrokinetic salts and

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(DHM C h«U O rt p 2: -h 00 +-> CD P O P > U P O P P m (/) .H P H GO hihtIh G o3 to o3 oj • H CD 0) C M +-> T3 H X V) P 0,(4-1 P CD & X p CD (/) CD .ri+J nj i— i •>£!/) h o a) ^ si P 13 +-> CD CD H O rt +-> rH U E 13 13 P 2 U G CD rH -H O fi t/5 O P • •HO (/) CD i— I P -H -i— , H CD CD P -eCD O T) rH ft ^ ^ O a, p '-d p Ph s (DOC O t) (fl d£ In C 13 P P O £ 03 >,-H O -H O £ 5 O +-> H U) ft rift P X 03 rH
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172 1

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173 Stern equation assuming constant N. (curve 1) corresponded to only about one-tenth of the change in citrate concentration found in the adsorption experiment. This experimental analysis shows that for the calcium oxalate citrate system, although there is a qualitative correspondence between the experimental and the theoretical curves, the NGS model as employed does not quantitatively predict adsorption. This suggests that either the NGS model is an inadequate theory for adsorption in the calcium oxalate citrate system or that the values of assumed constants in the Stern equation are inaccurate. In Eq. [5] the only arbitrarily set parameter was the maximum adsorption density, N, , which was estimated using crystal lattice parameters. To see if an inaccurate N, value could be causing the discrepancy between experiment and theory, we proceeded as follows. If the NGS model is valid we should be able to calculate simultaneously values of both 4>. and r that are consistent with both electrophoretic and solution depletion data, respectively, then the two unknown constants N, and <$>. should be determinable from the two sets of experimental data. To do this we *Note that in the analysis that follows it is assumed that the citrate adsorption is independent of the adsorption of calcium and oxalate ions because experimental

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174 determined numerically the . value for each of a series of N, values that gave a r equivalent to the experimental solution depletion for an arbitrary total citrate equilibrium concentration (3.7 x 10 M, pH = 6.5). This gave a curve for N, versus $. that fit the adsorption data at that citrate concentration. Analogously, we found values of <$> . for each of a series of Nj values that gave \\i & equivalent to the experimental ip & at another arbitrary _ 2 total citrate equilibrium concentration (1 x 10 M, pH 6.5). Figure 31 shows that the intersection of these 14 two curves yields the solution set Nj = 7.78 x 10 (sites/cm 2 ) and cf> . = -0.09148 (V). Assuming the NGS model is valid, with this adjustment in Nj and $., for the "adsorption data has not as yet been attained for these ions. NGS model calculations, however, indicate that the density of calcium and oxalate adsorption is only about 1% of Nt; therefore this assumption is probably reasonable. *In previous electrophoretic experiments (Chapter II) it was found that for citrate the trivalent species was the dominant species in determining citrate's effect on \p & . Thus, good agreement between experimental and theoretical i> s values was obtained by making j for monoand ivalent citrate to zero. For pyrophosphate no singli dsorbing species with nonzero j could produce good agreement between experimental and theoretical i|; 5 values. Good agreement was obtained, however, when all pyrophosphate species were given a nonzero j of equal value. The
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Figure 31. Determination of a unique solution set of N 1 and j theoretically valid for all citrate concentrations by using the NGS model and experimental electrophoretic and adsorption data.

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176 CM £ o en Q> "(7> i O i 1 r Electrophoretic datq_ Solution set Adsorption data 0.090 0.100 0.1 10 0j (Volt)

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177 calcium oxalate citrate system there should now be agreement between the experimental and theoretical curves for adsorption and Stern potential for all citrate concentrations. Figure 32 shows that, through the range of citrate concentration in that ^ 5 varies strongly, the experimental and theoretical curves for ijj 6 closely agree. Figure 33 (left) shows that over the pH range 4 through 10 the agreement remains good. Figure 30 (curve 2) shows that the adsorption data are now also accurately predicted by the NGS model. These results establish that when appropriate values are determined for the constants N, and . for the calcium oxalate citrate system both electrophoretic and adsorption phenomena can simultaneously be described by the NGS model. The Langmuir adsorption isotherm obtained by linear least squares fit of the citrate adsorption data is given in Fig. 30 (curve 3). It can be seen that a better fit to these data, especially at the higher citrate concentration, is given by the NGS model. Assuming the improvement is not a curve fitting artifact, we conclude that the Stern isotherm is a more precise model for adsorption in the calcium oxalate citrate system than the Langmuir isotherm. A comparison between the two models suggests two possible explanations

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c o u O EH Cd o t/)

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179 C O c G) O c o o CD o (AW) |DI|U8|0cJ UJ8JS

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X p* ^

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181

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for this fact. According to the Langmuir model AC = V [14] 1 + tT where AC is the solution depletion of adsorbate, AC^ is the maximum possible solution depletion of adsorbate, C F is the total equilibrium solution concentration of adsorbate, and A is a constant inversely related to the affinity of the adsorbate for the surface. Comparing the terms in the two isotherms — Eqs. [5] and [14] — we can state AC unit area AC M unit area " "1 and = N n : but z, e (i|>. (J)-) if we let B. {J exp — ^ *—, it is apparent that — xdoes not always equal £( g-) . Thus, two reasons 1 + TT j 1 + 1 E "j why the Stern model gives a better fit to the experimental adsorption data for citrate are: 1) the lumped-parameter approach used in the Langmuir model for the different citrate ionic species concentrations and affinities is less accurate than the NGS approach, and 2) the electrostatic term, t|> 6 , in the Stern isotherm is needed to

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183 characterize a change in the affinity of the adsorbate to the surface due to changing electrostatic forces as the citrate concentration is increased. To determine if the electrostatic term caused a significant change in the affinity, we calculated ty & using the NGS equations for the experimental conditions of the adsorption experiment. The result was that the total change in if) & due to citrate addition was only 1.5 mV. This change would have negligible effect upon the affinity term. These results indicate that an improved accuracy of the Stern isotherm over the Langmuir isotherm in modeling the adsorption data in Fig. 30 could be due to its consideration of the concentrations and affinities of the individual citrate species but not to changing ^ g . The significance of the value of N, (the number of adsorption sites) determined for citrate adsorption needs further discussion. It could be a unique parameter for the calcium oxalate surface, or it could only be valid for the calcium oxalate, citrate system. To eliminate one of these hypotheses, we compared the experimental and theoretical adsorption densities for the calcium oxalate pyrophosphate system. Using the N 1 value determined for the calcium oxalate citrate system we determined a value for . for pyrophosphate that gave the best

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184 fit for electrophoretic data at an arbitrary pyrophosphate concentration (1 x 10" 4 M at pH 7.7). The adsorption densities resulting from these calculations, as can be seen in Fig. 34 (curve 1), increased much more rapidly with pyrophosphate equilibrium concentration than did the experimental adsorption data. Thus, if the maximum adsorption density, N,, is a unique parameter for the calcium oxalate system then this result shows that pyrophosphate adsorption would not follow the NGS model. On the other hand, there may be a particular solution set for N, and <\> . for pyrophosphate such that the NGS model could satisfy all electrophoretic and adsorption data simultaneously. To test this possibility we determined the . for the pyrophosphate concentration ranges over which the variables experimentally experience the greatest rate of change. The resulting theoretical curves did give a fairly good fit for the

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Figure 34. Solution depletion adsorption data for pyrophosphate. The theoretical curves are: 1) adsorption density from NGS model with Nj determined for citrate system and j set by electrophoretic data, 2) adsorption density from NGS model with the solution set Nj and j determined by experimental adsorption and electrophoretic data, and 3) linear least squares fit of the Langmuir adsorption model.

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186 CD G> C a O c o c CD O c o O CD O 40 30 20 / I h — Curve I / / D D / Curve 2 — *rf L / / D / // //n // / / / /ACurve 3 / 20 Pyrophosphate Equilibrium Cone. (uM)

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187 electrophoretic and adsorption data through the range of pyrophosphate concentrations; as is shown in Figs. 32, 33 (left), and 34. These experimental analyses show that both adsorption density and electrophoretic phenomena can be described simultaneously by the NGS model for the calcium oxalate, pyrophosphate system; it also indicates that the maximum adsorption density, N n , is not a unique constant for the calcium oxalate surface but can change for different adsorbates. It would now be interesting to see how the adsorption parameters obtained by this method for the two systems compare to those obtained by the less elaborate Langmuir analysis. The adsorption parameters obtained by the two methods may be consistent. If the parameters given by the two models are inconsistent, this could possibly give insight into the range of validity of the models. We thus examined the relative values of the adsorption parameters found for the two adsorbates by these two models. The adsorption parameters (in comparable units when possible) are listed in Table XI. Direct comparison of the maximum adsorption densities found by the two models for citrate show that they agree within a factor of two. However, the maximum adsorption densities found by the two models for pyrophosphate differ by an order of

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o O a
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189 magnitude. Furthermore, the Langmuir model predicts a greater maximum adsorption density for the pyrophosphate system than for the citrate system, while the NGS model predicts the opposite trend. By comparing the affinity terms found by the two models, we see that for the Langmuir model the value of the term A is less in the citrate than the pyrophosphate system; this indicates that pyrophosphate has less affinity for the calcium oxalate surface than citrate. The NGS analysis, however, gives a more negative value of 6. for the pyrophosphate system than for the citrate system; this indicates that pyrophosphate — not citrate — has the greater affinity. The relatively close agreement between the values of maximum adsorption density found by the two methods of analysis for the calcium oxalate, citrate system indicates that the two models are fairly consistent in their treatment of that system; however, for the pyrophosphate system the adsorption parameters found by the two models are definitely inconsistent. Since the electrostatic contribution to adsorption in the two systems is approximately equal, it is not likely to cause the difference between the model's treatment of the two systems. The NGS analysis of electrophoretic data for the two systems (Chapter II), fortunately, suggests a more likely

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190 explanation. For citrate, it was found that the electrophoretic data could give a good fit to NGS theory with a nonzero . assigned only to the trivalent species. For pyrophosphate, however, a satisfactory agreement between experiment and theory required a nonzero value for more than one pyrophosphate species. This indicates that separate consideration of the different pyrophosphate species is necessary. These results show that the lumpedparameter aspect of the Langmuir model for the calcium oxalate pyrophosphate system makes it inadequate for quantitative determination of adsorption parameters. It also demonstrates the necessity of the more complex Stern model for modeling adsorption in these calcium oxalate systems. However, when comparably high adsorption densities of dissimilar species are present , a form of the Stern equation is needed that accounts for the dependence of N, upon the type of adsorbate. Conclus i ons The NGS double layer model (in the form described previously in Chapter II) can adequately predict calcium oxalate's electrophoretic properties in solutions of relatively low concentration containing many adsorbing species; however, when surface coverage consisting of

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191 comparable fractions of unlike adsorbed species increases, the model's predictions tend to become less accurate. This appears to be due to the inadequacy at high adsorption density of dissimilar ions of the Stern isotherm used because of its inherent assumption that intermolecular interactions between unlike adsorbed species are absent. The NGS model can describe both electrophoretic and adsorption data over the range of concentrations which were experimentally verifiable if a unique solution set for each ion is determined for the number of adsorption sites, N, , and the specific adsorption potential, $y The value of NL as well as cf>, is not determined by the calcium oxalate surface alone but by the surf ace-adsorbate system. The Stern equation provided a significant improvement in determining adsorption parameters over the basic Langmuir isotherm especially when more than one complex of the same species specifically adsorbed. A Stern isotherm must be used that accounts for the dependence of N, upon adsorbate when the interaction between adsorbed species cannot be neglected.

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APPENDIX APL COMPUTER PROGRAMS USED IN CHAPTERS II, III, AND VI FOR MAKING NGS MODEL DOUBLE LAYER CALCULATIONS

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1] 2] 3 ] 4] 5] 5] 7] 3] 9] 10 11 12 13 14; 15 16 17 18 19 20 21 22 23 24, 25 26 27 28 29 :3 :3 1 ]3 2 '.3 3 .3 4 .3 5 :3 6 [3 7 \3 8 ]3 9 4 41 42 43 .44 45 46 47 43 ' COMPUTE a THIS PROGRAM USES "7F NGS '!OD7 T , TO CALCULATE STERN nCHARGE(CHl)GOUY C I1ARGE(C 72) .TOTAL CHARGE(C NT ) , AND Q nFOR GIVEN INPIT VALUES OF STERN ^T" EN n TAL ( PS) ;A ND *ACT (CO) \VALENCE(Z) % AND SPECIFIC ADSORPTION n POTENT lAL(SAP) OF VPE ADDED SPECIES. a DATA VAA+VBB+VSS+O A a70 Af/fl Z ARE FED IN AS VECTORS, THE NUMBER OF SPECIES a IS MMM, MMM-*-p ^E A tuLOOP FOV CALCULATING 4 r , r , " ER'-fS AND BUILDING VECTORS. MM 1+1 RIGHT : PSR+PSi K 1M1 ] F-<-0 r/^-Zf ! z AA«-((ZxKl)*l + U2*7)x*(Zx?n x(PS*?-(SAP*?/) )) ) BB+-C x ( ( * ( ( Z*Kl xPSft ) ) -1 ) 7ffi-*-+/i4i4 77-H + //? 1 ? +(CCZ0) /ENOUGH t\TRIS GIVES A APPROXIMATE VALUE FOR 77 fi/ffEW ENTERED PS a J IK DS 4 ,V IMA SI NA R 7 7 7 1 , »(F>6) /ENOUGH CC+0 MM1 F-f-F+l ENOUGH', +(PSR=Q) /ONE +(PO = SAP=0) I ONE SS<-PSR* I P.?/? -*? ;,jn ONEiSS+1 TWO: VSS+VSS.SS VAA+VAA .CHI VBB+VBB ,77 MM1+MM1+1 -v ( MM1 '/RX G H " A SUM VECTORS t CAL 7, 7 7ffll-t-p 7/4 7fflll«-( i (7711-1) )+l 7ffl-t-7.4i4C7.7111 1 77+73BC 77111] SS-*-7SSC7/711l] 17 1 " V O ''F/P 193

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194 [49] CHT + -(.K&*(PO-PS)) [50] 7#2«-(-( (K5*XH)*Q,5) )x(:7C*0,5)xS5 [51] Q+CHT-(CH1+CH2) [52] BG4 '4A=ADSORPTION DENSITY FOR FA' 17 ' S^^^l T FS AND GAM AT [53] a" RE TOTAL ADSORPTION DENSITY IN IONS PER SQUARE CM [54] GAMAHAA*(Z*E)) [55] GAMAT++/GAMA VFTjOOPZUIV V FLOOP [I] BTffIS PEEPS I.V PS VALUES INTO COMPUTE AND FINDS [2] *TBE BEST VALUE, IT NEEDS AN IMPUT VALUE FOR [3 ] fl7 AND Z FOR EACH SPECIES FROM OBEEK, [4] B [5] B INITIAL VALUE OF PS [6] B [7] PlLOOP FOR SETTING THE VALUE OF " ?.E LIMIT AND THE INITIAL [3 ] kRANGE FOR PS [ 9 ] FIRST : PSH 4* X ) , ( X ) [10] COMPUTE [II] LIMIT +IE 11 [12] 3.?^.?[1]*?[2] [13 ] +{QQ<0)/FIX [14] X+2xX [15] +(X>5) /FINAL [16] +FIRST [17] FIX-.X+PS [13] nLOOP TO SELF'' 7 ' RIGHT V S FO 77 NGS MODEL FIT, [19] NN+Q [20] SECONDiXl<-(XLll+XL2] 3*2 [21] NN+NN+1 [22] + (;VV>3 0) /BAT:"' OM [23 ] PS^XC 1],H ,.?C2] [24] COMPUTE [25] ->( (Q[1]*Q[2]> SO) /THIRD [26] ->( (Q[l]*?[3 ]> <0)/FOURTH [27] Z , flISZ):^-»-P5C2] f P5Ci] [23] +FIFTH [29] FOURTH :X+PS12') ,PS[3 ] [3 0] PIP? ?7:/?2H/( 13) [3 1] +{RQ
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195 [40] nWE NOW HAVE 7.4 L" VALUES OF "HI, 7 "2, ?ff?, PS, Q [41] -*-0 [42] BOTTOM: '10ULD NOT REACH LIMP' [43] + [44] FINAL: *?OULD NOV EXPAND PS RANIS ENOUGH 1 VDATAlUlV V DAP A [I] aTHIS PROGRAM CONTAINS CONSTANTS USED IN COMPUTE, [2] nNl=SITES PER SQ CM, [3] nE=GHARGE ON ELECTRON (7 OULOMBS) , [ 4 ] a N=M(7j EG UL E5 PER MCr, E , [ 5 ] *K = BO r r Z MA NS 7 VST 4 IT . [6] A T=AB SOLUTE TEMPERATURE, [7] *D = DTE r 1 EGTRIG CONSTANT, [8] «/l =47 ZVr 71" 7U 77) OF POTENTIAL DETERMINING TON (PDI) [9] nAT THE POINT OF ZERO CHARGE (PZ7). [10] *A=ACT OF PDI, [II] nZA=VALENCE OF PDI, [12] *PO=SURFACE POTENTIAL, [13] /V*l<-4 0500000000000 [14] E+1.6E~19 [15] .V«-6. 23 723 [16] tf+18 [17] X+i .33,7 23 [13] 1*^-3 11.15 [19] K6-KL .157 5_ [20] D+8. 2093 47 11 [21] AQ+1 , 857 6 [22] P0«-( ( (Xx 71 )*(£*Z4 ) )*(«( (.4x6. 023 720) t ( ,4 x 6 , 23 72 ) ) ) ) [23 ] £1<-A'1*7 [24] K2+N*M [25] K3 -«-E*Ux?) [26] KU-f-Xx? [27] K5+DH 2x3 .1415 9) ' V 705E7.?[D]7 V OBEEK [I] a^.7IS PROGRAM FEEDS I N" FL OOP VALUE OF Z AND CO, [2] a.4:V7 INTERFACES WI" H USER, [3] 'Zj4' [4] Z4+-2 [5] 'Z' [6] Z«-l ,(-1) ,2 ,( -2) [7] 'PSOK' [ 8 ] PSO#-<-C [9] NNN+VPS4-VVC + VCH1+VCH2+VCHT + Q [10] 1^0.025 [II] '70* [12] VALUES

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196 [13] [14] [15] [16] [17] [13] [19] [20] [21] [22] [23 ] [24] [25] [26] [27] [23] [29] [3 0] [3 1] [3 2] [33 ] [3 4] [3 5] [3 6] [37] [3 3] [39] [40] [41] [42] [43] [44] [45] [46] [47] [43] [49] [50] [51] [52] [53] [54] [55] [56] [57] [53] [59] [60] [61] co+u 'SAP' GIT 4-0. 1 OLDSAP4-0. 2 OLDPS4-0. 6 SAP+u C *•" 0x6. 23 £2 ONE: M ' A+-U *TYPE % 1000' FOE A * OUT OF PROG, -+{A = 1000) /END BACK'.FL OOP *THIS LOOP FINDS SAP ' 7 ZT ' FOR < *TO BYPASS LOOP ENTER '+ST0P3AP -+ST0PSAP LIM4-5E~S ->( ( | {PS-P50K) )>LIM) /TOOHI +ST0PSAP TOOHI : NXSAp4-(. ( OL DSAP-C IF ) * ( PS 01 DSAP+CIT 0LDPS4-PS IT +-7I7 -NX SAP SAP4-0, 0,0. 08 9 2,7 TV PS SAP +BACK STOP SAP: a" HIS LOOP MULT VPS+VPS,PS V1HI+-VTHI ,7.71 VS. H 2+77 H 2, 7, H 2 VTHT + VOH v t "HV t /7-<-:t6. 23 E2 VV14-VVS, vc C4-1 0*7 NNN+NNN+l *(NNN>0) IS n OP ST OP: ' £?/Z) OF WORK 1 r\PS IN MILLIVCTj V S , PS4-1 Ox VPS CH 1+-1 OOOOOOx VG HI OH 2+-1 000000 xf/7 7 2 7 ff'Z 1 *•! x 1/7 .7" ;J7FA T DESIRED PS(PSOK) ' WFAT &J/I/E. PSOK) )i(CTj DPS-PS) BY 10 AND REGALULA m ES ( NNN>X)TIMES , HARGE IN •/!" ROGOULOMBS, nREPROI ESSES VECTORS C+-VVG GG+pPS HH<-( \ (GG-1) )+l PS+PsttiHl TO ELIMINATE r IRS v 4tfD F7\Y 77C

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197 CALCINATED VALUES USING LIBRARY PRINT PROG. [62] CH1+CH11HH] [63] CH2+CH2LHH] [64] CHT+CHTlHH] [65] fiSKIP THIS FORoV>2 [66] +HIGHV [67] II+pVV? [63] JJ+( i(IJ-l))+l [69] 7 T /7<-777[JJ] [70] ##+(pW))*2 [71] r J LK(2x{ l M))-l [72] L &2«-2x( iH) [73] 7/n«-K7'7[^ r J l] [74] CN2+VVC ILL 2] [75] »PO=' [76] HIGHV: [77] nPRINT [78] 'PC [7 9] PC [80] 'S4?' [31] S.4 ? [8 2] 'Cffl 7#2 ?//! p "' [33] CHI AND 7. •2 4iVD 7/7? AND PS [84] AT'/rS CALCULATES ADSORPTION DATA{'+END* TO BYPASS). [85] 'TOT ADS DEN M/CM2' [8 6] DATA [87] G<4M?-*-&4AM*/V [38] C j 4.V4:'
PAGE 206

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201 49. Smith, R. M. and Albertz, R. A., J. Phys . Chem. 60, 180 (1956). 50 Bjerrum, N. and Urmack, A., Kge. Danske. Videnskab Selskab Math.-Fys. Medd. 9 (T)~ , 141 C1959J . 51. Bee, R. P. and George, J. H. B. , Trans. Faraday Soc. 49, 619 (1956). 52. Jenkins, I. T. and Monk, C. B. , J. Am. Chem. Soc. 72, 2695 (1950). 53. Homes, W. J., J. Am. Chem. Soc. 56, 860 (1934). 54. Bates, R. G. and Pinching, G. D., J. Am. Chem. Soc. 71, 1274 (1949). 55. Davies, C. W. and Hoyle, B. E. , J. Chem. Soc. Part I , 1038 (1955). 56. Honig, E. P. and Henyst, J. H. Th . , J. Colloid Sci. 2_9, 510 (1968). 57. von Smoluchowski, M. , Bull. Acad. Sci. Cracovie , 183 (1903). 58. Hiickel, E., Physik Z. 25, 204 (1924). 59. Henrv, D. C, Proc. Roy. Soc. London 133 , 106 (1931). 60. Henry, D. C, Trans. Faraday Soc. 44, 1021 (1948). 61. Overbeek, J. Th. G., Kolloid Beihefte 54, 287 (1945) . 62. Booth, F., Trans. Faraday Soc. 44, 955 (1948). 63. Wiersema, P. H. , Locb, A. L. , and Overbeek, J. Th. G., J. Colloid Interface Sci. 22, 78 (1966). 64. Lyklema, J., J. Colloid Interface Sci. 58, 242 (1977). 65. Robinson, R. A. and Stokes, R. H. , "Electrolyte Solutions," p. 25, Butterworths , Toronto, 1970.

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202 66. Hitchcock, E. I., J. Gen. Physiol. 8, 61 (1925). 67. Lindau, G. and Rhodius, R. , Z. Phy. Chem. A172, 321 (1935). 68 Pearce, E. I. F. and Bibby, B. G., Arch. Oral Biol. 11, 825 (1966). 69. McLaren, A. D., J. Phy. Chem. 58, 129 (1954). 70. Brash, J. L. and Lyman, D. J., J. Biomed. Mater. Res. 3, 175 (1969). 71. Dillman, W. J. and Miller, I. F., J. Colloid Interface Sci. 44, 221 (1973). 72. Healy, T. W. and LaMer, V. K. , J. Colloid Interface Sci. 19, 323 (1964). 73. Leal, J. and Finlayson, B., Invest. Urol. 14, 278 (1977). 74. Mac Ritchie, F., J. Colloid Interface Sci. 58, 484 (1972). 75. Bijsterbosch, B. H. and Lyklema, J., Adv. Colloid Interface 9, 147 (1978). 76. Mac Ritchie, F. and Alexander, A. E., J. Colloid Interface Sci. 18, 464 (1963). 77. Hartley, G. S. and Roe, J. W. , Trans. Faraday Soc. 36, 101 (1940). 78. Dixon, J. K. , LaMer, V. K. , Casslon, L., Messinger, S., and Linford, H. B., J. Colloid Interface Sci. 2_3, 165 (1967). 79 Rubio, J. and Kitchener, J. A., J. Colloid Interface Sci. 57, 132 (1976). 80. Pinck, L. A., "Clays and Clay Minerals," Proc. Natl. Conf. Clays Clay Minerals 9, 520 (1962). 81. Malek, R. S. and Boyce, W. H. , J. Urol. 117, 336 (1977).

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203 82. Boyce, W. H. , Amer. J. Med. 45, 673 (1968). 83. Kentel, H. L. and King, J. S. , Jr., Invest. Urol. 2, 115 (1964). 84. Maxfield, M. , Ann. Rev. Med. 14, 99 (1963). 85. Boyce, W. H. and Swanson, M. , J. Clin. Invest. 34, 1581 (1955). 86. Gasser, G. , Kovanyi, G. , Hanke , D. , and Hak-Hagir, A., in "Urinary Calculi. Int. Symp . Renal Stone Res., Madrid, 1972," p. 285 (Delatte, L. C, Rapado, M. A., and Hodgkinson, A., Eds.), Karger, New York, 197 3. 87. Dent, C. E. and Sutor, D. J., Lancet , 7728 (1971). 88. Nakagawa, Y. , Kaiser, E. T. , and Coe, F. L., Biochem. Biophys. Res. Commun. 6_5_, 233 (1975). 89. Overbeek, J. Th . G., J. Colloid Interface Sci. 58, 408 (1977). 90. Finlayson, B. and Reid, F., Invest. Urol. 15, 442 (1978). 91. Mundav, K. A. and Mahy , B. W. J., Clin. Chim. Acta 10, 144 (1964). 92. Blatt, W. F. and Robinson, S. M. , Analytical Biochemistry 26, 151 (1968). 93. Overbeek, J. Th., "Advances in Colloid Science III," 129, Elsevier, New York (1950). 94. Ehrlich, J. and Stivala, S. S., Polymer 15, 204 (1974). 95. Wagner, M. and Finlayson, B. , Invest. Urol. 15 , 456 (1978). 96. Mackor, E. L. and Van der Waals , J. H. , J. Colloid Sci. 7, 535 (1952). 97. Shaw, D. J., "Electrophoresis," Academic Press, New York (1969) .

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204 98. Fleisch, H. , Kidney Int. 13, 361 (1978). 99. Robert, W. G. and Peacock, M. , Clin. Sci. 45 , 499 (1972). 100. Robertson, W. G., Peacock, M. , and Nordin, B. E. C, Clin. Chim. Acta 43, 31 (1973). 103. Fleisch, H. and Monod, A., in "Urinary Calculi" (Difuentes Deiatte, L., Rapado, A., and Hodgkinson, A., Eds.), p. 53, Karger, Basel (1973). 102. Felix, R. , Monod, A., Broge, L., Hansen, N. M. , and Fleisch, H. , Urol. Res. 5, 21 (1977). 103. Finlayson, B. , Kidney Int. 15, 355 (1978). 104. Harris, H. S. , Warren, M. , Kaufman, W. J., and Krone, B. , J. San. Eng. 92, 95 (1966). 105. Hubley, C. E. , Robertson, A. A., and Mason, S. G., Can. J. Research 28, 770 (1950). 106. Swift, D. L. and Friedlander, S. K. , J. Colloid Interface Sci. 19, 621 (1964). 107. Singer, J. M. , Vekemans , F. C. A., Lichtenbelt, J. W. Th. , Hesselink, F. Th. , and Wiersema, P. H. , J. Colloid Interface Sci. 45, 608 (1975). 108. Fleer, G. J. and Lyklema, J., J. Colloid Interface Sci. 46, 1 (1974). 109. Ives, K. J. and Bhole, A. G., Water Res. 9, 1085 (1975). 110. O'Melia, C. R. and Stumm, W. , J. Colloid Interface Sci. 25, 457 (1967). 111. Uhlmann, D. R. , in "Urolithiasis: Physical Aspects" (Finlayson, B. , Hench, L. L. , and Smith, L. H. , Eds.), National Academy of Sciences, Washington, D.C. (1972). 112. Kahlweit, M. , Adv. Colloid Interface Sci. 5, 1 (1975) .

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BIOGRAPHICAL SKETCH Peter Angelo Curreri was born June 22, 1952, in Brooklyn, New York. He received his early education at St. Malachy's School in Brooklyn. After graduating from Brooklyn Technical High School's aeronautical curriculum in June 1970, he entered York College of The City University of New York. In September 1972, he transferred to the University of Florida's College of Engineering, and in June 1975, received the degree of Bachelor of Science in Engineering Science and Mechanics. He received his Master of Engineering degree in June 1977, from the Department of Materials Science and Engineering at the University of Florida, and has been pursuing a Doctor of Philosophy degree in the same department since that time. He is a member of Pi Lambda Phi social fraternity. Professional societies include the National Society of Professional Engineers and the American Ceramic Society. Honorary memberships include Keramos and Alpha Sigma Mu. 207

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. 6/Y%Jl George Yc^Onod'a, J~r Chairman Professor of Materials Science and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. .arry y^/Hencr Professor of Materials Science and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree i_of Doctor of Philosophy. John 'J . Hren/ Professor of Materials //Science and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. C3^ 7 ^ vv ' &~-&v>—. son Birdwell Finlaysoi Professor of Surgery/Urology

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This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 1979 cr^\ Dean, Graduate School

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UNIVERSITY OF FLORIDA 3 1262 08553 1969