Group Title: electrokinetic properties of calcium oxalate monohydrate
Title: The electrokinetic properties of calcium oxalate monohydrate
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 Material Information
Title: The electrokinetic properties of calcium oxalate monohydrate
Physical Description: ix, 207 leaves : ill. ; 29 cm.
Language: English
Creator: Curreri, Peter Angelo, 1952-
Copyright Date: 1979
Subject: Calcium oxalate   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Peter Angelo Curreri.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 198-206.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00099385
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000095684
oclc - 06337170
notis - AAL1115


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Copyright 1979


Peter Angelo Curreri

To Dad


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 contri-

bution 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.


ACKNOWLEDGEMENTS........................................ vi

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

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

OXALATE MONOHYDRATE............................. 5
Introduction.................................. 5
Materials and Methods ........................ 10
Results ........................................ 12
Discussion ................................... 37
Summary ...................................... 49

OCCURRING MACROMOLECULES ....................... 50
Introduction................................. 50
Materials and Methods ........................ 55
Results and Discussion........................ 56
Conclusions...................... .......... 87

CALCIUM OXALATE MONOHYDRATE ....................... 89
Introduction ................................ 89
Materials and Methods ........................ 91
Results and Discussion ....................... 97
Conclusions ................................. 111

ARTIFICIAL URINES .............................. 112
Introduction................................. 112
Materials and Methods ........................ 115
Results and Discussion........................ 117
Conclusions ................................. 151


MONOHYDRATE DOUBLE LAYER ....................... 155
Introduction................................. 155
Results and Discussion ....................... 159
Conclusions .................................. 190

LAYER CALCULATIONS ............... ............. 193

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

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

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




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

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 arti-

ficial 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 pre-

dicted the electrophoretic data. However, at higher


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.


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 as-

pects 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

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. Flectrophoretic measure-

ments 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 electro-

static. 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 clec-

trophoretic behavior of calcium oxalate in these systems

to gain an understanding of the character of calcium

oxalate's double layer and to provide a basis for a better

understanding of the mechanisms of formation of renal


The main areas we investigated were the fol-


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


2) bc studied the effect of some natural macro-

molecules 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


3) We studied the modes of aggregation of super-

micron calcium oxalate to see if aggregation would

occur in high ionic strength solutions and to see

if the adsorption of macromolecules could induce


4) Mobilities of calcium oxalate in artificial

and natural urines were studied to see if significant

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 con-

trolling 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.



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 Nernst-Gouy-Stern-

Grahame (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 pre-

dicted (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 sug-

gested that there is a diffuse layer of charge in the

solid phase (14-17). For silver halides, the charged

species are lattice defects (vacancies and intorstitials).

The space charge in the solid can give rise to behavior

that might appear to be due to a Stern layer with variable


For oxides, the theoretical concept is further com-

plicated by the inapplicability of the Nernst equation in

describing the surface potential (o ) (18-20). Modifi-

cations (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 compli-

cation with some oxides is the presence of gel-like struc-

tures at the surface, which give rise to higher adsorption

densities (24-30).

The importance of complex ions in solution has been

stressed, particularly by Matijovic (31,32) in relation

to specific adsorption (reversal of charge). Any quanti-

tative test of double layer theory requires an identifica-

tion 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.

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 solid-

state 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 as-

sociated with the inner Helmholtz plane. Specific ad-

sorption 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

of hydrated counter-ions of the diffuse layer). In this

case, the simpler Stern model, with only one layer, might


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 solvationn 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 con-

stituent 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

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 concen-

trations and because of the low surface areas (%3.0 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

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); analytic-

grade 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 (Qcm) 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 precipi-

tate confirmed the whewellite form of CaC204H20. The

particles were around 5 om in diameter, as ascertained

by scanning electron microscopy and Coulter Counter mea-


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 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 constant-temperature chamber, held at 370C 10C, 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

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-Hickel 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.


Calcium and Oxalate Ions

Ions common to the solid and aqueous phases are Ca2+
and C204 The activities of these two species are

related through the solubility constant. The variations
2+ *
in mobility with (Ca ) were investigated ; CaC12 and

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

Table I
Stability Constants Used in
Ion Equilibrium Calculationsa

Reaction (M-1)
2+ 2- 4
Ca2 + C204- CaC204 0.274 x 104

Na+ 2- 2
Na + C204 NaC204 0.134 x 102

Ca2+ + CaC204 Ca2C204 2 0.714 x 102

H+ + 2- 2- 5
H 2 0 4 HC204 0.215 x 105

Ca2+ + OH- CaOH+ 0.295 x 102
K+ + 2- 2
S C204 KC204 0.134 x 102

NH4+ + C2042 NH4C204 0.130 x 10

2+ 2- 102
Ca2 + HPO4 CaHPO4 0.319 x 10

Ca2+ + H2PO4 CaH2PO4+ 0.319 x 102

H4 + HPO2 H2PO 0.152 x 108
4 4- 2P04

Na+ HP04 2- NaHPO4 0.129 x 102
H+ 3- 2- 13
+ PO4 HPO4 0.152 x 101

Ca2+ + P4 CaPO4 0.346 x 10

H + H2PO4 H3PO4 0.164 x 103

Mg2+ + C242 4 MgC204 0.402 x 104

Mg2+ + MgC204 g2C204 0.475 x 101
Mg2++ L2 4 N: i2 C 0



















Table I continued.

Reaction (M1 ) Reference

Mg2+ + OH- MgOH+ 0.380 x 103 45

Ca2 + SO4 2 CaSO4 0.200 x 103 51

Na + SO42 NaSO4 0.525 x 101 52

H 4 + S 2- HSO4 0.100 x 103 53

2+ 3 CaCH- 5
Ca2+ + C6H5073 CaC6 H507 0.600 x 10 46

3- ~ 2-7
H+ + C6H5073- HC6 5072 0.272 x 107 54

Ca2+ + HC6H5072 CaHC6H507 0.505 x 103 46

+ -6
H + HC6H507 H2C6H507 0.561 x 10 54

H + H2C61H507 H3C6H507 0.127 x 104 54

Ca2+ + H2C6H507O CaH2C H07+ 0.125 x 102 55
Ca 6H2C5HO7 2 6 5 7
4-- 3- 10
IH + P2074 HP2073- 0.615 x 100 46

S+ HP2073 HP 2072- 0.615 x 10 45

H+ + H2P207 H3P207 0.190 x 102 45

Ca2+ P2074- CaP 202- 0.562 x 105 45
Ca + P 07 CaHP207 0.550 x 103 45

3 8
CaOHI + 0. 269 x 10 45

aThe complex CaC204 has a concentration in solution at
380C of (6.16 0.38) x 10-6 M (43).



o- 0

*H o
U --

4 o

U )

o H
*H t






4 0



Na2C204 solutions were used to alter the activity. The

(Ca 2+) 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 cor-

responds to pC204 = 3.45 (because pK = 8.65). In the

only other known attempt (56) to measure the point-of-

zero 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 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).

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 in-

ference 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

(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.


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.


E >
3 -30 E
5- / theoretical 0

-- -20 o
"0, 0
El 11 0 10

Ca 2+
- --- a -


< o2

-5 C24
o / o

0 \


2 4 6 8 10 12


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 re-

sulting from these additions are discussed and presented


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 103 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 concentra-

tion 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
SO4 which is the dominant ionic form of the sulfate

(by many orders of magnitude) in the solution, specifical-

ly adsorbs to the surface.

0 U
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X *


S *1-

Ui d




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N *


0 N


CS *

Ln <
X *

o N


o o

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f- ri'



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rc< r

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T 4




n d

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C*- 0



bo m



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N o






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N- c

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Nj U
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Oi fi

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e 2O

On n

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HtC >!



O c
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(i_ ::) (10

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cc cOI

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c cd Ou*n

C) in

E -H 0

F- C)
S0 V) F-C
)( I--
M to

E u


4-i +
F- 0 c-

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C ti-1 0
L~ l

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1I e-
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S\ I -

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1 o I /

i / O
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(i-uo3 lOA/1_S Tun) A!l!iqoAj

OJ ro i

When trisodium citrate (Na3C6H 57) was added, a

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 (Ca2+) changed from 4.5 x 105 M to
8.6 x 10- M when the trisodium citrate concentration

varied from 105 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 C obtained. Therefore, it appears

likely that specific adsorption is occurring. The

principal ionic citrate species in the system were

C6H5073 and HC6H5072- 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-

_____ _

the increasing (C6H507-) shown in Fig. 5 (bottom), and

not by the decreasing (HC6C5072-). We conclude, therefore,

that the specific adsorption of the C6H5073- 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- 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
be attributed to the species H2P207 2, 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 mono-

basic (NaH2PO4) 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 p1 with 5 x 10-4 M Na4P207 addition.
Top, electrokinetic properties. Bottom, activity
of multivalent pyrophosphate species.


S+1- -O >

> 0 I I I i

E theoretical "

-2- 20 a.
*- experimental \
o \ -30 O
0 3 -3 c

a I

-4- H2p202-

-5 .

- -

0-8- / -

2 4 6 8 10 12

10-2 M. This behavior can be better understood by con-

sidering the complex ions formed. Under the conditions

of this experiment, most of the electrolyte was in the

H2PO4 form. The (HPO42-) was only a few percent of the
(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
2- 3-
precipitate, the activities of H2PO4 HPO and PO4
were as shown in Fig. 7 (bottom); the (HPO4 ) increased

with pH, with a corresponding decrease in the mobility.
This indicates the specific adsorbing role of HPOG4 (or

possibly P43-) and the absence of specific adsorption

by H2PO4 If precipitation of phosphate occurred,

however, this interpretation is not valid.

Magnesium chloride (MgCl2) 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.

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 103 M, as shown

in Fig. 4. For these changes, little variation in (Ca2+
was calculated (Table II) to occur until 4 x 10-2 M MgCl

addition. These results indicate the specific adsorption

role of Mg2


"Experimental" Stern Potential

The calculation of zeta potential, c, from electro-

phoretic mobility is often not straightforward. The

Smoluchowski equation (57) is valid only for some re-

stricted 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 4 (<<25 mV) or larger

Ka (>>l), 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
2 x 105 cm- (at the lowest ionic strengths). Because
2 x 10 cm (at the lowest ionic strengths). Because

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:

4 U,

where q is the viscosity, U is the electrophoretic

mobility, and e is the absolute permittivity of the

aqueous phase.

To relate 5 to double layer theory, we further

assume that c = *i. The validity of this assumption has

been debated; Lyklema (64) has recently provided some

strong arguments for justifying it. The Vi calculated

by setting c = ,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

6, 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.

The Nernst-Gouy-Stern Model
2+ 2-
The Ca+ and C204- 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 c (Ca2+) curve remains linear for over three

orders of magnitude (Fig. 1) and that the pH alters C

(Fig. 2) only according to what would be expected by its
effect on (Ca2+]. Admittedly, while the potential deter-

mining role of Ca2+ and C2042- is not proven conclusively,

the evidence is sufficient to warrant making this as-

sumption so that a double layer analysis could be carried


The Nernst equation is

kT (Ca2+
S- tI ln --2^- [1]
0 ze (Ca 2+) [i]

where (Ca ) is the activity at the thermodynamic
condition o = 0, po 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

D = E n (exp ze6 1), [2]
1i i

where oD is the charge in the diffuse layer, D is the
dielectric constant, D is equal to 1.112 x 10 coul
-1 -1
volt cm no and z. are the number of ions per cubic

centimeter and the valence of species i, and 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)

a ) [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 + D = 0 [4]

Without specific adsorption, the dependent variables are

a, aD' o and 6,, which can be determined from Eqs. [1-

4], 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

specific adsorption plane and the plane of closest ap-

proach 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)

Sj [5N1ze
s N 1 + z.e [
1 + n.mxp

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 j. is the specific

adsorption potential of species j. Also, Eq. [4] must

be modified to give

a + os + oD = 0. [6]

The five dependent variables a, as, oU, to, and -

can be determined from Eqs. [1], [2], [3], [5], and [6],

assuming values for (j and N1. A computer method of

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+ )zc = 6.31 x

10-6; D = 8.21 x I0-11 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 106 < (Ca2+) < 103. Significant deviations

occurred above and below this calcium activity range.
2+ -3
For (Ca ) > 10 the theoretical i~ drops with in-

creasing (Ca2+) because of the increasing ionic strength.

The experimental *6 does not exhibit this change, but

rather continues to increase (although more slowly) at
2+ 2+ -6
higher (Ca2+). At low values of (Ca2+), below 3 x 106

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.

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 06 at low and high (Ca +), but it also increases

46 throughout the intermediate range in such a way that
the theoretical p,-(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 significant-

ly from (Ca 2+ zc However, this is contrary to what was

found (or assumed) for silver iodide (6), where the

capacitance increased with more negative to values.

Another possible explanation for the discrepancy

is the specific adsorption of Ca and C2042-. 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

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 Ca2+ and C2042- species, the NGS theory

with specific adsorption can be applied, with the j ions
2+ 2-
(for Eq. [5]) being Ca2 and C2042. A value of
1013 -2
4.1 x 10 cm for N1 was used in the calculations on

the basis of estimates of average lattice spacings. The

two adjustable parameters are 4Ca2+ and 204 2-. These

were varied to give the best overall fit of theory to

data. The best-fitting values were rCa2+ = 130 mV and

C204 2- = -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 p6-pH curves, using

the same double layer parameters as above. The calculated

curve is given as the dashed line in Fig. 2. Essentially

the same curve is obtained regardless of whether or not
2+ 2-
we assume that Ca2+ and C2042- are specifically adsorbed.

The reason for this similarity is that the activities

of these ions remain in a range which gives a i, 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 ,.d 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 Ca and C204 2- 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 4 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


C202- 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- 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- 2-
The specific adsorption of SO42 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 deter-

mined by finding the best fit between theory and experi-

ment for the .-concentration curves. Values obtained
for 0j in this way were -93 mV for SO4-, -107 mV for
3- 2-
C6H5073-, -110 mV for HPO42, -113 mV for the multivalent
pyrophosphate species, and 112 mV for Mg The resulting
theoretical curves are compared with the data in Figs. 1,

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 calcula-

tions were possible. If so, quite different values of

|j | 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 hydra-

tion 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.

For all the specifically adsorbing ions studied

includingg 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 j expected

for various types of bonds, the experimental values of

. 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(QC + t), in contrast with

the convention used by Overbeek (61), where w is expressed

as ze6, + 4. Grahame's convention normalizes the specific

adsorption potential to unit valence; Overbeek's conven-

tion does not. Having used the former, we conclude that

the normalized specific adsorption potential is ap-

proximately the same for all the ions considered. There-

fore, the total chemical work term, ze4, is proportional

to the valence.

Ionic bonding depends on the valence of the adsorbing

ion. However, the specific adsorption energies, ze4, 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

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.


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 in-

volving 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.




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

on the surface. Because of the amphoteric nature of

proteins, their charge can usually be altered with solu-

tion 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 in-

fluenced 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 sur-

faces (76) due to its influence upon the adsorbate con-

centration near the surface (77).

The mechanisms of bonding of macromolecules to sur-

faces is the subject of much debate. Electrophoretic

studies of the adsorption of cationic synthetic polymer

on silica have shown evidence for specific adsorp-

tion (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

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 pos-

sibly with chemically bound mucopolysaccharides and

with serum albumin, alpha-globulin, and sometimes gamma-

globulin present (83,84). Urinary protein in general (85)

and urinary lysozyme in particular (86) are generally

higher than normal in concentration in stone former'


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

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 macro-

molecules 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 adsorbatee

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.

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 pre-

viously 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 106 (Qcm) 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 equi-

librated at least 2 hours at 370C before making electro-

phoretic measurements. The electrophoresis was carried

out using a commercial instrument in a constant tempera-

ture chamber at 37C (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 transmis-

sion 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





0 '0



0 cf





a o





CC <

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 (pm 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 spectro-

photometry at 280 nm for solution depletion of protein

I I_












Fi 11

S*H ti

UG e


S -'a)

O v
^3 ri

oc-) 0


a -4-4

--l c

3 o
r-i ci

H 0)

(D T
a.) U f

i- <-H

Pn H

0r-1 C
on. <


against standard solutions. Since the solids concentra-

tion 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 electro-

phoretic measurement. No evidence of precipitation was

found in any of the systems presented in this paper.

If calcium is removed from solution through com-

plexing 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- N 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 M by the solids con-

tent of our suspensions, the mobility change due to the

presence of the mucopolysaccharides cannot be explained

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 106 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 con-

clusion 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

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 sus-

pensions 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 102 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 pII.

Adsorbed proteins can sometimes maintain their integrity

and cause a covered particle to obtain surface properties

similar to the protein (93); conversely, adsorption could


0 H

0 01


4J 4a (

0 0
0 0 '-H



4444 0
0 0 ,

r-lri F:

L0 M 0
) 0
u 3
4 4r-r
- 0) 0

*flH C>i

4 +-i0

*itH Or-i

0U 0 *fl

Sr, 0 00








Mobility (umr

N) --

s-1/Volt Cm-')

+ +
) -- [

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 de-

creased with increasing pH approaching zero at ap-

proximately pH 11, which is the same is the isoelectric

point of lysozyme. The experiment was not extended to

high pll'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

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 concentra-

tion 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 muco-

polysaccharides. 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 macro-

molecules does not support a model that depicts large

alteration of the macromolecule's solution interface with


Since the natural macromolecules presented in this

study, as well as some small molecules studied pre-

viously (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

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

Figure 10.

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 sub-

stantially less negative than those without lysozyme for
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

E- 0
4* + 4-

0 .-
H 4, 3

.C ) O
S0 *0

-> C) rI
0 0 -
CJ O 0 0
-. 0 t-


0 ; 5
oO r 1

UH 0 0
r- 00 C

.- U 0 C

b U- O

.C 0
* 0

H I *H 4
-0U 45 0

uCo Co )

9 0 0n
*. o 0 N

0 orH C

0 0 rt
0 c u4 C CO
O 0. ) ,r



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
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 concentra-

tion 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

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,

F + [7]
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 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 macro-

molecule 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
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

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).

*H E

rH 0 0t -C
4'c) C) cl
C4-'0 04 -

3u ) 04-a
ZC U 3
4-'C OC 3

ti SC

VC) +C 0 C
H 0 -H I- 'V0

CC 0 O- 0

r 3t 3

4di UC
Oi d -1 o


U 0 n nC )O
+)H *0 CC'0

o 0 4- 0-
U0 0 o -

*4 [ 4-1
4 Ul -. 0 0
4[ -, .C- j 0

) H4UC 4
S0 0 0-

0O*cn 0
00) C0
C)0 0 M
4*HJ W < a

[4-3U *0
HO ri C)
0'0'-i 4-'C)

S 0000
0 H M U- C) 4-

r -4-43 C

in ni 0

03 D 0 3

D *H (/I 4- *
c3 e^ ^rt


fiM& jX

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 m /g. The molecular weight and density used

for serum albumin were 69,000 g/M and 0.73 g/cm re-

spectively. 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 2/g. The effective area covered by serum

albumin for each solution in Angstroms squared per liter


A = AC x Ap [8]

*This value for surface area gives a more conservative
estimate of crowding than the lowcr 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 con-
centration. Values obtained from a previous
study normalized by weight to our experimental






i I
en -4 -

-7 -6 -5 -4 -3 -2

Log [Calcium Concentration ( M )

The total surface area for 0.315 g/L calcium oxalate

is 6.3 x 1018 V2/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- M calcium there is likely

to be considerable physical crowding of adsorbed


This analysis of solution depletion data raises a

question of how the physical crowding of adsorbed

molecules affect their adsorption mechanism. One pos-

sibility 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 con-

tinued 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 electrostatical-

ly. Although solution depletion adsorption experiments

cannot differentiate between these two mechanisms, we


rj _

4- 1 a v o 0 o
E 0 0 C 0 0 0

EO 0 0 0 0 0 0 C

0o 3 X X X X! X

SU r1 L

CD CI 1 I 1 11
cO CU 0 0 0 0 0 CC 0)

0 u
3 'C C' v r- U'.

1r S4I I C I Ln I
40 : 0 0 0 (D 0 0 0

E o o-a ^

r- u C) 0 0Z 'D 0 r- C

H .

S- 0 CD N 0 0


* E3 N N t N N

- U U U u O O O
C r 0' N H I 'C C"
tC I I I I I I
3 0 0 0 0 0 0 0
< ~24 2- -

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.

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

+1 sites Molecules Molecules
(Ca) (MI) A2 T +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 104 6.7 x 10- 6.0 x 105 0.75

2.2 x 10-5 3.9 x 10-5 2.8 x 10-5 0.72

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 104 M sodium oxalate and at 104 M 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


U 4-

o o -H

F ,0 4-n

be cH

'--) .)
4H )
,' .

0 0 n1 0

o', E
O0 0 I
0 3H

in n
0-i 0 -. U

u ( 0 05
o F
rfl ) o

Ho r -,i
u u

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md .d -
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U i n ri
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S3 0L. 0

l0 0U d

*H i -' r

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.


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


pCa, the adsorption continues completely electrostatical

ly. 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.



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 lithia-

sis (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 super-

micron 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 in-

sufficient for perikinetic aggregation. However, for

super-micron particle suspensions the collision rate can

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 sur-

face, proteins and other macromolecules can either ac-

celerate 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 forma-

tion. In this work a comparison is made of the coarsening

calcium oxalate suspensions in saturated and super-

saturated systems. High particle density and high

electrolyte concentration are used in a nonturbulent

apparatus to examine the possibility of perikinetic ag-

gregation. 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

of polymeric macromolecules. We thus monitored particle

size information on calcium oxalate in various potential-

ly 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 super-

micron 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 nonohydrate crystals were prepared

as previously described in Chapter II. Water was de-

ionized 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 pm filter to

remove undissolved particles. Polyacrylamide and

polyethylene oxide, high molecular weight polymeric floc-

culants, were obtained commercially. The solution pH's

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

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