Nucleation of calcium oxalate monohydrate: use of turbidity measurements and computer-assisted simulations in characterizing early events in crystal formation

Journal of Crystal Growth 108 (1991) 455 464 North-Holland

Nucleation of calcium oxalate monohydrate: use of turbidity measurements and computer-assisted simulations in characterizing early events in crystal formation * Charles M. Brown, Daniel K. Ackermann, Daniel L. Punch and Birdwell Finlayson r Division of Urology, Department of Surgery, Box J 247 JHMHC, University of Florida, Gainesville, Florida 32610, USA

Received 2 July 1990; manuscript received in final form 2 October 1990

To examine the nucleation of calcium oxalate monohydrate (COM) crystallization, we have determined the time interval from initial formation of a supersaturated COM solution to the first appearance of turbidity or crystals. The turbidity measurments were conducted with the unaided eye, whereas crystal formation was analyzed using an inverted microscope and an image analysis system. The lag time kinetics were compared with previous nucleation studies using computer simulations with the Gibbs Thomson nucleation equation and the parabolic growth rate law. The nucleation behavior can be described as homogeneous or heterogeneous depending on the range of initial relative supersaturation. The calculated interfacial energies for homogeneous and heterogeneous nucleation agreed rather well with earlier investigations. Moreover, this investigation provided the opportunity to verify the utility of our particle size distribution program for simulating precipitating systems, and the experimentally determined surface energy was obtained from simulations of the nucleation kinetics.

I. Introduction

In the context of urolithiasis, the processes of crystal growth, its inhibition, as well as aggregation have been the most widely studied phenomena in crystal formation. Except for work with continuous crystallizers [1 4], nucleation has received scant attention even though there can be no crystals without it. In continuous crystallizers, the nucleation rate is calculated from the steady-state particle size distribution, and the main nucleation mechanism in this case is thought to be secondary nucleation arising from the influence of hydrodynamic forces on the particle suspension occurring at kinetic energy of magnitudes unlikely to be found in the urinary tract [5]. Studies of nucleation in aqueous solutions, perhaps, have been neglected as a result of unique observational difficulties. Yet, Mullin and Raven observed that *

Supported in part by NIH Grant AM20586. Deceased July 22, 1988.

0022-0248/91/$03.50 © 1991

“nucleation constitutes the first, and probably the least-understood, stage in the production of a new phase” [6]. To take an elementary look at the nucleation of calcium oxalate monohydrate (CaC2O4~H20, here abbreviated as COM), we have used an assay suggested by Christiansen and Nielsen [7] in which solutions supersaturated with respect to COM were observed to determine the interval (or lag-time) from formation of the solution to first appearance of either turbidity or crystals. First appearance of turbidity was determined by the unaided eye, and first appearance of crystals with a microscope. The validity of this approach to nucleation of COM formation was examined by comparison with previous nucleation studies that used a different approach and by comparison with computer simulations based on the Gibbs Thomson nucleation equation [8] and a parabolic growth rate law. Our simulations required an investigation of the relationship between measured and calculated turbidity. We further examined the relationship of

Elsevier Science Publishers B.V. (North-Holland)

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Nucleation of calcium oxalate monohydrate

lag-time to several system perturbations, including the addition of methylene blue, the presence of urine, and mechanical agitation.

2. Methods and materials 2.1. Macroscopic experiments

Water of 10 megohm purity or better was provided by a Milli-Q high purity water system. Chemicals were reagent grade. Glassware was acid-washed. The experiments were conducted at 37°Cin 25 ml glass-stoppered Erlenmeyer flasks in a shaker bath that had an adjustable shaking speed. The contents of each flask were made from equal amounts of two solutions: the first solution was calcium chloride (CaCl2~2H 20) in a buffer of 0.1OM NaCl and 0.O1M HEPES adjusted to pH 6.5 with 5N HC1; and the second solution was potassium oxalate (K2C204) in the same buffer. The CaC12 andand K2C204 concentrations equal to each other were selected to yieldwere a desired initial relative supersaturation (RSI) with respect to COM. R51 ranged from 10.5 to 32. Solutions were designed with the EQUIL ion speciation program [9]. All solutions were filtered through 0.22 ~tm Millipore filters and standardized with atomic absorption spectrophotometry of the cation. Stock solutions were equilibrated to 37°C before mixing. A typical run consisted of 33 crystallizers at 11 RSI values in triplicate. We observed the flasks at regular intervals for the first appearance of the finest particles discernable un der a strong white light with dark background and noted the time of appearance as the time of nucleation. For RSI below 20, the observation interval was 30 mm; for RSI values of 20 and higher, the interval was 1 mm. For experiments with urine, we used buffers which were 5% urine by volume. Four kinds of urine were used: whole human urine; filtered human urine; filtered urine of normal rats; and the filtered urine of rats treated with gentamycin (100 mg/kg of body weight per day). Under conditions which induce hyperoxaluria, gentamycin triggers COM deposition in rat kidneys. All urine samples were filtered through 0.22 ~smMillipore filters.

2.2. Microscopic experiments We prepared solutions for the microscopy ex periments as described for the turbidity experiments, except that RSI ranged between 11 and 18. Solutions were temperature-equilibrated at 37°C. After the mixing of CaCI2 and K2C204 solutions to the desired RSI, we placed drops of the mixed solution on glass slides for examination at a 200 x magnification with transmitted light in a Nikon inverted microscope. The temperature of the samplc was maintained with an incubator around the stage of the microscope. 2.3. Data reduction

The Gibbs Thomson equation relates the cxperimentally observed lag-time (T) to RSI, assuming the nucleation rate to be inversely proportional to T: j

2 16~rs~Lv A exp 3k3T3(m ln RS)2

‘

in which J is nucleation rate (s 1) taken as 1 /T, A is “pre-exponential factor”, s~L is crystal liquid interfacial tension (J m 2), v is molecular volume (for COM, 1.10 x 10 22 cmi), k is Boltzmann constant (1.38 x 10 23 j K I), T is absolute ternperature (in this work, 310 K), m is number of ions in neutral molecule (for COM, 2), and RS is relative supersaturation. Values for the pre-exponential factor, A, were derived from two sources: the first, termed A~, from our previous work involving particle counting [10], and the second, termed Ae, from the plots of ln(1/T) versus ln 2(RSI). The Gibbs Thomson equation predicts the nucleation rate, J, for a particular substance at temperature T and relative supersaturation RS. We define relative supersaturation as the calciumoxalate ion activity product divided by the solubility product. In these experiments, we took RS in eq. (1) as equal to the initial relative supersaturation (R51) of the solutions, assuming that the vast majority of particles are created at constant relative supersaturation before noticeable solution depletion of calcium or oxalate ions takes place.

G.M. Brown et at

/ Nucleation of calcium

That assumption is justifiable in the RSI range of these experiments (see fig. 4). COM crystal growth is assumed in this work to be governed by a parabolic rate law. This application is well established in the literature [11 15]. The growth rate constant occurs in two contexts. First, it is used to calculate crystal growth in our simulation program (see below). Second, it is used in the discussion as an alternative model for interpretation of the experimental results. Basic experimental data consisted of macroscopically observed nucleation lag-times (T) and initial relative supersaturation (RSI). We analyzed these data by making a linear regression of ln(1/T) on ln 2(RSI) and took the slope of the regression line as proportional to the cube of the interfacial surface energy term, s~L’ in the Gibbs Thomson equation. 2.4. Calibration of relative turbidity

In an effort to corroborate the turbidity-based arguments of this study, we calibrated the relative turbidity (as calculated with PSD, our particle size distribution program which simulates precipitating systems) to the more objective standard of optical density. The value, 7e1.d’ is relative turbidity based on an entire distribution (as opposed to an average particle size) and is considered proportional to measured turbidity. This value is calculated with PSD according to the following equation [16]: ~eI.d

2

~

(2)

~iIIi

where n, is the number of particles in size class i and v, is the average volume of particle size class i in cm3.

We prepared a series of solutions that were slightly supersaturated with respect to COM (RSI 6). Slurries were made from COM seeds (see preparation below) in concentrations ranging from 0.004 g 1 to 0.512 g 1 The slurries ranged in ~.

appearance from slightly milky to water-clear. We examined a 10 p.1 drop from each slurry under 400 x magnification with transmitted light in a Nikon inverted microscope, and we used an image analysis system (Image Technology Corporation)

457

oxalate monohydrate

to obtain between 10 and 20 measurements per drop. The optical densities of the slurries were measured in a Perkin-Elmer Model 559 UV Vis spectrophotometer at 530 nm. The image analysis system gave an apparent average projected area of 13 pixels for a single particle. That translated to an equivalent spherical diameter of 1.37 ~.tm. On the basis of that measurement of a single particle, we converted the total enhanced area of each measured field to a number of particles. The total enhanced area, the area of the measured field, and the total area of the drop yielded the number of particles per liter. An average equivalent spherical diameter of 1.20 ~tm was derived from the number of particles and the original mass. Because 1~I calculated from image analysis of slurries was based on one particle diameter and ‘eI for PSD was based on a distribution of particle sizes, we investigated the relationship between ‘elav’ the relative turbidity based on one particle size, and ‘el,d’ the relative turbidity based on a distribution whose average particle had a diameter equivalent to the one on which ‘eI.av was based. 7e1,av was calculated for monodisperse slurries with particle diameter of 1.37 p.m. and ‘eld from PSD-generated distributions with average diameter of 1.37 p.m. The ratio, 1e1.av/1e1.d was used to determine the proportionality between optical density (OD) and ‘~eId• Although that ratio was distribution-dependent, we observed that the distribution evolved very slowly in the range of macroscopic observability; thus, ~e1.av/1eI,d was practically constant with a value of approximately 1.73 x 10 ~. ‘ejd of the slurries ranged from 1 x 10 ~ to 2 x 10 6 The relationship between ‘ejd and OD was found to be OD(530 nm)

1.210

(3)

X 106 7eid•

On the basis of Fechner’s fraction [17], the minimal OD increment perceivable by the average human

eye is around 0.01 OD unit. The

‘ei.d

predicted

with PSD for macroscopic observation of lag-time was 1.66 X 10 ~. Eq. (3) transforms that to an OD(530) of 0.002. However, the lag-times were observed in 25 ml flasks whose pathlength was 3 4 cm, so the effective OD is about 0.008. We feel that this result provides one kind of internal

458

GM. Brown el al.

Nucleation of calcium oxalate monohydrate

consistency check between experimental and simulation results.

67 erg cm 2 [18]. The lower limb in fig. 2 gives an apparent interfacial energy of 31.1 erg cm 2 As indicated in eq. (1), the apparent interfacial energy

2.5. COM seed preparation for calibration experiments

We prepared seeds for our experiments by mixing 0.5M CaCl

2 and 0.5M K2C204. After the resulting slurry was allowed to settle, we decanted the supernatant fluid, and resuspended the seeds in high purity water. The process was repeated

until the potassium concentration was determined with atomic absorption spectrophotometry to be less than 1p.M. A final settling and decantation was followed by centrifugation and lyophilization. The seeds were stored dry under vacuum until used.

of the nucleation process can be obtained by multiplying the slope by 3.88 x 10 ~ (at 37°C) and taking the cube root. The data from this work yielded 27.3 erg cm 2 (shaker setting U in fig. 1; slope 70.0). The 3.8 erg cm 2 difference may be explained by the use of different systems of observation. The previous work on COM “crashes”

(i.e., unseeded, spontaneous precipitations) was carried out with a Coulter counter at a fixed time after formation of the supersaturated solution. and that analysis assumed that the particle count was a good indication of the number of nucleation events. The present work relied on turbidity of the solution as determined visually by an observer.

3. Results and discussion 3.1. Calculatton of apparent interfacial energy

6

-

To gain further insight into the relationship

between agitation and apparent interfacial energy, 2(RSI) for we made plots of ln(1/T) versus in some of the experimental data at several shaker settings. Fig. I shows these data overlain by the regression lines whose regression coefficients 0.97 or better. Past work from our laboratory indicated the nucleation observed in this experiment heterogeneous [10], and fig. 2 shows a plot of

were I..

that was

total particle production per ml versus ln 2(RSI). Two distinct regimes of particle production can be seen. The upper limb of the data has been attributed to the homogeneous nucleation expected at high relative supersaturations; the lower limb has been

SHAKER

0

6

12

Ia

SEUINGS

attributed to heterogeneous nucleation. The transition between the two processes appears to occur at RSI values of 80 100, although Walton placed the transition at an RSI of 31 [18]. Using eq. (1), the solid line in fig. 2 was ob tamed by a nonlinear fit to the two overlapping linear processes (i.e. homogeneous and heterogeneous nucleation). The interfacial energy calculated from the upper limb of fig. 2 is 69 erg cm 2

a value agreeing well with the published value of

0.10

0.15 -2

In

RSI

Fig. 1. Plot of ln(1 T) versus In 2(RSl) for the macroscopic observations of calcium oxalate monohydrate nucleation. These experiments were conducted at four shaker speed settings: (•) 0; (v) 6; (•) 12; (A) 18. The regression lines for these data are drawn as solid lines.

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Nucleation of calcium oxalate monohydrate

The lag-times for nucleation experiments at

Intercept ~.

459

integrated solution of eq. (4):

Slope=21

T). (5) (x, y) ([(RSI1 2_a)2 —1] shaker settings 0, 6, 12, and 18 were used in an ,

•~ 20 15

~

nal eq. solution of either ofcalcium or In (5), theconcentration a-term is a decrement the origioxalate, and this a-term accounts for a fixed amount of reacting species transformed to precipitate at the time of observation. Our simulations (unpublished) of crashing COM systems indicate that the assumption is reasonable for the early phase of precipitation. Fig. 3 depicts the data for shaker setting 0 plotted in the form of eq. (5), and the resulting non-linear plot demonstrates that these experimental findings do not conform to that predicted by eq. (5). Furthermore, the plot

Intercept=

~,

11.546

10

•

Slope=6.291

5

.

2

4

6

8

10I 12I

becomes increasingly nonlinear as the a-term increases, and would show even more curvature if

/n2(RSI) x 102 Fig. 2. Plot of the total particle production per ml versus In 2(RSI). The upper limb represents the homogeneous nucleation region, and the lower limb represents the heterogeneous nucleation range.

Both methods suffer from assumptions about the relation of the observable phenomena to the nucleation process. 3.2. Nucleation versus growth

Robertson and Peacock [19] have criticized the use of macroscopic lag-time to study nucleation, and they suggested that the macroscopically ob-

surface area were allowed to increase as it would in reality. Thus, we reject the notion that growth kinetics dominate in our experiments. Variation of growth rate in modeling simulations did perturb lag-time results, but the results were best fit by the nucleation kinetics. 3.3. Computer simulations of precipitation

Our experimental values of apparent surface energy were used in the PSD program that simulates precipitating systems, and fig. 4 shows such a

servable lag-time is dominated not by the nuclea-

tion rate, but rather by the time required for particles to grow to detectable size (i.e., the lagtimes are determined by the growth rate). Sohnel and Mullin [20] offered another view by suggest-

withthat ing tion. the If criticism following lag-times of are empirical the a valid above parabolic reflection approach growth of isnucleavalid, rate lag-times would be modeled more appropriately law: dRS/dt

Ks(RS

1)2,

(4)

where K and s are the growth rate constant and total surface area of particles, respectively,

2.O~—a

0.2505 I 0

10.0

08 -~

0.6

0.2 0.0

0.06

012

I(RSI

1/2

0.18 2

-a) -ii

0.24

0.30

—1

Fig. 3. Plot of the experimentally observed lag times T versus [(RSI1 2 0)2 1] as influenced by several computationally imposed values of the decrement, a.

460

C. M Brown et a!.

Nucleation of calcium oxalate monohydrate

I

RSk32.13 ~

1.0

Ntot SA

P

05

Turb

0.6

~ 0.4 ~

02

is assigned as the lag time for RSI of 20.31. A plot of the slopes of the lines joining various pairs of lag times is shown in fig. 5. Interpolation of growth fitted growth rate. rates to that intersection yields the simulationAt a growth rate constant of 3.902>< 10 6 cm 2 the lag-time for RSI of 32.13 was 601 s. as compared with 600 s found experimentally, and the lag-time for RSI of 20.31 was 2,460 s, as

RS

-J

0.0

I

0

200

400

600

800

1000

TIME(sec)

compared with 2,520 s experimentally. Those times were found at ‘eId 1.57 X 10 6 B derived with this procedure was 51.80 compared with the

Fig. 4. Simulation plots of RS, N

101, surface area (SA), and turbidity (turbl versus time for spontaneous precipitation of RSI 32.13 as computed using the PSD program. The vertical line represents the macroscopically observed lag time.

simulation. The main objective was to see whether experimentally determined surface energy would be returned from simulation results plotted according to eq. (1) if we3. simulated experiments like those shown in table

experimental value of 52.09 used as tnput in PSD. That is the second internal consistency between the experimental and simulation results. Although the growth rate constant used here was chosen empirically to match the experimental and simulation results, it was later found to agree very closely with the published growth rate constant for COM Nancollas of 6M given m 2 by mmSheehan [13].and When calcium 3.3 X 10 ion concentration is appropriately transformed to

PSD uses eq. (1) in a form (eq. (6)) that collects all exponential term parameters into one factor, B, that can be identified directly with the slope of graphs of ln(1/T) versus ln 2(RSI). This assumes that J is proportional to inverse lag-time. The preexponential factor, A is a measure of heterogeneous particle production in the theoretical limit of infinite RSI and can be found as the intercept of the lower limb of fig. 2.

RS in the RSI range of these experiments, the latter value converts to 3.94 .c 10 6 s cm 2 in good agreement with the 3.902 x 10 ~ cm 2 value noted above.

J

and the results are summarized in table 1. The slope obtained by microscopy is approximately half that observed with the unaided eye, hut the

A exp[B/1n2(RSI)].

(6)

The value of A derived from fig 2 (Ar) was 2.344 x iO~.B, as given by this work, was 52.09 (see table 3). The value 52.09 differs from the slope given earlier, because a more limited data set was used for comparison with the simulations. PSD simulations starting with RSI of 32.13 and RSI of 20.31 using these values of A and B were run at three growth rates to generate two points on plots similar to those in fig. 1. The location of the points depends heavily on the assumed lag-time with a given growth rate. To get a pair of points for a plot like fig. 1, a lag-time is assumed for RSI 7~1ei.d’ is matched of 32.13 and its turbidity value, with the comparable ‘d.d in a PSD simulation of RSI of 20.31; the time corresponding to this ‘el d

3.4. Microscopy studies Comparable nucleation experiments were carned out with a microscope to detect time (Tm),

expt T=600sec 30

-

ui a. ______ Rate

L_

15~

\

______ 50

10 1o9

2.0

\ 30

~exp~ slope— 52 09 4.0

10(9sec) for RSI=32 13

Fig 5. Evolution of slope B versus log(time) in the macroscopically observed RSI range at three growth rates.

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Nucleation of calcium oxalate monohydraze

Table 1 Slopes and intercepts as calulated from microscopically determined Tr,, at 25 and 37°C (observed at 200 X, no agitation) Slope, B 25°C 37°C Macroscopic, 37°C a) a)

461

cated by the vertical line in fig. 5), there is a broad plateau where B is not changing much and is definitely lower than in the region of macroscopic

Intercept, A~

observability. Third, simulations were done in the

0.59 + 1.73 2.14+0.86 2.14+0.38

RSI range of the microscope experiments (following the same outline as those for the macroscopic experiments in which B was calculated at points of equal turbidity) at RSI = 11.7 and 17.5. The

41.45 + 12.12 26.91 + 6.02 52.09+ 3.93

Macroscopic values at 37°C given for comparison,

x 10 6 1 cm 2~ At a lag-time of 192 s for RSI of 17.5, the lag time for RSI of 11.7 was 515 s compared to the experimental value of 648 s (see table 1). The predicted slope was 22.77 with intercept 2.477. Those growth rate constant was 3.902

intercepts are almost equal. Such a discrepancy may be resolved by the following three observations. First, when the complete set of four macroscopic points at SS of 0 (i.e., at RSI of 32.13, 28.04, 24.06, and 20.31) was used to calculate three slopes for each of the point-to-point segments, a slight but significant decrease in the absolute value of the slope occurred with decreasing RSI. That trend is also found at higher SS where the shorter lag times extended the range of observation down to RSI of 13.50 which overlaps with the RSI range of the microscopic experiments. Second, simulations with RSI over the 20 30 range for the microscope experiments, the absolute value of B would have been significantly lower. Fig. 5 shows the evolution of B with time for the macroscopic range of RSI. At times well

before macroscopic observation is possible (mdi-

values differ from the experimentally determined values by about 15%, but illustrate that predicted values of A~and B will be lower at lower RSI. Table 2 gives a comprehensive comparison of nucleation results without agitation as found cxperimentally, using the Gibbs Thomson treatment (eq. (6)), and as predicted by PSD simulations with turbidity used to determine lag-time.

3.5. Effect of mechanical agitation Estimates of parameter B in eq. (6) were calculated for series of experiments at different shaker settings. These values indicate that there is a strong

Table 2 Lag times for both microscopic and macroscopic examination in unagitated systems RSI

Lag times (s) Microscopic examination PSD

10.49 11.70 13.50 13.65 15.62 16.78 17.50 20.31 24.06 28.01 32.13 °~

b) C)

d)

Time B Time B

680 515 365 355

246 210 192 135 96 69 53

a)

Exp.

648 498 342 192

Macroscopic examination Gibbs Thomson b) 1104 724 450 435 298 250 226 165 121 96 79

at which relative turbidity is 2.82 x 10 26.91, lfl(Ae) 2.14. at which relative turbidity is 1.57x 10 52.09, ln(A~) 2.13.

14

~.

PSD

3070 3165 2460 1670 973 600

‘~

Exp.

Gibbs Thomson d)

9900

104708 46190 18393 17237 8310 5880 4859 2631 1450 916 637

2520 1560 960 600

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Nucleation of calcium oxalate monohydrate

Table 3 Nucleation times ‘r (in minutes) for a series of relative supersaturations over a range of shaker settings; for each shaker setting, parameters denved by linear regression are given

RSI

Initial concentration

[Cal, [C

204]

Shaker setting 0

3

6

9

12

15

18

M)

(~i

475 525 575 625 Linear slope, B 2 Regression intercept, ln(A~) R

Note: Observation interval is 2

20.31 24.06 28.01 32.13

42 26 16 10 52.09 0.99 2.13

34 20 12 9 48.91 1.00 1.90

28 18 12 8 45.55 0.99 1.66

27 17 11 7 48.98 0.99 2.06

24 16 10 6 50.22 0.97 2.29

19 11 7 5

49.21 1.00 2.48

16 10 7 5

42.38 1.00 1.89

mm.

association between mechanical energy input and

Their observed quantity was degree of “under-

apparent interfacial energy (see fig. 1). Table 3 includes the lag-times as a function of shaker speed and RSI, as well as the statistical parameters. The slope, y-intercept, and correlation coefficient (R2) are given for each linear least-squares fit of ln(1/T) to ln 2(RSI). Note that there is no monotonic relationship between these slopes and shaker speed indicating some effect of shaker speed on the exponential factor in the Gibbs Thomsen equation. We observed that the shaker setting (SS) was linearly correlated with cycles per minute (CPM) the shaker bath speed over the range of settings used in the experiments according to the relation:

cooling” before precipitation, as achieved by cooling solutions at a constant rate and recording the temperature at which particle scattering was first observed. Their observed biphasic response was interpreted as a superposition of the effects of reduction of diffusion barrier and increase of attrition secondary to mechanical impact.

CPM

{

16.63 SS ± 78.91, 2< SS < 20 0, Stroke displacement of the shaker was 2.94 cm. The response to degree of agitation found in this study is similar to that reported by Mullin and Raven [6] in which they studied the relationship between nucleation and mechanical agitation. Table 4 Effect of urine in macroscopic nucleation system (shaker set ting 9, temperature 37°C) Slope, B

Intercept, ln(A~)

3.6. Effects of additives

All of the above data were obtained for buffered solutions of calcium and oxalate ions in the absence of agents that are known to modulate COM crystallization. To gauge the impact of such agents as methylene blue or various urine samples, we conducted the following series of experiments. Methylene blue has been investigated as an inhibitor of COM growth both in vivo and in vitro [21 23]. In vitro experiments showed that methylene blue retardant of COM encrustation on synthetic polymers and growth. However, in the nucleation systems used in our work, we found methylene blue to have no discernable effect. We used four types of urine as additives in macroscopic nucleation experiments: unfiltered human urine (5% V/V); filtered human urine (5% V/V); filtered urine of normal rats (5% V/V), and filtered urine of rats receiving gentamycin (5%

2.01+0.22

V/V). Table 4 summarizes the results with all but the unfiltered human urine for which the effects

45.73+ 1.35

3.41 + 0.20 2.63+0.15

53.41 + 1.96

1.40+ 0.22

Control Human urine

49.27+1.44 40.89 + 1.76

Normal rat urine Gentamycin rat urine

_____________________________________________

were not found to differ from those values with filtered human urine in our experimental system. .

.

.

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Nucleation of cak ium oxalate monohydrate

463

The tabulations suggest that the urine of normal humans and normal rats reduces A and increases B with respect to control systems. In contrast, the urine of rats receiving gentamycin exhibited increased Ac and decreased B values,

hydrate [25], we produced graphs of ln(1/t) versus ln 2(RSI) and obtained slopes greater than four times those found in this work. Together, these observations give us reasonable confidence that the formation and accumulation of other hydrates was not a significant factor in these studies.

4. Conclusions

the nucleation event both in time and in size would, of course, be highly desirable. Nevertheless, the use of lag-times to investigate nucleation can be appropriately discriminating for characterizing nucleation phenomena and for defining the action of agents accelerating or retarding nucleation. For example, we note the failure of methylene blue to have any significant effect on nucleation of COM. This suggests that the action of other agents as nucleation promoters or inhibitors can be both qualitatively and quantitatively assessed.

In closing, any observation technique closer to

Any study of crystal nuclei formation in aqueous solution necessarily depends on the method of observation as well as the interpretation of data involving the convolution of nucleation, growth and aggregation. For our present analysis, we worked under conditions minimizing aggregation processes. For example, we limited our observations to very early times in crystallization, and we minimized shear through avoiding the use of an internal stirring device. We found that our experimental observations are interpretable by use of the Gibbs Thomson equation, and we were successful in applying an empirically calibrated simulation to investigate the reasonableness of our experimental approach. Because such calibrations were em pirical, some may regard the reasoning as a bit circular; nonetheless, the correspondence between empirical and computed macroscopic and microscopic lag-times, the correspondence between empirical and computed turbidity, and the correspondence between experiment and simulations to compute surface energy all attest to the basic suitability of our approach for calcium oxalate

monohydrate nucleation. In this report, we have not considered the formation of other hydrates of calcium oxalate. Although the trihydrate has been found to play a

role in the nucleation of calcium oxalate monohydrate, we saw no evidence of trihydrate formation under our experimental conditions. Indeed, using the light microscope, we found that COM in our experiments had the characteristic morphology of the monohydrate. The conversion of tnhydrate to monohydrate takes longer than the five-hour limit of our experiments [24], suggesting that any appreciable amount of trihydrate should have been observed. We cannot, however, rule out the formation of a small amount of trihydrate. Using Gardner’s lag-time data for the nucleation of tn-

References [1] GW Drach, S Thorson and A, Randolph, Trans. Am. Assoc. Genitourin. Surg. 71(1979) 62. [2] W.G. Robertson and D.S. Scurr, J. Urol. 135 (1986) 1322. [3] A.L. Rodgers and J. Garside, Invest. Urol. 18 (1981) 484.

14]

J. Garside, L.J. Brecevic and J.W. Mullin, J. Crystal

Growth 57 (1982) 233. [5] J. Garside, in: Biological Mineralization and Deminerali-

zation, Ed. G. Nancollas (Spnnger, Berlin, 1982). [6) J.W. Mullin and K.D. Raven, Nature 194 (1962) 35. [7] J.A. Christiansen and A.E. Nielsen, Acta Chem. Scand. 5 (1951) 673. [8] AG. Walton, The Formation and Properties of Precipitales (Kreiger, Huntington, NY, 1979) p. 5. [9] P. Werness, C. Brown, L. Smith and B. Finlayson, J. Urol. 134 (1985) 1242. [10] B. Fmnlayson, Kidney Intern. 13 (1978) 353. [11] G.L. Gardner, J. Phys. Chem. 82 (1978) 864. [12] Y. Nakagawa. H.C. Margolis, S. Yokoyama, F J. Kezdy and E. Thomas, J. Biol. Chem. 256 (1981) 3936. [13] ME. Sheehan and G.H. Nancollas, Invest. Urol. 17 (1980)

446. [14] J.L. Meyer and L.H. Smith, Invest. Urol. 13 (1975) 31. [15] B. Tomazic and G.H. Nancollas, J. Colloid Interface Sci. 75 (1980) 149.

[16] C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961). [17] A. Linksz, Physiology of the Eye, Vol. 2, Vision (Grune and Stratton, New York, 1952). [18] A.G. Walton, The Formation and Properties of Precipi tates (Kreiger, Huntington, NY, 1979) p. 30.

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C. M. Brown et a!.

/ Nucleation of calcium

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oxa!ate monohydrate

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