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Surface effects in the crystal growth of calcium oxalate monohydrate
Surface Effects in the Crystal Growth of Calcium Oxalate Monohydrate R.
P.
SINGH, S. S. G A U R , D. J. WHITE, 1 AND G. H. N A N C O L L A S Chemistry Department, State University of New York, Buffalo, New York, 14214
Received January 12, 1987;accepted March 23, 1987 The rates of growth of calcium oxalate monohydrate crystals have been measured under conditions of constant supersaturation overa range of concentrations and in the presence of an inhibitor, N,N,N',N'ethylenediaminetetra(methylene phosphonic) acid ENTMP. Changes in the measured specific surface area during the growthreactionsare consistent with the observedmorphologiesofthe developingcrystals. Well-aged seed crystals undergo a rapid crystal lattice perfection during the initial stages of the reaction which is accompanied by a marked decrease in specific surface area. Initial rates of crystallization are therefore markedly dependent upon the surface properties of the seed crystals. These results emphasize the importance of using well-developed pregrown crystal surfaces in designing experimental studies of the characterization of the mechanism of crystal growth. This is especially important when comparing the influence of adsorbinginhibitor moleculeson the crystalgrowthreactions. The adsorption of ENTMP at the crystal surfaces has been investigated by equilibrium and electrophoretic mobility measurements. © 1987 Academic Press, Inc.
INTRODUCTION The relatively high concentration of calcium ions in biological systems and in the environment has resulted in an increasing interest in the almost ubiquitous precipitation of sparingly soluble calcium salts. In biological mineralization (1) and in industrial scale formation (2), these involve the oxalates, phosphates, carbonates, and sulfates. Elucidation of the mechanism of precipitation presents a considerable challenge for the physical chemist. In biological mineralization, minute crystallites are frequently observed in urines of both normal and stone-forming subjects (3). However, the reasons for the retention of crystals in the kidneys of stone formers and their development to macroscopic size have not yet been explained. Here, there is little doubt that in an environment where supersaturation fluctuates with time (4), it is necessary to take into account growth, aggregation, and secondary nucleation as well as changes in the morphology of the developing crystals. 1Present address:Procter& Gamble Co., SharonWoods Technical Center, Cincinnati, OH 45241.
In most experimental studies aimed at the determination of the mechanisms of crystal growth, the reactions are induced by the addition of aged seed crystals. The rates are monitored by following the decrease in lattice ion concentrations. Where a weak acid anion is involved, the changes in pH have also been used to calculate reaction rates. Uncertainties in the variation of rate with supersaturation have led m a n y workers to base their conclusions entirely on initial rates of crystallization. However, in the present work, it is shown that aged seed crystals of calcium oxalate monohydrate (COM) undergo a rapid initial growth process which is followed by a slower but constant rate of crystallization when the reactions are carded out at sustained supersaturation. Moreover, when these pregrown crystals are used to inoculate metastable supersaturated solutions, no such initial growth surge is observed. These results on COM and in m a n y other sparingly soluble crystallization experiments suggest that meaningful conclusions regarding the mechanism of crystallization cannot be made simply on the basis of initial crystaUization measurements.
379 0021-9797/87 $3.00 Copyright @ 1987 by Academic Press, Inc. All fights of reproduction in any form reserved. Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
380
SINGH ET AL.
In the constant composition (CC) method used in the present work (5-7), following the addition of seed crystals to metastable supersaturated solutions, the activities of the crystal lattice ions were maintained constant by the simultaneous addition of titrant solutions from mechanically coupled burets. In this way, relatively large extents of crystallization can be achieved, even at very low supersaturations, as well as in the presence of inhibitors which may also be introduced in the titrant solutions in order to compensate for dilution effects. Since, as discussed above, conventional crystallization experiments provide an insufficient extent of reaction to achieve crystal perfection, the CC method has been used to investigate the influence of surface properties of COM crystals on the growth reaction.
metastable COM-supersaturated solutions (total molar concentrations, Tca= Tox = 4.5 X 10 -4 mole liter -1 in 0.15 mole liter-~ sodium chloride, a = 1.257, at 37°C). Seed crystals were examined by scanning electron microscopy (ISI Model II) and X-ray powder diffraction (Cu K~ radiation, Phillips X R G 3000 diffractometer) confirmed the monohydrate as the only phase present in both preparations. Specific surface areas (SSA) of the crystals were measured using single-point nitrogen adsorption (30% nitrogen, 70% helium, Quantasorb II, Quantachrome). Particle size distributions were determined using an Electrozone celloscope (Model III LTS CD/ADC, Particle Data Inc.). Specific surface areas and mean particle diameters were 3.05 + 0.09 m 2 g-1 and 4.4 _+ 1.3/~m for aged and 1.42 + 0.1 m 2 g-i and 4.1 + 2.5 #m for pregrown crystals. Crystallization experiments were made in EXPERIMENTAL metastable supersaturated solutions in magSolutions of calcium chloride, potassium netically stirred Pyrex double-walled reaction oxalate, sodium chloride, and potassium hy- vessels maintained at 37 + 0.1°C. Nitrogen droxide were prepared from reagent-grade gas, saturated at 37°C with respect to back(J. T. Baker Co.) chemicals, using triply dis- ground electrolyte (0.15 mole liter -1 sodium tilled deionized water which was filtered before chloride), was bubbled continuously through use (0.22-#m Millipore filters). The filters were the cell solution during the experiments to exprewashed in order to remove any residual clude carbon dioxide. The pH of the reactant wetting agents and surfactants. N,N,N',N'- solutions was monitored with a glass electrode ethylenediamenetetra(methylene phospho- (Corning 476024) and the calcium ion activnate), ENTMP, was donated by Monsanto ities in the supersaturated solutions were meaChemical Co. Analysis of this anion was made sured using a specific ion electrode (Radiusing a UV-catalyzed oxidation method (Hach ometer Model F2112). The common reference Co., P.O. Box 389, Loveland, CO 80539). So- electrode was a thermal electrolytic silver/sillutions were analyzed for cations by passing ver chloride probe immersed in 4 mole liter-1 aliquots through an ion exchange resin potassium chloride solution saturated with re(Dowex 50) in hydrogen form and titrating spect to silver chloride and separated from the the eluted acid with standardized potassium cell solution by means of a 0.15 mole liter-~ hydroxide. Calcium ion was also analyzed by sodium chloride salt bridge in order to avoid atomic absorption (Perkin-Elmer Model 503) changes in liquid junction potential. In the preparation of the supersaturated soand oxalate was determined by ion chromalutions, the calcium ion electrode was used to tography (8) (Dionex Q.I.C. analyzer). Crystals of COM, prepared by mixing 0.05 measure the free ion activity. The desired inimole liter-1 solutions of calcium chloride and tial supersaturation was achieved by the adpotassium oxalate at 70°C, were aged for at dition of solutions containing calcium chloleast 1 month before use (9). The pregrown ride, potassium oxalate, and sodium chloride. seed was prepared using the constant com- Following the addition of calcium oxalate position method by growing aged seeds in monohydrate seed crystals (usually 5-6 X 10 -3 Journal of Colloid and l~tdrface Science, Vol. 118, No. 2, August 1987
381
SURFACE EFFECTS IN CRYSTAL G R O W T H
g cm-3), titrant solutions containing calcium and oxalate ions at the required ionic strength (0.15 mole liter -l in sodium chloride) were added from mechanically coupled burets and controlled by means of a potentiostat (Metrohm Combititrator 3D, Brinkmann Instrument Co.). Titrants were prepared such that the total concentrations of calcium, oxalate, and sodium chloride were maintained constant during the reactions. Growth rates were calculated from the recorded titrant volume as a function of time. During the crystallization experiments, aliquots of reaction mixture were periodically filtered (0.22-#m Millipore filter) and the filtrate was analyzed for calcium and oxalate. Solid phases were characterized by X-ray powder diffraction, particle size distribution, SSA, zeta potential, and scanning electron microscopy. The determination of electrophoretic mobility (zeta potential) was made using a Rank M K II microelectrophoresis apparatus with a thin-walled, four-electrode cylindrical cell and platinum black electrodes. The suspensions were first ultrasonicated for 3 min and brought to the desired temperature (37°C). The velocities of COM particles were measured in 0.15 mole liter-i sodium chloride at both stationary levels in the capillary (10). At each depth, at least 20 particles were timed for each direction of the applied field. The coefficient of variation of the electrophoretic mobilities was less than 10%. Zeta potentials were calculated using the relationships of Wiersema et al. (11).
The rate of crystallization of COM has been shown (7) to be considerably less than that to be expected for bulk diffusion, indicating a surface-controlled reaction following the rate equation Rate = Rg = kgstr n. [1] In Eq. [ 1], kg is the rate constant, s is a function of the available growth surface area, and n is the effective order of the growth reaction. The relative supersaturation a is given by ( r / t o ) °'5 - 1 in which 7r is the ionic product (Ca2+)(C2042-) and 7r0 is the value at equilibrium (2.29 × 10 -9 mole liter -i) (15). Typical constant composition growth curves on well-aged seed crystals at different a values are shown in Fig. l in which the volume of titrant is plotted against time. The curves are characterized by a brief initial rapid growth surge followed by a decreased but constant growth rate. As can be seen in Table I, the dependence of initial growth surges, Ri, on a is striking. Differences between Ri and the subsequent (constant) growth rates, Rg, represented by the slopes of the linear portions of the growth curves in Fig. I were more than 50% at the lowest supersaturation and decreased continuously with increasing a until at a = 1.4 the difference was <10%. In all experiments, linear growth plots in Fig. 1 were
10 ~E Z [Z
RESULTS AND DISCUSSION
The activities of ionic species in the supersaturated solutions were calculated from mass balance and electroneutrality expressions as described previously by taking into account the formation of CAC204 and NaC204 ion pairs having association constants 1890 and 13.2 liters mole -1, respectively ( 12, 13). Ionic activity coefficients were calculated from the extended form of the Debye-Huckel equation proposed by Davies (14).
O >
O, 0
•
,
10
•
,
•
:
20 90 TIME / min
:
:
40
:
50
FIG. 1. Crystal growth of COM. Plots oftitrant volume against time. Titrant concentrations, Tc~ = Tox = 4.0 X 10 .3 mole liter -1 in 0.15 mole liter -~ NaC1. Aged seed, exps. 101A ([2]), 113A ( ), 109A (X). Pregrown seed, exps. 42P (O), 101P ( ) , 86P (0). Journal of Colloid and InterfaceScience, Vol. 118,No. 2, August1987
382
SINGH ET AL. TABLE 1 CC Crystal Growth of COM (37°C,
Exp. No.
Tca = Tc204 ,
Ionic Strength = 0.15 (NaC1))
Tca ( l 0-4 mole liter- 1)
a
Seed (mg)
Ri ( 10-~ mole min-J m-2)
R~ ( 10.2 mole min- i m -2)
Percentage reduction in P~
109 113 101 111 96
Aa A A A P"
3.50 3.80 4.00 4.50 3.00
0.775 0.921 1.017 1.257 0.531
5.7 5.7 5.7 5.7 5.0
6.7 8.9 9.5 b 11.4 1.1 c
3.3 5.2 7.0 b 10.4 1.1 c
50.7 41.6 26.3 8.8 0.0
86 88 101 42
P P P P
3.25 3.80 4.00 4.50
0.653 0.921 1.017 1.257
5.0 5.0 5.0 5.0
1.7 4.0 4.8 8.0
1.7 4.0 4.8 8.0
0.0 0.0 0.0 0.0
a A = aged, P = p r e g r o w n . b 101A: Ri = (9.4 _+ 0.60) × 10 -5, C V = 6.4%. Six d e t e r m i n a t i o n s . Rg = (7.0 + 0.29) × 10 -5, C V = 4.1%. Six determinations. c 9 6 P : R~ = Rg = (1.12 _ 0.05) × 10 -5, C V = 4.7%. F i v e d e t e r m i n a t i o n s .
generally obtained after about 30% of growth (G) with respect to the initial seed mass. Here, = 102(m - mo)/mo where m0 and m are the masses of crystals in the supersaturated solutions initially and at time t. The observed marked decrease in rate of crystallization after brief rapid periods may be attributed either to a reduction in crystal surface area due to agglomeration or aggregation, or to the annealing of the crystal surfaces. The first possibility was ruled out by the results of particle size measurements, summarized in Table II, which shows that the number of par-
ticles did not change during the crystallization experiments. SSA of the crystals grown at two supersaturations are shown in Fig. 2. It can be seen that the specific surface area of the seed crystals decreased dramatically (by approx. 40%) during the brief initial surges. Moreover, the reductions in specific surface area were considerably greater than the value of 8-10% expected for the 30-35% growth during these periods. The results therefore point to an initial annealing process. When well-aged crystals are added to metastable supersaturated solutions, the most rapid crystal growth should take place
TABLE II Particle Density during CC Experiments 242 (a = 0.831) and 244 (a = 1.056). Exp. No.
G (%)
Particle density (104 cm 3)
244 244 244 244 244 242 242 242 242 242
0.0 18.7 56.2 93.6 168.9 0.0 9.7 48.4 87.5 145.3
2.8 2.4 2.5 2.6 2.9 2.7 2.7 2.6 2.7 2.7
Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
'~0") ~E \
A
1t 0
510
I 100
i
I
150
200
FIG. 2. Plots o f specific surface a r e a as a f u n c t i o n o f g r o w t h extent for a g e d seed. a = 1.056 (O) a n d cr = 0.55
(m).
383
SURFACE EFFECTS IN CRYSTAL GROWTH
FIG. 3. Scanning electron micrographs of (a) aged (×6000) and (b) pregrown (×3000) COM crystals.
Journal of Colloid and Interface Science,
Vol. 118,No. 2, August1987
384
SINGH ET AL.
on the faces with the greatest number of kinks and steps. However, it is unlikely that large numbers of kinks would persist since scanning electron micrographs (Fig. 3) reveal that the seed crystals rapidly perfected their lattices in the initial stages of seeded growth. It is significant that when seed crystals removed from the reaction vessel after the initial surges were reintroduced into metastable supersaturated solutions of calcium oxalate, no initial rapid periods were observed. The rates of crystal growth, as shown in Table III, were close to those measured at the time of initial harvesting from the growth medium. The results of these studies clearly point to the importance of using well-perfected pregrown seeds which do not show a surge in the growth curves (Fig. 1 and Table I). It is interesting to compare the values of n in Eq. [ 1] which describe the growth of the aged seed crystals (the initial surge) and those of the pregrown material. The logarithmic plots in Fig. 4 confirm the second-order growth of the pregrown seed, indicating a surface-controlled mechanism. For the growth rate of the aged crystals, however, n is initially about 1 as can be seen in Fig. 4 and reaches a constant value of 2 after about 30% of growth. The overall reaction, therefore, appears to involve a change in mechanism of the aged crystals as the lattice is perfected. The differences in Fig. 4 could also be interpreted in terms of the s parameter in Eq. [ 1] at constant supersaturation. The influence of ENTMP is shown in Fig. 5. It can be seen that the additive is considerably more effective in reducing the rate of growth of pregrown as compared with aged seed. The rate of retardation may be interpreted in terms of a simple Langmuir model (16, 17) following
4°8-
~4.5CD
2 I 4.2.
3.9
, 4.2
: 4.4 - l 09
,
I 4.6
(W1/2-1~/2)
FIG. 4. Logarithmic plots of Eq. [1]. Aged seed (a), initial rates; ([3) rates at G ~ 30. Pregrown seed (O).
Ro/(Ro - R ' ) = (1 - b) -I + [K(1 - b)C] -1. [2] In Eq. [2], Ro and R' are the rates of crystallization in the absence and presence of inhibitor, respectively, bRo is the limiting rate in the presence of high concentrations of inhibitor (1 < b < 0), K is the adsorption affinity, and C is the concentration of ENTMP (18). The value of b, calculated from the intercept of the linear plots ofRo/(Ro - R') against [C] -1, is a measure of the effectiveness of the inhibitor when present at "infinite" concentration, at monolayer coverage, or its capability of completely inhibiting the growth at a concentration level below that required for monolayer coverage (18). Although ENTMP also complexes the calcium ion in solution (19), the low levels
0 25 I
.25 ,
t
ENTNP/ID-6 .5 t
tool ~] ,
.75 ,
"75
20-
%
1013
15-
~=
•
.5o ~.
10-
TABLE III r~"
Regrowth of COM Crystals Exp. No.
a
O (%)
Rs (10-4 mole min -l mg-')
R s (regrowth) (10 -4 mole min -t mg-')
282 283
1.30 1.06
86 27
1.35 2.05
1.37 2.26
Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
c~.
"25
0
.
25
50 75 ENTMP/IO8 too| t'1
*~
0
IO0
FIG. 5. Plots of P ( @ ) and (Ro - R')IRo in the presence of ENTMP. (I) pregrown and (~,) aged seed crystals.
385
SURFACE EFFECTS IN CRYSTAL GROWTH
of concentration in these studies would have little influence upon the values of a. Values of K from the linear plots of R o / ( R o - R') as a function of [C] -1 (Fig. 6) were 6 X l06 and 11.2 X l 0 6 liters mole -1 for aged and pregrown crystals, respectively. E N T M P was therefore almost twice as effective in inhibiting the growth of pregrown seed crystals, again suggesting that the initial annealing process eliminated active growth sites on the crystal surfaces during lattice perfection. The equilibrium adsorption of E N T M P (I?) is plotted as a function of additive concentration in Fig. 5. Although experiments showed that the uptake of E N T M P was completed in 10 min, a 24-h reaction time was used to ensure adsorption equilibrium. The initial plateau at an additive concentration of 0.2 X 10 -6 mole liter -1 is quite striking and, as can be seen in Fig. 7, is also reflected in the measured zeta potentials. In the crystallization experiments, the rate is reduced by about 90% at an E N T M P concentration of 0.8 X 10 -6 mole liter-L Assuming that the maximum area covered by an E N T M P molecule is 44 X 10 2o m 2 (20), the first plateau in Fig. 5 corresponds to about 7% coverage of the available crystal surface. The observed, almost complete inhibition of growth under these conditions suggests that crystallization proceeds through the development of a relatively small number of active growth sites. Similar conclusions were reached for other phosphonates during the
3-
o
2
0 0
I 4 [ENTMp'I
I 8 /
10 6 L m o l
ll2
115
1
FIG. 6. Langmuir plots (Eq. [2]) for aged (e) and pregrown (U]) seeds.
1B
\~ i15t
~2
14
13-113 .n
.25
.50 E N T M P / I O -6
.7~5 tool L-I
1. O0
FIG. 7. Plots of zeta potential of COM (aged) seed crystals in the presence of ENTMP.
growth of barium sulfate (21) and gypsum (22, 23). The results are in accordance with the parabolic kinetic equation of Burton et al. (24), in which growth takes place on active sites at dislocations on the crystal surfaces. The observed decrease in growth rate of the aged crystals therefore reflects a reduced growth site density, despite the fact that simple three-dimensional crystal growth with a concomitant increase in surface area would predict (e.g., in exp. 109, Fig. 1) an increase in growth rate from 2 3 X 10 -5 at G = 25 to 47 X 10 5 a t G = 250. In contrast, the experimental rates of crystallization decreased from 8 × 10 -5 to 2.9 X 10 -5 mole min - l m g -1 during the same growth period. In conclusion, it has been shown that the aging of crystals through slow dissolution/reprecipitation processes may be an inappropriate preparative technique for preparing surfaces for studying subsequent crystallization reactions in metastable supersaturated solutions. It is preferable to use pregrown (perfected) crystallites, especially for the investigation of the influence of growth inhibitors. Moreover, the rates of crystallization of the pregrown crystallites follow a rate law second order in relative supersaturation, suggesting a spiral growth mechanism with a relatively constant number of growth sites or spirals during growth. Aged COM crystals may be used only when the experiments are made at constant supersaturations so that reactions can be extended beyond the initial surges. Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
386
SINGH ET AL. ACKNOWLEDGMENTS
11. Wiersema, P. H., Loeb, A. L., and Overbeek, J. Th. G., J. Colloid Interface Sci. 22, 78 (1966). 12. Tomazic, B., and Nancollas, G. H., J. Cryst. Growth 46, 355 (1979). 13. Nancollas, G. H., "Interactions in Electrolyte Solutions." Elsevier, Amsterdam, 1966. REFERENCES 14. Davies, C. W., "Ion Association." Butterworths, Lon1. Nancollas, G. H., "Biological Mineralization and Dedon, 1962. mineralization." Springer-Verlag, Berlin, 1982. 15. White, D. J., and Nancollas, G. H., J. Cryst. Growth 2. van Rosmalen, G. M., Ph.D. thesis, Delft Univ. Press. 57, 267 (1982). 3. Werness, P. G., Bergert, J. H., and Smith, L. H., J. 16. Langmuir, J., J. Amer. Chem. Soc. 38, 2221 (1916). Cryst. Growth 53, 166 (1981). 17. Davies, C. W., and Nancollas, G. H., Trans. Faraday 4. Vahlensieck, E. W., Bach, D., and Hesse, A., Urol. Soc. 51, 818 (1955). Res. 10, 195 (1982). 18. Nancollas, G. H., and Zawacki, S. J., in "Industrial 5. Tomson, M. B., and Nancollas, G. H., Science 200, Crystallization '84" (S. J. Jancic and E. J. de Jong, 1059 (1978). Eds.). Elsevier, Amsterdam, 1984. 6. Koutsoukos, P., Arnjad, Z., Tomson, M. B., and 19. Westerback, S., Rajan, K. S., and Martell, A. E., J. Nancollas, G. H., J. Amer. Chem. Soc. 102, 1553 Amer. Chem. Soc. 87, 2567 (1965). (1980). 20. Meyer, J. L., and Nancollas, G. H., Calc. Tissue. Res. 7. Sheehan, M. E., and Nancollas, G. H., Invest. Urol. 13, 295 (1973). 17, 446 (1980). 21. Leung, W. H., and Nancollas, G. H., J. Cryst. Growth 8. Singh, R. P., and Nancollas, G. H., Anal. Lett. 19, 44, 163 (1978). 1487 (1986). 22. Weijnen, M. P. C., Marchee, W. G. T., and van Ros9. Nancollas, G. H., and Gardner, G. L., J. Cryst. Growth malen, G. M., Desalination 47, 81 (1983). 21, 267 (1974). 23. Gill, J. S., and Nancollas, G. H., Corrosion 37, 120 10. Overbeek, J. Th. G., in "Colloid Science" (H. R. (1981). Kruyt, Ed.), Vol. 1, p. 219. Elsevier, Amsterdam, 24. Burton, W. K., Cabrera, N., and Frank, F. C., Philos. 1952. Trans. A 243, 299 (1951). We thank the National Institute of Arthritis, Diabetes, Digestive and Kidney Diseases for a grant (AM19048) in support of this work and Dr. J. Budz for helpful discussions.
Journal of ColloidandInterfaceScience, Vol.118,No. 2, August1987
P.
SINGH, S. S. G A U R , D. J. WHITE, 1 AND G. H. N A N C O L L A S Chemistry Department, State University of New York, Buffalo, New York, 14214
Received January 12, 1987;accepted March 23, 1987 The rates of growth of calcium oxalate monohydrate crystals have been measured under conditions of constant supersaturation overa range of concentrations and in the presence of an inhibitor, N,N,N',N'ethylenediaminetetra(methylene phosphonic) acid ENTMP. Changes in the measured specific surface area during the growthreactionsare consistent with the observedmorphologiesofthe developingcrystals. Well-aged seed crystals undergo a rapid crystal lattice perfection during the initial stages of the reaction which is accompanied by a marked decrease in specific surface area. Initial rates of crystallization are therefore markedly dependent upon the surface properties of the seed crystals. These results emphasize the importance of using well-developed pregrown crystal surfaces in designing experimental studies of the characterization of the mechanism of crystal growth. This is especially important when comparing the influence of adsorbinginhibitor moleculeson the crystalgrowthreactions. The adsorption of ENTMP at the crystal surfaces has been investigated by equilibrium and electrophoretic mobility measurements. © 1987 Academic Press, Inc.
INTRODUCTION The relatively high concentration of calcium ions in biological systems and in the environment has resulted in an increasing interest in the almost ubiquitous precipitation of sparingly soluble calcium salts. In biological mineralization (1) and in industrial scale formation (2), these involve the oxalates, phosphates, carbonates, and sulfates. Elucidation of the mechanism of precipitation presents a considerable challenge for the physical chemist. In biological mineralization, minute crystallites are frequently observed in urines of both normal and stone-forming subjects (3). However, the reasons for the retention of crystals in the kidneys of stone formers and their development to macroscopic size have not yet been explained. Here, there is little doubt that in an environment where supersaturation fluctuates with time (4), it is necessary to take into account growth, aggregation, and secondary nucleation as well as changes in the morphology of the developing crystals. 1Present address:Procter& Gamble Co., SharonWoods Technical Center, Cincinnati, OH 45241.
In most experimental studies aimed at the determination of the mechanisms of crystal growth, the reactions are induced by the addition of aged seed crystals. The rates are monitored by following the decrease in lattice ion concentrations. Where a weak acid anion is involved, the changes in pH have also been used to calculate reaction rates. Uncertainties in the variation of rate with supersaturation have led m a n y workers to base their conclusions entirely on initial rates of crystallization. However, in the present work, it is shown that aged seed crystals of calcium oxalate monohydrate (COM) undergo a rapid initial growth process which is followed by a slower but constant rate of crystallization when the reactions are carded out at sustained supersaturation. Moreover, when these pregrown crystals are used to inoculate metastable supersaturated solutions, no such initial growth surge is observed. These results on COM and in m a n y other sparingly soluble crystallization experiments suggest that meaningful conclusions regarding the mechanism of crystallization cannot be made simply on the basis of initial crystaUization measurements.
379 0021-9797/87 $3.00 Copyright @ 1987 by Academic Press, Inc. All fights of reproduction in any form reserved. Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
380
SINGH ET AL.
In the constant composition (CC) method used in the present work (5-7), following the addition of seed crystals to metastable supersaturated solutions, the activities of the crystal lattice ions were maintained constant by the simultaneous addition of titrant solutions from mechanically coupled burets. In this way, relatively large extents of crystallization can be achieved, even at very low supersaturations, as well as in the presence of inhibitors which may also be introduced in the titrant solutions in order to compensate for dilution effects. Since, as discussed above, conventional crystallization experiments provide an insufficient extent of reaction to achieve crystal perfection, the CC method has been used to investigate the influence of surface properties of COM crystals on the growth reaction.
metastable COM-supersaturated solutions (total molar concentrations, Tca= Tox = 4.5 X 10 -4 mole liter -1 in 0.15 mole liter-~ sodium chloride, a = 1.257, at 37°C). Seed crystals were examined by scanning electron microscopy (ISI Model II) and X-ray powder diffraction (Cu K~ radiation, Phillips X R G 3000 diffractometer) confirmed the monohydrate as the only phase present in both preparations. Specific surface areas (SSA) of the crystals were measured using single-point nitrogen adsorption (30% nitrogen, 70% helium, Quantasorb II, Quantachrome). Particle size distributions were determined using an Electrozone celloscope (Model III LTS CD/ADC, Particle Data Inc.). Specific surface areas and mean particle diameters were 3.05 + 0.09 m 2 g-1 and 4.4 _+ 1.3/~m for aged and 1.42 + 0.1 m 2 g-i and 4.1 + 2.5 #m for pregrown crystals. Crystallization experiments were made in EXPERIMENTAL metastable supersaturated solutions in magSolutions of calcium chloride, potassium netically stirred Pyrex double-walled reaction oxalate, sodium chloride, and potassium hy- vessels maintained at 37 + 0.1°C. Nitrogen droxide were prepared from reagent-grade gas, saturated at 37°C with respect to back(J. T. Baker Co.) chemicals, using triply dis- ground electrolyte (0.15 mole liter -1 sodium tilled deionized water which was filtered before chloride), was bubbled continuously through use (0.22-#m Millipore filters). The filters were the cell solution during the experiments to exprewashed in order to remove any residual clude carbon dioxide. The pH of the reactant wetting agents and surfactants. N,N,N',N'- solutions was monitored with a glass electrode ethylenediamenetetra(methylene phospho- (Corning 476024) and the calcium ion activnate), ENTMP, was donated by Monsanto ities in the supersaturated solutions were meaChemical Co. Analysis of this anion was made sured using a specific ion electrode (Radiusing a UV-catalyzed oxidation method (Hach ometer Model F2112). The common reference Co., P.O. Box 389, Loveland, CO 80539). So- electrode was a thermal electrolytic silver/sillutions were analyzed for cations by passing ver chloride probe immersed in 4 mole liter-1 aliquots through an ion exchange resin potassium chloride solution saturated with re(Dowex 50) in hydrogen form and titrating spect to silver chloride and separated from the the eluted acid with standardized potassium cell solution by means of a 0.15 mole liter-~ hydroxide. Calcium ion was also analyzed by sodium chloride salt bridge in order to avoid atomic absorption (Perkin-Elmer Model 503) changes in liquid junction potential. In the preparation of the supersaturated soand oxalate was determined by ion chromalutions, the calcium ion electrode was used to tography (8) (Dionex Q.I.C. analyzer). Crystals of COM, prepared by mixing 0.05 measure the free ion activity. The desired inimole liter-1 solutions of calcium chloride and tial supersaturation was achieved by the adpotassium oxalate at 70°C, were aged for at dition of solutions containing calcium chloleast 1 month before use (9). The pregrown ride, potassium oxalate, and sodium chloride. seed was prepared using the constant com- Following the addition of calcium oxalate position method by growing aged seeds in monohydrate seed crystals (usually 5-6 X 10 -3 Journal of Colloid and l~tdrface Science, Vol. 118, No. 2, August 1987
381
SURFACE EFFECTS IN CRYSTAL G R O W T H
g cm-3), titrant solutions containing calcium and oxalate ions at the required ionic strength (0.15 mole liter -l in sodium chloride) were added from mechanically coupled burets and controlled by means of a potentiostat (Metrohm Combititrator 3D, Brinkmann Instrument Co.). Titrants were prepared such that the total concentrations of calcium, oxalate, and sodium chloride were maintained constant during the reactions. Growth rates were calculated from the recorded titrant volume as a function of time. During the crystallization experiments, aliquots of reaction mixture were periodically filtered (0.22-#m Millipore filter) and the filtrate was analyzed for calcium and oxalate. Solid phases were characterized by X-ray powder diffraction, particle size distribution, SSA, zeta potential, and scanning electron microscopy. The determination of electrophoretic mobility (zeta potential) was made using a Rank M K II microelectrophoresis apparatus with a thin-walled, four-electrode cylindrical cell and platinum black electrodes. The suspensions were first ultrasonicated for 3 min and brought to the desired temperature (37°C). The velocities of COM particles were measured in 0.15 mole liter-i sodium chloride at both stationary levels in the capillary (10). At each depth, at least 20 particles were timed for each direction of the applied field. The coefficient of variation of the electrophoretic mobilities was less than 10%. Zeta potentials were calculated using the relationships of Wiersema et al. (11).
The rate of crystallization of COM has been shown (7) to be considerably less than that to be expected for bulk diffusion, indicating a surface-controlled reaction following the rate equation Rate = Rg = kgstr n. [1] In Eq. [ 1], kg is the rate constant, s is a function of the available growth surface area, and n is the effective order of the growth reaction. The relative supersaturation a is given by ( r / t o ) °'5 - 1 in which 7r is the ionic product (Ca2+)(C2042-) and 7r0 is the value at equilibrium (2.29 × 10 -9 mole liter -i) (15). Typical constant composition growth curves on well-aged seed crystals at different a values are shown in Fig. l in which the volume of titrant is plotted against time. The curves are characterized by a brief initial rapid growth surge followed by a decreased but constant growth rate. As can be seen in Table I, the dependence of initial growth surges, Ri, on a is striking. Differences between Ri and the subsequent (constant) growth rates, Rg, represented by the slopes of the linear portions of the growth curves in Fig. I were more than 50% at the lowest supersaturation and decreased continuously with increasing a until at a = 1.4 the difference was <10%. In all experiments, linear growth plots in Fig. 1 were
10 ~E Z [Z
RESULTS AND DISCUSSION
The activities of ionic species in the supersaturated solutions were calculated from mass balance and electroneutrality expressions as described previously by taking into account the formation of CAC204 and NaC204 ion pairs having association constants 1890 and 13.2 liters mole -1, respectively ( 12, 13). Ionic activity coefficients were calculated from the extended form of the Debye-Huckel equation proposed by Davies (14).
O >
O, 0
•
,
10
•
,
•
:
20 90 TIME / min
:
:
40
:
50
FIG. 1. Crystal growth of COM. Plots oftitrant volume against time. Titrant concentrations, Tc~ = Tox = 4.0 X 10 .3 mole liter -1 in 0.15 mole liter -~ NaC1. Aged seed, exps. 101A ([2]), 113A ( ), 109A (X). Pregrown seed, exps. 42P (O), 101P ( ) , 86P (0). Journal of Colloid and InterfaceScience, Vol. 118,No. 2, August1987
382
SINGH ET AL. TABLE 1 CC Crystal Growth of COM (37°C,
Exp. No.
Tca = Tc204 ,
Ionic Strength = 0.15 (NaC1))
Tca ( l 0-4 mole liter- 1)
a
Seed (mg)
Ri ( 10-~ mole min-J m-2)
R~ ( 10.2 mole min- i m -2)
Percentage reduction in P~
109 113 101 111 96
Aa A A A P"
3.50 3.80 4.00 4.50 3.00
0.775 0.921 1.017 1.257 0.531
5.7 5.7 5.7 5.7 5.0
6.7 8.9 9.5 b 11.4 1.1 c
3.3 5.2 7.0 b 10.4 1.1 c
50.7 41.6 26.3 8.8 0.0
86 88 101 42
P P P P
3.25 3.80 4.00 4.50
0.653 0.921 1.017 1.257
5.0 5.0 5.0 5.0
1.7 4.0 4.8 8.0
1.7 4.0 4.8 8.0
0.0 0.0 0.0 0.0
a A = aged, P = p r e g r o w n . b 101A: Ri = (9.4 _+ 0.60) × 10 -5, C V = 6.4%. Six d e t e r m i n a t i o n s . Rg = (7.0 + 0.29) × 10 -5, C V = 4.1%. Six determinations. c 9 6 P : R~ = Rg = (1.12 _ 0.05) × 10 -5, C V = 4.7%. F i v e d e t e r m i n a t i o n s .
generally obtained after about 30% of growth (G) with respect to the initial seed mass. Here, = 102(m - mo)/mo where m0 and m are the masses of crystals in the supersaturated solutions initially and at time t. The observed marked decrease in rate of crystallization after brief rapid periods may be attributed either to a reduction in crystal surface area due to agglomeration or aggregation, or to the annealing of the crystal surfaces. The first possibility was ruled out by the results of particle size measurements, summarized in Table II, which shows that the number of par-
ticles did not change during the crystallization experiments. SSA of the crystals grown at two supersaturations are shown in Fig. 2. It can be seen that the specific surface area of the seed crystals decreased dramatically (by approx. 40%) during the brief initial surges. Moreover, the reductions in specific surface area were considerably greater than the value of 8-10% expected for the 30-35% growth during these periods. The results therefore point to an initial annealing process. When well-aged crystals are added to metastable supersaturated solutions, the most rapid crystal growth should take place
TABLE II Particle Density during CC Experiments 242 (a = 0.831) and 244 (a = 1.056). Exp. No.
G (%)
Particle density (104 cm 3)
244 244 244 244 244 242 242 242 242 242
0.0 18.7 56.2 93.6 168.9 0.0 9.7 48.4 87.5 145.3
2.8 2.4 2.5 2.6 2.9 2.7 2.7 2.6 2.7 2.7
Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
'~0") ~E \
A
1t 0
510
I 100
i
I
150
200
FIG. 2. Plots o f specific surface a r e a as a f u n c t i o n o f g r o w t h extent for a g e d seed. a = 1.056 (O) a n d cr = 0.55
(m).
383
SURFACE EFFECTS IN CRYSTAL GROWTH
FIG. 3. Scanning electron micrographs of (a) aged (×6000) and (b) pregrown (×3000) COM crystals.
Journal of Colloid and Interface Science,
Vol. 118,No. 2, August1987
384
SINGH ET AL.
on the faces with the greatest number of kinks and steps. However, it is unlikely that large numbers of kinks would persist since scanning electron micrographs (Fig. 3) reveal that the seed crystals rapidly perfected their lattices in the initial stages of seeded growth. It is significant that when seed crystals removed from the reaction vessel after the initial surges were reintroduced into metastable supersaturated solutions of calcium oxalate, no initial rapid periods were observed. The rates of crystal growth, as shown in Table III, were close to those measured at the time of initial harvesting from the growth medium. The results of these studies clearly point to the importance of using well-perfected pregrown seeds which do not show a surge in the growth curves (Fig. 1 and Table I). It is interesting to compare the values of n in Eq. [ 1] which describe the growth of the aged seed crystals (the initial surge) and those of the pregrown material. The logarithmic plots in Fig. 4 confirm the second-order growth of the pregrown seed, indicating a surface-controlled mechanism. For the growth rate of the aged crystals, however, n is initially about 1 as can be seen in Fig. 4 and reaches a constant value of 2 after about 30% of growth. The overall reaction, therefore, appears to involve a change in mechanism of the aged crystals as the lattice is perfected. The differences in Fig. 4 could also be interpreted in terms of the s parameter in Eq. [ 1] at constant supersaturation. The influence of ENTMP is shown in Fig. 5. It can be seen that the additive is considerably more effective in reducing the rate of growth of pregrown as compared with aged seed. The rate of retardation may be interpreted in terms of a simple Langmuir model (16, 17) following
4°8-
~4.5CD
2 I 4.2.
3.9
, 4.2
: 4.4 - l 09
,
I 4.6
(W1/2-1~/2)
FIG. 4. Logarithmic plots of Eq. [1]. Aged seed (a), initial rates; ([3) rates at G ~ 30. Pregrown seed (O).
Ro/(Ro - R ' ) = (1 - b) -I + [K(1 - b)C] -1. [2] In Eq. [2], Ro and R' are the rates of crystallization in the absence and presence of inhibitor, respectively, bRo is the limiting rate in the presence of high concentrations of inhibitor (1 < b < 0), K is the adsorption affinity, and C is the concentration of ENTMP (18). The value of b, calculated from the intercept of the linear plots ofRo/(Ro - R') against [C] -1, is a measure of the effectiveness of the inhibitor when present at "infinite" concentration, at monolayer coverage, or its capability of completely inhibiting the growth at a concentration level below that required for monolayer coverage (18). Although ENTMP also complexes the calcium ion in solution (19), the low levels
0 25 I
.25 ,
t
ENTNP/ID-6 .5 t
tool ~] ,
.75 ,
"75
20-
%
1013
15-
~=
•
.5o ~.
10-
TABLE III r~"
Regrowth of COM Crystals Exp. No.
a
O (%)
Rs (10-4 mole min -l mg-')
R s (regrowth) (10 -4 mole min -t mg-')
282 283
1.30 1.06
86 27
1.35 2.05
1.37 2.26
Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
c~.
"25
0
.
25
50 75 ENTMP/IO8 too| t'1
*~
0
IO0
FIG. 5. Plots of P ( @ ) and (Ro - R')IRo in the presence of ENTMP. (I) pregrown and (~,) aged seed crystals.
385
SURFACE EFFECTS IN CRYSTAL GROWTH
of concentration in these studies would have little influence upon the values of a. Values of K from the linear plots of R o / ( R o - R') as a function of [C] -1 (Fig. 6) were 6 X l06 and 11.2 X l 0 6 liters mole -1 for aged and pregrown crystals, respectively. E N T M P was therefore almost twice as effective in inhibiting the growth of pregrown seed crystals, again suggesting that the initial annealing process eliminated active growth sites on the crystal surfaces during lattice perfection. The equilibrium adsorption of E N T M P (I?) is plotted as a function of additive concentration in Fig. 5. Although experiments showed that the uptake of E N T M P was completed in 10 min, a 24-h reaction time was used to ensure adsorption equilibrium. The initial plateau at an additive concentration of 0.2 X 10 -6 mole liter -1 is quite striking and, as can be seen in Fig. 7, is also reflected in the measured zeta potentials. In the crystallization experiments, the rate is reduced by about 90% at an E N T M P concentration of 0.8 X 10 -6 mole liter-L Assuming that the maximum area covered by an E N T M P molecule is 44 X 10 2o m 2 (20), the first plateau in Fig. 5 corresponds to about 7% coverage of the available crystal surface. The observed, almost complete inhibition of growth under these conditions suggests that crystallization proceeds through the development of a relatively small number of active growth sites. Similar conclusions were reached for other phosphonates during the
3-
o
2
0 0
I 4 [ENTMp'I
I 8 /
10 6 L m o l
ll2
115
1
FIG. 6. Langmuir plots (Eq. [2]) for aged (e) and pregrown (U]) seeds.
1B
\~ i15t
~2
14
13-113 .n
.25
.50 E N T M P / I O -6
.7~5 tool L-I
1. O0
FIG. 7. Plots of zeta potential of COM (aged) seed crystals in the presence of ENTMP.
growth of barium sulfate (21) and gypsum (22, 23). The results are in accordance with the parabolic kinetic equation of Burton et al. (24), in which growth takes place on active sites at dislocations on the crystal surfaces. The observed decrease in growth rate of the aged crystals therefore reflects a reduced growth site density, despite the fact that simple three-dimensional crystal growth with a concomitant increase in surface area would predict (e.g., in exp. 109, Fig. 1) an increase in growth rate from 2 3 X 10 -5 at G = 25 to 47 X 10 5 a t G = 250. In contrast, the experimental rates of crystallization decreased from 8 × 10 -5 to 2.9 X 10 -5 mole min - l m g -1 during the same growth period. In conclusion, it has been shown that the aging of crystals through slow dissolution/reprecipitation processes may be an inappropriate preparative technique for preparing surfaces for studying subsequent crystallization reactions in metastable supersaturated solutions. It is preferable to use pregrown (perfected) crystallites, especially for the investigation of the influence of growth inhibitors. Moreover, the rates of crystallization of the pregrown crystallites follow a rate law second order in relative supersaturation, suggesting a spiral growth mechanism with a relatively constant number of growth sites or spirals during growth. Aged COM crystals may be used only when the experiments are made at constant supersaturations so that reactions can be extended beyond the initial surges. Journal of Colloid and Interface Science, Vol. 118, No. 2, August 1987
386
SINGH ET AL. ACKNOWLEDGMENTS
11. Wiersema, P. H., Loeb, A. L., and Overbeek, J. Th. G., J. Colloid Interface Sci. 22, 78 (1966). 12. Tomazic, B., and Nancollas, G. H., J. Cryst. Growth 46, 355 (1979). 13. Nancollas, G. H., "Interactions in Electrolyte Solutions." Elsevier, Amsterdam, 1966. REFERENCES 14. Davies, C. W., "Ion Association." Butterworths, Lon1. Nancollas, G. H., "Biological Mineralization and Dedon, 1962. mineralization." Springer-Verlag, Berlin, 1982. 15. White, D. J., and Nancollas, G. H., J. Cryst. Growth 2. van Rosmalen, G. M., Ph.D. thesis, Delft Univ. Press. 57, 267 (1982). 3. Werness, P. G., Bergert, J. H., and Smith, L. H., J. 16. Langmuir, J., J. Amer. Chem. Soc. 38, 2221 (1916). Cryst. Growth 53, 166 (1981). 17. Davies, C. W., and Nancollas, G. H., Trans. Faraday 4. Vahlensieck, E. W., Bach, D., and Hesse, A., Urol. Soc. 51, 818 (1955). Res. 10, 195 (1982). 18. Nancollas, G. H., and Zawacki, S. J., in "Industrial 5. Tomson, M. B., and Nancollas, G. H., Science 200, Crystallization '84" (S. J. Jancic and E. J. de Jong, 1059 (1978). Eds.). Elsevier, Amsterdam, 1984. 6. Koutsoukos, P., Arnjad, Z., Tomson, M. B., and 19. Westerback, S., Rajan, K. S., and Martell, A. E., J. Nancollas, G. H., J. Amer. Chem. Soc. 102, 1553 Amer. Chem. Soc. 87, 2567 (1965). (1980). 20. Meyer, J. L., and Nancollas, G. H., Calc. Tissue. Res. 7. Sheehan, M. E., and Nancollas, G. H., Invest. Urol. 13, 295 (1973). 17, 446 (1980). 21. Leung, W. H., and Nancollas, G. H., J. Cryst. Growth 8. Singh, R. P., and Nancollas, G. H., Anal. Lett. 19, 44, 163 (1978). 1487 (1986). 22. Weijnen, M. P. C., Marchee, W. G. T., and van Ros9. Nancollas, G. H., and Gardner, G. L., J. Cryst. Growth malen, G. M., Desalination 47, 81 (1983). 21, 267 (1974). 23. Gill, J. S., and Nancollas, G. H., Corrosion 37, 120 10. Overbeek, J. Th. G., in "Colloid Science" (H. R. (1981). Kruyt, Ed.), Vol. 1, p. 219. Elsevier, Amsterdam, 24. Burton, W. K., Cabrera, N., and Frank, F. C., Philos. 1952. Trans. A 243, 299 (1951). We thank the National Institute of Arthritis, Diabetes, Digestive and Kidney Diseases for a grant (AM19048) in support of this work and Dr. J. Budz for helpful discussions.
Journal of ColloidandInterfaceScience, Vol.118,No. 2, August1987