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Influence of amino acids on the precipitation kinetics of calcium oxalate monohydrate
Journal of Crystal North-Holland
Growth
,oulNAtor CRYSTAL GROWTH
132 (1993) 122-128
Influence of amino acids on the precipitation of calcium oxalate monohydrate Lj. Komunjer
kinetics
I, M. MarkoviC and H. Fiiredi-Milhofer
Rugjer Bockovic’ Institute, P.O. Box 1016, 41001 Zagreb, Croatia Received
15 March
1993
Precipitation kinetics of calcium oxalate monohydrate has been studied by monitoring the concentration variation of calcium ions in the solution with a selective electrode. The experimental data for both pure oxalate solutions and solutions containing 7 to 56 ppm of glutamic acid indicate that two-dimensional nucleation is likely to be the growth controlling mechanism. Supporting this assertion is the fact that the value of the ledge (interface) free energy, determined from the constant A, in the exponential law, agrees quite well with those obtained by other authors in similar systems. Furthermore, the same constant A, turns out to be independent of the presence of additives in the solution, their inhibiting effect being due to variations of the pre-exponential factor K, only. As in other known cases, the specific adsorption of additives at the ledges of the two-dimensional nuclei, leading to decrease of the ledge free energy, has not been evidenced.
Introduction Crystallization occurring in human beings and other natural environments is a special case of precipitation of slightly soluble salts. Although supersaturation with respect to certain species exists in urines of healthy persons, concretion does not take place unless pathological state is achieved. A variety of components present in urines (ions, organic molecules, macromolecules) are considered as presumable inhibitors of pathological mineralisation and different mechanisms of inhibition are expected, depending on the possible interactions of these species with the nascent crystals. In early work, Nancollas and Gardner [l] pointed out that volume diffusion of constituent ions toward the crystal is not the rate controlling mechanism of growth of calcium oxalate monohydrate (COM). They suggested an interfacial
i To whom all correspondence should be addressed. Present address: Laboratoire de Mineralogie-Cristallographie, Universites de Paris VI et VII, 4 Place Jussieu, Tour 16, F-75252 Paris Cedex 05, France. 0022-0248/93/$06.00
0 1993 - Elsevier
Science
Publishers
mechanism related to the dehydratation of calcium and oxalate ions at active growth sites, probably affected by preferential adsorption of nonconstituent ions on the crystal surface. The established quadratic dependence of the rate of growth on supersaturation did not change in presence of additives (citrate and urate ions), thus suggesting that mechanism remained the same. It has been pointed out that in these cases, as in the case of albumine inhibited COM crystallization, studied by the same group [21, the inhibitory effect is caused by adsorption of the additives on the charged crystal surface due to electrostatic interaction Hlady [3] studied the adsorption of poly-electrolytes (dextran and dextran sulfate) and the specific role of calcium ion activity on both the surface charge of COM crystals and the charge of dextran sulfate in solution. In the case of COM crystallization in presence of some aminoacids, Grases et al. [4] found that aspartic acid inhibited the growth by adsorption in the active growth site, while cysteine and threonine did not cause any significant effect. No satisfactory explanation of this result is given so
B.V. All rights reserved
123
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
far. It seems to indicate, however that the COM-aminoacid interaction is not purely electrostatic. SkrtiC et al. [5] studied the influence of the cationic surfactant dodecylammonium chloride (DDACl) on the crystallization of calcium oxalate, and concluded that adsorption of a surfactant on the surface with ionic headgroups oriented toward the liquid phase produces electrostatic repulsion between particles, thus preventing aggregation. By examining the surface structure of different facets of COM crystal [7], based on the models constructed from structure determination data, an attempt is made to correlate the detected inhibitory effects with this structure. In the present work we proposed to study the effect of glutamic acid (Glu) on the kinetics of crystallization of calcium oxalate monohydrate, and to discriminate the stage (nucleation, growth, aggregation) in which inhibition is most efficient. An attempt will be made to assess the governing growth mechanism.
2. Materials
and methods
The spontaneous COM precipitation was initiated by mixing equal volumes of solutions containing 8 x 10e4 mol dm-” calcium chloride and 8 x 1O-4 mol dm-” sodium oxalate. The ionic strength of both solutions was adjusted to a constant value of 0.3 mol dmP3 by addition of the necessary quantity of sodium chloride, while the pH of the oxalic component was adjusted to 6.5 &-0.1 by titration with sodium hydroxide of the initial oxalic (and eventually glutamic) acid solution. All solutions were prepared by dissolving p.a. chemicals in triply distilled water, and the solutions were filtered twice through 0.22 pm Millipore filter. The temperature of the system has been maintained at 25 f O.l”C. Changes in the solution were followed with calcium selective electrode connected to Ionometer 8.5 (Radiometer, Copenhagen). Supersaturation and total precipitated mass of COM were calculated from the data of calcium ion concentration, taking into account the equilibria summarized in table 1. It must be pointed out that while
Table 1 Equilibria in a solution containing Ca*+, C,Oi-, Ghl~ a)
Reaction No.
Equilibrium
PR
e H+ +HC,O; HC,O, = H+ + C,O,zCaC,O,O + Ca*+ + C,O,2+ Ca*+ +2C,O,2Ca(C,OJCa,C,O:+ + 2Ca2+ +C 2 O*4 CaC,O,.H,O (solid) + CaZf + C,Of - + H,O NaC,O, + Na+ + C,OiH,Glu +H++HGlu HGlu +H++GhrCaGlu’ + Ca*+ + Glu2~
1.252 4.266 3.187 0.008 3.897
(1) (2) (3) (4) (5)
7.610 1.035 2.130 4.310 2.000
(6) (7) (8) (9) (10)
H,GO,
‘) By Glu*ion.
Na+ and
we designate the doubly ionized glutamate an-
the reaction (6) of this table is supposed to have a finite rate which is subject to the present study, the rest of equilibria are considered as instantaneously established. The analytical solution of the system of eqs. (0, (21, (31, (5) and (6) was performed following the standard procedure [S-lo]. Eq. (4) was excluded because of the high dissociation constant of the complex ion Ca(C,O,):-. Five supplementary equations have been added, four of them expressing the conservation of mass of Ca, C,O,, Glu and Na, the fifth taking into account the equality of the total concentrations of Ca and C,O, at every stage of crystallization. In fig. 1, which gives the result of the calculation in absence of additive ([Glu] = 01, the total
Kh2+l Imol dm-3
109
Fig. 1. Calculated total concentration of calcium in solution as a function of measured ionic calcium concentration.
124
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
concentration, [Cal, of calcium in the solution is plotted versus the concentration, [Ca*+], measured with the electrode, in the range of concentrations between [Ca*+l = 3.23 x 10e4 mol dmP3, defined by the solubility product, LCaCzO, = 2.45 X lo-‘, and [Ca*+] = 6.45 X 10e4 mol dmP3 corresponding to the initial concentration of calcium in solution, [Cal,, = 8.0 X lop4 mol dmP3. Another result of the same calculation is the determination of the concentration, [C,O,2-], of free oxalate ions in the solution which, together with [Ca*‘] and L CaC204, defines the supersaturation u at any moment of the crystallization [S]:
(+=
[Ca”+][C,Oi-] L CaC,O,
- 1.
(1)
sion hi, and that the reaction yield can be expressed as V
h?
V,
h),’
(y=-_=
where V and V, are the total volumes of precipitated COM at the time t and after full precipitation, respectively, and hi,, is the final average linear dimension. Note that the latter expression is valid for any particle shape, under the sole condition that it remains homothetical during the entire growth period. The same condition leads to the conclusion that the growth rate of any facet can be deduced from Ri. From eq. (3) we have dh,
Calculation of the supersaturation (+ in absence and in presence of additives shows that: l (T is not exactly proportional to the measured concentration of calcium ions, [Ca*+]; l there is a non-negligible influence of the additive which increases the supersaturation u with respect to the measured concentration [Ca*+]. The physical interpretation of this result is that the formation of CaGlu’ in the solution is consuming calcium ions, thus increasing the concentration [C,O,2-I. In a similar way, the yield (Yof the precipitation reaction, i.e., the ratio between the crystallized mass and the total mass which can crystallize from the given solutions is calculated from the initial total concentration, [Cal,, the total concentration at time t, [Cal, and the final total concentration, [Cal,: [Cal0 - [Cal a = [Cal, - [Cal, ’
(4
The rate of growth of the ith facet of a particle, Ri = dh,/dt, where hi is the normal distance to it, is calculated under the assumption of invariant number of particles, formed during a short (non measurable) nucleation period, throughout the crystallization process. It follows that the growing particles are a quasi-monodisperse collection characterized by an average linear dimen-
(3)
Ri=
dt
=h,,,--
1
da
3a213 dt ’
which can be compared equation [8],
to the generalized
Ri = KiuP,
(4)
rate
(5)
where Ki and p are the “rate constant” and the “order” of the precipitation reaction, respectively. The relationship obtained by combination of eqs. (4) and (5) may be represented in the form
ln(&$)=ln($)+plnu,
(6)
which permits simultaneous experimental determination of the order of the reaction and the rate constant to be carried out. The latter is a measure of the “conductance” of the surface for transport of matter and should be related to the poisoning of growth sites or to the nonspecific adsorption of large molecules. While to values of p equal to 1. or 2 correspond well-known growth kinetics, bulk transport in the first case and surface diffusion (spiral growth) in the second case, the experimental finding of larger p values poses some problems. For this reason, we have compared the growth rate from eq. (4) also to the law Ri = Ki exp( -A,/v),
(7)
125
Lj. Komunjer et al. / InjTuence of amino acids on precipitation kinetics of COM
typical for growth kinetics governed by two-dimensional nucleation. In this case the constant Ai is proportional to the square of the ledge free energy of a two-dimensional nucleus on the ith facet. In the resulting linear relationship between ln(Ri/hi,,) and l/a,
7--1
(8) the constant Ai is related to the energetic barrier for nucleation on the ith facet of the crystal. It is clear that in this type of experiment the constant Ki cannot be dissociated from the final particle size h,,,. A separate measurement of this length is, therefore, necessary. For this reason, series of experiments have been carried out by monitoring the hydrodynamic radius of the precipitated particles through in situ quasi-elastic laser light scattering. Particle morphology and size changes were also determined by optical microscopy and Coulter counter on samples withdrawn from the solution 5 and 60 min after precipitation onset. Structure and state of hydratation of the as-grown crystals were determined by X-ray powder technique and thermal gravimetric analysis.
3. Results
and discussion
3.1. Crystallization
in pure solution
X-ray analysis of the precipitates showed that at early time calcium oxalate monohydrate prevails, with approximately 5% of calcium oxalate trihydrate, and that no transformations between different hydrates are taking place during the kinetic run. Fig. 2 shows the raw experimental results of [Ca2’] variation with time in a solution containing no additives. It is important to point out that the experimentally measured concentrations of calcium ions fit quite exactly with the values corresponding to the extremities of the curve of fig. 1 calculated from the set of equilibria of table 1, i.e., [Ca2’] = 6.5 x lop4 mol dme3 when the
Fig. 2. Raw experimental data showing change tion of ionic calcium with time during a typical COM precipitation.
of concentrakinetic run of
total concentration of calcium is the initial one, [Cal, = 8 x lop4 mol dmp3, and no precipitation has taken place, and [Ca2’] = 3.25 x 10V4 mol dmp3 at the end of the experiment when the solubility product is reached. In fig. 3, the term of the left-hand side of eq. (6) is plotted versus the logarithm of the supersaturation. Note on the upper abscissa axis the corresponding time of precipitation. Two linear parts, presumably corresponding to two different regimes, are clearly visible. The change takes place about 20 min after onset of the crystallization at a supersaturation u = 1.86. The ordinate at the origin of the right linear part is equal to -8.07, and its slope to p = 5.51. t [minutes1
Fig. 3. Logarithm of the scaled growth rate as given by eq. (6) versus logarithm of the supersaturation, showing a change in the initial power law. Upper abscissa denotes the related time of precipitation.
126
Lj. Komunjer et al. / Infzuence of amino acids on precipitation kinetics of COM
This result calls for the following comments: The regular alignment of experimental points only 2 min after the precipitation has begun favours the assumption that after this short time period, nucleation is already over, and that one has to deal further with a constant number of growing crystals. l Taking as average measured final linear dimension hi, the value of 12 pm, the rate constant is Ki = 1.4 X lo-’ cm s-r. l When supersaturation falls below u = 1.86, a new kinetic law seems to emerge. One cannot yet speculate on the mechanism in this stage, although it has been suggested [ll] that by decreasing supersaturation aggregation takes over the overall kinetics. The rather high value of the exponent p makes the application of the kinetic law of eq. (5) doubtful. As we shall see in the next section, the exponential relationship of eq. (7) seems more appropriate to interpreting the experimental data in both cases of growth in pure solution and in presence of additives. l
3.2. Znjhence
of additives
Fig. 4 shows the raw data of the experimenduring COM tally measured Ca*+ concentrations crystallization in a pure solution and in the presence of 7, 28 and 56 ppm of glutamic acid. The surprising result of this series of experiments is a
Fig. 4. Change of calcium ion concentration during kinetic run for three different Glu concentrations; curve b: 7 ppm; curve c: 28 ppm; curve d: 56 ppm, compared to crystallization from pure solutions (curve a).
I
Fig. 5. Logarithm of the scaled growth rate versus reciprocal supersaturation. Discontinuities are showing changes in the initial exponential law, as given by eq. (8); curves: b, c, and d: 7, 28 and 56 ppm Glu respectively; curve a: pure solution.
maximum inhibition of the precipitation rate at relatively small concentrations of glutamic acid (7 ppm). The approximate concentration range in which this strong inhibition occurs is 3-15 ppm of H,Glu. At higher concentrations the precipitation rate reaches a relative maximum (cf. the data of fig. 41, and decreases further with increasing additive concentration. A possible explanation of this unexpected behaviour could be the competition between two opposite effects: the blocking of growth sites on the COM surface, which can be effective at quite low H,Glu concentrations, and the already mentioned increase of the supersaturation at higher concentrations of additive. Unfortunately, this assumption had to be abandoned, since after replacement of the experimentally measured concentration [Ca2’l by the true supersaturation u, taking into account the effect of [H,Ght] on the ensemble of equilibria of table 1, the maximum inhibition of growth at low H,Glu concentrations still persisted. Other possible hypotheses, such as more effective blocking of growth sites by single adsorbed molecules of Glu*(or H,Glu?) species, rather than by their organized adsorption layers, have for the moment no serious experimental background. The data of fig. 4 are transformed into a ln(R,/h,,,) versus l/a plot in fig. 5. It can be stated that the linear fit for the data corresponding to growth in pure solution is just so good as that with the power law of fig. 3. The fit is fairly
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
127
Table 2 Parameters of eq. (7) for different concentrations of additive
4. Conclusions
GlU
InW, /&A
‘4,
0 7 28 56
2.97 2.62 3.10 1.57
12.00 13.24 13.15 11.66
Although the results of the present study on the relationship between the growth rate of calcium oxalate monohydrate and supersaturation can be fitted by an exponential law and by a power law as well (at least as regards the pure solutions), we are tempted to think that the exponential law, typical for 2D nucleation kinetics, describes better the growth mechanism. Following experimental facts are supporting this conclusion: (1) The exponent of the power law determined in the case of pure solution, equal to 5.5, does not correspond to any known growth kinetics. (2) The constant A, in the exponent of the exponential law has a reasonable value. The ledge and surface free energies of the COM-solution interface determined from this constant are in agreement with those already communicated for similar systems [12,13]. (3) The values of the same constant are not altered by the presence of glutamic acid in the solution, although the overall growth kinetics is sensibly affected. This result conforms to the results of previous studies showing that adsorption of additives rarely, if ever, decreases the surface (ledge) free energy (as it could be expected from purely thermodynamic considerations), but can decrease essentially the pre-exponential factor Ki. The unexpected maximum in the inhibitory effect at low concentrations of glutamic acid cannot be understood yet. To clarify this effect, more detailed studies on the structural and thermodynamic properties of calcium glutamate are necessary.
reasonable also for the data in presence of glutamic acid, and the values of the edge free energies estimated from the slope of the linear parts, K = (l-2) x 10P6 erg cm-’ (which correspond to interface free energies of COM-solution of 15-30 that the two-dimenerg cm -2) let us presume sional nucleation is the general mechanism responsible for the growth. Similar values of the interface free energy have already been obtained from measurement of the 3D nucleation rate in electrolyte solutions [12,131. In table 2 are given the parameters of eq. (7) determined from the linear fit of fig. 5. The constant Ai can be considered as being the same, within experimental error, for the pure solution and for all concentrations of glutamic acid. This important result indicates that the inhibition of growth is not due to variation of the ledge (interface) free energy, in agreement with former results on 3D nucleation [14]. The pre-exponential factor of eq. (7) decreases at the smallest amount of glutamic acid, and then varies in a irregular way. The presumption that the influence of additives is mainly due to hindrances during the transfer of molecules from the solution to the growth sites seems, thus, to be confirmed. The graphs of fig. 5 show another interesting feature, namely the slight but systematic increase, by increasing Glu concentration, of the growth rate at which a change of growth mechanism occurs. This effect can be explained by the takeover of passivation due to the adsorption of additive on the continuous refreshing of the surface during growth. The higher the growth rate, the larger must be the concentration of glutamic acid necessary to stop the growth.
Acknowledgements The authors are indebted to B. Mutaftschiev for fruitful discussions and suggestions concerning the present paper. Financial support of the Commission of the European Community, D.G. XII (grant No. CIl*-0345-YU(A)) and the Scientific Authorities of the Republic of Croatia is gratefully acknowledged. One of the authors
128
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
(Lj. K.) was enabled to complete this work while being a post-doctoral fellow at the Laboratoire de MinCralogie-Cristallographie, UniversitCs de Paris VI et Paris VII, Paris, France, in the framework of the post-doctoral programs of the European Community Commission for Science, Research and Development.
References [l] G.H. Nancollas and G.L. Gardner, J. Crystal Growth 21 (1974) 267. [2] S.A. Smesko, R.P. Singh, A.C. Lanzalaco and G.H. Nancollas, Colloids Surfaces 30 (1988) 361. [3] V. Hlady, J. Colloid Interface Sci. 98(2) (1984) 373.
141 F. Grases, J.G. March, F. Bibiloni and E. Amat, J. Crystal Growth 87 (1988) 299. [S] D. Skrtic, N. FilipoviC-Vincekovid and H. FtirediMilhofer, J. Crystal Growth 114 (1991) 118. [6] D. Skrtid, N. Filipovic-Vincekovid and V. Babid-Ivan&d, J. Crystal Growth 121 (1992) 197. [7] Lj. Komunjer, PhD Thesis, University of Zagreb, Zagreb (1990). 181 H.E. Lundager Madsen, Nephrologie 5 (1984) 151. [9] A.E. Nielsen and J.M. Toft, J. Crystal Growth 67 (1984) 278. [lo] A.E. Nielsen, J. Crystal Growth 67 (1984) 289. [ll] M. MarkoviC, Lj. Komunjer, H. Fiiredi-Milhofer, D. SkrtiC and S. Sarig, J. Crystal Growth 88 (1988) 118. [12] M. Kahlweit, Z. Physik. Chem. (NF) 25 (1960) 1. [13] B. Mutaftschiev and W. Platikanowa, Compt. Rend. Bulg. Acad. Sci. 14 (1961) 695. 1141 B. Mutaftschiev and S. Toschev, Bull. Inst. Phys. Chem. Bulg. Acad. Sci. 1 (1960) 59.
Growth
,oulNAtor CRYSTAL GROWTH
132 (1993) 122-128
Influence of amino acids on the precipitation of calcium oxalate monohydrate Lj. Komunjer
kinetics
I, M. MarkoviC and H. Fiiredi-Milhofer
Rugjer Bockovic’ Institute, P.O. Box 1016, 41001 Zagreb, Croatia Received
15 March
1993
Precipitation kinetics of calcium oxalate monohydrate has been studied by monitoring the concentration variation of calcium ions in the solution with a selective electrode. The experimental data for both pure oxalate solutions and solutions containing 7 to 56 ppm of glutamic acid indicate that two-dimensional nucleation is likely to be the growth controlling mechanism. Supporting this assertion is the fact that the value of the ledge (interface) free energy, determined from the constant A, in the exponential law, agrees quite well with those obtained by other authors in similar systems. Furthermore, the same constant A, turns out to be independent of the presence of additives in the solution, their inhibiting effect being due to variations of the pre-exponential factor K, only. As in other known cases, the specific adsorption of additives at the ledges of the two-dimensional nuclei, leading to decrease of the ledge free energy, has not been evidenced.
Introduction Crystallization occurring in human beings and other natural environments is a special case of precipitation of slightly soluble salts. Although supersaturation with respect to certain species exists in urines of healthy persons, concretion does not take place unless pathological state is achieved. A variety of components present in urines (ions, organic molecules, macromolecules) are considered as presumable inhibitors of pathological mineralisation and different mechanisms of inhibition are expected, depending on the possible interactions of these species with the nascent crystals. In early work, Nancollas and Gardner [l] pointed out that volume diffusion of constituent ions toward the crystal is not the rate controlling mechanism of growth of calcium oxalate monohydrate (COM). They suggested an interfacial
i To whom all correspondence should be addressed. Present address: Laboratoire de Mineralogie-Cristallographie, Universites de Paris VI et VII, 4 Place Jussieu, Tour 16, F-75252 Paris Cedex 05, France. 0022-0248/93/$06.00
0 1993 - Elsevier
Science
Publishers
mechanism related to the dehydratation of calcium and oxalate ions at active growth sites, probably affected by preferential adsorption of nonconstituent ions on the crystal surface. The established quadratic dependence of the rate of growth on supersaturation did not change in presence of additives (citrate and urate ions), thus suggesting that mechanism remained the same. It has been pointed out that in these cases, as in the case of albumine inhibited COM crystallization, studied by the same group [21, the inhibitory effect is caused by adsorption of the additives on the charged crystal surface due to electrostatic interaction Hlady [3] studied the adsorption of poly-electrolytes (dextran and dextran sulfate) and the specific role of calcium ion activity on both the surface charge of COM crystals and the charge of dextran sulfate in solution. In the case of COM crystallization in presence of some aminoacids, Grases et al. [4] found that aspartic acid inhibited the growth by adsorption in the active growth site, while cysteine and threonine did not cause any significant effect. No satisfactory explanation of this result is given so
B.V. All rights reserved
123
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
far. It seems to indicate, however that the COM-aminoacid interaction is not purely electrostatic. SkrtiC et al. [5] studied the influence of the cationic surfactant dodecylammonium chloride (DDACl) on the crystallization of calcium oxalate, and concluded that adsorption of a surfactant on the surface with ionic headgroups oriented toward the liquid phase produces electrostatic repulsion between particles, thus preventing aggregation. By examining the surface structure of different facets of COM crystal [7], based on the models constructed from structure determination data, an attempt is made to correlate the detected inhibitory effects with this structure. In the present work we proposed to study the effect of glutamic acid (Glu) on the kinetics of crystallization of calcium oxalate monohydrate, and to discriminate the stage (nucleation, growth, aggregation) in which inhibition is most efficient. An attempt will be made to assess the governing growth mechanism.
2. Materials
and methods
The spontaneous COM precipitation was initiated by mixing equal volumes of solutions containing 8 x 10e4 mol dm-” calcium chloride and 8 x 1O-4 mol dm-” sodium oxalate. The ionic strength of both solutions was adjusted to a constant value of 0.3 mol dmP3 by addition of the necessary quantity of sodium chloride, while the pH of the oxalic component was adjusted to 6.5 &-0.1 by titration with sodium hydroxide of the initial oxalic (and eventually glutamic) acid solution. All solutions were prepared by dissolving p.a. chemicals in triply distilled water, and the solutions were filtered twice through 0.22 pm Millipore filter. The temperature of the system has been maintained at 25 f O.l”C. Changes in the solution were followed with calcium selective electrode connected to Ionometer 8.5 (Radiometer, Copenhagen). Supersaturation and total precipitated mass of COM were calculated from the data of calcium ion concentration, taking into account the equilibria summarized in table 1. It must be pointed out that while
Table 1 Equilibria in a solution containing Ca*+, C,Oi-, Ghl~ a)
Reaction No.
Equilibrium
PR
e H+ +HC,O; HC,O, = H+ + C,O,zCaC,O,O + Ca*+ + C,O,2+ Ca*+ +2C,O,2Ca(C,OJCa,C,O:+ + 2Ca2+ +C 2 O*4 CaC,O,.H,O (solid) + CaZf + C,Of - + H,O NaC,O, + Na+ + C,OiH,Glu +H++HGlu HGlu +H++GhrCaGlu’ + Ca*+ + Glu2~
1.252 4.266 3.187 0.008 3.897
(1) (2) (3) (4) (5)
7.610 1.035 2.130 4.310 2.000
(6) (7) (8) (9) (10)
H,GO,
‘) By Glu*ion.
Na+ and
we designate the doubly ionized glutamate an-
the reaction (6) of this table is supposed to have a finite rate which is subject to the present study, the rest of equilibria are considered as instantaneously established. The analytical solution of the system of eqs. (0, (21, (31, (5) and (6) was performed following the standard procedure [S-lo]. Eq. (4) was excluded because of the high dissociation constant of the complex ion Ca(C,O,):-. Five supplementary equations have been added, four of them expressing the conservation of mass of Ca, C,O,, Glu and Na, the fifth taking into account the equality of the total concentrations of Ca and C,O, at every stage of crystallization. In fig. 1, which gives the result of the calculation in absence of additive ([Glu] = 01, the total
Kh2+l Imol dm-3
109
Fig. 1. Calculated total concentration of calcium in solution as a function of measured ionic calcium concentration.
124
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
concentration, [Cal, of calcium in the solution is plotted versus the concentration, [Ca*+], measured with the electrode, in the range of concentrations between [Ca*+l = 3.23 x 10e4 mol dmP3, defined by the solubility product, LCaCzO, = 2.45 X lo-‘, and [Ca*+] = 6.45 X 10e4 mol dmP3 corresponding to the initial concentration of calcium in solution, [Cal,, = 8.0 X lop4 mol dmP3. Another result of the same calculation is the determination of the concentration, [C,O,2-], of free oxalate ions in the solution which, together with [Ca*‘] and L CaC204, defines the supersaturation u at any moment of the crystallization [S]:
(+=
[Ca”+][C,Oi-] L CaC,O,
- 1.
(1)
sion hi, and that the reaction yield can be expressed as V
h?
V,
h),’
(y=-_=
where V and V, are the total volumes of precipitated COM at the time t and after full precipitation, respectively, and hi,, is the final average linear dimension. Note that the latter expression is valid for any particle shape, under the sole condition that it remains homothetical during the entire growth period. The same condition leads to the conclusion that the growth rate of any facet can be deduced from Ri. From eq. (3) we have dh,
Calculation of the supersaturation (+ in absence and in presence of additives shows that: l (T is not exactly proportional to the measured concentration of calcium ions, [Ca*+]; l there is a non-negligible influence of the additive which increases the supersaturation u with respect to the measured concentration [Ca*+]. The physical interpretation of this result is that the formation of CaGlu’ in the solution is consuming calcium ions, thus increasing the concentration [C,O,2-I. In a similar way, the yield (Yof the precipitation reaction, i.e., the ratio between the crystallized mass and the total mass which can crystallize from the given solutions is calculated from the initial total concentration, [Cal,, the total concentration at time t, [Cal, and the final total concentration, [Cal,: [Cal0 - [Cal a = [Cal, - [Cal, ’
(4
The rate of growth of the ith facet of a particle, Ri = dh,/dt, where hi is the normal distance to it, is calculated under the assumption of invariant number of particles, formed during a short (non measurable) nucleation period, throughout the crystallization process. It follows that the growing particles are a quasi-monodisperse collection characterized by an average linear dimen-
(3)
Ri=
dt
=h,,,--
1
da
3a213 dt ’
which can be compared equation [8],
to the generalized
Ri = KiuP,
(4)
rate
(5)
where Ki and p are the “rate constant” and the “order” of the precipitation reaction, respectively. The relationship obtained by combination of eqs. (4) and (5) may be represented in the form
ln(&$)=ln($)+plnu,
(6)
which permits simultaneous experimental determination of the order of the reaction and the rate constant to be carried out. The latter is a measure of the “conductance” of the surface for transport of matter and should be related to the poisoning of growth sites or to the nonspecific adsorption of large molecules. While to values of p equal to 1. or 2 correspond well-known growth kinetics, bulk transport in the first case and surface diffusion (spiral growth) in the second case, the experimental finding of larger p values poses some problems. For this reason, we have compared the growth rate from eq. (4) also to the law Ri = Ki exp( -A,/v),
(7)
125
Lj. Komunjer et al. / InjTuence of amino acids on precipitation kinetics of COM
typical for growth kinetics governed by two-dimensional nucleation. In this case the constant Ai is proportional to the square of the ledge free energy of a two-dimensional nucleus on the ith facet. In the resulting linear relationship between ln(Ri/hi,,) and l/a,
7--1
(8) the constant Ai is related to the energetic barrier for nucleation on the ith facet of the crystal. It is clear that in this type of experiment the constant Ki cannot be dissociated from the final particle size h,,,. A separate measurement of this length is, therefore, necessary. For this reason, series of experiments have been carried out by monitoring the hydrodynamic radius of the precipitated particles through in situ quasi-elastic laser light scattering. Particle morphology and size changes were also determined by optical microscopy and Coulter counter on samples withdrawn from the solution 5 and 60 min after precipitation onset. Structure and state of hydratation of the as-grown crystals were determined by X-ray powder technique and thermal gravimetric analysis.
3. Results
and discussion
3.1. Crystallization
in pure solution
X-ray analysis of the precipitates showed that at early time calcium oxalate monohydrate prevails, with approximately 5% of calcium oxalate trihydrate, and that no transformations between different hydrates are taking place during the kinetic run. Fig. 2 shows the raw experimental results of [Ca2’] variation with time in a solution containing no additives. It is important to point out that the experimentally measured concentrations of calcium ions fit quite exactly with the values corresponding to the extremities of the curve of fig. 1 calculated from the set of equilibria of table 1, i.e., [Ca2’] = 6.5 x lop4 mol dme3 when the
Fig. 2. Raw experimental data showing change tion of ionic calcium with time during a typical COM precipitation.
of concentrakinetic run of
total concentration of calcium is the initial one, [Cal, = 8 x lop4 mol dmp3, and no precipitation has taken place, and [Ca2’] = 3.25 x 10V4 mol dmp3 at the end of the experiment when the solubility product is reached. In fig. 3, the term of the left-hand side of eq. (6) is plotted versus the logarithm of the supersaturation. Note on the upper abscissa axis the corresponding time of precipitation. Two linear parts, presumably corresponding to two different regimes, are clearly visible. The change takes place about 20 min after onset of the crystallization at a supersaturation u = 1.86. The ordinate at the origin of the right linear part is equal to -8.07, and its slope to p = 5.51. t [minutes1
Fig. 3. Logarithm of the scaled growth rate as given by eq. (6) versus logarithm of the supersaturation, showing a change in the initial power law. Upper abscissa denotes the related time of precipitation.
126
Lj. Komunjer et al. / Infzuence of amino acids on precipitation kinetics of COM
This result calls for the following comments: The regular alignment of experimental points only 2 min after the precipitation has begun favours the assumption that after this short time period, nucleation is already over, and that one has to deal further with a constant number of growing crystals. l Taking as average measured final linear dimension hi, the value of 12 pm, the rate constant is Ki = 1.4 X lo-’ cm s-r. l When supersaturation falls below u = 1.86, a new kinetic law seems to emerge. One cannot yet speculate on the mechanism in this stage, although it has been suggested [ll] that by decreasing supersaturation aggregation takes over the overall kinetics. The rather high value of the exponent p makes the application of the kinetic law of eq. (5) doubtful. As we shall see in the next section, the exponential relationship of eq. (7) seems more appropriate to interpreting the experimental data in both cases of growth in pure solution and in presence of additives. l
3.2. Znjhence
of additives
Fig. 4 shows the raw data of the experimenduring COM tally measured Ca*+ concentrations crystallization in a pure solution and in the presence of 7, 28 and 56 ppm of glutamic acid. The surprising result of this series of experiments is a
Fig. 4. Change of calcium ion concentration during kinetic run for three different Glu concentrations; curve b: 7 ppm; curve c: 28 ppm; curve d: 56 ppm, compared to crystallization from pure solutions (curve a).
I
Fig. 5. Logarithm of the scaled growth rate versus reciprocal supersaturation. Discontinuities are showing changes in the initial exponential law, as given by eq. (8); curves: b, c, and d: 7, 28 and 56 ppm Glu respectively; curve a: pure solution.
maximum inhibition of the precipitation rate at relatively small concentrations of glutamic acid (7 ppm). The approximate concentration range in which this strong inhibition occurs is 3-15 ppm of H,Glu. At higher concentrations the precipitation rate reaches a relative maximum (cf. the data of fig. 41, and decreases further with increasing additive concentration. A possible explanation of this unexpected behaviour could be the competition between two opposite effects: the blocking of growth sites on the COM surface, which can be effective at quite low H,Glu concentrations, and the already mentioned increase of the supersaturation at higher concentrations of additive. Unfortunately, this assumption had to be abandoned, since after replacement of the experimentally measured concentration [Ca2’l by the true supersaturation u, taking into account the effect of [H,Ght] on the ensemble of equilibria of table 1, the maximum inhibition of growth at low H,Glu concentrations still persisted. Other possible hypotheses, such as more effective blocking of growth sites by single adsorbed molecules of Glu*(or H,Glu?) species, rather than by their organized adsorption layers, have for the moment no serious experimental background. The data of fig. 4 are transformed into a ln(R,/h,,,) versus l/a plot in fig. 5. It can be stated that the linear fit for the data corresponding to growth in pure solution is just so good as that with the power law of fig. 3. The fit is fairly
Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
127
Table 2 Parameters of eq. (7) for different concentrations of additive
4. Conclusions
GlU
InW, /&A
‘4,
0 7 28 56
2.97 2.62 3.10 1.57
12.00 13.24 13.15 11.66
Although the results of the present study on the relationship between the growth rate of calcium oxalate monohydrate and supersaturation can be fitted by an exponential law and by a power law as well (at least as regards the pure solutions), we are tempted to think that the exponential law, typical for 2D nucleation kinetics, describes better the growth mechanism. Following experimental facts are supporting this conclusion: (1) The exponent of the power law determined in the case of pure solution, equal to 5.5, does not correspond to any known growth kinetics. (2) The constant A, in the exponent of the exponential law has a reasonable value. The ledge and surface free energies of the COM-solution interface determined from this constant are in agreement with those already communicated for similar systems [12,13]. (3) The values of the same constant are not altered by the presence of glutamic acid in the solution, although the overall growth kinetics is sensibly affected. This result conforms to the results of previous studies showing that adsorption of additives rarely, if ever, decreases the surface (ledge) free energy (as it could be expected from purely thermodynamic considerations), but can decrease essentially the pre-exponential factor Ki. The unexpected maximum in the inhibitory effect at low concentrations of glutamic acid cannot be understood yet. To clarify this effect, more detailed studies on the structural and thermodynamic properties of calcium glutamate are necessary.
reasonable also for the data in presence of glutamic acid, and the values of the edge free energies estimated from the slope of the linear parts, K = (l-2) x 10P6 erg cm-’ (which correspond to interface free energies of COM-solution of 15-30 that the two-dimenerg cm -2) let us presume sional nucleation is the general mechanism responsible for the growth. Similar values of the interface free energy have already been obtained from measurement of the 3D nucleation rate in electrolyte solutions [12,131. In table 2 are given the parameters of eq. (7) determined from the linear fit of fig. 5. The constant Ai can be considered as being the same, within experimental error, for the pure solution and for all concentrations of glutamic acid. This important result indicates that the inhibition of growth is not due to variation of the ledge (interface) free energy, in agreement with former results on 3D nucleation [14]. The pre-exponential factor of eq. (7) decreases at the smallest amount of glutamic acid, and then varies in a irregular way. The presumption that the influence of additives is mainly due to hindrances during the transfer of molecules from the solution to the growth sites seems, thus, to be confirmed. The graphs of fig. 5 show another interesting feature, namely the slight but systematic increase, by increasing Glu concentration, of the growth rate at which a change of growth mechanism occurs. This effect can be explained by the takeover of passivation due to the adsorption of additive on the continuous refreshing of the surface during growth. The higher the growth rate, the larger must be the concentration of glutamic acid necessary to stop the growth.
Acknowledgements The authors are indebted to B. Mutaftschiev for fruitful discussions and suggestions concerning the present paper. Financial support of the Commission of the European Community, D.G. XII (grant No. CIl*-0345-YU(A)) and the Scientific Authorities of the Republic of Croatia is gratefully acknowledged. One of the authors
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Lj. Komunjer et al. / Influence of amino acids on precipitation kinetics of COM
(Lj. K.) was enabled to complete this work while being a post-doctoral fellow at the Laboratoire de MinCralogie-Cristallographie, UniversitCs de Paris VI et Paris VII, Paris, France, in the framework of the post-doctoral programs of the European Community Commission for Science, Research and Development.
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