CRYSTAL GROWTH & DESIGN
The Influence of Homo-Aza-Steroids on the Crystallization of Hydroxyapatite in Vitro
2001 VOL. 1, NO. 5 367-372
S. Koutsopoulos, Ch. Maniatis, C. D. Xenos, and E. Dalas* Department of Chemistry, University of Patras, GR-26500, Patras, Greece Received February 26, 2001
ABSTRACT: The effect of three homo-aza-steroids, 3-aza-A-homo-4R-androstene-4,17-dione, 4-oxo-3-aza-A-homo4R-androsteno[16,17-c]pyrazole, and 4-oxo-3-aza-A-homo-4R-androsteno[16,17-c]phenyl pyrazole, used as drugs with anticancer properties, on the crystal growth of hydroxyapatite is investigated at conditions of sustained supersaturation employing the constant composition technique. All three aza-steroids were found to inhibit the crystal growth of hydroxyapatite possibly through adsorption on the active sites available for crystal growth. A detailed kinetic analysis suggested a Langmuir-type adsorption of the polycyclic compound on the surface of hydroxyapatite. The apparent order for the crystallization reaction was determined to be ca. 2, thus suggesting a surface diffusion controlled spiral growth mechanism. Introduction Homo-aza-steroids are compounds with a steroid-like group, which differ from the general category of steroids on the left-hand-side seven-membered ring (Figure 1). This ring has one nitrogen atom and alters the chemical properties of the molecule, which are also defined by the structure and chemical composition of the substituent appearing in the antipodean position. These compounds have been tested successfully as anticancer drugs against several leukaemias, B16 melanosarcoma, C3HB angiosarcoma, and T8 Guerin tumor.1-3 It has been demonstrated that depending on the substituent they possess different tumor growth inhibiting activities.4-7 Hydroxyapatite (Ca5(PO4)3OH, HAP) is a calcium phosphate salt and the main inorganic component of bones and teeth. It can also be found in several cases of undesirable pathological mineralization in stones formed in the bladder and kidneys, atheromatic plaque formation, and arthritis.8-13 From the thermodynamic point of view, HAP has the lowest solubility product among other calcium phosphate salts, and it is the most stable calcium phosphate salt in aqueous media of pH > 4 and ambient conditions. Under well-defined physicochemical conditions, HAP is considered as the model compound for studies on biological calcification processes. In the present work, the effect of three representative compounds of the aza-steroid group, namely, the 3-azaA-homo-4R-androstene-4,17-dione (HAS1), 4-oxo-3-azaA-homo-4R-androsteno[16,17-c]pyrazole (HAS2), and 4-oxo-3-aza-A-homo-4R-androsteno[16,17-c]phenyl pyrazole (HAS3), on biological calcification phenomena will be studied. It is interesting to explore the effect of these compounds with the unusual structure and chemical groups on the crystallization phenomenon and how these factors alter the interaction process and adsorption with the crystal surface of HAP. For this reason, the constant composition method was employed, and the crystallization kinetics of HAP were investigated. This method is particularly suitable for crystal growth stud* To whom correspondence should be addressed.
ies especially when interaction of an additive with the crystal surface is involved. In such cases, the kinetics may be accurately determined with high reproducibility under well-defined pseudo-steady-state conditions.18-20 Experimental Section Solid reagent-grade (Merck) calcium chloride, potassium dihydrogen phosphate, sodium chloride, and triply distilled CO2-free water were used in the preparation of the solutions. Potassium hydroxide solutions were prepared from concentrated standards (Merck, Titrisol). The standardization of the stock solutions is described in detail elsewhere.18-20 The kinetic study was performed in supersaturated solutions of calcium phosphate at 37 ( 0.1 °C. Potentiometric titrations of the homo-aza-steroid complexes were performed at 0.15 M NaCl ionic strength in the presence and in the absence of total calcium 5 × 10-4 M at constant temperature 37 °C. The aqueous solutions were equilibrated for 1 h before titration.21 All titration experiments were performed in a CO2-free solution, and throughout the course of the titration water-saturated nitrogen gas was bubbled through the solution. The pH was recorded every 3 min as a function of the volume of titrant added. From the titration curves, it was concluded that no complexation occurred between the organic molecule and the calcium ions.22 It is therefore demonstrated that the reduction of the crystal growth rates is not ascribed to a decrease of the reactant concentration and lower solution supersaturation. The working solutions were prepared in a thermostated double-walled vessel of volume totaling 250 mL, which contained the appropriate volumes of potassium dihydrogen phosphate and sodium chloride solutions. The latter was to adjust the ionic strength at 0.15 M. The pH was monitored continuously with a combined glass/Ag/AgCl electrode (Metrohm, 6.0202.100) standardized before and after each experiment with NBS buffer solutions (i.e., 0.08695 M KH2PO4 + 0.03043 M Na2HPO4, and 0.025 M KH2PO4 + 0.025 M Na2HPO4, with pH values 7.384 and 6.841, respectively, at 37 °C).23 After 20 mg of well-characterized HAP seed crystals was injected, the pH was adjusted to 7.4 by the addition of dilute potassium hydroxide, and the supersaturation was attained by the addition of the calcium chloride salt solution. Before and during the crystal growth process, water-saturated nitrogen was bubbled through the working solution to preclude atmospheric carbon dioxide from dissolving. The HAP seed crystals were prepared by a method described elsewhere24 and had a specific surface area of 34.6 m2 g-1 as determined by a multiple-point BET method (Perkin-Elmer
10.1021/cg010005n CCC: $20.00 © 2001 American Chemical Society Published on Web 09/05/2001
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Figure 1. The homo-aza-steroids tested as possible HAP inhibitors: (a) 3-aza-A-homo-4-androsteno-3-17-dione (HAS1), (b) 4-oxo3-aza-A-homo-4a-androsteno[16,17-c]pyrazole (HAS2), and (c) 4-oxo-3-aza-A-homo-4a-androsteno[16,17-c]phenyl pyrazole (HAS3). sorptometer 212 D). The solid precipitates were analyzed by infrared spectroscopy (KBr pellet method, FT-IR Perkin-Elmer 16-PC), powder X-ray diffraction (Philips PW 1830/1840, Cu KR radiation, using aluminum as internal standard), and chemical analysis. The synthetic crystals displayed the characteristic powder X-ray diffraction pattern (ASTM card file no. 9-432), and the infrared spectrum of the stoichiometric HAP20 and the experimentally determined stoichiometric ratio of Ca:P was 1.67 ( 0.01. The homo-aza-steroids previously prepared and purified25 have been characterized by elemental chemical microanalysis, infrared, and ultraviolet spectroscopic methods. For the HAP crystal growth experiments in the presence of aza-steroid compounds, the latter were dissolved in the phosphate solutions of the desired pH value and ionic strength which contained the HAP seed crystals 1 h before the experiment started by the addition of calcium chloride. When following the above procedure, adsorption phenomena of the additive compound at the solid/liquid interface do not interfere with the kinetic measurements. HAP formation results in a pH drop thus offering a sensitive means of monitoring the crystallization reaction. A pH-meter (Radiometer 25c) was used for measuring the pH. An interface was built to connect the pH-meter to the pH-stat (Metrohm 614 Impulsomat, 654 Dosigraph). The modified pH-stat system accommodated two burettes, mechanically coupled and mounted onto the shaft of the piston burette allowing, through the simultaneous addition of exactly equal volumes of reagents, to achieve invariability of all species in the working solution. The composition of the two titrants is given in detail elsewhere.18-20 The monitoring of the crystal growth process and the constant supersaturation approach have been described in detail in other publications.18,19 At conditions of constant supersaturation, the recorded addition of reactants can be translated to crystal growth rates of moles of HAP formed per unit time and area of the introduced seed crystals (i.e., molHAP min-1 m-2). However, owing to the reduction of the specific surface area during the crystallization process,26 the rates were taken at the initial part of the reaction curve corresponding to 2% growth of the seed crystals. Experiments with different amounts of seed crystals (10, 15, and 20 mg) showed the same
initial rates normalized per unit surface area of the substrate. Also, changes in the stirring rate between 60 and 300 rpm had no effect on the initial crystallization rates, R. From these, it is concluded that crystallization took place exclusively on the surface of the introduced seed crystals.27 The experimental error on the measured rates using this method was less than 5%. During the crystallization process, samples were withdrawn (0.5, 1, 3, 6, and 12 h after the experiment start) and filtered through membrane filters (Millipore, 0.2 µm). The filtrates were analyzed for calcium by atomic absorption and for phosphate by spectrophotometric methods as the vanadomolybdate complex.18,24 The constancy of calcium and phosphate fell within 3% of the original concentrations in the working solution, indicating sustained supersaturation.
Results and Discussion The experimental conditions were chosen mimicking the physiological, namely, pH 7.4, ionic strength adjusted to 0.15 M in NaCl, and the working temperature set at 37 ( 0.1 °C. The kinetic results and thermodynamic data obtained from the study are summarized in Table 1. As may be seen from this table, the rate of HAP crystal growth was reduced upon the addition of the three homo-aza-steroid compounds in the supersaturated solution. Furthermore, upon increasing the solution concentration of the HAS1 homo-aza-steroid further inhibition was observed against HAP crystallization. Potentiometric titrations of the three aza-steroids HAS1, HAS2, and HAS3 heterocyclic compounds at the same experimental conditions employed in the kinetic studies (i.e., pH ) 7.4, 0.15 M NaCl, 37 °C) in the presence and in the absence of total calcium 5 × 10-4 M did not show any appreciable complexation. It is therefore suggested that the observed crystal growth rate inhibition is not due to a decrease of the solution supersaturation because of the Ca2+ sequestration by
Homo-Aza-Steroids and Hydroxyapatite Crystallization
Crystal Growth & Design, Vol. 1, No. 5, 2001 369
Table 1. Crystallization of HAP on HAP Seed Crystals in the Presence of Homo-aza-steroids at pH 7.40, 0.15 M NaCl, and Total Calcium (Cat)/Total Phosphate (Pt) ) 1.67' ∆G (J mol-1) exp no.
Cat (10-4 mol L-1)
homo-aza-steroids (10-6 mol L-1)
HAP ( × 103)
TCP
OCP
DCPD (× 103)
R (10-8 mol min-1 m-2)
HA1 HA5 HA7 HA9 HA11 HA15 HA16 HA17 HA18 P1-P5 30 31 32 33 HA12 HA13
5.0 5.0 5.0 5.0 5.0 4.0 3.5 3.0 2.5 5.0 4.0 3.5 3.0 2.5 5.0 5.0
HAS1/1.8 HAS1/3.6 HAS1/10.8 HAS1/18.0 HAS1/36.0 HAS1/3.6 HAS1/3.6 HAS1/3.6 HAS1/3.6 0 0 0 0 0 HAS2/10.8 HAS3/10.8
-4.43 -4.43 -4.43 -4.43 -4.43 -3.94 -3.63 -3.29 -2.88 -4.43 -3.94 -3.63 -3.29 -2.88 -4.43 -4.43
-3.99 × 102 -3.99 × 102 -3.99 × 102 -3.99 × 102 -3.99 × 102 -5.00 × 102 -8.90 × 102 -1.35 × 103 -3.99 × 103 -3.99 × 102 -5.00 × 102 -8.90 × 102 -1.35 × 103 -3.99 × 102 -3.99 × 102 -3.99 × 102
1.28 × 101 1.28 × 101 1.28 × 101 1.28 × 101 1.28 × 101 5.04 × 101 7.99 × 101 1.14 × 102 1.55 × 102 1.28 × 101 5.04 × 101 7.99 × 101 1.14 × 102 1.55 × 102 1.28 × 101 1.28 × 101
3.56 3.56 3.56 3.56 3.56 4.12 4.45 4.85 5.31 3.56 4.12 4.45 4.85 5.31 3.56 3.56
3.10 2.40 1.80 1.61 1.45 1.35 0.96 0.77 0.43 9.71 5.38 3.85 3.04 1.68 2.73 2.32
the homo-aza-steroids. The suppression of the crystal growth, observed within the kinetic study, is attributable to extensive blocking of the active growth sites on the seed crystals by the adsorbed aza-steroids. Fitting the kinetic results in a Langmuir-type isotherm may test this hypothesis. Assuming that the additives adsorb on the HAP seed crystals according to the simple Langmuir model, occupying a fraction θ, of the active growth sites (0 < θ < 1), then the rates of crystal growth in the absence, Ro, and in the presence, Ri, of the inhibitor may be given from the equation:29
Ri ) Ro(1 - Radsθ)
(1)
where Rads is a factor introduced in the adsorption isotherm equation to take into account deviations of the model. When Rads > 1, then complete cessation of the crystallization is expected even at low concentrations of the adsorbed molecules (irreversible and strong adsorption on the surface of the crystals).29 If Rads < 1, then the crystal growth may be remarkably reduced, but it will not stop completely even at very high concentrations of the additive in the working solution.29 According to the Langmuir model at equilibrium, the rates of adsorption and desorption of the additive compound on the surface are equal:28
ka(1 - Radsθ)ci ) Radsθkd
(2)
where ka and kd are the adsorption and desorption rate constants of the adsorbate on the adsorbent, respectively, and ci is the concentration of the additive. Combination of eqs 1 and 2 gives the crystal growth rates in the presence and in the absence of the inhibitor as a function of its concentration in the supersaturated solution, ci:
Ro 1 1 1 ) + Ro - Ri Rads Radskaff ci
(3)
where kaff (equal to ka/kd) is the affinity constant, and it is a measure of the affinity of the adsorbent for the surface. The kaff and RCV may be determined from the slope and the intercept, respectively, of the linear plots of Ro/(Ro - Ri) as a function of the 1/ci according to eq
Figure 2. Crystal growth rates of HAP in the presence of various concentrations of HAS1. Table 2. Affinity Constants for Various Inhibitors of HAP Crystal Growth inhibitor phytic acid 1-hydroxyethane-1,1-diphosphonic acid sodium pyrophosphate amino tris(methylene phosphonic acid) 1-hydroxyethylidene-1,1-diphosphonic acid melitic acid citric acid glucose bis(sulfonamides) 1,2-dihydroxy-1,2-bis(dihydroxyphosphonyl) ethane titanocenes [Cp2Ti(H2O)2]2+ zirconocenes [Cp2Zr(H2O)2]2+ vanadocenes [Cp2V(H2O)2]2+ hafnocenes [Cp2Hf(H2O)2]2+ 3-aza-A-homo-4-androstene-3-17-dione, HAS1
kaff (× 104 L mol-1) ref 8.4 208 20 62 130 160 1.5 10.2 3.5 216
34 34 35 35 35 35 35 36 37 38
68.9 57.8 11.9 10.0 213
39 40 41 42
3. This plot is shown in Figure 2. From the straight line, a value of 2.13 × 106 L mol-1 was obtained for the affinity constant of HAS1 for the surface of HAP and Rads was found to be 0.86. For comparison reasons, values of the affinity constants for other inhibitors of HAP formation are given in Table 2. A high value of the affinity constant indicates strong adsorption of the inhibitor on the surface.
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The driving force for the HAP formation is the change in Gibbs free energy, ∆G, for the transfer from the supersaturated solution to equilibrium. Thermodynamically speaking, the criterion for a physical process to take place is the change in the Gibbs free energy between the initial and final states. If the Gibbs free energy is found to be negative, then the process is spontaneous (i.e., ∆G < 0). It is also known that the difference in Gibbs energy refers to the corresponding change of the chemical potentials:
∆G ) ∆µHAP ) µHAP(sat) - µHAP(supersat)
(4)
For the crystal growth of HAP the chemical potential in the two states are
µHAP(sat) ) µ°HAP + 1/9 5 3 (5) RgT ln[RCa 2+,(sat)RPO 3-,(sat)ROH-,(sat)] 4
µHAP(supersat) ) µ°HAP +
Figure 3. Kinetics of HAP crystal growth in the presence of various concentrations of HAS1, according to the Langmuir kinetic model at pH 7.40, 37 °C, 0.15 mol/L NaCl (calcium concentration 5 × 10-4 M).
1/9 5 3 (6) RgT ln [RCa 2+,(supersat)RPO 3-,(supersat)ROH-,(supersat)] 4
where R(ion) is the ionic activity, Rg is the gas constant, and T is the absolute temperature. The difference between the chemical potential in the two states is
∆µHAP ) RgT ln
[
] [ ]
1/9
5 3 RCa 2+,(sat)RPO 3-,(sat)ROH-,(sat) 4
5 3 RCa 2+,(supersat) RPO 3-,(supersat)ROH-,(supersat) 4
K°sp,HAP RgT ln IPHAP
)
1/9
(7)
After substitution in eq 4, the Gibbs free energy for the crystallization of HAP is given by:
(
)
(8)
Figure 4. Kinetics of HAP crystallization in the absence (9) and in the presence (b) of 3.6 × 10-6 mol/L HAS1 at pH 7.40, 37 °C, and 0.15 M NaCl.
Similar equations may be derived for the other phosphate salts in the crystallization system, which takes the general form:
The dependence of the crystal growth rate, R, on the relative solution supersaturation, which is equal to σ ) S - 1, is given by eq 10:
∆GHAP ) -RgT ln
IPHAP K°sp,HAP
∆G ) -RgT ln S ) -RgT ln
1/9
( ) IP K°sp
1/ν
(9)
The ∆G values shown in Table 1 were calculated according to this equation, where S is the solution supersaturation, IP is the ionic product of the precipitating salt, K°sp is the corresponding solubility product (at 37 °C, K°sp,HAP ) 2.35 × 10-59,14 K°sp,OCP ) 5.01 × 10-50,15 K°sp,TCP ) 2.83 × 10-30,16 and K°sp,DCPD ) 1.87 × 10-7,17), and ν is the number of ions in the formula unit (e.g., 9 for HAP). For the calculation of the solution supersaturation, the mass balance and electroneutrality conditions had to be taken into account. A number of equations were created to include all chemical equlibria occurring in the supersaturated solution and possible salt formation. To solve this system of equations, a computer program was designed and the speciation in the supersaturated solution was computed after successive approximations for the ionic strength.30
R ) ksσn
(10)
where k is the crystallization reaction rate constant, s is a function of the active growth sites on the seed crystals, and n is the apparent order of the reaction. Kinetic plots according to eq 10 gave a satisfactory fit as may be seen in Figure 3. From the logarithmic plots of ln R vs ln σ, a linear dependence was obtained and values of n ) 2.1 ( 0.1 and n ) 1.8 ( 0.2 were calculated for the crystallization of HAP in the absence and in the presence of HAS1, respectively. A value of n ≈ 2 is indicative of a surface diffusion controlled spiral crystal growth mechanism.13,18,20,27,30-42 From the analysis above, it is suggested that the observed inhibitions result from the interaction of the HAP crystal surface with specific groups of the organic molecule. Stereochemical factors are important in the adsorption process.31-33 The three aza-steroids differ only in their side groups. The addition of side substit-
Homo-Aza-Steroids and Hydroxyapatite Crystallization
uents on HAS1 gave rise to crucial structural changes as may be seen in Figure 1. The structures were refined by the use of energy minimization software (i.e., thermodynamic refinement process). It is also important to note that even though electrostatic interactions are not predominant between the adsorbed molecule and the polar crystal surface of HAP, the adsorption is strong and results in a remarkable crystal growth inhibition. The calculated high value of kaff implies a high affinity between the aza-steroid and the surface of HAP. This means that the adsorbed molecules bind extensively on the crystals and stay there blocking further advancement of the step. From the fitting of the kinetic results to the Langmuir-type isotherm where a value of Rads was found to be less than unity, it can also be assumed that the aza-steroids adsorb reversibly on the surface of HAP. As demonstrated from the kaff value, the equilibrium between adsorption and desorption of the aza-steroids on the crystal is in favor of the adsorbed species. Therefore, the observed inhibition does not result from poisoning of the surface by the adsorbed compounds but from the delay caused in the advancement of the crystal steps, during the growth process, which squeeze between the adsorbed molecules to overcome the blockage.29,43 All three compounds have a carbonyl group in their seven-membered ring. Furthermore, HAS1 has another carbonyl group in the antipode that may interact strongly by electrostatic forces with the charged groups on the surface of HAP. In HAS2, the carbonyl group of HAS1 has been substituted by the five-membered ring with two nitrogen atoms in the aromatic chain. This renders the group an electron donor, which may interact with positively charged points on the surface of HAP. In the third case of HAS3, the molecule has a phenyl group that is a better electron donor system than the ring of HAS2 with the two nitrogen atoms which are quite electronegative and therefore retain strongly the electrons of the aromatic group. So, the HAS3 is expected to be a stronger inhibitor as compared to HAS2. On the other hand, the effect of the stereochemical configuration of the aza-steroid molecules should be also considered. As may be seen in Figure 1c, the HAS3 adopts a configuration shape of two intersecting planes in a right angle due to the presence of a methyl group connected to the second ring of the compound, and so it becomes more bulky. The two groups (i.e., the carbonyl and the phenyl group) which might act synergistically toward adsorption on HAP and crystal growth inhibition now are distant from each other and the molecule cannot unfold its structure and adapt to the same plane as the crystal surface. The molecule can adsorb in a sideways configuration only with one of its planes, while the other plane is vertical to the surface (end-on configuration). It can also adsorb via its phenyl group, but this would lead to weak interaction with the polar surface of HAP. The other alternative of both active sites for adsorption interacting with the HAP surface, which may happen in the case of HAS1, is not feasible for HAS3 due to rigidity of the molecular structure. HSA1 has both carbonyl groups on the same side of the molecule. Presumably, HAS3 cannot be as effective against HAP crystallization as HAS1 because it does not occupy a large area on the crystal and its
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inhibitory activity results mostly from blocking the structural growth units (e.g., the lattice ions) of HAP from easily approaching the crystal surface and incorporating therein. On the other hand, the fact that it sterically blocks a larger area after anchoring on the surface also plays a role, and hence a higher inhibiting effect is seen when compared to the smaller HAS2, which probably has the same mechanism of inhibition. Conclusions In the present work, the effect of three homo-azasteroids compounds on the crystallization of HAP was investigated in solutions supersaturated only with respect to HAP and at conditions of constant solution composition. The aza-steroids were found to be active against HAP crystallization even at very low concentrations of 10-6 mol L-1 and reduced the rates of crystal growth up to 85%. Adsorption and further blocking of the active growth sites may explain the inhibitory effect. The adsorption assumption was justified for one of the aza-steroids through the satisfactory fit of the results to a kinetic Langmuir-type model. On the basis of stereochemical considerations and access of the active sites for adsorption groups to the surface of HAP, the different inhibitory activities of the three homo-azasteroids were explained. References (1) Catsoulakos, P.; Boutis, L. Cancer Chemother. Rep. 1973, 57, 365. (2) Catsoulakos, P.; Wampler, G. L. Oncology 1982, 39, 109. (3) Wampler, G. L.; Catsoulakos, P. Cancer Treat. Rep. 1977, 61, 37. (4) Catsoulakos, P. Cancer Lett. 1984, 22, 199. (5) Moss, M. L.; Kuzmic, P.; Stuart, J. D.; Tian, G.; Peranteau, A. G.; Frye, S. V.; Kadwell, S. H.; Kost, T. A.; Overton, L. K.; Patel, I. R. Biochemistry 1996, 35 (11), 3457. (6) Greway, A. T.; Levy, M. A. J. Steroid Biochem. 1989, 33 (4A), 573. (7) Wright, J. N.; van Leersum, P. T.; Chamberlin, S. G.; Achtar, M., J. Chem. Soc., Perkin Trans. 1989, 1 (9), 1647. (8) Boskey, A. L.; Bullogh, P. G. Scanning Electron Micros. 1984, 28, 511. (9) Gordon, G. V.; Villanueva, T.; Shumacher, H. R.; Gohel, V. J. Rheumatology 1984, 11, 861. (10) Schoen, F. J.; Levy, R. J. Cardiol. Clin. 1984, 2, 713. (11) Valente, M.; Bortloti, U.; Thiene, G. Am. J. Pathol. 1985, 119, 12. (12) Koutsopoulos, S.; Kontogeorgou, A.; Petroheilos, J.; Dalas, E. J. Mater. Sci. Mater. Med. 1998, 9, 421. (13) Nancollas, G. H. J. Cryst. Growth 1977, 42, 185. (14) McDowel, H.; Gregory, T. M.; Brown, W. E. J. Res. Nat. Bur. Stand. 1977, 81, 273. (15) Shyu, L. J.; Perez, L.; Zawacki, S. J.; Heughebaert, J. C.; Nancollas, G. H. J. Dent. Res. 1983, 62, 398. (16) Gregory, T. M.; Moreno, E. C.; Patel, J. M.; Brown, W. E. J. Res. Nat. Bur. Stand. A 1974, 78, 667. (17) Marshall, R. Ph.D. Thesis, State University of New York at Buffalo, NY, 1970. (18) Koutsoukos, P. G.; Amjad, Z.; Tomson, M. B.; Nancollas, G. H. J. Am. Chem. Soc. 1980, 102, 1553. (19) Tomson, M. B.; Nancollas, G. H. Science 1978, 200, 1059. (20) Koutsoukos, P. G., Ph.D. Thesis, State University of New York at Buffalo, 1980. (21) Vordonis, L.; Koutsoukos, P. G.; Lycourghiotis, A. J. Catal. 1986, 98, 296. (22) Martell, A. E.; Motekaitis, R. J. Determination and Use of Stability Constants; VCH Publishers Inc.: New York, 1988. (23) Bates, R. G. Determination of pH. Theory and Practice; Wiley: New York, 1973. (24) Amjad, Z.; Koutsoukos, P. G.; Nancollas, G. H. J. Colloid Interface Sci. 1984, 101, 250.
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CG010005N
