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Amorphous to crystalline calcium phosphate phase transformation at elevated pH
Amorphous to Crystalline Calcium Phosphate Phase Transformation at Elevated pH JOHN L. MEYER AND CECILIA C. W E A T H E R A L L Laboratory o f Biological Structure, National Institute o f Dental Research, National Institutes o f Health, Bethesda, Maryland 20205 Received August 18, 1981; accepted January 21, 1982 The spontaneous precipitation of calcium phosphate was studied in the pH range 9.25-12.80. The first-formed solid phase was an amorphous calcium phosphate (ACP) which transformed after a reproducible induction period into a crystalline apatitic phase. The induction period for this transformation was shown to first increase and then decrease with increasing pH. The maximum stability of ACP occurred at a pH of about 10.25. At lower pH, ACP had a well-defined solubility-determining molecular unit, but in the pH range of this study, a material with a variable solubility was formed suggesting a breakdown in the short-range order of the amorphous phase. Although the amorphousto-crystalline transformation occurs via an octacalcium phosphate (OCP)-like phase in the morenearly physiological pH range 7-9, nucleation kinetics suggested that no such intermediate phase formed at high pH. In fact, thermodynamic considerations rule out the participation of OCP in the amorphous to crystalline transformation above pH 10.7. It is possible that either a different mechanism for the amorphous-crystalline transformation takes precedence at high pH or the variable thermodynamic properties of the ACP formed at high pH result in a substrate with varying ability to nucleate the first-formed crystalline form of calcium phosphate. INTRODUCTION
phous-crystalline transformation at higher pH's in order to determine whether other mechanisms or precursors might be involved in this reaction. This study presents experimental evidence which suggests that in the pH range studied, 9.25-12.80, OCP is no longer a probable intermediate phase and that other mechanisms indeed are involved when ACP converts to HAP.
The spontaneous precipitation of amorphous calcium phosphate (ACP) and its subsequent transformation to crystalline apatite have been extensively investigated (1-5). Most of the earlier studies have dealt only with the composition and structure of the solid phases and direct experimental evidence concerning the mechanisms for the solid-solid transformations was generally not available. Recent studies (5, 6), however, have focused on the thermodynamic properties of the intermediates involved in the phase transformations, and it was concluded that an octaealcium phosphate (OCP)-like phase is a necessary precursor to hydroxyapatite (HAP) when the amorphous-crystalline transformation occurs in the pH range 7-9. Since the OCP-like intermediate phase becomes extremely unstable above pH 9 (6), it was decided to investigate the amor-
EXPERIMENTAL
Reagent-grade chemicals were used without further purification. All solutions were prepared with deionized, distilled, carbonate-free water. All reactions were performed at 25°C in a double-walled glass reaction chamber kept at constant temperature by circulating water from a constant temperature bath. The reaction vessel was covered with polyethylene film and nitrogen was continuously bubbled through the reaction so257
Journalof Colloidand InterfaceScience, Vol.89, No. I, September1982
0021-9797/82/090257-11 $02.00/0 Copyright© 1982by AcademicPress,Inc, All rightsof reproductionin any formreserved
258
MEYER AND WEATHERALL
lution to minimize the uptake of carbon dioxide. The initially undersaturated calcium phosphate reaction solutions (pH ~ 5) were prepared by combining measured amounts of 78 m M calcium nitrate and 48 m M potassium dihydrogen phosphate with water to obtain a combined volume of 600 ml. Initial concentrations of calcium and phosphate, before precipitation, were approximately 6 and 4 raM, respectively. These were adjusted slightly, depending upon the pH of the final reaction solution, in order that approximately equimolar concentrations of calcium and phosphate would be left in solution immediately following precipitation. This was necessary, especially for the higher pH experiments, since the solubility of ACP decreases rapidly with increasing pH and an unmeasurable concentration of one ion would result if the other ion was present in excess. Once thermal equilibrium was obtained spontaneous precipitation was induced by the rapid addition ( ~ 1 sec) of sufficient 2 M potassium hydroxide to increase the solution pH, in the presence of the precipitating ACP, to the desired value. The pH was maintained at the preselected level, within ___0.01 pH unit, by means of a pH stat (Metrohm Combititrator 3-D) which added 2 N potassium hydroxide. The composition of the solution, in equilibrium with the precipitated calcium phosphate phase, was determined at various time intervals by withdrawing 5-ml aliquots, removing the solid phase by 0.22-#m Millipore filtration, and analyzing the resultant filtrate for calcium and phosphate. Filtration required about 10 sec. Calcium concentrations were determined by atomic absorption spectrophotometry (Perkin-Elmer Model 603) and phosphate concentrations were determined spectroscopically as a phosphomolybdate complex (7). The hydrogen-ion-sensitive electrode (Sargent-Welch Combination, Model $3007215) was standardized before each experiment over the pH range of interest by comparison with buffers preJournal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
pared according to NBS specifications (8). The slope of the electrode's pH response at 25°C was established with pH 6.86 (0.025 M Na2HPO4 + 0.025 M KH2PO4) and 9.18 (0.01 M Borax) buffers. The electrode was then checked against a saturated calcium hydroxide solution (pH 12.45) and small corrections were made when necessary. Since the pH values assigned to the solutions are sensitive to temperature, particularly with the calcium hydroxide buffer, both electrode and buffer were stored in the constant temperature bath. Specimens for transmission electron microscopy (TEM) were obtained for selected experiments by withdrawing samples from the precipitation experiments at various time intervals. Drops of the solution slurry were placed directly on Formvar-carbon grids, allowed to settle for about 30 sec, and the excess solvent was carefully removed by touching the edges of the grids with filter paper. The grids were air-dried, and then observed with a JEOL 100B TEM operated at 80 kV. RESULTS Fourteen experiments were performed in the range 9.25-12.50 at approximately 0.25 pH unit intervals. Complete analytical resuits for all these experiments are not presented here, but details from representative experiments are shown in Figs. la and lb for pH 9.25, 10.80, and 12.25. These data were the total analytical concentrations of calcium (Fig. la) and phosphorus (Fig. lb) in solution in equilibrium with the solid calcium phosphate phase. Initial concentrations present before precipitation were much higher. The first solid phase to separate under these conditions was ACP. The relatively fiat portions of the curves obtained within 5 min of spontaneous precipitation represent solutions in equilibrium with ACP. The sharp inflection observed in the curves, after this reproducible period of relative stability, signified the transformation of amorphous
CALCIUM PHOSPHATE PHASE CHANGES
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MINUTES FIG. la. Plot of total calcium concentration, Tca,vs time for three experiments performed at pH 9.25 (©), 10.80 (D), and 12.25 (A). The initial flat portions of the curves indicate solutions in equilibrium with freshly precipitated ACP. The sharp inflections in the curves represent the amorphous to crystalline transformation. Induction periods for those transformations are obtained from tangents to the curves drawn at the inflection points and are indicated on the figures by L Samples for TEM observation were removed from the pH 10.80 experiment at the times indicated (*).
to crystalline calcium phosphate (4). I n d u c tion p e r i o d s , / , for this t r a n s f o r m a t i o n were obtained f r o m the intersection of tangents d r a w n at the inflection points as illustrated in Fig. 1a. Estimation of I was not a t t e m p t e d for the phosphate curves because of their variability in shape at the point of transform a t i o n as shown in Fig. lb. Induction periods, as determined f r o m the analytical calcium curves, are presented in Fig. 2 for the p H range 9.25-12.50. O p e n symbols in this and subsequent figures represent results obtained for a previous study which covered the p H r a n g e 7.40-9.25 at 2 5 ° C (5). It is clear t h a t the induction period for the a m o r p h o u s to crystalline transform a t i o n reached a m a x i m u m at a p H of about 10.25. A f t e r this p H the kinetics of the trans-
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•
pH 10.80
•
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FIG. lb. Plot of total phosphate concentration, Tp, vs time for three experiments performed at pH 9.25 (O), 10.80 (11), and 12.25 (A). The initial flat portions of the curves indicate solutions in equilibrium with freshly precipitated ACP. The sharp inflections in the curves represent the amorphous to crystalline transformation.
formation rapidly increased and overall, a nearly bell-shaped curve was obtained. Free ionic calcium and phosphate activities were determined for all points in all experiments f r o m the pH, analytical calcium, and analytical phosphate concentration by the m e t h o d described previously (5). Corrections were m a d e for the f o r m a t i o n of calc i u m - p h o s p h a t e ion pairs in solution (9). Activity products were calculated for the solutions in equilibrium with the first-formed
4O0
i
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i 9
,
,
,
,
i 10
. . . .
i 11
12
pH
FIG. 2. The dependency of the induction period for the amorphous to crystalline transformation, I, on the pH of the solution. Open symbols represent results obtained in an earlier study (Ref. (5)) performed at lower pH's. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
260
MEYER AND WEATHERALL 11 10
o -Log (Ca)3(PO4)1'87(HPO4)0"2 - 25.00 ~. -Log (HAP) -- 40.00 a -Log (OCP) - 43.00 o -Log (TCP) -- 1 9 . 0 0
,¢.,t%., . r
4
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FIG. 3. The dependence of the log of the activity product at t = 0 for the calcium phosphate phases HAP (A), OCP (n), TCP (O), and Ca3(PO4)I.s7(HPO4)o. 2 (O) on the pH of the precipitating solution. The values are normalized by subtracting 40.00, 43.00, 19.00, and 25.00 from the negative logarithms of the above phases, respectively. Open symbols represent results obtained in an earlier study (Ref. (5)) performed at lower pH's.
data obtained at such high pHs were subject to considerable error because of the very low solubility of ACP at these pHs (see, for example, the lower curves in Figs. la and b). Products of the ion activity product and the induction period for the amorphous to crystalline transformation are given for all experiments in Fig. 4. The three curves represent the variation with pH of the products obtained considering molecular formulae for the calcium phosphate phases HAP, TCP, and OCP. Values obtained for HAP and TCP increased at low pH, reached maxima, and rapidly decreased as the pH further increased. Products obtained for OCP were essentially constant at the lower pHs but also rapidly decreased above pH 9.5. Again, the reliability of the data above pH 12 (dotted lines) was questionable although there may have been a change in chemistry in this region. 50 49 4~
ACP by extrapolation of the data to t = 0. Products were obtained for the molecular formulae of the calcium phases Cas(PO4)3OH (HAP), Caa(PO4)2 (tricalcium phosphate, TCP), Ca4H(PO4)3-2.5 H20 (OCP), and CaH(PO4)I.s7(HPO4)0.2. This latter formula was found to give an invariant ion product for ACP in a previous study in the pH range 7.40-9.25 (5). These initial ion activity products are plotted as a function of pH in Fig. 3. Ion products for OCP decreased throughout the whole range. Ion products for HAP increased initially, reached a maximum at pH 9.8, and then decreased rapidly. Ion products for phases with chemical compositions approximating TCP (including Ca3(PO4)I.s7(HPO4)o.2), were the least affected at low pH but decreased rapidly after pH 9.5. It was not certain if the change in slope observed at pH > 12 (dotted lines) was real since the chemical Journal of Colloid and Interface Science,
Vol. 89, No. 1, September1982
• I x (OCP) • I x (HAP)
/'~
.~'*
• I x (TCP)
/
/
~ 47
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~ 46 ~ 45
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FIG. 4. Variation of the products I X (OCP), I × (HAP), and I X (TCP) with the pH of the solution. I is the induction period for the amorphous to crystalline transformation. (OCP), (HAP), and (TCP) are the ion activity products for the calcium phosphate phases OCP, HAP, and TCP, respectively, obtained from solutions containing freshly precipitated ACP. Open symbols represent results obtained in an earlier study (Ref. (5))
performed at lower pH's.
CALCIUM PHOSPHATE PHASE CHANGES
261
FIG. 5a. TEM micrograph of freshlyprecipitated ACP obtained from an experimentperformed at pH 10.80 (see Figs. la and b). In this and subsequentmicrographsthe bar is 1 /~m in length.
Samples for TEM observations were taken from a number of experiments. Representative micrographs are presented as Figs. 5a-c and 6a-c. Samples shown in Fig. 5 were isolated from the pH 10.80 experiment described in Fig. 1 at the indicated times. Figure 5a shows ACP isolated immediately upon formation (5 min); the ACP was similar in appearance to that described in other studies (3, 10). Upon completion of the amorphous to crystalline transformation, (Fig. 5c; 480 min), only the characteristic morphology of an apatitic calcium phosphate phase was observed. At a point near the inflection of the calcium and phosphate curves, (Fig. 5b, 360 min) both crystalline and amorphous phases were observed. Samples were also taken from an experiment performed at pH 12.80. At this pH the amorphous to crystalline transformation could not be followed by solution chemistry
measurements because the solid phase was too insoluble. Inspection of Fig. 2 suggested a rapid amorphous to crystalline transformation, and indeed a sample isolated at t = 30 min showed both amorphous and crystalline particles (Fig. 6a). At 40 rain (Fig. 6b) most of the sample appeared crystalline, and at 50 rain (Fig. 6c) ACP was not observed in any of the samples. In Fig. 7, a plot of pH vs the free energy, AG, of the solutions in equilibrium with ACP with respect to a solution in equilibrium with each of three well-characterized calcium phosphate crystalline phases is presented. The free energy was calculated from the following equation AG : -(2.303RT/n) log (APi/APs); APi is the ionic activity product of the solution in equilibrium with freshly precipiJournal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
FIG. 5b. TEM micrograph of solid phase isolated from a spontaneous precipitation experiment performed at pH 10.80 at a point during the amorphous to crystalline transformation (360 rain, Figs. la and b). Crystalline and amorphous calcium phosphate phases are observed.
Journal of Colloid and Interface Science,
Vol.89, No. 1, September1982 262
CALCIUM PHOSPHATE PHASE CHANGES
263
FIG. 6a. TEM micrograph of solid phase isolated from a pH 12.80 spontaneous precipitation experiment after 30-min reaction time. Both amorphous and crystalline calcium phosphate phases are observed.
tated ACP, APt is the thermodynamic solubility product, R and T are the ideal gas constant and absolute temperature, respectively, and n is the number of ionic terms in the activity product expression. The log of the thermodynamic solubility products, at 25°C, used in the calculations were: TCP (fl-Ca3(PO4)2, Whitlockite), 28.94; (11) OCP, 47.22; (12), and HAP, 58.59; (13). Points above the solid line (AG < 0) represented solutions, in equilibrium with ACP, that were supersaturated with respect to the designated phase and are permitted phases. Points below the line (AG > 0) were undersaturated and represent phases that are not
thermodynamically permitted. Solutions saturated with respect to ACP were supersaturated with respect to OCP at low pH but became undersaturated at pH >-_ 10.7. Similar solutions were always supersaturated with respect to fl-Caa(PO4)2 and HAP but their dependency on pH differed. The value of AGrcv varied little in the low pH range but steadily decreased (AG less negative) at higher pHs with the inflection occurring at about pH 10.0. The value of AGHAp, however, increased (AG more negative) with increasing pH at the lower pHs, became relatively constant in the pH range 9.5-10.5, and then decreased slightly with increasing
FIG. 5c. TEM micrograph of crystalline calcium phosphate phase isolated from a spontaneous precipitation experiment performed at pH 10.80. Sample was isolated after 480-rain reaction time (see Figs. 1a and b) at a point when the solution chemistry indicated the amorphous to crystalline transformation was complete. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
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MEYER AND WEATHERALL
FIG. 6b. TEM micrograph of solid phase isolated from the pH 12.80 spontaneous precipitation experiment after 40-min reaction time. Most of the sample appears crystalline.
Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
265
CALCIUM PHOSPHATE PHASE C H A N G E S
pH. The dashed curve in this figure was a trace of the induction period vs pH curve taken from Fig. 2. DISCUSSION
The characteristics of the amorphouscrystalline transformation are similar to those described earlier (I-5). ACP is the first-formed solid calcium phosphate phase which transforms to a microcrystalline phase with an apatitic X-ray diffraction pattern after a reproducible induction period. In terms of the solution chemistry changes, the stability of ACP is marked by relatively steady concentrations of calcium and phosphate and the transformation is marked by a sharp drop in the ion activity products for the less soluble crystalline calcium phosphate phases. As seen in Fig. 1, however, this does not necessarily mean a decrease in both calcium and phosphate since the phosphate concentrations actually rise in some of the experiments. This occurs because the newly formed crystalline phase has a higher calcium:phosphate ratio than ACP. TEM observation of the solid phase confirms both the nature of the solid phase and the time course of the reaction as determined from the solution chemistry. Freshly formed ACP was found to have the same morphologic properties at high pH as has been reported for low pH preparations (3, 10). Furthermore, micrographs show both amorphous and crystalline materials at reaction times which correspond to inflections in the analytical data. Only crystalline material is observed when the chemical kinetics suggest that the amorphous-crystalline transformation is complete. In fact, TEM could be used to approximate induction periods for amorphous to crystalline transformations, if chemical data were too imprecise or unavailable (see Fig. 6a-c). ACP, in the pH range 7.4-9.25, appears to have a rather well-defined molecular unit
o HAP n OCP TCP 2
600
--
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c
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~.~..
// 7/ 8
x
200 \
£
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11
12
FIG. 7. The thermodynamic stability of solutions in equilibrium with freshly precipitated ACP compared to solutions in equilibrium with pure crystalline HAP (O), OCP (n), or TCP (fl-Ca3(PO4)2; A) as a function of pH. Points above the line AG = 0 (AG < 0) represent solutions supersaturated with respect to the phase indicated whereas points below the line (AG > 0) represent solutions undersaturated. The dashed line is a trace of the induction period,/, data taken from Fig. 2. Open symbols represent results from an earlier study (Ref. (5)) performed at lower pH's.
governing its solubility. A constant ion activity product could be assigned to the molecular formula, Ca3(PO4)I.sT(HPO4)0.2 (5). This composition was consistent with a previous chemical study which measured this amount of acid phosphate in purified ACP (2). The proposal that ACP contains a solubility-controlling structural unit is consistent with a radial distribution study which suggested that ACP consisted of small clusters with definite local order (14). At high pH, however, the structural unit seems to change (Fig. 3). Although solutions in equilibrium with the first-formed ACP precipitates in the pH range 7.4-9.25 have nearly invariant ion activity products when the phases Caa(POn)I.87(HPO4)o.2 or TCP, respectively, are considered, ion products for both of these phases decrease rapidly with increasing pH in the range 9.5-12.5. This suggests that neither of these molecular formulae, or any multiple thereof, is a good
FIG. 6c. TEM micrograph of solid phase isolated from a pH 12.80 spontaneous precipitation experiment after 50-min reaction time. Only crystalline calcium phosphate phase is observed. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
266
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AND WEATHERALL
representation of the structural unit of ACP. Similarly, a structure approximating HAP appears unlikely since its ion product first increases and then decreases with increasing pH. A molecular product approximating OCP is also a poor representation of the ACP structure since its ion product decreased through the pH range. Since these three model compounds, OCP, TCP, and HAP, represent acidic, neutral, and basic forms of calcium phosphate, it is unlikely that a molecular formula could be assigned to the ACP which forms at high pH which would yield a constant ion product. A form of calcium phosphate much more basic than HAP would have to be proposed and compounds of this type (containing the oxide ion) are unlikely to be formed from aqueous solution (15). The conclusion is that the ACP formed at high pH does not contain a definite structural unit but rather is highly dependent upon the conditions of preparation. In contrast ACP formed in the pH range 7-9.5 appears to contain a single, solubility-controlling molecular unit. Since the low pH form of ACP apparently requires a small amount of acid phosphate for stability (6), it is possible that high pH preparations exclude or neutralize the acid phosphate in the ACP resulting in a breakdown in the structure. Previous studies suggested that OCP is the first-formed crystalline phase that occurs in the amorphous-crystalline transformation at pH 7-9 (5, 6). Two pieces of evidence tend to support this conclusion. First, the kinetics of the transformation are best described assuming OCP as the first nucleated phase and, second, the first-formed crystalline material has a consistent solubility product similar to that of OCP. Although a measure of the solubility of the first-formed crystalline phase was not attempted in this study, a kinetic analysis, similar to that used earlier (5), was employed. For a large number of precipitation systems involving heterogeneous nucleation an empirical equation of Journal of Colloid and Interface Science, VoL 89, No. 1, September 1982
the form I C e = constant is obeyed (16-19); I is the induction period for the nucleation, C is a concentration product term, and P is an integer. The amorphous-to-crystalline transformation appears to be an example of a crystalline material nucleating on a heterogeneous substrate, ACP (3). In the pH range 7-9, only the concentration product for an OCP-like phase satisfies this relationship; however, above this range none of the forms of crystalline calcium phosphate discussed above gives a constant product. Other forms of the equation and other hypothetical molecular formulae were tried but inspection of Fig. 4 suggests it is unlikely that a constant product could be obtained with any combination. The same slope in the curves is observed, a decrease in I × C with increasing pH, whether an acidic, neutral, or basic calcium phosphate phase is proposed. The reason for the shape of the curves and the apparent failure of the nucleation rate law becomes clear if the thermodynamic state of the solutions in equilibrium with ACP is considered. The fact that OCP appears to be the first nucleated crystalline phase is logical in light of the fact that the induction period, in the pH range 7-9, increases with increasing pH, while AGocp, the free energy of the solution with respect to OCP, decreases. The driving force for the nucleation reaction is AGocP and a decrease in the driving force should result in an increased induction period. The value of AGTcp remains relatively constant and AGHAp increases with increasing pH; nucleation of a phase with TCP and HAP stoichiometry should result in a nearly constant or decreasing induction period, respectively, with increasing pH. This is contrary to experimental observation. In contrast, the free energy with respect to the formation of OCP, TCP, and HAP of the solutions in equilibrium with ACP at high pH are all seen to decrease with increasing pH in the high pH range (Fig. 7). However, in this range the induction period for the amorphous-crystalline transforma-
CALCIUM PHOSPHATE PHASE CHANGES
tion is seen to decrease. Thermodynamic considerations would predict an increase. One explanation for this anomalous result is that an unusual, highly basic, stoichiometric form of calcium phosphate is first nucleated which could have an ion activity product that increased with pH. This appears unlikely based upon the arguments presented above, although the transient formation of a more basic form of calcium phosphate, such as tetracalcium phosphate (Ca4(PO4)20), cannot be ruled out (20). Calcium:phosphate molar ratios of the ACP precipitates were found to be in the range 1.46-1.51 and were not particularly sensitive to pH. If significant quantities of a highly basic form of calcium phosphate were being formed the Ca:P ratios would be expected to be much higher. Another explanation is that the mechanism of the amorphous-crystalline transformation changes at high pH and that a solution-mediated, heterogeneous nucleation step is no longer the rate-controlling step. A final, perhaps more likely explanation, is that the same mechanism is involved but the nucleating ability of the ACP changes at high pH. TEM micrographs, at the point when the transformation occurs, show crystalline and amorphous particles in close proximity suggesting nucleation at the surface of ACP. Furthermore, the inability to obtain a constant ion activity product for the ACP at high pH suggests that the structure of this material (at least the solubility-regulating structure) is changing with pH. It is possible that ACP formed at high pH is more similar in nature to apatite and thus acts as a better substrate for nucleation.
267
ACKNOWLEDGMENT The authors would like to thank Elaine Lenk for her assistance in obtaining the TEM micrographs. REFERENCES 1. Eanes, E. D., and Posner, A. S., Trans. N.Y. Acad. Sci. 28, 233 (1965). 2. Termine, J. D., and Eanes, E. D., Calcif Tiss. Res. 10, 171 (1972). 3. Eanes, E, D., Termine, J. D., and Nylen, M. U., Calcif Tiss. Res. 12, 143 (1973). 4. Boskey, A. L., and Posner, A. S., J. Phys. Chem. 77, 2312 (1973). 5. Meyer, J. L., and Eanes, E. D., Calcif Tiss. Res. 25, 59 (1978). 6. Meyer, J. L., and Eanes, E. D., Calcif Tiss. Res. 25, 209 (1978). 7. Murphy, J., and Riley, J. P., Anal Chim. Acta 27, 31 (1962). 8. Bates, R. G., "Determination of pH. Theory and Practice," pp. 90-123. Wiley, New York, 1964. 9. Chughtai, A., Marshall, R., and Nancollas, G. H., J. Phys. Chem. 72, 208 (1968). 10. Nylen, M. U., Eanes, E. D., and Termine, J. D., Calcif Tiss. Res. 9, 95 (1972). 11. Gregory, T. M., Moreno, E. C., Patel, J. M., and Brown, W. E., J. Res. NatL Bur. Stand. A 78, 667 (1974). 12. Moreno, E. C., Brown, W. E., and Osborn, G., Soil Sci. Soc. Amer. Proc. 21, 99 (1960). 13. McDowell, H., Wallace, B. M., and Brown, W. E., abstracted, IADR Program and Abstracts of Papers, No. 340, 1969. 14. Betts, F., and Posner, A. S., Mat. Res. Bull. 9, 353 (1974). 15. Van Wazer, J. R., "Phosphorus and its Compounds. Volume I: Chemistry," p. 528. Interscience, New York, 1958. 16. Van Hook, A., J. Phys. Chem. 44, 751 (1940). 17. Christiansen, J. A., and Nielsen, A. E., Acta Chem. Scand. 5, 673 (1951). 18. Nielsen, A. E., J. Colloid Sci. 10, 576 (1955). 19. Walton, A. G., Science 149, 601 (1965). 20. Brown, W. E., and Epstein, E. F., J. Res. Natl. Bur. Stand. A 69, 547 (1965).
Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
phous-crystalline transformation at higher pH's in order to determine whether other mechanisms or precursors might be involved in this reaction. This study presents experimental evidence which suggests that in the pH range studied, 9.25-12.80, OCP is no longer a probable intermediate phase and that other mechanisms indeed are involved when ACP converts to HAP.
The spontaneous precipitation of amorphous calcium phosphate (ACP) and its subsequent transformation to crystalline apatite have been extensively investigated (1-5). Most of the earlier studies have dealt only with the composition and structure of the solid phases and direct experimental evidence concerning the mechanisms for the solid-solid transformations was generally not available. Recent studies (5, 6), however, have focused on the thermodynamic properties of the intermediates involved in the phase transformations, and it was concluded that an octaealcium phosphate (OCP)-like phase is a necessary precursor to hydroxyapatite (HAP) when the amorphous-crystalline transformation occurs in the pH range 7-9. Since the OCP-like intermediate phase becomes extremely unstable above pH 9 (6), it was decided to investigate the amor-
EXPERIMENTAL
Reagent-grade chemicals were used without further purification. All solutions were prepared with deionized, distilled, carbonate-free water. All reactions were performed at 25°C in a double-walled glass reaction chamber kept at constant temperature by circulating water from a constant temperature bath. The reaction vessel was covered with polyethylene film and nitrogen was continuously bubbled through the reaction so257
Journalof Colloidand InterfaceScience, Vol.89, No. I, September1982
0021-9797/82/090257-11 $02.00/0 Copyright© 1982by AcademicPress,Inc, All rightsof reproductionin any formreserved
258
MEYER AND WEATHERALL
lution to minimize the uptake of carbon dioxide. The initially undersaturated calcium phosphate reaction solutions (pH ~ 5) were prepared by combining measured amounts of 78 m M calcium nitrate and 48 m M potassium dihydrogen phosphate with water to obtain a combined volume of 600 ml. Initial concentrations of calcium and phosphate, before precipitation, were approximately 6 and 4 raM, respectively. These were adjusted slightly, depending upon the pH of the final reaction solution, in order that approximately equimolar concentrations of calcium and phosphate would be left in solution immediately following precipitation. This was necessary, especially for the higher pH experiments, since the solubility of ACP decreases rapidly with increasing pH and an unmeasurable concentration of one ion would result if the other ion was present in excess. Once thermal equilibrium was obtained spontaneous precipitation was induced by the rapid addition ( ~ 1 sec) of sufficient 2 M potassium hydroxide to increase the solution pH, in the presence of the precipitating ACP, to the desired value. The pH was maintained at the preselected level, within ___0.01 pH unit, by means of a pH stat (Metrohm Combititrator 3-D) which added 2 N potassium hydroxide. The composition of the solution, in equilibrium with the precipitated calcium phosphate phase, was determined at various time intervals by withdrawing 5-ml aliquots, removing the solid phase by 0.22-#m Millipore filtration, and analyzing the resultant filtrate for calcium and phosphate. Filtration required about 10 sec. Calcium concentrations were determined by atomic absorption spectrophotometry (Perkin-Elmer Model 603) and phosphate concentrations were determined spectroscopically as a phosphomolybdate complex (7). The hydrogen-ion-sensitive electrode (Sargent-Welch Combination, Model $3007215) was standardized before each experiment over the pH range of interest by comparison with buffers preJournal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
pared according to NBS specifications (8). The slope of the electrode's pH response at 25°C was established with pH 6.86 (0.025 M Na2HPO4 + 0.025 M KH2PO4) and 9.18 (0.01 M Borax) buffers. The electrode was then checked against a saturated calcium hydroxide solution (pH 12.45) and small corrections were made when necessary. Since the pH values assigned to the solutions are sensitive to temperature, particularly with the calcium hydroxide buffer, both electrode and buffer were stored in the constant temperature bath. Specimens for transmission electron microscopy (TEM) were obtained for selected experiments by withdrawing samples from the precipitation experiments at various time intervals. Drops of the solution slurry were placed directly on Formvar-carbon grids, allowed to settle for about 30 sec, and the excess solvent was carefully removed by touching the edges of the grids with filter paper. The grids were air-dried, and then observed with a JEOL 100B TEM operated at 80 kV. RESULTS Fourteen experiments were performed in the range 9.25-12.50 at approximately 0.25 pH unit intervals. Complete analytical resuits for all these experiments are not presented here, but details from representative experiments are shown in Figs. la and lb for pH 9.25, 10.80, and 12.25. These data were the total analytical concentrations of calcium (Fig. la) and phosphorus (Fig. lb) in solution in equilibrium with the solid calcium phosphate phase. Initial concentrations present before precipitation were much higher. The first solid phase to separate under these conditions was ACP. The relatively fiat portions of the curves obtained within 5 min of spontaneous precipitation represent solutions in equilibrium with ACP. The sharp inflection observed in the curves, after this reproducible period of relative stability, signified the transformation of amorphous
CALCIUM PHOSPHATE PHASE CHANGES
4~
259
3
3-
~/I l ~ ~
4"~ ~x 2~
2
o pH 9.25 a pH 10.80 ~ pH12,25
1 I-
0
0
100
I
Z
P
200
300
40O
I
5O0
600
MINUTES FIG. la. Plot of total calcium concentration, Tca,vs time for three experiments performed at pH 9.25 (©), 10.80 (D), and 12.25 (A). The initial flat portions of the curves indicate solutions in equilibrium with freshly precipitated ACP. The sharp inflections in the curves represent the amorphous to crystalline transformation. Induction periods for those transformations are obtained from tangents to the curves drawn at the inflection points and are indicated on the figures by L Samples for TEM observation were removed from the pH 10.80 experiment at the times indicated (*).
to crystalline calcium phosphate (4). I n d u c tion p e r i o d s , / , for this t r a n s f o r m a t i o n were obtained f r o m the intersection of tangents d r a w n at the inflection points as illustrated in Fig. 1a. Estimation of I was not a t t e m p t e d for the phosphate curves because of their variability in shape at the point of transform a t i o n as shown in Fig. lb. Induction periods, as determined f r o m the analytical calcium curves, are presented in Fig. 2 for the p H range 9.25-12.50. O p e n symbols in this and subsequent figures represent results obtained for a previous study which covered the p H r a n g e 7.40-9.25 at 2 5 ° C (5). It is clear t h a t the induction period for the a m o r p h o u s to crystalline transform a t i o n reached a m a x i m u m at a p H of about 10.25. A f t e r this p H the kinetics of the trans-
I
~
r
•
pH .25
•
pH 10.80
•
122.5pH
I
I
100 200 300 400 MINUTES
I
I
500 600
FIG. lb. Plot of total phosphate concentration, Tp, vs time for three experiments performed at pH 9.25 (O), 10.80 (11), and 12.25 (A). The initial flat portions of the curves indicate solutions in equilibrium with freshly precipitated ACP. The sharp inflections in the curves represent the amorphous to crystalline transformation.
formation rapidly increased and overall, a nearly bell-shaped curve was obtained. Free ionic calcium and phosphate activities were determined for all points in all experiments f r o m the pH, analytical calcium, and analytical phosphate concentration by the m e t h o d described previously (5). Corrections were m a d e for the f o r m a t i o n of calc i u m - p h o s p h a t e ion pairs in solution (9). Activity products were calculated for the solutions in equilibrium with the first-formed
4O0
i
8
i 9
,
,
,
,
i 10
. . . .
i 11
12
pH
FIG. 2. The dependency of the induction period for the amorphous to crystalline transformation, I, on the pH of the solution. Open symbols represent results obtained in an earlier study (Ref. (5)) performed at lower pH's. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
260
MEYER AND WEATHERALL 11 10
o -Log (Ca)3(PO4)1'87(HPO4)0"2 - 25.00 ~. -Log (HAP) -- 40.00 a -Log (OCP) - 43.00 o -Log (TCP) -- 1 9 . 0 0
,¢.,t%., . r
4
~
"t
3 2 1 0
I
I
I
I
I
i
8
9
10 pH
11
12
13
FIG. 3. The dependence of the log of the activity product at t = 0 for the calcium phosphate phases HAP (A), OCP (n), TCP (O), and Ca3(PO4)I.s7(HPO4)o. 2 (O) on the pH of the precipitating solution. The values are normalized by subtracting 40.00, 43.00, 19.00, and 25.00 from the negative logarithms of the above phases, respectively. Open symbols represent results obtained in an earlier study (Ref. (5)) performed at lower pH's.
data obtained at such high pHs were subject to considerable error because of the very low solubility of ACP at these pHs (see, for example, the lower curves in Figs. la and b). Products of the ion activity product and the induction period for the amorphous to crystalline transformation are given for all experiments in Fig. 4. The three curves represent the variation with pH of the products obtained considering molecular formulae for the calcium phosphate phases HAP, TCP, and OCP. Values obtained for HAP and TCP increased at low pH, reached maxima, and rapidly decreased as the pH further increased. Products obtained for OCP were essentially constant at the lower pHs but also rapidly decreased above pH 9.5. Again, the reliability of the data above pH 12 (dotted lines) was questionable although there may have been a change in chemistry in this region. 50 49 4~
ACP by extrapolation of the data to t = 0. Products were obtained for the molecular formulae of the calcium phases Cas(PO4)3OH (HAP), Caa(PO4)2 (tricalcium phosphate, TCP), Ca4H(PO4)3-2.5 H20 (OCP), and CaH(PO4)I.s7(HPO4)0.2. This latter formula was found to give an invariant ion product for ACP in a previous study in the pH range 7.40-9.25 (5). These initial ion activity products are plotted as a function of pH in Fig. 3. Ion products for OCP decreased throughout the whole range. Ion products for HAP increased initially, reached a maximum at pH 9.8, and then decreased rapidly. Ion products for phases with chemical compositions approximating TCP (including Ca3(PO4)I.s7(HPO4)o.2), were the least affected at low pH but decreased rapidly after pH 9.5. It was not certain if the change in slope observed at pH > 12 (dotted lines) was real since the chemical Journal of Colloid and Interface Science,
Vol. 89, No. 1, September1982
• I x (OCP) • I x (HAP)
/'~
.~'*
• I x (TCP)
/
/
~ 47
26
~ 46 ~ 45
24
N 43
41
_
i 8
~ 10 pH
1~1
22
1t2
20 13
FIG. 4. Variation of the products I X (OCP), I × (HAP), and I X (TCP) with the pH of the solution. I is the induction period for the amorphous to crystalline transformation. (OCP), (HAP), and (TCP) are the ion activity products for the calcium phosphate phases OCP, HAP, and TCP, respectively, obtained from solutions containing freshly precipitated ACP. Open symbols represent results obtained in an earlier study (Ref. (5))
performed at lower pH's.
CALCIUM PHOSPHATE PHASE CHANGES
261
FIG. 5a. TEM micrograph of freshlyprecipitated ACP obtained from an experimentperformed at pH 10.80 (see Figs. la and b). In this and subsequentmicrographsthe bar is 1 /~m in length.
Samples for TEM observations were taken from a number of experiments. Representative micrographs are presented as Figs. 5a-c and 6a-c. Samples shown in Fig. 5 were isolated from the pH 10.80 experiment described in Fig. 1 at the indicated times. Figure 5a shows ACP isolated immediately upon formation (5 min); the ACP was similar in appearance to that described in other studies (3, 10). Upon completion of the amorphous to crystalline transformation, (Fig. 5c; 480 min), only the characteristic morphology of an apatitic calcium phosphate phase was observed. At a point near the inflection of the calcium and phosphate curves, (Fig. 5b, 360 min) both crystalline and amorphous phases were observed. Samples were also taken from an experiment performed at pH 12.80. At this pH the amorphous to crystalline transformation could not be followed by solution chemistry
measurements because the solid phase was too insoluble. Inspection of Fig. 2 suggested a rapid amorphous to crystalline transformation, and indeed a sample isolated at t = 30 min showed both amorphous and crystalline particles (Fig. 6a). At 40 rain (Fig. 6b) most of the sample appeared crystalline, and at 50 rain (Fig. 6c) ACP was not observed in any of the samples. In Fig. 7, a plot of pH vs the free energy, AG, of the solutions in equilibrium with ACP with respect to a solution in equilibrium with each of three well-characterized calcium phosphate crystalline phases is presented. The free energy was calculated from the following equation AG : -(2.303RT/n) log (APi/APs); APi is the ionic activity product of the solution in equilibrium with freshly precipiJournal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
FIG. 5b. TEM micrograph of solid phase isolated from a spontaneous precipitation experiment performed at pH 10.80 at a point during the amorphous to crystalline transformation (360 rain, Figs. la and b). Crystalline and amorphous calcium phosphate phases are observed.
Journal of Colloid and Interface Science,
Vol.89, No. 1, September1982 262
CALCIUM PHOSPHATE PHASE CHANGES
263
FIG. 6a. TEM micrograph of solid phase isolated from a pH 12.80 spontaneous precipitation experiment after 30-min reaction time. Both amorphous and crystalline calcium phosphate phases are observed.
tated ACP, APt is the thermodynamic solubility product, R and T are the ideal gas constant and absolute temperature, respectively, and n is the number of ionic terms in the activity product expression. The log of the thermodynamic solubility products, at 25°C, used in the calculations were: TCP (fl-Ca3(PO4)2, Whitlockite), 28.94; (11) OCP, 47.22; (12), and HAP, 58.59; (13). Points above the solid line (AG < 0) represented solutions, in equilibrium with ACP, that were supersaturated with respect to the designated phase and are permitted phases. Points below the line (AG > 0) were undersaturated and represent phases that are not
thermodynamically permitted. Solutions saturated with respect to ACP were supersaturated with respect to OCP at low pH but became undersaturated at pH >-_ 10.7. Similar solutions were always supersaturated with respect to fl-Caa(PO4)2 and HAP but their dependency on pH differed. The value of AGrcv varied little in the low pH range but steadily decreased (AG less negative) at higher pHs with the inflection occurring at about pH 10.0. The value of AGHAp, however, increased (AG more negative) with increasing pH at the lower pHs, became relatively constant in the pH range 9.5-10.5, and then decreased slightly with increasing
FIG. 5c. TEM micrograph of crystalline calcium phosphate phase isolated from a spontaneous precipitation experiment performed at pH 10.80. Sample was isolated after 480-rain reaction time (see Figs. 1a and b) at a point when the solution chemistry indicated the amorphous to crystalline transformation was complete. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
264
MEYER AND WEATHERALL
FIG. 6b. TEM micrograph of solid phase isolated from the pH 12.80 spontaneous precipitation experiment after 40-min reaction time. Most of the sample appears crystalline.
Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
265
CALCIUM PHOSPHATE PHASE C H A N G E S
pH. The dashed curve in this figure was a trace of the induction period vs pH curve taken from Fig. 2. DISCUSSION
The characteristics of the amorphouscrystalline transformation are similar to those described earlier (I-5). ACP is the first-formed solid calcium phosphate phase which transforms to a microcrystalline phase with an apatitic X-ray diffraction pattern after a reproducible induction period. In terms of the solution chemistry changes, the stability of ACP is marked by relatively steady concentrations of calcium and phosphate and the transformation is marked by a sharp drop in the ion activity products for the less soluble crystalline calcium phosphate phases. As seen in Fig. 1, however, this does not necessarily mean a decrease in both calcium and phosphate since the phosphate concentrations actually rise in some of the experiments. This occurs because the newly formed crystalline phase has a higher calcium:phosphate ratio than ACP. TEM observation of the solid phase confirms both the nature of the solid phase and the time course of the reaction as determined from the solution chemistry. Freshly formed ACP was found to have the same morphologic properties at high pH as has been reported for low pH preparations (3, 10). Furthermore, micrographs show both amorphous and crystalline materials at reaction times which correspond to inflections in the analytical data. Only crystalline material is observed when the chemical kinetics suggest that the amorphous-crystalline transformation is complete. In fact, TEM could be used to approximate induction periods for amorphous to crystalline transformations, if chemical data were too imprecise or unavailable (see Fig. 6a-c). ACP, in the pH range 7.4-9.25, appears to have a rather well-defined molecular unit
o HAP n OCP TCP 2
600
--
/
c
\\
~.~..
// 7/ 8
x
200 \
£
10 pH
11
12
FIG. 7. The thermodynamic stability of solutions in equilibrium with freshly precipitated ACP compared to solutions in equilibrium with pure crystalline HAP (O), OCP (n), or TCP (fl-Ca3(PO4)2; A) as a function of pH. Points above the line AG = 0 (AG < 0) represent solutions supersaturated with respect to the phase indicated whereas points below the line (AG > 0) represent solutions undersaturated. The dashed line is a trace of the induction period,/, data taken from Fig. 2. Open symbols represent results from an earlier study (Ref. (5)) performed at lower pH's.
governing its solubility. A constant ion activity product could be assigned to the molecular formula, Ca3(PO4)I.sT(HPO4)0.2 (5). This composition was consistent with a previous chemical study which measured this amount of acid phosphate in purified ACP (2). The proposal that ACP contains a solubility-controlling structural unit is consistent with a radial distribution study which suggested that ACP consisted of small clusters with definite local order (14). At high pH, however, the structural unit seems to change (Fig. 3). Although solutions in equilibrium with the first-formed ACP precipitates in the pH range 7.4-9.25 have nearly invariant ion activity products when the phases Caa(POn)I.87(HPO4)o.2 or TCP, respectively, are considered, ion products for both of these phases decrease rapidly with increasing pH in the range 9.5-12.5. This suggests that neither of these molecular formulae, or any multiple thereof, is a good
FIG. 6c. TEM micrograph of solid phase isolated from a pH 12.80 spontaneous precipitation experiment after 50-min reaction time. Only crystalline calcium phosphate phase is observed. Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982
266
MEYER
AND WEATHERALL
representation of the structural unit of ACP. Similarly, a structure approximating HAP appears unlikely since its ion product first increases and then decreases with increasing pH. A molecular product approximating OCP is also a poor representation of the ACP structure since its ion product decreased through the pH range. Since these three model compounds, OCP, TCP, and HAP, represent acidic, neutral, and basic forms of calcium phosphate, it is unlikely that a molecular formula could be assigned to the ACP which forms at high pH which would yield a constant ion product. A form of calcium phosphate much more basic than HAP would have to be proposed and compounds of this type (containing the oxide ion) are unlikely to be formed from aqueous solution (15). The conclusion is that the ACP formed at high pH does not contain a definite structural unit but rather is highly dependent upon the conditions of preparation. In contrast ACP formed in the pH range 7-9.5 appears to contain a single, solubility-controlling molecular unit. Since the low pH form of ACP apparently requires a small amount of acid phosphate for stability (6), it is possible that high pH preparations exclude or neutralize the acid phosphate in the ACP resulting in a breakdown in the structure. Previous studies suggested that OCP is the first-formed crystalline phase that occurs in the amorphous-crystalline transformation at pH 7-9 (5, 6). Two pieces of evidence tend to support this conclusion. First, the kinetics of the transformation are best described assuming OCP as the first nucleated phase and, second, the first-formed crystalline material has a consistent solubility product similar to that of OCP. Although a measure of the solubility of the first-formed crystalline phase was not attempted in this study, a kinetic analysis, similar to that used earlier (5), was employed. For a large number of precipitation systems involving heterogeneous nucleation an empirical equation of Journal of Colloid and Interface Science, VoL 89, No. 1, September 1982
the form I C e = constant is obeyed (16-19); I is the induction period for the nucleation, C is a concentration product term, and P is an integer. The amorphous-to-crystalline transformation appears to be an example of a crystalline material nucleating on a heterogeneous substrate, ACP (3). In the pH range 7-9, only the concentration product for an OCP-like phase satisfies this relationship; however, above this range none of the forms of crystalline calcium phosphate discussed above gives a constant product. Other forms of the equation and other hypothetical molecular formulae were tried but inspection of Fig. 4 suggests it is unlikely that a constant product could be obtained with any combination. The same slope in the curves is observed, a decrease in I × C with increasing pH, whether an acidic, neutral, or basic calcium phosphate phase is proposed. The reason for the shape of the curves and the apparent failure of the nucleation rate law becomes clear if the thermodynamic state of the solutions in equilibrium with ACP is considered. The fact that OCP appears to be the first nucleated crystalline phase is logical in light of the fact that the induction period, in the pH range 7-9, increases with increasing pH, while AGocp, the free energy of the solution with respect to OCP, decreases. The driving force for the nucleation reaction is AGocP and a decrease in the driving force should result in an increased induction period. The value of AGTcp remains relatively constant and AGHAp increases with increasing pH; nucleation of a phase with TCP and HAP stoichiometry should result in a nearly constant or decreasing induction period, respectively, with increasing pH. This is contrary to experimental observation. In contrast, the free energy with respect to the formation of OCP, TCP, and HAP of the solutions in equilibrium with ACP at high pH are all seen to decrease with increasing pH in the high pH range (Fig. 7). However, in this range the induction period for the amorphous-crystalline transforma-
CALCIUM PHOSPHATE PHASE CHANGES
tion is seen to decrease. Thermodynamic considerations would predict an increase. One explanation for this anomalous result is that an unusual, highly basic, stoichiometric form of calcium phosphate is first nucleated which could have an ion activity product that increased with pH. This appears unlikely based upon the arguments presented above, although the transient formation of a more basic form of calcium phosphate, such as tetracalcium phosphate (Ca4(PO4)20), cannot be ruled out (20). Calcium:phosphate molar ratios of the ACP precipitates were found to be in the range 1.46-1.51 and were not particularly sensitive to pH. If significant quantities of a highly basic form of calcium phosphate were being formed the Ca:P ratios would be expected to be much higher. Another explanation is that the mechanism of the amorphous-crystalline transformation changes at high pH and that a solution-mediated, heterogeneous nucleation step is no longer the rate-controlling step. A final, perhaps more likely explanation, is that the same mechanism is involved but the nucleating ability of the ACP changes at high pH. TEM micrographs, at the point when the transformation occurs, show crystalline and amorphous particles in close proximity suggesting nucleation at the surface of ACP. Furthermore, the inability to obtain a constant ion activity product for the ACP at high pH suggests that the structure of this material (at least the solubility-regulating structure) is changing with pH. It is possible that ACP formed at high pH is more similar in nature to apatite and thus acts as a better substrate for nucleation.
267
ACKNOWLEDGMENT The authors would like to thank Elaine Lenk for her assistance in obtaining the TEM micrographs. REFERENCES 1. Eanes, E. D., and Posner, A. S., Trans. N.Y. Acad. Sci. 28, 233 (1965). 2. Termine, J. D., and Eanes, E. D., Calcif Tiss. Res. 10, 171 (1972). 3. Eanes, E, D., Termine, J. D., and Nylen, M. U., Calcif Tiss. Res. 12, 143 (1973). 4. Boskey, A. L., and Posner, A. S., J. Phys. Chem. 77, 2312 (1973). 5. Meyer, J. L., and Eanes, E. D., Calcif Tiss. Res. 25, 59 (1978). 6. Meyer, J. L., and Eanes, E. D., Calcif Tiss. Res. 25, 209 (1978). 7. Murphy, J., and Riley, J. P., Anal Chim. Acta 27, 31 (1962). 8. Bates, R. G., "Determination of pH. Theory and Practice," pp. 90-123. Wiley, New York, 1964. 9. Chughtai, A., Marshall, R., and Nancollas, G. H., J. Phys. Chem. 72, 208 (1968). 10. Nylen, M. U., Eanes, E. D., and Termine, J. D., Calcif Tiss. Res. 9, 95 (1972). 11. Gregory, T. M., Moreno, E. C., Patel, J. M., and Brown, W. E., J. Res. NatL Bur. Stand. A 78, 667 (1974). 12. Moreno, E. C., Brown, W. E., and Osborn, G., Soil Sci. Soc. Amer. Proc. 21, 99 (1960). 13. McDowell, H., Wallace, B. M., and Brown, W. E., abstracted, IADR Program and Abstracts of Papers, No. 340, 1969. 14. Betts, F., and Posner, A. S., Mat. Res. Bull. 9, 353 (1974). 15. Van Wazer, J. R., "Phosphorus and its Compounds. Volume I: Chemistry," p. 528. Interscience, New York, 1958. 16. Van Hook, A., J. Phys. Chem. 44, 751 (1940). 17. Christiansen, J. A., and Nielsen, A. E., Acta Chem. Scand. 5, 673 (1951). 18. Nielsen, A. E., J. Colloid Sci. 10, 576 (1955). 19. Walton, A. G., Science 149, 601 (1965). 20. Brown, W. E., and Epstein, E. F., J. Res. Natl. Bur. Stand. A 69, 547 (1965).
Journal of Colloid and Interface Science, Vol. 89, No. 1, September 1982