CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 2 639–645
PerspectiVes Calcium Phosphate Solubility: The Need for Re-Evaluation H.-B. Pan†,‡ and B. W. Darvell*,† Dental Materials Science, Faculty of Dentistry, The UniVersity of Hong Kong, and Department of Orthopaedics and Traumatology, The UniVersity of Hong Kong ReceiVed October 6, 2008; ReVised Manuscript ReceiVed October 30, 2008
ABSTRACT: The determination of the solubility of calcium phosphates by the conventional large excess of solid method has been demonstrated to be inappropriate. The problem lies in incongruent dissolution, leading to phase transformations, and lack of detailed solution equilibria: all calculations have been based on simplifications, which are only crudely approximate. The absolute solidtitration approach shows excellent reliability and reproducibility. Using solid titration, the true solubility isotherm of hydroxyapatite (HAp) has been found to lie substantially lower than previously reported. In addition, contrary to wide belief, dicalcium phosphate dihydrate (DCPD) is not the most stable phase below pH ∼4.2, where calcium-deficient HAp is less soluble. The misunderstanding here arises from the metastability of DCPD, which nucleates much more easily than HAp at low pH. Such results indicate that the Ca-P system is in need of complete reappraisal. The solid-titration method can be extended to other complex systems.
1. Introduction Calcium phosphates have attracted considerable interest over many years, and in particular hydroxyapatite (HAp), as it is the basis of the major inorganic component of many biological hard tissues (dental enamel, dentine, bone)1,2 as well as pathological calcifications (e.g., dental calculus).3-6 As perhaps the key property in the context, solubility determines the direction of many processes such as dissolution, precipitation, and phase transformation, and is also crucial in biological contexts such as the formation and resorption of hard tissues as well as pathological conditions,7 especially dental caries.8 This becomes of greater interest in studying the prospects for “remineralization”, the repair of dental carious lesions by external therapeutic treatment,9 mineralization of implant interfaces,10 and even bone repair.11 Although the solubility of HAp has been the subject of extensive investigations for several decades,12-22 little agreement on or precision for the solubility product (p)Ksp has been obtained (Figure 1), although a value of 58.4 has been partially accepted23 [HAp is variously referred to as Ca5 or doubled Ca10 formula. For consistency, only the equivalent Ca5 values for pKsp will be used in this paper, converted as necessary (i.e., divided by 2)]. The difficulties have been attributed to factors such as incongruent dissolution (phase transformation)24 and variable composition (calcium-deficient and calcium-rich).15 But such a value (i.e., 58.4) apparently cannot explain some phenomena in vitro; for example, Wang * To whom correspondence should be addressed. Tel: +852 2859 0303. Fax: +852 2548 9464. E-mail:
[email protected]. † Dental Materials Science, Faculty of Dentistry. ‡ Department of Orthopaedics and Traumatology.
et al.25 reported that dental enamel was protected by nanoscale HAp crystals against further dissolution such that the adjacent solution remained undersaturated with respect to HAp. Clearly, and according to well-established thermodynamic principles, below saturation all solids tend to dissolve (and especially allowing for the known particle-size effect of small scale driving dissolution); if the reported result is real, the solution should have already reached saturation. The confusion possibly arises from reliance on the reported solubility. However, detailed and accurate knowledge of the solid phase and its solubility is still lacking, and still less the effects of lattice substitutions such as fluoride, carbonate, and so on which characterize biological apatites. In the conventional method, solubility is determined through the addition of a large excess of solid into a given solution and stirring. If the analyzed solution ion concentration does not change with time, equilibrium is presumed to have been reached. However, for calcium phosphates this seems problematic, in part due to the limitation of the precision and accuracy of such analyses, but also the possibility of phase transformations: several other phases may also be involved [e.g., for HAp work: DCPD, octacalcium phosphate (OCP), or amorphous calcium phosphate (ACP)], thus complicating the situation. Although a number of papers26-34 have focused on the dissolution mechanism of calcium phosphates, seldom has there been discussion of the method itself. A detailed analysis is therefore necessary. To emphasize the point, it has been known since the 1930s that the solubility of calcium phosphates “depends on the amount of solid present”;35 this revealing remark has not been recognized for what it entails: incongruency.
10.1021/cg801118v CCC: $40.75 2009 American Chemical Society Published on Web 12/09/2008
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Figure 1. Solubility results for HAp by the conventional excess-solid method compared with isotherm from solid titration.63,77 The equivalent pKsp for the solid titration results below pH 3.9 is ∼63; it cannot be calculated for the region above pH 3.9.77
2. Problems of the Conventional Method 2.1. Incongruent Dissolution. Phase transformation occurring on particle surfaces is a critical problem. For the theory of solubility itself to be satisfied, it is essential for a measurement that the composition of the solid be completely unchanged; otherwise, the solution analysis does not correspond to that of the original solid. However, for calcium phosphates, incongruent dissolution is well documented.24,27,28,32 If heterogeneous nucleation occurs, an unknown, possibly more acidic, calcium phosphate, other than HAp, may form. In such a case, the calculated solubility cannot be a true value for the original material. In addition, Nordstrom et al.36 reported that calcium dissolution was much faster than for phosphate in calcium phosphates with Ca/P ratios between 1.67 and 2.0. Thus, if incongruent dissolution occurs from a (stoichiometric) HAp surface, the surface Ca/P ratio will become lower than for the bulk, and a calcium-deficient HAp must then be present, even if there is no phase change. Of course, to maintain charge balance in the solid, other species must also be involved: H+ and OH- at least, and the risk of a phase change is made greater. Brown and Martin37 concluded that if the Ca/P ratio in solution remained stoichiometric, the HAp had dissolved congruently (this, however, depends on the accuracy with which the analyses can be made). However, if the two values differed, a surface layer would have been formed. Thus the differing dissolution rates of calcium and phosphate ions possibly lead to the formation of a calcium-deficient HAp with composition varying from Ca10(PO4)6(OH)2 to ∼Ca9HPO4(PO4)4OH, that is, from the stoichiometric Ca/P ratio 1.67 to 1.5, the reported limit of a fully calcium-deficient material.37
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In addition, a surface complex with the composition of Ca2(HPO4)(OH)2 has been postulated according to the solution Ca/P ratio at equilibrium.15 However, no strong evidence was offered for such a phase; at least no confirmation from XRD or other technique was given, and there appears to be no other report of such a substance. Nevertheless, in view of what follows, the potential for such other phases should be kept in mind in such studies. Although in most previous work the (bulk) composition and constitution of the original solid has been analyzed carefully, similar analysis and identification of the solid material when equilibrium was attained have been very limited. Thus, it cannot be said with confidence what solid substance (i.e., in contact with the solution) is relevant to the equilibrium. In fact, the second phase covering the HAp surface may vary, as has been recognized. For example, OCP has been found to form on the surface of an HAp seed in a supersaturated calcium phosphate solution38-40 Eanes41 found that an amorphous phase, a calcium carbonate phosphate, may form spontaneously at pH 7.4, and this may eventually transform to a more stable crystalline apatite phase. DCPD may possibly also form as a transient phase.42-44 For example, Mahapatra et al.19 found wellcrystalline DCPD formed below pH 7.2 in 0.165 M NaNO3 solution during solubility work involving a large excess of solid HAp. This indicates that the solid surface may have already been contaminated with another phase; such conditions cannot permit a true solubility for HAp to be obtained. 2.2. Solubility Product. The calculation of the solubility product itself (Ksp) may also have a problem. The determination depends not only on the validity of a measured mass solubility, but also on the assumed solution speciation, as the distribution of an analyte across all species controls the activity of each of the representative entities inserted in the solubility product. That is to say, all ionic and neutral forms derived from the components of the solid during the dissolution process need to be taken into an account. Even in a “simple” solution, there may be more than a dozen equilibria involved. In particular, for the calcium phosphate system the case is rather more complicated due to the many known, assumed, or postulated species, and although attention has been drawn to such species,45 for example, CaH2PO4+, CaPO4-, seldom have they been involved in the calculations. Whether this is because of assumed insignificance, lack of recognition, or lack of the ability to do the calculation, the omission cannot be defended. Unless such species are accounted for fully (and it is by no means certain that we have as yet a full inventory), it is not possible to calculate a meaningful Ksp. Thus, the solubility product for HAp is ordinarily only expressed in the simplified form: pKsp ) -log([Ca2+]5[PO43-]3[OH-]) or Ksp ) [Ca2+]5[PO43-]3[OH-], where the concentrations “[X]” are essentially analytical, that is, assuming full dissociation, with no attempt to take into account other species. The importance of speciation is coupled with the need for good control at the relevant temperature. As has been reported,23 HAp has a retrograde solubility with respect to temperature increase. This presumably means that equilibria for solution complexes such as Ca2+ + PO43- S CaPO4- are driven to the left with increasing temperature, as would be expected, thereby increasing the concentrations (and so activities) of the ions involved in the statement of the solubility product, which thus leads to the suppression of the dissolution of the solid. If nothing else, this underlines the importance of solution speciation being recognized properly. Therefore, the calculation of solubility product simplified by using analytical calcium and phosphate ionic concentrations is
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a crude approximation, neglecting as it does the presence of a number of solution complexes. Such a value cannot express the true solution equilibrium for HAp itself, and it is made worse if phase transformation has already occurred. Indeed, Levinskas and Neuman46 reported that, due to incongruent dissolution, no constant pKsp could be calculated for HAp, which in fact means very simply that the solution speciation was not handled properly, but it also implies that the solid was not as intended, either in composition or constitution. 2.3. Ca/P Ratio. In a related matter, disagreement in published values may also possibly more directly arise from the effect of the Ca/P ratio. Early studies of solubility by Holt et al.,47 Bjerrum et al.,48 Elmore and Farr,49 and Clark14 did not mention the Ca/P ratio of the solid. The use or presence of nonstoichiometric HAp clearly may affect its actual solubility, but also its apparent solubility due to this being expressed solely according to a measured calcium ion concentration with the assumption of a stoichiometric solid, Ca5(PO4)3OH. Although it is normally noted that stoichiometric HAp has the ideal Ca/P ratio 1.67, the range for nonstoichiometric HAp remains uncertain. While it is generally accepted that the (lower) limiting value is 1.5, an even lower value of 1.33 has also been reported.50 However, such material may have been contaminated by other phases, such as OCP, whose crystal structure is similar to that of HAp. Generally, nonstoichiometric HAp can be precipitated using lower temperatures51 and lower pH.52 Since such material is not a mixture of stoichiometric HAp and other more acidic phases such as OCP, DCPA, or DCPD, calcium-deficient HAp must be thought of as a thermodynamically stable phase, but for the particular conditions of formation, which is why it could be formed stably on the surface of the stoichiometric phase when this is not actually stable. For example, Rootare et al.15 reported a substantially higher solubility product for nonstoichiometric HAp, with Ca/P between about 1.55 and 1.70, than did Moreno et al.,16 Wier et al.,12 Avnimelech et al.,21 Chuong,20 and Bell et al.17 for material close to the stoichiometric ratio of 1.67. Although Moreno et al.16 also calculated a higher solubility product value close to that of Rootare et al.,15 the powder was treated by heating in air, which possibly incorporated other ions, such as carbonate replacing hydroxide, although it still showed the stoichiometric Ca/P ratio. In addition, the formation of oxyapatite (Ca10(PO4)6O) due to dehydroxylation (actually, loss of water), at least above 900 °C, needs to be taken into account, and this may further decompose to tricalcium phosphate and tetracalcium phosphate.53 Driessens and Verbeeck54 reported pKsp(HAp) ∼ 42.5; however, comparing this with the more widely accepted value of ∼58.4,23 there is an obvious discrepancy. Thus, if it is real, how does a more soluble phase coat on a more stable phase at equilibrium spontaneously? Too many questions remain. 2.4. Contamination by Other Ions. Contamination by “foreign” ions should also be taken into an account. Here, “foreign” means other than derived from HAp itself. The most likely contamination is carbonate, which may partially replace both phosphate and hydroxide in the crystal,55 although recently such substitution has been found to occur spontaneously mainly on phosphate sites.56 The usual method for the preparation of pure HAp is the addition of a calcium solution dropwise into a phosphate solution, maintaining pH > 10. The possible incorporation of carbonate from air has been mentioned, and some attempts have been made to minimize this, such as by preparation under N257 or removing CO2 by boiling the solution.21 However, there is no evidence, such as from IR spectra, to
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confirm the efficacy of these attempts. In particular the solubility of carbon dioxide increases markedly with increase of pH, and thus the absorption of atmospheric CO2, and so potentially the incorporation of carbonate into the crystal structure must also increase. As reported by Tung et al.,58 carbonate was found in some prepared solids. Yoshimura and Okamoto59 said that carbonate partially substitutes at hydroxide sites in the hydrothermal synthesis of HAp, although it possibly still remained at the stoichiometric Ca/P ratio of 1.67. Even so, many descriptions of the preparation process do not mention whether the conditions were CO2-free or not. Although solubility work is commonly conducted carefully, contamination of the original test solid could be a serious problem. While the actual solubility of the solid may be affected by contamination, ultimately these endogenous contaminants must also be in the supernatant and so affect speciation just as would exogenous contaminants. In 1945, Greenwald60 first reported that the solubility of calcium phosphates was increased in the presence of solution carbonate. This increase was attributed to the formation of such solution complexes as Ca2HPO4CO3 and (Ca2PO4CO3)-, and although such an assumption had not been proven, similar results were also obtained later by Gron et al.61 Meanwhile, Ericsson62 had found a much higher solubility for HAp in saliva than in CO2-free solution in the physiological pH range, explained as possibly caused by the presence of carbonic acid, thus indicating that saliva is not generally supersaturated with respect to HAp to such a high degree as hitherto thought. The effect is in fact large: Chen et al.63 reported a 7-fold increase in solubility for HAp in 1 mM KCl at pH 5 when equilibrated with 3.5 vol% CO2 in air, while Leung and Darvell found a 10-fold difference in an artificial saliva system at the same pH.64 Therefore, the inclusion of carbonate during both the solid preparation and the solubility investigation has to be considered from both points of view: solid stability and solution speciation. Contamination by fluoride is also believed to be important. Fluoride has been found to reduce markedly and control dental caries,65,66 enhance the rate of crystal growth,67 and act as a key factor in the transformation of minerals.68 It can easily substitute at the site of the hydroxide of HAp as the two ions have the same charge and similar radius. Kamiya et al.69 reported that the substitution of hydroxide by fluoride significantly increased the stability of HAp, which was supported by Moreno et al.,70 who thought that it was due to surface effects. Hence, the inclusion of fluoride is expected to affect significantly the solution equilibrium. In addition, another widely neglected factor has to be mentioned: phosphate itself. Ca-P solubilities are strongly dependent on solution pH, and this is commonly adjusted by adding HCl or H3PO4. However, the possible formation of complexes by phosphoric acid has not been considered, referring back to the speciation problem discussed above. Chen et al.63 reported a clearly increased mass solubility for HAp in the presence of 1 mM phosphate as background, at least in the pH range from 4.2 to 5.2. This can only be due to the formation of complexes. More generally, solution Ca/P ratio has been little considered (Figure 2). It is now obvious that the Ca/P ratios of the solutions investigated by Moreno et al.,16 McDowell et al.,23 Verbeek et al.,57 Avnimelech et al.,21 and Tung et al.58 were significantly lower than the stoichiometric value for HAp due to the use of phosphate (as acid) to adjust the pH. Although Moreno et al.16 claimed that the dissolution of HAp was stoichiometric, the phosphate concentration used for the calculation was not the actual value at equilibrium, but adjusted by
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Figure 3. Schematic general layout of the apparatus in vertical section on the beam axis.
Figure 4. Typical detector recording and titration events (addition of HAp increments).
Figure 2. Solution conditions used for HAp and DCPD solubility determinations by the conventional excess-solid method.
simply subtracting the initial concentration of phosphate from the value at equilibrium. This is not the way solution equilibria work. In addition, the calcium concentrations reported in the absence of added phosphate by Avnimelech et al.,21 at pH 6.595 and 6.826, were significantly lower than the values obtained by adding phosphate at around the same pH range. This also shows that solution equilibria really are shifted by the presence of extra phosphate. Furthermore, the phosphoric acid added to adjust the pH brought the Ca/P ratio at “equilibrium” for HAp very close to the value reported for DCPD (1.5) by Gregory et al.,71 Patel et al.,72 Moreno et al.,73,74 Holt et al.,47 Strates et al.,75 Kugelmass and Shohl76 (Figure 2). Thus, the possibility of a phase transformation through the addition of phosphoric acid has to be considered. Mahapatra et al.19 has reported that the more acid phase of DCPD may be formed during the dissolution of HAp between pH 5.8 and 7.2 (but see above). Determination of the solubility of HAp has also been attempted by solution titration. However, homogeneous nucleation, whether for calcium added to phosphate solution, or vice versa, always needs great supersaturation to drive it and thus microscopic reversibility is not attained. Thus, the calculation for such a solution normally cannot yield true solubility, and in particular for HAp, where stoichiometry is uncertain, phase transformations may occur, and exposure to atmospheric CO2 represents a major risk of interference. In general, the conventional “large excess of solid” method is not suitable for the calcium phosphate system due at the very
least to incongruent dissolution, phase transformation, pKsp calculation difficulties, and contamination by other ions. Although some of these points have often been mentioned, seldom has any attempt been made so far to overcome them. The true solubility of HAp remains uncertain.
3. Solid Titration In 1980, one of us (B.W.D.) proposed a new approach to resolve the difficulties: solid titration (Figure 3), one which has proved its worth in a number of subsequent studies.63,64,77-81 In contrast to the “large excess” approach, it is based on the expectation of heterogeneous nucleation very close to the point of saturation. Very small increments of pulverized solid of the material of interest are added to a solution, and suspended by agitation with a magnetic stirrer. The titration process is followed by the use of a very sensitive, low-angle laser-scattering system to detect the presence of solid particles. Each addition of the solid, even if less than 0.5 mg, causes an obvious step-increase in the scattered light signal, which then decreases with time due to the dissolution of the solid. Attainment of a stable signal at or very close to the original baseline value is taken as indicating that the increment has completely dissolved, when the next addition can be made. The end-point of the titration is unambiguously detected by the output signal remaining higher than the original baseline, meaning that no more solid could dissolve or that a new solid had precipitated, or both (Figure 4). Sometimes, the signal then increases somewhat, which may indicate the possibility of crystal growth, that is, Ostwald ripening.82 On achieving stability, a further small increment may then be made to enable a better estimate of the actual end-point pH and titrant total by interpolation. The pH may then be adjusted by adding HCl solution (as a noninterfering acid) such
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that all solid is redissolved (normally a deliberately minute amount), as confirmed by the scattering signal returning to the baseline, to form the basis for the next titration to determine a new end-point. However, to obtain enough solid for analysis (a few milligrams), a few more small increments may be added beyond the end-point, ensuring that equilibration occurs for each one. The end-point condition may usefully be elaborated. There are two possibilities: first, that the titrant is exactly the stable phase, when simply no more solid can dissolve; second, and more probably, the titrant is less stable (more soluble). In this latter case, some addition will take the system beyond the true end-point, but while that solid takes time to dissolve it provides a chemically, if not crystallographically, similar surface on which the growth of the stable phase may be nucleated. Thus, even if an increment were to take the system to a point between the two isotherms, that is, of the stable phase and the titrant, there must be a time when solid is present beyond the stable phase isotherm, thus providing crystallization nuclei. The advantage of this approach in comparison with any electrochemical method is that it is extremely easy to detect the titration end-point to high precision, controlled only by the size of the increment that may be handled conveniently and the working volume of the solution. The solubility isotherm obtained is therefore necessarily more accurate than otherwise achievable. Both dissolution and precipitation after saturation can be clearly monitored using the laser signal output. It should be noted that although the dissolution of the added solid titrant may still be incongruent, this can only be the case while original solid persists; hence, the next addition is not made until all previous solid has dissolved so that it is small-scale but only temporary. Thus, even if the equilibrium solid is a different phase compared with the titrant, the method avoids completely the problem of phase transformation layers affecting the contact of solid and solution. The detected end-point is therefore really very much closer to the true solution equilibrium than can be realizable by the conventional method, and is in fact microscopically reversible; in principle, acid could be added to redissolve that infinitesimal precipitate. An alternative view of this process is that calcium and phosphate ions are being put into the test system, at a chosen ratio, as if in solution, but with the benefit of heterogeneous nucleation very close to the end point. The solution composition is therefore known as precisely as the weighing and the analysis of the original titrant solid permit. A second and major advantage is that the technique is absolute; it is a direct determination of mass solubility. It relies on the direct physical observation of the point of saturation, according to the well-understood concept of the definition of solubility. There are no assumptions about solution speciation, solution composition, equilibrium constants, analytical errors, or phase identifications; it requires no theory or elaborate calculation. In addition, it does not depend on the crystal perfection or otherwise of the titrant, as everything added must first dissolve, the increments being very small; indeed, crystal damage to drive dissolution is beneficial as this ensures higher “solubility” than the end-point solid, even if this is the same phase, guaranteeing full turnover. Although light-scattering is affected by particle size, and thus the sensitivity of the laser-scattering system may vary, the system is effective and reliable in that 0.5 mg of solid (HAp particle size ∼50 × 200 nm2) in 600 mL solution can provide a large signal even though not discernible by eye. Although the increment dissolution time tends to be long as equilbrium
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Figure 5. Solid titration solubility isotherms for HAp and (metastable) DCPD compared with solid titration curves for OCP, β-TCP, and TTCP (which produce HAp at the end-point).
is approached (on the order of a few to several hours), this is due to the very low dissolution rate of the solid itself, in the case of calcium phosphates, at least, even if pulverized. Over the course of several hundred determinations, under a variety of conditions, the method has proved reliable and highly reproducible for all crystalline calcium phosphates tested, in marked contrast to the conventional method.
4. Significance Using solid-titration, the solubility isotherm for HAp has been redetermined and confirmed to lie substantially lower than previously reported (Figure 1),77 and fluorapatite was shown to have a very similar behavior, only slightly less soluble than HAp.78 While there is a marked change of slope at pH ∼3.9, no DCPD was formed in the precipitate at equilibrium either side of this point. Instead, calcium-deficient HAp was found at both pH 3.20 and 3.60, while above pH 3.9 it was stoichiometric. HAp is therefore stable in the region where DCPD is widely believed to be the most stable phase.77 Even the reported solubility isotherm of DCPD supports this conclusion, lying always above that of HAp as now determined (Figure 5). But in a similar titration with solid DCPD the only phase found at the detected end-point at both pH 3.60 and 4.50 was DCPD itself. However, seeding with 1 mg of HAp at such “equilibrium” end-points for DCPD titration led to the formation of well-crystalline HAp at pH 3.30, 3.60, and 4.47, and the disappearance of the DCPD. Thus, the initial titration end-point for DCPD was a metastable equilibrium, possibly reflecting the difficulty of nucleating HAp on DCPD (knowing that homogeneous nucleation is not favored). It has also been found that the end-point precipitates in the solid titration of OCP, β-tricalcium phosphate (β-TCP), and tetracalcium phosphate (TTCP) were all HAp at pH 3.6, albeit calcium-deficient.79,80 Below about pH 3.9, the Ca/P ratio falls with pH. Thus, a ratio of 1.48 was found at pH 3.2,77 with no indication in the solubility isotherm of a phase change from there to pH ∼2.9, but with the implication of a further decrease in ratio. This is to be compared with the reports of the minimum Ca-P ratio discussed above. Illustrating the kinetic and thermodynamic complexity of the calcium-phosphate system is the observation that when a
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relatively large addition of OCP was made after the end-point of its titration at pH 3.6, when “equilibration” had been allowed to occur, well-crystalline DCPD was then found, while the pH had risen to ∼3.9.80 That is, driving supersaturation with respect to HAp with extra OCP prompted the precipitation of the moreeasily nucleated phase, DCPD. Seeding with HAp, again, results in HAp being formed in what would then be understood to be an Ostwald succession.80 Given that HAp seems to be the most stable phase over the pH range usually investigated, and in view of the evident complications arising from the metastable formation of DCPD, dependent variously on degree of supersaturation and ease of nucleation, it is not surprising that difficulties are encountered in the large excess of solid studies of Ca-P solubilities. In other words, extraordinary care has to be taken to avoid interference from surface layer transformations and “premature”, metastable precipitation. Nucleation clearly needs to be recognized as a controlling factor; it does not appear to have been mentioned before. In particular, no attempt has been made to allow for this in studies of the system with pH < 4.2 (Figure 1) (where DCPD is generally expected to form83), but above this value, HAp has simply been considered as the most stable phase, with the general assumption that there is no phase transformation, despite incongruous dissolutionsthe only consideration ever shown being the formation of complexes, and then rarely. It can be noted in passing that true solubility isotherms cannot be obtained under the present conditions for OCP, β-TCP, and TTCP (Figure 5) as HAp is most stable; their true positions must lie somewhat higher. Thus, any attempt at measuring their solubility in the conventional manner must fail. However, it is clear that the position of the isotherm for HAp is strongly dependent on solution Ca/P ratio, implying that if this is not taken into account, erroneous conclusions will be reached. The reliability and reproducibility of the solid titration method have been confirmed in a relatively simple system, CaF2,78 giving results consistent with theoretical calculations84-88 and close to those reported experimentally by others.89,90 In fact, the sensitivity of the method is such that to explain results above about pH 8, a new solid species, CaFOH, was postulated,78 no other known substance fitting. The method may therefore be applied generally for low-solubility systems. However, it is still not possible to reconcile the present Ca-P results with the HAp solubility isotherm calculated numerically. The only possibilities apparent are (a) a faulty solution speciation model, which seems to be rather likely, noting that all equilibrium constants need to be known, or (b) that what is precipitated is an unexpected, possibly a new solid, although the accumulating evidence is against this. It is the circularity of the argument of the equilibrium constants derived from excess-solid studies being used to calculate an isotherm to check solubility that needs to be broken, as has been outlined before.91 What are required are truly independent observations. Solid titration is independent. It is now clear that the “protection” phenomenon reported by Wang et al.,25 discussed earlier, has probably resulted from a false solubility product value, arising from any of the problems mentioned above, but the report itself betrays a significant misunderstanding of true solution equilibria. There is no contradiction between chemistry principles and the in vitro phenomena. But while no solubility product can be determined for HAp so far, due to lack of detailed knowledge of solution equilibria, it remains a direct and interpretable option to express solubility in terms of the calcium-carrying capacity of the solution or the total dissolved solid without prejudice to the explanation of the values.
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In general, solid titration has shown its value as a useful and reliable technique in solubility work on sparingly soluble solids, especially in systems complicated by kinetic effects. However, there is still a need for further work, at least for calcium phosphates, as the present results are rather distinct from those reported over more than 50 years, and a comprehensive mapping would be of great value. We would argue on several grounds that we are now, at last, making progress in this important area.
5. Conclusion The conventional method for studying solubility, through the addition of a large excess of solid, has been confirmed as inappropriate for the calcium phosphates. Solid titration may be the only viable approach to explore their true solution equilibria. The method can be extended to many other systems.
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