Metastable Equilibrium Solubility Distributions Research Articles

Quantitative Determination of Lattice Fluoride Effects on the Solubility and Crystallinity of Carbonated Apatites with Incorporated Fluoride

The purpose of this study was to evaluate quantitatively the effects of fluoride on the solubility and crystallinity of carbonated apatites (CAPs) after its incorporation into the crystal lattice using the metastable equilibrium solubility (MES) distribution method. Fluoride-incorporated CAPs (F-CAPs) of two different carbonate levels (3 and 5%) and fluoride contents from 0 to 20,000 µg/g were synthesized. X-ray diffraction experiments and Rietveld analysis were conducted to obtain crystallite microstrain and unit cell parameters. Acetate buffer MES solution media were prepared at two solution fluoride concentrations (0.2 and 2.0 mg/l) and at two pHs (5.0 and 5.7). The unit cell a-axis values of the F-CAPs were found to decrease as the fluoride content increased, consistent with the fluoride being incorporated into the crystal lattice. The fluoride concentrations in the MES solution media were high enough to provide a ‘swamping’ effect such that the fluoride released from the F-CAPs during dissolution was minimal in changing the solution fluoride concentration. Employing the MES distribution superposition method, it was shown that the surface complex possessing the fluorapatite (FAP) stoichiometry [Ca₁₀(PO₄)₆F₂] accounted for the MES distribution behavior of all experiments. In addition, the mean pI_FAP [the value of –log(a_Ca¹⁰a_PO_₄⁶a_F²) calculated from the ionic activity product based on FAP stoichiometry of the MES dissolution media in which 50% of the F-CAPs had dissolved] correlated well with the crystallite microstrain parameters of the F-CAPs. The incorporated fluoride in the F-CAPs showed only modest effects on F-CAP crystallinity and solubility.

A comparative study of the metastable equilibrium solubility behavior of high-crystallinity and low-crystallinity carbonated apatites using pH and solution strontium as independent variables

Using solution strontium and pH as independent variables, the metastable equilibrium solubility (MES) behavior of two carbonated apatite (CAP) samples has been examined, a high-crystallinity CAP (properties expected to be similar to dental enamel) and a low-crystallinity CAP (properties expected to be similar to bone mineral). CAP samples were prepared by precipitation/digestion: (CAP A: high-crystallinity, 1.3 wt% CO 3, synthesized at 85 °C; CAP B: low-crystallinity, 6.4 wt% CO 3, synthesized at 50 °C). Baseline MES distributions were determined in a series of 0.1 M acetate buffers containing only calcium and phosphate (no strontium) over a broad range of solution conditions. To assess the influence of strontium, MES profiles were determined in a similar fashion with 20, 40, 60, and 80% of the solution calcium being replaced on an equal molar basis by solution strontium. To determine the correct function governing CAP dissolution, ion activity products (IAPs) were calculated from the compositions of buffer solutions based on the hydroxyapatite template (Ca 10– n Sr n (PO 4) 6(OH) 2 ( n = 0 – 10 )) and the calcium/hydroxide deficient hydroxyapatite template (Ca 9– n Sr n (HPO 4)(PO 4) 5OH ( n = 0 – 9 )). Findings: (a) for CAP A, at high solution strontium/calcium ratios, the MES profiles were essentially superimposable when the solution IAPs were calculated using the stoichiometry of Ca 6Sr 4(PO 4) 6(OH) 2 and for CAP B by a stoichiometry of Ca 7Sr 2(HPO 4)(PO 4) 5OH; (b) for CAP A, at low strontium/calcium ratios, the stoichiometry yielding MES data superpositioning was found to be that of hydroxyapatite and for CAP B, that of calcium/hydroxide deficient hydroxyapatite. When other stoichiometries were assumed, good superpositioning of the data was not possible.

Effect of fluoride pretreatment on the solubility of synthetic carbonated apatite.

The purpose of this research was to address the following question: How is the solubility of fluoride-pretreated carbonated apatite (CAP) in aqueous acidic media related to the equilibrium solution fluoride and/or the CAP adsorbed fluoride levels? A CAP sample prepared by a precipitation method at 70 degrees C containing approximately 6% carbonate was fluoride-treated (F adsorption from neutral aqueous solutions) to yield a approximately 1000 ppm F CAP and a approximately 3300 ppm F CAP. Metastable equilibrium solubility distributions were determined in acetate buffers at pH 5.0. Solution fluoride, calcium, phosphate, and pH were determined from the equilibrated solutions. The equilibrium solution fluoride levels were extremely low, e.g., as low as approximately 0.10 ppb to approximately 0.30 ppb at 50% dissolved for the two CAP preparations. The approximately 3300 ppm F CAP yielded a lower solubility than the approximately 1000 ppm F CAP (shift in the mean pKHAP value of 1.5-2 units). This can be attributed to the lower solution F(-) for the sample containing approximately 1000 ppm fluoride compared with the approximately 3300 ppm fluoride-containing CAP. These important findings suggest that a fluoride treatment simply may provide an adsorption fluoride depot for subsequent release, providing a solution fluoride effect upon the CAP solubility and not necessarily any intrinsic alteration of the mineral solubility.

Metastable equilibrium solubility behavior of carbonated apatite in the presence of solution strontium.

The purpose of this study was to use the concept of metastable equilibrium solubility (MES) to describe the anomalous solubility behavior of carbonated apatite (CAP) in the presence of solution strontium. A CAP sample (4.8 wt% CO(3), synthesized at 70 degrees C) was prepared by precipitation. Baseline MES distributions were determined in a series of 0.1 M acetate buffers containing only calcium and phosphate (no strontium) over a broad range of solution conditions. In order to assess the influence of strontium, MES profiles were then determined in a similar fashion with 20, 30, 40, 50, 60, 70, and 80% of the solution calcium being replaced on an equal molar basis by solution strontium. From the compositions of the equilibrating buffer solutions, ion activity products (IAPs) of the form Ca(10-n)Sr(n)(PO(4))(6)(OH)(2) (n = 0-10) were calculated in an attempt to determine the correct function governing the dissolution of the CAP preparation. The results demonstrate the following important findings: (a) at high solution strontium/calcium ratios (i.e., when 60% or more of the solution calcium was replaced by strontium), the MES profiles in all the experiments were found to be essentially superimposable when the solution IAPs were calculated using the stoichiometry of Ca(6)Sr(4)(PO(4))(6)(OH)(2), and (b), at low solution strontium/calcium ratios (i.e., when 40% or less of the solution calcium was replaced by strontium), the stoichiometry yielding MES data superpositioning was found to be that of hydroxyapatite. When other stoichiometries were assumed, good superpositioning of the data was not possible.

Effect of age on rat bone solubility and crystallinity.

It has been shown that biominerals such as dental enamel and bone demonstrate a non-thermodynamic equilibrium state following initial dissolution where no further mineral dissolution or precipitation occurs; this state is termed metastable equilibrium solubility (MES). Furthermore, these minerals are composed of a distribution of domains each with their own MES. Recent studies have also demonstrated a linear relationship between crystallinity and the mean MES of these minerals, with solubility decreasing with increasing crystallinity. This study investigates the effect of age on the MES and crystallinity of rat bone mineral. The bone mineral samples were prepared by protein extraction with a series of hydrazine and alcohol solutions. The MES distributions of the bone mineral were measured by exposure to 0.1 M acetate buffers containing a range of calculated amounts of calcium (Ca) and phosphate for 48 h. The amount of mineral dissolved in each solution was determined from Ca and phosphate analyses of the undissolved residue. The full width of the half maximum (FWHM) of the 002 reflection of the X-ray powder diffraction was used as an indicator of crystallinity. The MES of mineral from bone of rats of different ages (1-25 months) were compared. Results of this study indicate that (l) there is a difference in the mean MES of bone mineral from rats of different ages, with older bone mineral being less soluble and more crystalline than bone mineral from younger rats; (2) the nature of the solubility distribution changes from a narrow to a broader distribution with age; and (3) all of the bone samples demonstrated an inverse-linear correlation between crystallinity and mean MES value consistent with previous results obtained with synthetic apatites and dental enamel.

Metastable Equilibrium Solubility Behavior of Carbonated Apatites in the Presence of Solution Fluoride

The aims of the present investigation were to assess the applicability of the metastable equilibrium solubility (MES) concept for the carbonated apatites (CAPs) over a range of pH and a wide range of solution fluoride concentrations and to examine the hypothesis that, in the presence of solution fluoride, a surface complex with the stoichiometry of fluorapatite (FAP) governs the MES behavior. Two CAP samples were prepared by precipitation from reaction media containing calcium nitrate (Ca(NO3)2·4H2O) and sodium phosphate (NaH2PO4·H2O) at two different levels of sodium bicarbonate. The MES distributions of the two CAP preparations were determined by equilibrating approximately 10 mg of CAP powder in 2 L of 0.1 M acetate buffers (ionic strength=0.50 M) at pH 4.5 and 5.5 and at various levels of calcium, phosphate, and fluoride. The fluoride concentrations ranged from 0.03 to 12 ppm. From the compositions of the equilibrating buffer solutions, ion activity products based upon the stoichiometries of hydroxyapatite (HAP) and FAP were calculated in an attempt to determine the correct function governing the dissolution of the CAP preparations. The results of this study demonstrated that both CAP preparations exhibit the MES distribution phenomenon in solution media of varying pH and fluoride concentrations. Furthermore, the experimental MES data obtained with both CAP preparations at the lower pH (4.5) and at higher solution fluoride levels (≥0.1 ppm) were essentially superimposable when plotted against the ion activity product based upon the stoichiometry of FAP, suggesting that in the presence of solution fluoride the MES governing surface complex may be an entity possessing a stoichiometry approximated by that of FAP. When the HAP stoichiometry was assumed to represent the surface complex, good superposition of the data was not possible.

Use of Dicalcium Phosphate Dihydrate as a Probe in an Approach for Accurate Calculations of Solution Equilibria in Buffered Calcium Phosphate Systems

Both synthetic and biological carbonated apatites have been shown to possess metastable equilibrium solubility (MES) distributions. Investigation of their MES behavior requires accurate knowledge of the activities of the relevant ions over a range of solution compositions. This in turn requires that the activity coefficients for these ions and the stability constants for the various solution complexes be accurately known. Since the solubility of dicalcium phosphate dihydrate (DCPD) can be easily determined, it can be used as a probe to study the appropriateness of proposed sets of stability constants and activity coefficients. In the present study, the solubility of DCPD was determined in acetate buffer solutions at pHs ranging from 4.5 to 6.5 and this allowed for the determination and evaluation of the stability constants of the NaHPO−4, CaHPO04, CaH2PO+4, and CaAc+ complexes. The activity coefficients were calculated by a modification of the extended Debye–Hückel method and also by Bockris and Reddy's method, in which the activity of water and the hydration numbers of ions are also considered. The solution conditions were controlled to simulate the dissolution media used for the determination of MES distributions of apatites in our laboratory. Both methods of activity coefficient determination gave very consistent DCPD solubility product (KDCPD) values, and values for the stability constants of the relevant complexes determined using the two methods were close to each other. This approach of determining the stability constants under a set of conditions similar to those in apatite dissolution studies offers an effective set of parameters which, though not necessarily always exactly correct in absolute terms, are internally consistent and should allow for the quantitative characterization of the MES behavior of apatites.

Metastable Equilibrium Solubility Distribution of Carbonated Apatite as a Function of Solution Composition

Previous studies have shown that carbonated apatites (CAPs) exhibit the phenomenon of metastable equilibrium solubility (MES) in weak acid media. The purpose of the present investigation was to examine two questions: first, whether the MES concept is applicable to a broader range of solution conditions and, second, whether a driving force function associated with a surface complex having a constant stoichiometry governs the dissolution of CAP and, if so, what is this stoichiometry. CAP preparations with carbonate contents of 1.8–5.7 wt% (synthesized by hydrolysis of dicalcium phosphate anhydrate in solutions of varying bicarbonate levels or by direct precipitation from supersaturated calcium/phosphate/carbonate solutions) were studied as follows. MES distributions for each of the CAP preparations were determined by equilibrating the CAP under stirred conditions in a series of acetate buffers (0.10 M) containing various levels of calcium and phosphate in the pH range 4.5–6.5 and a solution calcium/phosphate ratio in the range 0.1–10. The amount dissolved in each instance was regarded as the fraction of the CAP possessing an MES value greater than that corresponding to the ion activity product (IAP) of the equilibrating solution. The solution IAPs were calculated from the solution compositions using plausible calcium phosphate stoichiometries, viz., dicalcium phosphate dihydrate, octacalcium phosphate, tricalcium phosphate, hydroxyapatite, carbonated apatite (based on the bulk composition of the particular CAP involved in the experiment), and tetracalcium phosphate. The fraction of CAP dissolved was plotted against the solution IAPs for each experimental set using each of the six assumed stoichiometries for the surface complex. The results demonstrated that the MES concept was applicable to all of the CAP preparations in media of various solution compositions and different pH levels. The most important new outcome of this study was that MES profiles for each of the CAP preparations in all of the experiments were found to be superimposable when solution IAPs were calculated using the hydroxyapatite stoichiometry, while such was not the case when other stoichiometries were used to calculate the solution IAPs.

Relationships among carbonated apatite solubility, crystallite size, and microstrain parameters.

The use of the metastable equilibrium solubility (MES) concept to describe the solubility properties of carbonated apatites (CAPs) and human dental enamel (HE) has been well established in previous studies using a range of CAPs with varying carbonate contents and crystallinities. It was shown in these studies that the mean value of the CAP MES is directly related to the broadening parameter full width at half maximum (FWHM) of the 002 reflection of the X-ray diffraction profile. The apparent solubility of the CAPs increased monotonically with an increase in the broadening of the diffraction peaks, and when this peak broadening was taken into account, carbonate had no additional effect upon the MES. The broadening of the diffraction peaks has been used as an indicator of crystallinity, and is generally influenced by both crystallite size and microstrain. The purpose of the present study was to extract the crystallite size and microstrain parameters separately from the X-ray diffraction peaks and then to determine their relationships to the corresponding MES values. The samples studied were CAPs synthesized by precipitation from Ca(NO3)2 and NaH2PO4 solutions in carbonate containing media at temperatures of 95, 80, and 70 degrees C, and powdered HE. The crystallite size and microstrain parameters were determined simultaneously with the refinement of the structural parameters with the Rietveld method of whole-pattern-fitting structure-refinement. A modified pseudo-Voigt function was used to model the observed peak profiles. The MES distributions for the CAPs and HE were determined by a previously described method. The results of this study showed that the CAPs possessed an MES distribution and therefore provided further support that MES distribution is a common phenomenon, regardless of the method of CAP synthesis. The crystallite size decreased and the microstrain increased with increasing carbonate content and decreasing temperature of synthesis of the CAPs. A plot of the mean of the MES distribution versus the microstrain parameter showed that the apparent solubility of the CAPs and HE correlated very well with the microstrain parameter. On the other hand, a plot of the mean of the MES distribution versus the crystallite size parameter showed a poor correlation between MES and crystallite size. These findings support a view that microstrain, rather than crystallite size, is the dominant factor governing the effective solubility of the CAPs and dental enamel.

Effect of Carbonate Content and Crystallinity on the Metastable Equilibrium Solubility Behavior of Carbonated Apatites

The purpose of this investigation was to assess the applicability of the metastable equilibrium solubility (MES) concept, previously developed in our laboratory, over wide ranges of two independent variables, carbonate content and crystallinity, and also to examine the influences of these variables on the MES behavior of carbonated apatites (CAPs). The CAP samples were prepared by dicalcium phosphate dihydrate (DCPD) hydrolysis for 48 h in NaHCO3-containing media at 95, 70, and 50°C. This method of preparation gave CAP samples with varying carbonate contents and crystallinities. A previously developed technique with slight modification was used to determine the MES distribution for each of the CAP samples. The equilibration solutions were prepared both with and without extraction of fluoride with hydroxyapatite (HAP). From X-ray diffraction, the full width at half-maximum (FWHM) of the 002 reflection was used as a measure of crystallinity. The findings of this study showed that each of these preparations possessed an MES distribution and therefore provided further support that the MES distribution is a common phenomenon describing the dissolution behavior of CAPs, regardless of their carbonate content and crystallinities. The crystallinities of the CAPs decreased and the MES values increased with increasing carbonate content and decreasing temperature of synthesis. A plot of the mean MES value against CAP crystallinity revealed that the mean MES was a single-valued function of crystallinity; i.e., when crystallinity was taken into account, there was no additional effect of carbonate on the MES. When fluoride was not extracted from the equilibration solutions, the MES shifted to lower values. The concept of MES distribution and its dependence on the crystallinity of CAP may provide insight into the mechanism of dissolution of biological apatites, which may be considered imperfect crystalline substances.

Quantitative Relationship between Carbonated Apatite Metastable Equilibrium Solubility and Dissolution Kinetics

The purpose of this study was to compare the experimental dissolution rates of carbonated apatite (CAP) pellets in acidic acetate buffers under a variety of conditions with theoretical predictions. The theoretical predictions were made in the following way. Recently obtained data on metastable equilibrium solubility (MES) and MES distributions for CAP preparations were incorporated as input into a quantitative, physical model for nonsteady-state dissolution of CAP pellets. The model takes into account simultaneous diffusion and equilibria of all species in the pellet pores as well as in the adjacent hydrodynamic boundary layer. It also takes into account both porosity changes and MES distribution changes as a function of time and position in the CAP pellet as the dissolution reaction proceeds. The model assumes a first-order surface reaction and the driving force for this reaction is directly related to the ion activity product of a surface complex. The main findings of the study were that the theoretical predictions agreed well with all the experimental data when a surface complex with hydroxyapatite stoichiometry was used in the theoretical calculations. When the surface complex stoichiometries of dicalcium phosphate (DCP) or CAP itself were used in the calculations, the predictions failed in one way or another. When a surface complex with octacalcium phosphate (OCP) stoichiometry was assumed in the calculations, the agreement between the experiments and predictions was almost as good as with the hydroxyapatite stoichiometry; more work needs to be done for a better assessment of the OCP surface complex model. The present results are believed to be an important step in the ultimate mechanistic understanding of the dissolution rate behavior of apatites as they represent, for the first time, a direct correlation between dissolution kinetics and independently measured apatite solubilities within a quantitative physical model framework.

Metastable Equilibrium Solubility Behavior of Carbonated Apatites

The purpose of this investigation was to examine the heretofore not considered hypothesis that carbonated apatite (CAP) preparations exhibit the phenomenon) of metastable equilibrium solubility (MES). The MES phenomenon may arise when crystal dissolution rates are very much greater than crystal-growth/precipitation rates when compared at equal but opposite (in sign) chemical potential differences between a crystal phase and solution. Preliminary studies had suggested that CAP preparations may be expected to exhibit the MES phenomenon and yield apparent solubilities very far removed from true thermodynamic equilibrium solubility. CAP samples prepared in our laboratories as well as samples prepared elsewhere were studied in the following manner. MES and MES distributions were determined by equilibrating under stirred conditions each of the CAP samples in a series or acetate buffers containing various levels of calcium and phosphate ions corresponding to various magnitudes of the solution ion activity productKHAP = (aCa)10(aPO46(aOH)2.A large solution-to-solid ratio was used to ensure that changes in the solution KHAP before and after equilibration would be negligible. In a typical set of experiments, the residues were recovered after 1, 2, 4, and 8 days, dried, and weighed to determine whether MES had been attained. Generally, dissolution proceeded rapidly and, after 2 to 4 days, further CAP dissolution could not be detected. The resulting apparent solubilities were plotted as fraction of CAP dissolved versus pKHAP and, typically, a normal distribution function satisfactorily fitted the experimental data. In order to demonstrate that the results corresponded to a true MES and not a steady-state situation involving equal dissolution and precipitation rates, (a) IR spectra of the residues were obtained and (b) residues from lower KHAP equilibrations were reequilibrated in buffers with higher KHAP values. Both these procedures showed that the apparent CAP solubilities and solubility distributions were closely consistent with the MES phenomenon and not a steady-state condition. Importantly, it has been shown in a separate study in this laboratory (J. Hsu, in press) that the MESs and MES distributions of the CAPs also govern the surface-controlled kinetics of CAP crystallite dissolution in acetate buffers. One infers from this that the CAP MESs determined in the present study govern dissolution of CAPs over, at least, a time-scale range from seconds to 105 s. Also, this appears to be the first time that the driving force for dissolution of apatite crystallites has been independently and directly quantified via "solubility" measurements.