Quantitative Relationship between Carbonated Apatite Metastable Equilibrium Solubility and Dissolution Kinetics

Abstract

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.