Formation and transformation of calcium phosphate phases under biologically relevant conditions: Experiments and modelling

Abstract

The experimental data on calcium phosphates formation were collected in dilute solution at constant pH (7.40) and temperature (37.0 °C) at different levels of ionic strength (IS). The evolution of the solid phase formation is described in detail using a thermodynamic-kinetic model. The thermodynamic model takes into account all relevant chemical species as well as Posner's clusters; the kinetic model, based on the discretized population balance approach, accounts for the solid formation from solution. The experimental data are consistent with an initial formation of dicalcium phosphate dihydrate (DCPD, brushite), which dominates the nucleation rate, and its rapid transformation into octacalcium phosphate (OCP) or hydroxyapatite (HA), which dominates the growth rate. Depending on the experimental conditions and, including the influence of the IS level, OCP may be further transformed into apatite. The classical nucleation theory is able to describe the experimental results very well and the solid phase growth is limited by the diffusion of Ca²⁺ ions. The precipitation pathway described by a complete thermodynamic-kinetic model is expected to contribute to the understating of the in vivo osteogenesis.

Statement of significance: The formation mechanism of calcium phosphates under biomimetic conditions is unraveled. The formation pathway is mathematically described based on a thermodynamic-kinetic model in which (i) the nucleation stages (primary and secondary) are dominated by the formation of dicalcium phosphate dihydrate (DCPD) and (ii) the fast growth stage is limited by the diffusion of Ca²⁺ ions under the driving force of octacalcium phosphate (OCP), or hydroxyapatite (HA), solubility. The obtained solid phase seems correlated to the activity coefficient of phosphate ions, thus to the ionic strength and local phosphate speciation. The model, being able to highlight the details of the precipitation pathway, is expected to contribute to the understanding of the apatitic phase formation in the biomineralization-biodemineralization processes under in-vivo conditions.

Keywords: Calcium phosphates; Classical nucleation; Diffusion-limited growth; Modelling; Precipitation kinetics.