Kinetics of hydroxyapatite precipitation at pH 7.4 to 8.4

The rate of hydroxyapatite (HAP) precipitation was studied using a reproducible seeded growth technique under pH stat conditions. Thirty different experiments were performed at initial Ca²⁺ and PO₄^3- concentrations ranging from 0.37-0.86 and 0.29-1.0 mmol L^-1, respectively, ionic strengths from 0.015-0.043 mol L^-1, HAP seed concentrations from 7.1-28.4 m² L^-1, temperatures from 10-40°C, and pH from 7.4 to 8.4. Initial rates expressed as mole HAP L^-1 s^-1 were used to test several empirical rate equations and derive a rate equation based on experimentally determined reaction orders. The rate equation: R = k_fsγ₂γ₃[Ca²⁺][PO₄^3-], where R = rate of HAP precipitation (mol HAP L^-1 s^-1), k_f = rate constant (L² mol^-1 m^-2 s^-1), γ₂ and γ₃ = divalent and trivalent ion activity coefficients, s = surface area (m² L^-1), and brackets = concentrations of Ca²⁺ and PO₄^3- (mol L^-1), was derived based on the reaction orders with respect to S, [Ca²⁺] and [PO₄^3-]. The equation was also verified using the integral method, and the average value for the precipitation rate constant was 173 ± 11 L² mol^-1 m^-2 s^-1. The Arrhenius activation energy was 186 ± 15 kJ mol^-1, indicative of a surface controlled precipitation mechanism. We speculate that the rate limiting steps include migration of surface Ca²⁺ and HPO₄^2- into lattice vacancies, with subsequent dehydration and incorporation into the crystal lattice.