Crystallization in Aggregates of Calcium Phosphate Nanocrystals: A Logistic Model for Kinetics of Fractal Structure Development

Abstract

Calcium phosphate crystallization is of importance in medicine and materials science, and aggregation frequently happens at its early stage. Herein, we report a kinetic study of crystallization in particles of aggregated nanocrystals of calcium phosphate by in situ synchrotron small-angle X-ray scattering. The particles were random fractal aggregates, having diameters of 20–60 nm and comprising structural units of 2.5 nm in dimension. With the application of a logistic model, the structural changes of the particles were characterized by the successive developments of mass and surface fractal dimensions. The rate constant of mass fractal development was found to be 0.052 h–1, corresponding to the generation of crystallites on the pre-existing seeds inside an aggregate. These newly formed nanocrystals then detached from their seeds and fell into the voids. Afterward, the surface fractal structure developed at a rate of 0.11 h–1, making the particle surface less rough. During this period, a transition layer of 1.2-nm thickness emerged between a particle and the surrounding solution. Our findings present an advance toward understanding the crystallization in particles of aggregated nanocrystals and would be beneficial for preparing nanocrystals and recognizing the roles of other substances (such as proteins and metals) in both biological and synthetic systems.