Thermodynamic-Kinetic Precipitation Modeling. A Case Study: The Amorphous Calcium Carbonate (ACC) Precipitation Pathway Unravelled

Nine accurate experimental data sets on amorphous calcium carbonate (ACC) formation in dilute solution were collected varying temperature and pH. The entire precipitation process is described using a complete thermodynamic-kinetic model. The thermodynamic model includes two new complex chemical interactions whereas the kinetic model is based on the discretized population balance approach. Saturation, primary particles size distribution, average secondary particles size, nucleation, and growth rates, as well as a number of additional parameters on the ACC precipitation reaction, are reported. The excellent agreement among experiments, calculated results, and literature data demonstrates that a complete thermodynamic kinetic model can significantly contribute toward the understanding of a plausible pathway for precipitating systems. In this case study, the classical nucleation theory, which includes homogeneous nucleation, "true" secondary nucleation, and diffusion limited growth events, is able to completely describe the entire precipitation process. The calculated surface (gamma) and cohesion (beta) energies range from 28 to 35 and 30 to 42 mJ m(-2), respectively, as a function of pH and temperature. Clusters or prenucleation entities act as spectators and are not directly involved in the solid formation pathway. The general methodological approach presented can be readily applied to other solid phase formation processes.