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

Abstract

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 (γ) and cohesion (β) 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.

Water: How Does It Influence the CaCO3 Formation?

“…[36] In addition, clusters with aw ell-defined diameter of around 2nmh ave been observed by analytical ultracentrifugation (AUC), [36] cryogenic transmission electron microscopy (cryo-TEM), [39] and small-angle X-ray scattering (SAXS). [32,44,45] Even when PNCs were present under certain experimental conditions, their role in the formation of ACCr equires further clarification. [42] Experiments and simulations suggest that the formation of PNCs,t heir stability,a nd dynamic behavior are strongly influenced by the water molecules associated with these clusters.…”

“…[45,58] Thep referential formation of the ACCp hase during early stages of CaCO 3 crystallization might be thermodynamically driven:M olecular dynamics (MD) simulations indicate that the free energy of ACCp articles whose diameters do not exceed af ew nanometers is below that of their crystalline counterparts. [45,58] Thep referential formation of the ACCp hase during early stages of CaCO 3 crystallization might be thermodynamically driven:M olecular dynamics (MD) simulations indicate that the free energy of ACCp articles whose diameters do not exceed af ew nanometers is below that of their crystalline counterparts.…”

“…[62] The faster formation of small amorphous particles compared to that of crystalline counterparts is supported by MD simulations. [45,60,64,65] This growth or agglomeration reduces their surface-to-volume ratio such that, at some point, the free energy of ACC particles exceeds that of the crystalline polymorphs. [45,60,64,65] This growth or agglomeration reduces their surface-to-volume ratio such that, at some point, the free energy of ACC particles exceeds that of the crystalline polymorphs.…”

“…Thef ormation of ACCi si nfluenced by synthesis conditions including the formation time, [55] solute concentration, [38,48,58,65] pH, [36,45] temperature, [38,45,48,58] solvent, [77] and confinement. [78] These conditions also influence the structure and hydration of the resulting ACCparticles.…”

“…These parameters and hence the dissolution kinetics can be influenced by the size [61] and degree of hydration [47] of ACCp articles as well as the crystallization conditions such as the pH, [36,110] temperature, [45,111] and solvent [77,112,113] of the ACC-encompassing solution. These parameters and hence the dissolution kinetics can be influenced by the size [61] and degree of hydration [47] of ACCp articles as well as the crystallization conditions such as the pH, [36,110] temperature, [45,111] and solvent [77,112,113] of the ACC-encompassing solution.…”