A New Technique for Calculating Kinetic and Thermodynamic Barriers for Nucleation Rates and Interfacial Energy of CaCO₃ Prenucleation Nanoclusters at High Temperature Using TGA Models and In Situ Crystallization

Abstract

Nucleation at different temperature levels can provide quantitative insights into the energy barrier associated with sub-molecular nuclei. The accurate calculation of nucleation rates, thermodynamics, and interfacial energy for extremely small nanoclusters (1−2 nm) remains a challenge at high temperatures. Here, E 𝜶 , 𝚫G, 𝚫H, 𝚫S and A 𝜶 are computed to estimate the nucleation rate of ultra-small CaCO 3 pre-nucleation clusters (0.85 nm) from thermogravimetric analysis (TGA) experimental values in the temperature range from 555 to 795 K, by adopting the most accurate iterative iso-conversional method and random nucleation dependent differential function f (𝜶), respectively. On the basis of these analyses, four mathematical models are presented for computing nucleation rates (nuclei 𝛍m −2 min −1 ) and interfacial energy (mJ m −2 variation with temperature and conversion for CaCO 3 prenucleation clusters. Furthermore, experimental validation is also carried out in order to assess the existence of nucleation in CaCO 3 pre-nucleation clusters at high temperatures (500 °C) using X-ray diffraction and experimental z(𝜶) master plots. The TGA can be used to predict and understand nucleation rates for various nano systems.