High-Temperature-Driven Analysis of Nucleation Rates and Interfacial Energy in Cobalt Oxide Nanoclusters Investigated by In Situ Thermogravimetric Analysis

This research delves into the critical role of high temperature in overcoming both thermodynamic and kinetic barriers, essential for evaluating nucleation rates and interfacial energy during the formation of a large number of subatomic-sized nuclei from the heating of nanoclusters, a key factor in the synthesis and optimization of advanced materials. Therefore, herein, for the first time, we demonstrate a mathematical framework to compute and understand the nucleation rate and interfacial energy patterns under elevated temperature conditions for ultrasmall cobalt oxide nanoclusters (CONCs), which is also visualized through 2D mathematical simulations via MATLAB software. Further, to achieve this, a combination of precise isoconversional techniques, such as the Kissinger–Akahira–Sunose method and the advanced Vyazovkin approach, was employed to determine key kinetic parameters, including the pre-exponential factor (Aα) and apparent activation energy (Eα), using thermogravimetric analysis (TGA) data. These results were integrated to obtain the interfacial energy and nucleation rate of approximately 2 nm-sized CONCs over 555–780 K temperature range. The Z(α) master plot revealed that random nucleation predominantly occurred at higher temperatures, surpassing low conversion thresholds, within a chitosan matrix. To further enhance the understanding of the nucleation process, four distinct mathematical models were developed, linking the interfacial energy and nucleation rate with temperature and conversion. A logarithmic scale was adopted in the current work for a 2D simulation plot of predicted J with conversion and temperature, which typically helped to visualize a wide range of data effectively into a small segment and making nucleation rate patterns and differences more observable, with maxima and minima evinced through light yellow and blue coloration, respectively. Therefore, these models with visual representation provide valuable insights for predicting real-time process optimization, enabling controlled nucleation and advancing the design of CONCs for advanced material design applications investigated through TGA.