Statistical kinetic approach for modeling lifespan

Crystallization of Glycine During Freezing of a 40/60 w/w Sucrose/Glycine Excipient System: An Alternative to the Johnson–Mehl–Avrami (JMA) Equation for Modeling Dispersive Kinetics

The isothermal crystallization of glycine in a 40/60 (w/w) sucrose/glycine excipient system is examined with the goal of comparing the kinetic information obtained by using the Johnson-Mehl-Avrami (JMA) equation with that collected using a novel, dispersive kinetic model equation recently proposed by the author. It is found that while both models explain the experimental data reasonably well, the latter equation fits the data, collected at temperatures in the range 241-251 K, without the use of empirical parameters. The values of the activation energy and Arrhenius constant (frequency factor) for both models agree within experimental error.

A Collision Theory-Based Derivation of Semiempirical Equations for Modeling Dispersive Kinetics and Their Application to a Mixed-Phase Crystal Decomposition

In recent works, the author has shown the utility of new, semiempirical kinetic model equations for treating dispersive chemical processes ranging from slow (minute/hour time scale) solid-state phase transformations to ultrafast (femtosecond) reactions in the gas phase. These two fundamental models (one for homogeneous/deceleratory sigmoidal conversion kinetics and the other for heterogeneous/acceleratory sigmoidal kinetics; isothermal conditions), based on the assumption of a "Maxwell-Boltzmann-like" distribution of molecular activation energies, provide a novel, quantum-based interpretation of the kinetics. As an extension to previous work, it is shown here that the derivation of these dispersive kinetic equations is supported by classical collision theory (i.e., for gas-phase applications). Furthermore, the successful application of the approach to the kinetic modeling of the solid-state decomposition of a binary system, CO2.C2H2, is demonstrated. Finally, the models derived appear to explain some of the (solid-state) kinetic data collected using isoconversional techniques such as those often reported in the thermal analysis literature.