Simple approximate analytical solution for non-isothermal single-step transformations: kinetic analysis

TL;DR

This paper presents a simple analytical method for modeling non-isothermal single-step transformations, enabling easy curve fitting and revealing that transformed fraction evolutions are identical when scaled by a time constant.

Contribution

It introduces a new approximate analytical solution for non-isothermal transformations, simplifying system description and analysis compared to existing methods.

Findings

Analytical expressions for transformation rate peaks derived.

Evolutions at different heating rates are identical when scaled.

Method's accuracy is comparable to the Kissinger method.

Abstract

In this paper, we develop a method for obtaining the approximate solution for the evolution of single-step transformations under non-isothermal conditions. We have applied it to many reaction models and obtained very simple analytical expressions for the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the system's description allowing easy curve fitting to experiment. A remarkable property is that the evolutions of the transformed fraction obtained at different heating rates are identical when time is scaled by a time constant. The accuracy achieved with our method is checked against several reaction models and different temperature dependencies of the transformation rate constant. It is shown that its accuracy is closely related with that of the Kissinger method.