New Integral Method for the Combined Kinetic Analysis (ICKA) of Condensed Phase Reactions Using Truncated Šesták–Berggren Model

The truncated Šesták–Berggren (TSB) model has been demonstrated to reliably predict the conversion function of standard reaction models. However, when applying the TSB model to thermal analysis of condensed phase reactions using the integral method, an integration emerges that lacks an analytical solution. This integral can be expressed using special functions like the incomplete beta function and the Gaussian hypergeometric function. The integral method offers the capacity to utilize raw kinetic data directly, thereby obviating the potential for errors arising from the calculation of instantaneous reaction rates with noisy experimental data. In this study using a special function, we have developed a new integral method for combined kinetic analysis of simple reactions under nonisothermal conditions, enabling the estimation of kinetic parameters, including the activation energy, pre-exponential factor, and TSB-form of conversion function through a trial-and-error procedure with linear regression. The validity of the new approach was tested by applying it to the kinetic data of a simulated reaction and the thermal decomposition of poly(methyl methacrylate), yielding results closely matching those obtained using differential method. Furthermore, we provided GNU Octave/MATLAB codes for users to calculate TSB model coefficients for standard reaction models in both differential and integral forms, as well as to estimate kinetic parameters of reactions using their own kinetic data.