Determination of the Kinetic Parameters of Condensed Phase Reactions Using Chebyshev Series Expansion

Abstract In the investigation of condensed phase reactions, obtaining kinetic parameters is vital for understanding reaction behavior and optimizing conditions. To achieve this, differential methods have been devised, yet due to the instability of calculating instantaneous reaction rates through numerical differentiation, they have been less commonly utilized. In this study, the extraction of smooth reaction rate curves from highly noisy experimental data via the Chebyshev series expansion (CSE) approach is explained. Furthermore, a novel combined kinetic analysis is developed to determine reaction kinetic parameters utilizing the Chebyshev series expansion. By employing the new method, kinetic parameters can be accurately deduced by performing multiple linear regression analysis on kinetic data generated from reactions. The CSE has consistently exhibited exceptional accuracy in approximating the conversion function. The primary advantage of the new method lies in its ability to accurately determine unique values for kinetic parameters, including activation energy, pre‐exponential factor, and conversion function, without prior knowledge of the reaction mechanism. The new method has been validated using kinetic data from a simulated reaction and poly(methyl methacrylate) thermal degradation. To facilitate readers in applying the new methods to various kinetic data, the GNU Octave/MATLAB codes have been made publicly available.