Confidence intervals on the kinetic parameters of condensed-phase reactions

This study introduces a novel methodology for deriving the confidence intervals on the kinetic parameters—including the rate constant, conversion function, activation energy, and pre-exponential factor—in condensed-phase reactions. The approach employs multiple linear regression to factorize the reaction rate into a temperature-dependent rate constant and a conversion function. Confidence intervals for the rate constant and conversion function are approximated using the delta method. Activation energy and its interval estimator are obtained by the Friedman method. Additionally, confidence interval for the pre-exponential factor is computed using the distribution of the difference between means of two populations. The methodology accommodates both isothermal and nonisothermal conditions and is versatile for reactions exhibiting single- or multi-peak rate profiles. Validation on two simulated complex reactions demonstrated excellent agreement between estimated and exact parameter values, with true values consistently falling within the calculated 95\% confidence intervals. Application to experimental thermal degradation data of poly(methyl methacrylate) and a blend of poly(methyl methacrylate) with cyclic olefin copolymer further confirmed practical utility. GNU Octave/MATLAB codes and sample datasets have been provided to enable readers to apply the proposed methodology to their own experimental data.