Confidence interval on the kinetic parameters of simple condensed phase reactions

Abstract

Confidence intervals play a crucial role in statistical inference, as they provide a range of values within which a population parameter is likely to fall, thereby enabling researchers to quantify the uncertainty associated with their estimates. This study proposes a new approach for estimating the confidence intervals on kinetic parameters of simple condensed phase reactions using a combined kinetic analysis and multiple linear regression. The conversion function may be represented in the form of truncated Šesták-Berggren (TSB), Šesták-Berggren (SB), or discrete cosine transform (DCT) models. The confidence intervals are calculated for pre-exponential factor, activation energy, and reaction exponents directly from multiple linear regression. However, for rate constant and conversion function, we need to estimate the variance of these parameters using the delta method. The proposed method was applied to the kinetic data from a simulated reaction as well as those of thermal decomposition of a commercial poly(methyl methacrylate). The results revealed that the DCT model provides highly accurate estimates with extremely narrow confidence intervals for kinetic parameters of the simulated reaction, whereas the TSB and SB models may exhibit systematic errors. The research also includes GNU Octave/MATLAB codes enabling readers to generate smooth reaction rate curves from noisy experimental data using the Fourier cosine series expansion and discrete cosine transform, approximate conversion functions with TSB, SB, and DCT models, and determine kinetic parameters and their confidence intervals for simple reactions through the new combined kinetic analysis methods.