Principal component analysis for automatic extraction of solid-state kinetics from combined in situ experiments

Abstract

Solid-state reactivity is often studied by in situ experiments with a multi-technique approach, where complementarity of different probes is exploited. In situ data are usually analysed using a complex protocol: first the reaction model most suited to describe the specific solid-state reaction is chosen, second the reaction coordinate is obtained from the data, the order of reaction is then calculated by applying a specific kinetic equation, and finally kinetic parameters are obtained with an Arrhenius plot. The approach is both time consuming and subject to errors due to the arbitrariness of extraction of the reaction coordinate, typically from individual peak intensity variations during the reaction. In addition, application of the different kinetic equations to obtain the best fitting one is tedious and no general method to select the best model with an unbiased approach is available. Here we propose a new procedure based on principal component analysis to get kinetic information from in situ data, which simplifies and speeds up the process of kinetic parameter calculation from a three- to a two- or even a one-step form, reaching a high degree of automation and the ability to manage the huge amount of data produced by in situ multi-technique experiments. The new approach treats data as a whole, without biases introduced by manual methods of obtaining the reaction coordinate by peak intensity evaluation from individual patterns typical of the traditional approach. The procedure is described in its theoretical framework and applied to the formation of a molecular complex, monitored by in situ X-ray powder diffraction and Raman measurements.