Reaction rate ambiguities for perturbed spectroscopic data: Theory and implementation

The analysis of reaction systems and their kinetic modeling is important for both exploratory research and process design. Multivariate curve resolution (MCR) methods are state-of-the-art tools for the analysis of spectral series, but are also affected by an unavoidable solution ambiguity that impacts the obtained concentration profiles, spectra and model parameters. These uncertainties depend on the underlying model and the magnitude of the measurement perturbations. We present a general theoretical approach together with a computational method for the analysis of the solution ambiguity underlying arbitrary kinetic models. The main idea is to determine all those model parameters for which the corresponding pure component factorizations satisfy all given constraints within small error tolerances. This makes it possible to determine bands of concentration profiles and spectra that reflect the underlying ambiguity and circumscribes the potential reliability of MCR solutions. False conclusions on the uniqueness of a solution can be prevented. The procedure can be applied as a post-processing step to MCR methods as MCR-ALS, ReactLab or others. The Matlab program code is freely accessible and includes not only the proposed ambiguity analysis but also an MCR hard-modeling approach. Application studies are presented for two experimental data sets, namely for UV/Vis spectra on the relaxation of a photoexcited state of benzophenone and for Raman spectra on an aldehyde formation process.