Combining hard- and soft-modelling to solve kinetic problems

Abstract

A novel approach mixing the qualities of hard-modelling and soft-modelling methods is proposed to analyse kinetic data monitored spectrometrically. Taking as a basis the Multivariate Curve Resolution–Alternating Least Squares method (MCR–ALS), which obtains the pure concentration profiles and spectra of all absorbing species present in the raw measurements by using typical soft-modelling constraints, a new hard constraint is introduced to force some or all the concentration profiles to fulfill a kinetic model, which is refined at each iterative cycle of the optimisation process. This modification of MCR–ALS drastically decreases the rotational ambiguity associated with the kinetic profiles obtained using exclusively soft-modelling constraints. The optional inclusion of some or all the absorbing species into the kinetic model allows the successful treatment of data matrices whose instrumental response is not exclusively due to the chemical components involved in the kinetic process, an impossible scenario for classical hard-modelling approaches. Moreover, the possible distinct constraint of each of the matrices in a three-way data set allows for the simultaneous analysis of kinetic runs with diverse kinetic models and rate constants. Thus, the introduction of model-based and model-free features in the treatment of kinetic data sets yields more satisfactory results than the application of pure hard- or pure soft-modelling approaches. Simulated and real examples are used to confirm this statement.