Application of chemometrics methods with kinetic constraints for estimation of rate constants of second order consecutive reactions

To determine the rate constants for the second order consecutive reactions of the form U + V ->(k1) W ->(k2) P, a number of chemometrics and hard modeling-based methods are described. The absorption spectroscopic data from the reaction were utilized for performing the analysis. Concentrations and extinctions of components were comparable, and all of them were absorbing species. The number of steps in the reaction was less than the number of absorbing species, which resulted in a rank-deficient response matrix. This can cause difficulties for some of the methods described in the literature. The standard MATLAB(R) functions were used for determining the solutions of the differential equations as well as for finding the optimal rate constants to describe the kinetic profiles. The available knowledge about the system determines the approaches described in this paper. The knowledge includes the spectra of reactants and products, the initial concentrations, and the exact kinetics. Some of this information is sometimes not available or is hard to estimate. Multiple linear regression for fitting the kinetic parameters to the obtained concentration profiles, rank augmentation using multiple batch runs, a mixed spectral approach which treats the reaction using a pseudo species concept, and principal components regression are the four groups of methods discussed in this study. In one of the simulated datasets the spectra are quite different, and in the other one the spectra of one reactant and of the product share a high degree of overlap. Instrumental noise, sampling error are the sources of error considered. Our aim was the investigation of the relative merits of each method.