Estimating rate constants and pure UV-vis spectra of a two-step reaction using trilinear models

This paper describes the estimation of reaction rate constants and pure species UV-vis spectra of the consecutive reaction of 3-chlorophenylhydrazonopropane dinitrile with 2-mercaptoethanol. The reaction rate constants were estimated from the UV-vis measurements of the reacting system using the generalized rank annihilation method (GRAM) and the Levenberg–Marquardt/PARAFAC (LM-PAR) algorithm. Both algorithms can be applied in cases where the contribution of different species in the mixture spectra is of exponentially decaying character. From a single two-way array, two two-way datasets are formed by means of splitting such that there is a constant time lag between the two two-way datasets. By stacking these two two-way datasets, the reaction rate constants can be estimated very easily from the third dimension. GRAM, which is fast and non-iterative, decomposes the trilinear structure using a generalized eigenvalue problem (GEP). The iterative algorithm LM-PAR consists of a combination of the Levenberg–Marquardt algorithm and alternating least squares steps of the PARAFAC model using GRAM results as a set of initial starting values. Pure spectra of the absorbing species were estimated and compared with their measured pure spectra. LM-PAR performed the best, giving the lowest relative fit error. However, the relative fit error obtained with GRAM was acceptable. Since a lot of measurements are based on exponentially decaying functions, GRAM and LM-PAR can have many applications in chemistry.