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Estimating rate constants and pure UV‐vis spectra of a two‐step reaction using trilinear models
Author(s) -
Bijlsma Sabina,
Louwerse Ad D. J.,
Smilde Age K.
Publication year - 1999
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/(sici)1099-128x(199905/08)13:3/4<311::aid-cem539>3.0.co;2-9
Subject(s) - spectral line , reaction rate constant , dimension (graph theory) , least squares function approximation , gram , mathematics , constant (computer programming) , approximation error , chemistry , analytical chemistry (journal) , statistics , physics , kinetics , computer science , combinatorics , quantum mechanics , chromatography , estimator , biology , bacteria , genetics , programming language
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. Copyright © 1999 John Wiley & Sons, Ltd.