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

Abstract

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.

Modelling of spectroscopic batch process data using grey models to incorporate external information

“…The reaction used in this paper has been described previously in the literature [33]. A two-step consecutive reaction of 3-chlorophenylhydrazonopropane dinitrile (A) with 2-mercaptoethanol (B) forms an intermediate adduct (C) which is hydrolysed to give 3-chlorophenylhydrazonocyanoacetamide (D) and ethylene sulphide (E):…”

“…It has been shown previously [33] that applying a first-order kinetic reaction model to the measured spectra yields estimates of the rate constants (k 1 and k 2 in Equation (2)) for each batch. From these it is then possible to estimate both the compound spectra and the concentration time profiles for the reactant, intermediate and product.…”

“…The new NOC batches (30)(31)(32) are also within the confidence limits, indicating that despite the high percentage of variation described by the grey model, there is probably no significant degree of model overfit. Of the nine batches known to include process disturbances (33)(34)(35)(36)(37)(38)(39)(40)(41), all break the 95% confidence limit and only numbers 31 and 34 do not break the 99% confidence limit. The concentrations of NaOH used to disturb these batches were the lowest used (0⋅0251 and 0⋅1020 mol l 71 respectively), and so the effect of the process disturbance is not as large as for e.g.…”

Estimation of the rate constants of second order reactions using mean centering of ratio spectra

“…Most of these studies are oriented towards consecutive first-order reactions. These methods include non-linear least squares fitting [4], rank annihilation factor analysis (RAFA) [6], time shift trilinear models [7,8], target testing [9,10] and curve resolution [11]. The extended Kalman filter has been applied by Mok and Chau [12] to determine kinetic parameters of first-order consecutive reactions.…”

“…The extended Kalman filter has been applied by Mok and Chau [12] to determine kinetic parameters of first-order consecutive reactions. Estimation of the reaction rate constants from a twostep reaction and a comparison between the two-way and three-way methods have also been published [13][14][15][16]. Recently, a new multivariate analysis tool, namely DECRA (direct exponential curve resolution algorithm), that is based on the generalized rank annihilation method (GRAM), has been developed by Windig et al [17] for resolving consecutive first-order reactions.…”