Identifiability and distinguishability of first-order reaction systems

Abstract

barrier heights which increase as the solvent becomes more polar, in contrast to the normal equilibrium solvation picture where the barrier should decrease as the polarity increases, because of increased solvation of the polar transition state. Although models exist which discuss these ideas concerning nonequilibrium solvation, it is difficult to draw quantitative comparisons. Similar behavior to that observed for 4,4'-dimethoxystilbene in «-alkyl alcohols has been observed for irans-stilbene in «-alkyl alcohols by Eisenthal and co-workers,5 who also suggest nonequilibrium solvation as the cause of changing barrier heights.Acknowledgment. We thank J. Brady for the use of the SLM 8000 fluorimeter and Beckman DU7 absorption spectrometer as well as many discussions concerning solvation. We thank G. R. Fleming and A. J. Cross for the fitting programs used for the decay Curves. Finally, we thank J. Burkhardt for suggesting the minpak routines. This research was supported by the donors of the Petroleum Research Fund, administered by the American Chemical

Sufficient conditions for unique solutions within a certain class of curve resolution models

“…The second reaction is first-order, and if the reactant V is in large excess, then the first reaction is pseudofirst-order. This reaction scheme applies to several reactions [11][12][13][22][23][24][25][26][27][28]. When the reaction of Equation (10) is performed under (pseudo-)first-order kinetics, then the concentration profiles of U, W and Y can be solved analytically and become…”

“…This is a known permutation problem in first-order kinetics [28]. The correct permutation can be found using knowledge of e.g.…”

Hard‐modelled trilinear decomposition (HTD) for an enhanced kinetic multicomponent analysis

“…However, reaction schemes with only first-order reactions often cannot be uniquely identified from bilinear spectrophotometric data sets [3,4]. For example, the interchange of the two rate constants of a consecutive reaction`A→B→C' will result in different calculated absorption spectra for the intermediate`B', but identical residuals R [3].…”

“…For example, the interchange of the two rate constants of a consecutive reaction`A→B→C' will result in different calculated absorption spectra for the intermediate`B', but identical residuals R [3]. As long as there is no additional information on the spectrum of the intermediate, the two cases cannot be distinguished.…”

Constrained least squares methods for estimating reaction rate constants from spectroscopic data

“…Hence matrix F can be reconstructed if the reaction rate constants are given a value. For first-order kinetics the decomposition of Equation (1) is unique apart from a permutation of the kinetic constants [26,27] (also A. K. Smilde et al, submitted). Chemical knowledge is required to solve this permutation ambiguity.…”