title: On the ambiguity of the reaction rate constants in multivariate curve resolution for reversible first-order reaction systems.
abstract: If for a chemical reaction with a known reaction mechanism the concentration profiles are accessible only for certain species, e.g. only for the main product, then often the reaction rate constants cannot uniquely be determined from the concentration data. This is a well-known fact which includes the so-called slow-fast ambiguity. This work combines the question of unique or non-unique reaction rate constants with factor analytic methods of chemometrics. The idea is to reduce the rotational ambiguity of pure component factorizations by considering only those concentration factors which are possible solutions of the kinetic equations for a properly adapted set of reaction rate constants. The resulting set of reaction rate constants corresponds to those solutions of the rate equations which appear as feasible factors in a pure component factorization. The new analysis of the ambiguity of reaction rate constants extends recent research activities on the Area of Feasible Solutions (AFS). The consistency with a given chemical reaction scheme is shown to be a valuable tool in order to reduce the AFS. The new methods are applied to model and experimental data.
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
authors.forename: Henning
authors.initials: H
authors.lastname: Schröder
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
authors.forename: Mathias
authors.initials: M
authors.lastname: Sawall
authors.affiliation: Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Kubis
authors.affiliation: Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Detlef
authors.initials: D
authors.lastname: Selent
authors.affiliation: Evonik Performance Materials GmbH, Paul-Baumann Strasse 1, 45772 Marl, Germany.
authors.forename: Dieter
authors.initials: D
authors.lastname: Hess
authors.affiliation: Evonik Performance Materials GmbH, Paul-Baumann Strasse 1, 45772 Marl, Germany; Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany.
authors.forename: Robert
authors.initials: R
authors.lastname: Franke
authors.affiliation: Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Armin
authors.initials: A
authors.lastname: Börner
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany; Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany. Electronic address: klaus.neymeyr@uni-rostock.de.
authors.forename: Klaus
authors.initials: K
authors.lastname: Neymeyr
keywords: Area of feasible solutions; Factor analysis; Feasible rate constants; Kinetic modeling; Nonnegative matrix factorization; Spectral recovery