Matrix and convolution methods in chemical kinetics
The use of matrices in chemistry and chemical engineering allows the formulation of chemical models in an elegant and compact way. Nevertheless, the integration of kinetic rate equations is frequently presented without recourse to matrix algebra. The matrix formulation of the rate equations (a set of interconnected differential equations, one for the concentration time variation of each species) is particularly convenient since it allows the integration of the rate equations, using a uniform set of procedures. In addition, the time evolution of the concentrations of all species (reagents, products and intermediates) is obtained simultaneously. This topic is only briefly treated in basic texts on chemical kinetics and mathematics for chemistry, and has been recently reconsidered and further developed by different authors. This fact does not limit the definition of a set of rules that can help with the formulation of the rate matrix \({\mathbf K}\) in a direct way. Furthermore, numerical methods based on the same matrix approach can be used to solve the general case of kinetic systems composed by steps of any order. Analogous formalisms, based on matrices, find many other applications in chemistry and chemical engineering, namely in quantum chemistry (secular equation), spectroscopy (molecular vibrations) and chemical graph theory. The second part of the paper is devoted to the convolution approach that allows to write kinetic equations directly in the integrated form. However, this approach is limited to kinetic schemes composed of first-order or pseudo first-order elementary steps. The method has been recently used for the analysis of complex photochemical kinetic systems.
scientific article; zbMATH DE number 1129353