Calculation of the Spectrum of Chemical Relaxation Times for a General Reaction Mechanism

Abstract

Abstract A simple formalism is developed in which the determinantal equation for the reciprocal relaxation times of a reaction mechanism can be written down immediately from an inspection of the elementary chemical reactions in the mechanism. The reactions in the mechanism may be of any order; parallel reaction paths may be included. The determinantal equation can be solved for the relaxation times using the simple formalism and the expressions in terms of rate constants and equilibrium concentrations obtained at the end of the procedure. If the reactions are not thermodynamically independent then the order of the determinantal equation can be reduced directly in a simple way to that corresponding to the number of thermodynamically independent reactions. The procedure and the various approximational techniques are illustrated by a number of detailed examples. A number of general results are derived. It is pointed out that for kinetically elementary reactions, the matrix of Onsager coefficients is diagonal. The diagonal element is proportional to the exchange rate of the elementary reaction. It is shown that the transformation to normal coordinates can be done by using a product of a diagonal matrix and an orthogonal matrix. This simplifies the inversion of the transformation considerably. For systems with thermodynamically dependent reactions the explicit form of the time independent coordinates is derived. Some general relations between the elements of the transformation matrix are also derived.