The method of asymptotic approximations as applied to analyzing the mechanism of inhibited liquid‐phase oxidation

Abstract

AbstractA new method for analyzing the problems of chemical kinetics is elaborated involving the technique of mathematical modeling. Namely, the matching method of the asymptotic expansion is applied to analyzing the inhibition mechanism of oxidation. The proposed approach is an extension of the well‐known method of quasi‐stationary concentrations and may be applied to study a series of problems in the field of chemical kinetics. Three different time scales were established for the mechanism of inhibited oxidation under restrictions k7[InH]0/(2k6Wi)1/2 ⩽ 1 and k8 ≫ 2k6 ≫ k7. At the first time scale (that is very fast and is measured in second fractions) the concentration of radicals In only changes while [RO2] ≃ [RO2]0, [In H] ≃ [In H]0 are constants. At the second time scale (s), [RO2] changes while [In] ≃ [In]st, [In H] ≃ [In H]0 are constants. At the third time scale (min), [In H] changes. An asymptotic analysis of the differential equations allows us to find out both the time duration of each step and the variation of the component which changes at this step. After that the rate constants k8, 2k6, k7 are determined from comparison with the experimental measurements of [In], [RO2], and [In H]. Due to the simplicity and efficiency of the asymptotic method, one may be applied to treating the complex multicenter radical chain processes such as conjugated oxidation, radical copolymerization, sulfoxidation, etc. © 1993 John Wiley & Sons, Inc.