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The method of asymptotic approximations as applied to analyzing the mechanism of inhibited liquid‐phase oxidation
Author(s) -
Kalyakin L. A.,
Maslennikov S. I.,
Komissarov W. D.
Publication year - 1993
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/kin.550250902
Subject(s) - chemistry , mechanism (biology) , liquid phase , phase (matter) , computational chemistry , thermodynamics , organic chemistry , physics , philosophy , epistemology
A 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 oxidationunder restrictions k 7 [InH] 0 /(2 k 6 W i ) 1/2 ⩽ 1 and k 8 ≫ 2 k 6 ≫ k 7 . At the first time scale (that is very fast and is measured in second fractions) the concentration of radicals In only changes while [ R O 2 ] ≃ [ R O 2 ] 0 , [In H] ≃ [In H] 0 are constants. At the second time scale (s), [ R O 2 ] 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 k 8 , 2 k 6 , k 7 are determined from comparison with the experimental measurements of [In], [RO 2 ], 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.