Polybrusselator‐type models

In this paper, the possibility for autocatalysis in polymerization reactions is explored by introducing part of a polymerization mechanism in a model known as Brusselator. It is assumed that monomer concentration is practically constant. Four possibilities are examined: (1) a first radical propagator X, which has an isomer of position of the free electron, Y, dimerizes reversibly and this dimer catalyzes the isomerization of Y to X; (2) the radical propagator X is a polymer with a critical degree of polymerization and has an isomer of position of the free electron Y. This critical radical propagator catalyzes the conversion of Y to X; (3) any radical propagator has an isomer of position of the free electron, Y, and any polymer obtained by recombination of the radicals can catalyze the conversion of Y into its corresponding isomer X; and (4) any radical propagator with a critical degree of polymerization can catalyze the conversion of Y into its corresponding isomer. Isomorphism equations are obtained in all mechanisms, which implies the possibility of limit cycle oscillations (Brusselator model). © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 617–623, 2008