Harmonic oscillations in a polymerization

Abstract

A simple radical polymerization is proposed in this paper, with step-by-step chain growth (R i + M → R i+1), and termination by transfer to a third body (R i + S→polymer) such as the solvent. It is assumed that, for a certain critical degree of polymerization n, the propagator Rn reacts with substrate H to produce a deactivator (V ) of the first propagator (H + R n → R n + V ; V + R 1 → P 1) R 1. Assuming that monomer, M, and precursor concentrations are constant, and assuming that the deactivator reaches fast a steady state, the resulting kinetic equations are formally linear, but they admit, perturbations r j (t ) of the steady-state concentrations of the propagators R 1, R 2, . . . , R n, which are periodic functions of time. Even more, they can be purely sinusoidal functions (which have been called "harmonic," in analogy to the solutions of the well-known classical harmonic oscillator) with phase shift between perturbations r j (t ) = R j- (R j )0 and r j +1(t ) = R j+1- (R j+1)0. Based on these periodic solutions and aiming to a model as simple as possible, a theoretical analysis is made, resulting in that the minimum value for n would be n = 3. Of course, these harmonic oscillations "driven by trimer" are equally found in the group of all the remaining propagators with polymerization degree higher than 3 (variable Y = σ ∞ j =4 R j ). Int J Chem Kinet 41: 507-511, 2009 © 2009 Wiley Periodicals, Inc.