Harmonic oscillations in a polymerization

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 R n 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 = ∑   ∞ j =4R j ). © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 507–511, 2009