Abstract. In this paper, the subcritical, near-critical and supercritical asymptotic behaviour of a reversible Markov process as a chemical model for polymerization was studied. We establish the existence of three distinct stages (subcritical, near-critical and supercritical stages) of polymerization (in the thermodynamic limit as N → +∞), depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, N^a(1/2 < a < 1) and N, respectively. Especially, a = 2/2σ+1 when the coagulation (reaction) rate constant R_ij of the polymers satisfies R_ij = i^σ j^σ with 1/2 < σ < 3/2.

PACS numbers: 82.35.Jk, 02.50.Ga, 82.70.Gg

Print publication: Issue 27 (11 July 2003)
Received 14 January 2003, in final form 28 May 2003
Published 25 June 2003