End-evaporation kinetics in living-polymer systems

Abstract

We study theoretically the process of ‘‘end-evaporation’’ in living polymer systems, such as wormlike surfactant micelles. End-evaporation occurs when single monomers either break away from, or join onto, a chain end, the rates being described by the (mean-field) rate constants k and k′, respectively. Thus the chains can exchange material with one-another via a bath of free monomers. The relaxation of a system of living polymers after a small temperature jump (T-jump) is studied theoretically. The effect of a T-jump is to prepare the system with the wrong mean chain length, which relaxes to its equilibrium value L̄ by end-evaporation. It is found that the number of free monomers in the system relaxes almost completely in a time of order 1/kL̄, while the weight-average chain length, which is the quantity measured in light scattering experiments, relaxes on a time scale τD=4L̄2/k, which is three powers of L̄ longer. We also predict that the stress relaxation after a step strain is dominated by end-evaporation whenever τD≲τrep, where τrep is the reptation (disengagement) time for a chain of length L̄. In this case the stress relaxation is found to be ‘‘stretched exponential’’ for times smaller than τD and single exponential for longer times.