END-EVAPORATION KINETICS IN LIVING-POLYMER SYSTEMS

We study theoretically the process of ''end-evaporation'' in living po lymer systems, such as wormlike surfactant micelles. End-evaporation o ccurs when single monomers either break away from, or join onto, a cha in 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 liv ing polymers after a small temperature jump (T-jump) is studied theore tically. The effect of a T-jump is to prepare the system with the wron g mean chain length, which relaxes to its equilibrium value LBAR by en d-evaporation. It is found that the number of free monomers in the sys tem relaxes almost completely in a time of order 1/kLBAR, while the we ight-average chain length, which is the quantity measured in light sca ttering experiments, relaxes on a time scale tau(D) = 4 L2BAR/k, which is three powers of L longer. We also predict that the stress relaxati on after a step strain is dominated by end-evaporation whenever tau(D) less than or similar tau(rep), where tau(rep) is the reptation (disen gagement) time for a chain of length L. In this case the stress relaxa tion is found to be ''stretched exponential'' for times smaller than t au(D) and single exponential for longer times.