Monomer-mediated relaxation in living polymers

We study the relaxation kinetics in living polymer systems, such as poly(alpha-methylstyrene), where association-dissociation processes are monomer mediated. so that the molecular weight distribution adapts reversibly to the new thermodynamic parameters by monomer exchange at active sites at chain ends. Using both a system of rate equations for the concentration of l-mers, which is solved numerically, and Monte Carlo simulations in terms of a bond fluctuation model. we find a good description of the dynamic response of the system to large deviations from equilibrium in terms of a single relaxation tau(L) proportional to L-5, where L is the average chain length in equilibrium. The response itself is found to decay with time t as t(-1) in the late stages of relaxation. In contrast to wormlike micelles with scission-recombination kinetics. the: average lifetime tau(l) of chains of length I is found to be practically independent of I for l much greater than 1 for given rate of dissociation which map essentially determine the dynamics of such systems.