The relaxation spectrum of polymer length distributions

We study theoretically the behaviour of a system of « living polymers » (polymers that can break and recombine reversibly) whose molecular weight distribution (MWD) is perturbed from equilibrium and then allowed to relax. Two classes of chemical kinetics are considered: (a) reversible unimolecular scission, and (b) end-interchange. (Both yield equilibrium MWD's that are exponential). Assuming simple forms for the reaction-rate kernels in each case, we derive response functions that determine the relaxation of the system after an arbitrary (small) initial perturbation to the MWD. This is in general a complicated, non-exponential decay. However, for the special case of a temperature or pressure jump, which preserves the exponential form of the MWD but shifts its mean, a single exponential decay is predicted for the unimolecular scission case, whereas there is no decay at all in the case of end interchange. We expect our results to be relevant to the interpretation of T-jump experiments on flexible wormlike micelles.