Power-Law-Like Stress Relaxation of Block Copolymers: Disentanglement Regimes

We consider stress relaxation in a strongly segregated lamellar mesophase, where block copolymers are in the " brush " state with junction points confined to the interface between the adjacent lamellae and blocks stretched out away from it. If the molecular weight of the blocks is large enough, they entangle with their neighbors as well as with blocks from the opposite brush. The number of entanglements of one particular chain with the opposite brush varies from chain to chain even in the monodisperse system. We demonstrate that this dispersion of the number of entanglements leads to a very broad spectrum of relaxation times and to an effectively power-law-like stress relaxation function log G (log t)" with a = l/2 (a = 2) in the strong (weak) chain-stretching limit. We analyze various disentanglement mechanisms for diblocks and triblocks and the onset of the diffusion of copolymers along the interface. Another relaxation mechanism is due to the displacement of a block across the interface into the " enemy " phase. We conclude that for highly entangled copolymers it will be an important mode of stress relaxation (especially for triblock copolymers). For asymptotically long times the relaxation of stress along the perfectly ordered lamella will be liquidlike. In a system with defects in domain structure the relaxation of stress is controlled by the processes of equilibration of excess density along the layers. For the lamellar mesophase we found G(t) £ 1/2, while for the cylindrical mesophase, G(t) £ 1 4.