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We consider the effects of anisotropic diffusion and hydrodynamic flows onthe relaxation time scales of the lamellar phase of a diblock copolymer. Wefirst extend the two-fluid model of a polymer solution to a block copolymer,and include a tensor mobility for the diffusive relaxation of monomercomposition which is consistent with the uniaxial symmetry of the lamellarphase. The resulting equation is coupled to the momentum conservation equation,allowing also for a dissipative stress tensor for a uniaxial fluid. We thenstudy the linear relaxation of weakly perturbed lamellae, and the motion of atilt grain boundary separating two semi-infinite domains. We find thatanisotropic diffusion has a negligible effect on the linear relaxation of thelayered phase (in the long wavelenght limit), whereas the introduction ofhydrodynamic flows considerably speeds the decay to a rate proportional to$Q^{2}$, where $Q\ll 1$ is the wavenumber of a transverse perturbation to thelamellar phase (diffusive relaxation scales as $Q^{4}$ instead). On the otherhand, grain boundary motion is siginificantly affected by anisotropic diffusionbecause of the coupling between undulation and permeation diffusive modeswithin the grain boundary region.

Anisotropic diffusion and hydrodynamic effects on lamellar relaxation and grain boundary motion in a model of a block copolymer