Anisotropic linear response in block copolymer lamellar phases

We examine the linear response of a lamellar block copolymer phase in the weak segregation regime and focus on those effects that arise from the uniaxial symmetry of the phase. The classical two fluid model of a polymer solution is extended to allow for anisotropic monomer diffusion as well as hydrodynamic flows. The latter include constitutive laws for the stress that also reflect the symmetry of the phase. Transverse relaxation of weakly perturbed lamellae is the slowest mode, and is subdiffusive, in contrast to diffusive decay of longitudinal perturbations. Anisotropic diffusion can both enhance or reduce the rate of relaxation of long wavelength perturbations of lamellae depending on the relative magnitude of longitudinal and transverse mobilities. Hydrodynamic flows at the scale of the lamellae are negligible for most situations of interest, but not long ranged flows as would appear in, for example, multidomain configurations. We find that such flows accelerate linear decay, and even dominate diffusive relaxation in the long wavelength limit. We finally examine anisotropic effects on defect motion as exemplified by a tilt grain boundary. The boundary velocity is significantly affected by anisotropic diffusion through the coupling between undulation and permeation diffusive modes in the defect region.