__Grain
boundary motion in lamellar phases under oscillatory shear__

** Zhi-Feng Huang**, J. Vinals

Florida State University

We study a symmetric diblock copolymer below the order-disorder
threshold, which is in a polycrystalline state consisting of two differently
oriented lamellar domains. We focus on the motion of a single grain boundary
under an oscillatory shear flow for the special case of two sets of
semi-infinite ordered lamellar regions with different orientation. The motion
of the grain boundary is obtained through both multi-scale analysis and direct
numerical solution of a mesoscopic model. For a two dimensional system, the
grain boundary separating transverse and parallel lamellar regions is found to
exhibit simultaneously two types of motions: a rigid and oscillatory motion
along the imposed shear, and more importantly, a break-up of the transverse
lamella on the boundary followed by recombination with nearby parallel ones.
Consequently, the transverse region, although linearly stable in the absence of
the boundary, is invaded by parallel lamellae and finally disappears. We derive
amplitude equations by perturbation near threshold and for low shear
frequencies, and then calculate the velocity of the grain boundary. We compare
these results with direct numerical solution of an order parameter model. The
properties of a three-dimensional system, where the grain boundary is between
the perpendicular and parallel lamellar domains, are also investigated,
including the effect of viscosity contrast for different phases.