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.