Birefringence and depolarized light scattering from ordered block copolymers with anisotropic distributions of grain orientations produced by shear flow

We have observed birefringence and depolarized light scattering patterns with 2-fold symmetry from a cylindrical diblock copolymer solution that was ordered under shear flow. We have developed a theory to account for such 2-fold symmetric scattering patterns, based on a model that assumes an anisotropic orientation distribution of ellipsoidal grains in the sample. We also show how scattering patterns can be approximately reduced to the sum of three terms of the form C-n(theta) cos(nphi), where theta and phi are polar angles in the detection plane and n = 0, 2, and 4. By comparing the experimentally determined C-n(theta) functions with theoretical calculations, we estimated the fraction of the sample that is composed of misaligned grains, their size and eccentricity, and the angular range over which their optic axes were distributed (DeltaTheta). The analysis of the optical properties of these kinds of systems is complicated by the fact that the signal from misaligned grains diminishes extremely rapidly as DeltaTheta decreases.