Role of Dynamical Asymmetry on the Orientation of Block Copolymers in Shear Flow: Computer Simulation and Experiment

The ability of diblock copolymers to self-assemble into periodic microstructures with length scales in the nanometer range offers many opportunities for fundamental research and applications. For practical applications, it is often desirable that the microstructures have a high degree of order on macroscopic length scales and are oriented in a desired direction. This can be achieved in a large volume by shearing the copolymer melt. In experiments, different orientations are observed depending on the copolymer characteristics and the applied shear conditions. However, details of the orientation mechanism under shear are not completely understood. Studying structurally and thermodynamically symmetric, lamellae-forming diblock copolymers by molecular simulation using a highly coarse-grained model, we analyze the effect of dynamical asymmetry on the stable orientation in steady-shear flow. We control the dynamical asymmetry via (i) the segmental friction in our dissipative particle dynamics DPD simulation or via (ii) slip springs, which mimic physical entanglements of the polymers. We study the kinetics of structure formation after a quench from the disordered state in the presence of shear and the ordering of a system, initially comprised of two orthogonally oriented lamellar grains, under shear. In both simulation settings and for both mechanisms of dynamical asymmetry, the perpendicular orientation, where the lamellae normals are perpendicular to the shear gradient, is preferred for approximately equal dynamics of the two blocks, whereas the parallel orientation becomes stable when the ratio of the relaxation times of the blocks exceeds an order of magnitude. We rationalize this finding by the minimum of the Rayleighian, i.e., the energy dissipation rate of the nonequilibrium steady state. We compare these simulation results to experimental diblock copolymer model systems, polystyrene-b-poly-2-vinylpyridine, with slightly different glass transition temperatures of the two polymer blocks. Adjustment of the polymer block mobility by different temperatures for alignment experiments confirms the trend toward a parallel orientation with increasing dynamical asymmetry of the polymer blocks, when the rigid lamellae slide past the opposing brushes of the more mobile polymer block.