Influence of confinement on the orientational phase transitions in the lamellar phase of a block-copolymer melt under shear flow

In this paper, we incorporate some real-system effects into the theory of orientational phase transitions under shear flow [M. E. Cates and S. T. Milner, Phys. Rev. Lett. 62 1856 (1989) and G. H. Fredrickson, J. Rheol. 38, 1045 (1994)]. In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates, the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behavior. At lower temperatures, the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behavior might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.