Orientation selection in lamellar phases by oscillatory shears

Abstract

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shear. The resulting secondary flows break the degeneracy between parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.