Orientation selection in lamellar phases by oscillatory shears

TL;DR

This paper investigates how oscillatory shear influences lamellar orientation in block copolymers, revealing a hydrodynamic instability that favors perpendicular alignment under specific conditions.

Contribution

It introduces a constitutive model respecting lamellar symmetry and demonstrates how secondary flows select lamellar orientation through hydrodynamic instability.

Findings

Hydrodynamic instability favors perpendicular lamellar orientation.

Secondary flows break degeneracy between orientations.

Preferred orientation depends on polymer and shear parameters.

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.