Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

TL;DR

This paper develops a model for the stress tensor in lamellar block copolymers under oscillatory shear, revealing potential instabilities at domain boundaries that influence orientation selection.

Contribution

It introduces a uniaxial symmetry-based constitutive law for lamellar phases and analyzes the hydrodynamic stability of domain boundaries under shear.

Findings

The model predicts hydrodynamic instability at domain boundaries.

Instability can lead to secondary flows affecting lamellar orientation.

Orientation-dependent viscosity influences stability and flow behavior.

Abstract

We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicularly oriented lamellae in a uniform, oscillatory, shear flow, and show that the configuration can be hydrodynamically unstable for the constitutive law chosen. It is argued that this instability and the secondary flows it creates can be used to infer a possible mechanism for orientation selection in shear experiments.