Stability analysis of twist grain boundaries in lamellar phases of block copolymers

TL;DR

This paper investigates the stability of twist grain boundaries in lamellar phases of block copolymers using a mesoscopic model, numerical solutions, and stability analysis within the weak segregation regime.

Contribution

It introduces a detailed analysis of twist grain boundary stability, including a multiple scale approach and amplitude equations, in the context of block copolymer lamellar phases.

Findings

Boundary width scales as epsilon^{-1/4}

Two modes describe the boundary configuration

Planar boundary stability analyzed

Abstract

Twist grain boundaries are widely observed in lamellar phases of block copolymers. A mesoscopic model of the copolymer is used to obtain stationary configurations that include a twist grain boundary, and to analyze their stability against long wavelength perturbations. The analysis presented is valid in the weak segregation regime, and includes direct numerical solution of the governing equations as well as a multiple scale analysis. We find that a twist boundary configuration with arbitrary misorientation angle can be well described by two modes, and obtain the equations for their slowly varying amplitudes. The width of the boundary region is seen to scale as $\epsilon^{-1/4}$, with $\epsilon$ being the dimensionless distance to the order-disorder transition. We finally present the results of the linear stability analysis of the planar boundary.