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

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.