Defect dynamics in mesophases

Block copolymer phases are a fertile ground in which to investigate both equilibrium and nonequilibrium properties of mesophases (phases that exhibit partial broken symmetries, intermediate between a completely disordered fluid and a perfectly order crystal). We focus here on two particular phases: a lamellar phase (of smectic symmetry, solid like in one direction and fluid in the two other directions), and a columnar phase (a hexagonal solid in two dimensions, and fluid in the third dimension). Starting from a mesoscopic model of the copolymer, we present the amplitude equations of motion for tilt and twist grain boundaries, and the resulting equations of motion for slightly distorted boundaries. We also examine the assumptions underlying the separation of scales in the derivation of the amplitude equations, and analyze corrections to the equations due to the coupling to the 0(1) variation of the order parameter in the vicinity of the boundaries. These corrections can lead to defect pinning. The effect of pinning on defect motion depends on whether the bifurcation originating the mesophase is super or sub critical.