Coarse-Grained Modeling of Mesophase Dynamics in Block Copolymers

In this chapter we survey recent research on the theoretical description of the mechanisms controlling the dynamics of mesophases in extended block copolymer systems, including the motion of topological defects, coarsening of domains in partially ordered, nonequilibrium configurations, and the response of mesophases to external shear flows for the control of long range order. Our focus here is on a mesoscopic modeling of block copolymer dynamics, based on the fact that the characteristic spatial and temporal scales of structural evolution in nanostructured copolymer materials are far beyond the individual molecular dimension, and hence a coarse-grained, reduced description can be adopted to account for the complex behavior of the system. The mesoscopic model equations as well as the associated amplitude/envelope equations derived from a multiple scale analysis will be introduced below in Sect. 2. The applications to various issues in block copolymer mesophase dynamics are given in Sect. 3 and Sect. 4.