Multiscale modeling of grain-boundary motion in cylinder-forming block copolymers*

Structure formation in block copolymer systems typically results in a multigrain state and the late-stage morphology can be conceived as an assembly of grain boundaries that separate regions of the equilibrium phase that differ in their orientation and registration. The motion of grain boundaries dictates the late-stage coarsening kinetics.

Using the combination of (i) a soft, coarse-grained, particle-based model, (ii) a free-energy functional, and (iii) a lattice model of local, metastable states, we study the structure and motion of a grain boundary between two orthogonal grains of cylindrical domains in asymmetric block copolymers. The particle-based simulation provides direct insights into the elementary class of thermally activated transitions of the self-assembled morphology in the course of grain-boundary translation. These processes are correlated in space and time. We identify a minimal set of transitions, whose free-energy changes and barriers are obtained by describing the system by a free-energy functional and calculating the minimum free-energy path. The spatiotemporal correlation arises from the dependence of the free-energy characteristics on the local environment. We use this information to devise a lattice model of the correlated processes involved in grain-boundary motion. This allows us to investigate the grain-boundary motion by kinetic Monte-Carlo (kMC) simulation and determine its free-energy landscape. Grain-boundary motion proceeds by nucleating a two-dimensional, anisotropic cluster inside the plane of the grain boundary.