Characterizing the routes to nonequilibrium morphologies in two dimensional microphase formers

Striped patterns emerge in a variety of systems, ranging from diblock copolymers, magnetic and ferroelectric materials, and even in biological tissues. In tissues, in particular, different proposed mechanisms are known to generate similar steady-state structures, but their assembly dynamics can markedly differ. We here consider models, in which the emergence of striped patterns can be understood as a phase transition from an unstable ordered phase to a spatially modulated phase. The generic equilibrium behavior can be described by the Brazovskii free energy functional and their relaxational dynamics by the Swift-Hohenberg equation. On a lattice, microscopic interactions are described by short-range attractive and long-range repulsive interactions, such as in the canonical anisotropic next nearest neighbor Ising (ANNNI) model. Although the equilibrium behavior of these systems is fairly well understood, questions remain concerning their assembly dynamics.
We here describe and quantify the out-of-equilibrium self-assembly of two-dimensional microphase formers for various quenching protocols. We specifically investigate whether the associated modulated phases form via nucleation or through some alternate relaxation pathway.