Self-assembly of ternary cubic, hexagonal, and lamellar mesophases using the lattice-Boltzmann kinetic method

We use a kinetic lattice-Boltzmann method to simulate the self-assembly of the cubic primitive (P), diamond (D), and gyroid (G) mesophases from an initial quench composed of oil, water, and amphiphilic particles. Here, we also report the self-assembly of the noncubic hexagonal phase and two lamellar phases, one with periodic convolutions. The periodic mesophase structures are emergent from the underlying conservation laws and quasi-molecular interactions of the lattice-Boltzmann model. We locate regions of the model's parameter space where the sequence of appearance of mesophases lamellar --> primitive --> hexagonal is in agreement with pressure jump experiments and the sequence cubic --> lamellar is in agreement with compositional variations reported in the literature. The ability of our lattice-Boltzmann model to simulate self-assembly of cubic and noncubic phases in a unified and consistent manner opens the way for further investigations into the transition pathways and kinetics of the phase transitions between these states as well as of the rheology of these phases.