Self-assembly of the gyroid cubic mesophase: lattice-Boltzmann simulations

TL;DR

This paper uses lattice-Boltzmann simulations to study the self-assembly process of the gyroid cubic mesophase in a binary fluid, revealing transient phases, slow relaxation, and defect dynamics without macroscopic parameters.

Contribution

First microscopic simulation of gyroid mesophase self-assembly using a Boltzmann transport approach with emergent hydrodynamics.

Findings

Identification of transient microemulsion phase during self-assembly

Observation of slow relaxation towards ordered structure

Detection of grain boundaries and defect dynamics in larger lattices

Abstract

We present the first simulations of the self-assembly kinetics of the gyroid cubic mesophase using a Boltzmann transport method. No macroscopic parameters are included in the model and three-dimensional hydrodynamics is emergent from the microscopic conservation laws. The self-assembly arise from local inter-particle interactions in an initially homogeneous, phase segregating binary fluid with dispersed amphiphile. The mixture evolves in discrete time according to the dynamics of a set of coupled Boltzmann-BGK equations on a lattice. We observe a transient microemulsion phase during self-assembly, the structure function peaks and direct-space imaging unequivocally identifying the gyroid at later times. For larger lattices, highly ordered subdomains are separated by grain boundaries. Relaxation towards the ordered equilibrium structure is very slow compared to the diffusive and microemulsion-assembling transients, the structure function oscillating in time due to a combination of Marangoni effects and long-time-scale defect dynamics.