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

Centre for Computational Science, Department of Chemistry, University College London 20 Gordon Street, London WC1H 0AJ, UK

Corresponding authors: n.gonzalez-segredo@ucl.ac.uk p.v.coveney@ucl.ac.uk

Received: 7 October 2003
Accepted: 23 January 2004

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 arises 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.