Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations

TL;DR

This study uses lattice-Boltzmann simulations to explore how amphiphile concentration influences phase separation and self-assembly in ternary fluids, revealing new insights into the formation of complex mesophases and their dynamics.

Contribution

It demonstrates that periodically modulated structures can form without long-range amphiphile interactions and challenges previous claims about the necessity of chemically-specific models.

Findings

Amphiphile concentration slows domain growth, transitioning from algebraic to logarithmic to stretched-exponential.

Self-assembly of sponge and gyroid mesophases occurs in growth-arrested regimes.

Structural oscillations in the structure function are observed, linked to complex amphiphile dynamics.

Abstract

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic, to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically-specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wavenumbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behaviour to a combination of complex amphiphile dynamics leading to Marangoni flows.