Time dependent Ginzburg-Landau equation for an N-component model of self-assembled fluids

TL;DR

This paper investigates the dynamics of an N-component microemulsion model using a time-dependent Ginzburg-Landau equation, analyzing structure factor behavior under different conditions and conservation laws.

Contribution

It provides a comprehensive analysis of the dynamical structure factor in bicontinuous microemulsions with conserved and non-conserved dynamics in the large-N limit.

Findings

Multiscaling observed in unstructured phase at zero temperature for COP.

Ordinary scaling observed for NCOP.

Structured phase exhibits universal scaling form regardless of conservation law.

Abstract

We study the time evolution of an N-component model of bicontinuous microemulsions based on a time dependent Ginzburg-Landau equation quenched from an high temperature uncorrelated state to the low temperature phases. The behavior of the dynamical structure factor $\tilde C(k,t)$ is obtained, in each phase, in the framework of the large-$N$ limit with both conserved (COP) and non conserved (NCOP) order parameter dynamics. At zero temperature the system shows multiscaling in the unstructured region up to the tricritical point for the COP whereas ordinary scaling is obeyed for NCOP. In the structured phase, instead, the conservation law is found to be irrelevant and the form $\tilde C(k,t) \sim t^{\alpha / z} f((|k-k_m| t^{1/z})$, with $\alpha=1$ and $z=2$, is obtained in every case. Simple scaling relations are also derived for the structure factor as a function of the final temperature of the thermal bath.