Self-consistent solution of a continuum model for phase-ordering kinetics in self-assembled fluids

The time evolution of an N-component model of bicontinuous microemulsions based on a time-dependent Ginzburg-Landau equation is considered. The model is solved in the framework of the large-N limit approach with both conserved (COP) and non-conserved order parameter (NCOP) dynamics. The equilibrium phase-diagram displays a low-temperature ordered "ferromagnetic" phase with infinite correlation length and a disordered phase with finite coherence length. Within the disordered phase two different regimes can be identified corresponding to a "paramagnetic" and a microemulsion phase. The latter is divided in two regions by the Lifshitz line which separates a regime with a structure factor peaked around k(m) = 0 from one with k(m) > 0. Lamellar states are also observed at vanishing temperature in the structured region. The behavior of the dynamical structure factor C((k) over right arrow, t) is obtained, for a system quenched from a high-temperature uncorrelated state to the low-temperature phases. At zero temperature the system exhibits a behavior analogous to the one observed in simple fluids in the unstructured region. In the structured phase, instead, the conservation law is found to be irrelevant and the form C((k) over right arrow, t) similar to t(alpha / z) f(\k - k(m)\t(1 / z)), with alpha = 1 and z = 2 is obtained both for NCOP and COP. For quenches near the tricritical point an interesting pattern of different preasymptotic behaviors in identified. Simple scaling relations are also derived for the structure factor as a function of the temperature of the final state.