Fluctuating interfaces in microemulsion and sponge phases

A simple Ginzburg-Landau theory with a single, scalar order parameter is used to study the microscopic structure of microemulsions and sponge phases. The scattering intensity in both film and bulk contrast, as well as averages of the internal area S, the Euler characteristic ${\mathrm{\chi }}_{\mathit{E}}$, and the mean curvature squared 〈${\mathit{H}}^2$〉, are calculated by Monte Carlo methods. The results are compared with results obtained from a variational approach in combination with the theory of Gaussian random fields and level surfaces. The results for the location of the transition from the microemulsion to oil-water coexistence, for the scattering intensity in bulk contrast, and for the dimensionless ratio ${\mathrm{\chi }}_{\mathit{E}}$ ${\mathit{V}}^2$/${\mathit{S}}^3$ (where V is the volume) are found to be in good quantitative agreement. However, the variational approach fails to give a peak in the scattering intensity in film contrast at finite wave vector, a peak which is observed both in the Monte Carlo simulations and in experiment. Also, the variational approach fails to produce a transition from the microemulsion to the lamellar phase.