Random Interfaces and the Physics of Microemulsions

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Abstract
The Gaussian model of random interfaces is related to the statistical mechanics of microemulsions by a variational approximation to the free energy. This allows the prediction of the structure factor as a function of surfactant and water/oil concentrations and the bending modulus. Different scaling regimes for the behaviour of the structure factor (and the real-space structure) are identified and we predict how the structure changes from one with a well-defined length scale to one with no well-defined domain size as the surfactant concentration or the bending energy are decreased. Upon a further decrease in these quantities, the correlation length of the exponential decay diverges, signifying an instability of this system.