Statistical morphology of random interfaces in microemulsions

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Abstract
We introduce a phenomenological lattice model of interacting surfaces to relate the phase behavior of microemulsions with the random geometry and topology of microstructures formed by the self-assembling surfactants. The model rests upon an effective Hamiltonian whose morphological character is manifest. In contrast to earlier membrane models, we focus attention on energy parameters favoring multiply connected microstructures. By employing mean-field and related approximations supported by Monte Carlo simulations, we study phase diagrams, liquid structure factors, and macroscopic surface tensions to demonstrate that the model reflects prominent features of microemulsions.