Configurational entropy in a microemulsion: The error implicit in the use of a phenomenological lattice model

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Abstract
Lattice models of complex fluids (micellar solutions, microemulsions, etc.) have been an effective tool for the study of both the internal structures of various complex phases and the corresponding phase diagrams. In some approaches, e.g., the random-mixing model of a microemulsion, the lattice parameter is many times the dimension of a single molecule and has been used as a length scale for computing the configurational entropy (entropy of mixing) of the microemulsion. By investigating a one-dimensional model that can be solved exactly in the continuum, we show that the lattice scale is grossly inappropriate for the evaluation of the mixing entropy because of the omission of a very large number of configurations available in the continuum. Indeed, the proper length scale is of the order of the cube root of the free volume per molecule or much smaller. The lattice parameter is, however, an appropriate scale for the amplitude of interface roughness or persistence length. Since the proper scale leads to a much larger value of the mixing entropy, the microemulsion could be stable against a larger (nonzero value) of interfacial tension than is assumed at present.

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