CONFIGURATIONAL ENTROPY OF MICROEMULSIONS - THE FUNDAMENTAL LENGTH SCALE

Phenomenological models have been quite successful in characterizing b oth the various complex phases and the corresponding phase diagrams of microemulsions. In some approaches, e.g., the random mixing model (RM M), the lattice parameter is of the other of the dimension of an oil o r water domain and has been used as a length scale for computing a con figurational entropy, the so-called entropy of mixing, of the microemu lsion. In the central and material section of this paper (Sec. III), w e show that the fundamental length scale for the calculation of the en tropy of mixing is of the order of the cube root of the volume per mol ecule-orders of magnitude smaller than the dimension of such a domain. This length scale is specifically the scale for the configurational e ntropy-not that which measures either the curvature of the interface, the ''granularity'' of the microemulsion, or the persistence length. F urthermore, we demonstrate, in general, that mixing entropy, evaluated in configuration space as opposed to phase space, will not be physica lly correct unless it is made to be consistent with the phase space ev aluation. Following this core section, we give a one-dimensional illus tration of the problem (Sec. IV), and discuss the consequences of our general result with respect to the RMM (Sec. V). The RMM not only seri ously underestimates the entropy of mixing but exhibits a dependence o n composition that is qualitatively very different from the correct de pendence. Furthermore, for oil or water rich compositions of the micro emulsion, the correct mixing entropy reinforces effects that would nor mally be attributed to bending energy, i.e., it destabilizes the syste m.