
Phenomenological models have been quite successful in characterizing both the various complex phases and the corresponding phase diagrams of microemulsions. In some approaches, e.g., the random mixing model (RMM), the lattice parameter is of the order of the dimension of an oil or water domain and has been used as a length scale for computing a configurational entropy, the so‐called entropy of mixing, of the microemulsion. In the central and material section of this paper (Sec. III), we show that the fundamental length scale for the calculation of the entropy of mixing is of the order of the cube root of the volume per molecule—orders of magnitude smaller than the dimension of such a domain. This length scale is specifically the scale for the configurational entropy—not that which measures either the curvature of the interface, the ‘‘granularity’’ of the microemulsion, or the persistence length. Furthermore, we demonstrate, in general, that mixing entropy, evaluated in configuration space as opposed to phase space, will not be physically correct unless it is made to be consistent with the phase space evaluation. Following this core section, we give a one‐dimensional illustration of the problem (Sec. IV), and discuss the consequences of our general result with respect to the RMM (Sec. V). The RMM not only seriously underestimates the entropy of mixing but exhibits a dependence on composition that is qualitatively very different from the correct dependence. Furthermore, for oil or water rich compositions of the microemulsion, the correct mixing entropy reinforces effects that would normally be attributed to bending energy, i.e., it destabilizes the system.
