Length Scale for Configurational Entropy in Microemulsions

In this paper we study the length scale that must be used in evaluating the mixing entropy in a microemulsion. The central idea involves the choice of a length scale in configuration space that is consistent with the physical definition of entropy in phase space. We show that this scale may be sensitive to the model employed in the description of a microemulsion, but that in most cases it is of the order of the cube root of the average molecular volume in the system. We also show that other much larger length scales used by workers in the field can be partially reconciled with the fundamental scale through a consideration of the constraints to which the microemulsion is subject. We have attempted to perform the analysis in as rigorous a manner as possible. Many interesting features appear and the importance of using the correct length scale as well as methods (some of which are extensions of current theory) for incorporating it into theories of microemulsions are discussed.