SCALING OF THE INTERFACIAL-TENSION OF MICROEMULSIONS - A PHENOMENOLOGICAL DESCRIPTION

Recent experiments revealed a striking scaring behavior of the low and ultralow interfacial tension of microemulsions. A description of this behavior based on the Helfrich elastic free energy, which is symmetri c in the principal curvatures c(1) and c(2), appears to be inconsisten t. We show that, within the phenomenological theory of membrane bendin g elasticity, symmetry breaking between the two principal curvatures s eems to be required in order to explain the low, but nonzero, values o f the interfacial tension and its temperature dependence. We propose t wo simple generalizations of the Helfrich free energy which describe t he experimental results. The first considers a quadratic elastic free energy and anisotropy in the membrane which breaks the symmetry betwee n the two principal curvatures. In the second, which is applicable to systems with positive saddle-splay rigidities, the symmetry between th e two principal curvatures is spontaneously broken by inclusion of hig her-order terms in the curvatures in order to stabilize the free energ y of the system. This analysis provides a straightforward method to ob tain estimates of the bending elastic constants from interfacial tensi on measurements. Experiments confirming the theoretical picture are pr esented and values for kappa and <(kappa)over bar>, for a variety of s ystems, are obtained. (C) 1996 American Institute of Physics.