Theory of vesicles and droplet type microemulsions : Configurational entropy, size distribution, and measurable properties

Abstract

A model of vesicles and droplet type microemulsions is presented. It is shown that the size distribution of the droplets (either vesicles or microemulsions) coexisting with excess fluid is determined in general by only two terms : the free energy of the interface between the drops and the continuous phase, and a size dependent entropic factor commonly referred to as 'the entropy of mixing'. The last mentioned term arises from translational configurations of the droplets. In this work we use an estimate of the translational contribution as derived in earlier work. A conjecture of the finite size effects coupled to the entropy of the interfacial layer is made based on experimental data. We treat the summation over the size distribution as an 'effective partition function' from which all relevant measurable properties are calculated. The necessity of invoking a curvature dependence of the interfacial tension is proved. For vesicles, their average size is shown to scale as the volume fraction raised to a universal power, whereas their polydispersity is fully determined by a universal coefficient. Because of the existence of a finite preferred curvature, no such universal behavior is found for microemulsions. Approximate analytical expressions for their size, interfacial tension of the planar oil-water interface, and polydispersity are obtained. A limit (though not a physical one) is found at which universal behavior is recovered. The model is compared to experimental data found in the literature. Quantitative comparison reveals full agreement at a consistency level. Good agreement is found even when using only a single free parameter in the theory. However, this comparison points to an additional size independent term in the size distribution. Includes an erratum, published in vol. 101, issue 12, 1997, -p. 1963