BENDING MODULI AND SPONTANEOUS CURVATURE IN ONE-PHASE MICROEMULSION SYSTEMS - A MOLECULAR APPROACH

We use a lattice-based self-consistent field (SCF) theory to model one -phase microemulsion systems composed of solvents with limited miscibi lity and a non-ionic emulsifier. All relevant degrees of freedom are a ccounted for in a mean-field description; all molecules can distribute freely over the two bulk phases, accumulate at the interface and take all possible conformations, but cooperative fluctuations of the inter face are ignored. The only constraint imposed on the system is a fixed geometry of the droplets. The constraint equilibrium is based on the thermodynamics of small systems. We consider systems with equal compos itions of oil, water and surfactants in lamellar, cylindrical and sphe rical topology. We take the Gibbs energy of these three systems to eva luate the mechanical properties of the monolayers. We show that a Helf rich-type description of the microemulsion is possible in this SCF fra mework. However, the predicted mechanical properties of the system are not classical. Usually it is assumed that the mean bending modulus k( c) and the spontaneous curvature J(0) are surfactant-dependent constan ts. We find that k(c) and J(0) also depend strongly on the surfactant concentration. However, neither the product k(c)J(0) nor the saddle-sp lay modulus (k) over bar depend on the composition as long as the inte rfaces do not interact. These results can be rationalised, as both k(c ) J(0) and (k) over bar can be found from the lateral pressure profile of the flat, relaxed interface. Another important observation is that the Gibbs energy of the microemulsion is not exactly a quadratic func tion of the imposed curvature, causing k(c) to depend weakly on the to pology of the interface.