Bending moduli and spontaneous curvature in one-phase microemulsion systems. A molecular approach

Abstract

We use a lattice-based self-consistent field (SCF) theory to model one-phase microemulsion systems composed of solvents with limited miscibility and a non-ionic emulsifier. All relevant degrees of freedom are accounted 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 interface 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 compositions of oil, water and surfactants in lamellar, cylindrical and spherical topology. We take the Gibbs energy of these three systems to evaluate the mechanical properties of the monolayers. We show that a Helfrich-type description of the microemulsion is possible in this SCF framework. 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 J₀ are surfactant-dependent constants. We find that k_c and J₀ also depend strongly on the surfactant concentration. However, neither the product k_cJ₀ nor the saddle-splay modulus k depend on the composition as long as the interfaces do not interact. These results can be rationalised, as both k_cJ₀ and k 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 function of the imposed curvature, causing k_c to depend weakly on the topology of the interface.