Gaussian random fields with two level-cuts—Model for asymmetric microemulsions with nonzero spontaneous curvature?

Abstract

The microstructure of a microemulsion is dominated by the thermodynamics of the surfactantinterface between the oil and water domains. As the spontaneous curvature of this surfactantinterface is strongly temperature dependent the microstructure of microemulsions also becomes temperature dependent. In the present work we have assumed that the thermodynamics of the interface is determined by the Helfrich Hamiltonian and that the interface can be described by two appropriately chosen level-cuts of a Gaussian random field. It is then possible to express the free energy density of the interface as a functional of the spectral distribution of the Gaussian random field so that the microstructure which minimizes the free energy can be determined by performing a functional minimization of the free energy with respect to the spectral distribution of the Gaussian random field. The two level-cuts are an important feature of the model since they allow us to model microemulsions with nonzero spontaneous curvature and with unequal volume fractions of water and oil. This again makes it possible to simulate the temperature driven phase inversion of the microemulsions described above. The model furthermore allows us to predict the microstructure of the microemulsion for a given composition of water, oil and surfactant and input parameters H0, κ and κ̄ as well as to predict direct space structures and scattering structure factors. Microemulsions with bicontinuous structures, droplet structures or swollen sponge-like structures are predicted dependent on the input parameters and represented in direct and inverse space. Dilution plots for scattering peak positions are in good agreement with experimental results.