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

The microstructure of a microemulsion is dominated by the thermodynamics of the surfactant interface between the oil and water domains. As the spontaneous curvature of this surfactant interface 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...