Influence of a modulated surface on the properties of liquid-liquid interfaces

We present an extension to the linear Gouy-Chapman theory for an interface between two immiscible electrolytes (ITIES) with an interface that deviates from a planar geometry. This theory takes into account the proper boundary condition for an ITIES, i.e., neither the potential nor the surface charge is fixed at the boundary between the electrolytes. Instead, the dielectric displacement at the interface position is allowed to respond to the perturbation from a flat surface. The linear and quadratic response functions are calculated self-consistently. We derive a roughness function in terms of a height-height correlation function of the surface, which determines the behavior of the capacity and the free energy of a modulated ITIES. Furthermore, we calculate the appropriate electrostatic contribution to the elastic bending modulus of the interface. [S1063-651X(98)10410-5].