DESCRIPTION OF THE GEOMETRICAL AND TOPOLOGICAL-STRUCTURE IN AMPHIPHILIC SYSTEMS

A unified description of internal interfaces in oil-water-surfactant m ixtures is proposed. Surfactant degrees of freedom are explicitly take n into account in the form of a vector field. A general definition of average curvatures in terms of the vector field is given. They are ave rages of the mean and Gaussian curvatures and characterize globally th e geometrical and topological structure of the internal interface. It is argued that this definition can be applied to both sharp and diffus e oil-water interfaces, in ordered phases and in disordered microemuls ions. A few examples concerning ordered phases are considered, and the results for the average curvatures are compared with the standard app roach, in which the interface is modeled by an infinitely thin mathema tical surface. It is also shown that the approach reduces to the stand ard one in the case of well-defined surfactant monolayers. Finally, th e definition of average curvatures is extended to the case of microsco pic Hamiltonians.