Density functional theory beyond the surface tension. Interfacial width, elastic bending constants and line tension

The long wavelength behavior of the Ornstein-Zernike direct correlation function for nonuniform fluids c(r,r′) has provided important results that comprise our current understanding of fluid interfaces. As we know, the surface tension is obtained from the second moment of c(r,r′), and long-ranged correlations parallel to the surface stand among the main predictions. Also, conventional capillary wave theory leads to its notorious divergent results for the interfacial width when the surface tension cost of thermally excited fluctuations is considered. Here we discuss the consequences of the higher moments of c(r,r′) in the density functional theory of fluid interfaces. We find that in an appropriately extended capillary wave model the interfacial width is finite in the absence of external fields. We derive the expression for the elastic curvature energy and find that the bending moduli are given by the fourth moment of c(r,r′). We obtain too in the same fashion the line tension that originates when interfaces meet.