Theory of interfacial bending constants

We critically work over the density functional theoretical foundation of th e interfacial free energy with curvature terms. For a spherical interface d escribed by a free-energy functional with square-gradient and square-Laplac ian terms we find that the grand potentials of the stationary states are gi ven exactly (and only) by pressure-volume and interfacial tension contribut ions. On the other hand, when the density functional is partially optimized in the subspace of densities with fixed interface position, the resulting effective interface potential acquires in the limit of large radius the cus tomary form of Helfrich. We illustrate our findings with a description for the nucleation of micelles.