Bending rigidities and spontaneous curvature for a spherical interface

We report on a study of the free energy of a spherical interface described by a van der Waals density functional with a squared-Laplacian term. We examine the bulk, the surface tension and the bending rigidity terms, and find the position for the dividing surface that satisfies the Laplace equation generalized to nonvanishing bending energy. In doing this we have made explicit the connection between two previously derived but dissimilar sets of expressions for the interfacial coefficients that stem from the same free energy model (one by Romero-Rochín et al. (Phys. Rev. A 44 (1991) 8417; Phys. Rev. E 46 (1993) 1600) and the other by Gompper and Zschocke (Europhys. Lett. 18 (1991) 731) and by Blokhuis and Bedeaux (Mol. Phys. 80 (1993) 705).