VAN-DER-WAALS ENERGIES OF CYLINDRICAL AND SPHERICAL SINGLE-LAYER SYSTEMS

The van der Waals energies for cylindrical and spherical single layer systems are obtained, in the nonretarded limit, from the heuristic pro cedure of summing the normal surface electromagnetic mode frequencies. Both the zero and finite temperature results are presented. The geome trical dependence of the energies for the cylindrical and spherical sy stems is shown to satisfy inequalities involving simple model dielectr ic configurations. The exact energies have a first-order correction to the planar case, for a large inner radius in comparison to the film t hickness, which is proportional to the mean curvature with a new Hamak er coefficient. It is conjectured that this applies to arbitrarily sha ped smooth films with small curvature. In the two-body summation appro ximation the energies factorize into a geometrical factor, for which e xact analytical forms are found, and the standard Hamaker constant. Th e effect of geometry on the van der Waals energy is shown to be import ant, in that the effective Hamaker constants for curved films of inner radius r and layer thickness w rises rapidly at r approximately 2.6w for the cylindrical and at r approximately 1.8w for the spherical syst em.