Non-retarded dispersion energy between macroscopic spheres

Abstract The dispersion energy between two spheres A and B is calculated by expanding the field fluctuations in these spheres in terms of spherical harmonics. This yields an infinite Taylor series in the reduced radii (=radius/distance of centers). The exact dispersion energy is compared with its upper and lower limits, which correspond to a maximum screening by half-spaces (Lifshitz approach) and to no screening at all (Hamaker approach). The two limits are split into identical frequency and different geometric factors and differ by less than 1 per cent at separations characteristic of adhesion. In a second step we calculate the dispersion energy between spheres whose surface is covered with an adsorbed layer. The effect of such layers on the dispersion energy depends primarily on the cross-sections of the spheres at twice the separation d of the interacting partner. An exact treatment of adsorbed layers shows that the dispersion energy is no longer factorized into a frequency and a geometric term and hence depends sensitively on the frequency dependence of the dielectric constants involved. This affects the accuracy of computed results, in particular for separations smaller than and equal to the thickness of the adsorbed layer; for large separations the dielectric properties of the bulk material are predominant.