Non-retarded van der Waals energies between a finite rod and a planar substrate

Abstract

We calculate the non-retarded van der Waals interaction free energy for a rod of finite length immersed in an electrolyte and inclined at an arbitrary angle with respect to a plane dielectric substrate. The result is obtained by first calculating the interaction between a composite medium in which an array of rods is embedded and a dielectric substrate. The interaction between a single rod and the substrate is then obtained by letting the volume fraction of embedded rods tend to zero. The final interaction free energy retains all non-additive and many-body effects as well as effects due to electrolyte dissolved in the solvent. The complete free energy of interaction must, in general, be computed numerically for particular systems. We obtain some special results for pure dielectric systems and asymptotic expressions for the effect of dissolved electrolyte. Expressions for the torque exerted on the rod and the spring constant for torsional oscillations of the rod due to surface interactions are also obtained. Typical values for these oscillation frequencies lie in the microwave or far infra-red regions and should be accessible using modern spectroscopic methods.