First-Principles Theory of van der Waals Forces between Macroscopic Bodies

We present a first-principles method for the determination of the van der Waals interactions for a collection of finite-sized macroscopic bodies. The method is based on fluctuational electrodynamics and a rigorous multiple-scattering method for the electromagnetic field. As such, the method takes fully into account retardation, many-body, multipolar, and near-fields effects. By application of the method to the case of two metallic nanoparticles, we demonstrate the breakdown of the standard $1/r^2$ distance law as the van der Waals force decays exponentially with distance when the nanoparticles are too close or too far apart.

Figure 1

Spectrum $F(\omega )$ of the vdW force between two silver nanospheres ($S=10\mathrm{nm}$) for various surface-to-surface distances.

Figure 2

vdW force between two silver nanospheres of radius $S=10\mathrm{nm}$ as a function of their surface-to-surface distance, in log-log scale (a) and log-linear scale (b).