van der Waals interactions between nanostructures: Some analytic results from series expansions

The van der Waals force between objects of nontrivial geometries is considered. A technique based on a perturbation series approach is formulated in the dilute limit. We show that the dielectric response and object size can be decoupled and dominant contributions in terms of object separations can be obtained. This is a powerful method, which enables straightforward calculations of the interaction for different geometries. Our results for planar structures, such as thin sheets, infinitely long ribbons, and ribbons with finite dimensions, may be applicable for nanostructured devices where the van der Waals interaction plays an important role.