Nanoscale van der Waals interactions

Despite the fact that van der Waals (VDW) interactions are often considered to be weak, they dominate the behaviour of all neutral physical systems at separations of order 0.5 nm or larger. For simple geometries-geometric half spaces, spheres, cylinders, or points-VDW interactions are often calculated using a form of Lifshitz theory, which is based on continuum descriptions. But for nanoscale systems, it is often the case that the geometries involve corners, sharp edges, discrete atom placement or small sizes, so that bulk continuum models do not apply. In these cases it is common to compute the VDW interactions using two-body calculations, for instance from Lennard-Jones parameters, the Derjaguin or Hamaker approximation, or pairwise additivity. In this review, we show that none of these estimates predicts VDW interactions accurately; rather, one must use a 'nanoscale Lifshitz theory', which we call the 'coupled dipole method' (CDM). The CDM accounts for all many-body interactions in the nonretarded limit. The method uses an exact evaluation of the eigenmodes of the coupled dipole oscillators, which represent the charge fluctuations of the system. A key quantity determining the relative importance of many-body contributions is the dimensionless ratio (nu = alpha/alpha(3)) of the polarisability to the cube of the interparticle spacing. We assess the accuracy of two-body and three-body calculations against many-body predictions, and then briefly discuss the role of retardation. Several important research questions remain, and these are summarised.