Nanoscale van der Waals interactions

Abstract

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 (ν = α/a 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.

Keywords:

• van der Waals interactions
• coupled dipole method
• nanoscale

Acknowledgements

We would like to acknowledge primary support from DOE grant DE-FG02-07ER46414, as well as numerous discussions with other scientists, including Silvina Gatica, Jerry Mahan, Jorge Sofo, Kristen Fichthorn, Leonidas Gergidis, Slava Rotkin and Adrian Parsegian. Hye-Young Kim would like to acknowledge support from the Center of Nanophase Materials Sciences, which is sponsored at Oak Ridge National Lab by DOE.

Notes

^1. [email protected]

^2. He2 is bound by approximately 1027 eV.

^3. In one sense, the word rigorously is not correct. This expression for C3 is valid only to the first nonvanishing perturbation order in powers of the polarizability a(iv). In the Drude model of an atom interacting with a metal surface, the full result is a power series in the polarizability – that is, there are higher order terms in 1/z 6 and 1/z 9 and so on. When the metal is not perfect, such as when it responds through a dynamical image g(iw), the exact, nonretarded result can be obtained via an independent boson model (IBM) for the metal coupled harmonically to the Drude atom.

Additional information

Notes on contributors

Milton W. Cole

1 1. [email protected]