Effect of surface roughness on van der Waals and Casimir-Polder/Casimir attraction energies

Abstract

A theoretical model is devised to assess effects of surface roughness on dispersion interactions between macroscopic bodies, bounded by self-affine fractal surfaces and separated by a vacuum gap. The rough-surface profiles are described statistically by the saturation values of surface width and the correlation lengths; i.e., in terms of experimentally measurable quantities. The model devised takes into account the separation distance-dependent nature of dispersive interactions. The case of non-retarded van der Waals interactions, known to operate at smaller separation distances between the bodies, and that of retarded attractions, operative at larger separation length-scales, are treated separately in this work. Analytical formulae for the roughness corrections are deduced for the two aforementioned types of attractions. The model is employed to compute roughness corrections to interactions between an extended body, bounded by a self-affine surface, and: a) a point-like adherent; and b) a planar half-space. Furthermore, the roughness-induced corrections to dispersive interaction energies between half-spaces, both bounded by self-affine surfaces, are obtained under assumption that the corresponding surface profiles are not correlated. The predictions of the model are compared with some previously reported theoretical studies and available experimental data on the theme of dispersive adhesion between macroscopic bodies.