van der Waals interaction at a material wedge

The problem of evaluating the van der Waals attraction energy of an atom or microparticle adsorbed near the edge of a straight material wedge of arbitrary opening angle is considered. In order to disentangle more clearly the effect of the wedge geometry from the material parameters, a simple model is used in which the particle is represented by a harmonic oscillator and the substrate by a perfect conductor. By a straightforward extension of the method of images of classical electrostatics, the dipolar coupling of the particle to the substrate is constructed from which new oscillator frequencies can be determined as a function of its position relative to the edge and of the wedge angle. The van der Waals energy is given by the shift in zero-point energy of the oscillator coupled to itself via its images. For a physisorbed atom crossing the edge of a wedge material, the detailed shape of the van der Waals energy barrier (respectively, well) offered by a convex (respectively, concave) wedge is displayed and compared with approximate results deduced from a pairwise summation of Lennard-Jones interactions. The interest of these results for the dynamics and kinetics of sorption by microporous solids is briefly discussed.