Van der Waals interaction between an atom and a solid surface

Abstract

This paper contributes to the theory of the long-range attractive polarization force between a neutral atom and a crystalline solid surface in the nonrelativistic limit. The first two terms in the asymptotic expansion of the polarization energy are used to define an atom-solid potential of the form V~, = -C(Z -Zo) '. The constant C appearing in this expression is known from the earlier work of E. M. Lifshitz. The present paper gives a theory of the position of the "reference plane, " Zo, which is important in applications to physisorption.An explicit expression for Zo is first derived for atoms interacting with a jellium metal and with an insulating crystal consisting of atoms which interact via dipole-dipole forces. These model calculations are then incorporated into a computation of the polarization energies of rare-gas atoms physisorbed on noble-metal surfaces. The computed energies are found to be consistent with observed adsorption energies. I. INT ROD UCl IONA physisorbed atom can be considered as being bound to a solid surface under the combined action of two potentials: the long-ranged attractive polarization potential which, in the nonrelativistic limit, has the asymptotic formwhere Z is the distance from the surface; and a short-ranged repulsive potential arising from the overlap of the electronic clouds of the atom and of the surface. ' The present paper deals exclusively with the polarization potential.In a classic paper,~L ifshitz has given a macroscopic formulation of the attractive Van der Waals forces between two bodies characterized by spatially nondispersive, frequency-dependent dielectric functions. This formulation ' implicitly contains an exact expression for the constant C appearing in (1.1). Thus, the extreme asymptotic behavior of V", can be regarded as known. However, in applications to physisorption, the separation Z is typically of the order of 10 cm, a distance which is not large on the scale of the thickness of the "surface" itself. In this situation, it becomes important to know the reference plane with respect to which Z is to be measured. Because of the rapid variation of V", with Z, it is clear that a knowledge of the reference-plane position is crucial in obtaining a reliable estimate of the contribution of the polarization energy to the heat of adsorption.A precise definition of this reference plane can be obtained from the second term in the asymptotic expansion of the polarization energy VÃ1--C/Z -D/Z +~~Ẽ quivalently, we can write Vy"--C/(Z -Zo) thereby defining the reference-plane position, Zo. This procedure is clearly analogous to the one followed previously in defining the correct reference plane for the image potential. Our main objective in this paper is to develop a similar theory of the reference-plane position for the atom-surface polarization potential. Although the need for defining the reference-plane position has been indicated before,~the precise relationship between Zo and the microscopic details of the solid surface has not previously been given.In Sec. II we ...

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