Reduction of macroscopically derived dispersion forces to two-body interactions

Abstract

It is shown analytically and illustrated numerically that the magnitude of dispersion forces per unit area is the same according to two different methods of calculation, the Lifshitz macroscopic theory and the microscopic pair summation of London-Hamaker, for a geometry of two semi-infinite slabs separated by a thin film. Consequently, if the macroscopic approach is accepted, then at least for the given geometry and distances of separation studied, dispersion forces between bodies or particles may be obtained by a sum over pairs. This result may be useful in calculation of dispersion forces for geometries where lack of symmetry makes macroscopic derivations unworkable. Calculations on several systems in the framework of the Lifshitz theory illustrate that in most cases dispersion forces alone can account for the major part of van der Waals forces between macroscopic bodies at close distances of separation. An exception to this rule is exhibited in the case of the system water-benzene-water.