The effective attractive potential in the non-retarded regime for molecules of dielectric materials via Lifshitz theory

Abstract

A general theory of van der Waals forces developed by Lifshitz based on quantum electrodynamics theory is applied in the present paper to construct a van der Waals attractive potential between the molecules of sufficiently rarefied dielectric materials on the condition that R « λ0, where R is the distance between molecules and λ0 the principal wavelength of the absorption spectra of the medium under consideration, i.e. a theory that is valid in the non-retarded regime. The main objective of the efforts is to provide an effective attractive potential for analysing the interactive characteristics between molecules, including the molecule clusters having repeated structures. A closed form solution for the integral formulation of the attractive potential between particles is first obtained based on certain assumptions made in this work. The derived expression in terms of bulk properties is then compared with the well-known London formula, and is found to differ by a factor of or For identical dielectric media, the factor is reduced to 4/π or (4/π)((ε∞ + 2)/3)2. The validity of the effective potential can be verified by test cases composed of several types of dielectric materials. The computed results are presented in this paper, and comparisons with the results computed by London dispersion formula, as well as the recommended values of the experimental and theoretical techniques, are also presented. As an example, the effective potential of polyethylene is also calculated. The computed well depth of the effective potential is reasonable in comparison with the available experimental and calculated data.