Long range intermolecular forces between macroscopic bodies: Macroscopic and microscopic approaches

Abstract

Van der Waals energies of interaction are calculated by two methods, the macroscopic method of Lifshitz and the microscopic method of London-Casimir and Polder-Hamaker for the case of two semi-infinite slabs separated by a thin film. When retardation effects may be neglected, the London-Hamaker approach yields values of dispersion interactions which almost coincide with those of the Lifshitz approach, the magnitude of the former values being larger by approximately 10–25%, which is attributed to the effect of the molecular environment in condensed media. At 50–100 Å film thicknesses where retardation effects are small, dispersion terms are generally the major part of van der Waals forces in the Lifshitz formulation. Hence, for 50–100 Å film thicknesses the Hamaker approach, which only includes dispersion interactions is generally adequate. By accounting for retardation effects, which significantly reduce the magnitude of dispersion interactions at several hundred Å, there is a reasonable agreement between the values obtained by the macroscopic and microscopic approaches. When polar substances are present and for film thicknesses of several hundred Å, where dispersion interactions are significantly reduced, the major contribution to van der Waals forces may arise from orientation and induction terms. For such cases the Hamaker approach may lead to critical underestimates of the calculated magnitude of van der Waals forces. An ad hoc way to overcome this difficulty which is applicable to any geometry is proposed. This study presents a simple procedure for the determination of free energies of interaction between macroscopic bodies of various shapes. The procedure, which is applicable when the molecules of bodies and surrounding medium are isotropic, yields results which closely approximate those obtained with the Lifshitz theory.