Development of a picture of the van der Waals interaction energy between clusters of nanometer-range particles

The importance of the long-range Lifshitz--van der Waals interaction energy between condensed bodies is well known. However, its implementation for interacting bodies that are highly irregular and separated by distances varying from contact to micrometers has received little attention. As part of a study of collisions of irregular aerosol particles, an approach based on the Lifshitz theory of van der Waals interaction has been developed to compute the interaction energy between a sphere and an aggregate of spheres at all separations. In the first part of this study, the iterated sum-over-dipole interactions between pairs of approximately spherical molecular clusters are compared with the Lifshitz and Lifshitz-Hamaker interaction energies for continuum spheres of radii equal to those of the clusters' circumscribed spheres and of the same masses as the clusters. The Lifshitz energy is shown to converge to the iterated dipolar energy for quasispherical molecular clusters for sufficiently large separations, while the energy calculated by using the Lifshitz-Hamaker approach does not. Next, the interaction energies between a contacting pair of these molecular clusters and a third cluster in different relative positions are calculated first by coupling all molecules in the three-cluster system and second by ignoring the interactions between the molecules of the adhering clusters. The error calculated by this omission is shown to be very small, and is an indication of the error in computing the long-range interaction energy between a pair of interacting spheres and a third sphere as a simple sum over the Lifshitz energies between individual, condensed-matter spheres. This Lifshitz energy calculation is then combined with the short-separation, nonsingular van der Waals energy calculation of Lu, Marlow, and Arunachalam, to provide an integrated picture of the van der Waals energy from large separations to contact.