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 en ergy between condensed bodies is well known. However, its implementati on for interacting bodies that are highly irregular and separated by d istances varying from contact to micrometers has received little atten tion. 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 Lifs hitz and Lifshitz-Hamaker interaction energies for continuum spheres o f radii equal to those of the clusters' circumscribed spheres and of t he same masses as the clusters. The Lifshitz energy is shown to conver ge to the iterated dipolar energy for quasispherical molecular cluster s for sufficiently large separations, while the energy calculated by u sing the Lifshitz-Hamaker approach does not. Next, the interaction ene rgies between a contacting pair of these molecular clusters and a thir d cluster in different relative positions are calculated first by coup ling all molecules in the three-cluster system and second by ignoring the interactions between the molecules of the adhering clusters. The e rror 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 sp heres. This Lifshitz energy calculation is then combined with the shor t-separation, nonsingular van der Waals energy calculation of Lu, Marl ow, and Arunachalam, to provide an integrated picture of the van der W aals energy from large separations to contact.