CLUSTER-COLLISION FREQUENCY .1. THE LONG-RANGE INTERCLUSTER POTENTIAL

In recent years, gas-borne atomic and molecular clusters have emerged as subjects of basic physical and chemical interest and are gaining recognition for their importance in numerous applications. To calculate the evolution of the mass distribution of these clusters, their thermal collision rates are required. For computing these collision rates, the long-range interaction energy between clusters is required and is the subject of this paper. Utilizing a formulation of the iterated van der Waals interaction over discrete molecules that can be shown to converge with increasing numbers of atoms to the Lifshitz-van der Waals interaction for condensed matter, we calculate the interaction energy as a function of center-of-mass separation for identical pairs of clusters of 13, 33, and 55 molecules of carbon tetrachloride in icosahedral and dodecahedral configurations. Two different relative orientations are chosen for each pair of clusters, and the energies are compared with energies calculated from the standard formula for continuum matter derived by summing over pair interactions with the Hamaker constant calculated according to Lifshitz theory. The results of these calculations give long-range interaction energies that assume typical adhesion-type values at cluster contact, unlike the unbounded results for the Lifshitz-Hamaker model. The relative difference between the discrete molecular energies and the continuum energies vanishes for r* almost-equal-to 2, where r* is the center-of-mass separation distance in units of cluster diameter. For larger separations, the relative difference changes sign, showing a value of approximately 15%, with the difference diminishing for increasing-sized clusters. We argue that the details of the results of these calculations indicate that the deficiency in the continuum picture for small separations lies in the substitution of an averaged picture of the interaction for what is intrinsically the cumulative energy of discrete interactants.