Cluster-collision frequency. II. Estimation of the collision rate

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Abstract
Gas-phase cluster-collision rates, including effects of cluster morphology and long-range intermolecular forces, are calculated. Identical pairs of icosahedral or dodecahedral carbon tetrachloride clusters of 13, 33, and 55 molecules in two different relative orientations were discussed in the preceding paper [Phys. Rev. A 43, 5483 (1991)]: long-range interaction energies were derived based upon (i) exact calculations of the iterated, or many-body, induced-dipole interaction energies for the clusters in two fixed relative orientations; and (ii) bulk, or continuum descriptions (Lifshitz–van der Waals theory), of spheres of corresponding masses and diameters. In this paper, collision rates are calculated according to an exact description of the rates for small spheres interacting via realistic potentials. Utilizing the interaction energies of the preceding paper, several estimates of the collision rates are given by treating the discrete clusters in fixed relative orientations, by computing rotationally averaged potentials for the discrete clusters, and by approximating the clusters as continuum spheres. For the discrete, highly symmetric clusters treated here, the rates using the rotationally averaged potentials closely approximate the fixed-orientation rates and the values of the intercluster potentials for cluster surface separations under 2 Å have negligible effect on the overall collision rates. While the 13-molecule cluster-collision rate differs by 50% from the rate calculated as if the cluster were bulk matter, the two larger cluster-collision rates differ by less than 15% from the macroscopic rates, thereby indicating the transition of microscopic to macroscopic behavior.