Ion Clustering

Kinetic theory is employed in investigating the extent to which polarizable molecules attach themselves to slowly moving ions in a gas, the underlying picture being that commonly used in deriving the barometric equation, i.e., the aggregation of molecules in a constant field of force. A potential energy of the form -κr^-4 for r>~r₀ but ∞ for r<~r₀, leads to a large cluster formation. This hard-sphere potential, however, packs most of the clustered molecules into the sharp crevasse near r₀ and therefore falsifies the result. When the cusp is removed by the more adequate potential λr^-12-κr^-4, the tendency to cluster is reduced nearly 100-fold. Results are obtained in general agreement with experiment, except for Li⁺-Kr, where theory predicts a much smaller cluster than that inferred from mobility measurements.