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 $-\kappa r^{-4\mathrm{}}$ for $r>~r_0$ but $\infty$ for $r<~r_0$, leads to a large cluster formation. This hard-sphere potential, however, packs most of the clustered molecules into the sharp crevasse near $r_0$ and therefore falsifies the result. When the cusp is removed by the more adequate potential $\lambda r^{-12\mathrm{}}-\kappa r^{-4\mathrm{}}$, the tendency to cluster is reduced nearly 100-fold. Results are obtained in general agreement with experiment, except for ${\mathrm{Li}}^{+}$-Kr, where theory predicts a much smaller cluster than that inferred from mobility measurements.