The properties of ion clusters and their relationship to heteromolecular nucleation

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Abstract
Ion induced heteromolecular nucleation may be formulated in terms of either a kinetic or a steady‐state thermodynamic model. In the case of the former, nucleation is expressed in terms of the rate constants of the individual association reactions leading to the formation of the ion cluster prenucleation embryos. The thermodynamic approach, on the other hand, leads implicitly to the concept of an energy barrier to nucleation. The two formulations are examined in detail and shown to be complementary. An assessment of the validity of the classical charged liquid drop expression, referred to as the Thomson equation, is made by comparing predicted and experimental values. Although the equation is shown to be useful for calculating the enthalpies of ligand attachment to ions at moderate and larger cluster sizes, in the case of entropies it is only moderately successful for hydration reactions and totally fails for ammonia clustering about ions. It is concluded that the Thomson equation is inadequate for treating the general heteromolecular phenomenon and that methods which are able to effectively take large numbers of configurations into account offer the most promise in describing the molecular properties of clusters. Experimental entropy data indicate that the structures of certain ion clusters are more ordered than accounted for by the classical charged liquid drop formulations. Further examination of these data in light of the Sakur–Tetrode equation indicates the existence of low lying excited internal vibrational modes in ion clusters. These considerations suggest that vibrational frequencies on the order of 1.7×1012 sec−1 are present in clusters of two or more ligands.