INFERENCE OF CLUSTER PHASE FROM CONSIDERATIONS OF HOMOGENEOUS NUCLEATION IN AN EVAPORATIVE ENSEMBLE

It is possible to express the rate of freezing of molecular clusters of normal substances in terms of two dimensionless indexes, R1 and R2, related to the range of liquid existence and to the entropy of fusion. This can be done by incorporating into the classical nucleation theory for freezing Turnbull's relation for interfacial free energy, the Klots-Farges relation for the evaporative cooling temperature of clusters, Trouton's rule for heat of vaporization, and Ward's relation for activation energy of viscous flow. The two indexes R1 and R2 are just the two which had been invoked for purely heuristic reasons several years ago in a successful empirical criterion for the phase of clusters generated in supersonic expansions. Although the present treatment cannot be expected to yield precise nucleation rates for clusters of arbitrary compounds, the rate law derived is quite successful in discriminating between those substances which can freeze in the characteristic time of the supersonic experiments and those which are unable to. Moreover, the dividing line derived is closely related to that of the original criterion for cluster phase. The insight provided by the treatment makes it possible to extend the criterion to condensates produced under more general conditions and to correct the interpretation of certain observations.