A kinetic theory of cluster formation in the condensation of gases

Abstract

It is attempted to calculate the course of homogeneous condensation in a classical monatomic vapour from molecular rather than thermodynamic precepts. The growth and decay of physical clusters is described by simple models of energy exchange between degrees of freedom at a common temperature. Unimolecular and bimolecular reaction probabilities are obtained from the phase integrals for critical energy configurations, neglecting cross-terms in the Hamiltonian. Hard-sphere collision diameters and zero-temperature pair energies are introduced as parameters in place of potential functions. Two-atom clusters (dimers) form and decay by special mechanisms involving weak interaction with atoms of a permanent gas. Detailed balance yields size distributions of the Volmer kind. These either converge and are stable, or diverge above a certain size and are metastable. Examples are given for argon. Saturation pressures are calculable from parameters. Surface tension causes the minima in metastable curves and is calculated for argon clusters of up to ten atoms. The non-equilibrium problem is partially solved for distributions not too close to thermodynamic states. No information on the trans-critical sizes results, but concentrations at smaller sizes are found in terms of characteristic times. The threshold phenomenon is connected with the structure of growing clusters, confirming Volmer's conclusion. The behaviour after onset requires further investigation with a theory of the parameters.