The Kinetics of Evolution of Water Vapor Clusters in Air

Abstract
The kinetic theory of cluster formation in a condensing gas proposed by Buckle (1) attempts to calculate the course of homogeneous condensation from molecular rather than thermodynamic precepts. Here it is applied to the rapid nonequilibrium expansion of atmospheric water vapor in air. A method is established for demonstrating the validity of this theory, originally proposed for a mono-molecular gas, in the case of a complicated species such as water vapor. Cluster conditions in the temperature range 210-295 K and the vapor pressure are calculated throughout the collapse of a supersaturated metastable vapor. An effective molecular pair interaction energy and nearest neighbor coordination number is found based on the classical zero-point enthalpy of sublimation and by iteration to satisfy initial equilibrium limiting constraints at 273 K. The internal energy redistribution frequency results from close matching of the experimental pressure distribution. A method of determining the cluster size at which macroscopic properties become relevant is described; the size is found to be a cluster of about 122 molecules at 273 K based on a hard sphere model collision cross section. For the water vapor dimer an equilibrium constant of 4 x 10 to the -21st power/cc is found at 273 K compared to 3.1 x 10 to the -21st power/cc obtained from Keyes data. Two models for water vapor clusters result (from satisfying all constraints imposed on the theory) which are given in terms of number of nearest neighbors, pair interaction energy per molecule (2.9kcal/mol at 273 K) and possible structure on a cluster by cluster basis for a classical hard sphere model and for a model approximating a Pauling type clathrate.

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