A kinetic model for clustering of water on hydrated protons in a supersonic free jet expansion

A simple model with three variable parameters is developed for calculating observed clustering data from a free jet expansion. One parameter, σ_R1, can be associated with a reactive collision diameter for a monomer associating with a cluster to form a larger, excited cluster. A second parameter, σ_R3, can be associated with a reactive collision diameter for energy transfer from the excited cluster to the surrounding gas. The third parameter, K', is a constant in a unimolecular decay rate expression for the excited cluster. The reactive cross sections that give the best fit of experimental data are given by (π/4) σ²_R1 =9.90×10^-16 cm² and (π/4) σ²_R3=5.22 ×10^-17 cm². No value could be assigned to K'. Apparently the excited clusters are stabilized by energy exchange collisions in this particular flow field before there is appreciable unimolecular decay. Good fits of clustering data are obtained even though these same values are used for clusters varying in size from 6 to 26 water molecules. Since the clustering environment is radically different than in near-equilibrium experiments, it is not clear that these numbers can be used with other types of experimental data.