A Study of the Critical Cluster Size for Water Monolayer Clusters on a Model AgI Basal Substrate

We present a formalism and estimate a critical cluster size for water monolayer formation on a (rigid) model AgI basal substrate. The formalism is modified from that developed for vapor clusters [B. N. Hale and R. C. Ward, J. Stat. Phys. 28, 487 (1982)] and uses a Metropolis Monte Carlo method developed by Squire and Hoover [J. Chem. Phys. 50, 701 (1969)] to determine (Helmholtz) free energy differences for clusters containing n and n -1 molecules. Calculations for clusters of n =1, 2, 3, 4, 6, and 24 water molecules on a model AgI basal face at 265 K are used in a statistical mechanical formalism which assumes that the adsorbed clusters form a mixture of noninteracting ideal gases; the adsorbed monomer concentration is related to the vapor concentration at the same temperature. At water saturation and 265 K a critical cluster size of n *=3 molecules and a steady state nucleation rate (for monolayer formation) of 10 ²³ cm ^-2 s ^-1 is predicted. The implications of this for ice nucleation on the model AgI substrate under atmospheric conditions are discussed.