BINARY NUCLEATION KINETICS .1. SELF-CONSISTENT SIZE DISTRIBUTION

Using the principle of detailed balance, we derive a new self-consiste ncy requirement, termed the kinetic product rule, relating the evapora tion coefficients and equilibrium cluster distribution for a binary sy stem. We use this result to demonstrate and resolve an inconsistency f or an idealized Kelvin model of nucleation in a simple binary mixture. We next examine several common forms for the equilibrium distribution of binary clusters based on the capillarity approximation and ideal v apor behavior. We point out fundamental deficiencies for each expressi on. We also show that each distribution yields evaporation coefficient s that formally satisfy the new kinetic product rule but are physicall y unsatisfactory because they depend on the monomer vapor concentratio ns. We then propose a new form of the binary distribution function tha t is free of the deficiencies of the previous functions except for its reliance on the capillarity approximation. This new self-consistent c lassical (SCC) size distribution for binary clusters has the following properties: It satisfies the law of mass action; it reduces to an SCC unary distribution for clusters of a single component; and it produce s physically acceptable evaporation rate coefficients that also satisf y the new kinetic product rule. Since it is possible to construct othe r examples of similarly well-behaved distributions, our result is not unique in this respect, but it does give reasonable predictions. As an illustrative example, we calculate binary nucleation rates and vapor activities for the ethanol-hexanol system at 260 K using the new SCC d istribution and compare them to experimental results. The theoretical rates are uniformly higher than the experimental values over the entir e vapor composition range. Although the predicted activities are lower , we find good agreement between the measured and theoretical slope of the critical vapor activity curve at a constant nucleation rate of 10 (7) cm(-3) s(-2). (C) 1995 American Institute of Physics.