Two-dimensional kinetics of binary nucleation in sulfuric acid–water mixtures

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Abstract
Homogeneous nucleation theory for binary mixtures is developed as a two-component extension of the classical multistate kinetics rate theory. A matrix formulation, based on the stochastic model of Shugard and Reiss [J. Chem. Phys. 65, 2827 (1976)], provides the framework for solving the strongly coupled two-dimensional flux network associated with tracking the evaporation and growth kinetics of each component for several thousand binary clusters, of varying composition, throughout the region of critical size. This approach avoids the assumption of a single nucleation path, e.g., through the saddle point of the binary free-energy surface, and considers, instead, all possible paths whose current density contributes to the nucleation rate. Calculations are presented for the steady-state nucleation rate and, by a new method based on the negative eigenvalue theorem, for the distribution of relaxation times in sulfuric acid–water mixtures. At water relative humidities typical of the atmosphere, quantitative agreement with the predictions of a closed-form rate expression due to Shugard et al. is found. At high supersaturations, typical of diffusion cloud chamber operation, the nucleation current is found to bypass the saddle point, due to kinetic forcing, resulting in a higher-than-expected nucleation rate.