Using Jarzynski’s relation to calculate cluster free energies

Ian Ford and Hoi Yu Tang

A reliable theory of aerosol nucleation requires us to do several things. First, we need to conceive of a simplified kinetic pathway from supersaturated vapour to condensed droplets that can serve as an approximation to the real process. Traditionally, this means we introduce the idea of molecular clusters that are able to grow or evaporate by gain or loss of monomers. We approximate these kinetics with equations of the Becker-Döring type. Then we invoke equilibrium statistical physics ideas in the hope that they can provide us with accurate models of cluster growth and decay, in spite of these actually being non-equilibrium processes. In short, we devote our attention to cluster free energies. Then we need to decide on a level of approximation for the calculation of these free energies, and for molecular statistical mechanics, the detailed specification of the molecular clusters, and of the intermolecular interactions. Then the framework is complete, though it is clearly a very eleborate one!

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