Dynamical nucleation theory: Calculation of condensation rate constants for small water clusters

Abstract

In previous work we began the description of a molecular theory of homogeneous vapor-to-liquid nucleation based on the kinetics of cluster formation and decomposition. In this work we focused on a new theoretical approach to calculating rate constants for evaporation of molecules from clusters. In the present work, we present a molecular theory for calculating condensation rate constants that are consistent with the evaporation rate constants. The new method, which uses variational transition state theory (VTST), provides an expression for the evaporation rate constant that is proportional to the derivative of the Helmholtz free energy for cluster formation with respect to the radius of the spherical volume constraining the cluster. Furthermore, the theory provides a physically justified procedure for selecting a unique value of the radius of the spherical volume for each i-molecule cluster. Since VTST obeys detailed balance, condensation rate constants can be obtained from the evaporation rate constants and the corresponding equilibrium constants. In the present work, we provide a theoretical approach to obtain the equilibrium constants that are consistent with the evaporation rate constants. Monte Carlo methods are presented for calculating the dependence of the Helmholtz free energy of cluster formation on the radius of the constraining volume, which are needed for the evaporation rate constants. In addition, Monte Carlo methods are presented for calculating the relative differences in Helmholtz free energies for clusters of different sizes, which are needed for the equilibrium constants and condensation rate constants. The volume dependent Helmholtz free energies for the water dimer up to the decamer are calculated at 243 K.