where c n is the concentration (or probability) of a cluster of size n, c i is the concentration (or probability) of a cluster component i, p w and p ref are the partial pressures water and the equilibrium saturation vapor pressure of water, respectively, ∆G bind,n is the binding free energy associated with forming a cluster of size n, ∆G bind,i is the binding free energy associated with the cluster component, i, k B is the Boltzmann constant, and T is the temperature.