Fluctuations, temperature, and detailed balance in classical nucleation theory

The role of temperature in classical nucleation theory is examined. It is shown that while even small clusters are assigned a temperature in the classical theory, this must be a fluctuating quantity. Stochastic simulations of cluster evaporation and growth are presented to track the temperature fluctuations in time. The relation 〈‖δT‖2〉=kT20/Cν for the mean square temperature fluctuation is confirmed, where k is the Boltzmann constant, Cν is the cluster heat capacity, and T0 is the bath temperature. For small capillary drops (50–100 molecules), the resulting rms temperature fluctuations of 10°–20° might be expected to have a significant effect on the nucleation rate. However, the simulations reveal a cluster temperature distribution that is centered several degrees below T0. A theory is presented to explain this effect. To first order, which includes Gaussian fluctuations of the cluster temperature T, we find that the effective temperature for cluster evaporation is T−h/2Cν, where h is the latent heat. This temperature correction is precisely that required by detailed balance and results both in a centering of the cluster temperature distribution on T0 and a cancellation of any significant effect of temperature fluctuations on the nucleation rate.