Fluctuations, temperature, and detailed balance in classical nucleation theory
- Environmental Chemistry Division, Brookhaven National Laboratory, Upton, New York 11973 (United States)
- Idaho National Engineering Laboratory, P.O. Box 1625, Idaho Falls, Idaho 83415 (United States)
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 {l_angle}{vert_bar}{delta}{ital T}{vert_bar}{sup 2}{r_angle}={ital kT}{sup @2}{ital d}0/{ital C}{sub {nu}} for the mean square temperature fluctuation is confirmed, where {ital k} is the Boltzmann constant, {ital C}{sub {nu}} is the cluster heat capacity, and {ital T}{sub 0} is the bath temperature. For small capillary drops (50--100 molecules), the resulting rms temperature fluctuations of 10{degree}--20{degree} 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 {ital T}{sub 0}. A theory is presented to explain this effect. To first order, which includes Gaussian fluctuations of the cluster temperature {ital T}, we find that the effective temperature for cluster evaporation is {ital T}{minus}{ital h}/2{ital C}{sub {nu}}, where {ital 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 {ital T}{sub 0} and a cancellation of any significant effect of temperature fluctuations on the nucleation rate.
- Research Organization:
- Brookhaven National Laboratory
- DOE Contract Number:
- AC02-76CH00016; AC07-76ID01570; AC07-94ID13223
- OSTI ID:
- 46442
- Journal Information:
- Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 22 Vol. 102; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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