Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Abstract

Recent experimental [Diao et al., J. Am. Chem. Soc.2011133, 3756.] and simulation results [Sear, J. Phys. Cond. Matt.201224, 052205.] are not consistent with a nucleation rate that is in the thermodynamic limit. This has consequences, if the rate is not in the thermodynamic limit, the time for nucleation will not necessarily scale as one over system size. Here, I show how to analyze data for nucleation times to test for the existence of a well-defined nucleation rate. I also show how to estimate the scaling of the nucleation time with the number of nucleation sites. The prediction is that the farther the system is from the thermodynamic limit, the more rapidly the nucleation time varies with system size. To make this prediction, I use extreme-value statistics. I also show how nucleation data can be analyzed to extract information on the heterogeneity in the surfaces on which nucleation is occurring.