Scaling of the Nucleation Rate and a Monte Carlo Discrete Sum Approach to Water Cluster Free Energies of Formation


The intent of this work is to examine small cluster discrete size effects and their effect on the free energy of cluster formation. There is evidence that such terms can cancel in part the temperature dependence of the monomer flux factor of the classical nucleation rate and result in a scaled form for the nucleation rate. In this work, Monte Carlo configurational free energy differences between neighboring sized n molecule TIP4P water clusters are calculated and used in a Monte Carlo discrete summation (MCDS) technique to generate steady-state nucleation rates. The free energy differences, when plotted versus n-1/3, show evidence of a bulklike effective surface tension for n ≥ 10, and for the range of T examined the free energy differences appear to scale in temperature like (Tc/T - 1). This scaling can provide estimates of nucleation rates for arbitrary temperatures within the range of T simulated. Nucleation rates generated from the model TIP4P free energy differences are compared with the experimental water nucleation rate data of Wölk and Strey (J. Chem. Phys. 2001, 105, 11683) and with the data of Miller et al. (J. Chem. Phys. 1983, 78, 3204). The TIP4P MCDS results provide some evidence of the cancellation effect and generate the scaling of the nucleation rate data at higher temperatures. The magnitudes of the nucleation rates are, however, too large by a factor of 104. Other discrete sum models are also presented and give similar results.




National Science Foundation (U.S.)

Keywords and Phrases

Boltzmann constant; Magnitude; Monte Carlo discrete summation (MCDS); Temperature dependence; Approximation theory; Data reduction; Error analysis; Functions; Monte Carlo methods; Nucleation; Supersaturation; Surface tension; Free energy

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2004 American Chemical Society (ACS), All rights reserved.