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

Abstract

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 g 10, and for the range of T examined the free energy differences appear to scale in temperature like (T c /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 10 4 . Other discrete sum models are also presented and give similar results.

Modeling of H2O/D2O Condensation in Supersonic Nozzles

“…Finally, Hale (Hale 1992;Hale et al 2004;Hale 2005) developed a nucleation model based on scaling arguments that has a temperature dependence that matches the experimental results quite closely. Here the nucleation rate is calculated as,…”

“…Recent work combining small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) with pressure measurements has resulted in the first measurements of nucleation rates for both isotopes of water in supersonic nozzles (Khan et al 2003;Kim et al 2004;Wyslouzil et al 2007). In Figure 1, we compare the measured nucleation rates for D 2 O to the predictions of the temperature-corrected Wölk-Strey nucleation rate (Wölk and Strey 2001), J WS , and Hale's scaled nucleation model (Hale 1992;Hale et al 2004;Hale 2005), J HALE . Both expressions fit the experimental data quite well over a 20 K temperature range and for supersaturations ranging from 40 to 150.…”

Simultaneous effects of inlet stagnation pressure and heat transfer to the water vapor condensing flow of supersonic laval nozzle

“…Finally, Hale[14,15] developed a nucleation model based on scaling arguments which has a temperature dependence that matches the experimental results quite closely. Here the nucleation rate is calculated as:…”

Ordering in Two-Dimensional Lennard-Jones Clusters

“…The relaxation dynamics in Lennard-Jones(L-J) systems have been studied using Monte-Carlo(MC) method by various workers [1][2][3][4][5][6][7][8]. The study of cluster formation, growth, and ordering under different physical conditions is important both from theoretical and experimental point of view [1,3,8].…”