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.

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Abstract. The experimental homogeneous nucleation rate data, J exp (T,S), for water are compared with a steady state Monte Carlo nucleation rate model, J MC (T,S), in which the small cluster energies of formation are determined from a discrete sum of Monte Carlo generated Helmholtz free energy differences, ≤f c (n). This formalism includes the ≥ln(n) term of Fisher, where for the critical water clusters (n* > 20 molecules) we use ≥ = 2.2. It is shown that the ≤f c (n) scale like [T c /T -1] and that the discrete summation over n = 2,3,…8 produces a term that cancels the temperature dependence of the monomer flux factor. The result is a scaled form for the nucleation rate, J scaled (T,S) = J o exp[-(16↓/3)[τ(T c ./T-1)] 3 /(lnS) 2 , where J o = 10 26 cm -3 s -1 and τ = 1.47 (close to the value predicted by liquid water bulk surface tension). This form has the same T dependence as the data of Viisanen, Strey and Reiss and gives an improved prediction for the data of Miller, Kassner and Anderson.