Barbara N. Hale

Molecular model for ice clusters in a supersaturated vapor

A molecular model previously applied to prenucleation water clusters is used to examine ice Ih embryos. The canonical partition function is evaluated for clusters having from 6 to 64 water molecules. The intermolecular vibrational free energies are extrapolated to clusters containing up to 120 molecules and free energies of formation, nucleation rates, and critical supersaturation ratios are calculated and compared with experiment. For the clusters studied, the ice Ih structure appears to be much less stable at all temperatures than the more spherical clathratelike cluster.

The scaling of nucleation rates

The homogeneous nucleation rate,J, forT → Tc can be cast into a “corresponding states” form by exploiting scaled expressions for the vapor pressure and for the surface tension, δ. In the vapor-to-liquid case with δ= δ0[Tc -T], the classical cluster energy of formation /kT = [16π/3] • Ώ3 [Tc -1]3/(lnS)2 = [x0/x]2, where Ώ ≡ δ0/[k ñ2/3] and ñ is liquid number density. [1] The Ώ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications ofσ and Ώ.[2]) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data.[3,4] In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with lnJ ≈ const. -[x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), whereTc is the inverse thermal wavelength cubed per second atT =Tc. The ln (Γc) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at smalln, the discrete integer behavior ofn, and a configurational entropy term, τ ln (n), is presented.

Temperature dependence of homogeneous nucleation rates for water: Near equivalence of the empirical fit of Wölk and Strey, and the scaled nucleation model

It is pointed out that the temperature fitting function of Wölk and Strey [J. Phys. Chem. 105, 11683 (2001)], recently shown to convert the Becker-Döring [Ann. Phys. (Leipzig) 24, 719 (1935)] nucleation rate into an expression in agreement with much of the experimental water nucleation rate data, also converts the Becker-Döring rate into a form nearly equivalent with the scaled nucleation rate model, J(scaled)=J(oc) exp[-16piOmega(3)(T(c)T-1)(3)3(ln S)(2)]. In the latter expression J(oc) is the inverse thermal wavelength cubed/sec, evaluated at T(c).

Theory of Nucleation of Water. I. Properties of Some Clathrate-Like Cluster Structures

Abstract The tranquility of classical homogeneous nucleation theory has been disturbed by the introduction of statistical mechanical correction factors to a basically thermodynamic theory. These factors, which appear to be essential, destroy much of the agreement with experiment in the case of water vapor. A molecular model for the prenucleation water clusters is proposed with a view toward resolving some of these difficulties. As a first step, the properties of a few specific cluster configurations have, been examined. Clathrate-like structures containing 16 to 57 water molecules are discussed. The hydrogen bonds were treated as simple harmonic oscillators for the purpose of calculating normal mode frequencies. The Helmholtz free energy of formation of the cluster is calculated from the appropriate partition functions. For these clathrate-like structures the free energy of formation was not found to be a smoothly increasing function of the number of molecules but showed minima corresponding to closed cages.

Studies of H2O on β‐AgI surfaces: An effective pair potential model

Effective pair potential functions are used to study the adsorption of a water molecule on surfaces of β‐AgI. The water molecule is represented by a rigid point charge ST‐2 model and the AgI substrate by an array of point atoms with effective charge ±0.6e, Lennard‐Jones cores, and ionic polarizabilities. Maximal binding energy surfaces and optimal H2O configurations are generated for the water molecule adsorbed on the rigid and unrelaxed basal and prism AgI faces. Adsorption of the H2O above a two layer ledge, an iodine vacancy, and an H2O trapped in the vacancy are modeled for the iodine basal face and compared with results for the smooth substrates. These studies indicate the H2O adsorption is favored at ’’interstitial’’ sites where no substrate atoms lie directly below either in the first or second layer. The prism face is found to attract the water molecule more strongly and provide larger energy barriers to surface diffusion. The model predicts maximal binding energies of 20 and 16 kcal/mole for the ...

A study of the critical cluster size for water monolayer clusters on a model AgI basal substratea)

We present a formalism and estimate a critical cluster size for water monolayer formation on a (rigid) model AgI basal substrate. The formalism is modified from that developed for vapor clusters [B. N. Hale and R. C. Ward, J. Stat. Phys. 28, 487 (1982)] and uses a Metropolis Monte Carlo method developed by Squire and Hoover [J. Chem. Phys. 50, 701 (1969)] to determine (Helmholtz) free energy differences for clusters containing n and n−1 molecules. Calculations for clusters of n=1, 2, 3, 4, 6, and 24 water molecules on a model AgI basal face at 265 K are used in a statistical mechanical formalism which assumes that the adsorbed clusters form a mixture of noninteracting ideal gases; the adsorbed monomer concentration is related to the vapor concentration at the same temperature. At water saturation and 265 K a critical cluster size of n*=3 molecules and a steady state nucleation rate (for monolayer formation) of 1023 cm−2 s−1 is predicted. The implications of this for ice nucleation on the model AgI substra...

A monte carlo method for approximating critical cluster size in the nucleation of model systems

A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennetts Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n2/3] is used to predict critical cluster size and critical supersaturation ratio, S*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.

Analysis of experimental nucleation data for silver and SiO using scaled nucleation theory

The experimental vapor phase nucleation data of Nuth et al., for silver [J. A. Nuth, K. A. Donnelly, B. Donn, and L. U. Lilleleht, J. Chem. Phys. 77, 2639 (1982)] and SiO [J. A. Nuth and B. Donn, J. Chem. Phys. 85, 1116 (1986)] are reanalyzed using a scaled model for homogeneous nucleation [B. N. Hale, Phys. Rev. A 33, 4156 (1986)]. The approximation is made that the vapor pressure at the nucleation site is not diminished significantly from that at the source (crucible). It is found that the data for ln S have a temperature dependence consistent with the scaled theory ln S≊ΓΩ3/2 [Tc/T−1]3/2, and predict critical temperatures 3800±200 K for silver and 3700±200 K for SiO. One can also extract an effective excess surface entropy per atom Ω=2.1±0.1 and an effective surface tension σ≊1500−0.45T ergs/cm2 for the small silver clusters (assuming a range of nucleation rates from 105 to 1011 cm−3 s−1). The corresponding values for SiO are Ω≊1.7±0.1 and σ≊820−0.22T ergs/cm2 (assuming a range of nucleation rates from...

On Nucleation Phenomena I: A Molecular Model

Abstract Nucleation events involving water and ice play a vital role in many atmospheric processes. This paper describes a molecular model for prenucleation water clusters. Results are presented for the formation of these clusters from the supersaturated vapor. The temperature dependence of the model is shown to agree with the classical (liquid drop) model and nucleation rates are calculated and compared with experiment. This model has the advantage of being readily extended to homogeneous and heterogeneous nucleation of ice as well as being applicable to the description of ion-hydration processes. We believe the information inherent in the model concerning interactions on a molecular level can be applied to nucleation phenomena in the atmosphere and can enhance understanding of these processes. This introductory paper describes the progress which has been made and the areas of extended application of these results.

The water monomer on the basal plane of ice Ih: an effective pair, central force potential model of the static interaction

The H2O–H2O intermolecular central force potential of Lemberg and Stillinger is used to obtain optimal binding energy surfaces, vibrational frequencies, and bonding configurations of an adsorbed water monomer on a model basal plane of ice Ih. The monomer interacts (pairwise) with 50 molecules arranged in two layers of the unrelaxed bulk ice lattice. The results of calculations for three model surface sites of differing proton arrangement indicate the existence of diffusion barriers of the order of 2.5 kcal/mole and optimal monomer bonding sites at about 9 kcal/mole with nonepitaxial characteristics. Perspective computer‐drawn plots of the optimal monomer binding energy surfaces and the center of mass height of the monomer over each of the three sites are shown. Similar diagrams showing the variations in the monomer dipole orientation along ’’walks’’ across the sites are also presented. Mean residence times and mean path lengths of the monomer diffusing over the model ice surface are estimated from the mon...