Application of a Scaled Homogeneous Nucleation-Rate Formalism to Experimental Data at T≪T\u3csub\u3ec\u3c/sub\u3e

It is pointed out that for temperatures T\u3c0.5Tc, where Tc is the critical temperature, the classical steady-state nucleation-rate formalism of Becker and Doring predicts an approximate critical supersaturation ratio Scr (for the onset of nucleation) given by lnScr/Ω3/2~0.53(Tc/T-1)3/2. Ω is a material-dependent quantity approximately equal to the excess surface entropy per molecule. For most substances Ω ~ 2.0 and for associated liquids Ω ~ 1.5.The experimental data (for nucleation from vapor to liquid) from diffusion chamber and nozzle beam studies are found to be consistent with the above expression. The classical theory also predicts that for a supersaturation ratio S corresponding to constant J, lnS/lnScr-1 ~ lnJ/2lnJc, where lnJc is a quantity evaluated at the critical point and is ~ 72 for most materials. Expansion cloud-chamber data for nonane, toluene, and water are also found to be consistent with these approximate scaling laws

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, Jscaled=Joc exp[-16πΩ3(Tc/T-1)3/3(ln S)2]. In the latter expression Joc is the inverse thermal wavelength cubed/sec, evaluated at Tc

Scaled Vapor-to-Liquid Nucleation in a Lennard-Jones System

Scaling of the homogenous vapor-to-liquid nucleation rate, J, is observed in a model Lennard-Jones (LJ) system. The model uses Monte Carlo simulation-generated small cluster growth to decay rate constant ratios and the kinetic steady-state nucleation rate formalism to determine J at four temperatures below the LJ critical temperature, Tc. When plotted vs the scaled supersaturation, lnS/[Tc/T-1]3/2, the values of log J are found to collapse onto a single line. A similar scaling has been observed for the experimental nucleation rate data of water and toluene

Modified Phase Representation and Effects of Inelasticity in N/D Calculation of p-Wave Pion-Pion Scattering

An N/D formalism based on a modified phase representation is used to study the effects of inelasticity on the ρ-wave pion-pion amplitude. The effects of high-energy inelasticity are introduced in terms of the assumed behavior of the high-energy phase (not phase shift) of the partial-wave amplitude. Using a ρ-exchange input force with the experimental ρ mass and a ρ width of about 100 MeV, and the assumption that the average phase is (1/2)π, for total c.m. energies greater than about 8Mπ, we find that there is no appreciable reduction in the width of the calculated ρ-wave resonance. We also investigate the effects of low-energy inelastic channels that may contribute through the inelasticity parameter η for E ≤ Ei, where Ei is the energy above which the phase assumption is made. None of the forms for η that were used resulted in an output width less than about 280 MeV

Differential Cross Section for Charged A₁ Photoproduction Using the Regge Exchange Formalism

The Regge-pole formalism is applied to the calculation of the differential cross section for A1+ photo-production in the region |tmin| \u3c -t \u3c 10µ2. The p, A1, A1-daughter, A2, and π trajectory contributions are considered, and use is made of chiral dynamics to estimate the unknown coupling constants. We find that the π and the A2 trajectories provide the dominant contributions

Monte Carlo Study of a Simple Model Bulk-Ice-Ih System: P-T Melting Behavior at Constant Volume

An NVT Metropolis Monte Carlo computer simulation is used to examine the P-T behavior of a constant-density model periodic ice-Ih sample near melting. The ice unit cell with density 0.904 g/cm3 consists of 192 rigid water molecules interacting via the revised central-force potentials (RSL2) of Stillinger and Rahman [J. Chem. Phys. 68, 666 (1978)] with a cutoff. Intramolecular parameters are determined from a minimization of the total potential energy of the ice-Ih structure at 0 K. In the P-T plot, emergence of the liquid-solid coexistence region is signaled by a change in sign of dP/dT (when expansion occurs upon freezing) and gives an approximate value for the onset of constant-density melting. In this simulation, the expected pressure slope reversal occurs near 280 K. Internal energy, specific heat, and two-dimensional structure factors for the constant-density H2O system are also monitored at 14 temperatures from 100 to 370 K and support the P-T analysis

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 monomer vibrational modes and the estimated average diffusion barriers and binding energies. A sample diffusion path is discussed

Monte Carlo Simulations of Water-Ice Layers on a Model Silver Iodide Substrate: A Comparison with Bulk Ice Systems

Two water layers adsorbed on a model silver iodide basal face are simulated at nine temperatures from 150 to 425 K using Monte Carlo methods. The periodic unit cell of 96 internally rigid water molecules (interacting via the revised central-force potentials) couples to the rigid-substrate atoms via effective pair potentials with Lennard-Jones short-range and Coulomb long-range terms. The distribution of molecules perpendicular to the substrate exhibits layering, and individual layer structure factors, dipole moments, and pseudodiffusion coefficients are calculated. A complex temperature dependence with the two layers taking on different solidlike, quasiliquid, or liquid properties at the same T is observed. Both layers appear to be solid at the lowest T studied. But for T ≥ 265 K the upper layer becomes increasingly liquidlike with increasing T, whereas the lower layer of water molecules remains generally solidlike up to T=325 K. Comparisons are made with constant number, volume, and temperature bulk ice Monte Carlo simulations and (flexible molecule) molecular-dynamics simulations using the same water-water potentials. Pseudodiffusion coefficients are compared with experimental values for ice, water, and with a quasiliquidlike layer of water on ice

Molecular Model for Prenucleation Water Clusters

A molecular model applicable to prenucleation water clusters is described. As an illustration the model is applied to water clusters having clathrate-like structures composed of five-menibered rings. This work was motivated by the apparent inadequacies of the corrected liquid drop model which (in addition to applying bulk properties to small clusters) predicts nucleation rates which may be as much as 1017 larger than experiment. We present the energy of formation at a temperature of 277°K for our molecular model for clusters ranging in size from 5 to 57 molecules. These results agree qualitatively with experiment and, we believe, provide a motivation for further development of the molecular approach

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