Monte Carlo simulations of critical cluster sizes and nucleation rates of water

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.

A comparison of rigid and flexible water models in collisions of monomers and small clusters

In this study we have investigated the dynamics of small water clusters using microcanonical molecular dynamics simulations. The clusters are formed by colliding vapor monomers with target clusters of two and five molecules. The monomers are sampled from a thermal ensemble at T=300 K and target clusters with several total energies are considered. We compare rigid extended simple point charge water with flexible counterparts having intramolecular harmonic bonds with force constants 10(3) and 10(5) kcal(mol A2). We show that the lifetimes of the clusters formed via collision process are similar for the rigid model and the flexible model with the bigger force constant, if the translational temperatures of the target cluster molecules are equal. The model with the smaller force constant results in much longer lifetimes due to the stabilizing effect caused by the kinetic energy transfer into internal vibration of the molecules. This process may take several hundreds of picoseconds, giving rise to time-dependent decay rates of constant-energy clusters. A study of binary collisions of water molecules shows that the introduction of flexibility to the molecules increases the possibility of dimer formation and thus offers an alternative route for dimer production in vapors. Our results imply that allowing for internal degrees of freedom is likely to enhance gas-liquid nucleation rates in water simulations.

Analysis of nucleation ability of cluster configurations with Monte Carlo simulations of argon

We determine the nucleation ability of argon clusters from Monte Carlo simulations. The nucleation rate appears to be defined by a sole characteristic of the clusters, namely, the stability. The stability is calculated as the ratio of grand canonical growth and decay rates and can be assigned to individual cluster configurations. We study the connection between the stability of the cluster configurations and their volume and total potential energy. Neither the potential energy nor the volume of a cluster configuration has a clear relation to its stability, and thus to the nucleation ability. On the other hand, we show that it is possible to use a specific volume for each cluster size to calculate the work of the cluster formation. These clusters with a unique volume have the same average stability as the full set of clusters. Our simulation method allows us to study the effect of possible deviations from equilibrium in the cluster configuration distributions. We argue that the nucleation process itself can produce a source for such a deviation. We show that even a small deviation from equilibrium in the cluster configuration distribution can lead to a dramatic deceleration of the nucleation rate. Although our simulations may overestimate the magnitude of the effect, they give qualitative estimates for its importance.

Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems

Computer simulations are employed to obtain subcritical isotherms of small finite sized systems inside the coexistence region. For all temperatures considered, ranging from the triple point up to the critical point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from approximately 8 to approximately 21 molecular diameters. For the smallest system sizes, and more so close to the critical point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chemical potential-density plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the observed discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liquid side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qualitatively rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The analysis shows that the shape of the subcritical isotherms is dictated by a single characteristic volume (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system volumes, the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms observed in the simulations. When the liquid and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, especially for large systems (i.e., larger than about 15 molecular diameters) at low temperature (lower than about 0.85 times the critical temperature). This implies that the Laplace pressure differences can be predicted for drops as small as five molecular diameters, and as few as about 500 molecules. The theoretical study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse volume.

Molecular Dynamics Simulations of Atmospheric Oxidants at the Air−Water Interface: Solvation and Accommodation of OH and O3

A comparative study of OH, O3, and H2O equilibrium aqueous solvation and gas-phase accommodation on liquid water at 300 K is performed using a combination of ab initio calculations and molecular dynamics simulations. Polarizable force fields are developed for the interaction potential of OH and O3 with water. The free energy profiles for transfer of OH and O3 from the gas phase to the bulk liquid exhibit a pronounced minimum at the surface, but no barrier to solvation in the bulk liquid. The calculated surface excess of each oxidant is comparable to calculated and experimental values for short chain, aliphatic alcohols. Driving forces for the surface activity are discussed in terms of the radial distribution functions and dipole orientation distributions for each molecule in the bulk liquid and at the surface. Simulations of OH, O3, and H2O impinging on liquid water with a thermal impact velocity are used to calculate thermal accommodation (S) and mass accommodation (alpha) coefficients. The values of S for OH, O3, and H2O are 0.95, 0.90, and 0.99, respectively. The approaching molecules are accelerated toward the liquid surface when they are approximately 5 angstroms above it. The molecules that reach thermal equilibrium with the surface do so within 2 ps of striking the surface, while those that do not scatter into the gas phase with excess translational kinetic energy in the direction perpendicular to the surface. The time constants for absorption and desorption range from approximately 35 to 140 ps, and the values of alpha for OH, O3, and H2O are 0.83, 0.047, and 0.99, respectively. The results are consistent with previous formulations of gas-phase accommodation from simulations, in which the process occurs by rapid thermal and structural equilibration followed by diffusion on the free energy profile. The implications of these results with respect to atmospheric chemistry are discussed.

Simulations of vapor water clusters at vapor–liquid equilibrium

The Gibbs-ensemble Monte Carlo methods based on the extended single point charge [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987)] potential-energy surface have been used to study the clustering of vapor phase water under vapor-liquid equilibrium conditions between 300 and 600 K. It is seen that the number of clusters, as well as the cluster size, increase with temperature. This is primarily due to the increase in vapor density that accompanies the temperature increase at equilibrium. In addition, due to entropic effects, the percentage of clusters that have linear (or open) topologies increases with temperature and dominates over the minimum-energy cyclic topologies at the temperatures studied here. These results are insensitive to the number of molecules used in the simulations and the criterion used to define a water cluster.

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.

The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.

Simulating Vapor−Liquid Nucleation of Water: A Combined Histogram-Reweighting and Aggregation-Volume-Bias Monte Carlo Investigation for Fixed-Charge and Polarizable Models

The method of histogram-reweighting was integrated with a recently developed approach using aggregation-volume-bias Monte Carlo and self-adaptive umbrella sampling to develop the AVUS-HR algorithm that allows for exceedingly efficient calculations of nucleation properties over a wide range of thermodynamic conditions. Simulations were carried out for water using both fixed-charge and polarizable force fields belonging to the TIP4P family (namely, TIP4P, TIP4P-FQ, TIP4P-pol2, and TIP4P-pol3) to investigate the nucleation of water over a temperature range from 200 to 300 K and the concentration of water clusters in the atmosphere at elevations up to 15 km. It was found that the nucleation free energy barriers and atmospheric concentrations are extremely sensitive to the force field, albeit all of the models investigated in this study support the following general conclusions: (i) ice nucleation is not present under the thermodynamic conditions and cluster-size range investigated here, i.e., the critical nuclei possess liquidlike structures, and (ii) the atmospheric concentrations of water clusters under homogeneous conditions are very low with the mole fraction of hexamers being about 10(-10), a number probably too low to influence the solar radiation balance. Compared to the experimental data, the TIP4P-pol3 model yields the most accurate nucleation results, consistent with its excellent performance for the second virial coefficient and the minimum cluster energies.