Tests of the homogeneous nucleation theory with molecular-dynamics simulations. I. Lennard-Jones molecules

Two kinds of the homogeneous nucleation theory exist at the present: the classical nucleation theory and the semiphenomenological model. To test them, we performed molecular-dynamics (MD) simulations of nucleation from vapor to liquid with 5000-20,000 Lennard-Jones-type molecules. Simulations were done for various values of supersaturation ratios (from 2 to 10) and temperatures (from 80 to 120 K). We compared the size distribution of clusters in MD simulations with those in the theoretical models because the number density of critical clusters governs the nucleation rate. We found that the semiphenomenological model achieves excellent agreements in size distributions of the clusters with all MD simulations we done. The classical theory underestimates the number density of the clusters in the temperature range of 80-100 K, but overestimates in 100-120 K. The semiphenomenological model also predicts well the nucleation rate in MD simulations, while the classical nucleation theory does not. Our results confirmed the validity of the semiphenomenological model for Lennard-Jones-type molecules.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

Microscopic simulations of molecular cluster decay: Does the carrier gas affect evaporation?

We develop a kinetic theory of cluster decay by considering the stochastic motion of molecules within an effective potential of mean force (PMF) due to the cluster. We perform molecular dynamics simulations on a 50-atom argon cluster to determine the mean radial force on a component atom and hence the confining potential of mean force. Comparisons between isolated clusters and clusters thermostatted through the presence of a 100-atom helium carrier gas show that the heat bath has only a slight effect upon the PMF. This confirms the validity of calculations of cluster properties using isolated cluster simulations. The PMF is used to calculate the atomic evaporation rate from these clusters, and results are compared with the predictions of the capillarity approximation together with detailed balance, both components of the classical theory of aerosol nucleation.     

Comparative study on methodology in molecular dynamics simulation of nucleation

Gas-liquid nucleation of 1000 Lennard-Jones atoms is simulated to evaluate temperature regulation methods and methods to obtain nucleation rate. The Berendsen and the Andersen thermostats are compared. The Berendsen thermostat is unable to control the temperature of clusters larger than the critical size. Independent of the thermostating method the velocities of individual atoms and the translational velocities of clusters up to at least six atoms are accurately described by the Maxwell velocity distribution. Simulations with the Andersen thermostat yield about two times higher nucleation rates than those with the Berendsen thermostat. Nucleation rate is extracted from the simulations by direct observation of times of nucleation onset and by the method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)]. Compared to the direct observation, the nucleation rates obtained from the method of Yasuoka and Matsumoto are higher by a factor of 3.     

氟化钾团簇的相变、成核和重结晶的分子动力学模拟

我们利用Born-Mayer-Huggins相互作用势函数对(KF)_N(N=108，256，500和864)团簇进行了分子动力学(MD)模拟。为了避免周期性边界条件对相变、成核和重结晶的干扰作用，对体系采用了自由边界。基于MD模拟结果，对团簇的熔化温度、熔化焓、扩散系数、成核速率、固液界面自由能、临界核大小等进行了计算和讨论。在对(KF)₈₆₄双晶团簇的热退火模拟中，观察到了固态的重结晶和晶粒的生长。经典的成核理论成功地解释了(KF)₈₆₄双晶团簇的重结晶MD模拟结果。     

A stochastic simulation of nonisothermal nucleation

The results of stochastic simulations of growth and evaporation of small clusters in vapor are reported. Energy dependent growth rates are determined from the monomer-cluster collision rate and decay rates are found from a detailed balance, with the equilibrium size and energy distribution of clusters calculated using the capillarity approximation and the equilibrium vapor pressure. These rates are used in simulations of two-dimensional random walks in size and energy space to determine the fraction of clusters in supersaturated vapor of size (i(min)+1) that reach a size i(max). By assuming that clusters of size i(min) are in equilibrium, this fraction can be related to the nonisothermal nucleation rate. The simulated rates show good agreement with the previously published analytical results. In the absence of an inert carrier gas, the nonisothermal nucleation rates are typically between 1% and 5% of the isothermal rates.     

Molecular dynamics simulations of nucleation from vapor to solid composed of Lennard-Jones molecules

We performed molecular dynamics (MD) simulations of nucleation from vapor at temperatures below the triple point for systems consisting of 10(4)-10(5) Lennard-Jones (L-J) type molecules in order to test nucleation theories at relatively low temperatures. Simulations are performed for a wide range of initial supersaturation ratio (S(0) ? 10-10(8)) and temperature (kT = 0.2-0.6ε), where ε and k are the depth of the L-J potential and the Boltzmann constant, respectively. Clusters are nucleated as supercooled liquid droplets because of their small size. Crystallization of the supercooled liquid nuclei is observed after their growth slows. The classical nucleation theory (CNT) significantly underestimates the nucleation rates (or the number density of critical clusters) in the low-T region. The semi-phenomenological (SP) model, which corrects the CNT prediction of the formation energy of clusters using the second virial coefficient of a vapor, reproduces the nucleation rate and the cluster size distributions with good accuracy in the low-T region, as well as in the higher-T cases considered in our previous study. The sticking probability of vapor molecules onto the clusters is also obtained in the present MD simulations. Using the obtained values of sticking probability in the SP model, we can further refine the accuracy of the SP model.     

Evaporation rate of nucleating clusters

The Becker-D?ring kinetic scheme is the most frequently used approach to vapor liquid nucleation. In the present study it has been extended so that master equations for all cluster configurations are included into consideration. In the Becker-D?ring kinetic scheme the nucleation rate is calculated through comparison of the balanced steady state and unbalanced steady state solutions of the set of kinetic equations. It is usually assumed that the balanced steady state produces equilibrium cluster distribution, and the evaporation rates are identical in the balanced and unbalanced steady state cases. In the present study we have shown that the evaporation rates are not identical in the equilibrium and unbalanced steady state cases. The evaporation rate depends on the number of clusters at the limit of the cluster definition. We have shown that the ratio of the number of n-clusters at the limit of the cluster definition to the total number of n-clusters is different in equilibrium and unbalanced steady state cases. This causes difference in evaporation rates for these cases and results in a correction factor to the nucleation rate. According to rough estimation it is 10(-1) by the order of magnitude and can be lower if carrier gas effectively equilibrates the clusters. The developed approach allows one to refine the correction factor with Monte Carlo and molecular dynamic simulations.     

Molecular dynamics analysis of multiple site growth and coalescence effects on homogeneous and heterogeneous nucleations

Homogeneous and heterogeneous nucleations were simulated by molecular dynamics (MD). The behavior of Lennard-Jones molecules was studied inside a liquid-gas system where all dimensions of the wall were periodic and a soft core carrier gas within the system controlled the temperature. In this study, the classical nucleation theory was found to underestimate the homogeneous nucleation rate by five orders of magnitude, which complies with other MD studies. The discrepancy in the nucleation rate between theory and simulation was mainly caused by the fundamental assumption that there are no volumetric interactions in the growth process. In this particular case, however, growth was observed at multiple sites due to Ostwald ripening and coalescence between nuclei by Brownian motion. Furthermore, even though the supersaturation ratio is inadequate for homogeneous nucleation, once a seed is introduced to the system, a cluster can be created. The addition of seeds not only enhances nucleation but also renders coalescence as an important nucleation mechanism in the earlier stages compared to homogeneous nucleation.     

Study of Injection Angle and Carrier Gas Flow Rate Effects on Particles In-Flight Characteristics in Plasma Spray Process: Modeling and Experiments

This paper investigates the influence of particle injection angle on particle in-flight behaviors and characteristics at different primary and carrier gas flow rates through an integrated modeling and experimental approach. Particle in-flight status such as temperature, velocity, size and their distribution are analyzed to examine particle’s melting status before impact. Results from the experiments and numerical simulations both show that, when carrier gas flow rate is fixed, a small injection angle favors the particle melting and flattening. This behavior is independent of primary and secondary gas flow rates, spray distance and carrier gas flow rate. When both carrier gas flow and injection angle vary, a high carrier gas flow rate and a small injection angle are recommended for high particle temperature and velocity.     

Homogeneous nucleation and growth in supersaturated zinc vapor investigated by molecular dynamics simulation

Homogeneous nucleation and growth of zinc from supersaturated vapor are investigated by nonequilibrium molecular dynamics simulations in the temperature range from 400 to 800 K and for a supersaturation ranging from log S=2 to 11. Argon is added to the vapor phase as carrier gas to remove the latent heat from the forming zinc clusters. A new parametrization of the embedded atom method for zinc is employed for the interaction potential model. The simulation data are analyzed with respect to the nucleation rates and the critical cluster sizes by two different methods, namely, the threshold method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)] and the mean first passage time method for nucleation by Wedekind et al. [J. Chem. Phys. 126, 134103 (2007)]. The nucleation rates obtained by these methods differ approximately by one order of magnitude. Classical nucleation theory fails to describe the simulation data as well as the experimental data. The size of the critical cluster obtained by the mean first passage time method is significantly larger than that obtained from the nucleation theorem.     

Molecular dynamics of homogeneous nucleation in the vapor phase of Lennard-Jones. III. Effect of carrier gas pressure

A molecular dynamics simulation of vapor phase nucleation has been performed with 40,000 Lennard-Jones particles for the target gas and 0-160,000 particles for the carrier gas. Three carrier gas models are adopted, including a soft-core model, a Lennard-Jones model, and a modified Lennard-Jones model in which the attractive interaction can be adjusted. The effect of the carrier-gas pressure is assessed through computing and comparing the rate of nucleation and cluster size distribution. It is found that the effect of the carrier-gas pressure can be strongly dependent on the carrier-gas model. A positive effect (enhancement of the nucleation rate) is found with the soft-core potential model, whereas negligible effect is found with the Lennard-Jones potential model. For the modified Lennard-Jones potential with a weak attractive interaction, the carrier-gas effect is positive. However, the effect is negligible with a stronger attractive interaction between the target and carrier-gas particles. A reason for the negligible effect is that the carrier-gas particles are adsorbed on the cluster surface when the density of target and carrier-gas particles are comparable. When the density of carrier-gas particles are four times that of the target particles, the carrier-gas particles tend to mix with the target particles in the clusters.     

Implementation of dynamical nucleation theory effective fragment potentials method for modeling aerosol chemistry

In this work, the dynamical nucleation theory (DNT) model using the ab initio based effective fragment potential (EFP) is implemented for evaluating the evaporation rate constant and molecular properties of molecular clusters. Predicting the nucleation rates of aerosol particles in different chemical environments is a key step toward understanding the dynamics of complex aerosol chemistry. Therefore, molecular scale models of nanoclusters are required to understand the macroscopic nucleation process. On the basis of variational transition state theory, DNT provides an efficient approach to predict nucleation kinetics. While most DNT Monte Carlo simulations use analytic potentials to model critical sized clusters, or use ab initio potentials to model very small clusters, the DNTEFP Monte Carlo method presented here can treat up to critical sized clusters using the effective fragment potential (EFP), a rigorous nonempirical intermolecular model potential based on ab initio electronic structure theory calculations, improvable in a systematic manner. The DNTEFP method is applied to study the evaporation rates, energetics, and structure factors of multicomponent clusters containing water and isoprene. The most probable topology of the transition state characterizing the evaporation of one water molecule from a water hexamer at 243 K is predicted to be a conformer that contains six hydrogen bonds, with a topology that corresponds to two water molecules stacked on top of a quadrangular (H(2)O)(4) cluster. For the water hexamer in the presence of isoprene, an increase in the cluster size and a 3-fold increase in the evaporation rate are predicted relative to the reaction in which one water molecule evaporates from a water hexamer cluster.     

Molecular dynamics studies to understand the mechanism of heat accommodation in homogeneous condensing flow of carbon dioxide

Using molecular dynamics (MD), we have studied the mechanism of heat accommodation between carbon dioxide clusters and monomers for temperatures and cluster size conditions that exist in homogeneous condensing supersonic expansion plumes. The work was motivated by our meso-scale direct simulation Monte Carlo and Bhatnagar-Gross-Krook based condensation simulations where we found that the heat accommodation model plays a key role in the near-field of the nozzle expansion particularly as the degree of condensation increases [R. Kumar, Z. Li, and D. Levin, Phys. Fluids 23, 052001 (2011)]. The heat released by nucleation and condensation and the heat removed by cluster evaporation can be transferred or removed from either the kinetic or translational modes of the carbon dioxide monomers. The molecular dynamics results show that the time required for gas-cluster interactions to establish an equilibrium from an initial state of non-equilibrium is less than the time step used in meso-scale analyses [R. Kumar, Z. Li, and D. Levin, Phys. Fluids 23, 052001 (2011)]. Therefore, the good agreement obtained between the measured cluster and gas number density and gas temperature profiles with the meso-scale modeling using the second energy exchange mechanism is not fortuitous but is physically based. Our MD simulations also showed that a dynamic equilibrium is established by the gas-cluster interactions in which condensation and evaporation processes take place constantly to and from a cluster.     

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.     

Computational study on the properties and structure of methyl lactate

A theoretical study on the properties and molecular level structure of the very important green solvent methyl lactate is carried out in the gas phase and methanol and water solutions, with the solvent treated both explicitly and as a continuum. Torsional barriers giving rise to different conformers by rotation of the hydroxyl and methyl groups were analyzed using density functional theory (DFT) to establish the most stable conformer both in gas phase and solution. DFT computations on lactate dimers were also done to study short-range features, and the effect of the surrounding solvent on intra- and intermolecular hydrogen bonding was analyzed according to the polarizable continuum model approach. We have also studied lactate/water and lactate/methanol small clusters together with the corresponding binding energies. Moreover, classical molecular dynamics simulations (MD) were carried out to study medium- and large-range effects at lower computational cost. MD simulations at different pressure and temperature conditions on pure lactate were carried out, and mixtures with water and methanol of different compositions were also studied. Structural information, analyzed through the radial distribution functions, together with dynamic aspects of pure and mixed fluids were considered. The intramolecular hydrogen bonding ability of methyl lactate together with the possibility of homo- and hetero-intermolecular association determines the behavior of this molecule in pure fluids or in mixed.     

A molecular dynamics study of water nucleation using the TIP4P/2005 model

Extensive molecular dynamics simulations were conducted using the TIP4P/2005 water model of Abascal and Vega [J. Chem. Phys. 123, 234505 (2005)] to investigate its condensation from supersaturated vapor to liquid at 330 K. The mean first passage time method [J. Wedekind, R. Strey, and D. Reguera, J. Chem. Phys. 126, 134103 (2007); L. S. Bartell and D. T. Wu, 125, 194503 (2006)] was used to analyze the influence of finite size effects, thermostats, and charged species on the nucleation dynamics. We find that the Nose?-Hoover thermostat and the one proposed by Bussi et al. [J. Chem. Phys. 126, 014101 (2007)] give essentially the same averages. We identify the maximum thermostat coupling time to guarantee proper thermostating for these simulations. The presence of charged species has a dramatic impact on the dynamics, inducing a marked change towards a pure growth regime, which highlights the importance of ions in the formation of liquid droplets in the atmosphere. It was found a small but noticeable sign preference at intermediate cluster sizes (between 5 and 30 water molecules) corresponding mostly to the formation of the second solvation shell around the ion. The TIP4P/2005 water model predicts that anions induce faster formation of water clusters than cations of the same magnitude of charge.     

Molecular dynamics study of phase transition and nucleation in supercooled clusters of potassium iodide

In a series of molecular dynamics (MD) runs on (KI)₁₀₈ clusters, the Born–Mayer–Huggins potential function is employed to study structural, energetic, and kinetic aspects of phase change and the homogeneous nucleation of KI clusters. Melting and freezing are reproducible when clusters are heated and cooled. The melted clusters are not spherical in shape no matter the starting cluster is cubic or spherical. Quenching a melted (KI)₁₀₈ cluster from 960 K in a bath with temperature range 200–400 K for a time period of 80 ps both nucleation and crystallization are observed. Nucleation rates exceeding 10³⁶ critical nuclei m⁻³ s⁻¹ are determined at 200, 250, 300, 350, and 400 K. Results are interpreted in terms of the classical theory of nucleation of Turnbull and Fisher and of Buckle. Interfacial free energies of the liquid–solid phase derived from the nucleation rates are 7–10 mJ m⁻². This quantity is 0.19 of the heat of transition per unit area from solid to liquid, or about two-thirds of the corresponding ratio which Turnbull proposed for freezing transition. The temperature dependence of σ_sl(T) of (KI)₁₀₈ clusters can be expressed as σ_sl(T)∝T^0.34.     

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.     

Molecular Dynamics Studies of the Kinetics of Phase Changes in Clusters II: Crystal Nucleation from Molten (RbCl)256 and (RbCl)500 Clusters

Molecular dynamics computer simulations have been carried out to study the effects of cluster size and temperature on the nucleation rate of rubidium chloride clusters in the temperature range of 500-650 K. Clusters with 256 and 500 RbCl molecules have been studied and the results are compared with those obtained from 108 molecule clusters. The melting point (MP) of the clusters was observed to increase with the size of the clusters and can be described by a linear equation MP=997-405 N^−1/3, where N is the number of molecules in the cluster. The nucleation rate is found to decrease with increasing cluster size or increasing nucleation temperature. Both classical nucleation theory and diffuse interface theory are used to interpret our observed results.