Simulation of droplet heating and desolvation in inductively coupled plasma—part II: coalescence in the plasma

A numerical model is developed to consider for the first time droplet coalescence along with transport, heating and desolvation in an argon inductively coupled plasma (Ar ICP). The direct simulation Monte Carlo (DSMC) method and the Ashgriz–Poo model are used, respectively, to compute droplet–droplet interactions and to determine the outcome of droplet collisions. Molecular dynamics (MD) simulations support the use of the Ashgriz–Poo coalescence model for small droplet coalescence. Simulations predict spatial maps of droplet number and mass densities within an Ar ICP for a conventional nebulizer-spray chamber arrangement, a direct injection high efficiency nebulizer (DIHEN), and a large bore DIHEN (LB-DIHEN). The primary findings are: (1) even at 1500 W, the collisions of the droplets in the plasma lead primarily to coalescence, particularly for direct aerosol injection; (2) the importance of coalescence in a spray simulation exhibits a complex relationship with the gas temperature and droplet size; (3) DIHEN droplets penetrate further into the Ar ICP when coalescence is considered; and (4) droplets from a spray chamber or the LB-DIHEN coalesce less frequently than those from a DIHEN. The implications of these predictions in spectrochemical analysis in ICP spectrometry are discussed.     

Unisized two-dimensional platinum clusters on silicon(111)-7x7 surface observed with scanning tunneling microscope

Uni-sized platinum clusters (size range of 5-40) on a silicon(111)-7 x 7 surface were prepared by depositing size-selected platinum cluster ions on the silicon surface at the collision energy of 1.5 eV per atom at room temperature. The surface thus prepared was observed by means of a scanning tunneling microscope (STM) at the temperature of 77 K under an ambient pressure less than 5 x 10(-9) Pa. The STM images observed at different cluster sizes revealed that (1) the clusters are flattened and stuck to the surface with a chemical-bond akin to platinum silicide, (2) every platinum atom occupies preferentially the most reactive sites distributed within a diameter of approximately 2 nm on the silicon surface at a cluster size up to 20, and above this size, the diameter of the cluster increases with the size, and (3) the sticking probability of an incoming cluster ion on the surface increases with the cluster size and reaches nearly unity at a size larger than 20.     

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.     

Growth of Co clusters on thin films Al2O3NiAl(100)

We present a scanning tunnel microscopy study of Co clusters grown through vapor deposition on Al(2)O(3) thin films over NiAl(100) at different coverages and temperatures. Formation of Co clusters was observed at 90, 300, 450, and 570 K. At the three lower temperatures, we find narrow cluster size distributions and the mean sizes (with a diameter of 2.6 nm and a height of 0.7 nm) do not change significantly with the coverage and temperature, until the clusters start to coalesce. Even on 3-4-nm-wide crystalline Al(2)O(3) strips where the deposited Co atoms are confined, the same features sustain. Only at 570 K the normal growth mode where the cluster size increases with the deposition coverage is observed, although the data are less conclusive. A simple modeling of kinetic surface processes on a strip confirms the normal growth mode, but fails to show a favored size unless additional energetic constraints are applied on the cluster sizes. Increasing Co coverages to cluster coalescence, a larger preferable size (mean diameter of 3.5 nm and height of 1.4 nm) appears for growth at 450 K. These two sizes are corroborated by morphology evolution of high Co coverages deposited at 300 K and annealed to 750 K, in which the coalescence is eliminated and the two preferable geometries appear and coexist.     

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.     

Application of scaling and kinetic equations to helium cluster size distributions: Homogeneous nucleation of a nearly ideal gas

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected.     

Effects of Ag Atomic Segregation from Different Planes on the Size-Dependent Melting of Ag–Pd Clusters

This paper studies the effects of Ag atomic segregation from the inner (100) or (111) planes on the melting of Ag–Pd clusters with different sizes by a molecular dynamics simulation. The results show that Ag segregation leads to the atomic energy decreases with increasing the temperature. Furthermore, the effect of the (100) segregation is larger than that of the (111) segregation. Meanwhile, the influence of segregation on the energy decreases with increasing the cluster size. The melting points of the clusters without segregation are the largest, followed by the clusters with a (111) and (100) segregation.     

Molecular simulation study of cavity-generated instabilities in the superheated Lennard-Jones liquid

Previous equilibrium-based density-functional theory (DFT) analyses of cavity formation in the pure component superheated Lennard-Jones (LJ) liquid [S. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10224 (2003); M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007)] revealed that a thermodynamic limit of stability appears in which no liquidlike density profile can develop for cavity radii greater than some critical size (being a function of temperature and bulk density). The existence of these stability limits was also verified using isothermal-isobaric Monte Carlo (MC) simulations. To test the possible relevance of these limits of stability to a dynamically evolving system, one that may be important for homogeneous bubble nucleation, we perform isothermal-isobaric molecular dynamics (MD) simulations in which cavities of different sizes are placed within the superheated LJ liquid. When the impermeable boundary utilized to generate a cavity is removed, the MD simulations show that the cavity collapses and the overall density of the system remains liquidlike, i.e., the system is stable, when the initial cavity radius is below some certain value. On the other hand, when the initial radius is large enough, the cavity expands and the overall density of the system rapidly decreases toward vaporlike densities, i.e., the system is unstable. Unlike the DFT predictions, however, the transition between stability and instability is not infinitely sharp. The fraction of initial configurations that generate an instability (or a phase separation) increases from zero to unity as the initial cavity radius increases over a relatively narrow range of values, which spans the predicted stability limit obtained from equilibrium MC simulations. The simulation results presented here provide initial evidence that the equilibrium-based stability limits predicted in the previous DFT and MC simulation studies may play some role, yet to be fully determined, in the homogeneous nucleation and growth of embryos within metastable fluids.     

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.     

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

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Numerical Study of a Lifshitz-Slyozov-like Metastable Dewetting Model

A Lifshitz-Slyozov-type of model of the coalescence of dry zones in the process of metastable dewetting proposed in V. S. Mitlin (J. Colloid Interface Sci. 227, 371, 2000) is applied to simulating the evolution of the probability distribution of holes by sizes. For the model considered, the average size of a hole increases linearly with time, the surface fraction of holes grows as the time squared, and the maximum value of the probability distribution decreases as the inverse square root of time. Copyright 2001 Academic Press.     

不同温度下炉内喷射氨水脱除NOx的模拟与试验研究

在一台小型沉降炉上进行了氨水喷射还原烟气中NOx的SNCR（Selective Non-Catalytic Reduction）实验研究，同时结合化学反应动力学模型研究了NH3还原NO过程中的关键影响因素，结果发现，过高的温度引起氨水的氧化，过低的温度不利于NO的还原，存在一个单一的温度区间，在该试验台上最佳的氨水喷射温度范围为850 ℃～1 100 ℃，最高达到了82％的NO还原率；采用均相反应模型与试验结果进行了对比，在高温区吻合情况较好；当温度高于950 ℃时，NH3残留量可以忽略；NH2的两类支链反应对于整个反应起重要作用。     

Extended study of molecular dynamics simulation of homogeneous vapor-liquid nucleation of water

Using the simple point charge/extended water model, we performed molecular dynamics simulations of homogeneous vapor-liquid nucleation at various values of temperature T and supersaturation S, from which the nucleation rate J, critical nucleus size n(*), and the cluster formation free energy DeltaG were derived. As well as providing lots of simulation data, the results were compared with theories on homogeneous nucleation, including the classical, semi-phenomenological, and scaled models, but none of these gave a satisfactory explanation for our results. It was found that two main factors made the theories fail: (1) The average cluster structure including the nonspherical shape and the core structure that is not like the bulk liquid and (2) the forward rate which is larger than assumed by the theories by about one order of magnitude. The quantitative evaluation of these factors is left for future investigations.     

Ring-polymer Molecular Dynamics Simulation for the Adsorption of H2 on Ice Clusters (H2O)n (n=8, 10, and 12)

In the interstellar medium, the H₂ adsorption and desorption on the solid water ice are crucial for chemical and physical processes. We have recently investigated the probabilities of H₂ sticking on the (H₂O)₈ ice, which has quadrilateral surfaces. We have extended the previous work using classical MD and ring-polymer molecular dynamics (RPMD) simulations to the larger ice clusters, (H₂O)₁₀ and (H₂O)₁₂, which have pentagonal and hexagonal surfaces, respectively. The H₂ sticking probabilities decreased as the temperature increased for both cluster cases, whereas the cluster-size-independent profiles were observed. It is thought that the size independence of the probabilities is qualitatively understood from the similar binding energies for all the three cluster systems. Furthermore, the RPMD sticking probabilities are smaller than the classical ones because of the reduction in the binding energies owing to nuclear quantum effects, such as vibrational quantization.     

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.     

A Study About Nanocluster Deposition of Thin-film Formation by Molecular Dynamics Simulation

The thin-film growth has been confirmed to be assembled by an enormous number of clusters in ICBD method. In sequence of clusters’ depositions proceeds to form the thin-film to understand quantitatively the interaction mechanisms between the cluster atoms and the substrate atoms, we use molecular dynamics simulation with EAM potential. The quantitative of flatness of deposition and percent of disordered atoms were proposed to evaluate the property of thin-film. In this simulation, three different Co cluster sizes of 55, 70, and 100 atoms with different velocities (100 up to 800 m/s) were deposited on a Al(0 0 1) substrate whose temperatures were set between 300 and 500 K. The simulations begin at specific equilibrium temperature of clusters and the substrate. The simulations are performed at different temperatures of the clusters and substrate and for different sizes of clusters. We showed that the percent of disordered atoms of substrate are affected by the cluster size and velocity of the clusters. Temperature dependence of the number of disordered atoms for different cluster’s velocity was observed. We investigated the effect of cluster size and initial velocity of cluster on the value of flatness.     

Brownian dynamics simulation study of self-assembly of amphiphiles with large hydrophilic heads

We have studied the effect of shape of an amphiphilic molecule on micellization properties by carrying out stochastic molecular dynamics simulation on a bead-spring model of amphiphiles for several sizes of hydrophilic head group with a fixed hydrophobic tail length. Our studies show that the effect of geometry of an amphiphile on shape and cluster distribution of micelles is significant. We find the critical micelle concentration increases with the increasing size of the hydrophilic head. We demonstrate that the onset of micellization is accompanied by (i) a peak in the specific heat as found earlier in the simulation studies of lattice models, and (ii) a peak in the characteristic relaxation time of the cluster autocorrelation function. Amphiphiles with larger hydrophilic head form smaller micelles with sharper cluster distribution. Our studies are relevant to the controlled synthesis of nanostructures of desired shapes and sizes using self-assembling properties of amphiphiles.     

Car-Parrinello molecular dynamics simulation of Fe 3+ (aq)

The optimized geometry and energetic properties of Fe(D2O)n 3+ clusters, with n = 4 and 6, have been studied with density-functional theory calculations and the BLYP functional, and the hydration of a single Fe 3+ ion in a periodic box with 32 water molecules at room temperature has been studied with Car-Parrinello molecular dynamics and the same functional. We have compared the results from the CPMD simulation with classical MD simulations, using a flexible SPC-based water model and the same number of water molecules, to evaluate the relative strengths and weaknesses of the two MD methods. The classical MD simulations and the CPMD simulations both give Fe-water distances in good agreement with experiment, but for the intramolecular vibrations, the classical MD yields considerably better absolute frequencies and ion-induced frequency shifts. On the other hand, the CPMD method performs considerably better than the classical MD in describing the intramolecular geometry of the water molecule in the first hydration shell and the average first shell...second shell hydrogen-bond distance. Differences between the two methods are also found with respect to the second-shell water orientations. The effect of the small box size (32 vs 512 water molecules) was evaluated by comparing results from classical simulations using different box sizes; non-negligible effects are found for the ion-water distance and the tilt angles of the water molecules in the second hydration shell and for the O-D stretching vibrational frequencies of the water molecules in the first hydration shell.     

Molecular dynamics and kinetic study of carbon coagulation in the release wave of detonation products

We present a combined molecular dynamics and kinetic study of a carbon cluster aggregation process in thermodynamic conditions relevant for the detonation products of oxygen deficient explosives. Molecular dynamics simulations with the LCBOPII potential under gigapascal pressure and high temperatures indicate that (i) the cluster motion in the detonation gas is compatible with Brownian diffusion and (ii) the coalescence probability is 100% for two clusters entering the interaction cutoff distance. We used these results for a subsequent kinetic study with the Smoluchowski model, with realistic models applied for the physical parameters such as viscosity and cluster size. We found that purely aggregational kinetics yield too fast clustering, with moderate influence of the model parameters. In agreement with previous studies, the introduction of surface reactivity through a simple kinetic model is necessary to approach the clustering time scales suggested by experiments (1000 atoms after 100 ns, 10 000 atoms after 1 μs). However, these models fail to reach all experimental criteria simultaneously and more complex modelling of the surface process seems desirable to go beyond these current limitations.     

Argon cluster-ion sputter yield: Molecular dynamics simulations on silicon and equation for estimating total sputter yield

Argon Gas Cluster-Ion Beam sources have become widely-used on X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry (SIMS) instruments in recent years, but there is little reference data on sputter yields in the literature as yet. Total sputter yield reference data is needed in order to calibrate the depth scale, of XPS or SIMS depth profiles. We previously published a semi-empirical ‘Threshold’ equation for estimating cluster total sputter yield from the energy-per-atom of the cluster and the effective monatomic sputter threshold of the material. This has been shown to agree extremely well with sputter yield measurements on a range or organic and inorganic materials for clusters of around a thousand atoms. Here we use the molecular dynamics (MD) approach to explore a wider range of energy and cluster size than is easy to do experimentally to high precision. We performed MD simulations using the ‘Large-scale Atomic/Molecular Massively Parallel Simulator’ (LAMMPS) parallel MD code on high-performance computer (HPC) systems. We performed 1150 simulations of individual collisions with a silicon (100) surface as an archetypal inorganic substrate, for cluster sizes between 30 and 3000 argon atoms and energies in the range 5 to 40 eV per atom. This corresponds to the most important regime for experimental cluster depth-profiling in SIMS and XPS. Our MD results show a dependence on cluster size as well as energy-per-atom. Using the exponent previously suggested by Paruch et al., we modified the Threshold model equation published previously to take this into account. The modified Threshold equation fits all our MD results extremely well, building on its success in fitting experimental sputter yield measurements. This work is submitted to the volume dedicated to Dr. Martin P Seah, MBE, who was a great influence on the early career of one of the authors (PJC) and who himself made many valuable contributions to the literature on sputtering as it relates to surface and interface analysis.