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.     

Water absorption in polyethylene under external electric fields

Monte Carlo simulations of the solubility and structure of water in polyethylene in thermodynamic equilibrium with liquid water were performed in external fields ranging from 2 x 10(5) to 4 x 10(9) V/m. For a given equilibrium temperature and pressure, the water solubility decreases at higher fields. This occurs since it is energetically favorable for water molecules to be in the pure water phase than in the polyethylene matrix at high field strengths, and results in an increased density in the water phase. However, fields relevant to high voltage conduction (in the absence of defects that can lead to large local field strengths) do not change the solubility. In addition, at large fields the number of water clusters decreases for all cluster sizes. The rate of decrease is highest for large clusters, and a larger fraction of water molecules exist as monomers in the polyethylene matrix at high fields. Large fields also cause alignment of the water molecules, which leads to more clusters with linear topologies and hence an increase in the cluster radius of gyration.     

Interatomic Lennard-Jones potentials of linear and branched alkanes calibrated by Gibbs ensemble simulations for vapor-liquid equilibria

We propose Lennard-Jones potential parameters for interatomic interactions of linear and branched alkanes based on matching the results of Gibbs ensemble simulations of vapor-liquid equilibria to experimental data. The alkane model is similar as in the OPLS-AA, but multiple atom types for carbon based on the number of covalently bonded hydrogen atoms are necessary to accurately reproduce liquid densities and enthalpies of vaporization with the errors of 2.1% and 3.3%, respectively, for hydrocarbons of various chain lengths and structures. We find that the attraction energies of the carbon atoms are almost proportional to the number of covalent hydrogen atoms with each increasing the carbon energy parameter by approximately 0.033 kcal/mol. Though the present force field outperforms the OPLS-AA force field for alkanes we studied, systematic deviations for vapor pressures are still observed with errors of 15%-30%, and critical temperatures are slightly underestimated. We think that these shortcomings are probably due to the inadequacy of the two-parameter Lennard-Jones potential, and especially its behavior at short distances.     

Formation of rodlike structures of water between oppositely charged ions in decane and polyethylene

The Gibbs ensemble Monte Carlo method has been combined with the connectivity altering osmotic Gibbs ensemble to study water solubility and clustering in decane and polyethylene. We show that the presence of oppositely charged ion pairs that have fixed positions in the hydrocarbon matrices leads to an order of magnitude increase in the water solubility. This is important to a wide range of technical applications, since the uptake of the water leads to an increase in volume--or expansion--of the hydrocarbon phase which, in the case of polyethylene, may change the polymer properties and lead to water treeing. The increase in solubility is largest when the ions are sufficiently close so that rod-shaped clusters of water molecules form between the ions.     

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.     

GEMC和GDI方法计算流体气液相平衡的比较

考察采用TraPPE联合原子和OPLS全原子力场两种分子力场, Gibbs系综蒙特卡罗(GEMC)方法和Gibbs-Duhem积分(GDI)方法计算流体气液相平衡的适用性、计算速度、计算精度等问题. 结果表明, 在采用全原子力场情况下, GDI方法比GEMC方法极大地节省了计算时间. 从计算结果来看, 两种方法各有适用范围, 在使用时可互为补充. 在给定力场的前提下, 两种方法所得到的液相密度、蒸发焓、临界温度和临界密度相差不大, 而当力场中的缺陷导致蒸发焓的计算不够准确时, 两种计算方法得到的气体的压力和密度明显不同,进而导致预测的临界压力也明显不同.     

Solvation of sodium-chloride ion pair in water cluster at atmospheric conditions: grand canonical ensemble Monte Carlo simulation

Open statistical ensemble simulations are used to study the mechanism of nucleation of atmospheric water on sodium-chloride ion pair in a wide range of temperature and relative humidity values. The extended simple point-charge model is used for water molecules. Ions-water nonadditive interactions are taken into account by introducing the mutual polarization of ions and water in the field of each other. Gibbs free-energy variations are calculated from Na+-Cl- pair-correlation function and used as a criterion for determining the possible stable states of the cluster. In this relation, it was found that the dissociation of ion pairs in water clusters occurs even at vapor pressures of only a few millibars. In the conditions under consideration solvent-separated ion-pair states are found to be more probable than contact ion-pair configurations. The susceptibilities of water and ions are found to play an essential role in the stabilization of ions at large separations. The structure of ion-induced clusters is analyzed in terms of binary correlation functions. The non-pair interactions influence essentially the structure of ion solvation shells. The results of simulation show that the separation of the charges in water clusters containing simple ions can take place under atmospheric conditions.     

Electron trapping by polar molecules in alkane liquids: cluster chemistry in dilute solution

Experimental observations are presented on condensed-phase analogues of gas-phase dipole-bound anions and negatively charged clusters of polar molecules. Both monomers and small clusters of such molecules can reversibly trap conduction band electrons in dilute alkane solutions. The dynamics and energetics of this trapping have been studied using pulse radiolysis-transient absorption spectroscopy and time-resolved photoconductivity. Binding energies, thermal detrapping rates, and absorption spectra of excess electrons attached to monomer and multimer solute traps are obtained, and possible structures for these species are discussed. "Dipole coagulation" (stepwise growth of the solute cluster around the cavity electron) predicted by Mozumder in 1972 is observed. The acetonitrile monomer is shown to solvate the electron by its methyl group, just as the alkane solvent does. The electron is dipole-bound to the CN group; the latter points away from the cavity. The resulting negatively charged species has a binding energy of 0.4 eV and absorbs in the infrared. Molecules of straight-chain aliphatic alcohols solvate the excess electron by their OH groups; at equilibrium, the predominant electron trap is a trimer or a tetramer, and the binding energy of this solute trap is ca. 0.8 eV. Trapping by smaller clusters is opposed by the entropy that drives the equilibrium toward the electron in a solvent trap. For alcohol monomers, the trapping does not occur; a slow proton-transfer reaction occurs instead. For the acetonitrile monomer, the trapping is favored energetically, but the thermal detachment is rapid (ca. 1 ns). Our study suggests that a composite cluster anion consisting of a few polar molecules imbedded in an alkane "matrix" might be the closest gas-phase analogue to the core of solvated electron in a neat polar liquid.     

Phase behavior of C60 by computer simulation using ab‐initio interaction potential

A first‐principles intermolecular potential recently proposed by Pacheco and Ramalho [Phys Rev Lett 1997, 79, 3873–3876] has been used with the Gibbs ensemble and Gibbs–Duhem integration Monte Carlo methods to simulate the vapor–liquid and fluid–solid coexistence properties of C₆₀. The critical properties were calculated by fitting the results to the laws of rectilinear diameters and order parameter scaling. The triple‐point properties were determined from the limiting behavior of the Gibbs ensemble vapor–liquid simulations at the lowest temperature range. A stable liquid phase is predicted for temperatures between 1570±20 and 2006±27 K and densities between 0.444±0.003 and 1.05±0.01 nm^?3. The estimated critical and triple‐point pressures are, respectively, 35±6 and 5±16 bars. We show for the first time, to our knowledge, that it is possible, strictly by computer simulation, to estimate a triple point for C₆₀ in accordance with the predictions of theoretical methods and the basic concepts of thermodynamics. The liquid and fluid radial distribution functions indicate the presence of solid or glasslike features. This may support the suggestion of a more cooperative interaction of clusters in C₆₀. A comparison of our results with the data obtained by other authors is presented and discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 375–387, 2001     

Solvent-Polymer Interaction. II. Measurements of Liquid Solvent Molecules Associating with Polymer Sites and of Their Transport Behavior in Polymer Membrane by Thermogravimetry,GLC, and Mass Spectrometry

The measurement of sorption and diffusion behavior of liquid ethanol and water solvent mixtures in polyurethane membrane were made simultaneously by thermogravimetry. The individual amounts of sorbed water and ethanol in the polymer membrane were estimated by thermogravimetry and differentiated by mass spectrometry. In addition, from a single dynamic thermogravimetric experiment the activation energy for solvent molecules desorbing from the polymer membrane was also determined. The thermodynamic activity of ethanol vapor in equilibrium with the ethanol-water-polyurethane system was determined by gas-liquid chromatography. The clustering functions, the mean numbers of solvent molecules in the clusters, and those associating with polymer sites were evaluated by applying simplified mathematical derivatives using the experimentally determined values of activity and volume fraction of solvent molecules. It was found that at lower ethanol concentration the tendency for ethanol molecules to cluster together is high. At higher ethanol activity, ethanol-polymer site interactions predominantly occurred.

Similar results were observed for ethanol-water molecules. However, water molecules in this particular system did not exhibit a self-associating tendency nor interact with the polymer sites. It was concluded that the Zimm-Lundberg clustering theory can be adequately applied to the interpretation of sorption and diffusion behavior of liquid ethanol-water mixtures in the polymer membrane.     

Prediction of thermodynamic properties of heavy hydrocarbons by Monte Carlo simulation

In this study, Monte Carlo simulation techniques based on the anisotropic united atom (AUA) potential have been used to predict thermodynamic properties, comprising saturation pressures, vaporization enthalpies and liquid densities, at different temperatures for several isoalkanes (2,3-dimethylpentane, 2,4-dimethylpentane), alkylbenzenes (propylbenzene and hexylbenzene), alkyl-substituted cycloalkanes (propylcyclohexane and propylcyclopentane), polycyclic alkanes (trans-decalin), and naphtenoaromatics (tetralin and indan), representing gasoil range fractions of hydrocarbons. This variety of hydrocarbons with different molecular structures served to demonstrate the transferability of the AUA potential parameters. For this purpose, two types of Monte Carlo algorithm were used: the Gibbs ensemble algorithm to predict equilibrium properties at high temperatures, and the NPT algorithm followed by the thermodynamic integration to extend the prediction to lower temperatures. Techniques increasing the efficiency of the algorithms such as configuration bias, reservoir bias, and parallel tempering were also implemented in the algorithms. Based on available experimental information, good predictions of equilibrium properties were obtained for all the hydrocarbon families studied, and small differences between isomers were represented with a good accuracy.     

Clusterization of water molecules on crystalline β-AgI surface. Computer experiment

The free energy and the work of formation of the clusters of water molecules from the vapor on the ideal continuous crystalline surface of silver iodide at 260 and 300 K are calculated with the Monte Carlo method for a bicanonical statistical ensemble. Long-range electrostatic and polarization interactions with the surface are calculated with the two-dimensional Ewald method. It is shown that the adsorption of water molecules is accompanied by their intense clusterization. At negative Celsius temperatures, hydrogen-bonded molecules form the chains on the crystal surface. The closure of chains into rings begins with the clusters containing five molecules. As cluster sizes increase, the competition between five-and six-membered cycles is ended in favor of six-membered cycles. The substrate field stimulates the formation of six-membered cycles. Entropic effects strongly level the influence of clusterization on the probability of adsorption. Within the size interval 1 < N < 15, there are two clusterization barriers whose heights are negligible and equal to about 2k _B T. The presence of a substrate lowers the vapor pressure of clusterization by more than an order of magnitude.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Structural transition in the OH<Superscript>−</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> cluster in water vapors

The hydration of hydroxyl ion in water vapors at temperatures corresponding to seasonal variations in natural air medium is studied by the Monte Carlo simulation in grand canonical statistical ensemble using the detailed model of intermolecular forces that takes into account many-particle covalent interactions, polarization, and charge transfer. An increase in the number of water molecules in a cluster is accompanied by a structural transition from strongly asymmetric ion environment of water molecules to the formation of enveloping shell composed of these molecules. This transition is accompanied by an abrupt increase in cluster size and qualitative changes in its structural characteristics. The displacement of ion on the surface of clusters with extremely small sizes is an entropy effect. Results of simulation are compared with data on the hydration of hydroxonium at which similar structural transition is not observed, and with data of quantum-chemical calculations.     

Vapor–liquid equilibrium of systems containing alcohols,water, carbon dioxide and hydrocarbons using SAFT

The statistical associating fluid theory (SAFT) equation of state is employed for the correlation and prediction of vapor–liquid equilibrium (VLE) of eighteen binary mixtures. These include water with methane, ethane, propane, butane, propylene, carbon dioxide, methanol, ethanol and ethylene glycol (EG), ethanol with ethane, propane, butane and propylene, methanol with methane, ethane and carbon dioxide and finally EG with methane and ethane. Moreover, vapor–liquid equilibrium for nine ternary systems was predicted. The systems are water/ethanol/alkane (ethane, propane, butane), water/ethanol/propylene, water/methanol/carbon dioxide, water/methanol/methane, water/methanol/ethane, water/EG/methane and water/EG/ethane. The results were found to be in satisfactory agreement with the experimental data except for the water/methanol/methane system for which the root mean square deviations for pressure were 60–68% when the methanol concentration in the liquid phase was 60 wt.%.     

Critical comparison of classical and quantum mechanical treatments of the phase equilibria of water

The Gibbs ensemble Monte Carlo simulation technique was used to compare the phase equilibria of the rigid TIP4P water model [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)] utilizing classical and quantum statistical mechanics. The quantum statistical mechanical treatment generally resulted in lower liquid densities and higher vapor densities, narrowing the phase envelope. As a result, the calculated critical temperatures and normal boiling points were lower from the quantum simulations than the classical by 22 and 17 K, respectively, but the critical densities were equal within the estimated uncertainties. When the phase diagram from the quantum statistical mechanical treatment was increased by 22 K, it agreed with the classical results quite well throughout the entire simulated temperature range. A semiclassical treatment, involving a low order expansion in Planck's constant, resulted in good agreement with the path integral results for second virial coefficients, but gave densities and vapor pressures that fluctuated between the values for the classical and quantum statistical mechanics values, with no definite agreement with either.     

Chain conformation and solvent partitioning in reversed-phase liquid chromatography: Monte Carlo simulations for various water/methanol concentrations

Many structural models for the stationary phase in reversed-phase liquid chromatography (RPLC) systems have been suggested from thermodynamic and spectroscopic measurements and theoretical considerations. To provide a molecular picture of chain conformation and solvent partitioning in a typical RPLC system, a particle-based Monte Carlo simulation study is undertaken for a dimethyl octadecyl (C(18)) bonded stationary phase on a model siliceous substrate in contact with mobile phases having different methanol/water concentrations. Following upon previous simulations for gas-liquid chromatography and liquid-liquid phase equilibria, the simulations are conducted using the configurational-bias Monte Carlo method in the Gibbs ensemble and the transferable potentials for phase equilibria force field. The simulations are performed for a chain surface density of 2.9 micromol/m(2), which is a typical bonded-phase coverage for mono-functional alkyl silanes. The solvent concentrations used here are pure water, approximately 33 and 67% mole fraction of methanol and pure methanol. The simulations show that the chain conformation depends only weakly on the solvent composition. Most chains are conformationally disordered and tilt away from the substrate normal. The interfacial width increases with increasing methanol content and, for mixtures, the solvent shows an enhancement of the methanol concentration in a 10 Angstrom region outside the Gibbs dividing surface. Residual surface silanol groups are found to provide hydrogen bonding sites that lead to the formation of substrate bound water and methanol clusters, including bridging clusters that penetrate from the solvent/chain interfacial region all the way to the silica surface.     

Thermodynamic properties of ionic liquids-a cluster approach

We describe a method for calculating thermodynamic properties of ionic liquids by using standard quantum statistical thermodynamics as characterized by ab initio techniques. We review briefly how thermochemical properties for different sized clusters of ionic liquids are calculated by standard ab initio programs. The cluster partition functions allow one to calculate energies, enthalpies and Gibbs energies. Assuming that the ionic liquid exists exclusively as isolated ion-pairs in the gaseous phase and regarding the largest clusters as possible liquid structures, we could estimate vapor pressures, enthalpies of vaporization and entropies of vaporization. For possible boiling points it is shown how they vary with pressure.