Molecular-dynamics study of the density scaling of inert gas condensation

The initial stages of vapor condensation of Ge in the presence of a cold Ar atmosphere were studied by molecular-dynamics simulations. The state variables of interest included the densities of condensing vapor and gas, the density of clusters, and the average cluster size, while the temperatures of the vapor and the clusters were separately monitored with time. Three condensation processes were explicitly identified: nucleation, monomeric growth, and cluster aggregation. Our principal finding is that both the average cluster size and the number of clusters scale with the linear dimension of the computation cell, L, and Ln, with the scaling parameter n approximately 4, corresponding to a reaction order of nu approximately 2.33. This small value of n is explained by an unexpected nucleation path involving the formation of Ge dimers via two-body collisions.     

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.     

Evanescent high pressure during hypersonic cluster-surface impact characterized by the virial theorem

Matter under extreme conditions can be generated by a collision of a hypersonic cluster with a surface. The ultra-high-pressure interlude lasts only briefly from the impact until the cluster shatters. We discuss the theoretical characterization of the pressure using the virial theorem and develop a constrained molecular-dynamics procedure to compute it. The simulations show that for rare-gas clusters the pressures reach the megabar range. The contribution to the pressure from momentum transfer is comparable in magnitude and is of the same sign as that ("the internal pressure") due to repulsive interatomic forces. The scaling of the pressure with the reduced mechanical variables is derived and validated with reference to the simulations.     

Strain-induced yielding in bubble clusters

We study how shearing clusters of two or four bubbles induces bubble separation or topological rearrangement. The critical deformation at which this yielding occurs is measured as a function of shear rate, liquid composition, and liquid content in the cluster. We establish a geometrical yield criterion in the quasistatic case on the basis of these experimental data as well as simulations. In the dynamic regime, the deformation where the cluster yields increases with the strain rate, and we derive a scaling law describing this phenomenon based on the dynamical inertial rupture of the liquid meniscus linking the two bubbles. Our experiments show that the same scaling law applies to two- and four-bubble clusters.     

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.     

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.     

水分子簇在聚丙烯酰胺膜中的渗透研究

在不同蒸气活度下,通过吸附动力学实验,测定了蒸气状态的水分子簇在聚丙烯酰胺(PAM)膜中的动态吸附曲线,改进了ENSIC模型并用于计算水分子簇在膜内的扩散系数。结果显示,随着水蒸气活度的增加,膜内水分子簇尺寸增大,并在膜的微孔内产生多层吸附甚至毛细管冷凝,导致扩散系数迅速降低。     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

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.     

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.     

Thermodynamics of d-dimensional hard sphere fluids confined to micropores

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.     

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.     

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.     

Monte Carlo simulations of equilibrium solubilities and structure of water in n-alkanes and polyethylene

Gibbs ensemble Monte Carlo methods based on a force field that combines the simple point charge [Berendsen et al., in Intermolecular Forces, edited by Pullman (Reidel, Dordrecht, 1981), p. 331] and transferable potentials for phase equilibria [Martin and Siepmann, J. Phys. Chem. B 102, 2659 (1998)] models were used to study the equilibrium properties of binary systems consisting of water and n-alkanes with chain lengths from hexane to hexadecane. In addition, systems where extended linear alkane chains (up to 300 carbon units long) were used to represent amorphous polyethylene were simulated in the presence of water using a connectivity altering osmotic Gibbs ensemble. In these simulations the equilibrium between a liquid water phase and a polymer phase into which water was inserted was studied. The predicted solubilities, which were determined between 350 and 550 K, are in good agreement with experiment, where experimental results are available, and the density of water molecules in the hydrocarbons is approximately 63% as high as in saturated water vapor under the same conditions. At the lower temperatures most of the water exists as monomers; increasing the temperature leads to an increase in the density of water in the alkane phase and hence in the fraction of molecules that participate in clusters. Dimers are the most prevalent clusters in all hydrocarbons and at all temperatures studied, and the fraction of clusters of given size decrease with increasing cluster size. A large fraction of trimers, tetramers, and pentamers, which are the cluster sizes for which topologies have been studied, are cyclic at low temperatures, but at higher temperatures linear structures predominate. The same properties are observed for pure water vapor clusters in equilibrium with the liquid phase, showing that the cluster topologies are not significantly affected by the surrounding hydrocarbon.     

Effect of amino acid sorption on formation of water clusters in ion-exchange membranes

The average size and number of water clusters inside ion-exchange membranes are calculated from experimental isotherms of water vapor sorption as a result of considering the sorption in terms of the clusterization theory. It is established that, in MK-40 heterogeneous cation-exchange membrane, water clusters are not formed, while, inside MF-4SK perfluorinated homogeneous membrane, intense cluster formation takes place. The effect of amino acid sorption on cluster water is considered. An increase in the membrane hydrophobicity as a result of the incorporation of amino acid ions leads to prevailing interaction of water molecules with one another rather than with the polymer phase, which is evident from an enlargement of water clusters.     

Water sorption characteristics of poly(2‐hydroxyethyl acrylate)/silica nanocomposite hydrogels

Water sorption in hydrogels based on nanocomposites of poly(2‐hydroxyethyl acrylate) (PHEA) and silica, prepared by simultaneous polymerization and sol‐gel process, were studied gravimetrically over wide ranges of silica content, both below and above the percolation threshold of about 15% wt for the formation of a continuous inorganic network interpenetrated with the organic network. Measurements were performed at room temperature from the vapor phase, both at equilibrium and dynamic, for selected values of water activity α_w between 0 and 0.95, and from the liquid phase. In the nanocomposite hydrogels, the overall water uptake from the vapor phase is practically the same as in pure PHEA below the percolation threshold, whereas it is reduced above the percolation threshold, in particular at high α_w values where swelling becomes significant. Water clustering sets in at around 14 vol % (10 wt %) of water independently of composition, whereas the mean value of water molecules in a cluster decreases at high silica contents. In immersion experiments water uptake decreases as silica content increases to the percolation threshold of about 15 wt % and is then almost independent of composition. A scheme is proposed, which explains these results in terms of the existence of micelles, where a number of hydrophilic hydroxy groups are linked together, and their disentaglement by immersion into water. Diffusion coefficients of water depend on water content and are reduced on addition of silica above the percolation threshold. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Intermolecular potential energy surface and second virial coefficients for the water-CO2 dimer

A five-dimensional potential energy surface is calculated for the interaction of water and CO(2), using second-order M?ller-Plesset perturbation theory and coupled-cluster theory with single, double, and perturbative triple excitations. The correlation energy component of the potential energy surface is corrected for basis set incompleteness. In agreement with previous studies, the most negative interaction energy is calculated for a structure with C(2v) symmetry, where the oxygen atom of water is close to the carbon atom of CO(2). Second virial coefficients for the water-CO(2) pair are calculated for a range of temperatures, and their uncertainties are estimated. The virial coefficients are shown to be in close agreement with the available experimental data.     

Percolation transition in supercritical water: a Monte Carlo simulation study

Computer simulations of water have been performed on the canonical ensemble at 15 different molecular number densities, ranging from 0.006 to 0.018 A-3, along the supercritical isotherm of 700 K, in order to characterize the percolation transition in the system. It is found that the percolation transition occurs at a somewhat higher density than what is corresponding to the supercritical extension of the boiling line. We have shown that the fractal dimension of the largest cluster and the probability of finding a spanning cluster are the most appropriate properties for the location of the true percolation threshold. Thus, percolation transition occurs when the fractal dimension of the largest cluster reaches 2.53, and the probability of finding a cluster that spans the system in at least one dimension and in all the three dimensions reaches 0.97 and 0.65, respectively. On the other hand, the percolation threshold cannot be accurately located through the cluster size distribution, as it is distorted by appearance of clusters crossing the finite simulated system even far below the percolation threshold. The structure of the largest water cluster is dominated by a linear, chainlike arrangement, which does not change noticeably until the largest cluster becomes infinite.     

Lifetimes of cagelike water clusters immersed in bulk liquid water: a molecular dynamics study on gas hydrate nucleation mechanisms

Molecular dynamics simulations were performed to observe the evolution of cagelike water clusters immersed in bulk liquid water at 250 and 230 K. Totally, we considered four types of clusters--dodecahedral (5(12)) and tetrakaidecahedral (5(12)6(2)) cagelike water clusters filled with or without a methane molecule, respectively. The lifetimes of these clusters were calculated according to their Lindemann index (delta) using the criterion of delta> or =0.07. The lifetimes of the clusters at 230 K are longer than that at 250 K, and their ratios are the same as the ratio of structure relaxation times of bulk water at these temperatures. For both the filled and empty clusters, the lifetimes of 5(12)6(2) cagelike clusters are similar to that of 5(12) cagelike clusters. Although the methane molecules indeed make the filled cagelike water clusters live longer than the empty ones, the empty cagelike water clusters still have the chance of being long lived. These observations support the cluster nucleation hypothesis for the formation mechanisms of gas hydrates.