Hard-wall potential function for transport properties of alkali metal vapors

This study demonstrates that the transport properties of alkali metals are determined principally by the repulsive wall of the pair interaction potential function. The (hard-wall) Lennard-Jones (LJ) (15-6) effective pair potential function is used to calculate the transport collision integrals. Accordingly, reduced collision integrals of K, Rb, and Cs metal vapors are obtained from the Chapman-Enskog solution of the Boltzmann equation. The law of corresponding states based on the experimental transport reduced collision integral is used to verify the validity of a LJ(15-6) hybrid potential in describing the transport properties. LJ(8.5-4) potential function and a simple thermodynamic argument with the input PVT data of liquid metals provide the required molecular potential parameters. Values of the predicted viscosity of monatomic alkali metal vapor are in agreement with typical experimental data with average absolute deviations of 2.97% for K in the range of 700-1500 K, 1.69% for Rb, and 1.75% for Cs in the range of 700-2000 K. In the same way, the values of predicted thermal conductivity are in agreement with experiment within 2.78%, 3.25%, and 3.63% for K, Rb, and Cs, respectively. The LJ(15-6) hybrid potential with a hard-wall repulsion character conclusively predicts the best transport properties of the three alkali metal vapors.     

Correlations among residual multiparticle entropy, local atomic-level pressure, free volume and the phase-ordering rule in several liquids

A modified Wang-Landau density-of-states sampling approach has been performed to calculate the excess entropy of liquid metals, Lennard-Jones (LJ) system and liquid Si under NVT conditions; and it is then the residual multiparticle entropy (S(RMPE)) is obtained by subtraction of the pair correlation entropy. The temperature dependence of S(RMPE) has been investigated along with the temperature dependence of the local atomic-level pressure and the pair correlation functions. Our results suggest that the temperature dependence of the pair correlation entropy is well described by T(-1) scaling while T(-0.4) scaling well describes the relationship between the excess entropy and temperature. For liquid metals and LJ system, the -S(RMPE) versus temperature curves show positive correlations and the -S(RMPE) of liquid Si is shown to have a negative correlation with temperature, the phase-ordering criterion (based on the S(RMPE)) for predicting freezing transition works in liquid metals and LJ but fails in liquid Si. The local atomic-level pressure scaled with the virial pressure (σ(al)/σ(av)) exhibits the much similar temperature dependence as -S(RMPE) for all studied systems, even though simple liquid metals and liquid Si exhibit opposite temperature dependence in both σ(al)/σ(av) and -S(RMPE). The further analysis shows that the competing properties of the two effects due to localization and free volume on the S(RMPE) exist in simple liquid metals and LJ system but disappear in liquid Si, which may be the critical reason of the failure of the phase-ordering criterion in liquid Si.     

A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000?K and at pressures ranging from vapour pressure up to 40,000?bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.     

Prediction of the surface tension of cesium in the whole liquid range

Surface tension is an important quantity, both as physical and technological features. We applied the general form of Lennard-Jones potential model, LJ (m-n), and some thermodynamic arguments in the Kirkwood and Buff equation to calculate the surface tension of liquid cesium. To find out the surface tension in a wide temperature range, only pVT data are required. By this method, we investigated the influence of the potential model on the surface tension. For two selected potential models [LJ (6–3) and LJ (8.5–4)], the values of the calculated surface tension and the predicted surface energy agree with the experimental values.     

On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface

The long-range corrections (LRCs) to the configurational energy have been taken into consideration in the Monte Carlo simulation of the vapor-liquid interface for a pure Lennard-Jones (LJ) fluid. The simulated bulk densities agree satisfactorily with those obtained from the Gibbs ensemble method, and the simulated surface tension values agree reasonably well with those reported in the literature for a larger number of molecules and a larger cut-off distance. To compare the influence of the potential forms on the simulation results, a truncated LJ potential, and a shifted and truncated LJ potential have been examined. Although the bulk densities and surface tensions calculated for different model fluids are strongly affected by the LRC, the different potentials essentially lead to similar density values and similar surface tension values when the respective calculated values are compared on the basis of a reduced temperature scale.     

Validation of intermolecular pair potential model of SiH4: molecular-dynamics simulation for saturated liquid density and thermal transport properties

We demonstrate a validation of the intermolecular pair potential model of SiH(4), which is constructed from ab initio molecular-orbital calculations and expressed as the sum of the exponential and the London dispersion terms. The saturated liquid densities of SiH(4) are calculated for temperatures from 100 to 225 K by molecular-dynamics (MD) simulation. The average deviation between the experiment and the MD simulation using the present potential model is 3.9%, while the deviations exceed 10% for other well-known potential models such as the five-center Lennard-Jones (LJ) model. Subsequently, the shear viscosity, the thermal conductivity, and the self-diffusion coefficient of liquid SiH(4) are calculated by an equilibrium MD simulation with the Green-Kubo formula from 100 to 225 K. The average deviations from experiment are 11.8% and 13.7% for the shear viscosity and the thermal conductivity, respectively. Comparing the present model with an empirical one-center LJ model, it turns out that the rotational energy transfer through the intermolecular potential energy, which comes from the anisotropic potential energy, plays an important role in the thermal conductivity of liquid SiH(4). These results indicate that the present intermolecular potential model has an ability to give realistic pictures for liquid SiH(4) through molecular simulations.     

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.     

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.     

A perturbed hard-sphere equation of state for alkali metals

A perturbed hard-sphere equation of state, employing a basic frame proposed by Eslami [H. Eslami, J. Nucl. Mater. 336 (2005) 135–139] has been developed for alkali metals. Following the approach introduced by Ihm et al. [G. Ihm, Y. Song, E.A. Mason, J. Chem. Phys. 94 (1991) 3839–3848], the temperature dependence of the parameters a and b has been fitted to liquid density data for potassium. The scaling parameters that are used to reduce the temperature are the temperature and density at normal boiling point. The important improvement is to omit the adjustable parameters, the well depth and the location of the minimum of pair potential, which are required to apply the earlier equation of state of Eslami. The present EoS, which can be used without fitting parameters, reproduces the volumetric behavior of liquid alkali metals with a very good accuracy. Six hundred and ninety four data points at different pressures and temperatures are examined and the average absolute deviation of predicted liquid density data compared to experiment is 1.41%.     

The calculation of vapor-liquid coexistence curve of Morse fluid: application to iron

The vapor-liquid coexistence curve of Morse fluid was calculated within the integral equations approach. The critical point coordinates were estimated. The parameters of Morse potential, fitted for elastic constants in solid phase, were used here to apply the results of present calculations to the determination of iron binodal. The properties of copper and sodium were considered in an analogous way. The calculations of pair correlation functions and isobars at liquid phase have shown that only for sodium these potential parameters allow one to obtain agreement with the measurements data. For iron another parameters are necessary to get this agreement in liquid phase. However, they give rise to very low critical temperature and pressure with respect to the estimates of other authors. Consequently, one can suppose that Morse potential is possibly inapplicable to the calculation of high temperature properties of non-alkali metals in disordered phases.     

Approximation of the Dymond-Rigby-Smith potential function using the Lennard-Jones form

Due to the mathematical similarities between the Dymond-Rigby-Smith (DRS) function with the conventional Lennard-Jones (LJ) functions, modification to the LJ indices is made herein in order to approximate the DRS energy curve. It is herein shown that the LJ(9-6) potential approximates well the DRS curve for interatomic distance shorter than the equilibrium distance. For interatomic distance longer than the equilibrium distance, a pair of LJ indices, based on the equal mean stretching energy, was found to give very good agreement with the DRS curve. Modification to the conventional LJ functions for describing the DRS energy, rather than the replacement of the LJ potentials with DRF function, allows numerous computational chemistry softwares to quantify the DRS energy with minimal hard-coding of their algorithms.     

Corresponding-states correlation for the compressed liquid density of metals

Applying the previous correlation for the saturated liquid density of metals, we have developed a corresponding-states correlation for the prediction of their compressed liquid densities. The correlation needs the values of the melting and boiling point parameters of metals plus an adjustable parameter, used to predict the saturated liquid densities. In this work, we have shown that by employing the Tait equation together with the previous correlation, for saturated liquid densities, it is possible to develop an accurate method for the prediction of the compressed liquid density of metals. The agreement of the predicted density values with the experimental ones for alkali metals, mercury, bismuth, tin, and lead over a wide range of temperatures, from melting point up to several hundred degrees above the boiling point, and pressures ranging from the vapor pressure up to 4000 bar, is quite good. From 821 data points examined for the aforementioned metals the average absolute deviation for the calculated densities compared with experiment is 0.72%. The correlation is also examined against a number of existing regularities for the liquid phase.     

Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids

The vapor-liquid phase envelope of Mie(14,7) fluids is determined by the Gibbs ensemble Monte Carlo (MC) simulation technique. The NVT-MC simulation method is then utilized to compute the equation of state and the pair correlation function over a wide range of densities and temperatures. The effective diameters are calculated via the virial minimization method and the results are applied as the repulsion-attraction splitting distance within the generic van der Waals (GvdW) theory to compute the mean free volume. The density and temperature dependence of these parameters are studied and discussed. The results for the effective diameter, and the GvdW parameters are fitted to analytical functions of density and temperature. An examination of the results for the fluid phase equilibria of argon shows excellent agreement with empirical data for the densities of the coexisting phases, the vapor pressure, and the critical point. The computed free volumes are used to compute the diffusion coefficient of argon and the results are compared with experimental data.     

Mixing rules for binary Lennard–Jones chains: theory and Monte Carlo simulation

Theoretically-based van der Waals one-fluid (vdW1) mixing rules are derived for Lennard–Jones (LJ) chain mixtures. The rules provide equivalent one-fluid segment parameters for LJ size (σ) and energy () parameter as well as chain length (m) based on the parameters of the individual mixture components and the component mole fractions. The mixing rules are tested by performing Monte Carlo simulations of eight different binary mixtures and the equivalent vdW1 pure fluid, each at three densities. The simulations test the effects of changing LJ size parameter, LJ energy parameter and chain length individually and together. The effects of mole fraction and density are also examined. The mixing rules are tested for accuracy in predicting compressibility factors and radial distribution functions. It is found that the vdW1 rules provide excellent agreement when size and energy parameter are varied. Good agreement is found for mixtures with different chain lengths. The discrepancy is worst at very high densities when all component parameters are varied simultaneously.     

The free energy of the metastable supersaturated vapor via restricted ensemble simulations. II. Effects of constraints and comparison with molecular dynamics simulations

Extensive restricted canonical ensemble Monte Carlo simulations [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)] were performed. Pressure, excess chemical potential, and excess free energy with respect to ideal gas data were obtained at different densities of the supersaturated Lennard-Jones (LJ) vapor at reduced temperatures from 0.7 to 1.0. Among different constraints imposed on the system studied, the one with the local minimum of the excess free energy was taken to be the approximated equilibrium state of the metastable LJ vapor. Also, a comparison of our results with molecular dynamic simulations [A. Linhart et al., J. Chem. Phys. 122, 144506 (2005)] was made.     

Transition state dynamics of N2O4 <==> 2NO2 in liquid state

Transition state dynamics of dissociation and association reactions N2O4 <==> 2NO2 in liquid state are studied by classical molecular dynamics simulations of reactive liquid NO(2) at 298 K. An OSPP+LJ potential between NO(2) molecules proposed in paper I [J. Chem. Phys. 115, 10852 (2001)], which takes into account the orientational sensitivity of the chemical bond, has been used in the simulation. The trajectory and energy evolution of various reactions are studied in the OSPP+LJ liquid, which reproduces both the observed liquid phase equilibrium constant and Raman band shape of the dissociation mode. It is found that a NO(2) pair in reactive liquid NO(2) is bound when E(T)<0 and dissociates when E(T)>0, and the dissociation of a reactant pair occurs when the transition state (TS) surface of E(T)=0 is crossed from negative to positive, where E(T) is the sum of the potential and kinetic energies of intermolecular motion of the pair. Two types of dissociation are found depending on the source of energy for dissociation; the first type D is the dissociation via collisional activation of the reactive mode by solvent molecules, and the second type T is the dissociation via bond transfer from a dimer to a monomer NO(2) through the TS of NO(2) trimer. It is concluded that the type T dissociation is found to be much more probable than the type D dissociation because of easy energy conservation. The reactant experiences the TS of NO(2) trimer for a long time (1-10 ps) in NO(2) mediated bond transfer reactions, and crossing and recrossing trajectories and dynamics in the TS neighborhood are studied.     

Vapor-phase chemical equilibrium for the hydrogenation of benzene to cyclohexane from reaction-ensemble molecular simulation

The reaction-ensemble Monte-Carlo (REMC) molecular simulation method was used to study the vapor-phase chemical equilibrium for the reaction of hydrogenation of benzene to cyclohexane. A one-center modified Buckingham exponential-6 (1CMBE6) effective pair potential model (that had already been used to predict thermodynamic properties and liquid–liquid equilibria of helium+hydrogen mixtures) was used for hydrogen. Six-center modified Buckingham exponential-6 (6CMBE6) effective pair potential models (that had already been used to reproduce the saturated liquid and vapor densities, vapor pressures, second virial coefficients, and critical parameters of the six-membered ring molecules), were used for benzene and cyclohexane. No binary adjustable parameters were needed to compute the unlike-pair Buckingham exponential-6 interactions in the ternary system. Simulation results were obtained for the effect of some operating variables such as temperature (from 500 to 650 K), pressure (from 1 to 30 bar), and hydrogen to benzene feed mole ratio (from 1.5:1 to 6:1) on the reaction conversion, molar composition, and mass density of the ternary system at equilibrium. These results were found to be in excellent agreement with calculations using the predictive Soave–Redlich–Kwong (PSRK) group contribution equation of state.     

A new equation of state for metal alloys

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model volumetric properties of molten metals and their alloys considering a trimer expression obtained from the statistical associating fluid theory. The van der Waals dispersion forces were applied as perturbation term. Two parameters appeared in the PHT EOS, reflecting the dispersive energy among trimers, ε and the hard-core diameter σ were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the saturated and isobaric densities of 16 molten metals including alkali metals, alkali earth and refractory metals over the temperature range within 234–7400 K and pressures up to 436 MPa. From 677 data points examined, the average absolute deviation (AAD) of the predicted densities from the experimental ones was found to be 1.60%. Furthermore, the estimated uncertainties of predicted densities of alloys were ±3.00%.