Scaled equations for the coexistence curve,the capillary constant and the surface tension of n-alkanes

A review of experimental data of several fluids shows that their coexistence curve follows a power law in reduced temperature at the approach of the critical point, with an universal exponent equal to 0.325, their capillary constant a power law with an universal exponent equal to 0.925 and their surface tension a power law with an universal exponent equal to 1.26. In the critical region, the concept of two-scale-factor universality was used to predict the density difference amplitude, the capillary constant amplitude, and the surface tension amplitude between near critical vapor and liquid phases. A comparison with amplitudes determined from experimental data is given. In order to extend this universality all along the liquid–gas coexistence curve from the triple point to the critical point for n-alkanes, a mean field approximation was used far away from T_C. We show that the density difference, the capillary constant and the surface tension can be calculated with a reasonable accuracy by generalized scaled equations adding only two empirical constants. A comparison between calculated and experimental data is presented.     

Vibrational energy relaxation of high density HCl fluid in the 150–345 K range

The vibrational lifetime of liquid hydrogen chloride alone the liquid—vapor coexistence curve and of high density hydrogen chloride above the critica anti-Stokes Raman scattering technique. The results obtained above the critical temperature show a gas-liKe behaviour with a larger relaxation rate con is consistent with a contribution of van der Waals dimers to vibrational relaxation. The results obtained along the liquid—vapor coexistence curve ar model.     

General correlation model for some physical properties of saturated pure fluids

In this work, we use a general expression to accurately correlate the liquid density, the vaporization enthalpy, the surface tension, and the isobaric heat capacity of a saturated liquid versus temperature along the whole coexistence curve. The general expression used is the same for the four thermodynamic properties, and uses both critical and triple point values as reference. As representative examples of the use of the model, results are given for a set of 22 pure substances. We find that this general expression correlates the data with smaller or similar overall deviations when compared with other published models whose number of coefficients are the same or greater.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

A New Technique for Modelling the Structure of Expanded Liquid Metals Along the Liquid-Vapour Coexistence Curve

Abstract

We have developed a simple technique for modelling the structure of expanded liquid metals along the liquid vapour coexistence curve which may be characterised as a ‘correlated percolation’ method. Starting from a model for the liquid at high density, e.g. near the triple point, obtained either by molecular dynamics simulation or reverse Monte Carlo modelling, we keep the size of the model and the atomic positions fixed and remove atoms, according to criteria which depend on the coordination number distribution, until the required lower density, corresponding to a higher temperature, is reached. Small random Gaussian displacements are then added to the position of each atom to account for the increased temperature. The structure factor of the resulting model is quite close to that measured experimentally. Changes in the structure factor as the liquid expands can thus be separated into the effects of density fluctuations and temperature (or entropy).     

Measurements of the isochoric heat capacity,the critical point (TC, ρC) and vapor–liquid coexistence curve (TS, ρS) of high-purity toluene near the critical point

Isochoric heat capacities (C_V, V, T), phase boundary properties (T_S, ρ_S) and the critical (T_C, ρ_C) parameters for high-purity (0.9999+ mole fraction) toluene have been measured with a high temperature, high pressure, nearly constant volume adiabatic calorimeter and quasi-static thermogram technique. Measurements were made at three selected liquid and vapor isochores 777.8, 555.25, and 214.64 kg m⁻³ in the temperature range from 379 to 591 K. For five near-critical isochores 268.68, 281.68, 296.62, 301.52, and 318.28 kg m⁻³, the measurements were made in the immediate vicinity of the coexistence curve in order to accurately determine the phase transition temperatures (T_S, ρ_S) (shape of the coexistence curve near the critical point) and the critical parameters (T_C, ρ_C). The total combined uncertainty of heat capacity, density, and temperature measurements were estimated to be less than 2%, 0.06%, and 15 mK, respectively. The uncertainties reported in this paper are expanded uncertainties at the 95% confidence level with a coverage factor of k = 2. The uncertainty of the phase transition and the critical temperature value was 0.02 K. The Krichevskii parameter for some toluene-containing binary mixtures was calculated. The derived values of the Krichevskii parameter were used to estimate the effect of dilute impurities on the critical parameters of toluene. The measured values of saturated density near the critical point were interpreted in terms of the “complete scaling” theory in order to study singularity behavior of the coexistence curve diameter. The measured isochoric heat capacities and saturated densities were compared with the data reported by other authors and values calculated from an equation of state and other correlations.     

Low density observations of Rb and Cs chains along the liquid–vapour coexistence curves to the critical point in relation to quantum-chemical predictions on the metal-insulator transitions in Li and Na rings

Recent ab initio predictions concerning the metal-insulator (MI) transition in rings of the light alkali atoms, Li and Na, are compared and contrasted with experimental facts concerning diluted Rb and Cs alkalis. The main focus here is on the local coordination number as a function of density as these two heavy alkali metallic fluids are taken along the liquid–vapour coexistence curve towards the critical point, which in these cases coincides with the MI transition. Also recorded are the results of experiments in which Cs chains are observed at large interatomic spacing outside semiconducting substrates of InSb and GaAs.     

Extension of the exp-6 model to the simulation of vapor-liquid equilibria of primary alcohols and their mixtures

Configurational-biased Gibbs ensemble Monte Carlo simulations were performed to obtain the phase behavior of the homologous series of primary alcohols from ethanol to 1-heptanol. Molecular interactions in these systems are modeled by a newly developed exp-6 potential in combination with a Coulombic intermolecular potential. Some of exp-6 potential parameters required to describe these alcohols were taken from the previous literature data reported for methanol and n-alkanes. The oxygen's potential parameters were optimized to fit the coexistence curve of these alcohols to the experimental data. Simulated values of saturated liquid and vapor densities, vapor pressures and critical constants of the alcohols are in good agreement with experimental data. The efficiency of the new model in the prediction of binary phase diagram of water/ethanol and n-hexane/1-propanol mixtures is also evaluated. The calculated mole fractions in the vapor and liquid phases of these binary mixtures also show satisfactory agreement with the experimental data.     

Vibrational energy relaxation of high-density HBr fluid in the 186–366 K range

We have measured the vibrational lifetime of dense fluid hydrogenn bromide slightly above the critical temperature and of liquid-phase hydrogen bromide along the liquid—vapor coexistence curve. The results obtained above the critical temperature are interpreted in terms of a contribution of van der Waals dimers to vibrational relaxation. The liquid-phase results are interpreted in terms of the Delalande and Gale model using the same approximations as in the case of hydrogen chloride.     

纳米尺度氩液体线物性的分子动力学模拟

运用分子动力学模拟方法,对纳米尺度氩液体线的物理性质进行了研究。文中模拟计算了纳米线的熔点温度以及气液平衡状态下液态区密度、气态区密度和液体线的半径,并分析了模拟盒子尺寸和模拟温度对液体线物性的影响。结果表明,由于在初始结构中增加了气体分子,当模拟温度不变时,随模拟盒子尺寸的增加,液态区密度增大,气态区密度减小。但模拟盒子尺寸较小时,液体线半径不随模拟盒子尺寸发生变化。模拟计算所得的液态区密度十分接近宏观尺度氩液体密度时,模拟盒子的尺寸较合适。当模拟盒子尺寸固定不变时,液态区密度和气态区密度随温度的变化趋势与文献中宏观尺度氩液体和气体密度的变化趋势相同。结论可以为进一步系统地分析纳米尺度液体线的稳定性提供一定的依据。     

Low-coordination phases of both crystalline and fluid states of alkali metals under extreme conditions of high and low densities,respectively

After a brief summary of early work, involving the present authors, relating to low coordination phases of some alkalis in either dense crystalline states at high pressure (e.g. Li) or low density metallic fluids near criticality (Cs and Rb), contact is made with the very recent density functional study by Pickard and Needs (Phys. Rev. Lett. 102, 146401 (2009)). Whereas these authors predict three- and four-fold coordination numbers for extremely high pressure crystalline phases of Li, we stress here the remarkable behaviour of the heavy alkali metallic fluids Cs and Rb along the liquid–vapour coexistence curve towards the critical point. Coordination numbers ～8?10 near melting then reduce, as the density is lowered, to 2 at or near the critical point.     

Estimation of spinodals from the density profile of the vapor–liquid interface

An extension of a recently proposed method for the calculation of the spinodals in pure fluid systems from the interfacial properties is elaborated, which requires the density profile as only input. The foundation of this approach is the so-called Fuchs-transformation which gives an estimate for the tangential pressure profile from the density profile. Using molecular dynamics simulation data for argon and carbon dioxide as well as lattice Boltzmann simulation data for the argon-like Shan–Chen fluid, the accuracy of the approach is analyzed. The Fuchs-transformation is qualitative, however it is possible to estimate the temperature–density projection of the spinodal. Depending on the underlying correlation function for the interfacial density profile reasonable results are obtained for the liquid and the vapor spinodal. The advantage of this method is that equilibrium data can be used to estimate the spinodal which is experimentally impossible to access because it is a highly non-equilibrium property. In the final consequence of this approach only the coexistence vapor and liquid densities are required to estimate the temperature–density projection of the spinodals.     

A new cubic equation of state for reservoir fluids

A new three-parameter cubic equation of state is developed with special attention to the application for reservoir fluids. One parameter is taken temperature dependent and others are held constant. The EOS parameters were evaluated by minimizing saturated liquid density deviation from experimental values and satisfying the equilibrium condition of equality of fugacities simultaneously. Then, these parameters were fitted against reduced temperature and Pitzer acentric factor. For calculating the thermodynamic properties of a pure component, this equation of state requires the critical temperature, the critical pressure, the acentric factor and the experimental critical compressibility of the substance. Using this equation of state, saturated liquid density, saturated vapor density and vapor pressure of pure components, especially near the critical point, are calculated accurately. The average absolute deviations of the predicted saturated liquid density, saturated vapor density and vapor pressure of pure components are 1.4%, 1.19% and 2.11%, respectively. Some thermodynamic properties of substances have also been predicted in this work.     

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.     

A predictive vapor-pressure equation

A simple equation is presented for predicting the temperature dependence of the vapor-pressure of a pure substance along the entire (liquid + vapor) coexistence curve, from the triple point to the critical point. The proposed equation is based on the use of a dimensionless temperature reduced by using critical and triple point values, and of the Clausius–Clapeyron equation as a zeroth-order approximation. The pressure and temperature at the triple point, the normal boiling temperature, and the pressure and temperature at the critical point are required as input data. The proposed equation is verified for 53 fluids by using NIST data. These data are reproduced with an overall average deviation of 0.55%.     

Empirical Relationships between Transport Coefficients of Liquid Metals over a Range of Thermodynamic States

Abstract

Assuming the Wiedemann-Franz law, measured data for electrical conductivity α of liquid Cs and Rb is converted to λ_e , the electronic contribution to the thermal conductivity A. While the major part of the measured thermal conduction is thereby accounted for, the “residual” ionic contribution, denned as (^λ-1—λ_e ^?1)^?1, does not simply increase as the metal-insulator transition is approached along the coexistence curve.

Since λ is dominated by _λe, it is surprising that a hard sphere model, which predicts λ/n = 5k_B/2M with n the shear viscosity and M the ionic mass, still gives correctly a relatively constant ratio, though a difference in behaviour of λ/n as a function of thermodynamic state is noted for liquid Rb and Cs compared with liquid argon.

A generalization of Andrade's formula for shear viscosity at the melting point is also discussed, including the work of Zwanzig relating the self-diffusion coefficient D to n via the bulk viscosity.     

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE‐D3, BLYP‐D3, PBE0‐D3, M062X‐D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP‐D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP‐D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO₂ and SO₂. © 2017 Wiley Periodicals, Inc.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.