Molecular dynamics investigations on Lennard–Jones systems near the gas–liquid critical point

NVT simulations on Lennard–Jones (L–J) systems near the gas–liquid critical point were performed by a direct approach. As a result, the two necessary conditions for simulating the systems in accordance with the thermodynamic limit were proposed: (i) L/ξ≳20 (L: the box-length, ξ: the correlation length), (ii) the total time of evolution, t_E>500 L–J units, for ξ≈3.5. The proposed conditions are probably very close to the sufficient ones. The influence of finite-size effects on pressure and density of small systems was qualitatively predicted. The prediction was confirmed by the simulations but only for L markedly lower than the length of typical critical wave, 2πξ. For L markedly higher, the evolutions were dominated by an effect called here the instability effect. The effect became negligible just when the condition for L/ξ was fulfilled. The ξ₀′ constant for L–J fluid was estimated from direct measurements of ξ to be 0.27±0.02 (L–J units). The thermodynamic parameters of the critical point, obtained from extrapolation, were in agreement with the results of other authors. The β_C exponent was estimated from minimization for a high range of temperatures to be 0.346. A comparison of the efficiency of NVT and NpT methods was also performed and no distinct differences were noted.     

Isothermal vapor–liquid equilibria and excess molar volumes for the ternary mixtures containing 2-methyl pyrazine

Isothermal vapor–liquid equilibrium (VLE) data at 353.15 K and excess molar volumes (V^E) at 298.15 K are reported for the binary systems of ethyl acetate (EA)+cyclohexane and EA+n-hexane and also for the ternary systems of EA+cyclohexane+2-methyl pyrazine (2MP) and EA+n-hexane+2MP. The experimental binary VLE data were correlated with common g^E model equations. The correlated Wilson parameters of the constituent binary systems were used to calculate the phase behavior of the ternary mixtures. The calculated ternary VLE data using Wilson parameters were compared with experimental ternary data. The experimental excess molar volumes were correlated with the Redlich–Kister equation for the binary mixtures, and Cibulka’s equation for the ternary mixtures.     

Thermodynamics of the multicomponent vapor–liquid equilibrium under capillary pressure difference

We discuss the two-phase multicomponent equilibrium, provided that the phase pressures are different due to the action of capillary forces. We prove the two general properties of such an equilibrium, which have previously been known for a single-component case, however, to the best of our knowledge, not for the multicomponent mixtures. The importance is emphasized on the space of the intensive variables P, T and μⁱ, where the laws of capillary equilibrium have a simple geometrical interpretation. We formulate thermodynamic problems specific to such an equilibrium, and outline changes to be introduced to common algorithms of flash calculations in order to solve these problems. Sample calculations show large variation of the capillary properties of the mixture in the very neighborhood of the phase envelope and the restrictive role of the spinodal surface as a boundary for possible equilibrium states with different pressures.     

Vapor–liquid equilibria for the system 1-propanol+n-hexane near the critical region

Vapor–liquid equilibria and critical point data for the system 1-propanol+n-hexane at 483.15, 493.15, 503.15 and 513.15 K are reported. The critical pressures determined from the critical opalescence of the mixture were compared with published data for the system 2-propanol+n-hexane. Phase behavior measurements were made in a modified circulating type apparatus with a view cell. These mixtures are highly nonideal because of the hydrogen bonding of 1-propanol. Modeling of the experimental data has been performed using the multi-fluid nonrandom lattice fluid with hydrogen-bonding (MF-NLF-HB) equation of state and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with Wong–Sandler mixing rule. The critical points and the critical locus were also calculated.     

Refined semi-empirical formula for liquid–vapour critical point exponent δ and its relevance to the random field Ising model

Recent work in D.J. Klein and N.H. March, Phys. Lett. A 372, 5052 (2008) has considered, by a semi-empirical approach, the critical exponent δ at the liquid–vapour critical point as a function of dimensionality D. Here we first refine δ(d′), again semi-empirically, but with better results for other critical exponents, especially η(d′). The resulting form of δ(d′) is then utilised to discuss the random field Ising model. Systems with random fields are expected to exhibit drastically modified critical properties. We discuss the relation between a d-dimensional spin system in a random field with a d′-dimensional spin assembly in a zero magnetic field. A further matter focused in here concerns effective reduced dimensionality and hyperscaling relations. We conclude by assessing the way in which the available experimental results relate to the issues raised above.     

Dynamics of the Goldstone mode near the point of polarization sign reversal in ferroelectric liquid crystal–aerosil mixtures

Dielectric spectroscopy was used to study the influence of random disorder in aerosil–ferroelectric liquid crystal dispersions on the dynamics of the Goldstone mode near the point of polarization sign reversal and the relaxation rate and dielectric strength of the collective modes. In general, the dielectric strength and the relaxation frequency of the Goldstone mode decrease, in comparison with the bulk, with increasing aerosil density near a point of polarization sign reversal. However, the characteristic frequency of the Goldstone mode varies with silica density in an opposite manner on each side of this point. This can be explained as a different sensitivity on the spatial confinement of different molecular conformers above and below the point of polarization sign reversal. The experimental results of temperature and frequency dependence of the complex dielectric constant are compared with predictions of the generalized Landau model for ferroelectric liquid crystals.     

Soft-SAFT modeling of vapor–liquid equilibria of nitriles and their mixtures

Nitriles are strong polar compounds showing a highly non-ideal behavior, which makes them challenging systems from a modeling point of view; in spite of this, accurate predictions for the vapor–liquid equilibria of these systems are needed, as some of them, like acetonitrile (CH₃CN) and propionitrile (C₂H₅CN), play an important role as organic solvents in several industrial processes. This work deals with the calculation of the vapor–liquid equilibria (VLE) of nitriles and their mixtures by using the crossover soft-SAFT Equation of State (EoS). Both polar and associating interactions are taken into account in a single association term in the crossover soft-SAFT equation, while the crossover term allows for accurate calculations both far from and close to the critical point. Molecular parameters for acetonitrile, propionitrile and n-butyronitrile (C₃H₇CN) are regressed from experimental data. Their transferability is tested by the calculation of the VLE of heavier linear nitriles, namely, valeronitrile (C₄H₉CN) and hexanonitrile (C₅H₁₁CN), not included in the fitting procedure. Crossover soft-SAFT results are in excellent agreement with experimental data for the whole range of thermodynamic conditions investigated, proving the robustness of the approach. Parameters transferability has also been used to describe the isomers n-butyronitrile and i-butyronitrile. Finally, the nitriles soft-SAFT model is further tested in VLE calculation of mixtures with benzene, carbon tetrachloride and carbon dioxide, which proved to be satisfactory as well.     

Isobaric vapor–liquid–liquid equilibrium and vapor–liquid equilibrium for the system water–ethanol-1,4-dimethylbenzene at 101.3 kPa

An all-glass, dynamic recirculating still equipped with an ultrasonic homogenizer has been used to determine vapor–liquid (VLE) and vapor–liquid–liquid (VLLE) equilibria. Consistent data have been obtained for the ternary water + ethanol + p-xylene system at 101.3 kPa for temperatures in the range of 351.16–365.40 K. Experimental results have been used to check the accuracy of the UNIFAC, UNIQUAC and NRTL models in the liquid–liquid region of importance in the dehydration of ethanol by azeotropic distillation.     

Application of the Wilson—Wegner expansion to represent vapor—liquid equilibrium surfaces of binary and ternary systems from the critical locus to the vapor pressure of the heavier component

The Torquato—Stell modification of the Wilson—Wegner expansion has been used to present and to represent the vapor—liquid equilibrium surfaces of several binary methane—alkane mixtures and one ternary system from the critical locus to the heavier component's vapor pressure within the experimental accuracy of the data. Inconsistent phase compositions are revealed without recourse to equations of state computations. Since the critical point of the mixtures are not precisely known, an isothermal regression analysis of the data is first used to obtain an improved estimate of the critical point of mixtures using the scaled expressions. Then, along isotherms, the phase compositions are analyzed in terms of the reduced proximity to the critical pressure. Subsequently, the entire compositional surfaces are presented in terms of both the reduced proximity to the critical pressure of the mixture and the reduced proximity to the critical temperature of the heavier component.     

Isothermal vapor–liquid equilibria for mixtures composed of 1,2-dimethoxybenzene, 2-methoxyphenol,and diphenylmethane

Diphenylmethane was found to be a potential entrainer for separating the closely boiling mixtures of 2-methoxyphenol+1,2-dimethoxybenzene via extractive distillation. To gain insight into the capability of this auxiliary agent, isothermal vapor–liquid equilibrium data were measured for the binary and the ternary mixtures containing 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane at temperatures from 433.15 to 463.15 K. All the binary data passed thermodynamic consistency tests. However, there exhibits a large discrepancy between the experimental values and the predicted results from the UNIFAC model. The new data were correlated with the Wilson, the NRTL, and the UNIQUAC models, respectively. The model parameters determined from the binary data were applied to predict the phase equilibrium behavior of the ternary system.     

Monte Carlo simulations of vapor–liquid–liquid equilibrium of some ternary petrochemical mixtures

The aim of this study was to determine the capability and accuracy of Monte Carlo simulations to predict ternary vapor–liquid–liquid equilibrium (VLLE) for some industrial systems. Hence, Gibbs ensemble Monte Carlo simulations in the isobaric–isothermal (NpT) and isochoric–isothermal (NVT) ensembles were performed to determine vapor–liquid–liquid equilibrium state points for three ternary petrochemical mixtures: methane/n-heptane/water (1), n-butane/1-butene/water (2) and n-hexane/ethanol/water (3). Since mixture (1) exhibits a high degree of mutual insolubility amongst its components, and hence has a large three-phase composition region, simulations in the NpT ensemble were successful in yielding three distinct and stable phases at equilibrium. The results were in very good agreement with experimental data at 120 kPa, but minor deviations were observed at 2000 kPa. Obtaining three phases for mixture (2) with the NpT ensemble is very difficult since it has an extremely narrow three-phase region at equilibrium, and hence the NVT ensemble was used to simulate this mixture. The simulated results were, once again, in excellent agreement with experimental data. We succeeded in obtaining three-phase equilibrium in the NpT ensemble only after knowing, a priori, the correct three-phase pressure (corresponding to the force fields that were implemented) from NVT simulations. The success of the NVT simulation, compared to NpT, is due to the fact that the total volume can spontaneously partition itself favorably amongst the three boxes and only one intensive variable (T) is fixed, whereas the pressure and the temperature are fixed in an NpT simulation. NpT simulations yielded three distinct phases for mixture (3), but quantitative agreement with experimental data was obtained at very low ethanol concentrations only.     

Molecular simulation of the phase behaviour of ternary fluid mixtures: the effect of a third component on vapour–liquid and liquid–liquid coexistence

The Gibbs ensemble algorithm is implemented to determine the vapour–liquid and liquid–liquid phase coexistence of dilute ternary fluid mixtures interacting via a Lennard–Jones potential. Calculations are reported for mixtures with a third component characterised by different intermolecular potential energy parameters. Comparison with binary mixture data indicates that the choice of energy parameter for the third component affects the composition range of vapour–liquid substantially. The addition of a third component lowers the energy of liquid phase while slightly increasing the energy of the vapour phase.     

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.     

Proposed relationship between the exponents γ and η at liquid–vapour critical point via the dimensionality d

In earlier work, Ma [S.K. MA, Phys. Rev. Lett., 29, 1311 (1972)] has studied the critical exponents γ and η for charged and neutral Bose gases. Here we use the result of Ma, valid for general dimensionality d but only to O(m ^?1), where m is the number of components of the Bose field, to write a relation between γ(d) and η(d) to O(m ^?1). This then motivates, but now for the Ising model, a relationship between the critical exponents γ and η, via the dimensionality d. We finally demonstrate a connection between the two renormalisation group eigenvalues y _t and y _h , via the critical exponent δ with a dimensional dependence.     

An approach to calculate solid–liquid phase equilibrium for binary mixtures

An approach is presented to calculate solid–liquid phase equilibrium for binary mixtures, using expressions for the temperature as a function of the molar fraction. For Margules model the expression gives explicitly the temperature, while for other liquid phase activity models an iterative procedure is required to calculate the temperature. The method is very easy to apply and it can be used for mixtures that have peritectic and eutectic points, or just a eutectic point. The approach was applied to five case studies with binary mixtures of fatty acids and triglycerides. The results were in good agreement with experimental data.     

Modification of the Furter equation and correlation of the vapor–liquid equilibrium for mixed-solvent electrolyte systems

Isobaric vapor–liquid equilibrium values at 1 atm pressure were measured for the systems 1-propanol–water–potassium acetate and 2-propanol–water–potassium acetate under fixed salt mole fractions using a modified Othmer recirculation still. A modified Furter equation, ln(α_s/α)=k₁z+k₂z², was proposed for correlating the effect of dissolved salts on vapor–liquid equilibrium (VLE). The modified equation contains two parameters that are applicable to the entire salt/solvent composition range. Correlation of VLE for 15 mixed-solvent electrolyte systems was made by means of the proposed modified equation with better results than those obtained from the original equation.     

Molecular models for 267 binary mixtures validated by vapor–liquid equilibria: A systematic approach

By assessing a large number of binary systems, it is shown that molecular modeling is a reliable and robust route to vapor–liquid equilibria (VLE) of mixtures. A set of simple molecular models for 78 pure substances from prior work is taken to systematically describe all 267 binary mixtures of these components for which relevant experimental VLE data is available. The mixture models are based on the modified Lorentz–Berthelot combining rule. Per binary system, one state independent binary interaction parameter in the energy term is adjusted to a single experimental vapor pressure. The unlike energy parameter is altered usually by less than 5% from the Berthelot rule. The mixture models are validated regarding the vapor pressure at other state points and also regarding the dew point composition, which is a fully predictive property in this work. In almost all cases, the molecular models give excellent predictions of the mixture properties.     

High pressure vapor–liquid equilibria for carbon dioxide + tetrahydrofuran mixtures

Vapor–liquid equilibria and saturated density for carbon dioxide + tetrahydrofuran mixtures at high pressures were measured by the analytical method at the temperatures 298.15 and 313.15 K. The experimental apparatus equipped with three Anton Paar DMA 512S vibrating tube density meters was previously developed for measuring vapor–liquid–liquid equilibrium at high pressures. The equilibrium composition and saturated density of each phase were determined by gas chromatograph and vibrating tube density meters, respectively. The bubble point pressure at the temperature 313.15 K was further measured by the synthetic method. The experimental data were correlated with Soave–Redlich–Kwong (SRK) equation of state and the pseudocubic equation of state.