Modelling the volumetric properties of ionic liquids using a modified perturbed hard-sphere-chain equation of state

In this paper, a modified perturbed hard-sphere-chain equation of state (EOS) by Eslami [H. Eslami, Fluid Phase Equilib. 216 (2004) 21–26], is applied for modelling the thermodynamic properties of some ionic liquids (ILs). Two reliable scaling constants are used to determine two temperature-dependent parameters in the proposed EOS. The unique adjustable parameter that is reflecting the number of segments per molecule, r, compensates the uncertainties in the calculated temperature-dependent parameters. The reliability of the proposed EOS has been checked by comparing the results with 1561 experimental data points for 18 ILs over a broad range of pressures and temperatures. The overall average absolute deviation is 0.35%. A comparison of the predicted results, using the present EOS with the results of some previous models, indicates that the determined results of this EOS are in more accordance with experimental data than those.     

A modified perturbed hard-sphere-chain equation of state: consideration of attractive contribution

We adapted a new perturbation term reported by Bokis et al. for the modified perturbed hard-sphere-chain (PHSC) equation of state. The new model better agrees with the simulation data for illustrating both repulsive and attractive contributions than those of the PHSC equation of state. Three characteristic parameters, r, σ, and , are obtained from thermodynamic properties of pure saturated species and directly used to calculate coexistence curves of given binary systems. Vapor–liquid equilibria and liquid–liquid equilibria of fluids are remarkably well predicted by the model even in the case of polymer solution that shows non-ideal phase behavior.     

A simplified hard-sphere equation of state meeting the high and low density limits

A simplified hard-sphere equation of state has been developed, which meets the correct limit for close-packed conditions. It is shown that the proposed equation of state for hard spheres can represent accurately the computer simulation compressibility factor data and virial coefficients over a wide density range. The comparison of the results of the calculations using this equation, the Carnahan-Starling equation, and the two equations proposed by Iglesias-Silva and Hall, shows that the equation proposed here represents the compressibility factor data and the virial coefficients with better accuracy.     

A perturbed hard-sphere-chain equation of state for nematic liquid crystals and their mixtures with polymers

A perturbed hard-sphere-chain (PHSC) equation of state is presented to compute nematicisotropic equilibria for thermotropic liquid crystals, including mixtures. The equation of state consists of an isotropic term and an anisotropic term given by the Maier-Saupe theory whose contribution disappears in the isotropic phase. The isotropic contribution is the recently presented PHSC equation of state for normal fluids and polymers which uses a reference equation of state for athermal hard-sphere chains and a perturbation theory for the squarewell fluid of variable well width. The PHSC equation of state gives excellent correlations of pure-component pressure-volume-temperature data in the isotropic region and, combined with the Maier-Saupe theory, correlates the dependence of nematic-isotropic transition temperature on the pressure. Theory also predicts a nematic-isotropic biphasic region and liquid-liquid phase separation in a temperature-composition diagram of binary mixtures containing a nematic liquid crystal and a normal fluid or polymer. Theory and experiment show good agreement for pure fluids as well as for mixtures.     

Liquid-liquid equilibria and theta temperatures in homopolymer-solvent solutions from a perturbed hard-sphere-chain equation of state

The perturbed hard-sphere-chain (PHSC) equation of state is used to calculate liquid-liquid equilibria of binary nonpolar solvent/homopolymer systems exhibiting both an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST). Systems studied include polyisobutylene, polyethylene, and polystyrene solutions. Equation-of-state parameters of homopolymers are obtained by regressing the pressure-volume-temperature data of polymer melts. In polymer solutions, however, theory overestimates the equation-of-state effect which causes the LCST at elevated temperature. To correct the overestimated equation-of-state effect, an empirical adjustable parameter is introduced into the perturbation term of the PHSC equation of state. An entropy parameter is also introduced into the Helmholtz energy of the mixture to correlate quantitatively the dependence of critical temperatures on polymer molecular weight. For systems exhibiting a LCST, two adjustable parameters are required to obtain quantitative agreement of theoretical critical temperatures with experiment as a function of polymer molecular weight. For systems exhibiting both an UCST and a LCST, three adjustable parameters may be necessary. The need for so many empirical binary parameters is probably due to the oversimplified perturbation term which is based on the mean-field assumption. © 1996 John Wiley & Sons, Inc.     

An analytical perturbed equation of state for hard chain fluids: Application to n-alkanes and n-perfluoroalkanes

A completely analytical equation of state for pure hard chain fluids, derived on the basis of perturbation theory and reported in our previous work, is applied for the calculation of pVT properties and the prediction of vapour–liquid equilibria of n-alkanes and n-perfluoroalkanes. The molecules are treated as a chain formed from freely joined spheres which interact via an extended site-site square-well potential. The molecular parameters of compounds are obtained from the experimental compressibility factor data above the critical temperature. These parameters are capable of relatively satisfactory prediction of the vapour–liquid equilibrium coexistence curves of compounds. Linear relationships have been found between the potential parameters of fluids and their molecular weight, which make it possible to predict the pVT data and vapour–liquid phase equilibria of heavier compounds.     

Excess volume of mixing and equation of state theories

Equation-of state theories of Flory and of Sanchez and Lacombe describe both enthalpy and volume of mixing of binary systems using single component properties and only one binary parameter X₁₂. We have evaluated this parameter from literature enthalpy data for numerous mixtures of two aromatic hydrocarbons, of alkanes with aromatic compounds, and of alkanes with carbonyl compounds. We have used this X₁₂ for calculation of excess volumes and compared the results with our previously measured experimental data. The agreement was fair for mixtures of two nonpolar components. Nevertheless, mixtures containing either cyclohexane or benzene displayed anomalies that could be traced to special packing of molecules in these compounds when pure. For mixtures of carbonyl compounds with alkanes, the theories predicted the qualitative trends correctly, but the quantitative agreement was rather poor. These results tend to support a model in which the enthalpy(cohesive energy) is inversely proportional to volume (as in the theories considered) only for dispersive interaction. When polar-polar interactions are involved, the dependence of excess volume on the excess enthalpy is much weaker.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

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%.     

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%.     

Simulation and model development for the equation of state of self assembling non-additive hard chain–hard monomer mixture

Molecular dynamics simulations for a short hard chain composed of a head and three tail groups interacting with non-additive size interactions with a hard sphere solvent were performed. Different densities and non-additivities were used. The equation of state for this mixture was investigated and models based on the first-order thermodynamic perturbation theory (TPT1) and the polymeric analog of the Percus–Yevick approximation (PPY) were developed to predict the compressibility factor of the mixture. The models predicted the compressibilities of the mixtures accurately at zero and negative non-additivities. However, at positive non-additivities, the models overpredicted the compressibilities especially at high densities. The TPT1 model was generally more accurate in predicting the compressibility factor than the PPY model. Microphase separation was observed at high densities and positive non-additivities.     

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%.     

Experimental densities,vapor pressures,and critical point,and a fundamental equation of state for dimethyl ether

Densities, vapor pressures, and the critical point were measured for dimethyl ether, thus, filling several gaps in the thermodynamic data for this compound. Densities were measured with a computer-controlled high temperature, high-pressure vibrating-tube densimeter system in the sub- and supercritical states. The densities were measured at temperatures from 273 to 523 K and pressures up to 40 MPa (417 data points), for which densities between 62 and 745 kg/m³ were covered. The uncertainty (where the uncertainties can be considered as estimates of a combined expanded uncertainty with a coverage factor of 2) in density measurement was estimated to be no greater than 0.1% in the liquid and compressed supercritical states. Near the critical temperature and pressure, the uncertainty increases to 1%. Using a variable volume apparatus with a sapphire tube, vapor pressures and critical data were determined. Vapor pressures were measured between 264 and 194 kPa up to near the critical point with an uncertainty of 0.1 kPa. The critical point was determined visually with an uncertainty of 1% for the critical volume, 0.1 K for the critical temperature, and 5 kPa for the critical pressure. The new vapor pressures and compressed liquid densities were correlated with the simple TRIDEN model. The new data along with the available literature data were used to develop a first fundamental Helmholtz energy equation of state for dimethyl ether, valid from 131.65 to 525 K and for pressures up to 40 MPa. The uncertainty in the equation of state for density ranges from 0.1% in the liquid to 1% near the critical point. The uncertainty in calculated heat capacities is 2%, and the uncertainty in vapor pressure is 0.25% at temperatures above 200 K. Although the equation presented here is an interim equation, it represents the best currently available.     

A simple method for evaluation of parameters of the Bender equation of state from experimental data

A simple numerical method for evaluation of parameters (constants) of Bender equation of state for pure fluids is proposed. The minimisation of the objective function leads to a set of linear equations. The method employs experimental data on state behaviour (p–ρ–T) of fluid phases, vapour–liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas–liquid critical point. Results of the tests using data for two fluids (methane and n-pentane) are presented.     

An equation-of-state-based viscosity model for non-ideal liquid mixtures

A viscosity model based on the Eyring’s theory and a cubic equation of state (Peng–Robinson–Stryjek–Vera) has been applied to the correlation and prediction of experimental liquid viscosities of binary mixtures containing polar fluids within a wide range of temperature, pressure and composition (encompassing low-pressure and compressed liquid conditions). Highly non-idealities of the binary mixtures considered in this study were conveniently handled via the application of the Wong–Sandler approach for the mixing rules used in the cubic equation of state. The results obtained were highly satisfactory for various non-ideal binary mixtures over the whole composition range at a low pressure. The predictive capabilities of the present approach were also verified in the representation of liquid viscosities at elevated pressures preserving the same model parameters previously obtained at low pressure.     

A perturbed Yukawa chain equation of state for refractory liquid metals

The perturbed Yukawa chain equation of state (EoS) has been employed to calculate the liquid density of refractory metals over a wide range of temperatures and pressures. The model uses three independent parameters: m-segment number, σ-segment size, and ε/k-segment energy. For pure components, parameters have been obtained by fitting the models to experimental data on liquid densities. Our calculations on the liquid density of tantalum, rhenium, molybdenum, titanium, zirconium, hafnium and niobium from undercooled temperatures up to several hundred degrees above the boiling point and pressures ranging from 0 to 200?MPa reproduces very accurately the experimental pVT data.     

A proposed equation of correlation for the study of thermodynamic properties (density,viscosity, surface tension and refractive index) of liquid binary mixtures

The literature on the physicochemical properties of liquid binary mixtures shows that most such systems exhibit nonlinear behavior. As a result, rigorous data and equations capable of affording a reliable estimate of the behavior of such mixtures are needed.     

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Prediction of gas condensate properties by Esmaeilzadeh–Roshanfekr equation of state

The Esmaeilzadeh–Roshanfekr (ER) equation of state (EOS) is used to predict the PVT properties of gas condensate reservoir fluids. Three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as five samples from literature have been used to check the validity of the ER EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. In order to have an unbiased comparison between the ER and the Peng–Robinson (PR) equation of state, van der Waals mixing rules are used without using any adjustable parameters (k_ij = 0). Also, no pure component parameters are adjusted. The critical properties and acentric factor for plus-fraction are estimated by the Kesler–Lee, Pedersen et al. and Riazi–Daubert characterization methods. The results of dew point pressure calculations show that the ER EOS has smaller error than the PR EOS. For some mixtures, relative volume, gas compressibility factor and condensate drop-out in CVD and CCE test were also predicted. Comparison results between experimental and calculated data indicate that the ER EOS has smaller error than the PR EOS. The total average absolute deviation was found to be 0.82% and 2.97% for calculating gas compressibility factor and gas specific gravity in CVD test. Also, the total average absolute deviation was found to be 2.06% and 3.42% for calculating gas compressibility factor and relative volume in CCE test.