A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

Quintic equation of state for pure substances in sub- and supercritical range

A new quintic equation of state (EOS) for pure substances and mixtures is proposed. The equation is based on critical parameters and one saturation point. The proposed Q5EOS is a generalisation of many cubic equations of state. Equation Q5 has five parameters, four of which are temperature-independent. The temperature-dependent parameter a is expressed by a relation based on a simple power function. Parameters defining this function can be calculated from saturation data, Boyle temperature and supercritical data.     

Modification of the Peng–Robinson equation of state for helium in low temperature regions

Helium shows the nearest behaviour to ideal gas in the room conditions. In contrast, thermodynamic behaviour of helium in the critical region, in which its liquefaction is possible, is extremely complicated. The equation of state (EOS), which is in common use for helium, is the modified Benedict–Webb–Rubin (MBWR) EOS developed by McCarty and Arp which is a 13th-order equation with 32 substance-dependent parameters. MBWR is a complicated EOS and its use is time consuming. In this work, the modified Peng–Robinson EOS introduced by Feyzi et al. is customised with 10 adjustable parameters for helium in the temperature range of 2.20–15.20 K and pressures up to 16 bar. The proposed EOS is able to predict the properties of helium in the vapour–liquid equilibrium (VLE) conditions and in the single gas-phase region. In addition, a temperature-dependent correlation for constant pressure heat capacity of helium from very low up to normal temperatures is proposed. The liquefaction process of helium, which is being done by cooling it to very low temperatures by passing through a Joule–Thomson valve, is predicted by the proposed EOS. Very accurate results are observed.     

Use of heat capacities for the estimation of cubic equation-of-state parameters—application to the prediction of very low vapor pressures of heavy hydrocarbons

Improvement in the prediction of very low vapor pressures is checked by introducing heat capacity data into the estimation of cubic equation-of-state (EOS) parameters. As the key parameter is the temperature-dependent parameter a, several expressions (mainly of exponential form) were investigated. All of them were chosen in order to show a consistent behavior for the two considered properties (vapor pressures and heat capacities). The cubic EOS used as an illustration is of the Peng–Robinson type applied to heavy hydrocarbons. No satisfactory refinement in the prediction of the very low vapor pressures was observed in comparison with the results obtained by extrapolating the EOS from medium to very low pressures. This work has, however, the following benefits: (1) to point out the changes that should be made to improve these predictions; (2) to inform on the accuracy that may be obtained if vapor pressures of heavy organic compounds are predicted from heat capacity data as the sole alternative for estimating the temperature-dependent parameter a of a cubic EOS; (3) to confirm the reliability of the cubic group-contribution (GC)-based EOS proposed by Coniglio et al. [Ind. Eng. Chem. Res. 39 (2000) 5037] when extrapolated for modeling crude oils or gas condensates encountered in the petroleum industry.     

Modification of PSRK mixing rules and results for vapor–liquid equilibria, enthalpy of mixing and activity coefficients at infinite dilution

The predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) is a well-established method for the prediction of thermodynamic properties required in process simulation. But there are still some problems to be solved, e.g. the reliability for strong asymmetric mixtures of components which are very different in size. The following modifications are introduced in the PSRK mixing rules: the Flory–Huggins term in the mixing rule for the EOS parameter a, and the combinatorial part in the UNIFAC model are skipped simultaneously; a nonlinear mixing rule for the EOS parameterb, instead of the linear mixing rule, is proposed. With these two modifications better results are obtained for vapor–liquid equilibria and activity coefficients at infinite dilution for alkane–alkane systems, specially for asymmetric systems. In order to obtain better results for enthalpy of mixing, temperature-dependent parameters are used. Group interaction parameters have been fitted for several groups, and the results are compared with the Modified UNIFAC (Dortmund), and the PSRK methods.     

PVT properties of imidazolium-, phosphonium-, pyridinium- and pyrrolidinium-based ionic liquids using critical point constants

Song and Mason equation of state (EOS) with a simple modification has been extended to modelling PVT properties of ionic liquids (ILs). The considered ILs are [C₁mim][MeSO4], [C₁mim][CH₃OC₂H₅SO₄], [C₁mim][(CH₃)₂PO₄], [C₂mim][MeSO4], [C₂mim][BF₄], [C₂mim][SCN], [C₂eim][NTf₂], [C₄mim][C(CN)₃], [C₄mim][CF₃SO₃], [C₄mim][SCN], [C₅mim][NTf₂], [C₈mim][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Cl], [(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Ac], [C₃mpyr][NTf₂], [C₄mpyr][NTf₂] and [Py][C₂H₅OC₂H₄SO₄]. Three temperature-dependent parameters in the proposed EOS have been scaled as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just critical temperature and critical density is sufficient to predict the PVT properties of these ILs. The overall average absolute deviation of calculated densities from literature values for 1347 data points of 18 ILs was found to be 0.58%. The predicted density of ILs from proposed EOS has been compared with those obtained by other literature work. Moreover, we indicate that the Zeno line regularity can well be predicted by proposed model for ILs.     

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%.     

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 Density,Surface Tension,and Viscosity of Quaternary Ammonium-Based Ionic Liquids ([N222(n)]Tf2N) by Means of Artificial Intelligence Techniques

In this work, thermophysical properties of quaternary ammonium-based ionic liquids (ILs) including density, surface tension, and viscosity are produced by two powerful artificial intelligence techniques: genetic function approximation (GFA) and artificial neural network (ANN). In proposed GFA and ANN models, the critical temperature and water content of studied ILs ([N_222(n)]Tf₂N with n = 5, 6, 8, 10, and 12) as well as operation temperature were given as the input parameters and the density, surface tension, and viscosity were predicted as the output results. The obtained results reveal that the selected input parameters are appropriate for prediction of thermophysical properties of quaternary ammonium-based ILs. In addition, the high statistical quality represented by various criteria and the low prediction errors of the presented models indicate that they can accurately predict the density, surface tension, and viscosity of new ILs without recourse to experimental data.     

Towards understanding the effect of electrostatic interactions on the density of ionic liquids

In order to have a better understanding on the electrostatic contribution to the thermodynamic property of ionic liquids (ILs), a two-parameter equation of state (EOS) is developed on the basis of hard sphere perturbation theory by accounting for the dispersion interaction with Cotterman et al.’s EOS for L-J fluid and electrostatic interaction with mean spherical approximation (MSA) approach. The EOS is applicable for the density correlation of molecular liquids, and the resulting parameters, viz. Lennard–Jones dispersive parameter ?/k and soft-core diameter σ, can be used to predict the density of molecular mixtures and the corresponding ILs. The results indicate that the density of IL is always about 10% higher than the corresponding stoichiometric molecular mixture with which the IL is produced as an ionic adduct, for example, IL 1-methyl-3-methylimidazolium dimethylphosphate ([MMIM][DMP]) versus equimolar mixture of 1-methylimidazole (MIM) and trimethylphosphate (TMP). Furthermore, the density enhancement of ILs with respect to their corresponding stoichiometric molecular mixtures can be well represented by the electrostatic contribution among ionic species involved.     

Synthesis and Computational Study of Phosphorus Ionic Liquids

The synthesis of six tetraalkylammonium bromopentachlorophosphoride ionic liquids (ILs) is reported here. Their structures were determined by IR, ¹H NMR, and ¹³C NMR spectroscopy. Moreover, thermogravimetric (TG) and differential thermal analysis (DTA) were used to investigate the thermal behavior of these compounds. The results show that these ILs have excellent thermal stability below 145°C, and by decreasing the size of the alkyl groups, the thermal stabilities will increase. Along with the experimental study, these compounds have been studied computationally at the B3LYP/LANL2DZ level of theory using the PC GAMESS/Firefly program package. From these calculations, optimized geometries, molecular parameters, and vibrational spectra of ILs have been calculated. In addition, calculated frequencies are compared with the experimental frequencies after correction by the appropriate scaling factor. This comparison shows that our theoretical data are in good agreement with the experimental results.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

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.     

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 three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Extremely Low Vapor-Pressure Data as Access to PC-SAFT Parameter Estimation for Ionic Liquids and Modeling of Precursor Solubility in Ionic Liquids

Precursor solubility is a crucial factor in industrial applications, dominating the outcome of reactions and purification steps. The outcome and success of thermodynamic modelling of this industrially important property with equations of states, such as Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), vastly depends on the quality of the pure-component parameters. The pure-component parameters for low-volatile compounds such as ionic liquids (ILs) have been commonly estimated using mixture properties, e. g. the osmotic pressure of aqueous solutions. This leads to parameters that depend on the solvent, and transferability to other mixtures often causes poor modeling results. Mixture-independent experimental properties would be a more suitable basis for the parameter estimation offering a way to universal parameter sets. Model parameters for ILs are available in the literature [10.1016/j.fluid.2012.05.029], but they were estimated using pure-IL density data. The present work focuses on a step towards a more universal estimation strategy that includes new experimental vapor-pressure data of the pure IL. ILs exhibit an almost negligible vapor pressure in magnitude of usually 10⁻⁵ Pa even at elevated temperatures. In this work, such vapor-pressure data of a series of 1-ethyl-3-methyl-imidazolium-based [C₂mim]-ILs with various IL-anions (e. g. tetrafluoroborate [BF₄]⁻, hexafluorophosphate [PF₆]⁻, bis(trifluoromethylsulfonyl)imide [NTf₂]⁻) were experimentally determined and subsequently used for PC-SAFT parameter estimation. The so-determined parameters were used to predict experimental molecular precursor solubility in ILs and infinitely diluted activity coefficients of various solvents in ILs. The parameters were further compared to modeling results using classical parametrization methods (use of liquid-density data only for the molecular PC-SAFT and the ion-based electrolyte PC-SAFT). As a result, the modeled precursor solubilities using the new approach are much more precise than using the classical parametrization methods, and required binary parameters were found to be much smaller (if needed). In sum, including the pure-component vapor-pressure data of ILs opens the door towards parameter estimation that is not biased by mixture data. This procedure might be suitable also for polymers and for all kind of ionic species but needs extension to ion-specific parametrization in the long term.     

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%.     

由L-J流体的FMSA状态方程计算流体的PVT性质

运用Tang等提出的Lennard-Jones (L-J)流体两参数的一阶平均球形近似(FMSA)状态方程, 计算了流体的汽液共存相图和饱和蒸汽压曲线, 以及非饱和区的PVT性质, 并与文献数据进行比较. L-J参数由Tr＜0.95的汽液相共存数据回归得到. 计算结果表明, 对于分子较接近球形的流体, 除临界点附近外, 该方程可以在较大的温度和压力范围内计算真实流体的PVT性质, 结果满意. 对于球形分子, 该方程的精确度随分子尺寸的变大基本保持稳定. 该方程不适用于强极性物质. 在高密度区, 该方程的计算结果明显优于P-R方程. 对于分子偏离球形较远的流体, 该方程的适用性变差, 此时要考虑分子形状的影响, 可采用三参数的FMSA状态方程进行计算.     

Finite-element simulation of temperature-dependent three-point bending process of glass

Simulation of strains and stresses distributions in the glass subjected to a bending load during heat treatment is presented in the paper. The main objective of the work is to combine the temperature-dependent experimental test of three-point bending with simulation of this test and to apply inverse analysis to determine the properties of glass. The thermo-mechanical analysis (TMA) was used to test a temperature-dependent glass deformation. The Adina finite element software was used for simulations of the viscous flow. Two parameters in the Williams–Landell–Ferry (WLF) equation were identified by optimization of the square root error between measured and predicted deflection of the sample. Performed experiments and simulations yielded the values of these coefficients: C ₁ = 26.3 and C ₂ = 62.7. The proposed model with the optimized coefficients confirmed good agreement with the experimental data.     

羟烷基胺功能化离子液体吸收SO_2的量子化学计算(英文)

采用量子化学中的密度泛函理论(DFT)对羟烷基胺离子液体(HyAAILs)与二氧化硫(SO2)的相互作用进行了研究.通过几何结构优化,电荷分布和热力学参数计算等来确定离子液体中能够有效吸收SO2的官能团.HyAAILs与SO2反应形成平均距离为0.240nm的S—N键,导致电荷从ILs转移到SO2以及S—O键长和O—S—O键角的改变.气态和液态模型的计算结果表明,标准吉布斯函数变(△G苓)主要取决于阳离子的结构和分子质量.阳离子结构影响了吸收反应能垒,对于三种阳离子体系的反应活化能顺序为:Ea(secondary)Ea(tertiary)Ea(primary).理论计算结果得到了实验数据的验证,羟乙基伯胺离子液体吸收的SO2理论摩尔分数与文献中的实验数据非常接近.本研究提供了一种预测和验证功能离子液体性质的有效方法.     

Ionic liquid-alkane association in dilute solutions

Enthalpies and entropies of transfer were measured by gas chromatography for dilute solutions of a homologous series of eight even n-alkanes (from octane to docosane) into six different ionic liquids (ILs) (namely, 1-butyl-3-methylimidazolium chloride, bromide, iodide, triflate and hexafluorophosphate; plus N-butylmethylpyridinium bis {(trifluoromethyl) sulfonyl}-imide) over the 80–150 °C temperature range, all ILs being in the liquid state. Over a narrow concentration range, the entropic change may be consistent with a solvophobic association model of n-alkanes in ILs. A very simple model is proposed to account for the thermodynamic data. This approach can be used to approximate interionic distances and possible dielectric constants for ILs. Although the model may have some use in dilute alkane-IL solutions, more sophisticated models, particularly for the enthalpic contributions, are desirable.