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.     

Modelling aqueous solutions near the critical point of water

We review the thermodynamic properties of dilute solution near the critical point of the solvent. Two examples are discussed, a solution of a non-electrolyte and a solution of an electrolyte. The limiting behavior of the electrolyte solutions is modelled with a Debye-Huckel term in the Helmholtz free energy. The partial molar properties, in particular the volume and isobaric thermal expansion are examined in detail. The derivation of these properties is introduced by considering the geometry of the thermodynamic surfaces near to and far from the critical point of the solvent. We conclude that the properties of solutions near the solvent critical point are dominated by that feature; solution properties cannot be adequately modelled without including the functional forms associated with the critical point.     

Calculation of surface tension of metals using density gradient theory and PC-SAFT equation of state

The Cahn-Hilliard theory was combined with PC-SAFT equation of state (EOS), in order to describe both the phase behaviors and the surface tension of different types of metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Fe, Zn, Cd, In, Sn, Pb, and Bi). The only two inputs of the theory are the Helmholtz free-energy density and the influence parameter. The PC-SAFT equation of state was applied to determine Helmholtz free-energy density and bulk properties. The influence parameter is obtained by fitting to the experimental data of surface tension. The results show a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data.     

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%.     

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.     

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.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

Simulation studies on mixtures of dipolar with nonpolar linear molecules II. A mixing rule for the dipolar contribution to the Helmholtz energy

In recent equations of state an explicit expression for the dipolar contribution to the Helmholtz energy F_D is used. If such equations are applied to mixtures the problem of mixing rules for F_D arises. As a solution, a “one-fluid dipole moment μ_x” is introduced which is based on perturbation theory. The accuracy of the approach is tested by simulation results for mixtures of dipolar with nonpolar linear molecules. In addition to the simulation runs from Part I (Müller et al. (1994)), results from 97 new NVT simulations are presented. Comparisons of pressures, internal energies, dipole energies and excess free energies from simulations with those obtained from the equation for F_D in combination with the one-fluid dipole moment μ_x shows good to excellent agreement.     

New volume translation for cubic equations of state

Peneloux's volume translation is found of not equal benefit depending on pressure and temperature ranges for which volumetric properties are represented (some ranges being unfortunately worse described after correction than before).     

Effect of combining rules for cubic equations of state on the prediction of double retrograde vaporization

In this work, the phenomenon of double retrograde vaporization (DRV) is simulated using the Peng–Robinson equation of state with the classical mixing rules and several combining rules for the cross-energy and cross-co-volume parameters. The binary interaction parameters are set equal to zero in all cases, i.e., the calculations are entirely predictive. An interesting conclusion is that the predictions using the classical combining rules (geometric mean rule for a_ij and arithmetic mean rule for b_ij) provide the best agreement with the experimental data for all the systems tested: methane + n-butane, methane + n-pentane, ethane + limonene, and ethane + linalool. Another interesting observation is that several combining rules for b_ij, other than the arithmetic mean rule, predict the existence of three phases in equilibrium in a very narrow temperature range close to the critical temperature of methane in the methane + n-pentane system, even though, literature data indicates that n-hexane is the first n-alkane to present partial liquid phase immiscibility with methane.     

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Examining the effect of binary interaction parameters on VLE modelling using cubic equations of state

Vapor-liquid equilibrium (VLE) data are important in the optimization of thermodynamic cycles. As energy concerns continue to grow, improving the efficiencies of power and refrigeration cycles is increasingly important. Numerical simulations using empirical equations of state provide an excellent alternative to time consuming experimental measurement of VLE data. However, it is important to understand the limitations of using correlative equations for data prediction. In this study, a water-ethanol mixture is simulated with various VLE models. Non-optimal binary interaction parameters are considered and model accuracy is evaluated in terms of average absolute percent deviation (%AAD) between simulated and experimental bubble and dew point pressures. For this system, it is found that as the correlative accuracy of a model increases, the predictive ability decreases. Specifically, the temperature dependence of the binary interaction parameters is shown to be an important consideration for the water-ethanol system when more complex combining rules are implemented.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

On the compatibility between vapor pressure data and the critical constants: Use of the van der Waals family of cubic equations of state to study the cases of 2-methoxyethanol and 2-ethoxyethanol

The performance of five cubic equations of state (EOSs) for the correlation of vapor-pressure data of 2-methoxyethanol and 2-ethoxyethanol are compared. The cubic EOSs considered are the van der Waals EOS, modified with Soave's approach (MvdW), the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR), and the two versions of the Peng-Robinson-Stryjek-Vera EOSs: PRSV and PRSV2. Three sets of critical constants for 2-methoxyethanol are considered and new acentric factor is proposed for this compound. New critical constants and acentric factor for 2-ethoxyethanol are proposed. Pure compound parameters for the PRSV and the PRSV2 EOSs for 2-methoxyethanol and 2-ethoxyethanol are evaluated using a genetic algorithm (GA) optimization technique. The results show the importance of using compatible information in vapor liquid equilibrium studies.     

Prediction of the thermodynamic properties of {ammonia + water} using cubic equations of state with the SOF cohesion function

The SOF cohesion function for cubic equations of state is based on the behavior of the residual energy of pure fluids. It contains two adjustable parameters for each component, which have been obtained for over 800 substances by regression of pure-fluid saturation pressures, and correlated in terms of a four-parameter corresponding states principle. In the present work, we compare the performance of this function and of the original Soave cohesion function with the Redlich-Kwong and Peng-Robinson equations of state in the prediction of vapor-liquid equilibria and enthalpy-composition diagrams for the polar system {ammonia + water}. We use simple van der Waals one-fluid mixing rules, linear for the covolume and quadratic for the cohesion parameter with one (symmetric) and two (asymmetric) binary interaction parameters. The non-linear least squares minimization algorithm lsqnonlin, in Matlab^®, is used to adjust the interaction parameters to phase equilibrium and enthalpy data taken from the IAPWS fundamental formulation. Upper and lower bounds of the optimized interaction parameters are obtained using Matlab^®bootstrap with 95% confidence of a normal distribution sampling. The validity of the parameters as functions of temperature is between the triple point of water and the critical point of ammonia. At lower temperatures, a rapid increase of statistical uncertainties is observed that can be attributed to the scarcity of phase equilibrium data.The two-parameter SOF cohesion function and the cubic equations of state are shown to give accurate predictions of the VLE and enthalpies of {ammonia + water}. Both equations of state give very similar results. Statistical analysis of the interaction parameters shows that their values (within the range of validity mentioned above) are effectively the same for both cohesion functions. At higher temperatures, however, extrapolation of the two cohesion functions gives different results, and correspondingly requires different interaction parameters.     

Association equation of state (AEOS) based on aggregate formation for pure substance

Based on the statistical mechanical theories and by using the concept of grand canonical ensemble a new equation of state for aggregate formations in the association fluids has been proposed. The compressibility factor for aggregate formation in an association fluid is represented by the following equation:

Z=Z^dis+Z^agg-1$Z=Z^{\text{dis}}+Z^{\text{agg}}-1$

Vapor–liquid equilibrium data and critical points for the system H2S+COS. Extension of the PSRK group contribution equation of state

Isothermal vapor–liquid equilibrium data for the binary system hydrogen sulfide+carbonyl sulfide were measured in the temperature range from 232 to 293 K using the static-synthetic technique. From the isothermal P−x data, the azeotropic conditions were derived. The critical line of this system was visually detected in a flow apparatus. Interaction parameters for this binary system were fitted simultaneously to all the experimental VLE and critical data for the Predictive Soave–Redlich–Kwong group contribution equation of state.     

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: Binary mixtures with CO2

In Part I of this series of articles, the study of H₂S mixtures has been presented with CPA. In this study the phase behavior of CO₂ containing mixtures is modeled. Binary mixtures with water, alcohols, glycols and hydrocarbons are investigated. Both phase equilibria (vapor-liquid and liquid-liquid) and densities are considered for the mixtures involved. Different approaches for modeling pure CO₂ and mixtures are compared. CO₂ is modeled as non self-associating fluid, or as self-associating component having two, three and four association sites. Moreover, when mixtures of CO₂ with polar compounds (water, alcohols and glycols) are considered, the importance of cross-association is investigated. The cross-association is accounted for either via combining rules or using a cross-solvation energy obtained from experimental spectroscopic or calorimetric data or from ab initio calculations. In both cases two adjustable parameters are used when solvation is explicitly accounted for. The performance of CPA using the various modeling approaches for CO₂ and its interactions is presented and discussed, comparatively to various recent published investigations. It is shown that overall very good correlation is obtained for binary mixtures of CO₂ and water or alcohols when the solvation between CO₂ and the polar compound is explicitly accounted for, whereas the model is less satisfactory when CO₂ is treated as self-associating compound.     

Theoretical investigations on analytical potential energy function and spectroscopic parameters for the state b3Πu of dimer 7Li2

The SAC‐CI (symmetry‐adapted‐cluster configuration‐interaction) method presented in Gaussian 03 program package is applied to investigate the adiabatic potential energy curves (PECs) of ⁷Li₂(b³Π_u). These calculations are performed at numbers of basis sets, such as 6‐311++G(3df,3pd), 6‐311++G(2df,2pd), 6‐311++G(df,pd), D95V++, D95(3df,3pd), D95(d,p), cc‐PVTZ, 6‐311++G and 6‐311++G(d,p). All the ab initio calculated points are fitted to the analytic Murrell‐Sorbie functions and then used to compute the spectroscopic parameters. The analytic potential energy function (APEF) for this b³Π_u state is reported. By comparison, the spectroscopic parameters reproduced by the APEF attained at 6‐311++G(2df,2pd) are found to be very close to the latest experimental findings. With the APEF obtained at the SAC‐CI/6‐311++G(2df,2pd) level of theory, a total of 62 vibrational states is found when J = 0. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants for these vibrational states are also reported. The reasonable dissociation limit for this state is deduced using the calculated results at present. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007