Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λ _ij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.     

Development of a perturbed hard-sphere equation of state for pure and mixture of ionic liquids

A perturbed hard-sphere equation of state (PHS EOS) was previously proposed to present the volumetric properties of ionic liquids by employing a variable parameter β being a function of acentric factor to justify the range of vdW dispersion forces (M. M. Papari, J. Moghadasi, S. M. Hosseini, F. Akbari, J. Mol. Liq. 158 (2011) 57–60). The main aim of the present study is to revise an attractive part of the preceding EOS by re-evaluating the above-mentioned variable parameter as well as the repulsive term. Two temperature-dependent parameters appearing in the revisited EOS have been determined from the corresponding states correlations using the interfacial properties of ILs, i.e., surface tension and liquid density, both at room temperature. The revisited EOS has been employed to model the volumetric properties of ionic liquids (ILs). The predictive power of the proposed model has been assessed by comparing the results obtained with 2189 experimental data points related to 24 ILs over a broad range of pressures and temperatures. The overall average absolute deviation (AAD) of the calculated densities from literature data was found to be 0.62 %. Furthermore, the revisited PHS EOS has been employed to model the volumetric properties of 23 mixtures including IL + IL and IL+ solvent over the vast range of temperatures. From 1580 data points of the binary mixtures of interest, the AAD of the correlated densities from the measurements was found to be 0.47 %.     

Thermodynamic properties of some ionic liquids using a simple equation of state

In this work, we have used a simple equation of state (EoS) to predict the density and other thermodynamic properties such as isobaric expansion coefficient, α_P , isothermal compressibility, κ_T, and internal pressure, P_i, for nine ionic liquids including trihexyl (tetradecyl) phosphonium chloride ([(C₆H₁₃)₃P(C₁₄H₂₉)][Cl]), trihexyl (tetradecyl) phosphonium acetate ([(C₆H₁₃)₃P(C₁₄H₂₉)][Ac]), trihexyl (tetradecyl) phosphonium bis {(trifluoromethyl) sulfonyl} amide ([(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂]), 1-butyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([bmim][NTf₂]), 1-hexyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([hmim][NTf₂]), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF₄]), 1-butyl-3-octylimidazolium tetrafluoroborate ([omim][BF₄]), 1-butyl-3-octylimidazolium hexafluorophosphate ([omim][PF₆]), and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF₆]) at different temperatures and pressures. A wide comparison with experimental and literature data has been made. The results show that this EoS can be used to reproduce and predict different thermodynamic properties of ionic liquids within experimental errors.     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Thermodynamic properties of the mixtures of some ionic liquids with alcohols using a simple equation of state

In the present work, we have used a simple equation of state called the GMA EoS to calculate the density of three ionic liquid mixtures including 1-butyl-3-methylimidazolum hexafluorophosphate, [BMIM] [PF₆] + methanol, 1-butyl-3-methylimidazolum tetrafluoroborate, [BMIM] [BF₄] + methanol, and [BMIM] [BF₄] + ethanol at different temperatures, pressures, and compositions. The isothermal compressibility, excess molar volumes, and excess Gibbs molar energy of these mixtures have been computed using this equation of state. The values of statistical parameters show that the GMA EoS can predict these thermodynamic properties very well within the experimental errors. The results show that isothermal compressibility of ionic liquids is lower than alcohols and the effect of temperature and pressure on the isothermal compressibility of ionic liquids is lower than alcohols. The excess molar volumes and excess molar Gibbs energy for these ionic liquid mixtures with alcohols are all negative at various temperatures and pressures over the whole composition range. The results have been interpreted in terms of intermolecular interactions and structural factors of the ionic liquids and alcohols.     

A perturbed hard-sphere equation of state for phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids

In this work, a perturbed hard-sphere equation of state has been employed to predict the pressure–volume–temperature properties of some phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids in compressed states. Two temperature-dependent parameters that appeared in the equation of state have been determined using the critical properties of abovementioned ionic liquids as the scaling constant, i.e., knowing only two available scaling constants is sufficient to utilize the proposed equation of state to this class of fluids. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 1 to 65 MPa. From 550 data points examined for the aforementioned ionic liquids, the total average absolute deviation, AAD was found to be 1.12%.     

Correlation of volumetric properties of binary mixtures of some ionic liquids with alcohols using equation of state

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to pure ionic liquids. Here we apply TM EOS based on statistical?Cmechanical perturbation theory to binary mixtures of ionic liquids. Three temperature-dependent quantities are needed to use the equation of state: the second virial coefficient, B ₂, effective van der Waals co-volume, b, and a scaling factor, ??. The second virial coefficients are calculated from a correlation that uses the normal boiling temperature and normal boiling density. ?? and b can also be calculated from the second virial coefficient by scaling. In this procedure, the number of input parameters, for calculation of B ₂, ??, and b reduced from 5 (i.e., critical temperature, critical pressure, acetric factor, Boyle temperature T _B, and the Boyle volume ?? _B) to 2 (i.e., T _bp and ?? _bp). At close inspection of the deviations given in this work, the TM EOS predicts the densities with a mean AAD of 1.69%. The density of selected system obtained from the TM EOS has been compared with those calculated from perturbed-hard-sphere equation of state. Our results are in favor of the preference of the TM EOS over another equation of state. The overall average absolute deviation for 428 data points that calculated by perturbed-hard-sphere equation of state is 2.60%.     

Modified equation of state extended to imidazolium-, phosphonium-, pyridinium-, pyrrolidinium- and ammonium-based ionic liquids

An analytical equation of state (EoS) has been previously employed by Hosseini and Sharafi (Ionics 17:511, 2011) for modelling of PVT data of some ionic liquids (ILs). In this work, we have extended the mentioned model to five classes of ILs by the use of alternative scaling constants for corresponding states correlation procedure. For this purpose, ILs involving imidazolium, phosphonium, pyridinium, pyrrolidinium and ammonium cations have been taken into account. From these, 1,294 experimental data points examined to show the reliability of the modified EoS. The comparison of predicted densities with the measured values over a broad range of temperature 293?C452 K and pressures up to 150 MPa led to the encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.73%. Moreover, to establish the predictive power of proposed model, the reproduced densities have been compared with those obtained by another literature work. Moreover, we have demonstrated the density behaviour of studied ILs in terms of alkyl chain length of imidazolium cation via proposed model.     

Modelling the phase equilibria of multicomponent mixtures containing CO2, alkanes,water, and/or alcohols using the quadrupolar CPA equation of state

ABSTRACT

In this work, a quadrupolar cubic plus association (qCPA) equation of state is evaluated for its ability to predict the phase equilibria of multicomponent mixtures containing CO₂ and alkanes, alcohols, and/or water. A single binary interaction parameter is employed in qCPA for all binary combinations. All parameters are based solely on pure fluid or binary mixture data and multicomponent data are used only to evaluate the predictions. The performance of qCPA is, for all mixtures, compared to CPA where CO₂ is considered to be either non-associating (inert), solvating or self-associating. In the latter two approaches, an additional adjustable parameter is employed for binary pairs of CO₂ and an associating compound. The results show that the predictions with qCPA are very similar to the best performing CPA approaches, even though the model uses fewer adjustable binary parameters. The predictions with qCPA and the best CPA approaches are typically satisfactory and predict the general behaviour of the systems. As expected, qCPA and CPA with solvation or association typically performs better than inert CPA for two- and three phase vapour–liquid and vapour–liquid–liquid equilibria. However, inert CPA yields the best results of all the models for the prediction of dew point pressures.     

Modelling interfacial properties of ionic liquids with ePC-SAFT combined with density gradient theory

Highlights

• Combination of ePC-SAFT with density gradient theory

• Calculation of interfacial properties of pure ILs in broad temperature range

• Quantitative predictions of surface tensions for ILs not used in κ parameter fitting

     

Theoretical study of Raman scattering from pure liquids

A theory is presented to study the Raman spectra of liquids formed by diatomic molecules in the fundamental spectral region. This theory is based on the fact that the Hamiltonian of a liquid sample is invariant under the operations of the full N-symmetric group. It is found, in particular, that the isotropic Raman scattering is a partially coherent and, if the vibrational rotational correlation is neglected, the anisotropic Raman scattering is a totally incoherent process.     

The self-consistent average phonon equation of state for ionic crystals

The self-consistent average phonon (SCAP) approximation was successful in describing the thermodynamic properties of monatomic solids. This formalism was extended to ionic crystals (specifically sodium chloride) at two levels of approximation: (1) the phonon frequencies replaced by a single average frequency, and (2) the phonon frequencies replaced by two average frequencies corresponding to the usual acoustic and optic phonons. In order to compare with earlier calculations and with experiments various forms of the interatomic potential (with polarization neglected) were used. The SCAP calculation is in good agreement with experiment at low and medium temperatures but underestimates the high temperature thermal expansion. It is concluded that the SCAP formalism with polarization included should give a good approximation to the thermodynamic properties of simple ionic crystals over the entire temperature range.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

Temperature effects on a new equation of state of solids

Recently we have proposed an isothermal equation of state of solids, and applied it to a variety of substances to show that it agrees with the isothermal pressure-volume data quite accurately up to ultrahigh pressures, and that its agreement with data is superior to the existing equations of state. Further, it has been shown that the bulk modulus and its first pressure derivative, extracted by it, are in excellent agreement with experiment. In the present study, temperature effect is added on this new equation of state, following a widely used approach involving the input of zero-pressure bulk moduli parameters and thermal expansion, all evaluated at a single reference temperature. The resultant temperature-dependent equation of state is applied to predict the isotherms over a wide range of temperature, the thermal expansion as a function of temperature, and the temperature dependence of the isothermal bulk modulus and its pressure derivative. These predictions are tested using literature data for four solids: sodium chloride, gold, molybdenum and tungsten. Good agreement is obtained between theory and data. Furthermore, the predictions are compared with those obtained from a similar temperature-dependent equation of state recently proposed, and the superior prediction capability of our model, in the P-V-T space, is demonstrated.