Extended Real Associated Solution Research Articles

Application of ERAS-model and PFP theory on excess and deviation properties for binary systems of ionic liquid + amine derivatives

Thermodynamics of mixtures includes ionic liquid 2-hydroxyethylammonium propionate [2-HEAPr] + 1-propanol, 3-amino-1-propanol [AP], 1-amino-2-propanol [MIPA], and monoethanolamine [MEA] were studied. Density ρ, speed of sound u, and refractive index nD of pure and mixtures were measured at T = (298.15, 308.15, 318.15) K. Excess molar volume VmE, excess partial molar volume Vm,iE, excess thermal expansion coefficient αE, isothermal coefficient of excess molar enthalpy (∂Hm∂P)T,x, deviations in isentropic compressibility Δ ks, and refractive index Δ nD were calculated and data correlated with Redlich-Kister polynomial relation. The Prigogine-Flory-Patterson (PFP) and Extended Real Associated Solution (ERAS) models were applied to analyze intramolecular and intermolecular interactions between like and unlike molecules. The accuracy of theoretical models were found to be in agreement with empirical results. Finally, the study confirmed the structures of the ILs using FT-IR and HNMR analysis.

Physicochemical and acoustic characterization of binary mixtures of tetraalkylammonium bromide: PEG based DES and water

In modern green chemistry, Deep eutectic solvents (DESs) have gain appreciable recognition as an analogues of ionic liquids (ILs) due to inexpensive and easy to handle preparation method. DESs exhibit similar physiochemical properties to ILs and considered as a suitable alternative to volatile organic solvents. In present study, DESs were formulated by complexing HBA: Tetraethylammonium bromide and Tetrapropylammonium bromide and HBD: Polyethylene glycol of average molecular weight (200/400/600) in 1:2 M ratio. The densities (ρ), speeds of sound (u) of pure DESs and their binary mixtures with H2O were collected as a function of DES concentration and temperature. The excess molar properties: VmE and Ks,mE were calculated using these data and fitted to the Redlich-Kister equation to estimate standard deviation between the experimental and calculated values of excess molar properties. The trends of variation in calculated values of VmE and Ks,mE were interpreted in light of temperature and DES: H2O interactions occurring within the binary mixtures. The PFPT (Prigogine-Flory-Patterson Theory) and ERAS (Extended Real Associated Solution Model) were applied to evaluate the validity of theories to predict VmE for presently studied binary mixtures.

Relevance of the thermodynamic ERAS model for liquid mixtures with components exhibiting a small degree of self-association

The thermodynamic extended real associated solution (ERAS) model is reviewed and modified to accommodate weakly associating components. ERAS is a theoretical scheme applied to binary liquid mixtures whereby certain physically meaningful parameters such as the association equilibrium constants, species reduced volume and energy terms may be determined by optimization against the experimental excess molar volumes and enthalpies. The implicit assumption used for any non-associating molecule B is to routinely set the hydrogen-bonding energy ΔhB*, reaction volume ΔvB* and association constants KB to zero. It is proven here that such assignments lead to singularities in the ERAS parameters that are featured in the excess state functions used. A series of optimizations using the results of conductor-like screening model for real solvents (COSMO-RS) on the excess enthalpy HE of dimethoxymethane in binary mixtures with a series of alcohols are determined, and the parameters ΔhB*, ΔhAB* (mixed enthalpy of reaction) and XAB (interaction parameter) are determined. It is shown that the stipulated range of XAB values from ERAS theory requires minor modification if the above assumptions are not made. The magnitude of the computed variables are shown to be physically reasonable. The Bondi group averaged estimates for si, the ratio of the van der Waals (vdW) surface area to the vdW volume for molecule i, are contrasted against the more specific and reliable derivations from quantum calculations when calculating the excess functions. The degree of correlation is improved using the latter si values. We conclude that the results of the optimizations indicate that the ERAS model can be extended even to weakly self-associating components previously considered impossible in especially engineering thermodynamical applications, with the above modifications and refinements.

Experimental and theoretical excess molar properties of imidazolium based ionic liquids with isomers of butanol

The experimental densities (ρ), speeds of sound (u), and refractive indices (nD) of binary mixtures of 1-octyl-3-methylimidazolium tetrafluoroborate ([C8mim][BF4]) with isomers of butanol (1-butanol, 2-methyl-1-propanol, and 2-methyl-2-propanol) were measured at 0.1MPa and at 298.15, 308.15 and 318.15K. Excess molar volumes (VmE), excess molar isentropic compressibilities (Ks,mE), and deviations in refractive index (ΔϕnD) were calculated from the experimental data and were fitted to the Redlich–Kister polynomial equation. The results have been interpreted in terms of interstitial accommodation, ion–dipole interactions, formation of the hydrogen bonds, and structural factors involved in the mixture of ionic liquid and molecular organic solvents. Various mixing rules were used to predict the refractive indices and the data have been compared with the experimental results. In addition, analysis of the present VmE data were done through the Prigogine–Flory–Patterson (PFP) theory and the extended real associated solution (ERAS) model.

Volumetric behavior of the ternary system (methyl tert-butyl ether + methylbenzene + butan-1-ol) and its binary sub-system (methyl tert-butyl ether + butan-1-ol) within the temperature range (298.15 to 328.15) K

Values of the density and speed of sound were measured for the ternary system (methyl tert-butyl ether+methylbenzene+butan-1-ol) within the temperature range (298.15 to 328.15)K at atmospheric pressure by a vibrating-tube densimeter DSA 5000. Two binary sub-systems were studied and published previously while the binary sub-system (methyl tert-butyl ether+butan-1-ol) is a new study in this work. Excess molar volume, adiabatic compressibility, and isobaric thermal expansivity were calculated from the experimental values of density and speed of sound. The excess quantities were correlated using the Redlich–Kister equation. The experimental excess molar volumes were analyzed by means of both the Extended Real Associated Solution (ERAS) model and the Peng–Robinson equation of state. The novelty of this work is the qualitative prediction of ternary excess molar volumes for the system containing auto-associative compound and two compounds that can hetero-associate. The combination of the ERAS model and Peng–Robinson equation of state could help to qualitatively estimate the real behavior of the studied systems because the experimental results lie between these two predictions.

Thermodynamics of mixtures containing amines: XIII. Application of the ERAS model to cyclic amine + alkane mixtures

Primary or secondary cyclic amine+alkane mixtures have been investigated in the framework of the ERAS (Extended Real Associated Solution) model. The corresponding ERAS parameters are reported. All the amines considered have the same equilibrium constant (KA=0.75). Cyclopropylamine, cyclopentylamine, cyclohexylamine and pyrrolidine are characterized by the same enthalpy of self-association (ΔhA*=−15 kJ mol−1). Piperidine and hexamethyleneimine show a less negative ΔhA* value (−13kJmol−1). Experimental data on excess enthalpies, HmE, volumes, VmE, and isobaric heat capacities, CpmE, reveal the existence of physical interactions and structural effects in the studied solutions. The latter lead to values of self-association of pure amines, ΔvA*, which may depend on the solvent in systems with a given amine. Although the model overestimates the ΔhA* values, the relatively high values of the physical parameters XAB remark the importance of physical interactions. ERAS describes correctly the excess functions HmE, VmE, CpmE and GmE (molar Gibbs energy), and the enthalpy of vaporization of pure amines. Nevertheless, discrepancies with experimental data are found for the concentration dependence of VmE and GmE of some mixtures including cyclic primary amines.

Isobaric, isothermal theoretical investigation and examination of different prediction equations on some physicochemical properties in PEG liquid polymer system

Densities, viscosities and refractive indices of the {poly(ethylene glycol) 200+ethanol} binary liquid system were determined at three temperatures of (298.15, 303.15, and 308.15)K. From the experimental results, the excess molar volume was obtained and correlated with the Prigogine–Flory–Patterson (PFP) and Extended Real Associated Solution (ERAS) models. Several isobaric and isothermal properties consisting of the isobaric thermal expansion coefficient, excess molar isobaric expansion, excess molar isobaric heat capacity, isothermal coefficient of excess molar enthalpy, activation energy of flow, electron polarizibility, and Gibbs energy of activation were calculated from the experimental measurements. Moreover, the viscosity and refractive index values were correlated and predicted with different semi-empirical equations. To assess the validity of these proposed equations, comparisons were made between the experimental and predicted values.

Volumetric behaviour of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system and its binary sub-systems within the temperature range (298.15–328.15) K

Densities and speeds of sound of the (2,2,4-trimethylpentane+methylbenzene+butan-1-ol) ternary system as well as all its binary sub-systems were measured at four temperatures, namely 298.15K, 308.15K, 318.15K, and 328.15K at atmospheric pressure by a vibrating-tube densimeter DSA5000. The binary (isooctane+toluene) system was studied previously. Excess quantities (molar volume, adiabatic compressibility, and isobaric thermal expansivity) of the mixtures studied were calculated from the experimental densities and speed of sounds. The excess molar volume data were correlated using the Redlich–Kister equation. Both the positive and S-shaped excess molar volume curves were found for the systems studied. The excess molar volumes versus concentration of binary systems differed in the shape and temperature dependence. The experimental binary data were compared with literature data. The experimental excess molar volumes were analyzed by means of the Extended Real Associated Solution (ERAS) model. The experimental data and the ERAS model can help to estimate real behaviour of the systems studied.

The excess molar properties of {x1[C6min][BF4] + x22-propanol}: Application of ERAS model

Density, ρ, and viscosity, η, of pure 1-hexyl-3-methylimidazoliumtetrafluoroborate ([C6mim][BF4]), 2-propanol, and binary mixture of {x1[C6mim][BF4]+x22-propanol} were measured at atmospheric pressure and in the temperature range of (293.15 to 333.15) K. The excess molar volume, VmE, thermal expansion coefficient, αp, excess thermal expansion coefficient, αpE, and isothermal coefficient of excess molar enthalpy (∂HmE/∂p)T, x, were calculated from the experimental values of density. The excess molar volumes are negative over the entire mole fraction range for this mixture and increase with increasing temperature. These data have been used to examine the applicability of Extended Real Associated Solution (ERAS) model in correlating the excess molar volume of the binary mixture. The viscosity values of the binary mixture were calculated via McAllister equation and the obtained results show a good agreement between the experimental and the calculated values in the whole composition range and all temperatures, so that the relative deviations are rarely more than 2%. The excess molar properties were correlated with the Redlich–Kister equation.

Volumetric properties of binary mixtures of tributylamine with benzene derivatives and comparison with ERAS model results at temperatures from (293.15 to 333.15) K

Binary mixtures of tributylamine with aromatics (toluene, ethylbenzene, o-xylene, m-xylene, p-xylene and nitrobenzene) were selected in order to investigate intermolecular interactions by calculation of their excess molar volume V m E , from density measurements. Thermal expansion coefficients α p , and their excess values of α E , were obtained from the density data. The V m E values were positive for all the mixtures except for the (tributylamine + nitrobenzene) binary mixture over the entire range of composition and lower temperatures and become more positive with rising temperature. At high temperatures, sigmoidal behavior was observed for the mixture of (tributylamine + o-xylene). The mixture of (tributylamine + nitrobenzene) shows negative values for V m E and become more negative with increasing temperature. The experimental data were correlated to Redlich–Kister equation. In order to characterize the V m E values, the extended real associated solution (ERAS) model was applied at different temperatures.

Application of the extended real associated solution (ERAS) theory to excess molar enthalpies of benzaldehyde + 1-alkanols (C1 to C5) at T = 298.15 K

This paper reports excess molar enthalpies, HmE, for the binary mixtures of {1-alkanols (2), namely, {methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol} with benzaldehyde (1)} at T=298.15K at ambient pressure over a whole range of mole fraction. The sign of HmE for all systems are positive and the magnitude of HmE values with increasing of chain length, increase. The Redlich–Kister polynomial equation was used to correlate HmE. The excess partial molar enthalpies of benzaldehyde, Hm,1E, excess partial molar enthalpies of 1-alkanols (C1 to C5), Hm,2E, and excess partial molar enthalpies at infinite dilution, Hm,iE,0, are calculated according to experimental excess molar enthalpies and Redlich–Kister polynomial equation. The extracted date were used to evaluated the so-called intermolecular interaction functions ∂Hm,iE/∂xi and ∂Hm,iE/∂xj in terms of enthalpy. The ERAS, Wilson and NRTL models have been applied for describing the HmE.

Volumetric and viscometric properties of binary mixtures of {methyl tert-butyl ether (MTBE) + alcohol} at several temperatures and p = 0.1 MPa: Experimental results and application of the ERAS model

Densities and viscosities of binary mixtures of {methyl tert-butyl ether (MTBE) + methanol, or +ethanol, or +1-propanol, or +2-propanol, or +1-butanol, or +1 -pentanol, or +1 -hexanol} have been determined as a function of composition at several temperatures and atmospheric pressure. The temperatures studied were (293.15, 298.15, 303.15, and 308.15) K. The experimental results have been used to calculate the excess molar volume ( V m E ) and viscosity deviation (Δ η). Both V m E and Δ η values were negative over the entire range of mole fraction for all temperatures and systems studied. Moreover, the V m E values have been used to test the applicability of the Extended Real Associated Solution (ERAS) model.

Application of the ERAS model to volumetric properties of binary mixtures of banana oil with primary and secondary alcohols (C1–C4) at different temperatures

The densities of binary mixtures of {isoamyl acetate + alcohols (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, and 2-butanol)}, including those of pure liquids, over the entire composition range were measured at temperatures (293.15 to 333.15) K and atmospheric pressure by means of a vibrating-tube densimeter. The excess molar volume, V m E , thermal expansion coefficients, α, and their excess values, α E, were calculated from density data. The V m E values are positive over the entire range of composition and temperature and become more positive with increasing temperature for all of the mixtures except for the (isoamyl acetate + methanol) mixture. The V m E values were correlated by Redlich–Kister equation and the extended real associated solution (ERAS) model was used for describing V m E values at T = 303.15 K.

Densities and Excess Molar Volumes of Binary and Ternary Mixtures Containing Acetonitrile + Acetophenone + 1,2-Pentanediol: Experimental Data, Correlation and Prediction by PFP Theory and ERAS Model

Densities were determined experimentally over the entire range of composition at 298.15 K for the ternary system acetonitrile (1) + acetophenone (2) + 1,2-pentanediol (3) and for the three corresponding binary systems. Excess molar volumes were calculated for the binary and the ternary systems. These results were fitted to variable-degree polynomials. Further, the Prigogine-Flory-Patterson (PFP) theory and Extended Real Associated Solution (ERAS) model were applied to \(V_{m}^{\mathrm{E}}\) for the binary mixtures of acetonitrile + acetophenone, acetonitrile + 1,2-pentanediol and acetophenone + 1,2-pentanediol, and the findings compared with the experimental results.

Application of the extended real associated solution (ERAS) model to excess molar volumes of binary mixtures of (alkoxyethanols + 1-alkanol)

Excess molar volumes of binary mixtures of diethylene glycol monomethyl ether or triethylene glycol monomethyl ether or diethylene glycol monoethyl ether or triethylene glycol monoethyl ether + 1-alkanol at 298.15 K and atmospheric pressure over whole composition range have been used for application of extended real associated solution (ERAS) model which accounts for hydrogen bonding effects as well as for free volume effects in associating mixtures. The ERAS model results obtained by adjusting the model parameters indicates strong hydrogen bonding effects between unlike molecules. The value of cross association constant K AB illustrates the fact that cross associates are more pronounced in mixture of lower 1-alkanol.

Volumetric, transport, and acoustic properties of binary mixtures of 2-methyl-1-propanol with hexadecane and squalane at T = (298.15, 303.15, and 308.15) K: Experimental results, correlation, and prediction by the ERAS model

Density ρ, speed of sound u, and viscosity η of the binary systems 2-methyl-1-propanol + hexadecane and 2-methyl-1-propanol + squalane (2,6,10,15,19,23-hexamethyltetracosane) have been measured over the entire range of composition at T = (298.15, 303.15, and 308.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyzer Anton Paar model DSA-5000 and Ubbelohde suspended level viscometer. Excess molar volume V m E , excess molar isentropic compressibility K S , m E , and deviations of the speed of sound u D from their ideal values u id and excess thermal expansion coefficient α E were evaluated from the experimental results obtained. These derived properties were fitted to variable-degree polynomials. Further, the Extended Real Associated Solution (ERAS) model has been applied to V m E for the present binary mixtures along with (2-methyl-1-propanol + hexane, + octane and + decane) and the findings are compared with the experimental results.

Response to “Comment on ‘New statistical mechanical model for calculating Kirkwood factors in self-associating liquid systems and its application to alkanol+cyclohexane mixtures’ ” [J. Chem. Phys. 127, 047101 (2008)

A short summary of our theoretical concept for predicting Kirkwood factors in associating liquids system is presented which is based on the so-called extended real associated solution model involving the dipole correlations of chainlike associated alcohol molecules including a cyclic tetramer. Our model is discussed by comparing it with a different, alternative approach developed by Durov et al. Critical agreements and incorrect statements made by Durov have been discussed and tried to clarify.

Volumetric and transport properties of ternary mixtures containing 1-propanol, triethylamine or tri- n-butylamine and cyclohexane at 303.15 K: Experimental data, correlation and prediction by ERAS model

The excess molar volumes ( V m E ), viscosity deviations (Δ η), and excess Gibbs energies of activation (Δ G* E) of viscous flow have been investigated from densities and viscosities measurements for two ternary mixtures 1-propanol + triethylamine + cyclohexane and 1-propanol + tri- n-butylamine + cyclohexane and corresponding binaries at 303.15 K and atmospheric pressure over the entire range of composition. The empirical equations due to Redlich–Kister, Kohler, Rastogi et al., Jacob–Fitzner, Tsao–Smith, Lark et al., Heric–Brewer, and Singh et al., have been employed to correlate V m E , Δ η, and Δ G* E of ternary mixtures with their corresponding binary parameters. The results are discussed in terms of the molecular interaction between the components of the mixture. Further, the Extended Real Associated Solution (ERAS) model has been applied to V m E for the present binary and ternary mixtures and the results are compared with the experimental data.

Excess properties for binary systems ionic liquid + ethanol: Experimental results and theoretical description using the ERAS model

Density, isobaric molar heat capacity and excess molar enthalpy were experimentally determined at atmospheric pressure for a set of binary systems of ionic liquids and ethanol. Density and heat capacity were obtained within the temperature range (293.15–318.15 K) whereas excess molar enthalpy was measured at 303.15 K; excess molar volume and excess molar isobaric heat capacity were calculated from experimental data. The Extended Real Associated Solution (ERAS) model is applied to extract information about the association capability of each ionic liquid with ethanol molecules through hydrogen bonds. The chemical nature of the anion is revealed as the main factor that determines the thermodynamic behavior of the studied systems.

Excess molar enthalpy of 1-alkanol + 1-octene mixtures at 298.15 K : Experimental results and theoretical description by means of the ERAS and TB models

Excess molar enthalpies ( H E) measured at 298.15 K for the systems: 1-propanol + 1-octene, 1-butanol + 1-octene, 1-hexanol + 1-octene, 1-octanol + 1-octene and 1-decanol + 1-octene are reported. In this series of mixtures the H E values are positive in the whole concentration range. The H E curves are asymmetric and their values decrease with increasing chain length of 1-alkanol molecule. Two versions (with (I) and without (II) cross-association) of the extended real associated solution (ERAS) model and Treszczanowicz–Benson (TB) model have been applied to describe experimental H E data and literature excess molar volume ( V E) data for these mixtures. This paper points to the weak hydrogen bonds between 1-alkanol hydroxyl and 1-alkene vinyl groups.