Modeling pVT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State

Abstract

Abstract: Combining Peng-Robinson (PR) equation of state (EoS) with an association model derived from shield-sticky method (SSM) by Liu et al., a new cubic-plus-association (CPA) EoS is proposed to describe the thermodynamic properties of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall average deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their molecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter k_ij, satisfactory correlations of vapor-liquid equilibria (VLE) for binary mixtures of ILs + non-associating solvents and + associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs + non-associating mixtures from CPA, lattice-fluid (LF) and square-well chain fluids with variable range (SWCF-VR) EoSs are compared.

Key words: cubic-plus-association, equation of state, ionic liquids, vapor-liquid equilibrium

摘要： Combining Peng-Robinson (PR) equation of state (EoS) with an association model derived from shield-sticky method (SSM) by Liu et al., a new cubic-plus-association (CPA) EoS is proposed to describe the thermodynamic properties of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall average deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their molecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter k_ij, satisfactory correlations of vapor-liquid equilibria (VLE) for binary mixtures of ILs + non-associating solvents and + associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs + non-associating mixtures from CPA, lattice-fluid (LF) and square-well chain fluids with variable range (SWCF-VR) EoSs are compared.

关键词: cubic-plus-association, equation of state, ionic liquids, vapor-liquid equilibrium

MA Jun, LI Jinlong, FAN Dongfu, PENG Changjun, LIU Honglai, HU Ying. Modeling pVT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State[J]. , 2011, 19(6): 1009-1016.

马俊, 李进龙, 范冬福, 彭昌军, 刘洪来, 胡英. Modeling pVT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State[J]. , 2011, 19(6): 1009-1016.

References

1 Shariati, A., Peters, C.J., “High-pressure phase behavior of systems with ionic liquids: measurements and modeling of the binary system fluoroform+1-ethyl-3-methylimidazolium hexafluorophosphate”, J. Supercritical Fluids, 25, 109-117(2003).
2 Shiflett, M.B., Yokozeki, A., “Solubility of CO₂ in room temperature ionic liquid [hmim][Tf₂N]”, J. Phys. Chem. B, 111, 2070-2074(2007).
3 Carvalho, P.J., álvarez, V.H., Machado, J.J.B., Pauly, J., Daridon, J.L., Marrucho, I.M., Aznar, M., Coutinho, J.A.P., “High pressure phase behavior of carbon dioxide in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids”, J. Supercritical Fluids, 48, 99-107(2009).
4 Trindade, C.A.S., Visak, Z.P., Bogelukasik, R., Bogelukasik, E., da Ponte, M.N., “Liquid-liquid equilibrium of mixtures of imidazolium-based ionic liquids with propanediols or glycerol”, Ind. Eng. Chem. Res., 49, 4850-4857(2010).
5 Arce, P.F., Robles, P.A., Graber, T.A., Aznar, M., “Modeling of high-pressure vapor-liquid equilibrium in ionic liquids+gas systems using the PRSV equation of state”, Fluid Phase Equilib., 295, 9-16(2010).
6 Fumino, K., Wulf, A., Ludwig, R., “The cation-anion interaction in ionic liquids probed by far-infrared spectroscopy”, Angew. Chem. Int. Ed., 47, 3830-3834(2008)
7 Chang, H.C., Jiang, J.C., Chang, C.Y., Su, J.C., Hung, C.H., Liou, Y.C., Lin, S.H., “Structural organization in aqueous solutions of 1-butyl-3-methylimidazolium halides: a high-pressure infrared spectroscopic study on ionic liquids”, J. Phys. Chem. B, 112, 4351-4356(2008)
8 Gao, Y., Zhang, L.Q., Wang, Y., Li, H.R., “ Probing electron density of H-bonding between cation-anion of imidazolium-based ionic liquids with different anions by vibrational spectroscopy”, J. Phys. Chem. B, 114, 2828-2833(2010).
9 Andreu, J.S., Vega, L.F., “Capturing the solubility behavior of CO₂ in ionic liquids by a simple model”, J. Phys. Chem. C, 111, 16028-16034(2007).
10 Andreu, J.S., Vega, L.F., “Modeling the solubility behavior of CO₂, H₂, and Xe in [C_n-mim][Tf₂N] ionic liquids”, J. Phys. Chem. B., 112, 15398-15406(2008).
11 Wang, T.F., Peng, C.J., Liu, H.L., Hu, Y., “Equation of state for the vapor-liquid equilibria of binary systems containing imidazoliumbased ionic liquids”, Ind. Eng. Chem. Res., 46, 4323-4329(2007).
12 Geng, Y.F., Wang, T.F., Yu, D.H., Peng, C.J., Liu, H.L., Hu, Y.,“Densities and viscosities of the ionic liquid [C₄mim][PF₆]+N,N-dimethylformamide binary mixtures at 293.15 K to 318.15 K”, Chin. J. Chem. Eng., 16, 256-262(2008).
13 Ji, X.Y., Adidharma, H., “Thermodynamic modeling of CO₂ solubility in ionic liquid with heterosegmented statistical associating fluid theory”, Fluid Phase Equilib., 293, 141-150(2010).
14 Kontogeorgis, G.M., Voutsas, E.C., Yakoumis, I.V., Tassios, D.P., “An equation of state for associating fluids”, Ind. Eng. Chem. Res., 35, 4310-4318(1996).
15 Peng, D.Y., Robinson, D.B., “A new two-constant equation of State”, Ind. Eng. Chem. Fundam., 15, 59-64(1976).
16 Liu, H. L., Hu, Y., “Equation of state for systems containing chainlike molecules”, Ind. Eng. Chem. Res., 37, 3058-3066(1998).
17 Valderrama, J.O., Robles, P.A., “Critical properties, normal boiling temperatures, and acentric factors of fifty ionic liquids”, Ind. Eng. Chem. Res., 46, 1338-1344(2007).
18 Valderrama, J.O., Sanga, W.W., Lazzús, J.A., “Critical properties, normal boiling temperature, and acentric factor of another 200 ionic liquids”, Ind. Eng. Chem. Res., 47, 1318-1330(2008).
19 Valderrama, J.O., Rojas, R.E., “Critical properties of ionic liquids. revisited”, Ind. Eng. Chem. Res., 48, 6890-6900(2009).
20 Krummen, M., Wasserscheid, P., Gmehling, J., “Measurement of activity coefficients at infinite dilution in ionic liquids using the dilutor technique”, J. Chem. Eng. Data, 47, 1411-1417(2002).
21 Gardas, R.L., Freire, M.G., Carvalho, P.J., Marrucho, I.M., Fonseca, I.M.A., Ferreira, A.G.M., Coutinho, J.A.P., “PρT measurements of imidazolium-based ionic liquids”, J. Chem. Eng. Data, 52, 1881-1888(2007).
22 Esperanca, J.M.S.S., Visak, Z.P., Plechkova, N.V., Seddon, K.R., Guedes, H.J.R., Rebelo, P.N., “Density, speed of sound, and derived thermodynamic properties of ionic liquids over and extender pressure range. 4. [C₃min][NTf₂] and [C₅min][NTf₂]”, J. Chem. Eng. Data, 51, 2009-2015(2006).
23 de Azevedo, R.G., Esperanca, J.M.S.S., Szydlowski, J., Visak, Z.P., Pires, P.F., Guedes, H.J.R., Rebelo, L.P.N., “Thermophysical and thermodynamic properties of ionic liquids over an extended pressure range: [bmim][NTf₂] and [hmim][NTf₂]”, J. Chem. Thermodyn., 37, 888-899(2005).
24 Tomé, L.I.N., Carvalho, P.J., Freire, M.G., Marrucho, I.M., Fonseca, I.M.A., Ferreira, A.G.M., Coutinho, J.A.P., Gardas, R.L., “Measurements and correlation of high-pressure densities of imidazoliumbased ionic liquids”, J. Chem. Eng. Data, 53, 1914-1921(2008).
25 Fredlake, C.P., Crosthwaite, J.M., Hert, D.G., Aki, S.N.V.K., Brennecke, J.F., “Thermophysical properties of imidazolium-based ionic liquids”, J. Chem. Eng. Data, 49, 954-964(2004).
26 Kilaru, P., Baker, G.A., Scovazzo, P., “Density and surface tension measurements of imidazolium-, quaternary phosphonium-, and ammonium-based room temperature ionic liquids: data and correlations”, J. Chem. Eng. Data, 52, 2306-2314(2007).
27 Gardas, R.L., Freire, M.G., Carvalho, P.J., Marrucho, I.M., Fonseca, I.M.A., Ferreira, A.G.M., Coutinho, J.A.P., “High pressure densities and derived thermodynamic properties of imidazolium-based ionic liquids”, J. Chem. Eng. Data, 52, 80-88(2007).
28 Sanmamed, Y.A., González-Salgado, D., Troncoso, J., Cerdeiriňa, C.A., Romaní, L., “Viscosity-induced errors in the density determination of room temperature ionic liquids using vibrating tube densitometry”, Fluid Phase Equilib., 252, 96-102(2007).
29 Alavi, S., Thompson, D.L., “Molecular dynamics studies of melting and some liquid-state properties of 1-ethyl-3-methylimidazolium hexafluorophosphate [emim][PF₆]”, J. Chem. Phys., 122, 154704(2005).
30 Tekin, A., Safarov, J., Shahverdlyev, A., Hassel, E., “(p, ρ, T) properties of 1-butyl-3-methylimidazolium tetrafluoroborate and 1-butyl-3methylimidazolium hexafluorophosphate at T =(298.15 to 398.15) K and pressures up to p = 40 MPa”, J. Mol. Liq., 136, 177-182(2007).
31 Go don, A., Daübrowska, K., Hofman, T., “Densities and excess volumes of the 1,3-dimethylimidazolium methylsulfate+methanol system at temperatures from(313.15 to 333.15) K and pressures from(0.1 to 25) MPa”, J. Chem. Eng. Data, 52, 1830-1837(2007).
32 Fernández, A., García, J., Torrecilla, J.S., Oliet, M., Rodríguez, F., “Volumetric, transport and surface properties of [bmim][MeSO₄] and [emim][EtSO₄] ionic liquids as a function of temperature”, J. Chem. Eng. Data, 53, 1518-1522(2008).
33 Li, J.L., He, Q., He, C.C., Peng, C.J., Liu, H.L., “Representation of phase behavior of ionic liquids using the equation of state for square-well chain fluids with variable range’, Chin. J. Chem. Eng., 17(6), 983-989(2009).
34 Xu, X.C., Peng, C.J., Liu, H.L., Hu, Y., “Modeling pVT properties and phase equilibria for systems containing ionic liquids using a new lattice-fluid equation of state”, Ind. Eng. Chem. Res., 48, 11189-11201(2009).
35 Blas, F.J., Vega, L.F., “Thermodynamic behaviour of homonuclear and heteronuclear Lennard-Jones chains with association sites from simulation and theory”, Mol. Phys., 92, 135-150(1997).
36 Daubert, T.E., Danner, R.P., Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Hemisphere Publishing Corporation, New York(1989).
37 Smith, B.D., Srivastava, R., Thermodynamic Data for Pure Compounds, Elsevier, Amsterdam(1986).
38 Paulechka, Y.U., Kabo, G.J., Blokhin, A.V., “Thermodynamic properties of 1-butyl-3-methylimidazolium hexafluorophosphate in the ideal gas state”, J Chem Eng Data, 48, 457-462(2003).
39 Safarov, J., Verevkin, S.P., Bich, E., Heintz, A., “Vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with 1-methyl-3-butyl-imidazolium octyl sulfact and 1-methyl-3butyl-imidazolium tetrafluoroborate”, J. Chem. Eng. Data, 51, 518-525(2006).
40 Kato, R., Krummen, M., Gmehling, J., “Measurement and correlation of vapor-liquid equilibria and excess enthalpies of binary systems containing ionic liquids and hydrocarbons”, Fluid Phase Equilib., 224, 47-54(2004).
41 Kato, R., Gmehling, J., “Systems with ionic liquids: measurement of VLE and γ∞ data and prediction of their thermodynamic behavior using original UNIFAC, mod. UNIFAC(Do) and COSMO-RS(Ol)”, J. Chem. Thermodyn., 37, 603-619(2005).
42 Kato, R., Gmehling, J., “Measurement and correlation of vapor-liquid equilibria of binary systems containing the ionic liquids [Emim][(CF₃SO₂)₂N], [Bmim] [(CF₃SO₂)₂N], [Mmim][(CH₂)₂PO₄] and oxygenated organic compounds respectively water”, Fluid Phase Equilib., 231, 38-43(2005).
43 Nebig, S., Bolts, R., Gmehling, J., “Measurement of vapor-liquid equilibria(VLE) and excess enthalpies(HE) of binary systems with 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and prodiction of these properties and γ∞ using modified UNIFAC(Dortmund)”, Fluid Phase Equilib., 258, 168-178(2007).
44 Verevkin, S.P., Safarov, J., Bich, E., Hassel, E., Heintz, A., “Thermodynamic properties of mixtures containing ionic liquids vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with 1-methyl-3-butyl-imidazolium bis(trifluoromethylsulfonyl) imide”, Fluid Phase Equilib., 236, 222-228(2005).

[1]	Eileen Katherine Coronado-Aldana, Cindy Lizeth Ferreira-Salazar, Nubia Yineth Piñeros-Castro, Rubén Vázquez-Medina, Felipe A. Perdomo. Thermodynamic analysis, synthesis, characterization, and evaluation of 1-ethyl-3-methylimidazolium chloride: Study of its effect on pretreated rice husk [J]. Chinese Journal of Chemical Engineering, 2023, 60(8): 143-154.
[2]	Zhonghao Li, Yuanyuan Yang, Huanong Cheng, Yun Teng, Chao Li, Kangkang Li, Zhou Feng, Hongwei Jin, Xinshun Tan, Shiqing Zheng. Measurement and model of density, viscosity, and hydrogen sulfide solubility in ferric chloride/trioctylmethylammonium chloride ionic liquid [J]. Chinese Journal of Chemical Engineering, 2023, 59(7): 210-221.
[3]	Chen Chen, Qiong Tang, Hong Xu, Mingxing Tang, Xuekuan Li, Lei Liu, Jinxiang Dong. Alkyl-tetralin base oils synthesized from coal-based chemicals and evaluation of their lubricating properties [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 20-28.
[4]	Yutong Jiang, Yifeng Chen, Fuliu Yang, Jixue Fan, Jun Li, Zhuhong Yang, Xiaoyan Ji. Efficient SO₂ removal using aqueous ionic liquid at low partial pressure [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 355-363.
[5]	Jialei Sha, Chenyi Liu, Zhihong Ma, Weizhong Zheng, Weizhen Sun, Ling Zhao. Understanding the interfacial behaviors of benzene alkylation with butene using chloroaluminate ionic liquid catalyst: A molecular dynamics simulation [J]. Chinese Journal of Chemical Engineering, 2023, 54(2): 44-52.
[6]	Yifeng Chen, Hang Yu, Jingjing Chen, Xiaohua Lu, Xiaoyan Ji. Viscous behavior of 1-hexyl-methylimidazolium bis(trifluoromethylsulfonyl)imide/titanium dioxide/polyethylene glycol [J]. Chinese Journal of Chemical Engineering, 2023, 54(2): 280-287.
[7]	Mi Feng, Bin He, Xinyan Chen, Junli Xu, Xingmei Lu, Cai Jia, Jian Sun. Separation of chitin from shrimp shells enabled by transition metal salt aqueous solution and ionic liquid [J]. Chinese Journal of Chemical Engineering, 2023, 53(1): 133-141.
[8]	Xinqiang You, Kai Zhao, Ling Li, Ting Qiu. Ionic liquids as entrainer in extractive distillation for effectively separating 1-propanol–water azeotropic mixture [J]. Chinese Journal of Chemical Engineering, 2022, 49(9): 224-233.
[9]	Minjie Shi, Hangtian Zhu, Cheng Yang, Jing Xu, Chao Yan. Chemical reduction-induced fabrication of graphene hybrid fibers for energy-dense wire-shaped supercapacitors [J]. Chinese Journal of Chemical Engineering, 2022, 47(7): 1-10.
[10]	Song Hu, Jinlong Li, Qihua Wang, Weisheng Yang. Design and optimization of an integrated process for the purification of propylene oxide and the separation of propylene glycol by-product [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 111-120.
[11]	Alireza Afsharpour. A new approach for correlating of H₂S solubility in [emim][Lac], [bmim][ac] and [emim][pro] ionic liquids using two-parts combined models [J]. Chinese Journal of Chemical Engineering, 2022, 44(4): 521-527.
[12]	Haiyan Jiang, Lu Bai, Bingbing Yang, Shaojuan Zeng, Haifeng Dong, Xiangping Zhang. The effect of protic ionic liquids incorporation on CO₂ separation performance of Pebax-based membranes [J]. Chinese Journal of Chemical Engineering, 2022, 43(3): 169-176.
[13]	Wenjie Xiong, Mingzhen Shi, Yan Lu, Xiaomin Zhang, Xingbang Hu, Zhuoheng Tu, Youting Wu. Efficient conversion of H₂S into mercaptan alcohol by tertiary-amine functionalized ionic liquids [J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 197-204.
[14]	Yuxin Wu, Zhuo Chen, Xiaohui Zhang, Jian Chen, Yundong Wang, Jianhong Xu. Kinetic study of CO₂ fixation into propylene carbonate with water as efficient medium using microreaction system [J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 247-253.
[15]	Lianzheng Zhang, Jie Wang, Lin Yang, Dongmei Xu, Yixin Ma, Jun Gao, Yinglong Wang. Separation of isopropyl alcohol + isopropyl acetate azeotropic mixture: Selection of ionic liquids as entrainers and vapor-liquid equilibrium validation [J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 326-334.