Thermodynamic interpretation and prediction of CO2 solubility in imidazolium ionic liquids based on regular solution theory

Thermodynamic interpretation and prediction of CO2 solubility in imidazolium ionic liquids based on regular solution theory

Journal of Molecular Liquids 291 (2019) 110477 Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier...

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Journal of Molecular Liquids 291 (2019) 110477

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Thermodynamic interpretation and prediction of CO2 solubility in imidazolium ionic liquids based on regular solution theory Bartosz Dębski a,⁎, Andreas Hänel a, Robert Aranowski a, Stefan Stolte b, Marta Markiewicz b, Thomas Veltzke b, Iwona Cichowska-Kopczyńska a a b

Gdańsk University of Technology, Faculty of Chemistry, Department of Chemical Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland University of Bremen, Center for Environmental Research and Sustainable Technology, Leobener Strasse 6, 28359 Bremen, Germany

a r t i c l e

i n f o

Article history: Received 22 January 2018 Received in revised form 5 February 2019 Accepted 15 February 2019 Available online 1 March 2019 Keywords: Gas solubility Ionic liquids Henry constants Regular solution theory Solvation entropy Solvation enthalpy

a b s t r a c t Regular solution theory (RST) is the most popular model for the interpretation of the interaction between CO2 and ionic liquids. In the present work, the parameters of this model were determined for the CO2 absorption in eleven imidazolium ionic liquids. The y-intercept (A) of the RST model for the investigated imidazolium liquids increases with increasing temperature whereas the slope (B) remains constant. The values of RST parameters strongly depend on the Hildebrand parameters of the ionic liquids. It has been shown that ionic liquids surface tension and molar volume are the decisive parameters. The influence of the type of fluorinated anion and the length of the alkyl substituent on the solubility of CO2 was investigated. The dispersion of charge and the free space between the ions are key parameters determining the gas dissolution. The partial molar entropy and enthalpy of solvation were determined using a modified temperature dependent function of Henry's constant. It has been shown, that determination coefficient of the Henry's relation has to be larger than 0.9999 in order to estimate heat of salvation reliably. The molar enthalpy of solvation ranged from −11.6 to −14.7 kJ mol−1 at 298 K. Moreover, it is proposed that the entropy is composed of two parts, which explains the decrease in system order along with the elongation of the alkyl chain of the imidazolium substituent. Thus, the decrease of the gas condensation entropy component explains the increase of the partial molar entropy of solvation with temperature. It was shown that the molar volume of theoretically liquefied CO2 in the ionic liquid is lower than the actual value. © 2019 Published by Elsevier B.V.

Symbols

A parameter of regular solution equation (Pa) B parameter of regular solution equation (mol−1 cm3) B22 second virial coefficient for the pure gas (m) A′, B′, C′, D′, E′, F′ coefficients of the equation for temperature dependent Henry's constant (-) c′,d′ coefficients of the equation for molar volume dependent Henry's constant (-) Evap evaporation energy (J mol−1) f fugacity (Pa) G′ coefficient of temperature dependence of parameter A (Pa K−1) H Henry's constant (Pa) ⁎ Corresponding author. E-mail address: [email protected] (B. Dębski).

https://doi.org/10.1016/j.molliq.2019.02.076 0167-7322/© 2019 Published by Elsevier B.V.

H′ I′, J′, K′ Ks M n NA p p0 pΔV R R2 T V VB Vmol r y x z

coefficient of temperature dependence of parameter A (Pa) coefficients of second degree polynomial equation for Henry's constant dependent on molar volume (-) proportional coefficient for liquid Hildebrand parameter (-) molar mass (g mol−1) amount of substance (mol) Avogadro constant (6,022140857 1023 mol−1) partial gas pressure above ionic liquid (Pa) initial pressure (Pa) pressure change (Pa) universal gas constant (J mol−1 K−1) coefficient of determination temperature (K) volume (m3) Boyle volume (cm3) molar volume (cm3 mol−1) ion radius (Å) mole fraction in gas (-) mole fraction in liquid (-) ion charge (-)

2

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Z compressibility factor (-) δ Hildebrand parameter ((J cm−3)1/2) ∞ ΔGsol free energy of gas absorption (J mol−1) Δh∞ enthalpy of solvation in the infinite volume (J mol−1) sol2, 1 ∞ Δssol2, 1 entropy of solvation in the infinite volume (J mol−1 K−1) ΔV change of the chamber volume (m3) Ϛ density (g cm−3) σ surface tension (N cm−1) ϕ volume fraction (-) φ fugacity coefficient (-) Index

1 2 a abs c ch IL sol

liquid gas anion absorbed cation chamber ionic liquid solubility

1. Introduction Although ionic liquids (ILs) have been described the first time in 1914 by P. Walden [1], an abrupt rise of interest can be observed during the last three decades. Ionic liquids are compounds characterized by a large organic cation and an organic/inorganic anion, which have their melting temperature below 100 °C [2]. Due to their unique properties like low vapour pressure [3], stability in a wide temperature range [4] and a large electrochemical window [5], ILs have a high potential in different kind of industrial applications e.g.: as electrolyte in fuel cells [6] or batteries [7], cellulose dissolution, as catalyst [8] or as absorbent of acidic gases like CO2, H2S or SO2 [9]. Due to the proceeding global warming, which is caused to 86% by the burning of fossil fuels, new technologies are highly needed to reduce the emission of CO2 e.g. by carbon capture technologies [10]. For this reason, the current research is focusing on the application of ionic liquids as absorbent of CO2 and the modelling of the absorption thereof. Several thermodynamic models have been proposed to describe the properties of CO2 in ILs, which are 1) regular solution theory (RST) [11–14], 2) statistical models e.g. statistical associating fluid theory (SAFT) equation of state, perturbed-chain SAFT (PC-SAFT), soft-SAFT, heterosegmented-SAFT and SAFT-γ [15–18], 3) conductor-like screening model for real solvents (COSMO-RS) [19–21] or 4) stochastic simulation methods e.g. Monte Carlo [22–24]. The SAFT EOS is a highly advanced model, which considers a plurality of binary parameters of mutual dependency, which limits the application of it for engineering problems. In turn, the COSMO-RS model is a new method, which predicts the thermodynamic properties of pure and mixed liquids on the base of quantum chemical calculations of individual molecules or ions. However, this model shows discrepancies between the calculated and experimental measured results [21]. In difference, the regular solution theory is a simple and sufficient model to predict the solubility of gases in liquids at low pressures and depends only on a few temperature dependent parameters [25].

electron clouds of two different substances overlap each other [27]. RST is contained in PHSC model (PHSC - Perturbed Hard Sphere Chain Equation of State), which uses the modified Chiew equation of state, a van der Waals type perturbation term, and Song-Mason method. The PHSC model takes the following parameters into account: the number of effective hard-spheres per molecule, the non-bonding interaction energy and the segmental diameter [29,30]. Ionic liquids are liquid at room temperature due to low lattice energy, which is mainly caused by the delocalization of ions, especially due to delocalized charges at the big asymmetric cation [30]. Since the long-ranged columbic forces are weak and scattered the short-ranged van der Waals forces of hydrogen bonds are favoured [13]. Therefore RST can be used for the absorption modelling of gases in ionic liquids [31]. Systems consisting of an IL and therein solute gas are not ideal, which favours short-ranged interactions between solute and solvent. Hildebrand discovered that the difference between short-ranged forces can be used to predict and interpret the solubility which is expressed in the following equation [14]: ln H2;1 ½atm ¼ A þ Bðδ1 −δ2 Þ2

ð1Þ

Here, H is the Henry's constant of the gas absorption in ionic liquid (where the indices 1 and 2 are the liquid and gas, respectively), δ is the Hildebrand solubility parameter, A and B are RST model constants determined experimentally for given temperature [26]. The solubility parameter δ is equal to the square root of the evaporation energy of the compound in the liquid (Evap) divided by the molar volume of this compound (Vmol) in the ideal gas state (Eq. (2)). The evaporation energy is required to create free space between the ions of the ionic liquid, so that the gas can migrate through the IL. sffiffiffiffiffiffiffiffiffiffiffiffiffi −Evap δ¼ V mol

ð2Þ

The exact determination of the evaporation energy is impossible due to the low volatility of the ILs. Hildebrand considered the correction of the IL surface tension to calculate the solubility parameter. Zaitsau et al. related the experimentally determined IL evaporation energy with its surface tension and molar volume [3]. Therefore, the total interaction energy of the gas molecules with the ion pair is proportional to the surface tension, which is directly estimated by the interaction of the two components at the surface. Thus, the Hildebrand parameter was estimated on the base of the equation by Kilaru et al. [32]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  1 u ∙K ∙σ u 3 s 1 t 1 3 −8 V mol;1 δ1 ¼ 4:78∙10 ∙NA

ð3Þ

where NA is the Avogadro constant, Ks is the proportionality coefficient (equal 20 for imidazolium IL determined by Kilaru et al. [32]), σ1 is the surface tension (N cm−1), Vmol,1 is the molar volume of ionic liquid (cm3·mol−1). The Hildebrand parameter (δ1) for liquid (Eq. (3)) was determined by using the physicochemical parameters shown in Table S1 of Appendix A. It can be seen that Hildebrand parameters determined in this study are similar to the values found in the literature. The solubility parameter of CO2 at different temperatures can be estimated by the following equation [33]:

1.1. Regular solution theory

δ2 ¼ −0:535∙T þ 28:26

The RST is intrinsically designed for determination of solubility of nonpolar substances in nonpolar liquids at room temperature and at regular pressure [26]. Furthermore, the RST is one of the simplest and common applied models to describe the solubility of CO2 in ILs. In this theory the gas constitutes a regular network in the liquid, where

where T is the temperature (K). On the base of this model the Hildebrand parameter for CO2 gas δ2 is 13.1, 12.6, 12.0, 11.5 and 10.9 (J cm−3)1/2 at 283, 293, 303, 313 and 323 K, respectively. The coefficients A and B from Eq. (1) depend on the temperature, the type of solvent and gas. In the current paper, the coefficients A and B

ð4Þ

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

were determined for the absorption of CO2 in imidazolium ILs at temperatures of 283, 293, 303, 313 and 323 K. The constants A and B in Eq. (1) were interpreted by Kilaru et al. as [34]: A ¼ ln ð f 2 Þ B¼

ð5Þ

V mol;2 ϕ1 2 RT

ð6Þ

where f2 corresponds to the fugacity of dissolved gas being hypothetically in liquid state, Vmol,2 is the hypothetical liquid molar volume of the solute and ϕ1 is the volume fraction of ionic liquid and ϕ1 = (x1Vmol,1)/(x1Vmol,1 + x2Vmol,2) ≈ 1. 1.2. Thermodynamics of the physical absorption of a gas in a liquid Along with the change of temperature, the change of the gas solubility occurs and it can be quantified by the Henry's constant. At low pressures, this parameter is directly related to the thermodynamic absorption properties. The change of the free energy of gas absorption in an infinite volume depends on the Henry's constant (H2,1) according to the following equation [35]: ΔG∞sol2;1 ¼ RTln

  H2;1 p1

ð7Þ

Here, p1 is the partial gas pressure above ionic liquid and R is the universal gas constant. Inserting Eq. (7) into the Gibbs-Helmholtz equation gives the solvation enthalpy of gas in the infinite volume of an ionic liquid: ∞

Δhsol2;1

  ∂ ln H 2;1 ¼R ∂ ð1=T Þ p

ð8Þ

The entropy of gas solvation can be determined based on the Van't Hoff Eq. (7) or on the equation of Gibbs free energy Eq. (8) [26,36,37]:   ∂ lnH 2;1 Δs∞sol2;1 ¼ −R ∂ðlnT Þ p Δs∞sol2;1 ¼

ð9Þ



ΔG∞sol2;1 −Δhsol2;1 T

ð10Þ

Both equations indicate that the entropy of the gas solvation decreases with increasing temperature. Partial molar enthalpy and entropy can be calculated from the Henry's constant vs temperature dependence: lnH ¼ A0 þ

B0 C 0 þ T T2

ð11Þ

lnH ¼ D0 þ E0 lnT þ F0ðlnT Þ

2

ð12Þ

Calculating the derivatives of Eqs. (11) and (12) gives the molar enthalpy and entropy of CO2 solvation as a function of temperature, respectively: ∞

Δhsol2;1 ¼ R

 0 2C þ B0 Þ T

  Δs∞sol2;1 ¼ −R 2 F 0 ∙lnT þ E0

and (12). An attempt to explain the changes of parameters values was made taking into account high uncertainty of measurement. The solvation enthalpy enables the prediction of interaction between CO2 and IL, or more strictly between CO2 and IL anion. The determined entropy was fitted to the theory of Finotello et al., which explains the arrangement disorder of CO2-IL system [37]. However, one of the RST model limitations is the estimation of the Hildebrand parameter, since different methods of determining the Hildebrand parameters produce divergent RST model parameters A and B (Eq. (1)). It was also investigated if the determined parameters A and B adopt similar values at the equilibrium condition at certain temperature. In the literature these parameters are determined at certain temperatures, where Hildebrand parameters are calculated by various methods, e.g. based on surface tension, molar volume or viscosity. Commonly, the coefficients of RST equation are calculated based on one temperature point [14,26,32]. Moganty et al. determined the coefficients at three temperature points 283, 298, 313 K, this is the broadest range so far [38].In order to investigate more deeply the impact of temperature on the A and B parameters, the investigated temperature range was increased from 283 to 323 K, every 10 degrees. In presented research RST parameters obtained at 5 temperature points allowed to determine linear slope of this dependence. Furthermore, it was estimated which group of ionic liquids gives more contribution to free molar gas volume Vmol,2. 2. Materials and methods The room temperature ILs used in this study were: − 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C2mim][Tf2N]), − 1-buthyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C4mim][Tf2N]), − 1-hexyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C6mim][Tf2N]), − 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([C2mim] [TfO]), − 1-buthyl-3-methylimidazolium trifluoromethanesulfonate ([C4mim][TfO]), − 1-hexyl-3-methylimidazolium trifluoromethanesulfonate ([C6mim] [TfO]), − 1-ethyl-3-methylimidazolium tetrafluoroborate ([C2mim][BF4]), − 1-buthyl-3-methylimidazolium tetrafluoroborate ([C4mim][BF4]), − 1-buthyl-3-methylimidazolium hexafluorophosphate ([C4mim] [PF6]).

All ILs were obtained from Ionic Liquid Technologies (Iolitec), Germany with purity 99% and halides concentration below 100 ppm. The NMR spectrum corresponds in 99% to the spectrum of a standard. Carbon dioxide was obtained from Oxygen S.C. Gdansk with purity grade 5.0. The gas solubility, expressed by Henry's law constant, was determined by the change of the CO2 pressure above the ionic liquid surface according to the method described by Husson-Borg et al. [39]. φ2 y2 p2 x2

ð13Þ

H 2;1 ðP; T Þ ¼

ð14Þ

  p B22 φ2 ðp; T Þ ¼ exp 2 RT

The aim of this work was to determine the enthalpy, entropy and the RST parameters for CO2 absorption in imidazolium ionic liquids for the temperatures 283, 293, 303, 313 and 323 K. The reliability of the estimated thermodynamic parameters for given temperatures was verified on the basis of accuracy of the designed models described with Eqs. (11)

3

ð15Þ

ð16Þ

where x2 is the gas mole fraction in liquid, y2 is the gas mol fraction above liquid (y2 = 1 since pure CO2 was used), φ2 is the fugacity coefficient of gas component and B22 is the second virial coefficient for the pure gas. The second virial coefficient was calculated based on equation

4

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

of Sengers et al. [40]: B22 ¼ −1636:75 þ 12:04081T−3; 27957∙10−2 T 2 þ 3:16528∙10−5 T 3

ð17Þ

The scheme of the gas solubility measurement setup is shown in Fig. 1. The main part is the measuring chamber (1) and tubular gas reservoir (2). The pressure was monitored by a MSD pressure sensor (3) with a standard deviation of 0.16% over the whole measurement range from 0 to 250 kPa. Three valves (Swagelok, SS-6P4T-MM) (4) separated both equilibrated parts of the setup. All specified parts were placed in a water bath (5), where the temperature was kept constant with an accuracy of ±0.25 K. The Thermostat LS (PolyScience) (6), connected to the water bath, enabled measurements in the temperature range from 283 to 323 K. The water bath temperature was measured with a Pt 100 resistance temperature sensor (8). The ILs in the measuring chamber was agitated with magnetic stirrer (7). Prior to the measurements, the ionic liquids were degassed and dried under vacuum at 343 K for 24 h. Then, a volume VIL of 1 cm3 of IL was injected into the measurement chamber. Subsequently, ambient air was evacuated from the measurement chamber by an oil vacuum pump until a pressure of 10 Pa was reached. Subsequently, the chamber was filled with CO2 to a pressure of 2.5 bar. After adjusting the temperature the system was left untouched for at least 12 h in order to achieve equilibrium between gas phase and liquid phase. When the pressure change was b1 Pa during 10 s, it was assumed that equilibrium was achieved. The amount of absorbed CO2 nabs,2 equals the difference between the introduced amount of gas to the measurement chamber and the gas above the ionic liquid being in equilibrium. The amount of CO2 in the gas phase can be easily calculated using measured pressure, temperature and volume of the gas phase (head space volume over IL corresponds to the chamber volume minus the volume of injected IL): nabs;2 ¼

p2 ðV ch −V IL Þ RTZ

ð18Þ

The general gas Eq. (18) can be assumed as being valid for CO2 pressures of up to 5 bar [34,35] at investigated temperature range. Considering the compressibility factor Z, the deviation from the ideal gas law is 1% and 2.5% for the pressures of 1 bar and 5 bar, respectively [41,42]. The gas solubility was calculated considering its compressibility: Z ¼1þ

B22 p2 RT

ð19Þ

The chamber volume Vch was 7.8 cm3 and was determined by Boyle– Mariotte method, where the volume of constant gas amount is proportional to the pressure at constant temperature (Eq. (20)). Density and volume of ILs at different temperatures were taken into account. A septum was mounted to the valve (4), which was penetrated by a gas tight syringe with a volume of 5 cm3. When the chamber volume was

Fig. 1. Measurement setup for gas solubility in ionic liquids. 1 – measurement chamber, 2 tubular gas reservoir, 3 - pressure transducer, 4 – valves, 5 – water bath, 6 – thermostat, 7 – magnetic stirrer, 8 – temperature sensor, 9 – vacuum pump, 10 – gas supply.

increased by pulling the plunger in steps of 0.2 cm3, the pressure dropped (pΔV). Fig. S2 of Appendix A shows the change of the active volume (ΔV) every 0.2 cm3 step as a function of the pressure difference for the system with a constant amount of gas. The linear function intersects the ordinate at that point, at which the Boyle volume is equal to the chamber volume. VB ¼

 ΔV  po p −pΔV  1þ o Þ po −pΔV po

ð20Þ

3. Results 3.1. Carbon dioxide solubility in ionic liquids The Henry's constants in Table 1 and Fig. 2 indicate that the CO2 solubility depends on the type of anions in imidazolium ILs. The Henry's constant for CO2 absorption in ILs with the [C4mim]+ cation increases as follows: [Tf2N]− b [PF6]− ~ [TfO]− b [BF4]−. The observed effect can be explained by the delocalisation of the negative charge from N− caused by the higher electronegativity of fluorine in the bis (trifluoromethanesulfonyl)imide anion, which diminishes the interactions between the liquid ions and allows Lewis interactions between the S_O group and CO2. The Lewis interactions are directly proportional to the alkalinity of the anion, which leads to distorted linearity of the CO2 molecule [43,44]. In the [TfO]− anion the negative charge is delocalized by three oxygen atoms, assumable resulting in the formation of physical bonding between the oxygen of the anion and the carbon of CO2. Although CO2 is non-polar, it exhibits a considerable quadrupole moment [45]. The absorption of CO2 increases with increasing number of fluorine atoms in the anion and hence increases when the total electronegativity of ion increases ([Tf2N]− = 46, [PF6]− = 26.1, [TfO]− = 28, [BF4]− = 18). Furthermore, symmetric anions are characterized by strong cationanion interactions due to equally distributed charge, which leads to strong inter-ion attraction. Thus, the CO2 absorption in ILs with [BF4]− or [PF6]− anions is low, because CO2 cannot interpose between the ions. While the symmetry of [PF6]− anion is high, ILs containing this anion exhibit a greater absorption of CO2 than compounds with the [BF4]− anion. This can be explained by stronger Lewis acid and base interactions which was confirmed by ATR-FTIR measurements of Kazariana et al. [43,44]. The [Tf2N]− anion is characterized by a larger delocalization of the charge, which results in weaker cation-anion interaction. This leads to the formation of larger space between the ions and results in a higher CO2 absorption [43,46]. In most cases obtained results occurred to be slightly higher than those reported in literature, however there are some that are lower, ex. [C2mim][BF4] in 313 K, [C4mim][Tf2N] in 303 K. Literature authors do not always give a measurement errors, which is not a full description. Taking into account, errors obtained in this research which are also higher than those from literature, results are very close to literature data. According to research conducted by Fu et al. water content in ionic liquids has significant impact on CO2 solubility. The deviation at the same temperature and pressure, with different water mass fraction can reach 15% [57]. They found that Henry's constant is increasing when water mass fraction increases to 0.89% and is drastically decreasing at 1.6%. The impact of water content on CO2 solubility was also mentioned by Hasib-ur-Rahman et al. [53]. Prior to experiments ionic liquids were kept in 343 K for 24 h but this could not be enough to remove strongly associated water. Authors reporting solubility data ex. [58,59] do not give specific results on water content in ILs, the water content is usually measured after degassing or estimated at the time of purchase, and is not measured after the experiments, therefore it is difficult to estimate the difference. We assume our deviations from literature data are caused by water content. Moreover the discrepancy in the

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5

Table 1 Solubility of CO2 in ionic liquids. Ionic liquid

Henry's constant 10−5 [Pa]

Temperature [K]

283

293

303

313

323

[C2mim][Tf2N] [C4mim][Tf2N]

34.7 ± 2.1 30.0 [37] –

41.4 ± 1.4 35.8 [37] 40.0 ± 0.5

58.7 ± 0.8 50.7 ± 0.1 [37] 54.7 ± 1.2

68.9 ± 1.9 63.8 ± 0.1 [37] 63.0 ± 2.6 48.7 ± 0.9 [47]

[C6mim][Tf2N]



51.4 ± 1.3

58.2 ± 2.3 49.6 [37]

[C2mim][TfO]

49.7 ± 0.3

37.9 ± 0.4 34.5 ± 0.3 [37] 31.2 [37] 60.0 ± 2.9 51.3 [48]

50.6 ± 3.3 49.1 [34] 46.9 ± 0.5 55.4 [34] 42 [46] 44.1 ± 0.5

85.6 ± 1.4 78.2 [48]

99.1 ± 0.6 90.3 [48]

[C4mim][TfO]

45.4 ± 1.0

55.3 ± 1.2

73.3 ± 2.0 68.7 [34] 65.1 [48] 66.8 ± 1.9

78.1 ± 2.4 80.2 [49]

[C6mim][TfO]

41.9 ± 0.7

46.9 ± 2.0

59.9 ± 1.8

[C2mim][BF4]

61.1 ± 1.8 61.8 [37]

75.6 ± 2.4 72.5 [37]

92.1 ± 2.8 85.4 [37]

[C4mim][BF4]

53.6 ± 1.7 41.8 ± 2.3 [47] 48.3 ± 0.4 38.8 ± 0.2 [47]

65.8 ± 1.9

80.1 ± 2.3

70.4 ± 2.3 61 [51] 109.8 ± 3.3 100.6 [37] 125.24 [52] 95.1 ± 2.9

88.5 ± 4.3 75.7 [50] 106.2 [49] 80.9 ± 3.4

55.7 ± 2.0 56.5 in 298 K [53]

68.0 ± 2.9 59 [46] 59.8 [13]

[C4mim][PF6]

solubility measurements may be caused to the instability of anion for example [PF6]− and other grounds: different experimental techniques, impurities, uncertainties. The dependence of CO2 solubility in imidazolium ILs on the alkylchain length in the cation is shown in Fig. 3. For the ILs with [BF4]−, [TfO]− or [Tf2N]− anion the Henry's constant diminishes with the increasing length of the alkyl-chain of the cation. It means that the CO2 solubility in ILs with larger molar volume is higher. Steric obstructions in the form of alkyl groups or fluoroalkyl chains minimize the interactions of the liquid ions, which enables the formation of free intermolecular space for absorbed gas [45,46]. Shannon et al. used computational method taking into account 165 imidazolium based ILs and observed a

79.4 ± 4.5 68.3 [35]

[C4mim][Tf2N] [C4mim][TfO] [C4mim][BF4] 80

5

Henry's constant ·10 (Pa)

[C4mim][PF6]

60

40

20 280

290

300

111.2 ± 3.4 88.6 ± 1.9 [47] 92.7 ± 5.0 81.3 ± 0.8 [47] 88.5 ± 1.8 [54] 84.8 [55] 80.53 [35] 81.3 [46]

dependency between fractional free volume and gas solubility and selectivity in ionic liquids [60]. They conclude that highest CO2 solubility and selectivity is achieved with small cations and large, delocalized anions, which exhibit a large fractional free volume with simultaneously small molar volume. Such cations are [C2mim]+ and [C4mim]+ with a molar volume of 1.015·10−27 m3 and 1.291·10−27 m3, respectively [61]. For this reason, these ILs should be most effective in separation of CO2 from gas mixtures, since the molar CO2 fraction in the ILs is inversely proportional to their molar volume. The largest change of the Henry's constant is observed for ILs containing [BF4]− anion, when the substituent alkyl chain length increases. The lowest change was observed for ILs containing [Tf2N]− anion. In the

120

100

129.2 ± 3.4 118 [37]

310

320

330

Temperature (K) Fig. 2. Temperature dependency of the Henry's constant for the absorption of CO2 in imidazolium ionic liquids with different anions.

6

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150

130

[C2mim][Tf2N]

[C2mim][BF4]

[C4mim][Tf2N]

[C4mim][BF4]

[C2mim][TfO]

110

[C4mim][TfO]

5

Henry's constant · 10 (Pa)

[C6mim][Tf2N]

[C6mim][TfO]

90

70

50

30 280

290

300

310

320

330

Temperature (K) Fig. 3. Temperature dependence of the Henry's constant for the absorption of CO2 in imidazolium ionic liquids with different alkyl chain in cation.

case of [Tf2N]−, it can be observed that for the alkyl chain of the cation (containing from 2 to 6 carbon atoms) the Henry constant decreases by 12.8% at 303.15 K. Increasing the chain length by two carbon atoms in the IL containing [BF4]− anion the Henry's constant decreases by 13.0%. Extending the alkyl-chain gives an increase of van der Waals interaction between the substituents and hence interactions between the ions are diminished. A greater distance between the ions increases the quadrupole moment in the ionic liquid and further increases the intermolecular space, which increases the CO2 absorption [10]. This is confirmed with linear relationship between Henry's constant and molecular volume of ionic liquid. Shannon et al. reported, that absorbed CO2 mole fraction in ILs decreases as the length of the alkyl chain is increasing from C1 to C14 [62]. Elongation of the alkyl substituent in the cation results in a decrease of the volume of dissolved gas in the same ionic liquid volume. For example, increasing the chain length by two carbon atoms of [C2mim]+ cation having [Tf2N]− or [BF4]− anion will

decrease the volume of dissolved gas by 76.6 and 96.5 cm3, respectively. However, taking into account Henry's constant, the mole fraction of CO2 in ILs increases with the extension of the alkyl substituent in the cation. Considering the solubility in the unit volgas/volliquid the solubility is increasing with reducing the substituent length, which can be caused by the change of IL's density and molar mass. Increasing the anion or expanding the cation substituents results in increase of ionic liquid molar volume. Taking into account literature data and results obtained in this research, it is proposed to describe the relationship between Henry's constant and the molar volume following equation (Fig. 4):   ln H 2;1 ¼ I0 V mol 2 þ J 0 V mol þ K 0

ð21Þ

On the basis of Eq. (21) and data presented in Fig. 4 the molar volume of selected imidazolium ionic liquids with the highest CO2

Fig. 4. Henry's constant vs molar volume of IL.

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

absorption capacity was estimated and was equal 390, 491, 464, 478 cm3·mol−1 at 293, 303, 313, 323 K, respectively. The R2 regression coefficient for particular temperatures was 0.950, 0.948, 0.942, 0.954, respectively. Camper et al. observed the largest solubility of CO2 in ILs for liquids with Vmol, 1 ≈ 300 cm3·mol−1 [51]. Depending on the anion, free space in the ionic liquid structure may be available also for other gases as CH4 and N2 or favour interaction with CO2. Therefore, Shannon et al. analyzing 165 ionic liquids, did not achieve a better line fit regression than R2 = 0.97 [48]. They simplified it to the exponential using Eq. (1) and (2) and linear dependence of Evap vs Vmol.  0  c 0 H 2;1 ¼ d exp V mol

ð22Þ

The authors noticed that Haenry's constant decreases above molar volume of 275 cm3·dm−3. Coefficients c′ and d′ in Eq. (22) were 175,6 cm3·mol−1 and 18,87·105 Pa, respectively. For ionic liquids meeting the condition Vmol ≫ c′ H2,1 will approach d' value. Expanding substituent alkyl chain of the cation above 8 carbon atoms, not only increases global steric effects but also increases Van der Waals forces between substituents, resulting in viscosity increase [63]. The increase of molar volume of ILs above the maximum of CO2 solubility point results in further solubility decrease according to Eq. (21). The solubility of CO2 in all investigated ILs decreased with increasing temperature. This tendency complies with most of gases except of special systems (e.g. hydrogen–[C4mim][PF6] or hydrogen–[C2mim][BF4]) as it was stated by Afzal et al. [64] and Finotello et al. [37], where the solubility increased with increasing temperature and stayed constant in the case of methane. The most significant increase of the Henry's constant was observed for [C4mim][BF4] with 53.6·105 Pa (107%), when temperature increased from 293 to 323 K. The lowest increase was observed for [C4mim][Tf2N] with 23.0·105 Pa (58%). The increase of temperature from 298 to 308 K caused a solubility decrease of 18 ± 4% for the investigated ionic liquids. Increasing the temperature sequentially from 283 to 313 and 323 K the molar ratio of gas in [C2mim][TfO] is decrease of 30 ± 4% and 39 ± 3% of the starting value, respectively. The decline of the inner energy of the system is entailed by exothermal processes, which results in the emission of heat and can explain the decrease of CO2 solubility with increasing temperature. The coefficients of the Eqs. (11) and (12) are presented in Table 2 and 3, they are required for the calculation of the molar enthalpy and entropy of solution. The coefficient of determination of [C4mim][Tf2N] is higher than 0.9999, therefore solubility parameters can be calculated with high accuracy over the investigated temperature range.

7

Table 3 Coefficients of the Eq. (12). Ionic liquid

D′

E′

F′

R2

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C4mim][TfO] [C6mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

−177.828 −75.882 −136.245 −187.270 −306.304 −110.336 −175.043 −176.358 −39.929

62.205 27.201 48.480 65.705 107.512 39.069 61.081 61.626 14.435

−4.968 −1.966 −3.843 −5.279 −8.953 −2.980 −4.838 −4.897 −0.822

0.99773 0.99998 0.99861 0.99785 0.99889 0.99988 0.99977 0.99958 0.99965

ideal selectivity (CO2/CH4) for investigated ionic liquids are shown in Tables 4, 5. The determined values for the Henry's constant of CO2 are ten times lower than those of methane that can be found in literature. The calculated ideal selectivity is approximated for binary systems (ILone gas) and it is assumed, that there are no tertiary solute effects (ILCO2-CH4). These values suggest a high separation selectivity between CO2 and CH4 and confirm the possible application of ionic liquids for the biogas treatment. The lowest ideal absorption selectivity was observed in ionic liquids with [Tf2N]− anion (Table 5), which is caused by the high solubility of CH4 in ionic liquid. It is assumed that the solubility of CH4 increases with the number of fluoroalkyl groups in the anion [36]. The highest ideal absorption selectivity was obtained for ionic liquids with [EMIM]+ cation possessing [PF6]− or [BF4]− anion. Methane solubility in ILs can increase strongly with increasing temperature under specific conditions. This discrepancy from the ideal behavior was observed by Carvalho et al. [67] for almost all investigated ionic liquids at high pressure. For highly polarized ionic liquids, the decrease of absorption is observed along with increase of temperature at low pressure (e.g. for N-methyl-2-hydroxyethylammonium Propionate p N 1 MPa). The inversion of solubility in relation to the temperature was observed at higher pressures for low polarized phosphonic ionic liquids (e.g. hexyltetradecylphosphonium bis(trifluoromethanesulfonyl)imide p N 4.5 MPa). The non-ideality of a solution depends on a delicate balance between the solute–solute, solvent–solvent and solute–solvent interactions. Ionic liquids with large phosphate cation alkyl chain feature similar interactions with the CH4. Other ionic liquids, which are strongly polarizable, would exhibit strong unfavourable solute–solvent interactions [67]. Finotello et al. observed negligible increase of methane solubility in [C2mim][TfO] and [C2mim][BF4] with increasing temperature. Thus the decrease of ideal selectivity with increasing temperature is mainly caused by decrease of CO2 solubility, whereas the change of CH4 solubility is negligible. Also the selectivity of CO2 absorption relatively to H2 and CH4 decreases with increasing temperature [37].

3.2. Absorption selectivity 3.3. Thermodynamics of gas absorption in ionic liquids The gas solubility in ILs is controlled by free space between the ions and thus depends on the ionic liquid structure. In order to maximize the ideal selectivity between CO2 and CH4, the solubility of CH4 has to be minimized. The values of the Henry's constant (H2,1) for the CH4 and Table 2 Coefficients of the Eq. (11).

The values of the partial molar solvation enthalpy and entropy over the investigated temperature range are shown in Table 6. The determined solvation enthalpy of CO2 in the investigated imidazolium ILs ranged from −11.6 to −14.7 kJ·mol−1 at 298 K. The highest solvation Table 4 Henry constants of CH4 for the investigated ionic liquids.

Ionic liquid

A′

B′

C′

R2

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C4mim][TfO] [C6mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

18.6 20.5 18.3 18.7 14.7 20.1 19.9 19.5 22.5

−295.1 −1672.7 −414.1 −115.5 2198.4 −1218.2 −596.4 −494.8 −2544.7

−204,440.9 36,009.2 −146,599.5 −228,668.2 −570,738.2 −45,350.1 −175,422.2 −184,665.3 153,745.8

0.99773 0.99998 0.99857 0.99779 0.99875 0.99989 0.99976 0.99956 0.99965

Ionic liquid

Henry's constant for CH4 10−5 (Pa) 283 K

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

293 K

303 K

313 K

342 [65] 579 [36] 2600 [37] 965 [58] 1687 [66]

560 [37] 507 [23] 362 [65] 1310 [36] 2000 [37] 1114 [58] 1572 [66]

580 [37]

499 [36] 794 [58] 1480 [66]

321 [65] 452 [36] 3200 [37] 843 [58] 1657 [66]

323 K

381 [65]

1313 [58] 1310 [66]

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477 0

293 K

303 K

313 K

8.4 8.7 30.7 12.2 24.8

10.4 9.3 7.7 16.8 19.8 11.9 19.8

13.7

11.0 15.0 30.6

9.2 8.2 41.5 13.0 29.7

323 K

7.1

12.0 14.1

enthalpy and entropy of CO2 of all investigated ILs was observed for [C2mim][BF4]. Sequence of molar solvation enthalpy at 298.15 K is as following: [BF4]− b [TfO]− b [PF6]− b [Tf2N]−. It corresponds to a great extent to the increased number of fluorine atoms in the anion. The [BF4]− anion forms the strongest physical bonds between the fluorine atom and the CO2 with the energy of 19.9 kJ·mol−1. Due to the greater dispersion of the negative charge in the [PF6]− than in the [BF4]− anion the binding energy is lower, which is indicated by a lower solvation enthalpy. In comparison with the [BF4]− anion, the amount of binding energy of CO2 with the [TfO]− or [Tf2N]− anion is lower by 5.7 and 10 kJ·mol−1, respectively [43]. The difference of absorption enthalpy between the [BF4]− and the [Tf2N]− or [TfO]− anion does not exceed 3.9 kJ·mol−1. This difference can result from the delocalization of negative charge by the strong electronegative oxygen and fluorine atoms, which causes the withdrawal of the IL anion from the cation. The formed free space enables better contact between the CO2 molecule and the anion and creates more physical Lewis acid-base interactions between the oxygen of the [TfO]− anion and the carbon of the CO2. The enthalpy values for [C2mim][TfO] and [C2mim][Tf2N], which are estimated with high uncertainty, cast in doubt the possibility of binding two CO2 molecules to the two S_O groups of a [Tf2N] anion, like it was suggested by Reveendran i Wallen [68]. The solvation entropy is the lowest for the IL with the shortest alkylchain in the cation. For example for [C2mim][Tf2N], [C4mim][Tf2N], [C6mim][Tf2N] the entropy at 298 K is −46.6; −39.9 and −39.0 J mol−1 K−1, respectively. This can be explained by the presence of two entropic components next to one another. The first results from the condensation of the gas and adopts negative values. The second one results from the disruption of the ordered structure of the ILs and takes positive

solvation entropy

-1

-1

Ideal absorption selectivity CO2/CH4 (mol mol−1) 283 K

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

Partial molar solvation enthalpy (kJ mol )

Ionic liquid

0

solvation enthalpy -5

[C4mim][Tf2N]

[C4mim][Tf2N]

[C6mim][TfO]

[C6mim][TfO]

-10

-10

-20

-15

-30

-20

-40

-25 280

290

300

310

320

-1

Table 5 Selectivity of CO2/CH4 absorption for the investigated ionic liquids in dependence on temperature.

Partial molar solvation entropy (J mol K )

8

-50 330

Temperature (K) Fig. 5. Temperature dependency of the partial molar enthalpy and entropy for the absorption of CO2 in [C4mim][Tf2N] and [C6mim][TfO], dashed lines – entropy, continuous lines – enthalpy. Partial molar solvation enthalpy and entropy ware estimated on the basis of Eqs. (13) and (14).

values. In the case of CO2 the component of condensation is most important, thus the total absorption entropy takes negative values [37]. The long alkyl-chain in the cation is a steric hindrance, which hinders the arrangement of the IL structure. Consequently, this liquids exhibit higher entropy of the system. Probably the entropy increases as a result of the solvation of condensed gas. ILs with short alkyl-chain in the cation have a more structured molecular system and they probably form a more ordered system with CO2 [69]. Thus, these ILs exhibit a higher entropy. It is possible that the entropy increase is less significant due to the solvation of condensed gas. Obtained values are similar to the values determined by Finotello et al. ([C2mim][Tf2N] = −41 ± 5, [C6mim][Tf2N] = −38 ± 6, [C2mim][BF4] = −42 ± 2 J mol−1 K−1) [37], which are however burdened with a large standard deviation. The temperature dependency of the partial molar enthalpy and entropy of carbon dioxide solvation in [C4mim][Tf2N], [C6mim][TfO] is shown in Fig. 5. The calculated thermodynamic parameters of these ionic liquids exhibit the best regression fit of Eqs. (11) and (12) (R2 ≈ 0.9998). The solvation enthalpy of these ionic liquids decreases with increasing temperature. The functions of the Henry's constant of the remaining ionic liquids [BF4]−, [Tf2N]− and [TfO]− exhibit a smaller

Table 6 Molar solvation enthalpy and entropy of CO2 in imidazolium ILs. Ionic liquid Temperature change

283 K

293 K

298 K

303 K

313 K

323 K

−13.3 ± 3.4 −12.0 ± 0.4 −11.2 ± 1.8 −13.1 ± 1.7 −12.0 ± 0.7 −14.2 ± 0.9 −14.3 ± 1.4 −13.9 ± 2.1 −13.8 ± 0.6

−13.0 ± 3.3 −12.1 ± 0.4 −11.0 ± 1.8 −12.7 ± 1.6 −11.1 ± 0.6 −15.0 ± 1.0 −14.0 ± 1.4 −13.6 ± 2.1 −14.4 ± 0,7

−42.5 ± 3.8 −38.3 ± 0.4 −35.9 ± 1.7 −41.8 ± 3.4 −38.3 ± 1.3 −40.1 ± 1.0 −45.6 ± 5.8 −44.4 ± 5.6 −41.5 ± 5.6

−40.0 ± 3.5 −37.3 ± 0.4 −33.8 ± 1,6 −39.2 ± 3.2 −33.9 ± 1.1 −38.6 ± 0.9 −43.2 ± 5.5 −42.0 ± 5.3 −41.1 ± 5.5

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C4mim][TfO] [C6mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

−14.4 ± 3.6 −11.8 ± 0.4 −12.1 ± 1.9 −14.4 ± 1.8 −15.2 ± 0.9 −11.3 ± 0.7 −15.2 ± 1.5 −14.9 ± 2.2 −11.5 ± 0.5

−14.0 ± 3.5 −11.9 ± 0.4 −11.8 ± 1.9 −13.9 ± 1.8 −14.0 ± 0.8 −12.4 ± 0.8 −14.9 ± 1.5 −14.6 ± 2.2 −12.3 ± 0.6

−1 ) Δh∞ sol2, 1 (kJ mol −13.9 ± 3.5 −13.7 ± 3.5 −11.9 ± 0.4 −11.9 ± 0.4 −11.6 ± 1.9 −11.5 ± 1.8 −13.7 ± 1.7 −13.5 ± 1.7 −13.6 ± 0.8 −13.0 ± 0.7 −12.8 ± 0.8 −13.3 ± 0.9 −14.7 ± 1.4 −14.6 ± 1.4 −14.4 ± 2.2 −14.2 ± 2.1 −12.7 ± 0.6 −13.0 ± 0.6

[C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] [C2mim][TfO] [C4mim][TfO] [C6mim][TfO] [C2mim][BF4] [C4mim][BF4] [C4mim][PF6]

−50.7 ± 4.5 −41.5 ± 0.5 −42.2 ± 2.0 −50.5 ± 4.1 −53.1 ± 1.8 −45.0 ± 1.1 −53.5 ± 6.8 −52.5 ± 6.6 −42.9 ± 5.7

−47.8 ± 4.2 −40.5 ± 0.5 −40.1 ± 1.9 −47.4 ± 3.8 −47.9 ± 1.6 −43.3 ± 1.0 −50.7 ± 6.5 −49.7 ± 6.3 −42.4 ± 5.7

−1 −1 K ) Δs∞ sol2, 1 (J mol −46.6 ± 4.1 −45.2 ± 4.0 −39.9 ± 0.4 −39.4 ± 0.4 −39.0 ± 1.8 −37.9 ± 1.8 −46.1 ± 3.7 −44.6 ± 3.6 −45.7 ± 1.5 −43.2 ± 1.5 −42.5 ± 1.0 −41.7 ± 1.0 −49.6 ± 6.3 −48.2 ± 6.2 −48.5 ± 6.1 −47.1 ± 5.9 −42.2 ± 5.6 −41.9 ± 5.6

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

9

b)

a) 5.0

5.0

[C2mim][Tf2N]

[C2mim][Tf2N]

[C4mim][Tf2N]

[C4mim][Tf2N]

[C6mim][Tf2N]

4.5

[C6mim][Tf2N]

4.5

[C2mim][TfO] 4.0

ln(H2,1)

ln(H2,1)

4.0

3.5

3.0

1)

1)

[C4mim][PF6]

[C4mim][BF4]

[C4mim][TfO]

[C6mim][PF6]

[C6mim][BF4]

[C2mim][BF4]

3.0

4)

2)

[C6mim][TfO]

3.5

[C4mim][PF6]

[C4mim][BF4]

[C4mim][PF6]

[C4mim][BF4]

[C4mim][PF6]

1)

1)

6)

[C2mim][EtSO4]

[C8mim][BF4]

[C2mim][BF4]

[C4mim][TfO]

[C4mim][BF4]

[C4mim][TFO]

5)

3)

[C2mim][TfO]

2)

[C6mim][TfO]

[C6mim][BF4]

4)

[C6mim][PF6]

5)

[C2mim][EtSO4]

2.5

2.5 0

60

120

180

240

0

300

c)

60

120

180

240

300

d) 5.0

5.0

[C2mim][Tf2N]

[C2mim][Tf2N]

[C4mim][Tf2N]

7)

[C2mim][Tf2N] 4.5

4.5

[C4mim][Tf2N]

4.0

ln(H2,1)

ln(H2,1)

4.0 1)

[C4mim][BF4]

2)

7)

3.5

[C4mim][Tf2N]

[C4mim][TfO]

[C6mim][Tf2N]

[C4mim][TfO]

6)

[C4mim][PF6]

[C2mim][TfO]

[C2mim][BF4]

[C6mim][PF6]

[C4mim][BF4]

[C4mim][Pf2N]

7)

3.0

4)

6)

8)

1)

[C6mim][TfO]

[C2mim][TfO]

3)

3.5

[C4mim][PF6]

[C6mim][Tf2N]

7)

3.0

[C6mim][BF4]

2)

[C6mim][BF4] [C4mim][Tf2N]

[C4mim][TfO]

[C6mim][Tf2N]

[C6mim][TfO]

[C2mim][TfO]

[C2mim][BF4]

[C2mim][TfO]

[C4mim][BF4]

[C4mim][TfO]

[C4mim][BF4]

9)

7)

1)

[C8mim][BF4] [C4mim][PF6]

1)

[C4mim][PF6]

4)

[C6mim][PF6]

5)

[C2mim][EtSO4]

2.5

2.5 0

60

120

180

240

300

0

60

120

180

240

300

e) 5.0

4.5

ln(H2,1)

4.0 1)

[C2mim][TfO] 3.5

[C4mim][TfO]

3.0

6)

[C4mim][BF4]

2)

[C6mim][BF4] [C4mim][PF6]

[C2mim][Tf2N]

[C4mim][TfO]

[C4mim][Tf2N]

[C6mim][TfO]

[C4mim][PF6]

[C4mim][Tf2N]

[C2mim][BF4]

[C6mim][PF6]

[C6mim][Tf2N]

[C4mim][BF4]

[C2mim][EtSO4]

8)

1) 4) 5)

2.5 0

60

120

180

240

300

Fig. 6. Natural logarithm of the Henry's constants for CO2 versus the squared difference of the solubility parameters at: a) 283 K, b) 293 K, c) 303 K, d) 313 K, e) 323 K, 1) – Cadena et al. [54], 2) – Costantini et al. [71], 3) – Moganty et al. [38], 4) – Shariati et al. [72], 5) – Carvalho et al. [73], 6) – Jalili et al. [50], 7) – Kilaru et al. [34], 8) – Jacquemin et al. - [74], 9) – Camper et al. [14]. Dash lines mark 6% limit of uncertainty ln (H2,1), which was computed based on RST.

10

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

coefficient of determination, which yields in an ostensibly increase of solvation enthalpy with increasing temperature. According to Finotello et al. [37], Jacquemin et al. [35] and Anthony et al. [53,57] the enthalpy as well as entropy of solvation of gases in ionic liquids does not change or slightly declines with increasing temperature. For [BMIM][PF6], the Henry law characterizes the absorption of CO2 at low pressures better than in comparison to other investigated ILs due to the weaker hydrogen bonding [57]. Thus, despite the lower coefficient of determination R2 = 0,99965 it was observed, that the enthalpy declines with increasing temperature. The partial molar entropy of solvation rises with temperature within the investigated range of 283 K to 323 K, e.g. for [C4mim][PF6], [C4mim] [Tf2N], [C6mim][TfO] it increases the least by 1.8, 4.3 and 6.5 K−1 mol−1, respectively. The highest increase was observed for [C4mim][TfO] and [C2mim][TfO] with 19,9 JK−1·mol−1 and 11.3 JK−1·mol−1, respectively. Thus, it can be concluded that the entropy rises with temperature, because the solubility of CO2 in ILs decreases and at the same time the significance of condensation component of entropy decreases. This means that with increasing temperature less CO2 condensates in the IL. 3.4. Parameters of regular solution theory model Fig. 6 show the linear dependence of ln (H) on the square root of the Hildebrand parameters difference (δ1 − δ2)2 for the temperatures 283, 293, 303, 313, and 323 K. The parameters A and B of the RST are given in Table 7. High uncertainty (R2 between 0.75 and 0.81) can be explained by the presence of hydrogen bonds, polarization of ILs and uncertainty of measured values. For the temperatures 283 and 313 K, both parameters are approaching the parameters determined by Moganty et al. [38] (see Table 7), whereas they have determined the Hildebrand parameters on the base of the liquid viscosity activation energy. Blath et al. [30] observed, that [C4mim] [BF4] exhibits a higher viscosity activation energy in comparison to liquids with comparable molecular mass and for this reason this IL was excluded by them from the equation of the regular solution theory. We find that the solubility of CO2 in [C6mim] [BF4] falls within the error range of the Hildebrand function of imidazolium ILs over the investigated temperature range. Thus, the use of the RST model for all imidazolium ILs is justified. With increasing temperature the parameter A is increasing meanwhile the slope B is nearly constant (average of determined B equals 0.00322 ± 0.00071) (Fig. 7). This phenomenon is caused by the property of imidazolium ILs. The Hildebrand parameter of imidazolium ionic liquids is constant or insignificantly drops along temperature increases from 273 to 373 K. The increase of Henry constants with temperature is compensated in the equation by increase of parameter A [38]. This dependency is expressed by Eq. (23) exhibiting a coefficient of determination R2 = 0.9907: A ¼ 0:0144  0:0007  T−0:659  0:021

ð23Þ

At the same time, the fugacity of CO2 (f2) in the theoretical liquid phase is increasing, whereupon the molar volume of CO2 (Vmol,2) is nearly unchanged (see Table 7). The determined fugacity is close to the fugacity mentioned in literature (32·105 Pa at 283 K, 48·105 Pa at 298 K, 59·105 Pa at 313 K [38]). The theoretical molar gas volume in the IL condensed phase is five times smaller than in comparison to the values by Prausinitz et al. [70], which can result from lower condensation of CO2 in the free space between the liquid elements. More suitable seems the determination of liquid Hildebrand parameters on the basis of interfacial interactions like the surface tension (σ1) and the molar volume (Vmol,1) of the ILs. Additionally, the linear solubility of CO2 in ILs also depends on these two interfacial interactions [32]. However, Kilaru et al. [32] obtained lower values for the parameter A and higher values for the parameter B of the solubility of CO2 in ILs. This discrepancy can be explained by an extenuated value of the proportional coefficient (Ks) from Eq. (3) for calculation of the Hildebrand parameter of the IL (δ1). Diminishing δ1 minimizes the difference (δ1 − δ2)2 and increases the slope of the line describing ln (H2,1). The high divergence of both parameters results from the usage of different methods for the estimation of the Hildebrand parameters for the ILs. This parameter can be calculated on the basis of viscosity activation energy, surface tension and molar volume of the IL, evaporation energy for the vacuum, or density of cohesion energy [56,62–64]. Bara et al. and Camper et al. obtained nearly two-times higher value for the Hildebrand parameter [14,28]. For example, for [C2mim][TfO] it gives 47.2 (J cm−3)1/2, whereas the determined parameter does not exceed 24 (J cm−3)1/2 [11,25]. The Kapustinski equation (Eq. (24)) was used for the calculation of the crystal lattice energy [14,65,66]: 2

Evap

3   Â J e za zc 6 7 ¼ 2:40  106 4  5 mol rc þ ra

1−

 0:345 Å Þ rc þ ra

ð24Þ

where z are the numbers of elementary charge on the ions and r are the radii of the ions. In the case of ionic liquids, the charge is delocalized on the ion, which lowers the value of the Hildebrand parameter. Moreover, the polarizability of the aromatic ring of the cation should be taken into account, which is missing in the Kapustinski equation. The polarizability is greater, the more C2 positions of aromatic ring are occupied by hydrogen than by an alkyl substitute. Similarly, the difference (δ1 − δ2)2 is greater for crystalline salts in comparison to ILs for constant ln (H), which causes a decrease of the slope coefficient in the RST equation and a decrease of the solubility. However, Camper et al. and Bara et al. obtained higher R2 values of the RST model based on the Kapustinski equation of 0.92 and 0.85, respectively, than in comparison to R2 = 0.78 at 313 K [14,28]. Both presumed a nearly two times larger δ2 = 21.8 (J cm−3)1/2 for CO2. The curve linearity of the RST equation confirms the simple proportional dependency of ln (H) from the difference of Hildebrand parameters. The Hildebrand parameter of ILs depends inversely proportional on

Table 7 Comparison of the parameters of the regular solution theory model. Temperature (K)

A (Pa)

B 103 (mol cm-3)

f2 105 (Pa)

Vmol,2 (cm3 mol-1)

R2

283

3.42 ± 0.10 3.1 ± 0.2 3.56 ± 0.08 3.3 ± 0.2 3.74 ± 0.10 3.35 ± 0.055 3.87 ± 0.10 3.7 ± 0.2 3.26 ± 0.14 3.58 3.98 ± 0.11

3.06 ± 0.83 3.4 ± 1.5 3.22 ± 0.64 3.0 ± 1.3 3.23 ± 0.70 4.82 ± 0.35 3.25 ± 0.70 2.4 ± 1.3 0.84 ± 0.12 1.13 3.35 ± 0.69

28.9 ± 1.1 22 ± 1 33.3 ± 1.1 27 ± 1 39.5 ± 1.1 28.5 ± 1.1 45.4 ± 1.1 41 ± 1

7.7 ± 2.0 8.0 ± 3.5 8.5 ± 1.6 7.4 ± 3.2 8.7 ± 1.8 12.1 ± 0.9 9.0 ± 1.8 6.2 ± 3.4

0.75 0.79 0.80 0.73 0.78

51.0 ± 1.1

9.3 ± 1.9

293 298 303 313

323

Reference

[38] [38] [32]

0.78 0.68 0.92 0.86 0.81

[38] [14] [26]

B. Dębski et al. / Journal of Molecular Liquids 291 (2019) 110477

11 -3

4.5

5.0x10

A line fit to A -3

4.2

4.0x10

3.9

3.0x10

3.6

2.0x10

-3

-3

-3

3.3

3.0 280

B line fit to B 290

300

310

320

1.0x10

0.0 330

Fig. 7. Temperature dependency of parameters A and B of RST model.

the molar volume of liquid and directly proportional on the surface tension. The first dependence was confirmed by many researchers and the exponent of the molar volume is −1, 4/3 or −1/3 [56,62]. Researchers stated, that ln (H) is inversely proportional to Vmol,1, with an exponent of order one [63,67]. According to Eq. (3), the most important factor for the solubility is the surface tension of IL. Most likely, a decrease of the surface tension by a surfactant can yield an increase of the absorption of gases in the IL.

4. Conclusion In the current work the solubility of CO2 in nine imidazolium ionic liquids was determined and the slope B and y-intercept A of RST equation were calculated for eleven imidazolium ionic liquids within the temperature range from 283 K to 323 K. It was shown that the determined coefficients A and B of RST equation are reasonable for imidazolium ILs of low molecular volume. However, RST coefficients strongly depend on the method of calculating the IL Hildebrand parameter (δIL). For the investigated temperature range, the parameter A of the RST model increases with increasing temperature, whereas the slope B stays nearly constant. This confirms that the decrease of CO2 solubility in ILs results from the decrease of gas fugacity (f2) with temperature, if the theoretical liquid molar volume of the dissolved gas (Vmol,2) stays constant. The molar volume of ILs and surface tension are keyparameters, which was confirmed by CO2 solubility analysis depending on ILs structure. It was observed that the anion in imidazolium ILs influences the CO2 absorption more than the cation. The solubility of CO2 increases with increasing number of fluorine atoms and rising delocalized negative charge in anion. If molar volume of ionic liquids is increasing, the larger is the free fractional volume in IL and gases can easily penetrate between ions. Imidazolium ionic liquids with [Tf2N]− anion and longest alkyl chain in cation are the best solvents among investigated ILs. The selectivity of CO2 absorption relatively to H2 and CH4 decreases with increasing temperature. The absorption selectivity between CO2 and CH4 ranges from 7.1 to 41.5 and confirms the possible application of ionic liquids for the biogas treatment. The solubility of CO2 in all investigated ionic liquids decreased with increasing temperature. The decline of the inner energy of the system is entailed by exothermal processes, which results in the emission of heat and can explain the decrease of CO2 solubility with increasing temperature. The temperature dependent function of Henry constant for [C4mim] [Tf2N] and [C6mim][TfO] were determined with coefficients of

determination close to one (R2 ≈ 0.9999) by which partial molar solvation enthalpy and entropy can be determined with high accuracy. With increasing temperature the partial molar enthalpy of solvation of gases in ILs decreases. Furthermore, solvation enthalpy of CO2 in infinite ILs volume decreases with the amount of fluorine atoms in the anion. Low enthalpy differences exclude the direct interaction between the anions of IL and gas. Ionic liquids create with CO2 diffuse scattered physical interaction. It is proposed that this results from the delocalization of negative charge by the strong electronegative oxygen and fluorine atoms, which cause the withdrawal of the IL anion from the cation. The formed free space enables higher contact between the CO2 molecule with the anion and creates more physical Lewis acid-base interactions. The partial molar solvation entropy of CO2 increases with increasing temperature due to decline of CO2 solubility in ILs as well as decline of the entropy component, which corresponds to gas condensation in ILs. Furthermore, long alkyl-chain in the cation hinders the arrangement of the IL structure and thus such ILs exhibit higher entropy. In future prospect, the RST coefficients of CO2 absorption should be determined for several more ILs, e.g. pyridinium, pyrrolidinium, ammonium and phosphonium ionic liquids. This gives the possibility of choosing the group of ILs, where the condensed CO2 exhibits the highest molar volume proportional to parameter B. Furthermore, this helps in designing ILs with a high CO2 anion interaction from the group of ILs with the highest coefficient B. Acknowledgement This research was supported financially by the National Science Centre of Poland (7570/B/H03/2011/40, 2011) the National Centre for Research and Development (Task 4: Development of integrated technologies for the production of fuels and energy from biomass, agricultural waste and other resources, 2009). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2019.02.076. References [1] P. Walden, Ueber die Molekulargrösse und elektrische Leitfähigkeit einiger geschmolzenen Salze, Bull. l'Academie Imp. Des Sci. St. Petersbg. (1914) 405–422.

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