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Ind. Eng. Chem. Res. 2010, 49, 5846–5853
Regular Solution Theory for Low Pressure Carbon Dioxide Solubility in Room Temperature Ionic Liquids: Ionic Liquid Solubility Parameter from Activation Energy of Viscosity Surya S. Moganty† and Ruth E. Baltus* Department of Chemical and Biomolecular Engineering, Clarkson UniVersity, Potsdam, New York 13699-5705
The low pressure solubility of carbon dioxide in eight commercially available room temperature ionic liquids was measured at 10, 25, and 40 °C using a transient thin liquid film technique. In this paper, carbon dioxide solubility is reported as the Henry’s law constant for each system. Experimental results were interpreted using regular solution theory where Eyring’s reaction rate theory was successfully applied to estimate the solubility parameter of each ionic liquid from its activation energy of viscosity. Consistent with the regular solution theory, the carbon dioxide solubility was found to be inversely proportional to the solubility parameter of the ionic liquid, and Henry’s law constants were successfully correlated with the square of the difference between ionic liquid and carbon dioxide solubility parameters. Introduction Room temperature ionic liquids (RTILs) are organic salts consisting of a bulky cation and an inorganic anion with melting points below 100 °C. The large cation size allows for delocalization and screening of charges, resulting in a reduction in the lattice energy and thereby the melting or glass transition temperature. RTILs exhibit many interesting properties, which make them suitable for applications such as chemical synthesis, catalysis, electrochemical applications, and gas separations. Knowledge of the solubilities of gases in different RTILs is important for the design and development of ionic liquid-based reaction and separation processes as well as for understanding gas-liquid interactions that govern solubility. Among different gases, carbon dioxide is the most widely studied because its relatively high solubility in many RTILs has focused attention on RTIL-based separation processes for carbon capture from flue gases generated in coal-fired power plants.1-5 A number of different techniques have been used to measure gas solubilities in RTILs. These include a gravimetric method,6-10 a quartz crystal microbalance method,11 and equilibrium pressure and volume techniques.12,13 In recent years, work in our laboratory has focused on measuring gas solubility and diffusivity in RTILs using a technique involving gas uptake into a thin ionic liquid film.14-16 Efforts have also been directed toward the development of thermodynamic models for predicting gas solubilities in RTILs. Shiflett and Yokozeki7,9,17,18 developed a Redlich-Kwong cubic equation of state as well as different activity coefficient models to describe NH3, CO2, and hydrofluorocarbon solubilities in RTILs. Quantitative structure-properties relationship models have also been developed for modeling solubilities in RTILs.19 However, these approaches require experimental data for each RTIL-gas pair to determine the model parameters. This problem can be avoided with regular solution theory (RST) because model parameters involve only pure component properties. Shi and Maginn20 compared RST predictions with results from molecular modeling simulations and concluded that RST was * To whom correspondence should be addressed. E-mail: baltus@ clarkson.edu. † Present address: School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14850.
the most useful predictive tool for correlating low pressure gas solubilities. Using different approaches to relate measurable properties to RTIL solubility parameters, Noble and co-workers21-24 and Scovazzo and co-workers25-27 successfully applied RST to interpret and predict the solubilities of a variety of gases in different RTILs. In this paper, we report results from measurements of the low pressure solubility of CO2 in eight different RTILs at 10, 25, and 40 °C. Results are interpreted using RST, where an alternative approach for estimating the RTIL solubility parameters is presented. In this approach, RTIL solubility parameters are estimated from activation energies of RTIL viscosity, building upon Eyring’s absolute reaction rate theory of the liquid state, which relates the energy of vaporization to the activation energy of viscosity.28 This approach is similar yet different than the approach used by Kilaru and Scovazzo27 for interpreting carbon dioxide and hydrocarbon solubilities in RTILs. The resulting expression allows one to estimate the Henry’s law constant for CO2 in an ionic liquid from viscosity measurements at several different temperatures. Regular Solution Theory RST assumes that at constant temperature and pressure, the excess entropy of mixing vanishes and that forces of attraction between molecules are primarily short-range dispersion forces. Low columbic interactions are expected for RTILs because the large cation size delocalizes the charge. Hence, it is reasonable to assume that RTIL solutions are dominated by short-range forces. The vapor liquid equilibrium of carbon dioxide dissolved in an RTIL can be expressed in terms of the fugacity of carbon dioxide: fCO2G ) fCO2IL
(1)
Because RTILs are nonvolatile and only CO2 is introduced into the experimental cell, the gas phase is pure CO2 and is assumed to be ideal. Therefore, the fugacity of CO2 can be assumed to be equal to the gas pressure. The CO2 fugacity in the liquid phase can be written in terms of an activity coefficient:
10.1021/ie901837k 2010 American Chemical Society Published on Web 05/17/2010
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010
P ) xCO2 γCO2 fCO2
0
(2)
where xCO2 is the mole fraction of carbon dioxide in the RTIL solution phase, γCO2 is the activity coefficient of carbon dioxide in the RTIL phase, and fCO20 is the fugacity of pure CO2 at standard state, defined to be a hypothetical pure liquid at the solution temperature. Rearranging eq 2 and applying logarithms yields -ln xCO2 ) ln
( ) fCO20 P
+ ln γCO2
(3)
According to the Scatchard-Hildebrand RST, the logarithm of the activity coefficient is proportional to the squared difference in solubility parameters between solute and solvent:29-31 ln γCO2 )
VCO2φIL2 RT
(δIL - δCO )2
(4)
2
where VCO2 is the molar volume of hypothetical liquid carbon dioxide at the solution temperature and pressure, φIL is the volume fraction of RTIL, and δILand δCO2 are the solubility parameters for pure RTIL and pure CO2. Substituting eq 4 into eq 3 yields -ln xCO2 ) ln
( ) fCO20
+
P
VCO2φIL2 RT
(δIL - δCO )2
(5)
2
Applying Henry’s law (P ) HCO2xCO2), eq 5 can be rearranged to: ln HCO2 ) ln fCO2 + 0
VCO2φIL2 RT
(δIL - δCO )2 ) A + B(δIL - δCO )2 2
2
(6)
where A and B are parameters that depend only on temperature. RTIL Solubility Parameter The applicability of RST to RTIL-gas systems requires an estimation of the solubility parameter of the RTIL. In the Hildebrand treatment of RST, the solubility parameter is the square root of the cohesive energy density, which is defined as the ratio of the energy of vaporization, ∆Uvap, to the molar volume, V: δ)
∆Uvap V
(7)
Because RTILs are nonvolatile, experimental measurement of their energy of vaporization is difficult. For this reason, reports from experimental measurements of ∆Uvap have been very limited. Alternative approaches have been considered for relating the cohesive energy density to measurable parameters that characterize the intermolecular forces in RTILs. Assuming that the intermolecular forces that dictate melting point temperatures are related to the intermolecular forces that control vaporization, Camper et al.21 used RTIL melting temperatures to estimate the δIL. However, this approach is limited because few RTILs have a melting point. Assuming that the lattice energy density characterizes intermolecular interactions in ionic liquids, Camper et al.23 used the Kapustinskii equation to estimate the lattice energy density of RTILs. In the Kapustinskii equation, the lattice
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energy density for the ion pairs is estimated from the charge and molar radii of the ions, ignoring ion polarizability.32 Lee and Lee33 report δIL values that were determined from intrinsic viscosity measurements performed with ionic liquid solutions prepared with solvents of known δ. The RTIL solubility parameter was assumed to be equal to the solubility parameter of the solvent that yielded the maximum intrinsic viscosity. Recently, Kilaru et al.27 estimated Hansen solubility parameters of RTILs from surface tension values. Similarly, Jin et al.34 estimated Hildebrand solubility parameters for ionic liquids from surface tension measurements using correlations developed for RTILs with measured values of ∆Uvap. In another approach, Kilaru and Scovazzo27 estimated RTIL solubility parameters from the free energy of activation of viscosity using Eyring’s absolute reaction rate theory. The proportionality constant relating the free energy of activation of viscosity to the energy of vaporization was estimated using the solubility parameter values reported by Lee and Lee.33 It was found that a different proportionality constant was needed for Tf2N-based RTILs and for non-Tf2N-based RTILs. As an alternative approach, we have examined estimation of the energy of vaporization of RTILs from the activation energy for viscosity, which is also suggested by Eyring’s absolute reaction rate theory.35 Note that the activation energy for viscosity differs from the free energy of activation for viscosity by the entropy change that accompanies activation for viscous flow.28 Eyring and co-workers used reaction rate theory to model the liquid state and to develop equations for estimating transport properties of liquids.28,35,36 In Eyring’s approach, the liquid is considered to be made up of “holes”, and the process of flow is assumed to be a unimolecular rate process. For a molecule to take part in flow, a suitable “hole” or vacant site must be available, but this “hole” is not necessarily of molecular size. Hence, the activation energy for viscous flow, Eavis, is assumed to be related to the work required to form a “hole” in the liquid. Similarly, the energy of vaporization is the work required to remove a molecule from the liquid phase, that is, to form a molecular size hole in the liquid. Therefore, Eyring argued that the activation energy of viscosity is related to, but a fraction of, the energy of vaporization. For nonspherical molecules, Eyring reported that ∆Uvap ) 4Eavis.36 Energy of vaporization values for a few RTILs have been measured and reported by Armstrong et al.37 who used mass spectrometry, by Santos et al.38 who used a vacuum microcalorimeter, and by Luo et al.39 who used thermogravimetric analysis. There is general agreement between values measured using these different techniques. Using literature values for RTIL viscosity as a function of temperature, the activation energy of viscosity was determined for the RTILs investigated in the vaporization studies. A plot of the energy of vaporization versus the activation energy of viscosity was prepared and is shown in Figure 1. A linear regression fit yields a slope of 4.3. This is in very good agreement with the Eyring prediction that ∆Uvap is a factor of 4 times larger than Eavis. We have opted to use the Eyring factor of 4, recognizing that the difference in δIL predicted with the two different proportionality factors is less than 3%. Using the Eyring relationship, the RTIL solubility parameter can be estimated from the activation energy of viscosity: δIL )
4Evis a VIL
(8)
The solubility parameter for carbon dioxide at different temperatures can be estimated from the following correlation:40
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δCO2 ) -0.0535T + 28.26
(9)
where T is in K. This expression predicts δCO2 ) 13.1 (J/cm3)1/2 at 10 °C, δCO2 ) 12.3 (J/cm3)1/2 at 25 °C, and δCO2 ) 11.5 (J/cm3)1/2 at 40 °C. Experimental Section The experimental system used for solubility measurements involves tracking the decrease in pressure that results following the introduction of target gas (CO2 in this work) into a small closed chamber containing a thin film of RTIL. The solubility, characterized using Henry’s law constant, H, and diffusivity, D, of the target gas are determined by fitting the pressure decay to a one-dimensional diffusion model of gas transport in the RTIL film. Details of the experimental setup and operating principles for our measurements are described in detail elsewhere.14-16 By combining Fick’s law for diffusion in the RTIL film with a mass balance on gas above the liquid, the pressure decay can be related to system parameters and gas properties by ln
P 8 VIL FIL RT · ) 2 P0 π V MWIL H
∞
∑ (2n +1 1)
[ (
n)0
exp -
2
·
) ]
(2n + 1)2π2Dt - 1 (10) 4L2
where V is the volume of gas, VIL is the volume, FIL is the density, MWIL is the molecular weight, and L is the thickness of the RTIL film. In developing eq 10, it is assumed that the physical properties (i.e., density and viscosity) of the ionic liquid film do not change during the gas dissolution process. Mathematical details of the derivation of eq 1 are presented in Hou and Baltus.14 The final model includes two unknowns, H and D. Using a nonlinear least-squares method in the MATLAB curve fitting tool box, the experimental P vs time data were fit to eq 10 to determine H and D. In all cases, there was excellent agreement between experimentally measured pressure values and model predictions over the entire experimental time, supporting the assumption that the properties of the ionic liquid are constant throughout the process. In this paper, we focus exclusively on solubility values. Diffusion coefficient values will be reported and discussed in a subsequent paper.41 Materials. Eight different ionic liquids were studied in this work: 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (Emim Tf2N) (Solvent Innovation, 99% purity), 1-ethyl-3-methylimidazolium bis(pentafluoroethylsufonyl)imide
Figure 1. Comparison of the relationship between ∆Uvap and Eavis: Experimental measurements vs best fit line with slope ) 4.3 (dashed) and Eyring prediction36 with slope ) 4.0 (solid). Data were taken from Armstrong et al.37 ((), Santos et al.38 (b), and Luo et al.39 (9).
Table 1. Experimentally Measured Henry’s Law Constants (H) for Carbon Dioxide in Ionic Liquidsa H (bar) RTIL
10 °C
25 °C
40 °C
Bmpy BF4 Omim BF4 Hmim BF4 Hmim Tf2N Emim Tf2N Emim BETI Emim TfA Emim TfO
52 ( 4 32 ( 3 42 ( 4 23 ( 1 22 ( 1 25 ( 1 33 ( 5 40.1 ( 0.2
60 ( 6 43 ( 5 57 ( 4 28.2 ( 0.6 31.3 ( 0.4 33 ( 3 43 ( 6 50 ( 12
71 ( 14 56 ( 3 75.5 ( 0.1 42 ( 3 45 ( 6 46 ( 7 54 ( 3 68 ( 14
a
Uncertainty limits represent 95% confidence limits.
Table 2. Comparison of Henry’s Law Constants for CO2 Measured in This Study to Literature Reports from Others H (bar) RTIL
T (°C)
this work
literature report
ref
Hmim Tf2N Hmim Tf2N Hmim Tf2N Hmim Tf2N Hmim Tf2N Emim Tf2N Emim Tf2N Emim Tf2N Emim Tf2N Emim TfA Emim TfO
10 25 25 40 40 10 25 25 40 25 40
23 ( 1 28.2 ( 0.6 28.2 ( 0.6 42 ( 3 42 ( 3 22 ( 1 31.3 ( 0.4 31.3 ( 0.4 45 ( 6 43 ( 6 68 ( 14
24.2 31.6 34 45.6 43 25.3 35.6 39 50 55 70
6 6 49 6 49 48 48 49 49 50 22
(Emim BETI) (Covalent Associates, 99% purity), 1-ethyl-3methylimidazolium trifluoromethylsulfonate (Emim TfO) (Sigma Aldrich, 98% purity), 1-ethyl-3-methylimidazolium trifluoroacetate (Emim TfA) (EMD Merck, 98% purity), 1-hexyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide (Hmim Tf2N) (EMD Merck, 99% purity), 1-hexyl-3-methylimidazolium tetrafluoroborate (Hmim BF4) (Sigma Aldrich, 98% purity), 1-octyl-3-methylimidazolium tetrafluoroborate (Omim BF4) (Solvent Innovation, 99% purity), and 1-butyl-3-methylpyridinium tetrafluoroborate (Bmpy BF4) (Sigma Aldrich, 97% purity). High-purity nitrogen (N2) and carbon dioxide (CO2) were obtained from Merriam-Graves Co. (Charlestown, NH) with purities of 99.998 and 99.995%, respectively. (Nitrogen gas was used for RTIL regeneration following CO2 uptake measurements.15) Results and Discussion Carbon Dioxide Solubility. The values of the Henry’s law constant for CO2 in the RTILs are presented in Table 1. For a limited number of these RTILs, exact comparison with literature reports of H for CO2 can be made. These comparisons are summarized in Table 2, showing generally good agreement between Henry’s law constants measured in this work to values reported by others using different techniques. The solubility of CO2 in each RTIL at 1 bar CO2 pressure is listed on both a mole fraction basis as well as in mol CO2/L of RTIL in Table 3. When expressed as a mole fraction, a comparison of CO2 solubilities in the tested ionic liquids shows solubility in Hmim Tf2N > Emim Tf2N ∼ Emim BETI > Emim TfA ∼ Omim BF4 > Emim TfO > Hmim BF4 > Bmpy BF4. A comparison of carbon dioxide solubilities in Hmim Tf2N and Hmim BF4 clearly shows that CO2 is significantly more soluble in Hmim Tf2N than in Hmim BF4. This is consistent with previously reported observations that CO2 solubility is higher in RTILs with Tf2N anion than in RTILs with BF4 anion.6 CO2 solubility in the Emim RTILs is highest in Emim Tf2N and
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a
Table 3. CO2 Solubility in Ionic Liquids at 1 bar CO2 Pressure
mol CO2/L
mol CO2/mol IL RTIL
10 °C
25 °C
40 °C
10 °C
25 °C
40 °C
Bmpy BF4 Omim BF4 Hmim BF4 Hmim Tf2N Emim Tf2N Emim BETI Emim TfA Emim TfO
0.019 ( 0.001 0.031 ( 0.003 0.024 ( 0.002 0.043 ( 0.002 0.045 ( 0.002 0.040 ( 0.002 0.030 ( 0.004 0.025 ( 0.001
0.017 ( 0.002 0.023 ( 0.003 0.018 ( 0.001 0.035 ( 0.001 0.032 ( 0.001 0.030 ( 0.003 0.023 ( 0.003 0.020 ( 0.005
0.014 ( 0.003 0.018 ( 0.001 0.013 ( 0.001 0.024 ( 0.002 0.022 ( 0.003 0.022 ( 0.003 0.019 ( 0.001 0.015 ( 0.003
0.10 ( 0.01 0.12 ( 0.01 0.11 ( 0.01 0.14 ( 0.01 0.18 ( 0.01 0.13 ( 0.01 0.18 ( 0.03 0.13 ( 0.01
0.089 ( 0.009 0.093 ( 0.011 0.080 ( 0.006 0.11 ( 0.002 0.13 ( 0.002 0.099 ( 0.009 0.14 ( 0.02 0.11 ( 0.02
0.074 ( 0.014 0.070 ( 0.003 0.060 ( 0.001 0.073 ( 0.005 0.086 ( 0.011 0.071 ( 0.011 0.11 ( 0.006 0.077 ( 0.016
a
Uncertainty limits represent 95% confidence limits.
Table 4. Activation Energy of Viscosity and Molar Volumes for the RTILs Examined in This Studya vis
RTIL
VIL (cm3/mol)
Ea (kJ/mol) 10 °C 25 °C 40 °C
Bmpy BF4
42
189.0 190.7 192.4
Omim BF4 Hmim BF4
40 39
253.1 254.7 258.1 219.8 221.9 224.1
Hmim Tf2N
31
323.0 324.7 329.5
Emim Emim Emim Emim
Tf2N BETI TfA TfO
24 36 23 23
255.2 305.7 185.1 171.8
Bmim Tf2N
32
289.0 291.8 294.7
Pmmim Tf2N
35
285.3 287.7 290.2
Bmpy Tf2N
34
301.3
Bmim BF4
35
186.6 188.3 190.1
257.8 308.8 186.7 173.5
260.4 312.2 188.3 175.1
ref viscosity: 51 density: 52 viscosity and viscosity and viscosity: 51 density: 54 viscosity and viscosity and viscosity and viscosity and viscosity: 15 density: 47 viscosity: 15 density: 57 viscosity: 51 density: 15 viscosity and
density: 53 density: 53 density: density: density: density:
55 55 56 56
density: 58
a
The activation energy of viscosity values were calculated from viscosity at different temperatures.
Emim BETI, with comparable H values in these ionic liquids. The poorest CO2 solubility among the Emim RTILs was observed in Emim TfO. The comparable H values determined for CO2 in Emim Tf2N and Emim BETI were counter to expectations that the additional fluorines (and therefore electronegativity) in the BETI anion would improve CO2 solubility relative to the Tf2N RTIL. The difference in CO2 solubility between Emim TfA and Emim TfO was also unexpected, given the similar structure in these two anions. A comparison of CO2 solubility in Omim BF4 and Hmim BF4 supports previous observations that CO2 solubility increases with an increase in the alkyl chain length on the cation.6,42,43 It is speculated that this increase in solubility arises from an increase in free volume introduced with the longer alkyl chain. When expressed as mol CO2/L, solubility is considerably higher in Emim Tf2N and Emim TfA when compared to the other ionic liquids. Solubility is lowest in the three ionic liquids with BF4- anion, consistent with the trends observed when solubility is expressed on a mole fraction basis. RST. To consider the application of RST (eq 6) to the observed CO2 solubilities in RTILs, solubility parameter values for RTILs were estimated using eq 8. Values for the activation energy of viscosity were calculated from viscosity values reported in the literature and are listed in Table 4. RTIL molar volume values from the literature were used in these calculations, and these values are also listed in Table 4. In this analysis, we have included results for several other ionic liquids that were examined and previously reported by our group.14 The Hildebrand solubility parameters were determined from these parameters using eq 8 and are listed in Table 5. Examination of the values in Table 5 shows that the solubility parameters are
Table 5. Hildebrand Solubility Parameters Determined Using Eq 8 δIL (J/cm3)1/2 RTIL
10 °C
25 °C
40 °C
Bmpy BF4 Omim BF4 Hmim BF4 Hmim Tf2N Emim Tf2N Emim BETI Emim TfA Emim TfO Bmim Tf2N Pmmim Tf2N Bmpy Tf2N Bmim BF4
29.8 25.2 26.7 19.6 19.4 21.7 22.1 23.1 21.0 22.2
29.7 26.6 27.5 19.5 19.3 21.6 22.2 23.0 20.9 22.1 21.2 24.8
29.6 26.5 27.4 19.4 19.2 21.5 22.3 22.9 20.8 22.0
24.9
24.7
generally insensitive to temperature, consistent with the results from molecular simulations.44 As noted earlier, energy of vaporization values have been determined for several of the ionic liquids examined in this study.37-39 Solubility parameters were calculated for these ionic liquids using reported ∆Uvap values and eq 7. Solubility parameters have also been determined by Scovazzo and coworkers for selected ionic liquids from surface tension and free energy of activation for viscosity.26,27 These values are compared to values estimated using the approach that we propose (eq 8) in Table 6. There is generally very good agreement between δIL values calculated from ∆Uvap measurements and δIL values calculated in this work from activation energy of viscosity values. Solubility parameter values estimated using other approaches (surface tension and free energy of viscosity) are generally larger than the δIL values determined using our approach, with the largest values estimated from the free energy of viscosity, as reported by Kilaru and Scovazzo.27 CO2 solubility as a function of the RTIL solubility parameter at 25 °C is shown in Figure 2. When δIL < 25 (J/cm3)1/2, the observed solubility is inversely proportional to the solubility parameter. The observed trend can be explained by understanding the definition of the solubility parameter from a molecular level. Hildebrand defined the solubility parameter as the square root of the cohesive energy density, which is related to intermolecular interactions in the pure substance. Hence, CO2 solubility is expected to be a maximum in RTILs with cohesive energy density equal to that of CO2. Therefore, RTILs with solubility parameters close to the solubility parameter for CO2 [12.3 (J/cm3)1/2] at 25 °C are expected to have high CO2 solubility. According to the RST, a semilog plot of Henry’s law constant of carbon dioxide versus (δIL - δCO2)2 should yield a straight line at each temperature (eq 7). Plots prepared using the solubility data measured in this study with the predictions for δIL are shown in Figure 3 for data at 10, 25, and 40 °C. As predicted from RST (eq 7), generally, linear plots are observed,
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Table 6. Hildebrand Solubility Parameters for RTILs Estimated Using Different Approachesa δIL (J/cm3)1/2 vap
from measured ∆U
(eq 7)
RTIL
this work
ref 38
ref 37
ref 39
Emim Tf2N Bmim Tf2N Hmim Tf2N Bmim BF4 Omim BF4 Bmim PF6 Emim BETI
19.3 20.9 19.5 24.8 26.6 22.7 21.6
22.8 22.9 22.9
22.7 21.4 20.6
21.3 19.8 19.0 24.8
a
25.2
from surface tension measurements, ref 34
Hansen solubility parameter from surface tension measurements, ref 26
from free energy of activation of viscosity, 27
22.7 20.6
27.5 26.5 25.2
25.3
26.6 29.5
21.3 26.5 26.6 25.1
18.7
Values are at 25 °C, except those estimated by Kilaru et al.26 and Kilaru and Scovazzo,27 which are at 30 °C. Table 7. Fitted Parameters in the Regular Solution Model (Eq 6)a RST parameter
10 °C
25 °C
40 °C
A B × 103 fCO20(bar) VCO2 (cm3/mol)
3.1 ( 0.2 3.4 ( 1.5 22 ( 1 8.0 ( 3.5
3.3 ( 0.2 3.0 ( 1.3 27 ( 1 7.4 ( 3.2
3.7 ( 0.2 2.4 ( 1.3 41 ( 1 6.2 ( 3.4
a The molar volume of CO2 as a hypothetical liquid was calculated from the fitted values for B, assuming φCO2 ) 1. Uncertainty values represent 95% confidence intervals.
Figure 2. Solubility parameter vs measured CO2 solubility in various RTILs at 25 °C.
Figure 3. Logarithm of the Henry’s law constant vs the square of the difference in solubility parameters between RTIL and CO2 at 10, 25, and 40 °C.
with slope and intercept values (A and B) listed in Table 7. Observed deviations from linearity may result from complex interactions between the CO2 and the RTIL that are not captured by the RST approach. Using eq 8 to estimate δIL from Eavis may also lead to deviations from RST predictions. The fitted values for A and B can be used to estimate values for the standard state fugacity of CO2 as well as the molar
volume of CO2 as a hypothetical liquid. The standard state fugacity was calculated directly from the fitted values for A (eq 6), and these values are included in Table 7, with values ranging from 22 bar at 10 °C to 41 bar at 40 °C. Prausnitz and Shair correlated low pressure solubility data for a collection of gases in nine different organic solvents (not ionic liquids) and developed a corresponding states relationship between the reduced fugacity (standard state fugacity relative to the critical pressure) and the reduced temperature.45 Using this relationship, the standard state fugacity for CO2 was estimated to be 32 bar at 10 °C, 48 bar at 25 °C, and 59 bar at 40 °C. The agreement between these estimates and the fugacity values determined from a fit of the experimentally determined solubility values is reasonably good and provides further evidence of the validity of the approach used to estimate the ionic liquid solubility parameters. The parameter B is proportional to both the molar volume of CO2 as a hypothetical liquid, VCO2, and φIL2. With CO2 mole fractions in these ionic liquids less than 0.05 (Table 3), it is reasonable to assume φIL ) 1. With this assumption, the molar volume of the hypothetical liquid was calculated for CO2 at each temperature, and these values are included in Table 7. Prausnitz and Shair45 report a value of 55 cm3/mol for the liquid molar volume of CO2. Hildebrand and Scott46 report a value of 40 cm3/mol. These values are 5-10 times larger than the values determined from the fit of the solubility data reported here. This agreement is reasonable, given the uncertainty arising from the linear fit and the assumptions made in deriving the regular solution model and the approximations involved in estimating the solubility parameters for each ionic liquid. A comparison of experimental and predicted Henry’s law constant values is shown in Figure 4, where predicted values were determined using A and B values determined at each temperature. Excellent agreement is observed between the predicted and the experimental values. Most of the predictions fall within 10% of measured values, with all predictions within 27% of experimental values. The largest deviation between prediction and experiment is found for Emim TfO, with deviations of 23-27%. It is not clear why this particular ionic liquid might behave differently than the others with respect to intermolecular interactions governing viscosity and CO2 solubility. The agreement between RST prediction and experimental observation in this study (Figure 4) is generally comparable to
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010
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6,10,47-49
Figure 4. Comparison between the predicted Henry’s law constant and the measured Henry’s law constant for CO2 in a variety of ionic liquids. Values were predicted using RST with the RTIL solubility parameter estimated from the activation energy of viscosity (eq 8) and A and B values from Table 7 for each temperature (eq 6). Table 8. Partial Molar Enthalpy and Partial Molar Entropy of Absorption for CO2 in RTILsa ∆sjCO2 (J/mol K) RTIL ∆hjCO2 (kJ/mol) Bmpy BF4 Omim BF4 Hmim BF4 Hmim Tf2N Emim Tf2N Emim BETI Emim TfA Emim TfO Bmim Tf2N Pmmim Tf2N Bmpy Tf2N Bmim BF4
-8 ( 3 -13 ( 3 -14.6 ( 0.6 -14.7 ( 0.7 -18 ( 3 -15 ( 4 -12 ( 4 -13 ( 5 -12 ( 4 -11 ( 1 -10.4 ( 0.9 -14 ( 1
-27 ( 10 -42 ( 12 -50 ( 2 -50 ( 2 -59 ( 10 -50 ( 13 -41 ( 15 -42.6 ( 0.2 -40 ( 13 -36 ( 5 -34 ( 3 -44 ( 5
a Values for Bmim Tf2N, Pmmim Tf2N, Bmpy Tf2N, and Bmim BF4 were reported by Hou and Baltus.14 Uncertainty values represent 95% confidence intervals.
agreement reported by others who have used other approaches for determining solubility parameters for RTILs from different measured properties.26,27,34,37-39 Measuring the activation energy of viscosity involves a relatively simple and inexpensive approach for estimating δIL when compared to measuring surface tension or energy of vaporization. Therefore, the approach presented here provides a simple yet reasonably accurate means to predict low pressure solubility of CO2 in RTILs. Effect of Temperature on Solubility. In all of the tested RTILs, CO2 solubility was found to decrease with increasing temperature, in agreement with other reports in the literature for CO2 solubility in different RTILs. The sensitivity of H to temperature can be related to the partial molar enthalpy and partial molar entropy due to CO2 absorption: ∂ln H ∆hjCO2 ) R ∂(1/T)
(
)
H ( ∂ln ∂ln T )
∆sjCO2 ) -R
(11)
P
(12)
Values for ∆hjCO2 reflect energetic interactions between CO2 and the RTIL, while ∆sjCO2 values provide an indication of ordering resulting from absorption of CO2 into the RTIL. Values for ∆hjCO2 and ∆sjCO2 were determined from appropriate plots of H versus T and are listed in Table 8. These values are in general agreement with values reported by others for the same ionic
liquids. A table showing a comparison of values is in the Supporting Information. As discussed by Finotello et al,49 the negative values for both ∆hjCO2 and ∆sjCO2 are consistent with expectations developed from thermodynamic arguments for relatively high solubility gases. With data collected at only three temperatures, the uncertainty in ∆hjCO2 and ∆sjCO2 values is relatively large, making it difficult to draw conclusions about any effect of RTIL structure on these parameters. However, it does appear that both ∆hjCO2 and ∆sjCO2 are smaller for the two pyridinium-based RTILs (Bmpy BF4 and Bmpy Tf2N) when compared to the other imidazolium-based RTILs. With the larger ring in the pyridinium cation compared to imidazolium, the positive cation charge can be more delocalized, reducing the strength of the interaction between the CO2 and the RTIL, consistent with the smaller values for ∆hjCO2. Similarly, the more delocalized charge is also expected to impact the ordering or structure resulting from introduction of CO2 into the RTIL, yielding smaller values for ∆sjCO2 for the pyridinium-based ionic liquids. Conclusions The solubility of carbon dioxide in eight different commercially available RTILs was measured at three different temperatures using a transient liquid thin film method. Measurements were performed at low CO2 pressures, with solubility reported as the Henry’s law constant for each system. Of the tested ionic liquids, CO2 solubility on a mole fraction basis was found to be highest in Hmim Tf2N and lowest in Bmpy BF4. Experiments were performed with four different ionic liquids with Emim cation. Carbon dioxide solubility was comparable in Emim Tf2N and Emim BETI and lowest in Emim TfO. Consistent with previous reports, the solubility was found to increase as the length of the alkyl chain on the cation increased. This can be attributed to the increasing free volume and the reduction in cation-anion columbic forces that result with a longer alkyl chain length. RST was applied to interpret CO2 solubility with RTIL solubility parameters estimated using Eyring’s reaction rate theory to relate the RTIL solubility parameter to the activation energy of viscosity. Solubility parameters estimated using this approach were found to be in very good agreement with values determined from literature values for the energy of vaporization. Carbon dioxide solubility was found to be inversely proportional to the ionic liquid solubility parameter and correlated well with the square of the difference in solubility parameter between ionic liquid and carbon dioxide. The temperature sensitivity of the Henry’s law constant was used to determine the partial molar enthalpy and partial molar entropy of CO2 absorption. Values for ∆hjCO2 and ∆sjCO2 were not strongly dependent on ionic liquid structure for the ionic liquids with imidazolium cation. A comparison of ∆hjCO2 and ∆sjCO2 in pyridinium-based ionic liquids to values in imidazolium-based ionic liquids shows smaller values for the ionic liquids with pyridinium cation, indicating weaker RTIL-CO2 interactions for the pyridinium-based ionic liquids. The transient thin liquid film technique used to determine gas solubility also yields the infinite dilution diffusion coefficient for carbon dioxide in the tested ionic liquids. Diffusion coefficient values will be reported and discussed in a subsequent publication.41 Acknowledgment We acknowledge the financial support from the National Science Foundation through Grant No. CTS-0522589.
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Supporting Information Available: Tables of partial molar enthalpy and partial molar entropy of absorption for CO2 in RTILs. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature A ) regular solution theory constant in eq 6 B ) regular solution theory constant in eq 6 D ) diffusion coefficient of target gas in RTIL (m2/s) Eavis ) activation energy for viscosity (kJ/mol) fCO20 ) fugacity of pure CO2 at standard state conditions (bar) fCO2G ) fugacity of pure CO2 in the gas phase at system temperature and pressure (bar) fCO2G ) fugacity of CO2 in RTIL at system temperature and pressure (bar) H ) Henry’s law constant (bar) ∆hjCO2 ) partial molar enthalpy of absorption for CO2 in RTIL (kJ/mol) L ) thickness of RTIL film (m) MWIL ) molecular weight of RTIL (g/mol) P ) gas pressure (bar) P0 ) gas pressure at t ) 0 (bar) R ) universal gas constant (8.314 Pa m3 mol-1 K-1) ∆sjCO2 ) partial molar entropy of absorption for CO2 in RTIL (kJ/mol K) t ) time (s) T ) temperature (°C or K) ∆Uvap ) internal energy change of vaporization (kJ/mol) V ) molar volume (m3/mol) V ) volume of gas (m3) VCO2 ) molar volume of hypothetical liquid CO2 (cm3/mol) VIL ) molar volume of RTIL (m3/mol) VIL ) volume of RTIL sample (m3) xCO2 ) mole fraction of CO2 in RTIL γCO2 ) activity coefficient of CO2 in RTIL δ ) solubility parameter [(J/cm3)1/2] δCO2 ) solubility parameter of CO2 [(J/cm3)1/2] δIL ) solubility parameter of RTIL [(J/cm3)1/2] FIL ) density of RTIL (g/cm3) φIL ) volume fraction of RTIL
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ReceiVed for reView November 19, 2009 ReVised manuscript receiVed April 12, 2010 Accepted April 28, 2010 IE901837K
