A High-Pressure Quartz Spring Method for Measuring Solubility and

Article pubs.acs.org/IECR

A High-Pressure Quartz Spring Method for Measuring Solubility and Diffusivity of CO2 in Ionic Liquids Yanan Gong, Hongtao Wang, Yifan Chen, Xiaohui Hu, Abdul-Rauf Ibrahim, Ako-Rajour Tanyi, Yanzhen Hong, Yuzhong Su, and Jun Li* Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, National Engineering Laboratory for Green Chemical Productions of Alcohols, Ethers and Esters, Xiamen University, Xiamen 361005, P. R. China ABSTRACT: A high-pressure gravimetric apparatus using a quartz spring for measuring solubility and diffusivity of CO2 in ionic liquids (ILs) was established for the first time. The time-dependent amounts of CO2 were recorded with a telescopic cathetometer and analyzed by using a one-dimensional diffusion model to obtain diffusion coefficients of CO2 in two ILs, namely, 1-n-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF6]) and 1-butyl-3-methyl imidazolium tetrafluoroborate ([bmim] [BF4]) at pressures up to 10 MPa. Solubility data of CO2 in the two ILs up to 20 MPa were also obtained from its equilibrium masses and compared with those reported in the literature. The Peng−Robinson equation of state with the van der Waals one-fluid mixing rules was employed to correlate the experimental solubility data, revealing satisfactory calculation results. The measured diffusion coefficients of CO2 in [bmim][PF6] and [bmim][BF4] separately increase from 3.550 × 10−10 to 6.064 × 10−10 m2/s and from 7.184 × 10−10 to 9.880 × 10−10 m2/s following the pressure increase from 2.0 to 10.0 MPa at 323.2 K, while those at 5.0 MPa and different temperatures follow the Arrhenius equation, providing the diffusion activation energies of 25.53 and 20.30 kJ/mol for the [bmim][PF6]−CO2 and [bmim][BF4]−CO2 systems, respectively.

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INTRODUCTION Ionic liquids (ILs) are salts composed of organic cations and inorganic/organic anions. Unlike other liquid media, they have many extraordinary features such as negligible vapor pressure, wide liquid range, high thermal stability, and wide electrochemical window; with universal industrial applications, including chemical synthesis, polymerization, and catalysis.1 Nonetheless, there are challenges in their applications in certain areas. For example, in traditional separations such as distillation, separating products from reactants or catalysts in ILs has not been successful due to their extremely low vapor pressure.2 On the other hand, supercritical CO2 (sc−CO2), as an effective solvent has attracted research attention due to not only its lower critical pressure and temperature compared with most gases but also its nontoxicity and abundance among other properties.3 sc− CO2 is highly soluble in ILs while ILs have hardly any solubility in sc−CO2;4 therefore, employing binary systems involving sc− CO2 and ILs can mitigate several separation challenges by tapping the extraction power of sc−CO2. Consequently, many researchers have focused on exploiting the potential of IL−CO2 binary systems. Blanchard et al. used CO2 to extract naphthalene from 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6])2 and later demonstrated that CO2 was also able to separate numerous solutes from the IL with recovery rates higher than 95%.5 Results showed that separation problems were settled without cross-contamination with the assistance of CO2 in their system, which was thus seen as a promising procedure to meet the “green chemistry” requirement. In the meantime, Ibrahim et al. showed recently that coupling a solid IL with a system that used CO2 as reactant could enhance the synthesis of rhombohedral calcite.6 The growing applications have made studies of the thermodynamic and diffusion behavior of these systems all the more paramount. © 2013 American Chemical Society

Accordingly, lots of researches including experimental measurement and theoretical modeling have been conducted to explore the phase behavior of the IL/CO2 systems at high pressure.7 Experimental methods used to determine the phase equilibrium in the literature can be divided into two main categories: analytical and synthetic methods.7 This classification is mainly dependent on whether the overall mixture composition of the system in question is precisely known (synthesized) or not (analyzed). Shariati et al. used the synthetic method to visually determine bubble point pressures and vapor−liquid equilibrium (VLE) data for the IL/CO2 binary systems involving several ILs ([bmim][PF6], [emim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4]).8−10 Blanchard et al. employed both synthetic and analytic methods to explore the phase behaviors of ILs ([bmim][PF 6 ], [C 8 mim][BF 4 ], [bmim][NO 3 ], [emim][EtSO4], [N-bupy][BF4]) and CO2 binary systems.2 Baltus et al. applied the analytical method with a quartz crystal microbalance to obtain the solubility data of CO2 in a series of imidazolium-based room-temperature ionic liquids.11 Their apparatus was able to detect the frequency response of a typical IL-coated crystal exposed to CO2. Meanwhile, Anthony et al. employed an analytical gravimetric microbalance to acquire the solubility data of nine different gases in [bmim][PF6].12 It is important to note however that there are deviations in the results reported in the literature which may due to differences in experimental methods as well as the purity of precursors. Although the quartz spring-based gravimetric approach has been widely applied to study phase equilibrium and diffusion behaviors of systems at low pressures,13 to the best of our Received: September 28, 2012 Accepted: February 12, 2013 Published: February 12, 2013 3926

dx.doi.org/10.1021/ie400267h | Ind. Eng. Chem. Res. 2013, 52, 3926−3932

Industrial & Engineering Chemistry Research

Article

knowledge, the procedure has not been extended to high pressure systems. As a result, in this work, a high pressure procedure based on a quartz spring was developed and employed to obtain simultaneously, the solubility and diffusivity data for CO2 in two imidazolium-based ILs ([bmim][PF6] and [bmim][BF4]). This is important because the literature reports on diffusivity of CO2 in IL, particularly, at high pressure, are few.14 Nevertheless, Shiflett et al. measured diffusivities of CO2 in two ILs ([bmim][PF6] and [bmim][BF4]) up to 2 MPa using experimental data from a commercial gravimetric microbalance,15 while Ferguson et al. provided diffusivities of several gases in phosphonium-based ionic liquids at near ambient pressures.16 In terms of theoretical modeling for the phase behavior of IL− CO2 binary systems, the cubic equation of state (EoS) has been widely applied. For example, the Peng−Robinson (PR) EoS combining a quadratic mixing rules with two binary interaction parameters has been used to model the high-pressure solubility of CO2 in [Cnmim][Tf2N].17 Valderrama et al. employed the PR EoS with the Wong−Sandler mixing rules to describe the VLE of eight IL−CO2 binary systems.18 Arce et al. reported the modeling of 17 IL−CO2 binary mixtures by using Peng− Robinson/Stryjek−Vera (PRSV) EoS with the Wong−Sandler mixing rules and the one-fluid van der Waals mixing rules (vdW1), showing that the latter mixing rules gave good results.19 Yokozeke et al. used the Redlich−Kwong EoS to correlate the [bmim][PF6]−CO2 and [bmim][BF4]−CO2 binary systems,15 and recently a generic van der Waals EoS to model the solubilities of several gases in imidazolium-based ionic liquids, indicating that all “cubic” modified EoS work equally well for the systems.20 Ally et al. employed a semiempirical irregular ionic lattice model with two parameters to correlate and predict the solubilities of CO2 in several ILs.21 Kroon et al. utilized the truncated perturbed chain polar statistical associating fluid theory (tPC-PSAFT) EoS to model the phase behavior of IL−CO2 systems.22 In this work, the modeling of solubility of CO2 in ILs was carried out by using PR EOS combined with vdW-1 for comparison with the experimental data from the established quartz spring-based gravimetric approach.

Figure 1. Schematic diagram of the procedure with a quartz spring at high pressure: (1) CO2 cylinder; (2) compressor; (3) air thermostat; (4) high pressure visual cell; (5) quartz spring; (6) sample basket; (7) preheater; (8) telescopic cathetometer; (BPR) back pressure regulator; (V-1) entrance/check valve; (V-2) exhaust valve.

the initial position of the bottom of the sample basket, giving a system measurement error of 3.1811 × 10−6 mol for CO2. After the initial measurement, CO2 (from the gas cylinder) was introduced into the visual cell by passing a coil until a desired pressure with the help of the back pressure regulator with a maximum variation of ±0.3 MPa. In the meantime, the temperature of the cell was maintained by the air bath at a desired value with a maximum variation of ±0.5 K (high variation was caused by the introduction of high pressure CO2). The pressure and temperature monitors were carefully calibrated by standard pressure gauge and thermometer prior to use. The position of the basket was recorded with the cathetometer after the stability of the desired temperature and pressure, and its successive change in positions were subsequently recorded over a period of time until phase equilibrium.

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CALCULATION METHODS Solubility. To calculate the amount of CO2 dissolved in IL at any time or solubility at equilibrium, force analysis of the sample basket is conducted with the assumption that the ILs have negligible solubility in CO2.3 When the system is vacuumed, the total mass of the basket and sample is equal to the tension of the spring. Thus,

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m1g = T1

EXPERIMENTAL SECTION Materials. Carbon dioxide with purity >99.9% was purchased from Linde Gas, Xiamen-China. The ILs ([bmim][BF4] and [bmim][PF6]) both with purity >99% and water content 0

and

t>0

and

(12)

(13)

2

aiaj (1 − kij) (14)

2

∑ ∑ 0.5xixj(bi + bj) (15)

i=1 j=1

(6)

where Tc, pc, and ω are the critical temperature, critical pressure, and acentric factor, respectively; xi is the mole fraction of component i (namely, x1 is the solubility of CO2 in IL in molar fraction); and kij is the binary interaction parameter for the (i, j) pair which can be regressed by correlating the experimental data. For the correlation, an average absolute relative deviation of x1 (AARDx) was defined as the objective function

z=0

boundary condition 2: ∂C1 =0 ∂z

2

RTci pci

∑ ∑ xixj 2

b=

and

⎞⎤ ⎟⎟⎥ ⎠⎥⎦

where si = 0.37464 + 1.54226ωi − Meanwhile, the vdW-1 mixing rules for a and b can be written as

boundary condition 1: C1 = Cs

T Tci

i=1 j=1

t=0

(11)

0.26992ωi2.

initial condition: at

RT a − V−b V (V + b) + b(V − b)

where T, p, and V are the temperature, pressure, and molar volume, respectively, with the parameters a and b of component i defined as

∂C1 ∂ 2C = D 21 ∂t ∂z C1 = 0

(10)

z=L

where C1 is the concentration (in molarity) of CO2 in IL at time t, L is the thickness of the IL film, Cs is the solubility (in molarity) of CO2 in IL (see Assumption b), and D is the diffusion coefficient under given temperature and pressure. When applying the Laplace transform, eq 6 gives13

AARDx =

1 n

n

∑ |x1i ,exp − x1i ,cal|/x1i ,exp i=1

(16)

where the subscripts “exp” and “cal” represent the experimental and calculated data, respectively, and n is the total number of the 3928



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experimental data. The physical properties (Tc, pc, and ω) for the pure CO2 and ILs are listed in Table 1. Table 1. Physical Properties of the Pure Compounds Used for Correlation26 compound

Tc (K)

pc (MPa)

ω

[bmim][PF6] [bmim][BF4] carbon dioxide

708.9 632.3 304.19

1.73 2.04 7.382

0.7553 0.8489 0.2276

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RESULTS AND DISCUSSION Solubility Results. The solubility data of CO2 in [bmim][PF6] at different temperatures and pressures from this work and those from literature are indicated in Figure 3, indicating the Figure 4. The p−x diagram of the [bmim][BF4]−CO2 system at different temperatures. Data from this work: ▲, 313.2 K; ●, 323.2 K; ■, 333.2 K. Data from Lim et al.:29 Δ, 313.15 K; ○, 323.15 K; □, 333.15 K. Data from Aki et al.:30 ×-triangle, 313.15 K; ×-square, 333.15 K. Data from Kroon et al.:9 crossed circle, 320 K; crossed square, 330 K.

larger than that in [bmim][BF4] at the same experimental conditions, in accordance with the literature report.31 Correlating Solubility Data. The correlation results from eq 10 with PR EoS and the vdW-1 mixing rules are shown in Figures 5 and 6. These figures show good agreement between the

Figure 3. The p−x diagram of the [bmim][PF6]−CO2 system at different temperatures. Data from this work: ▲, 313.2 K; ●, 323.2 K; ■, 333.2 K. Data from Liu et al.:27 Δ, 313.15 K; ○, 323.15 K; □, 333.15 K. Data from Blanchard et al.:2 crossed triangle, 313.15 K; crossed circle, 323.15 K; crossed square, 333.15 K. Data from Pérez-Salado et al.:28 ×-triangle, 313.15 K; ×-square, 333.15 K.

experimental data from this work are in good agreement with those reported by Liu et al.27 and have relatively large discrepancies with data from Blanchard et al.2 and Pérez-Salado et al.28 at higher pressures although the consistence is good at low pressures. These deviations can be attributed to the purities of [bmim][PF6] used: the water content in the IL (0.1 wt %) used here is about the same as the one used by Liu et al.27 but different from that used by Blanchard et al.,2 suggesting the method can offer accurate measurements. The solubility data of CO2 in [bmim][BF4] are shown in Figure 4, indicating the experimental data from this work are in acceptable agreement with the data from Kroon et al.9 and Aki et al.30 at relatively low pressures, but have obvious deviations from those reported by Lim et al.29 at pressures larger than about 6 MPa. The differences can also be attributed to the different water contents in [bmim][BF4] (the anion [BF4]− is more hygroscopic than [PF6]−, so the water content in the loading procedure for IL to experimental apparatus can be different). Figures 3 and 4 also reveal that the solubility of CO2 in ILs decreases with increasing temperature at fixed pressure but increases with increasing pressure at constant temperature. Moreover, the solubility of CO2 in [bmim][PF6] is

Figure 5. Comparison of the experimental and modeled results for the [bmim][PF6]−CO2 system. Experimental results: ▲, 313.2 K; ●, 323.2 K; ■, 333.2 K. Modeled results: dash line, 313.2 K; dotted line, 323.2 K; solid line, 333.2 K.

experimental solubility data of CO2 in IL with those from the calculations, supporting that “cubic”-modified equations of state work equally well for modeling the solubilities of gases in imidazolium-based ionic liquids.20 The interaction parameter k12 increases with the increase of temperature as shown by eqs 17 and 18, respectively, for the [bmim][PF6]−CO2 and [bmim][BF4]−CO2 systems. The corresponding k12 and AARDx are listed in Table 2. k12 = 0.464 − 3929

109.4 T

(17)



Article

coefficients of CO2 in both ILs can be calcualted using eq 8. Following this, the obtained diffusitivities at different temperatures and two typical pressures are shown in Figure 9 while those at different pressures and 323.2 K are indicated in Figure 10. The figures show that the diffusion coefficient increases with increasing temperature and pressure, whereas the diffusivities are not that sensitive to pressure within the range invesitgated. In addition, the diffusion coefficient, as a function of temperature, is expressed by the Arrhenius equation in the form15 ln D = A −

109.3 T

(18)

Table 2. Correlating Results for Experimental Solubility Data systems [bmim] [PF6]− CO2 [bmim] [BF4]− CO2

313.2 K

323.2 K

333.2 K

k12 = 0.115

k12 = 0.125

k12 = 0.136

AARDx = 0.0182 k12 = 0.128

AARDx = 0.0147 k12 = 0.137

AARDx = 0.0262 k12 = 0.149

AARDx = 0.0252

AARDx = 0.0373

AARDx = 0.0117

(19)

where A is the pre-exponential factor, R is the universal gas constant in kJ/(mol K), Ea is the diffusion activation energy in kJ/ mol, and T is the temperature in Kelvin. Accordingly, the diffusivity data were fitted to the Arrhenius equation in order to calculate the activation energy, Ea, for both [bmim][PF6]−CO2 and [bmim][BF4]−CO2 systems, which yielded 25.53 and 20.30 kJ/mol, respectively, with the correlated results shown in Figure 9. The activation energies realized are comparable to the reported Ea values15 (27.2 and 24.3 kJ/mol, respectively) for the two binary systems at 2 MPa. As shown in Figure 10, although the solubility data of CO2 in the ILs were measured up to about 20 MPa, the diffusion coefficients obtained are only at pressures up to 10 MPa due to the obvious swaying of the quartz spring at the beginning several minutes when introducing CO2 and the fast diffusion of CO2 in IL at relatively high pressures. Therefore, further improvement for fast recording the time-dependent amounts of CO2 dissolved in IL is necessary by using the high-pressure quartz spring method at relatively high pressures.

Figure 6. Comparison of the experimental and modeled results for the [bmim][BF4]−CO2. Experimental results: ▲, 313.2 K; ●, 323.2 K; ■, 333.2 K. Modeled results: dash line, 313.2 K; dotted line, 323.2 K; solid line, 333.2K.

k12 = 0.476 −

Ea RT

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CONCLUSIONS

A high-pressure quartz spring method for measuring solubility and diffusivity of CO2 in ILs was developed, and studies for [bmim][PF6] and [bmim][BF4] at three different temperatures (313.2, 323.2 and 333.2 K) and various pressures were implemented. The solubility data were modeled using PR EOS with the vdW-1 mixing rules. From the studies, it can be

Diffusivity Results. The time-dependent amounts of CO2 dissolved in each IL were recorded from the experiments and are shown in Figures 7 and 8, revealing a good linear relationship between Mt/Ms and t0.5, and indicating that the diffusion

Figure 7. Amounts of CO2 in [bmim][PF6] at 313.2 K over time: (a) 5.0 MPa; (b) 8.3 MPa; solid line, linear correlation. 3930



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Figure 8. Amounts of CO2 in [bmim][BF4] at 313.2 K over time: (a) 5.1 MPa; (b) 8.1 MPa; solid line, linear correlation.

the accuracy and potential of the proposed procedure, and (3) the proposed phase equilibrium models described well the solubility data of CO2 in the two ILs. However, further work is necessary to more conveniently record the amount of CO2 in IL instead of using the telescopic cathetometer at the moment of introduction of CO2, particularly at relatively high pressures.

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: (+86)-592 2183055. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by NSFC (No.21276212) and SRFDP (No. 20100121110009). Figure 9. Diffusivities of CO2 in ILs at 5.0 ± 0.1 MPa and different temperatures: ■, [bmim][PF6]; ●, [bmim][BF4]; solid lines, correlated with eq 19.

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Figure 10. Diffusivities of CO2 in ILs at 323.2 K and different pressures: ■, [bmim][PF6]; ●, [bmim][BF4].

concluded that (1) the diffusivities and solubilities of CO2 in the two ILs at high pressures can be obtained at the same time by using the new apparatus, (2) the experimental results are in agreement with experimental data from the literature, indicating 3931



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A High-Pressure Quartz Spring Method for Measuring Solubility and

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