Carbon Dioxide Solubilities and Diffusivities in 1-Alkyl-3

Article pubs.acs.org/jced

Carbon Dioxide Solubilities and Diffusivities in 1‑Alkyl-3methylimidazolium Tricyanomethanide Ionic Liquids: An Experimental and Modeling Study Lawien F. Zubeir,*,† Tim M. J. Nijssen,† Theodora Spyriouni,§ Jan Meuldijk,‡ Jörg-Rüdiger Hill,§ and Maaike C. Kroon*,†,∥ †

Separation Technology Group, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, Groene Loper 5, 5612 AE Eindhoven, The Netherlands ‡ Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, Groene Loper 5, 5612 AE Eindhoven, The Netherlands § Scienomics GmbH, Professor-Messerschmitt-Straße 3, 85579 Neubiberg, Germany ∥ Department of Chemical Engineering, The Petroleum Institute, P. O. Box 2533, Abu Dhabi, United Arab Emirates S Supporting Information *

ABSTRACT: The solubility and diffusivity of CO2 in a series of 1-alkyl3methylimidazolium tricyanomethanide ionic liquids ([Cnmim][TCM] with n = 2, 4, 6, 7, 8; ILs) was studied using a magnetic suspension balance at temperatures ranging from 298 to 353 K and pressures up to 2 MPa. The effects of temperature, pressure, and alkyl chain length on CO2 solubility and diffusivity were examined. The electrolyte PC-SAFT (ePC-SAFT) equation of state was used to describe the solubility of CO2 in the ILs. The Henry’s law constant and the excess properties of solvation (Gibbs free energy, enthalpy, and entropy) were calculated. A series of equations derived from Fick’s second law were evaluated, and a Fourier expansion of Fick’s second law of diffusion was found to be the most suitable model for deriving diffusivities from gravimetric data. The diffusivities range from 10−10 to 10−9 m2·s−1 in the temperature and pressure ranges applied. The activation energies for CO2 diffusion (12−16 kJ· mol−1) were found to be in the range of traditional solvents.

1. INTRODUCTION

and diffusivities in these ILs is highly important for the development and evaluation of gas separation processes. There are numerous methodologies used by different groups to measure gas solubilities and diffusivities in different liquid media including ILs. Brennecke and co-workers9 reported the high pressure phase behavior of gases in solvents using the stoichiometric phase equilibrium apparatus. De Loos’ and Peters’ groups10,11 as well as Maurer and co-workers12 conducted their phase behavior measurements based on the synthetic method by means of different types of the Cailletet apparatus and the high pressure view cell technique, respectively. Chen et al.13 used the thermogravimetric analysis for determining the CO2 absorption rate and capacity in ILs. Other applied methods for evaluating the gas diffusivities are the pressure drop of the gas in a closed system containing the absorbent material,14,15 following the dissolving gas bubbles injected in microchannels,16 using online time-resolved FTIR

Ionic liquids (ILs), which are liquids consisting entirely of ions, have attracted a lot of interest in the past decade as potential candidates for CO2 capture to overcome the disadvantages related to volatile organic compounds (e.g., methanol and amines). ILs are mostly renowned because of their negligible vapor pressure, tunability, and stability. In the present work CO2 solubilities and diffusion coefficients in the low-viscous 1alkyl-3-methylimidazolium tricyanomethanide ([C nmim][TCM]) ILs family (with n = 2, 4, 6, 7, 8) are thoroughly investigated using the established thermogravimetric method.1−3 In addition to their low viscosity,4,5 the ILs studied show a high CO2/N2 selectivity,6 and in mixtures with amines they act as effective corrosion inhibitors and reduce toxicity.7 Moreover, in binary mixtures of [TCM]−-based ILs with water, enhanced CO2 solubilities are reported.8 In our previous work5 the dependence of the thermophysical properties on temperature and the alkyl chain length of these ILs have been systematically evaluated and compared to other imidazoliumbased ILs paired with a different anion. Combination of a complete set of data comprising thermophysical properties and thermal behavior of these ILs together with CO2 solubilities © XXXX American Chemical Society

Special Issue: Proceedings of PPEPPD 2016 Received: July 21, 2016 Accepted: November 8, 2016

A

DOI: 10.1021/acs.jced.6b00657 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Specifications of the Chemicals Used in This Work water content/(wt %)

a

compd

M/g·mol‑1

source

puritya

before drying

after drying

[C2mim][TCM] [C4mim][TCM] [C6mim][TCM] [C7mim][TCM] [C8mim][TCM] CO2

201.23 229.28 257.33 271.37 285.39 44.01

IoLiTec IoLiTec IoLiTec IoLiTec IoLiTec Hoek Loos

>0.98 >0.98 >0.98 >0.98 >0.98 0.99995

0.105 0.11 0.06 0.12 0.05

0.011 0.003 0.013 0.004 0.008

Purity (mole fraction) as reported by the manufacturer.

measurements by recording the characteristic IR spectra of the CO2 and the IL,17 or dynamic light scattering from bulk fluids containing dissolved CO2 in IL.18 Thermodynamic models able to model accurately the CO2 solubility in ILs are essential for the design and optimization of such processes. The electrolyte PC-SAFT (ePC-SAFT) is an equation of state (EoS) with a robust physical basis. It was developed by Cameretti et al.,19 as an extension of PC-SAFT20 that accounts explicitly for electrostatic interactions between charged species by using the Debye−Hückel theory. Since its appearance, it has been successfully applied in charged systems such as aqueous electrolytes19,21 and ILs.22 For ILs, in particular, a comparative study22 between various SAFT-based models was conducted for calculating the CO2 solubility in imidazolium-based ILs. That study concluded that ePC-SAFT was the most accurate model and that accounting for electrostatic interactions allows for predictive calculations without the need of adjustable binary interaction parameters. In this work, the solubilities and diffusion coefficients of CO2 in the above stated homologous series of imidazolium-based [TCM]− ILs are measured by means of the magnetic suspension balance. The effects of temperature, pressure, and alkyl chain length on CO2 solubility are examined and the results compared to available literature data. The ePC-SAFT is used to calculate the CO2 solubility in the [Cnmim][TCM]) ILs (n = 2, 4, 6, 8) as a function of temperature and pressure. Results with and without adjustable parameters kij are shown against the experimental data. Additionally, the Henry’s law constant and the Gibbs free energy, enthalpy and entropy of CO2 solvation are calculated. Diffusion models derived from Fick’s second law are applied in different regimes, and their window of application is established. The effect of the size of pressure steps on the diffusion coefficient is investigated. In addition, a selection of the most frequently used semiempirical correlations is implemented to estimate the diffusion coefficients of CO2 in ILs. To test the feasibility of these approaches for assessing the CO2 diffusivities in the studied ILs, the results are compared to the experimentally obtained values from the transient curves.

Figure 1. Molecular structure of 1-alkyl-3-methylimidazolium tricyanomethanide, where R represents the alkyl chain.

content of the delivered ILs was measured using a 795 KFT Titrino Metrohm Karl Fischer coulometer. The ILs were dried at 323 K under vacuum before usage so that the water has no effect on the measurements. The moisture content of the ILs before and after drying is listed in Table 1. Ultrahigh-purity CO2 (>99.995%) was purchased from Hoek Loos, Schiedam, The Netherlands. 2.2. Experimental Procedure. The solubility and diffusivity of CO2 in the [Cnmim][TCM] ILs (n = 2, 4, 6, 7, 8) were determined using a magnetic suspension balance (MSB; Rubotherm GmbH) over a wide temperature range from 288 to 353 K and pressures up to 2 MPa. A short description of the measuring method is given below. A detailed explanation of the measuring procedures, equipment, and sample preparation has been presented elsewhere.3,23 A systematic approach is required to obtain accurate solubility data. In this study the following steps were taken in order to determine the solubility of CO2 in [Cnmim][TCM] ILs. Prior to CO2 solubility measurements, the IL sample was thoroughly dried at 323 K under vacuum (Table 1), and the density as a function of temperature was determined. Then, the sample was introduced into the MSB to measure the absorption isotherms. Because no sample mixing is possible within the MSB, the step time must be sufficient to ensure that equilibrium has been reached. The experimental procedures mentioned above were tested to verify the reliability of the MSB to reproduce CO2 solubility data using the reference IL 1hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C6mim][Tf2N]). This IL was assigned by the IUPAC (Committee on the Thermodynamics of Ionic Liquids, Ionic Liquid Mixtures, and the Development of Standardized Systems) as the standard IL so that experimental data reported by different research laboratories could be compared and unexplained disagreements could be discussed.24 Our measurements of the CO2 + [C6mim][Tf2N] system are compared to the recommended reference values in a previous study.3 The main advantages of the MSB are as follows. (i) There is contactless magnetic coupling of the balance to the measuring cell: Therefore, the balance itself is not subjected to extreme conditions. Besides, the balance is not in contact with the gases to be measured, and, hence, absorption of corrosive gases (e.g.,

2. EXPERIMENTAL WORK 2.1. Materials. Table 1 shows the chemicals used in this work. The ILs 1-ethyl-3-methylimidazolium tricyanomethanide ([C2mim][TCM]), 1-butyl-3-methylimidazolium tricyanomethanide ([C4mim][TCM]), 1-hexyl-3-methylimidazolium tricyanomethanide ([C6mim][TCM]), 1-heptyl-3-methylimidazolium tricyanomethanide ([C7mim][TCM]), and 1-methyl3-octyl-imidazolium tricyanomethanide ([C8mim][TCM]) with a purity of >98% were kindly supplied by Ionic Liquids Technologies GmbH (IoLiTec); see Figure 1. The water B



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based on the perturbation theory for fluids according to which the free energy of a fluid is written as the sum of a reference fluid (repulsive interactions) and a perturbation term (attractive contributions). For PC-SAFT the reference fluid is the hardchain ahc and perturbation accounts for dispersion adisp and association (aassoc). ePC-SAFT adds one more contribution that accounts for electrostatic interactions of charged species (aion). For ePC-SAFT the residual Helmholtz free energy (ares) can be written as:19,21

H2S and NH3) can be measured. (ii) Only small sample sizes are required (∼0.5 g). (iii) A sequence of measurements (reactivation/degassing of the sample and actual absorption isotherm and desorption) can be programmed and the measurements run automatically: When the experiments are designed properly (i.e., maximizing the number of data points per unit of time without disturbing the system), both CO2 solubilities and diffusivities are assessed. (iv) The density of the gas phase surrounding the sample is directly measured using the MSB: This is done by weighing the sinker (a Ti-cylinder) with calibrated volume. The accuracy of direct measurement has advantages over using an EoS, since the measuring accuracy of the balance is higher than the accuracies of the standard temperature and pressure gauges and the impurities in the technical gases are not covered by EoS. (v) The balance is tared and calibrated periodically under process conditions, which improves the long-term stability and accuracy of the MSB: This so-called zero point correction is needed to correct for the external conditions (e.g., T, P, and humidity) causing a drift in the balance mechanics and due to internal changes causing zero point jumps, because of changes in the pressure after each step. During the measurements, the mass of the sample is weighed using a high-resolution mass balance (0.01 mg). To measure the absorption isotherms (i.e., Px diagram), the sample is held at a constant temperature (u(T) = 0.01 K) and the pressure (u(p) = 0.005 MPa) is changed stepwise and kept constant for a sufficient period of time until the sample is saturated with CO2 and equilibrium is reached (i.e., thermal, mechanical, and chemical equilibrium). This procedure is repeated from 0.1 up to 2 MPa in steps of 0.1 MPa. The mass of the dissolved CO2 (mCO2), taking the buoyancy effect into account, is obtained by:

ares = ahc + adisp + aassoc + aion

(3)

The aion contribution is derived from the primitive model of Debye−Hückel that treats the ions as charged spheres in a dielectric continuum: aion = −

κ 12πε

∑ xiqi 2χi

(4)

i

in which xi and qi are the mole fraction and the charge of ion i, respectively, ε is the dielectric constant of the medium, and χi is defined as: χi =

3 ⎡3⎤ 1 2 ⎢ ⎥ + ln(1 + κai) − 2(1 + κai) + (1 + κai) 2 (κai)3 ⎣ 2 ⎦ (5)

where ai is the ion diameter, κ is the inverse Debye screening length given by: κ=

mCO2 = mbal (P , T ) − (msc + s) + (Vsc + s + CO2) ρCO (P , T )

NA ∑ q 2ci kBTε i i

(6)

2

(1)

NA is Avogadro’s constant, kB is the Boltzmann constant, and ci is the molar concentration of ion i. 3.2. Parametrization. The ILs were considered to be fully dissociated into cation and anion. Each ion was characterized by the segment number (m), the segment diameter (σ), the dispersion energy (u/kB), and its charge. The associative interactions were not taken into account; therefore, the number of association sites (N) was set to zero. The parameters for the [Cnmim]+ cations, with n = 2, 4, 6, 8, were taken from a work of Sadowski and co-workers,22 where they were fitted against density data of pure ILs consisting of the anions [BF4]−, [PF6]−, and [Tf2N]−. Keeping the same parameters would allow one to test their transferability to ILs with different anions. The parameters for the [TCM]− anion were fitted against density data, measured by some of the authors of this work,5 for the [Cnmim][TCM] ILs at various temperatures and pressure equal to 0.1 MPa. It should be noted that the parameters were only fitted to liquid density data and not to other properties such as vapor pressure. This may affect the robustness of the model prediction for other properties that are more sensitive toward the dispersion energy parameter. The regression was performed by using the SciTherm module in the MAPS platform of Scienomics.25 The results of the fitting with ePC-SAFT are shown in Figure 2. The percent average relative error (ARE%) between the experimental and fitted data for [Cnmim][TCM] is 0.68, 0.11, 0.02 and 0.27%, for n = 2, 4, 6, and 8, respectively. The parameters for all species are presented in Table 2. The Lorentz−Berthelot combining rules were used for the cross-interactions:

where mCO2 is the mass of CO2 absorbed, mbal is the balance reading, (msc+s) is the total mass of the loaded sample container, (Vsc+s+CO2) is the volume of the sample with the absorbed gas and the sample container and ρCO2(P,T) is the density of CO2 at the operating conditions. Assuming that the volume of the CO2 absorbed is insignificant, eq 1 reduces to: mCO2 = mbal (P , T ) − (msc + s) + (Vsc + s) ρCO (P , T ) 2

(2)

where Vsc+s is the volume of the sample container and the sample. The product of the volume of the loaded sample container and the CO2 density is included to quantify and correct for the buoyancy phenomenon. The buoyancy effect cannot be reduced or prevented as a disturbance and acts on a body that is located in a fluid atmosphere with density ρ. To determine the volume of the sample, isothermal buoyancy of the sample in an inert gas environment at different pressures must be either measured or simply calculated from the mass of the evacuated sample and its density. Densities as a function of temperature for the ILs were measured using an Anton Paar SVM 3000 Stabinger viscometer. The experimental data are reported elsewhere.5

3. THERMODYNAMIC MODELING USING ePC-SAFT 3.1. Model. The electrolyte perturbed chain statistical associating fluid theory (ePC-SAFT)19 EoS was used in this work. ePC-SAFT is an extension of PC-SAFT20 that accounts explicitly for electrostatic interactions. The PC-SAFT EoS is C



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xCO2 =

V ϕCO (T , P ) 2

L ϕCO (T , P , xCO2)

(9)

2

4. RESULTS AND DISCUSSION 4.1. Density and Viscosity. Table 3 shows the densities, ρ, viscosities, η, and molar volumes, V̅ , of the [Cnmim][TCM] ILs at 298.15 K after drying the sample.5 The first two properties are measured using the Anton Paar (SVM 3000 Stabinger) viscometer. The densities are needed for the prediction of the molar volumes of CO2 (eq 14) and the viscosities for the prediction of the diffusivities using the correlations in section 4.5. The density of the ILs decreases with increasing temperature and the alkyl chain length. The latter can be explained by an increase in free volume, due to the steric hindrance caused by the alkyl chain and the increase in distance between the cation and the anion.26 However, viscosity increases with increasing alkyl chain length, due to the larger attractive intermolecular interactions of the alkyl chains.27 These two dependencies are expected to have opposing effects on the diffusion coefficients in the ILs. An elaborate evaluation of the densities and viscosities of [TCM]−-based ILs is given elsewhere.5 4.2. Solvent Expansion. Nearly all methods applied for measuring gas solubilities require a correction of the raw experimental data to include the actual volume or density of the sample. When the sample volume is constant during the measurement, it is sufficient to measure the volume in a separate experiment before and after the absorption measurement is conducted. However, if this is not the case and the sample expands upon gas absorption, additional measurements or assumptions are needed for the data correction. For instance, in volumetric measuring methods, an adequate determination of the volume occupied by the sample is required. In gravimetric experiments, the buoyancy effect acting on the sample is proportional to the volume of the sample. The buoyancy is the main source of deviations using the gravimetric method. Therefore, the dilation of the ILs has to be taken into account to represent the sample volume correctly. The following correction method,28 only applicable for relatively low pressures ( 0

concentration increase in the IL has to be caused by diffusion.

dC = 0 for z = L dz

Furthermore, to minimize the effect of concentration on the diffusion, the stepwise pressure increase is limited to 0.1 MPa.

where D is the diffusion coefficient (m2·s−1), C is the CO2 concentration (kg·m−3), t is the time (s), z is the diffusion distance (m), and L is the height (m) of the sorbent medium (i.e., the IL). Equation 19 can be readily solved if appropriate boundary conditions are provided that apply to a specific experiment. Furthermore, modern computational methods allow for a numerical solution of eq 19. In gravimetric absorption measurements the mass of the sorbed penetrant is measured over time. Appropriate solutions of Fick’s second law for these types of measurements include series solution that converge promptly over the long period of time (needed to reach the equilibrium). For this purpose solutions have been derived, such as eq 21 by Carslaw and Jaeger40 and the Gaussian error function eq 22.41

The assumptions made to describe the diffusion rate-controlled gas absorption in liquid films exhibiting one gas−liquid interface and the analysis to correct for the height of the sample upon CO2 absorption are thoroughly described in our previous work.3 For the one-dimensional diffusion of gas molecules in a liquid with a constant diffusion coefficient, Fick’s second law reads:

∂C ∂ 2C =D 2 ∂t ∂z

(20)

(19)

with the following boundary conditions: I



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for D. Equations 23 and 24 are respectively the so-called shortterm43 (mt/m∞ ≤ 0.5) and long-term44 (mt/m∞ ≥ 0.5) approximations of eq 21. The relative deviation of these equations is supposed to be in the order of 0.1% compared to eq 21.44 1/2 mt − m 0 2 ⎛D⎞ = ⎜ ⎟ t 1/2 m∞ − m0 L⎝ π ⎠

(23)

⎛ −Dπ 2t ⎞ mt − m 0 8 = 1 − 2 exp⎜ ⎟ m∞ − m0 ⎝ 4L2 ⎠ π

(24)

In order to confirm the validity of these approximations for the regimes they are designed for and to evaluate the numerical values obtained for D, the percent absolute relative deviation (ARD, %) has been calculated; see eq 25. The numerical solution to Fick’s second law (eq 20) was used as a reference, using 1000 spatial and temporal grid points. This solution has been obtained using MATLAB’s built-in partial differential equation solver.

Figure 11. Calculated diffusivities and the relative uncertainties (k = 1) of CO2 in [C6mim][TCM] at 308.15 K for different pressure step sizes (where, for example, 7E-10 represents 7 × 10−10): (open up-triangles) ΔP = 0.1 MPa; (black filled up-triangles) ΔP = 0.5 MPa; (open downtriangles) ΔP = 1 MPa. Dashed lines are a guide for the eye.

ARD/% = 100

D − Dref Dref

(25)

The relative error calculated for the different derivations and simplifications of Fick’s second law of diffusion, eqs 21−24, are shown in Figure 7 as a function of the Fourier number, Fo (eq 26). The summations in eqs 21 and 22 were terminated when the difference in the argument of the subsequent terms was sufficiently small ( 0.1 are most suitable for the data obtained using the magnetic suspension balance.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00657. All the CO2 solubility and diffusivity data in the different [TCM]−-based ILs (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(L.F.Z.) E-mail: [email protected]. Phone: +31 40 247 8235. *(M.C.K.) E-mail: [email protected]. Phone: +971 2 607 5317. M



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ORCID

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Maaike C. Kroon: 0000-0002-5985-986X Funding

European Union seventh Framework project “IOLICAP” (Grant Agreement No. 283077). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the European Union Seventh Framework Poject “IOLICAP” (Grant Agreement No. 283077) is gratefully acknowledged.

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Carbon Dioxide Solubilities and Diffusivities in 1-Alkyl-3

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