Mutual and Thermal Diffusivity of Binary Mixtures of the Ionic Liquids

Article pubs.acs.org/JPCB

Mutual and Thermal Diffusivity of Binary Mixtures of the Ionic Liquids [BMIM][C(CN)3] and [BMIM][B(CN)4] with Dissolved CO2 by Dynamic Light Scattering Michael H. Rausch,†,‡ Andreas Heller,†,‡ Jonas Herbst,† Thomas M. Koller,†,‡ Matthias Bahlmann,§ Peter S. Schulz,§ Peter Wasserscheid,§ and Andreas P. Fröba*,†,‡ †

Erlangen Graduate School in Advanced Optical Technologies, University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, D-91052 Erlangen, Germany ‡ Department of Chemical and Biological Engineering, Institute of Engineering Thermodynamics, University of Erlangen-Nuremberg, Am Weichselgarten 8, D-91058 Erlangen, Germany § Department of Chemical and Biological Engineering, Institute of Chemical Reaction Engineering, University of Erlangen-Nuremberg, Egerlandstraße 3, D-91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Ionic liquids (ILs) are promising solvents for gas separation processes such as carbon dioxide (CO2) capture from flue gases. For the design of corresponding processes and apparatus, thermophysical properties of ILs containing dissolved gases are required. In the present study, it is demonstrated that with a single optical setup, mutual and thermal diffusivities as well as refractive indices can be measured quasi-simultaneously for such mixtures. Dynamic light scattering (DLS) from bulk fluids was applied to determine mutual and thermal diffusivities for mixtures of 1-butyl-3-methylimidazolium tricyanomethanide ([BMIM][C(CN)3]) or 1-butyl-3-methylimidazolium tetracyanoborate ([BMIM][B(CN)4]) with dissolved CO2 at temperatures from 303.15 to 333.15 K and pressures between 2 and 26 bar in macroscopic thermodynamic equilibrium. Good agreement with literature data and only slight differences between the diffusivities measured for the two systems at the same temperature and comparable mole fractions of CO2 were found. Increasing mutual diffusivities with increasing mole fractions of CO2 are consistent with decreasing viscosities reported for other IL−CO2 mixtures in the literature and can be attributed to weakening of molecular interactions by the dissolved gas. For the conditions studied, no dependence of the thermal diffusivity on the temperature or the mole fraction of CO2 could be found.

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INTRODUCTION The separation of carbon dioxide (CO2) from flue gases and its subsequent storage is a controversially discussed option to reduce CO2 emissions to the atmosphere.1−4 For efficient gas separation processes, selective solvents with high CO2 solubility and diffusivity are required. Because of their potential to be tailored to specific applications by combining appropriate anions and cations, ionic liquids (ILs) are promising candidates to fulfill this profile without being volatile,5−7 which is a major drawback of currently used amines.3 At present, 1-alkyl-3methylimidazolium-based ILs carrying the anions tricyanomethanide ([C(CN)3]−) or tetracyanoborate ([B(CN)4]−) are discussed for this task because of their high CO2/N2 selectivity and comparatively low viscosity.8,9 Besides solubility data and other thermophysical properties, mutual diffusivities of mixtures of these ILs with dissolved CO2 and other gases are of special interest for the evaluation of the efficiency and kinetics of gas separation processes. Mutual diffusivities for CO2 and other gases dissolved in ILs available in the literature were predominantly obtained by analyzing the transient absorption process of the gas in the pure © 2014 American Chemical Society

IL. The most prominent methods are based on the analysis of the pressure drop of the gas in a closed system containing the IL10−14 or the mass change during gas absorption in the IL at constant gas pressure.8,15−21 Furthermore, mutual diffusivities were determined from the permeability of immobilized IL membranes either directly by a lag-time technique22−25 or by combining permeability results with solubility data obtained from separate experiments.26−28 Other approaches rely on the changing size of gas bubbles injected into the IL flowing in a microchannel,29 voltammetric measurements,30 or the temporal change of infrared spectra when the gas diffuses into the IL.31,32 For most of these methods, a considerable number of assumptions regarding the boundary conditions of the transient mass transfer process has to be made for data evaluation. Furthermore, the absence of convective effects superimposing the molecular diffusion process is usually assumed. Typical reported uncertainties in the resulting mutual-diffusivity data Received: February 25, 2014 Revised: March 28, 2014 Published: April 3, 2014 4636

dx.doi.org/10.1021/jp501973s | J. Phys. Chem. B 2014, 118, 4636−4646

The Journal of Physical Chemistry B

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range from questionable values of less than 1% up to 40%.10,12−14,20−25,29,32 Shiflett et al.18,19 even estimate the uncertainty to be within a factor of 2 in some of their diffusivity data whereas other authors do not specify uncertainties at all.8,11,15−17,26−28,30,31 In contrast to the methods summarized above, dynamic light scattering (DLS) can be used to measure transport properties such as mutual and thermal diffusivity33 and other thermophysical properties34,35 of fluid mixtures in macroscopic thermodynamic equilibrium. Here, strictly valid working equations are applied without the need for debatable assumptions. In context with ILs, DLS has successfully been tested for the precise measurement of the mutual diffusivity of their binary mixtures with molecular liquids.36,37 For the ILs 1butyl-3-methylimidazolium tricyanomethanide ([BMIM][C(CN)3]) and 1-butyl-3-methylimidazolium tetracyanoborate ([BMIM][B(CN)4]), it is demonstrated that a quasi-simultaneous determination of mutual and thermal diffusivity for ILs containing dissolved CO2 can be realized by DLS.

ppm equivalent to water mole fractions xCO2 of 0.006 and 0.012 were found for [BMIM][C(CN)3] and [BMIM][B(CN)4]. n-Hexadecane (n-C16H34) utilized as a reference fluid for checking the beam-displacement method for measuring the refractive index was purchased from Merck Schuchardt with a nominal purity of 99 mol % and used without further purification. For the same purpose, 1-hexyl-3-methylimidazolium tricyanomethanide ([HMIM][C(CN)3]) was synthesized similar to the procedure described for [BMIM][C(CN)3] using 1-hexyl-3-methylimidazolium chloride ([HMIM]Cl) as starting material. After drying on a vacuum line, a water content of 467 ppm (xCO2 = 0.007) was measured for [HMIM][C(CN)3]. The sample cell used in the present study exhibits a total inner volume of 40 mL and was designed for temperatures up to 573 K and a maximum pressure of 80 bar. It is made of hydrogen-resistant steel and was chemically nickel coated to anticipate corrosion effects. Four optical accesses allow the application of optical metrology. The cell temperature is measured with two calibrated Pt 100 Ω resistance probes with an absolute uncertainty (k = 2) of less than 0.01 K. The temperature control of the sample cell is realized by resistance heating where a temperature stability of better than 3 mK can be achieved. The temperature control loop is based on a temperature probe placed in the wall of the cell close to the resistance heating. The sample temperatures given within this study refer to the second probe. It is also positioned inside the cell material, but located close to the fluid. The pressure in the sample cell is recorded by a pressure transducer with an absolute uncertainty (k = 2) of 15 mbar. Approximately 30 mL of the filtered and dried IL was filled into the sample cell. Vacuum (0.5 mbar) was applied to the sample inside the cell for at least 30 min to remove any gases. Then, CO2 with a purity of 99.999 vol % provided by Linde was dosed into the sample cell via a bellow-type valve. Because of the negligible vapor pressure of the ILs studied, it can be assumed that only CO2 is present in the gas phase. Starting from about 50 bar, the pressure in the cell decreased as long as CO2 diffused into the IL. For [BMIM][B(CN)4], Figure 1 exemplarily depicts that directly after adding CO2 to the IL, streaks indicating convective mass transfer were formed. A movie in avi format showing the movement of the streaks is also available as Supporting Information. Similar convective contributions to mass transfer may also be present when smaller concentration gradients are applied to determine mutual diffusivities by transient measurement methods. In this case, erroneous mutual diffusivities are obtained if such effects are neglected for data evaluation. In our experiments, no more streaks could be observed visually after about 50 min. Large fluctuations in the scattered light intensity, however, still indicated the presence of significant convective effects. After about 24 h, these fluctuations disappeared and a constant system pressure was reached. At that time, equilibrium conditions could be assumed and first measurements of the molecular diffusion modes were performed. After varying the temperature or the CO2 pressure in the sample cell, waiting times of about 12 h proved to be sufficient to obtain steady-state conditions indicated by constant pressure at constant temperature. Measurements were performed at temperatures between 303 and 333 K in steps of 10 K and at least at two CO2 pressures in the range from about 2 to 26 bar. In the case of [BMIM][B(CN)4], CO2 was purged from the sample cell after the investigation of the

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EXPERIMENTAL SECTION Materials and Sample Preparation. The reactants for the synthesis of [BMIM][B(CN) 4] and [BMIM][C(CN) 3 ] summarized in the following were purchased from industrial suppliers. 1-Butyl-3-methylimidazolium chloride ([BMIM]Cl) was purchased from Solvent Innovation GmbH and washed with acetone prior to use. Potassium tetracyanoborate (K[B(CN)4]) was obtained from Merck KGaA and used as received. Sodium tricyanomethanide (Na[C(CN)3]) was purchased from Lonza. For cleaning Na[C(CN)3], a 0.25 M aqueous solution was stirred with activated carbon for 24 h. The activated carbon was filtered off using a filter with a pore size of 0.2 μm. Then, Na[C(CN)3] was recrystallized and received as a colorless solid. [BMIM][B(CN)4] was synthesized by reacting equimolar amounts of a 0.5 M aqueous solution of [BMIM]Cl and K[B(CN)4] suspended in distilled water under rigorous stirring for 24 h. The formed upper aqueous phase was decanted while the lower IL phase was washed with distilled water three times and dried at about 10−3 mbar and 333.15 K for at least 16 h. For the synthesis of [BMIM][C(CN)3], a similar procedure with the following differences was applied. Here, a 0.5 M aqueous solution of Na[C(CN)3] was used due to its solubility in water. Furthermore, the resulting IL was extracted with dichloromethane from the aqueous phase. Then, the organic phase was washed with distilled water three times before drying and removing dichloromethane by evaporation. Both ILs were obtained as colorless liquids with a purity of >99 mol % as proven by 1H NMR analysis (JEOL, ECX +400 spectrometer) and ion chromatography (DIONEX, Ultimate 3000 with separating column Acclaim Trinity P1). As the produced ILs still showed traces of particle-like impurities which would disturb the DLS experiments due to the strong light scattering intensities caused by particle scattering, the ILs were filtered again with a syringe filter with a pore size of 0.2 μm. Then, the ILs were dried on a vacuum line (0.5 mbar) at about 323.15 K for a time period of at least 4 h. Karl Fischer coulometric titration (Metrohm, 756 KF Coulometer) was used to measure the water content of the dried ILs with an expanded relative uncertainty (k = 2) of less than 20%. Values of 532 and 901 4637



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temperatures and pressures were used to calculate corresponding mole fractions of CO2 in [EMIM][B(CN)4] and [HMIM][B(CN)4] from the fit equations. These results were arithmetically averaged to approximate the mole fraction of CO2 in [BMIM][B(CN)4]. It should be mentioned that the averaged results deviate by up to 43% from those calculated from the Henry coefficient given by Mahurin et al.39 for 298.15 K and pressures from 1 to 10 bar. Also for CO2 dissolved in [EMIM][B(CN)4], the solubility data obtained corresponding to a further Henry coefficient reported by Mahurin et al.39 and those measured by Mota-Martinez et al.41 differ by up to 20%. Relying on the data of Mota-Martinez et al.,40,41 which are the only available data allowing a rough estimation of the solubility of CO2 in [BMIM][B(CN)4] at the experimental conditions investigated in the present study, an expanded uncertainty (k = 2) of 0.04 is estimated for the solubility data obtained by the approximation procedure. To estimate this uncertainty, the maximum difference of the solubility data for CO2 in [EMIM][B(CN)4] and [HMIM][B(CN)4] calculated from the fit equations at the investigated temperatures and pressures was divided by 2. Mutual and Thermal Diffusivity by DLS. With DLS, the scattered light intensity containing information on the dynamics of microscopic fluctuations in pressure, temperature, and concentration in case of a binary fluid mixture is analyzed in the time domain. It is a noninvasive method allowing the determination of various thermophysical properties of fluids in macroscopic thermodynamic equilibrium. Details on the DLS method42−44 and its application for the determination of mutual and thermal diffusivities37,45−47 are given in the literature. Only the features which are important in context with the present study are summarized in the following. The equilibration of microscopic fluctuations in temperature and concentration is governed by the thermal and the mutual diffusivity. The mean decay times of both types of fluctuations are analyzed by calculating the time-dependent intensity correlation function. For a heterodyne detection scheme where the scattered light is superimposed with much stronger coherent reference light, the normalized intensity correlation function takes the form

Figure 1. Visual observation of the IL [BMIM][B(CN)4] during the sample preparation: (a) pure IL; (b) directly after dosing CO2; (c) after 3 min; (d) after 50 min. A movie in avi format showing the movement of the streaks is also available as Supporting Information.

IL-gas mixtures to determine the thermal diffusivity of the pure IL. After the experiments, the IL samples were removed from the sample cell at atmospheric conditions and the water mass fraction was measured again. Presumably due to the purging procedure, a reduced water mass fraction of 205 ppm (xCO2 = 0.003) was found for [BMIM][B(CN)4]. For the more hygroscopic [BMIM][C(CN)3], an increased water mass fraction of 1873 ppm (xCO2 = 0.023) was measured, which is probably caused by the contact of the IL with ambient air after opening the sample cell. Nevertheless, the water content of [BMIM][C(CN)3] during the measurements is believed to be close to that measured after the initial drying procedure because the sample cell was evacuated for at least 30 min after filling the dried IL sample and charged with CO2 directly afterward. Solubility data from literature were used to estimate the mole fraction of CO2 in the ILs based on the measured temperatures and pressures. For [BMIM][C(CN)3], data obtained by a Cailletet apparatus over a pressure range from 5.8 to 61 bar at the same temperatures as studied here were applied.38 The data set for each temperature was fitted with a second-order polynomial and used to calculate the mole fractions of CO2 corresponding with the pressures measured in our experiments. The expanded uncertainty (k = 2) in the resulting mole fractions are estimated to be 0.01. For mixtures of [BMIM][B(CN)4] with dissolved CO2, only one Henry coefficient determined at 298.15 K could be found in the literature.39 Consequently, solubility data published for CO2 in 1-ethyl-3methylimidazolium tetracyanoborate ([EMIM][B(CN)4]) at temperatures from 278 to 343 K and pressures from 5.9 to 114 bar as well as in 1-hexyl-3-methylimidazolium tetracyanoborate ([HMIM][B(CN)4]) from 288 to 363 K and 2.7 to 83 bar were utilized.40,41 For both ILs, the experimental data were correlated with a two-dimensional fit. Our experimental

g(2)(τ ) = b0 + bt exp( −τ /τC,t) + bc exp(−τ /τC,c)

(1)

Here, the decay times of the two exponential functions, τC,t and τC,c, reflect the mean lifetimes of the temperature and concentration fluctuations in the binary mixture. The experimental constants b0, bt, and bc are mainly determined by the intensities of the scattered and the reference light as well as by effects that are caused by imperfect signal collection. τC,t and τC,c are related to the thermal diffusivity a and the mutual diffusivity D12 according to τC,t =

1 aq2

(2)

1 D12q2

(3)

and

τC,c =

For the systems studied here, D12 is by about two orders of magnitude smaller than a. Thus, the two decay times can be observed on different time scales. The scattering vector q can be determined from the refractive index of the fluid nfluid, the laser wavelength in vacuo λ0, and the scattering angle Θs by 4638


The Journal of Physical Chemistry B q=

4πn fluid sin(Θs /2) λ0

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of ±0.01°. A scattering angle of Θs = Θi = (90 ± 0.3)° (k = 2) can be realized by installing the mirrors M8 and M9 and adjusting backreflection from the windows of the sample cell (chain line). The 90° arrangement is also used for the measurement of the refractive index of the sample, for which a prism-shaped cell window and a measurement screen are installed. During the DLS experiments, the scattered light superimposed with reference light is detected by two photomultiplier tubes (PMTs). Their signals are amplified, discriminated, and fed to a single-tau and a multi-tau correlator for the calculation of the pseudocross correlation function. A multi-tau structure means that the sample times of the correlator channels increase with increasing lag time. With this quasi-logarithmic channel structure, sample times span over a range from a few nanoseconds up to many seconds so that processes on completely different time scales can be measured simultaneously. The single-tau correlator allows the manual adjustment of a fixed sample time for all 255 channels to access maximum information on the time range where one of the studied diffusion modes can be found. Hence, mutual and thermal diffusivity can be accessed consecutively by changing the sample time for the same scattering angle. In the present study, at least six small scattering angles in the range from 2.6° to 6.0° as well as a scattering angle of 90° were applied for each sample state. With the latter angle, only concentration fluctuations could be analyzed because the decay time of the temperature fluctuations is too small to be resolved by the correlators. For the mixtures of CO 2 and [BMIM][C(CN)3], mutual-diffusivity data could only be obtained for Θs = 90° because for the small scattering angles, strong disturbing signals probably caused by particle scattering were observed in the same time range as the signals associated with the concentration fluctuations. The data obtained from both correlators were evaluated regarding the decay times τC,t and τC,c with nonlinear regression. For the regression of the data from the multi-tau correlator, a theoretical model according to eq 1 was used. For the regression of the data from the single-tau correlator, the model was reduced to one single exponential focusing on only one of the diffusion modes. Various disturbing effects such as vibrations, particle scattering, incoherent external stray light, or convection in the sample can give rise to additional disturbing signals in the long-time range of the correlation functions. Such disturbances could be described by expanding the theoretical models by a linear and/or a quadratic term. A multifit procedure detailed by Heller et al.33 was used to check the applied regression models. Refractive Index by a Beam-Displacement Method. For the evaluation of the DLS experiments, refractive-index data for the studied sample mixtures at the corresponding thermodynamic states and at the wavelength of the used laser of 532 nm are required. For their measurement by a beamdisplacement method, the optical arrangement for Θs = 90° was used employing the prism-shaped quartz glass window in the sample cell and the measurement screen indicated in Figure 2. The optical path of the main beam through the prism for the case nprism > nfluid is illustrated in Figure 3. The zero-position on the screen, which corresponds to the optical axis, is determined when the sample cell is not installed. After that, the sample cell is positioned so that the initial laser beam following the optical axis is perpendicular to the outer surface of the prism-shaped window. The angle of incidence γ1

(4)

Θs is the angle between the directions of the incident light and the analyzed scattered light in the fluid. In the present study, measurements were performed at small scattering angles (Θs ≤ 6°) as well as at Θs = 90°. For the latter case, the uncertainty in the used refractive-index data directly affects the uncertainty in q. For small scattering angles, Θs can be deduced from the easily accessible incident angle Θi which is measured between the incident laser light outside the sample cell and the detection

Figure 2. Optical and electronic setup. The abbreviations in the figure are explained in the text.

direction of the scattered light, c.f. Figure 2. Θs and Θi are related by Snell’s law n fluid sin Θs = nair sin Θi

(5)

where the refractive index of air is assumed to be nair = 1. In this case, knowledge on the refractive index of the fluid nfluid with an uncertainty of about 10% is sufficient to obtain q from the combination of eqs 4 and 5 with an uncertainty of less than 0.2%. A schematic of the optical and electronic setup is shown in Figure 2. It allows the investigation of the thermal and the mutual diffusivity by DLS as well as of the refractive index by a beam-displacement method. A frequency-doubled Nd:YVO4 laser operated at output powers between 0.5 and 2 W is used as a light source. Mirrors (M) are used to guide the different beams within the setup. With a beam splitter (BS), the initial beam is separated into the main beam (solid line) and the reference beam (dashed line) ensuring heterodyne conditions. The intensity of both beams can be adjusted by combinations of half-wave plates (λ/2 retardation) and polarization beam splitters (PBS) and, for the reference beam, by an additional gray filter (GF). A lens (L) with a focal length of 2 m is used to focus the laser light into the sample cell (SC). The detection direction is defined by two stops (P1, P2) with apertures of 1 mm and a distance of about 1 m. When the mirror M8 is not installed, incident angles Θi between the main beam and the detection direction ranging from 3° to 9° from either side can be realized with mirror M6. The incident angle can be measured with a rotational table using the autocollimation technique with an uncertainty (k = 2) 4639



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Figure 4. Refractive-index data for n-hexadecane and [HMIM][C(CN)3] at a wavelength of 532 nm obtained with the beamdisplacement method in comparison with reference data49 and a correlation based on experimental data from an Abbe refractometer. Figure 3. Optical path for the measurement of the refractive index for nprism > nfluid.

measured with the beam-displacement method as well as the reference data are depicted in Figure 4. For [HMIM][C(CN)3] and n-hexadecane, temperature-independent deviations of 0.4 and 0.2% from the reference data were found. This may indicate that these deviations are originating from a slight misalignment of the sample cell with respect to the optical path. On the basis of the reference measurements and the worst-case analysis, an expanded relative uncertainty (k = 2) of less than 1% is estimated for the measurement of the refractive index using the beam-displacement method.

= 20° is then defined by the wedge angle of the prism. At the interfaces between the sample fluid and the glass prism as well as between the glass prism and the ambient air, the incident light is refracted according to Snell’s law. A caliper is used to measure the resulting displacement of the laser beam on the screen with respect to the optical axis Δy. The refractive index of the prism at the laser wavelength of 532 nm can be interpolated from the dispersion curve of the window material,48 resulting in nprism = 1.461. The length of the prism L is 29.762 mm, while the distance d between the prism and the screen was measured to be 2406 mm. With these data, nfluid can be determined iteratively from the equations n fluid sin γ1 = n prism sin γ2 (6) n prism sin γ3 = nair sin γ4

(7)

γ3 = γ1 − γ2

(8)

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RESULTS AND DISCUSSION A typical set of correlation functions recorded for the measurement of the mutual and thermal diffusivity is illustrated in Figure 5. Here, [BMIM][B(CN)4] was investigated at Θs = 5.883°, T = 303.12 K, and pCO2 = 12.377 bar, which corresponds with a mole fraction of CO2 of 0.254. In the presented normalized correlation functions, disturbing signals described by additional linear and/or quadratic terms in the correlation model were subtracted to give a clear impression of the light scattering signals related to fluctuations in concentration and temperature. In Figure 5a, the correlation function recorded with the multi-tau correlator featuring a quasi-logarithmic channel structure is shown. The faster exponentially decaying mode associated with the thermal diffusivity can be found in the short-time range, while the exponential function describing the decay of concentration fluctuations expands over a distinctly broader time range. The decay times evaluated from the correlator data by applying eq 1 as regression model and the corresponding uncertainties (k = 2) are given in Figure 5. Simultaneously with the multi-tau correlator, the single-tau correlator was operated with appropriate sample times to provide data from more correlator channels for the description of each exponential function. The correlation function in Figure 5b recorded with the single-tau correlator represents the slower diffusion mode related to the mutual diffusivity in a time range of about 4 ms. The correlator data were fitted to a single

and Δy = L tan γ3 + d tan γ4

(9)

A worst-case analysis taking into account uncertainties in L, Δy, and d of 1 mm, 3 mm, and 10 mm, respectively, showed that depending on the absolute value of nfluid, the method can provide refractive-index data with uncertainties ranging from about 0.3 to 0.7%. The method was also checked by comparing measured refractive-index data for [HMIM][C(CN)3] at temperatures between 293 and 333 K as well as for nhexadecane at temperatures between 303 and 373 K with reference data. For [HMIM][C(CN)3], results from measurements performed within the present study with an Abbe refractometer were used as reference data. Details on the Abbe method, the measurement results, and the corresponding correlation are summarized in the Supporting Information. The reference values for n-hexadecane were obtained by interpolating between the refractive-index data available for varying wavelength at the given temperatures.49 The refractive indices 4640



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represent the standard deviation (k = 2) of all single results contributing to the final value. For all single measurements, the combined standard uncertainties in D12 and a were additionally calculated according to the law of propagation of uncertainties. For this, the uncertainties in Θi, τC, and nfluid were taken into account on a confidence level of more than 95%. In all cases, agreement between the single measurements and the averaged results was found within combined uncertainties. For the mutual diffusivity of the [BMIM][C(CN)3]-based mixtures where only measurements for Θs = 90° could be performed with the single-tau correlator, the given uncertainties correspond with the results of the error propagation calculations. All measurements at small scattering angles were performed at an overall laser power of 0.5 W. Because of small light scattering intensities, a laser power of 2 W was applied for all measurements at Θs = 90°. For proving that laser heating does not affect the present results, the signals from concentration fluctuations were studied as a function of the laser power ranging from 0.5 to 2 W. Figure 6 shows the corresponding results for τC,c as a function of the measuring time for [BMIM][C(CN)3] at T = 303.01 K and pCO2 = 7.428 bar, which corresponds with xCO2 = 0.126.

Figure 5. Normalized correlation functions for a mixture of [BMIM][B(CN)4] and CO2 measured by a multi-tau correlator (a) as well as by a single-tau correlator in different time ranges (b and c) at Θs = 5.883°, T = 303.12 K, and pCO2 = 12.377 bar.

exponential function. Figure 5b depicts that the first data point slightly exceeds the fit curve. The reason for this behavior is a significant contribution of light scattering signals from temperature fluctuations in the short-time range. In consequence, the data from the first two to five correlator channels were not considered for the evaluation of τC,c. By reducing the sample time of the single-tau correlator, the correlation function shown in Figure 5c containing information on the thermal diffusivity could be recorded at the same experimental conditions. Here, the contribution of the slower diffusion mode associated with the mutual diffusivity is included in the description of all other disturbing signals. The stronger scatter of the correlator data, see Figure 5c, compared to those resulting from concentration fluctuations, see Figure 5b, can be explained by the smaller amplitudes of the light scattering signals caused by temperature fluctuations. Within the present study, 8 to 28 single results determined for varying scattering angles with the different correlators were averaged arithmetically to obtain the reported D12 and a data. This procedure was applied for the mutual diffusivity for the [BMIM][B(CN)4 ]-based mixtures and for the thermal diffusivity for all mixtures. Here, the uncertainties given in the data tables and illustrated in the corresponding figures

Figure 6. Measured mean lifetime of concentration fluctuations as a function of measuring time for different laser powers for a mixture of [BMIM][C(CN)3] and CO2 at Θs = 90°, T = 303.01 K, and pCO2 = 7.428 bar.

After comparable measurement times, distinctly smaller uncertainties in τC,c could be achieved with higher laser powers. All evaluated decay times agree within combined uncertainties, demonstrating that increased laser powers do not affect the sample. To prove that the evaluated light scattering signals are related to the molecular diffusion modes, the corresponding working equations, eqs 2 and 3, have to be verified. For this, the reciprocal of the determined decay times can be plotted as a function of the squared moduli of the related scattering vectors. Figure 7 exemplarily shows such diagrams for both diffusion modes where all relevant single measurement results for small scattering angles are included together with linear fits considering all data with the same statistical weight. 4641



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The trend of decreasing refractive indices with increasing temperature generally observed for fluids can also be noticed for pure [BMIM][B(CN)4] and each of the ILs containing comparable amounts of CO2. At constant temperature, the refractive index seems to decrease with increasing mole fraction of CO2 in the ILs. These tendencies, however, are within combined uncertainties in most cases. To our knowledge, no studies regarding the effect of dissolved CO2 on the refractive index of ILs can be found in the literature so far. The relative uncertainty in the mutual diffusivity tends to decrease with increasing mole fraction of CO2. This can be attributed to increasing amplitudes in the light scattering signals related to concentration fluctuations and corresponds with our results from previous studies focusing on binary mixtures of ILs with molecular liquids.36,37 The measured mutual diffusivities for both ILs studied here are shown as a function of the mole fraction of CO2 at different temperatures in Figure 8. All D12 values are larger than self-diffusion coefficients measured for the pure ILs by pulsed-field gradient spin−echo NMR where 1H or 11B nuclei were used according to the procedure described by Koller et al.50 At a temperature of 313.15 K, self-diffusion coefficients of 0.081 × 10−9 m2 s−1 for [BMIM]+ and 0.079 × 10−9 m2 s−1 for [B(CN)4]− were measured with a relative uncertainty (k = 2) of 10%. For [BMIM][C(CN)3], only a value of 0.090 × 10−9 m2 s−1 for the cation could be determined at the same temperature because [C(CN)3]− contains neither boron nor hydrogen atoms. The described behavior of D12 being larger than the self-diffusion coefficients of the pure IL is consistent with other results in literature. For example, the mutual diffusivities for mixtures of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][NTf2]) with CO2 reported by Gonzales-Miquel et al.16 and Hou and Baltus11 are larger than self-diffusion coefficients measured and simulated by Hazelbaker et al.51 Our results for [BMIM][C(CN)3] can be directly compared with those of Labropoulos et al.8 They calculated mutual diffusivities from temporally resolved mass-uptake data during the transient process of CO2 absorption applying a number of assumptions such as the absence of convective effects. For gas pressures of up to 1 bar, they found mutual diffusivities of about 0.08 × 10−9 m2 s−1 for 308 K and 0.13 × 10−9 m2 s−1 for 323 K without any noticeable tendency regarding the pressure dependence and without stating any uncertainties. These values are in the range of the self-diffusion coefficients of the ions and thus seem to be extremely low although they refer to CO2 mole fractions of less than 0.02. For [BMIM][B(CN)4] at 298.15 K, a mutual diffusivity of 0.45 × 10−9 m2 s−1 could be deduced from the solubility and permeability data measured by Mahurin et al.39 in a CO2 mole fraction range between 0.03 and 0.31. This value is in good agreement with our data measured by DLS. The mutual diffusivities found for both ILs studied here correspond well, which goes along with comparable dynamic viscosities for pure [BMIM][C(CN)3] (21.7 mPa s at 303.15 K8) and pure [BMIM][B(CN)4] (25.5 mPa s at 303.15 K measured by surface light scattering according to the procedure described by Koller et al.50). This observation seems to be associated with the similar structures of the ILs consisting of the same large cation and compact anions. The viscosity of 1ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM][NTf2], 27.2 mPa s at 303.15 K52) is also similar to the viscosities of the ILs studied here. Most mutual diffusivities reported in the literature for CO2 dissolved in [EMIM][NTf2]

Figure 7. Reciprocal of the mean lifetime of concentration and temperature fluctuations versus the squared modulus of the scattering vector for all single measurements for a mixture of [BMIM][B(CN)4] and CO2 at T = 323.01 K and pCO2 = 22.034 bar.

As expected, the single data are in accordance with the linear fit within their uncertainties and the intercepts of the linear fits are close to zero. For the slower diffusion mode related to the mutual diffusivity, the reciprocal decay time measured at Θs = 90° with the single-tau correlator also agrees with the value extrapolated from the linear fit equation determined from the results for small angles. The slopes of the linear fits represent the mutual and thermal diffusivity values which are given in the figure. They are consistent with the reported data averaged from the single measurements. The measured refractive indices as well as the mutual and thermal diffusivities for [BMIM][C(CN)3] and [BMIM][B(CN)4] containing dissolved CO2 at the studied temperatures, pressures, and estimated mole fractions of CO2 are summarized in Table 1. For the diffusivities, also the relative uncertainties (k = 2) are given for each datum. The listed temperatures and pressures represent mean values over the complete measurement period. For [BMIM][C(CN)3], only mutual or thermal diffusivity were measured in a first phase of the experiments and the corresponding results are given in the table as well. The thermal diffusivity was also measured for virtually pure [BMIM][B(CN)4] at very low pressures after purging CO2 from the sample cell. 4642



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Table 1. Refractive Index at the Laser Wavelength (532 nm) nfluid, Mutual Diffusivity D12, and Thermal Diffusivity a as well as the Relative Uncertainties (k = 2) of the Diffusivities Measured for [BMIM][C(CN)3] and [BMIM][B(CN)4] Containing Dissolved CO2 at Different Temperatures, Pressures, and the Corresponding Mole Fractions of CO2 T (K)

pCO2 (bar)

xCO2

nfluid

303.01 303.01 303.11 303.03 303.02 312.91 312.96 313.00 322.77 322.92 322.89 332.52 332.63 332.76

2.341 7.482 10.272 14.804 33.950 2.528 5.376 11.675 2.730 6.123 13.132 2.834 6.940 14.636

0.041 0.126 0.167 0.228 0.393 0.037 0.077 0.158 0.035 0.075 0.151 0.033 0.074 0.146

1.516 1.510 1.500 1.504 1.483 1.505 1.500 1.497 1.499 1.496 1.494 1.496 1.494 1.491

303.13 303.12 303.10 313.02 313.04 313.08 313.05 322.96 323.07 323.10 323.01 332.89 333.07 333.08 333.03

5.368 12.377 16.272 0.051 6.062 14.203 19.153 0.050 6.741 16.094 22.034 0.045 7.449 18.076 26.178

0.133 0.254 0.309 0.000 0.124 0.251 0.311 0.000 0.115 0.246 0.308 0.000 0.105 0.239 0.312

1.451 1.444 1.442 1.452 1.447 1.442 1.439 1.448 1.444 1.440 1.436 1.445 1.441 1.434 1.433

D12 (10−9 m2 s−1) [BMIM][C(CN)3] 0.440 0.584 0.571 0.616 0.813 − 0.573 0.718 − 0.884 0.938 1.059 0.952 0.965 [BMIM][B(CN)4] 0.553 0.721 0.799 − 0.785 0.836 0.959 − 0.949 0.996 1.151 − 1.171 1.260 1.404

(0.17 × 10−9 m2 s−1 at 293.15 K,25 0.66 × 10−9 m2 s−1 at 303.15 K,24 0.8 × 10−9 m2 s−1 at 303.15 K,10 and 0.65 × 10−9 m2 s−1 at 313.15 K13) are close to those measured for [BMIM][C(CN)3] and [BMIM][B(CN)4] by DLS. The results of Kortenbruck et al.32 obtained by online Fourier transform infrared spectroscopy (FTIR) during the uptake of CO2 into thin films of [EMIM][NTf2], however, suggest mutual diffusivities of about 22 × 10−9 m2 s−1 at 303.15 K. Although a relative uncertainty of less than 2.6% is stated by the authors, these data seem to be erroneous because they are at least by one order of magnitude larger than all other reported mutual diffusivities for CO2 dissolved in ILs at similar conditions.10−17,20,22−29,31 In comparison with our previous DLS studies regarding binary mixtures of ILs with molecular liquids at comparable mole fractions,36,37 the measured mutual diffusivities for the mixtures containing CO2 are larger. For example, D12 = 0.18 × 10−9 m2 s−1 at xethanol = 0.101 and D12 = 0.20 × 10−9 m2 s−1 at xacetone = 0.103 were measured for [EMIM][NTf2] at 303.15 K.36 Assuming comparability based on the similar viscosities of the pure ILs, molecular interactions such as Coulomb or van der Waals forces as well as steric effects between CO2 and [BMIM][B(CN)4] or [BMIM][C(CN)3] seem to be weaker than those between ethanol or acetone and [EMIM][NTf2]. Except for the mixtures of CO2 with [BMIM][C(CN)3] at 332.61 K, there is an increasing trend of D12 with increasing mole fraction of CO2 for both ILs studied here. The same trend

100 × ΔD12 × D12−1

a (10−9 m2 s−1)

100 × Δa × a−1

20.1 8.2 6.5 4.6 3.1 − 13.8 6.4 − 18.6 8.7 27.8 13.3 10.0

− − 72.8 − 82.8 77.4 79.3 74.1 77.3 77.9 75.3 79.7 81.4 74.9

− − 13.4 − 7.1 11.6 4.7 7.1 6.9 3.4 13.4 11.4 18.7 11.4

14.6 14.1 9.8 − 10.3 21.3 12.7 − 10.4 11.4 5.9 − 13.6 11.6 7.2

85.2 88.4 86.9 83.0 84.0 85.8 87.3 84.5 84.1 85.9 85.0 89.5 84.3 86.8 84.3

15.1 8.6 13.6 7.4 21.1 6.0 13.0 12.9 20.4 4.9 10.5 20.4 8.4 14.3 6.2

was observed by Labropoulos et al.8 for [BMIM][C(CN)3] and [EMIM][C(CN)3] with dissolved CO2 at pressures up to 20 bar as well as by other researchers studying the effect of CO2 pressure on the mutual diffusivity at constant temperature.15−17 These results are also consistent with those of our previous investigations on binary mixtures of ILs and molecular solvents36,37 as well as the study of Richter et al.53 regarding mixtures of 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF 6 ]) with methanol applying digital image holography. For [BMIM][PF6]54,55 as well as for other ILs,56−58 it was found that physically absorbed CO2 distinctly decreases the viscosity. Furthermore, Hazelbaker et al.51 concluded from their molecular dynamics simulations for mixtures of [BMIM][NTf2] with CO2 that the dissolved gas fluidizes the mixture, which results in decreasing density and increasing self-diffusion coefficients. In summary, the strength of molecular interactions tends to decrease with increasing mole fraction of CO2 dissolved in ILs, which also enhances the mutual diffusivity. For approximately constant xCO2, the mutual diffusivities measured in the present study increase with increasing temperature, which can also be related to decreasing viscosity. Indeed, it cannot be deduced reliably from the data measured here in a limited temperature range if the temperature dependence for the mixtures shows Arrhenius-like behavior as 4643



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Figure 9. Thermal diffusivities for [BMIM][C(CN)3] and [BMIM][B(CN)4] as a function of the mole fraction of dissolved CO2 for different temperatures.

Figure 8. Mutual diffusivities for [BMIM][C(CN)3] and [BMIM][B(CN)4] as a function of the mole fraction of dissolved CO2 for different temperatures.

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CONCLUSIONS It was demonstrated that mutual and thermal diffusivities for ILs containing dissolved CO2 can be measured reliably and quasi-simultaneously in a single optical setup at macroscopic thermodynamic equilibrium by DLS. For mixtures of [BMIM][C(CN)3] or [BMIM][B(CN)4] with CO2, there are only slight differences of less than 22% between the diffusivities measured at constant temperature and similar mole fractions of CO2. The results agree well with literature data for the same or comparable systems. The observed trend of increasing mutual diffusivities with increasing mole fraction of CO2 due to weakening of molecular interactions goes along with decreasing viscosities reported for other ILs containing CO2 in the literature. For the thermal diffusivity, no dependence on the temperature or the mole fraction of CO2 could be found.

it was found for mixtures of ILs with dissolved CO210,11,13,15,20,24,28 or liquid solvents.36,37,59 The thermal diffusivities measured for pure [BMIM][B(CN)4] as well as for both ILs containing dissolved CO2 are depicted as a function of the mole fraction of CO2 in Figure 9. Small amplitudes in the light scattering signals related to temperature fluctuations in the studied systems are the reason for expanded relative uncertainties up to 21.1%. In many cases, distinctly smaller uncertainties of less than 3% can be achieved by DLS, e.g., for refrigerant mixtures.34,35 Still being within combined uncertainties, the measured values tend to be somewhat larger for the [BMIM][B(CN)4]-based system. Neither the temperature nor the mole fraction of CO2 seems to have any noticeable effect on the thermal diffusivity in the investigated range of conditions. In the literature, only thermal diffusivities for pure ILs measured by a transient grating technique can be found. Frez et al.60 reported values between 58 and 86 × 10−9 m2 s−1 for various 1-alkyl-3-methylimidazolium-based ILs at 296.85 K, which corresponds well with the data measured by DLS here.

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ASSOCIATED CONTENT

S Supporting Information *

Details on the Abbe method, the measurement results, and the corresponding correlation for the refractive index of [HMIM][C(CN)3] and a movie in avi format showing the movement of streaks after dosing CO2 to the IL. These materials are available free of charge via the Internet at http://pubs.acs.org. 4644



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AUTHOR INFORMATION

Corresponding Author

*(A.P.F.) Telephone: +49-9131-85-29789. Fax: +49-9131-8529901. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative. In addition, financial support from the Seventh European Commission Framework Program for Research and Technological Development for the project “Novel Ionic Liquid and Supported Ionic Liquid Solvents for Reversible Capture of CO2″ (IOLICAP project no. 283077) is gratefully acknowledged.

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Mutual and Thermal Diffusivity of Binary Mixtures of the Ionic Liquids

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