Article pubs.acs.org/JPCB
Mutual and Self-Diffusivities in Binary Mixtures of [EMIM][B(CN)4] with Dissolved Gases by Using Dynamic Light Scattering and Molecular Dynamics Simulations Thomas M. Koller,† Andreas Heller,† Michael H. Rausch,†,‡ Peter Wasserscheid,§ Ioannis G. Economou,∥ and Andreas P. Fröba*,†,‡ †
Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, D-91052 Erlangen, Germany ‡ Department of Chemical and Biological Engineering, Institute of Engineering Thermodynamics (LTT), 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 ∥ Chemical Engineering Program, Education City, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar ABSTRACT: Ionic liquids (ILs) are possible working fluids for the separation of carbon dioxide (CO2) from flue gases. For evaluating their performance in such processes, reliable mutualdiffusivity data are required for mixtures of ILs with relevant flue gas components. In the present study, dynamic light scattering (DLS) and molecular dynamics (MD) simulations were used for the investigation of the molecular diffusion in binary mixtures of the IL 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM][B(CN)4]) with the dissolved gases carbon dioxide, nitrogen, carbon monoxide, hydrogen, methane, oxygen, and hydrogen sulfide at temperatures from 298.15 to 363.15 K and pressures up to 63 bar. At conditions approaching infinite dilution of a gas, the Fick mutual diffusivity of the mixture measured by DLS and the self-diffusivity of the corresponding gas calculated by MD simulations match, which could be generally found within combined uncertainties. The obtained diffusivities are in agreement with literature data for the same or comparable systems as well as with the general trend of increasing diffusivities for decreasing IL viscosities. The DLS and MD results reveal distinctly larger molecular diffusivities for [EMIM][B(CN)4]−hydrogen mixtures compared to mixtures with all other gases. This behavior results in the failure of an empirical correlation with the molar volumes of the gases at their normal boiling points. The DLS experiments also showed that there is no noticeable influence of the dissolved gas and temperature on the thermal diffusivity of the studied systems.
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membranes are loaded with ILs.7−9 For the proper design of such systems, reliable data for solubilities and mutual diffusivities of mixtures of ILs with dissolved gases are required. Although many studies on gas solubilities in ILs are available in the literature,10 experimental mutual diffusivities are very rare and often questionable regarding the applied boundary conditions for data evaluation and/or their specified uncertainties.11 By using dynamic light scattering (DLS), which is based on a strictly valid theory, we could recently demonstrate that the mutual and thermal diffusivity of binary mixtures of distinctly differing liquid solvents with dissolved gases are accessible at macroscopic thermodynamic equilibrium.11,12 For binary systems of two different IL solvents
INTRODUCTION The reduction of greenhouse gas emissions generated by the combustion of fossil fuels represents an ubiquitous challenge.1,2 For the separation of carbon dioxide (CO 2 ) mainly contributing to the current global warming, amine-based solvents are frequently used.3,4 Their disadvantage of solvent loss during the gas desorption stage4 stimulated the investigation of ionic liquids (ILs) as alternative working fluids due to their low volatilities and relatively large CO2 absorption capacities. In this context, low-viscosity ILs based on the tetracyanoborate anion are promising absorbents. Mahurin et al.5,6 found that, for selected 1-alkyl-3-methylimidazolium-based ILs with different anions, those carrying the tetracyanoborate anion show the largest CO2 solubility and CO2/nitrogen (N2) separation selectivity. Gas separation processes can be realized with supported ionic liquid membranes where the pores of the solid © 2015 American Chemical Society
Received: March 19, 2015 Revised: June 9, 2015 Published: June 15, 2015 8583
DOI: 10.1021/acs.jpcb.5b02659 J. Phys. Chem. B 2015, 119, 8583−8592
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The Journal of Physical Chemistry B
and after the measurements, the water content of the investigated samples yielding an average value of 588 ppm on a mass basis was analyzed by Karl Fischer coulometric titration (Metrohm, 756 KF Coulometer) with an expanded relative uncertainty (k = 2) of less than 20%. This value corresponds to a water mole fraction of 0.007. All gases used in this study were provided by Linde AG. The purity for CO2, N2, carbon monoxide (CO), and hydrogen (H2) are specified with 99.999, 99.999, 99.997, and 99.9999 vol %, respectively. The experimental setup used in the present study is presented in detail in our previous studies.11,12 Here, only the relevant information regarding the sample preparation and the measurement conditions are reported. The applied sample cell with a total inner volume of 40 mL provides four optical accesses. The cell temperature was measured with two calibrated Pt 100 Ω resistance probes with an absolute uncertainty (k = 2) of less than 0.01 K. For the temperature control of the sample cell, resistance heating was employed where a temperature stability of better than 3 mK could be achieved. The temperature control loop is performed with a temperature probe placed in the wall of the cell close to the resistance heating. A second probe, which is also located inside the cell material but close to the fluid, records the sample temperatures reported within this study. The pressure in the sample cell was recorded by a pressure transducer with an absolute uncertainty (k = 2) of 15 mbar. After approximately 30 mL of the filtered and dried IL [EMIM][B(CN)4] were added into the sample cell, a vacuum (0.5 mbar) was applied to the sample inside the cell to remove any gases. Then, gas was dosed into the sample cell via a bellow-type valve adjusting initial pressures between 10 and 70 bar. Due to the negligible vapor pressure of the IL, only the added gas is assumed to be present in the gas phase. The pressure in the cell decreased as long as gas diffused into the IL. Convective mass transfer could be observed in the form of streaks in the fluid. Though the streaks disappeared visually after about 30−60 min, first experiments still indicated the presence of distinct convective effects in the form of large fluctuations in the scattered light intensity. After a waiting period of about 12−24 h, these fluctuations vanished and the equilibrium conditions could be verified by the stable system pressure. At that time, DLS measurements of the molecular diffusion modes were performed. After variations in the temperature or the CO2 pressure in the sample cell, waiting intervals of about 12 h were sufficient to obtain steady-state conditions. Measurements were performed at temperatures from about 303 to 338 K in three steps. For all gases and temperatures, one stable pressure condition in the range from about 3−63 bar was applied. At about 318 K, also the pressure of CO2 was varied between 3 and 21 bar in four approximately equidistant steps. For the measurements with H2, N2, and CO, new samples from the flask with the degassed IL [EMIM][B(CN)4] were used. After the measurements with CO, the gas was purged from the sample with the vacuum pump for about 3 h before adding CO2 to the sample cell. For a rough estimation of the mole fraction of CO2 in [EMIM][B(CN)4] at the measured temperatures and pressures, solubility data published by Mota-Martinez et al.17 at temperatures from 278 to 343 K and pressures from 5.9 to 114 bar were adopted. These data are preferable in comparison with the single Henry coefficient given by Mahurin et al.6 for pressures between 1 and 10 bar at one specific temperature of
containing CO2, mutual diffusivities with typical uncertainties of less than 10% (k = 2) were determined at various compositions.11 Given the huge number of possible IL combinations and the experimental effort associated with the investigation of IL−gas systems at any relevant thermodynamic state, computational approaches are useful alternatives. In detail, molecular dynamics (MD) simulation is a valuable method for the prediction of various thermophysical properties and also allows for an interpretation of experimental data through an insight into the molecular structure of the probed systems. Nevertheless, the quality of each predictive method needs to be validated by comparison with experimental results. In previous studies,13,14 we showed that equilibrium and transport property data for two tetracyanoborate-based ILs obtained from our MD simulations and experiments were in good agreement. In the present study, DLS experiments and MD simulations are combined to investigate the molecular diffusion in binary mixtures of 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM][B(CN)4]) with seven dissolved gases typically present in flue gas. By DLS, one single Fick mutual diffusivity D12 is determined, which entirely characterizes the diffusive mass transport in IL−solute systems.15 According to Fick’s first law of diffusion, this collective property of the gas (species 1) and the IL (species 2) relates the molar flux of one species to a driving force, i.e., the gradient in the molar concentration of this component. The Fick mutual diffusivity can be connected with the Maxwell−Stefan (MS) mutual diffusivity Đ12 by the thermodynamic factor.16 In the MD simulations performed here, the self-diffusivity of the gas in the IL, D1,self, is calculated. It describes the random motion of the gas molecules in the mixture in the absence of a driving force for diffusion. Only in the limit of an infinite dilution of the gas in the IL, the different diffusivity types D12, Đ12, and D1,self are identical.16 This means that the self-diffusivity D1,self, which is more easily accessible in MD simulations than the Fick and MS diffusivity, can be directly compared with experimental D12 data for small gas mole fractions. Besides a discussion of the diffusivity data in connection with the physicochemical characteristics of the involved components, the results are compared to available literature data and used for the analysis of empirical correlations.
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EXPERIMENTAL SECTION Materials and Sample Preparation. The reactants for the synthesis of [EMIM][B(CN)4] were potassium tetracyanoborate (K[B(CN)4]) obtained from Merck KGaA and 1-ethyl-3methylimidazolium chloride ([EMIM]Cl) purchased from Solvent Innovation GmbH (now Merck KGaA). The latter substance was washed with acetone prior to use. [EMIM][B(CN)4] was synthesized by reacting equimolar amounts of a 0.5 M aqueous solution of [EMIM]Cl and K[B(CN)4] suspended in distilled water under rigorous stirring for 24 h. The upper aqueous phase formed was disposed while the lower IL phase was washed with distilled water three times and dried at 10−3 mbar and 333.15 K for at least 16 h. The purity of the colorless liquid [EMIM][B(CN)4] of more than 99 mol % was proven by 1H NMR analysis (JEOL, ECX +400 spectrometer). To avoid disturbances of the DLS measurements originating from traces of particle-like impurities in the sample, the IL was filtered twice with a syringe filter with a pore size of 0.2 μm. Then, the IL was dried on a vacuum line (0.5 mbar) at about 323.15 K for a time period of at least 4 h. Before 8584
DOI: 10.1021/acs.jpcb.5b02659 J. Phys. Chem. B 2015, 119, 8583−8592
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The scattering vector, q = (4πnfluid/λ0)·sin(Θs/2), can be determined from the refractive index of the fluid nfluid, the laser wavelength in vacuo λ0, and the scattering angle Θs. For small scattering angles that were adjusted in all present measurements (Θs ≤ 7°), Θs can be deduced from the easily accessible incident angle Θi with the help of Snell’s law, nfluid·sin Θs = nair· sin Θi. Here, the refractive index of air is assumed to be nair = 1. The optical and electronic setup is the same as that employed in our previous study.11 It includes a Nd:YVO4 laser (wavelength in vacuo λ0 = 532 nm; operated at 0.5 W), a single-tau and a multi-tau correlator, as well as optical and electro-optical components. The scattered light superimposed with reference light in the form of stray light from the cell windows was detected by two photomultiplier tubes at small scattering angles between 2° and 7°. For their determination, the incident angle was measured with a rotational table using the autocollimation technique with an uncertainty (k = 2) of ±0.01°. At least two and usually six different scattering angles were applied at each sample state during the DLS measurements. For the measurement of the refractive index with the aid of a prism-shaped sample cell window by a beam-displacement method,11 a scattering angle of Θs = Θi = 90 ± 0.3° (k = 2) was used. The normalized pseudo-cross correlation functions g(2)(τ) obtained from both correlators were evaluated by nonlinear regression to extract the decay times τC,t and τC,c. Because the mutual diffusivity is by about 2 orders of magnitude smaller than the thermal diffusivity for all studied systems, the decay time of the hydrodynamic mode associated with concentration fluctuations τC,c can be observed on a much larger time scale. Disturbing effects, which may arise from vibrations, particle scattering, incoherent external stray light, or convection in the sample and cause superimposing signals in the long-time range of the correlation functions, could be well described by additional linear and/or quadratic terms in the theoretical model. Typical correlation functions recorded by both correlator types at T ≈ 318 K are illustrated in Figure 1 for the binary mixtures of [EMIM][B(CN)4] with dissolved CO2 at Θi = 6.005° and p = 20.55 bar as well as with H2 at Θi = 9.000° and p = 35.38 bar. Here, disturbing signals described by an additional quadratic term in the correlation model were subtracted to illustrate the light scattering signals related to fluctuations in concentration and temperature. For the regression of the data from the multi-tau correlator featuring a broad sample time range between a few nanoseconds up to many seconds, a theoretical model according to eq 1 could be used for the simultaneous evaluation of τC,t and τC,c for all studied IL−gas systems. As exemplarily shown in Figure 1a for the [EMIM][B(CN)4]−CO2 system, the exponential mode governed by the mutual diffusivity (dashed line) decays much more slowly than the exponential mode associated with the thermal diffusivity (dotted line). 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 1. For the regression of the data from the single-tau correlator with a fixed sample time for all 255 correlator channels, the sample time was adjusted to access maximum information on the time range where the mutual diffusion mode can be found. In the case of the binary mixtures of [EMIM][B(CN)4] with dissolved CO2, N2, and CO, g(2)(τ) is reduced to one single slowly decaying exponential characterized by τC,c. This is shown in Figure 1b for the correlation function of [EMIM][B(CN)4]
298.15 K, which is outside our investigated experimental conditions. From the correlation of the experimental data of Mota-Martinez et al.17 by a two-dimensional fit as well as our experimental pressures and temperatures, the corresponding CO2 mole fractions were calculated and also extrapolated for pressures between about 3.7 and 5.9 bar. The expanded uncertainty (k = 2) in the resulting mole fractions is estimated to be 0.02. For the binary systems of [EMIM][B(CN)4] with dissolved N2, CO, and H2, no solubility data are available in literature. The small changes between the initial and equilibrium pressure in the measurement cell during the sample preparation procedure were comparable for N2, CO, and H2 and implicate their very low solubilities in the IL. For the system [EMIM][B(CN)4] and N2, this finding is corroborated by permeability measurements of Mahurin et al.5 From their reported CO2/N2 selectivity at 298.15 K and the mutual diffusivities obtained in this study, the solubility of N2 in [EMIM][B(CN)4] is presumably more than 40 times smaller compared to that of CO2 for the same pressures. Taking into account also the experimental database for gas solubilities in other ILs provided by Lei et al.,10 the mole fractions of dissolved N2, CO, and H2 in [EMIM][B(CN)4] are estimated to be smaller than 0.05 for the present measurements. Mutual and Thermal Diffusivity by DLS. With DLS from the bulk of fluids, microscopic statistical fluctuations in temperature, pressure, and concentration in the case of a binary fluid mixture are studied in macroscopic thermodynamic equilibrium. From the analysis of the time-dependent scattered light intensity reflecting the dynamics of these fluctuations, various thermophysical properties of fluids can be determined in an absolute way. A fundamental description of the DLS method especially in connection with the determination of mutual and thermal diffusivities can be found in literature.18−22 In the following, only the main information relevant for the present study is given. For binary fluid mixtures studied here, the relaxation of microscopic fluctuations in temperature and concentration is governed by the thermal diffusivity and the mutual diffusivity. The mean relaxation times of both hydrodynamic modes are analyzed in the time domain by the calculation of the correlation function of the scattered light intensity. 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 g(2)(τ ) = b0 + bt exp( −τ /τC,t) + bc exp(−τ /τC,c)
(1)
The decay times of the two exponentially decaying hydrodynamic modes, τC,t and τC,c, represent 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,t are related to the thermal diffusivity a and the mutual diffusivity D12 according to τC,t =
1 aq2
(2)
and
τC,c =
1 D12q2
(3) 8585
DOI: 10.1021/acs.jpcb.5b02659 J. Phys. Chem. B 2015, 119, 8583−8592
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statistical ensemble, equilibrium and transport properties are accessible for virtually every desired state. The fundamentals of the MD simulation method23 and its application to pure [B(CN)4]−-based ILs13,14 can be found in earlier work. In this section, only the features important in context with the present study are summarized. Recently, we developed a computationally efficient force field (FF) for [EMIM][B(CN)4].13 This nonpolarizable unitedatom (UA) model is based on a pair-additive potential energy function considering electrostatic and nonelectrostatic interactions. Details on the functional form of the FF and the parameters of the various terms can be found in our previous study.13 The reliability of the MD model was confirmed by the good agreement with our experimental data with deviations of less than ±0.3% for density and less than ±20% for dynamic viscosity as well as self-diffusivities of both ions. The transfer of the nonelectrostatic FF of [EMIM][B(CN)4] to the longerchained IL [HMIM][B(CN) 4 ] resulted also in good predictions with comparable deviations from our experiments.14 For the gas molecules, established literature models consistent with the functional form of the used FF were applied. Details on these FFs are given in the respective literature. In the following, only the essential features of the FFs are described. For CO2, an accurate three-site model from the transferable potentials for phase equilibria (TraPPE) FF developed by Pothoff and Siepmann24 was used by applying flexible C−O bond and O−C−O angle constants. Partial point charges qi of atom i are centered at each Lennard-Jones (LJ) site of the carbon (qC = +0.7e) and the two oxygen atoms (qO = −0.35e). For N2, the noncharged two-center FF developed by Rivera et al.25 was adopted in which a flexible N−N bond is implemented. The CO and H2 molecules were modeled as noncharged LJ spheres as proposed by Hirschfelder et al.26 The widely used TraPPE FF of Martin and Siepmann27 was applied for CH4, which interacts as noncharged UA through a LJ potential. The O2 model from Miyano28 consists of a twocenter LJ potential with a flexible O−O bond. The MD model of H2S is based on the FF reported by Nath29 and assumes three interaction sites for the three atoms. Point charges of qS = −0.248e and qH = +0.124e are used on each LJ site. For consistency, the simulation details are the same as used in our previous studies on [B(CN)4]−-based ILs13,14 and, thus, are only abstracted here. The Gromacs 4.0.7 simulation package30 was used for all MD simulations. The Nose−Hoover thermostat31,32 and the Parrinello−Rahman barostat33,34 with coupling times τT = 0.03 ps and τP = 0.7 ps were used to maintain constant temperature and pressure conditions. The full electrostatic interactions were calculated using the particle mesh Ewald (PME) summation.35 To speed up calculations, cutoffs for Coulomb and van der Waals interactions of 1.2 nm, which are smaller than half of the simulation box length, were employed. Long-range LJ corrections for energy and pressure were also considered. A classical leapfrog algorithm with a time step of 2 fs was used to integrate the equations of motion. Periodic boundary conditions in all directions were employed to mimic the bulk behavior. Starting from energetically minimized and equilibrated configurations of N = 58 IL molecules in a cubic simulation box, the density of pure [EMIM][B(CN)4] was extracted from 5 ns production runs in the NpT ensemble at a pressure p of about 1 bar; see details in ref 13. For each of the gases CO2, N2, CO, H2, CH4, O2, and H2S, three molecules were dispersed randomly in the equilibrated IL system adjusting a mole
Figure 1. Normalized correlation functions for binary mixtures of [EMIM][B(CN)4] with dissolved CO2 measured by a multi-tau correlator (a) and a single-tau correlator (b) as well as with dissolved H2 measured by a single-tau correlator (c): (− − −) exponential mode related to mutual diffusivity; (■) exponential mode related to thermal diffusivity.
with dissolved CO2. The datum of the first correlator channel clearly exceeds the fit of the slower mutual diffusion mode and is attributable to a light scattering signal from temperature fluctuations in the short-time range. Thus, the first two to five correlator channels were not considered for the evaluation of τC,c. For the mixtures of [EMIM][B(CN)4] with dissolved H2, the D12/a ratio increases mainly due to the significantly larger mutual diffusivities for the H2-based systems compared to the other gases. The smaller difference between τC,c and τC,t allowed for the evaluation of both exponential modes also with the aid of the single-tau correlator, which is illustrated in Figure 1c by a measurement example for the [EMIM][B(CN)4]−H2 system.
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MOLECULAR DYNAMICS (MD) SIMULATION Equilibrium MD simulation provides the means to analyze the dynamics of molecules at a microscopic level. On the basis of an accurate atomistic model of the studied multiparticle system and the solution of the equations of motion in a selected 8586
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(k = 2) are given in Figure 2. Comparable self-diffusivities of CO2, N2, and CO in [EMIM][B(CN)4] at a given temperature are indicated by the similar slopes in Figure 2. In accordance with the mutual diffusivities obtained by DLS, also our MD simulations reproduce the significantly faster dynamics for the H2-based systems.
fraction of the dissolved gas of 0.049. Though this mole fraction is most probably larger than the bulk solubilities of all gases except for H2S,10 it was used to obtain statistically meaningful results. Furthermore, a clustering of gas molecules, which may provide evidence for a gradually occurring phase, was not observed in the simulations. For the binary IL−gas mixtures, NpT simulations on the order of 10 ns were carried out to equilibrate and calculate the density. After that, 30 ns NVT simulations at the simulated density and a pressure of about 1 bar were performed for temperatures between 298.15 and 363.15 K to compute the self-diffusivities of the gases. The self-diffusivity of the gas molecules (species 1), D1,self, was calculated from the linear part of their mean square displacement (MSD) in the IL (species 2) according to the Einstein equation36 1 d 2 lim ⟨[ rk⃗ ,1(t ) − rk,1 ⃗ (0)] ⟩ 6 t →∞ dt d(MSD) 1 lim = 6 t →∞ dt
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RESULTS AND DISCUSSION First, the diffusivity results for binary mixtures of [EMIM][B(CN)4] with dissolved gases obtained by DLS and MD simulations are presented. Then, the calculated selfdiffusivities are compared to the experimental mutual diffusivities for the systems with CO2 and with the other gases. Besides their comparison with available literature data, the results are discussed in connection with thermodynamic as well as structural influences and empirical correlations. Summary of Diffusivity Data. For the determination of D12 and a of the investigated systems by DLS, the refractive index of the fluid nfluid is required. Here, even an uncertainty in nfluid of about 10% is sufficient to obtain q values with an uncertainty of less than 0.2%. With the DLS setup, the refractive index of virtually pure [EMIM][B(CN)4] was measured with an expanded relative uncertainty (k = 2) of less than 1% according to the beam-displacement method detailed by Rausch et al.11 The refractive-index value nfluid = 1.451 obtained at λ0 = 532 nm, T = 318.05 K, and p = 0.063 bar agrees within combined uncertainties with the value calculated from the correlation in our previous study37 of 1.445 for the same IL at atmospheric pressure and the same wavelength. Because the temperature and the dissolved gas showed no significant effect on the measured refractive index, nfluid = 1.451 was used for the evaluation of all DLS measurements reported in this study. The reported D12 and a data were averaged arithmetically on the basis of 2−12 independent measurements recorded by the different correlators for varying scattering angles. The uncertainties given in the data tables and illustrated in the corresponding figures represent the standard deviation (k = 2) of all single results. For all single measurements, the combined standard uncertainties in D12 and a were additionally calculated according to the law of error propagation taking into account the uncertainties in Θi , τC , and nfluid 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. The measured mutual and thermal diffusivities for [EMIM][B(CN)4] containing dissolved CO2, N2, CO, and H2 as well as their relative uncertainties (k = 2) are summarized in Table 1 at the studied temperatures T, pressures p, and estimated mole fractions of the gases x. The listed temperatures and pressures represent mean values over the complete measurement period. Very small amplitudes in the light scattering signals associated with temperature fluctuations allowed no reliable determination of the thermal diffusivity for mixtures of [EMIM][B(CN)4] with CO2 and CO at about 303 K. The thermal diffusivity was also measured for virtually pure [EMIM][B(CN)4] at very low pressures. No distinct effect of the temperature or amount of dissolved CO2 on the thermal diffusivities of the [EMIM][B(CN)4]based systems could be found within combined uncertainties for the studied conditions. This is in agreement with our observations made for the ILs 1-butyl-3-methylimidazolium tetracyanoborate ([BMIM][B(CN)4]) and 1-butyl-3-methyl-
D1,self =
(4)
In eq 4, rk⃗ ,1(t) represents the center-of-mass vector position of the kth gas molecule at simulation time t. The brackets indicate time and particle average. For data evaluation, the values for D1,self were generally calculated within the first 15 ns of each simulation run to exclude disturbing contributions from statistical artifacts found within the last few nanoseconds of the simulations. In Figure 2, MSDs of CO 2 , N 2 , CO, and H 2 in [EMIM][B(CN)4] are exemplarily plotted as a function of t
Figure 2. Mean square displacement (MSD) of dissolved gases in [EMIM][B(CN)4] as a function of the simulation time t at T = 318.15 K and p ≈ 1 bar.
at T = 318.15 K and p ≈ 1 bar. All functions show an approximately linear behavior exhibiting the Fickian diffusive regime for which eq 4 is valid. A noticeable sublinear diffusive regime at short diffusion times, which could be observed for the self-diffusion of cations and anions in pure [EMIM][B(CN)4],13 was not found for the self-diffusion of the gases in the IL. This behavior might be attributed to the distinctly larger mobilities of the small gas molecules compared to the more bulky ions, diminishing the presence of a sublinear regime. The D1,self data evaluated from the fit based on eq 4 between 0 and 5 ns as well as the corresponding uncertainties 8587
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The Journal of Physical Chemistry B Table 1. Mutual Diffusivity D12 and Thermal Diffusivity a as Well as Their Relative Uncertainties (k = 2) Measured by DLS for [EMIM][B(CN)4] Containing Dissolved CO2, N2, CO, and H2 at Different Temperatures, Pressures, and the Corresponding Mole Fractions of Dissolved Gases T (K)
p (bar)
318.05
0.059
x
D12 (10−9 2 −1 m s )
100 × ΔD12 × D12−1
a (10−9 m2 s−1)
100 × Δa × a−1
96.0
5.7
Table 2. Self-Diffusivities D1,self of CO2, N2, CO, H2, CH4, O2, and H2S in [EMIM][B(CN)4] and the Relative Uncertainties (k = 2) Obtained from MD Simulations at a Pressure of p ≈ 1 bar and a Gas Mole Fraction of x = 0.049
303.06 318.04 318.04 318.04 318.03 337.99
3.650 4.583 9.720 15.303 20.552 5.882
303.08 318.14 338.03
56.658 60.066 62.738
303.00 317.90 337.61
28.875 31.628 32.575
303.12 318.08 337.98
30.138 35.767 35.512
D1, self (10−9 m2 s−1)
298.15 318.15 338.15 363.15
0.548 0.978 1.582 2.493
298.15 318.15 338.15 363.15
0.721 1.277 1.908 3.274
298.15 318.15 338.15 363.15
0.609 1.145 1.983 2.779
298.15 318.15 338.15 363.15
3.331 4.962 6.970 9.939
298.15 318.15 338.15 363.15
0.563 1.131 1.734 2.854
298.15 318.15 338.15 363.15
1.056 1.588 2.351 3.976
298.15 318.15 338.15 363.15
0.607 0.955 1.489 2.240
100 × ΔD1, self × D1, self−1
CO2
[EMIM][B(CN)4] [EMIM][B(CN)4] + CO2 0.09 0.844 26.2 0.07 0.882 8.1 0.16 0.978 6.4 0.23 1.091 2.7 0.28 1.153 4.6 0.04 1.517 15.1 [EMIM][B(CN)4] + N2
