Transport Properties and Ionic Association in Pure Imidazolium-Based

May 12, 2014 - Oscar NordnessLuke D. SimoniMark A. StadtherrJoan F. Brennecke .... Douglas R. MacFarlane , Luís P. N. Rebelo , Isabel M. Marrucho...
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Transport Properties and Ionic Association in Pure ImidazoliumBased Ionic Liquids as a Function of Temperature B. E. Mbondo Tsamba, S. Sarraute, M. Traïkia, and P. Husson* CNRS, UMR 6296, Institut de Chimie de Clermont-Ferrand, 24 Avenue des Landais, BP 80026, Aubière F-63171, France Clermont Université, Université Blaise Pascal, Institut de Chimie de Clermont-Ferrand, BP 10448, F-63000 Clermont-Ferrand, France S Supporting Information *

ABSTRACT: In this work, three transport properties (viscosity, diffusion coefficient, and electrical conductivity) were experimentally determined from 298 K to 343 K in four pure imidazolium-based ionic liquids with two anions and different alkyl chain lengths on the cation: 1-ethyl-3-methylimidazolium methylsulfate, [C1C2Im][CH3SO4], 1-butyl-3-methylimidazolium methylsulfate, [C1C4Im][CH3SO4], 1-ethyl-3-methylimidazolium triflate, [C1C2Im][CF3SO3] and 1-butyl-3-methylimidazolium triflate, [C1C4Im][CF3SO3]. Higher viscosities, lower diffusion coefficients, and electrical conductivities were measured when the alkyl chain length was increased or a sulfate anion was present. From these experimental data, the ionic association was discussed using the qualitative approach of the Walden plots and the quantitative ionicity concept. An increased ionic association was observed when the alkyl chain length on the cation was increased, while comparable ionicities were measured for both anions. Finally, the applicability of the Stokes−Einstein equation (relation between the diffusion coefficient and the viscosity) was also discussed in these systems.

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INTRODUCTION Ionic liquids are interesting liquids for many applications in various domains.1 They are entirely composed of ions and exhibit modular physicochemical properties by simply changing the anion−cation combination. Because of the great number of possible combinations, these components are often considered as designer solvents. It is thus theoretically possible to choose the most adequate ionic liquid for a given application. At the same time, this means that it is not possible to experimentally characterize the properties of all the possible existing ionic liquids. For this reason, a molecular understanding of these systems is necessary. To design chemical operations with ionic liquids, the mass and energy transport have to be characterized. In this paper, we will focus on the first point with the experimental determination of three transport properties (viscosity, electrical conductivity, and diffusion) in a selection of pure imidazolium-based ionic liquids as a function of temperature. The objective is to contribute at two levels to a better description of ionic liquids and help in the choice of the best ionic liquid for a given application. First, for chemical engineers and specialists in fluid mechanics, such data are necessary tools for the description of mass transport phenomena in a process and consequently for the industrial design.34 Given the selection of ionic liquids, conclusions concerning the alkyl chain length on the cation and the effect of changing the anion can be assessed with these data. The aim of this work is also to contribute to a description at the molecular level, in particular © 2014 American Chemical Society

of ionic association. Such information is helpful for the selection of an adequate system for a particular purpose. Viscosity is the parameter describing the hydrodynamics of a system, namely the flow resistance of the liquid. In ionic liquids, the mass transport is mainly studied through this property, which has been the subject of a significant number of papers even if some disprecancy can be observed between some sets of data. This can be attested by a study of the NIST IL database.2 These deviations between different works are often explained by the purity of the samples. In contrast, diffusion (both self-diffusion and mutual diffusion) is far less studied. Diffusion is caused by random molecular motion and leads, in the case of binary systems, to complete mixing. The macroscopic flux resulting from this motion and observed in the presence of a concentration gradient can be calculated by the Fick’s law. Molecular motion also occurs in pure components. In this case, the diffusion coefficient is called the self-diffusion coefficient, whereas in mixtures, it is classically referred to as the interdiffusion (or mutual diffusion) coefficient.34 However, confusions appear in literature concerning the use of this terminology. At the molecular level, there is no difference between these two coefficients, provided, in the case of interdiffusion, that the diffusing specie is sufficiently diluted in the solvent. We are Received: September 17, 2013 Accepted: April 1, 2014 Published: May 12, 2014 1747

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molecular structure of anion and cation of the ionic liquid and on the temperature. Four, fully miscible with water, imidazolium-based ionic liquids were selected for this study: two with the methylsulfate anion (CH3SO4−), 1-ethyl-3-methylimidazolium methylsulfate ([C1C2Im][CH3SO4]) and 1-butyl-3-methylimidazolium methylsulfate ([C1C4Im][CH3SO4]), and two with the triflate anion (CF3SO3−), 1-ethyl-3-methylimidazolium triflate ([C1C2Im][CF 3 SO 3 ]) and 1-butyl-3-methylimidazolium triflate ([C1C4Im][CF3SO3]). The idea was to study the influence of the alkyl chain length on the cation and the influence of the anion. First, electrical conductivity and viscosity were simultaneously measured. The relationship between these two transport properties is presented in the Walden plots.9 In a second step, the DOSY NMR spectroscopy was used to measure the ions self-diffusion coefficients. The ratio of the molar conductivity measured by electrochemical methods and of the conductivity estimated by pulse field gradient spin echo NMR constitutes a quantitative measurement of the ionicity of the system that can be compared to the qualitative results observed with the Walden plot approach.

interested in the diffusion coefficients of the anion and of the cation in pure ionic liquids. These parameters can be calculated by molecular dynamics simulation using force fields. If the polarization is not included in the force field, the calculated selfdiffusion coefficients are typically 1 order of magnitude smaller compared to the experimental coefficients.4 For this reason, polarizable force fields are now developed by some groups.3 Pulsed-field-gradient spin−echo (PFGSE) nuclear magnetic resonance (NMR), also named diffusion ordered spectroscopy (DOSY) NMR, which is probably the most used technique for the experimental determination of self-diffusion coefficients of ionic species,4 was used in the present work. Finally, the ionic character of ionic liquids is a reason for their development, in particular in electrochemical processes (lithium batteries, capacitors, fuel cells...).5 The electrical conductivity, corresponding to a measurement of the number and mobility of available charge carriers is thus an important parameter to characterize transport in these media. Typically, it has to be as high as possible. A low viscosity is associated with high ionic conductivity and fast diffusion. Indeed, these three transport properties are related through Nernst−Einstein (conductivity and diffusion) and Stokes−Einstein (SE) (diffusion and viscosity) equations.34 The applicability of these equations will be discussed in this paper. At the molecular level, these properties describe the motion of the ions in the liquids. It was first thought that ionic liquids were only composed of totally dissociated ions. As observed by MacFarlane et al.,6 some of them exhibit much lower conductivity than others, even with comparable viscosities. This lower-than expected conductivity indicates that not only the viscosity is the property responsible for the electrical conductivity. In particular, the formation of neutral ions pairs or aggregates, provided they are sufficiently long-lived, can lower the electrical conductivity of the ionic liquid.6 Ionic association phenomena will have impact not only on the conductivity of ionic liquids but also on properties like the vapor pressure or solvation properties.7 In this context, their quantification is of particular relevance for the understanding of the diffusion and more generally physico-chemistry in ionic liquid media. Angell et al.7 first used the Walden plot approach, initially developed for electrolytes solutions, to characterize ionic association in ionic liquids. In this graphical representation (molar conductivity as a function of the fluidity), the line x = y (ideal Walden line) represents 0.01 M aq KCl that is fully dissociated. Angell et al.7 have then proposed a classification of ILs depending on their position from this reference line that is related to ionic association. This approach is considered as a qualitative indicator of the association of the system. The quantitative concept of ionicity was introduced by Tokuda et al.8 It corresponds to the quantity of ions available for ionic conduction among the diffusing species. It is equivalent to the degree of dissociation, a term that is used in dilute electrolyte solutions.8 The ionicity is calculated as the molar conductivity ratio Λimp/ΛNMR. It compares the molar conductivity calculated by impedancemetry (Λimp) and the molar conductivity obtained from the ion diffusion coefficients (ΛNMR). Our objective is to use these two different tools (Walden plots and ionicity concept) to describe cation−anion association and identify some of the parameters that influence this phenomenon. In particular, we have focused on the

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EXPERIMENTAL METHODS The four ionic liquids were purchased from Solvionic with a minimum stated mole fraction purity of 0.995. All the samples were degassed and dried under vacuum for at least 15 h. Their water quantity was measured by coulometric Karl Fischer titration (Mettler Toledo DL31) just after this conditioning step and also before and after each series of measurement. No variation of this quantity was depicted. Typical water quantities between 50 ppm and 100 ppm were measured. Particular attention was paid to a possible degradation of the sulfate-based ionic liquids in the presence of water as this phenomenon is mentioned in the literature.10,11 The samples used in this work were always kept dry, and their stability was regularly checked by NMR analysis. With the water quantities previously indicated, no degradation was observed during the experiments on these samples. Density measurements. The densities were experimentally measured using a vibrating-tube densimeter (Anton Paar, model DMA 512) according to a procedure previously described12 with a standard uncertainty of 10−4 g·cm−3. Viscosity Measurements. The dynamic viscosities, η, were measured using an Anton Paar microviscosimeter (AMVn) with a procedure previously described.13 The estimated standard uncertainty of the viscosity measurement is 1.5 %. Conductivity Measurements. The electrical conductivity, κ, was experimentally determined, with an uncertainty of 0.6 %, by impedancemetry (AC impedance bridge) according to a procedure described in the literature. 13 The standard uncertainty of the molar conductivity is 2 %. NMR Measurements. The pulsed-field gradient spin−echo NMR technique was used to measure the self-diffusion coefficients of both the cation and anion species by observing 1 H and 19F nuclei. For [C1C2Im][CH3SO4] and [C1C4Im][CH3SO4] a Bruker Avance III 500 spectrometer operating at 500.13 MHz for 1H with a 5 mm pulsed-field gradient TXI probe was used. For [C1C2Im][CF3SO3] and [C1C4Im][CF3SO3] a Bruker Avance III 400 spectrometer operating at 400.13 MHz for 1H and at 376.46 MHz for 19F with a 5 mm pulsed-field gradient QNP probe was used. It was checked that for the same sample the same diffusion coefficients were 1748

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Table 1. Parameters A and B of eq 1, Used To Fit the Experimental Densities (ρ) of the Pure Ionic Liquids at Atmospheric Pressure as a Function of Temperature along with the Standard Error of the Fit, SE (Standard Deviation between the Experimental and Calculated Densities) −1

−3

A/10 kg·m ·K B/103 kg·m−3 SE/10−4

−1

[C1C2Im][CH3SO4]

[C1C4Im][CH3SO4]

[C1C2Im][CF3SO3]

[C1C4Im][CF3SO3]

−6.585 1.478 23 0.8

−6.358 1.400 04 0.9

−8.206 1.623 31 1

−7.775 1.526 50 3

measured by observing 1H with both spectrometers. Details of the experimental procedure were previously described.14 We particularly took care to limit convection effects. The precision of the experimental diffusion coefficient is estimated to be less than 1 % (standard deviation of diffusion coefficients calculated using different protons of the same molecule).

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RESULTS AND DISCUSSION Density. The densities of the four investigated ionic liquids (Supporting Information, Table 1-SI) are between 1210 kg·m−3 and 1380 kg·m−3 at 25 °C and between 1180 kg·m−3 and 1340 kg·m−3 at 70 °C. A linear decrease of this parameter is observed as a function of temperature: ρ = AT /K + B

Figure 1. Viscosity, η, of the pure ionic liquids as a function of temperature from 298 K to 343 K: △, [C1C2Im][CF3SO3]; ▲, [C 1 C 4 Im][CF 3 SO 3 ]; □ , [C 1 C 2 Im][CH 3 SO 4 ]; ■ , [C 1 C 4 Im][CH3SO4]. Lines correspond to the fits with eq 2

(1)

The parameters A and B of the fit are presented in Table 1, together with the error associated with the fit. The liquids containing the CF3SO3− anion are denser (6−7% denser) than the two others with the CH3SO4− anion. For both anions the increase of the alkylchain length on the cation decreases the density of the ionic liquid. Jacquemin et al.15 have built a group contribution method for the estimation of ionic liquid densities as a function of temperature at 0.1 MPa. The main idea is to consider the molar volume of an ionic liquid as the addition of the molar volumes of the anion and cation. For example, the molar volume of [C1C4Im][CF3SO3], Vm[C1C4Im][CF3SO3], is the sum of the contribution to the molar volume of the methylimidazolium cation [C1C0Im]+, of the 4 −CH2− groups present in the alkyl chain and of the CF3SO3− anion. The contribution of these three groups is given by Jacquemin et al.15 as a function of temperature. From the contributions proposed by these authors, it was possible to calculate the molar volumes of the four ionic liquids considered in this work as a function of temperature. Average absolute deviations less than 0.9 % between the experimental molar volumes and the predicted values were obtained which is coherent with the uncertainty of 0.5 % claimed by Jacquemin et al. According to our experimental results, the contribution at 298.15 K to the molar volume of the −CH2− group is 16.55.10−6 m3·mol−1 that corresponds to the contribution of 16.967.10−6 m3·mol−1 proposed by Jacquemin et al.15 Viscosity. Viscosity is the transport property that characterizes the hydrodynamics of a fluid and its resistance to flow. It was measured in the four ionic liquids as a function of temperature from 298 K to 343 K. The results are presented in Supporting Information, Table 2-SI and in Figure 1. A dramatic decrease of the viscosity is observed for each sample when temperature increases, which is commonly observed with ionic liquids.16 The variation of the viscosity with temperature was correlated using the Vogel Fulcher Tamman (VFT) equation:17 ⎛ k ⎞ η = A T exp⎜ ⎟ ⎝ T − T0 ⎠

where A, k, and T0 are adjustable parameters given in Table 2 along with the standard error of estimation of the fit. At 298.15 K, the viscosities are between 46.10−3 mPa·s for [C1C2Im][CF3SO3] and 223.10−3 Pa·s for [C1C4Im][CH3SO4] and are divided by a factor 4 to 7 at 343.15 K, varying from 12.10−3 Pa·s for [C1C2Im][CF3SO3] and 31.10−3 Pa·s for [C1C4Im][CH3SO4]. The increase of the alkyl chain length on the imidazolium ring increases the viscosity, which was already observed in literature with other anions (NTF2−,16,18 BF4−,19 I−20). This can be explained by an increase of the van der Waals interactions when the size of the alkyl chain length on the cation is increased. Similarly the presence of the anion CH3SO4− leads to more viscous ionic liquids. An increased viscosity was already observed in literature with sulfate anions. As an example, while [C1C4Pyrro][NTf2] exhibits a 77.10−3 Pa· s viscosity at 298 K,21 this property is increased by more than a factor of 10 (934.10−3 Pa·s at the same temperature) when the anion is changed for a butyl sulfate.22 The viscosity of [C1C4Im][CH3SO4] was measured as a function of temperature by three other authors.23−25 In the temperature range 298 K to 343 K, two references23,25 present results that are similar to those presented in this work (relative deviations of −5 % and +5 %), while in the third paper,24 the measured viscosity is systematically lower (15 % lower). Supporting Information Figure 1-SI presents these deviations. The viscosity of [C1C4Im][CF3SO3] was measured by Tokuda et al.26 and Ge et al.27 Deviations with these authors (−3 % and −6 %, respectively) are coherent with the experimental errors. In the case of [C1C2Im][CF3SO3], an acceptable 8 % deviation between our experimental set and the results of Rodriguez28 was observed. Deviations of 6 % are observed with the set of data measured by Costa et al.29 on the [C1C2Im][CH3SO4] as a function of temperature. Conductivity. The electrical conductivity of the four ionic liquids was measured as a function of temperature from 298 K to 343 K. The results are presented in Supporting Information

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Table 2. Parameters A, k, and T0 of eq 2, Used To Fit the Experimental Viscosities from Supporting Information Table 2-SI as a Function of Temperature along with the Standard Error of the Fit, SE A/10−6 Pa·s·K1/2 k/K T0 /K SE

[C1C2Im][CH3SO4]

[C1C4Im][CH3SO4]

[C1C2Im][CF3SO3]

[C1C4Im][CF3SO3]

5.04 979 153 0.06

6.99 910 177 0.4

5.68 946 144 0.1

7.44 841 169 0.3

Table 3-SI and in Figure 2. An increase of the electrical conductivity is observed when temperature is increased. This

These data are presented in Supporting Information Table 3-SI. With the simultaneous measurement of the viscosity and of the molar conductivity, the Walden plots can be used as a tool to estimate, at least qualitatively, the ionic association in the ionic liquids. This graphical representation is in Figure 3. The points presented in this graph were calculated using the VFT equation.

Figure 2. Electrical conductivity, κ, of the pure ionic liquids as a function of temperature from 298 K to 343 K: △, [C1C2Im][CF3SO3]; ▲, [C1C4Im][CF3SO3]; □, [C1C2Im][CH3SO4]; ■, [C1C4Im][CH3SO4]. Lines correspond to the fits with eq 2 Figure 3. Walden plot of the pure ionic liquids as a function of temperature from 298 K to 343 K: △, [C1C2Im][CF3SO3]; ▲, [C 1 C 4 Im][CF 3 SO 3 ]; □ , [C 1 C 2 Im][CH 3 SO 4 ]; ■ , [C 1 C 4 Im][CH3SO4]; black line, reference line (KCl, 0.01 M).

variation was correlated using the VFT equation, in which A′, k′ and T′0 are adjustable parameters, given in Table 3 along with the standard error of estimation of the fit. The electrical conductivity is related to the viscosity of the fluid. It is thus logical to observe higher conductivities in the triflate-based ionic liquids, compared to the more viscous sulfate-based ionic liquids. Similarly, the increase of the alkyl chain length of the cation, as it increases the viscosity of the liquid, decreases its electrical conductivity. The electrical conductivity of [C1C4Im][CF3SO3] can be found in literature. The data measured by Tokuda et al.26 and Zech et al.30 are respectively 5 % and 4 % lower than our data, which is acceptable. In contrast, the work of Yu et al.31 presents electrical conductivities for [C 1 C 4 Im][CH 3 SO 4 ] and [C1C4Im][CF3SO3] that are systematically very different from the one presented here. The molar conductivity measured by impedancemetry, Λimp, can be calculated from the ionic conductivity, κ, and the ionic liquid concentration (molarity of the ionic liquid), cIL, according to κ Λ imp = c IL (3)

[C1C2Im][CF3SO3] and [C1C2Im][CH3SO4] have very similar positions in this graph. They are placed just below the reference line (KCl) and above [C1C4Im][CF3SO3] and [C1C4Im][CH3SO4]. This last point indicates more ionic association when the alkyl chain length of the ionic liquid is increased. This observation is in agreement with the work of Tokuda et al.8 on NTf2− based ionic liquids. According to the classification of Angell et al.7 all these ionic liquids belong to the group of good ionic liquids, as they cluster the ideal line. When temperature is increased (from left to right on the Walden plot) the distance between the experimental points and the reference line increases for all the samples indicating increased ionic association. This effect is more pronounced in the two shorter alkyl chain imidazolium ([C1C2Im][CF3SO3] and [C1C2Im][CH3SO4]) based ionic liquids. Diffusion. Finally, the pulse-field gradient spin echo or DOSY NMR spectroscopy was considered as another experimental tool to characterize structure and dynamics in the ionic liquids. The diffusion coefficients of the anions and

Table 3. Parameters A′, k′ and T′0 of eq 2, Used To Fit the Experimental Electrical Conductivities from Supporting Information Table 3-SI as a Function of Temperature along with the Standard Error of the Fit, SE −1

A′/S·m ·K k′/K T′0/K SE

1/2

[C1C2Im][CH3SO4]

[C1C4Im][CH3SO4]

[C1C2Im][CF3SO3]

[C1C4Im][CF3SO3]

1.807 −372.7 204.2 0.02

1.460 −496.1 204.9 0.009

0.776 −214.7 218.1 0.03

1.500 −445.7 198.0 0.0009

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Table 4. Self-Diffusion Coefficients of Cations and Anions, Molar Conductivity by 1H NMR and Ionicity in the Pure [C1C2Im][CH3SO4] and [C1C4Im][CH3SO4] as a Function of Temperature from 298 K to 343 K T/K 298.15 303.15 313.15 323.15 333.15 343.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

1011Dcation/m2·s−1 2.8 3.4 4.9 7 9.6 13.3 0.75 0.99 1.3 1.7 2.1 2.6 3.3 4.0 4.8 5.7

1011Danion/m2·s−1

104ΛNMR/S.m2.mol−1

ionicity

1.04 1.26 1.78 2.44 3.25 4.15

0.60 0.60 0.58 0.56 0.54 0.48

0.526 0.695 0.909 1.17 1.50 1.84 2.31 2.80 3.39 3.99

0.48 0.48 0.48 0.47 0.45 0.45 0.43 0.42 0.40 0.39

[C1C2Im][CH3SO4] 1.8 2.2 3.3 4.6 6.5 9.5 [C1C4Im][CH3SO4] 0.65 0.86 1.1 1.4 1.9 2.3 2.9 3.5 4.2 4.9

Table 5. Self-Diffusion Coefficients of Cations and Anions, Molar Conductivity by 19F NMR and Ionicity in the Pure [C1C2Im][CF3SO3] and [C1C4Im][CF3SO3] as a Function of Temperature from 298 K to 343 K T/K

1011Dcation/m2·s−1

298.15 303.15 313.15 323.15 333.15 343.15

4.1 4.8 7.1 10.2 14.7 19.9

298.15 303.15 313.15 323.15 333.15 343.15

1.7 2.2 3.6 5.8 8 11.3

1011Danion/m2·s−1

104ΛNMR/S.m2.mol−1

ionicity

2.52 3.04 4.58 6.57 9.65 13.4

0.68 0.67 0.59 0.52 0.44 0.37

1.13 1.50 2.48 4.05 5.63 8.03

0.60 0.56 0.50 0.43 0.41 0.37

[C1C2Im][CF3SO3] 2.6 3.3 5.1 7.3 11.0 15.7 [C1C4Im][CF3SO3] 1.3 1.8 3 5 7 10.1

cations were measured by 1H and 19F NMR from 298 K to 343 K, in the pure ionic liquids. The results are presented in Tables 4 and 5. Prior to these experiments, diffusion coefficients of 2.6·10−11 2 −1 m ·s and 2.0·10−11 m2·s−1 were measured for the cation and the anion, respectively, in [C1C4Im][NTf2] at 298 K. This is in good agreement with the values of 2.82·10−11 m2·s−1 and 2.16· 10−11 m2·s−1 proposed by Nama et al.32 in this ionic liquid at 300 K. In Tables 4 and 5, the diffusion coefficients of the anions vary from 0.65·10−11 m2·s−1 for [C1C4Im][CH3SO4] at 298 K to 15.7·10−11 m2·s−1 for [C1C2Im][CF3SO3] at 343 K. The diffusion coefficients of the cations vary from 0.75·10−11 m2·s−1 for [C1C4Im][CH3SO4] at 298 K to 19.9·10−11 m2·s−1 for [C1C2Im][CF3SO3] at 343 K. These orders of magnitude, smaller than what is observed in molecular liquids, are classical for ionic liquids.4 It was not possible to directly compare these data with literature as, to the best of our knowledge, the diffusion coefficients of the ionic liquids considered here are measured for the first time in the present work.

For all the samples the diffusion coefficients of the cation and anion are the same order of magnitude with the cation diffusing always slightly faster than the anion. This result can be surprising given the relative sizes of the cation and anion, but it was already observed and can be explained by the boardlike shape of the imidazolium ring that would be more appropriate for fast diffusion.4 The diffusion coefficients are higher in the less viscous triflate-based ionic liquids and in the ionic liquids with the smaller alkyl chain (C1C2Im). An increase of the diffusion coefficients was observed when temperature was increased, following an Arrhenius law.33,38 ⎛ −E ⎞ D = A exp⎜ A ⎟ ⎝ RT ⎠

(4)

The activation energies are presented in Table 6. They are between 29 kJ mol−1 and 39 kJ mol−1, higher in the two ionic liquids with the longer alkyl chains, which is coherent with their higher viscosities. The same was observed by Alam et al.38 in butyl and octyl methyl pyrrolidinium bis(trifluoromethanesulfonyl)imide (activation energies for the cation diffusion coefficients of 32.9 kJ mol−1 and 40.4 kJ mol−1, 1751

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Table 6. Activation Energies Calculated from Arrhenius Equation of the Diffusion Coefficients as a Function of Temperature Ea/kJ mol−1 ionic liquid [C1C2Im][CF3SO3] [C1C4Im][CF3SO3] [C1C2Im][CH3SO4] [C1C4Im][CH3SO4]

anion 33.8 39 31 38

± ± ± ±

0.7 3 1 1

cation 30.3 36 29.4 38

± ± ± ±

0.8 2 0.3 1

respectively for butyl and octyl chain on the pyrrolidinium cation). Lower activation energies (similar for the cation and the anion) were calculated by Anouti et al.33 for the diffusion coefficients in pyrrolidinium hydrogen sulfate and pyrrolidinium trifluoroacetate (14.5 kJ mol−1 and 13.3 kJ mol−1, respectively). In the case of pyrrolidinium trifluoroacetate, for temperatures higher than 328 K, four times higher activation energies (mean value of 41 kJ mol−1) were calculated. The diffusion coefficient, characterizing mass transport, can be related to the hydrodynamics of the system (viscosity) through the Stokes−Einstein (SE) equation:34 D=

kBT CπηrS

Figure 4. Relationship between the ion diffusion coefficients and T/η for the pure ionic liquids as a function of temperature from 298 K to 343 K: ▽, C1C2Im+ in [C1C2Im][CF3SO3]; △, CF3SO3− in [C 1C2Im][CF3 SO3]; ▼, C 1C4 Im+ in [C1 C4Im][CF 3SO3]; ▲, CF3SO3− in [C1C4Im][CF3SO3]; □, C1C2Im+ in [C1C2Im][CH3SO4]; ○, CH3SO4− in [C1C2Im][CH3SO4]; ●, C1C4Im+ in [C1C4Im][CH3SO4]; ■, CH3SO4− in [C1C4Im][CH3SO4]. The lines correspond to linear fits.

hydrodynamic radius calculated from the intercept of the lines with the y-axis by considering C as equal to 6 are underestimated as already observed in literature. As an example, the hydrodynamic radius of C1C4Im+ and CF3SO3− in [C1C4Im][CF3SO3] equal 0.13 nm and 0.15 nm, respectively, while the van der Waals radius of these ions are 0.33 nm and 0.267 nm.36 Values of 2.4 (C1C4Im+) and 3.4 (CF3SO3−) for C would be necessary to obey the Stokes−Einstein equation. These different C values for the anion and cation confirm that not only the size of the ion is responsible for its diffusion coefficient. Indeed, even if the two ions would have the same radius, their diffusion would be different, because of different solute−solvent interactions. Ionicity. From the diffusion coefficients, the molar conductivity can be calculated according to Nernst−Einstein equation:

(5)

where rS is the hydrodynamic radius of the diffusing particle and kB is the Boltzmann constant. The C factor is a constant affected by the strength of the interactions between the diffusing specie and the medium. It is typically taken as 6 but can be reduced to 4. Indeed, depending on the relative size of the solute and solvent, eq 5 can fail. Moreover, this equation breaks down in high-viscosity solvents.34 The Stokes−Einstein (SE) equation is derived from classical hydrodynamics (Stokes’ law) and assumes that the diffusing species is a rigid sphere in a continuum of solvent.34 These assumptions are not correct in ionic liquids. For this reason, the applicability of this equation in these systems is debated. For example, Koddermann et al.,35 from molecular dynamic simulations of diffusion coefficients, have concluded to its nonapplicability in pure [C1C2Im][NTf2] explaining this by the presence of dynamical heterogeneities. The variation of the diffusion coefficient as a function of T/η is often found linear, but the hydrodynamic radius and volumes calculated from the slope of the line are underestimated in some cases which is a signature of SE deviations.36 In some ionic liquids, fractional SE relation was observed with the diffusion coefficient being proportional to (T/η)m where m is lower than unity.37 A combined measurement of translational and rotational diffusion is a way to explore in more detail the validity of the SE equation. Indeed, from the ratio of these two parameters the molar volume of the molecule can be calculated and its variation with temperature is a signature of the breakdown of the SE equation in ionic liquids. Such a study is proposed by Alam et al.38 on ammonium- and pyrrolidinium-based ionic liquids, and the authors conclude that the equation is not applicable in these ionic liquids. In the present study, the evolution of the logarithm of the diffusion coefficients as a function of the logarithm of T/η was found linear as illustrated in Figure 4. The slopes of the lines typically equal 1, indicating that the diffusion coefficients are directly proportional to T/η. This is coherent with an application of the Stokes−Einstein equation; however, the

ΛNMR = NAe 2

D+ + D− kBT

(6)

where NA is Avogadro’s number, e is the electronic charge on each ionic carrier, D+ and D− are the diffusion coefficients of the ions, kB is the Boltzmann constant, and T is the temperature. If all ions are available for ionic conduction (which means there is no association), the molar conductivity calculated from eq 6 equals the molar conductivity obtained from the electrical conductivity (eq 3). In the case of ionic association, there are deviations from the Nernst−Einstein equation. The molar conductivities, ΛNMR and Λimp are different, and Λimp/ΛNMR represents the proportion of charged species contributing to ionic conduction. This ratio is called the ionicity and was calculated for each ionic liquid as a function of temperature. Results are presented in Tables 4 and 5. The ionicities are lower than unity, confirming the presence of ionic association in these systems, varying from 0.37 in [C1C4Im][CF3SO3] at 343 K to 0.68 in [C1C2Im][CF3SO3] at 298 K. Both for sulfate-based and triflate-based ionic liquids, an increase of the alkyl chain on the cation ring leads to a decrease of the ionicity. The same result was obtained by Tokuda et al.39 on an NTf2−-based ionic liquid 1752

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ionic liquid electrolytes for lithium−air batteries. J. Power Sources 2013, 243, 19−23. (6) Mac Farlane, D. R.; Forsyth, M.; Izgorodina, E. I.; Abbott, A. P.; Annat, G.; Fraser, K. On the concept of ionicity in ionic liquids. Phys. Chem. Chem. Phys. 2009, 11, 4962−4967. (7) Angell, C. A.; Byrne, N.; Belieres, J. P. Parallel developments in aprotic and protic ionic liquids: Physical chemistry and applications. Acc. Chem. Res. 2007, 40, 1228−1236. (8) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. Physicochemical properties and structures of room temperature ionic liquids. 2. Variation of alkyl chain length in imidazolium cation. J. Phys. Chem. B 2005, 109, 6103−6110. (9) Walden, P. Uber organische losungs-und ionisierungsmittel. III. Teil: Innere reibung und deren zusammenhang mit dem leitvermongen. Z. Phys. Chem. 1906, 55, 207−246. (10) Wasserscheid, P.; Van Hal, R.; Bösmann, A. 1-n-butyl-3methylimidazolium ([bmim]) octylsulfateAn even “greener” ionic liquid. Green Chem. 2002, 4, 400−404. (11) Ficke, L. E.; Rodríguez, H.; Brennecke, J. F. Heat capacities and excess enthalpies of 1-3ethyl-3-methylimidazolium-based ionic liquids and water. J. Chem. Eng. Data 2008, 53, 2112−2119. (12) Almantariotis, D.; Gefflaut, T.; Padua, A. A. H.; Coxam, J. Y.; Costa Gomes, M. F. Effect of fluorination and size of the alkyl sidechain on the solubility of carbon dioxide in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ionic liquids. J. Phys. Chem. B 2010, 114, 3608−3617. (13) Canongia Lopes, J. N.; Costa Gomes, M. F.; Husson, P.; Pádua, A. A. H.; Rebelo, L. P. N.; Sarraute, S.; Tariq, M. Polarity, viscosity and ionic conductivity of liquid mixtures containing [C4C1im][Ntf2] and a molecular component. J. Phys. Chem. B 2011, 115, 6088−6099. (14) Andanson, J. M.; Traïkia, M.; Husson, P. Ionic association and interactions in aqueous methylsulfate alkyl-imidazolium-based ionic liquids. J. Chem. Thermodyn. 2014, under press, doi: http://dx.doi.org/ 10.1016/j.jct.2014.01.031. (15) Jacquemin, J.; Ge, R.; Nancarrow, P.; Rooney, D. W.; Costa Gomes, M. F.; Padua, A. A. H.; Hardacre, C. Prediction of ionic liquid properties. I. Volumetric properties as a function of temperature at 0.1 MPa. J. Chem. Eng. Data 2008, 53, 716−726. (16) Jacquemin, J.; Husson, P.; Padua, A. A. H.; Majer, V. Density and viscosity of several pure and water-saturated ionic liquids. Green Chem. 2006, 8, 172−180. (17) Vogel, H. The law of relation between the viscosity of liquids and the temperature. Phys. Z. 1921, 22, 645−646. Tamman, G.; Hesse, W. The dependence of viscosity upon the temperature of supercooled liquids. Z. Anorg. Allgem. Chemie 1926, 156, 645−657. Fulcher, G. S. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 1925, 8, 339−355. (18) Tariq, M.; Carvalho, P. J.; Coutinho, J. A. P.; Marrucho, I. M.; Canongia Lopes, J. N.; Rebelo, L. P. N. Viscosity of (C2−C14) 1-alkyl3-methylimidazolium bis(trifluoromethylsulfonyl)amide ionic liquids in an extended temperature range. Fluid Phase Equilib. 2011, 301, 22− 32. (19) Rilo, E.; Vila, J.; Garcia, M.; Varela, L. M.; Cabeza, O. Viscosity and electrical conductivity of binary mixtures of CnMIM-BF4 with ethanol at 288 K, 298 K, 308 K, and 318 K. J. Chem. Eng. Data 2010, 55, 5156−5163. (20) Ghatee, M. H.; Zare, M.; Moosavi, F.; Zolghadr, A. R. Temperature-dependent density and viscosity of the ionic liquids 1alkyl-3-methylimidazolium iodides: Experiment and molecular dynamics simulation. J. Chem. Eng. Data 2010, 55, 3084−3088. (21) Pereiro, A. B.; Veiga, H. I. M.; Esperanca, J. M. S. S.; Rodriguez, A. Effect of temperature on the physical properties of two ionic liquids. J. Chem. Thermodyn. 2009, 41, 1419−1423. (22) Wu, T. Y.; Hao, L.; Chen, P. R.; Liao, J. W. Ionic conductivity and thermophysical properties of 1-butyl-1-methylpyrrolidinium butyl sulfate and its binary mixtures with poly(ethylene glycol) at various temperatures. Int. J. Electrochem. Sci. 2013, 8, 5067−5085.

and this is coherent with our observations on the Walden plots (Figure 3). The ionic character is the result of two opposite effects: the electrostatic attraction between ions and the van der Waals interactions, increased with the alkyl chain length on the cation. The increased ionicity with the alkyl chain length on the cation is the signature of a larger contribution of the van der Waals interactions in these systems, according to Tokuda et al.39 Increasing the temperature has no significant effect on the ionic association of these pure ionic liquids. Only a slight decrease of the ionic character is observed when increasing temperature, this is coherent with our previous observations on the Walden plots.

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CONCLUSION In this work, three transport properties (viscosity, diffusion coefficient, and electrical conductivity) were experimentally determined from 298 K to 343 K in four pure imidazoliumbased ionic liquids with two anions and different alkyl chain lengths on the cation. Higher viscosities, lower diffusion coefficients, and electrical conductivities were measured when the alkyl chain length was increased or the sulfate anion was present. An increased ionic association when the alkyl chain length on the cation was increased was observed, and comparable ionicities were measured for both anions. Typical ionicities between 0.4 and 0.6 were calculated in these systems. These results are confirmed (at least qualitatively) by the position of the experimental data on the Walden plot. Finally, the applicability of the Stokes−Einstein equation (relation between the diffusion coefficient and the viscosity) was discussed in these systems. A linear variation of the diffusion coefficients as a function of T/η was observed but the hydrodynamic radius calculated using the Stokes−Einstein equation are underestimated, which is the signature of a breakdown of this equation.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental densities, viscosities, and electrical conductivities; figure of relative deviations of the literature viscosities from the experimental data of this work. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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