J. Phys. Chem. B 2010, 114, 16329–16336
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Origin of the Low-Viscosity of [emim][(FSO2)2N] Ionic Liquid and Its Lithium Salt Mixture: Experimental and Theoretical Study of Self-Diffusion Coefficients, Conductivities, and Intermolecular Interactions Seiji Tsuzuki,*,† Kikuko Hayamizu,† and Shiro Seki*,‡ National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan, and Materials Science Research Laboratory, Central Research Institute of Electric Power Industry (CRIEPI), 2-11-1 Iwado-kita, Komae, Tokyo 201-8511, Japan ReceiVed: May 21, 2010; ReVised Manuscript ReceiVed: October 25, 2010
The temperature-dependent viscosity, ionic conductivity, and self-diffusion coefficients of an ionic liquid, 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)amide ([emim][FSA]), and its Li salt mixture were studied with reference to emim bis(trifluoromethyl-sulfonyl)amide ([emim][TFSA]) systems. The stabilization energies for the formation of the FSA- complexes with emim+ and Li+ were calculated by the MP2/6-311G** level ab initio method. The stabilization energies calculated for the FSA- complexes with emim+ and Li+ (-77.0 and -134.3 kcal/mol) were smaller than those for the corresponding TFSA- complexes (-78.8 and -137.2 kcal/mol). The weaker electrostatic and induction interactions are the causes of the smaller interaction energies for the FSA- complexes. The weaker interaction between the FSA- and emim+ can be one of the causes of the lower viscosity of the [emim][FSA] ionic liquid compared with that of the [emim][TFSA] ionic liquid. The weaker interaction between the FSA- and Li+ compared with that between the TFSA- and Li+ explains the fact that the addition of Li salt to the [emim][FSA] ionic liquid induces a little increase of the viscosity and a little decrease of the ionic conductivity and self-diffusion coefficients of ions. The FSA- in the Li[FSA] complex prefers the cis form due to the stronger attraction and smaller deformation energy of the cis-FSAcompared with the trans-FSA-. Introduction Room-temperature ionic liquids (RTILs) have attracted increasing interest in many fields of chemistry.1-4 RTILs have the potential to become important industrial solvents for synthesis, catalysis, extraction, and purification as they have low vapor pressure and unusual catalytic properties. Many RTILs also show the potential for applications to electrochemical devices, including batteries, capacitors, and solar cells, due to their high ionic conductivity and electrochemical stability.5-9 Especially, some RTILs have desirable characteristics for large lithium battery electrolyte media, owing to their low volatility and low flammability. The reduction of the viscosity of RTILs is one of the important issues for developing electrolytes for lithium secondary batteries and electric double-layer capacitors. For example, the diffusion of Li+ is an important factor controlling the charge-discharge property. The viscosity of RTILs is 2 or 3 order higher than that of conventional organic solvents (molecular liquids). In particular, the addition of Li salt to RTILs significantly increases the viscosity. In these situations, the (FSO2)2N anion (FSA-)-based ionic liquids attract much interest due to their low viscosity and high ionic conductivity.10-31 Matsumoto et al. reported11 the viscosity and conductivity of the FSA--based RTILs at 298 K. The viscosity is about 40% lower than that of the corresponding (CF3SO2)2N anion (TFSA-)based RTILs, and actually, the FSA--based RTILs have larger ionic conductivity. The addition of Li salt to the TFSA--based * To whom correspondence should be addressed. E-mail s.tsuzuki@aist. go.jp (S.T.);
[email protected] (S.S.). † AIST. ‡ CRIEPI.
RTILs increases the viscosity significantly (66-119%), while the increase in the viscosity of the FSA--based ionic liquids is remarkably smaller (28-33%). Recently, several studies were reported on the performance of the FSA--based ionic liquids as electrolytes for electrochemical devices.10,16,19,22-25,27,29,32-37 The liquid structures of FSA--based ionic liquids were studied both by experimental and theoretical methods, such as the measurements of IR, Raman spectra, and X-ray scattering.12,15,20 Also, ionic liquid aggregates were studied by the measurements of electrospray ionization mass spectra.38-43 Molecular dynamics simulations on FSA--based ionic liquids were reported.13,44-47 Despite the recent studies on the FSA--based ionic liquids, the cause of their low viscosity is still unclear. The intermolecular interactions between ions are one of the important factors determining transport properties of RTILs. The detailed information on the interactions is important for the elucidation of the cause of the low viscosity of the FSA--based ionic liquids. Unfortunately, however, the precise intermolecular interactions of the FSA- with cations are still unclear. In this paper, we studied the temperature dependence of various physical parameters of the [emim][FSA] ionic liquid and calculated the intermolecular interaction energies for the FSA- complex with emim+ by ab initio molecular orbital methods. The calculated interaction energies were compared with those for the [emim][TFSA] complex. We will discuss the relationship between the calculated interaction energies and the viscosity of the FSA-based ionic liquid. In addition, we calculated the interaction energies for the Li[FSA] and Li[TFSA] complexes. We will discuss the causes of various effects of the Li salt addition on the viscosity of the [emim][FSA] ionic liquid compared with that of the [emim] [TFSA] ionic liquid.
10.1021/jp106870v 2010 American Chemical Society Published on Web 11/16/2010
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Experimental Methods Samples. Ionic liquid samples ([emim][TFSA] and [emim] [FSA]) and Li[FSA] were purchased from Dai-ichi Kogyo Seiyaku Co., Ltd. Li[TFSA] was purchased from Kishida Chemicals. The Li-salt-doped samples were prepared to be 0.32 mol kg-1 by weight. The Li-salt-doped binary samples were prepared by adding the Li[TFSA] and Li[FSA] to the [emim][TFSA] and [emim][FSA], respectively. The samples were dried in a vacuum chamber at 323 K for more than 48 h and stored in a dry argon-filled glovebox ([O2] < 0.4 ppm, [H2O] < 0.1 ppm, Miwa Mfg. Co., Ltd.) before measurements. Density and Viscosity Measurements. Density (F) and viscosity (η) were measured using a thermoregulated Stabingertype density/viscosity meter (SVM3000G2, Anton Paar). The temperature was controlled in the range of 80-10 °C while cooling. Ionic Conductivity Measurements. Ionic conductivity (σ) was measured on SUS/electrolyte/SUS hermetically closed cells and determined by the complex impedance method using an ac impedance analyzer (Princeton Applied Research, PARSTAT2263, 200 kHz-50 mHz; applied voltage 10 mV) at temperatures between 80 and -39 °C while cooling. The samples were thermally equilibrated at each temperature for at least 90 min prior to the measurements. Diffusion Coefficient Measurements. The self-diffusion coefficients of ions were measured by pulsed-gradient spin-echo (PGSE) NMR methods by a Tecmag Apollo with a 6.35 T wide bore magnet using a JEOL PFG probe controlled by a JEOL console. The emim+ (1H), FSA- and TFSA- (19F), and Li+ (7Li) NMR spectra were measured at 270.2, 254.2, and 105.0 MHz, respectively. The NMR spectra did not include any extra peaks. The self-diffusion coefficients (Demim, DFSA, DTFSA, and DLi) were measured from 80 to -20 °C in the cooling process. The largest PFG used was 14 T/m, and the longest duration of time was 4 ms. Convection effects in the high-temperature region were carefully excluded by varying the PFG interval times. Computational Methods. The Gaussian 03 program48 was used for the ab initio molecular orbital calculations. The basis sets implemented in the Gaussian program were used. The geometries of complexes were fully optimized at the HF/6311G** level. The interaction energy between the cation and anion (Eint) was calculated at the MP2/6-311G**//HF/6-311G** level by the supermolecule method.49,50 Our previous calculations of the [emim][BF4] and Li[TFSA] complexes51,52 show that the basis set effects on the calculated interaction energies of the complexes are very small, if basis sets including polarization functions are used, and that the effects of electron correlation beyond MP2 are negligible. Therefore, we calculated the interaction energies of complexes at the MP2/6-311G** level in this work. The basis set superposition error (BSSE)53 was corrected for all of the interaction energy calculations using the counterpoise method.54 The stabilization energy by the formation of a complex from isolated ions (Eform) was calculated as the sum of the Eint and the deformation energy (Edef), which is the sum of the increase of energies of ions by deformation of the geometries associated with the complex formation.52 The electrostatic energy was calculated using the ORIENT version 3.2.55 The electrostatic energy of the complex was calculated as interactions between distributed multipoles of ions. Distributed multipoles56,57 up to hexadecapole on all atoms were obtained from the MP2/6-311G** wave functions of an isolated ion using the GDMA program.58 The induction energy was calculated as interactions of polarizable sites with the electric field produced by the distributed multipoles of monomers.59 The
Figure 1. Temperature dependence of the density (F) for the [emim][TFSA] and [emim][FSA] ionic liquids with and without Li salt (0.32 mol kg-1) upon cooling (80-10 °C).
atomic polarizabilities of carbon (R ) 10 au), nitrogen (R ) 8 au), oxygen (R ) 6 au), fluorine (R ) 3 au), and sulfur (R ) 20 au) were used for the calculations.60 Distributed multipoles were used only to estimate the electrostatic and induction energies. Results and Discussion Density. Figure 1 shows the temperature dependence of the density for neat RTIL samples and binary electrolyte samples with the Li salt. A strong linear relationship (r > 0.999) with temperature is obtained for all samples. The density of the [emim][TFSA] ionic liquid is larger than that of the [emim][FSA] ionic liquid at all temperatures. The density of the binary electrolyte samples (0.32 mol kg-1 Li[TFSA]) is larger than that of the neat RTIL samples. The density increases with the increase of molecular weight of the anion in the neat RTILs,61 and the addition of Li salt increases the density. Recently, the densities of the ionic liquids composed of the FSA- and N-butylN-methyl pyrrolidinium (Py14+) or N-methyl-N-propyl pyrrolidinium (Py13+) were reported.30 The density of the ionic liquids composed of the FSA- is smaller than the corresponding one composed of the TFSA-. Viscosity. Figure 2a shows the temperature dependence of the viscosity (η) for the neat RTIL samples and binary electrolyte samples. The viscosity for the neat [emim][FSA] and [emim][TFSA] ionic liquids at 30 °C is 17 and 28 mPas, respectively. The Li salt addition increases the viscosity up to 21 and 46 mPas at 30 °C, respectively. The relative viscosity (Li-salt-doped sample/neat RTIL sample) is depicted in Figure 2b. The increment of the viscosity of the [emim][FSA] ionic liquid by the addition of Li salt shows small temperature dependence and is always smaller than that of the [emim][TFSA] ionic liquid. Especially the increment at low temperature is remarkably smaller. The relative viscosity for the [emim][FSA] ionic liquid at 10 °C is only 1.2, while it is about 1.9 for the [emim][TFSA] ionic liquid. The viscosity of the FSA--based ionic liquids was measured by several groups.11,14,19,22-26,28,29 SeveralgroupsreportedtheviscosityoftheirLisaltmixtures.11,19,26,29 Very recently, two groups reported the temperature dependence of the viscosity of the FSA--based ionic liquids and their Li salt mixtures.26,29 Unfortunately, however, the temperature dependence of the viscosity of the [emim][FSA] ionic liquid doped with Li salt was not reported. Ionic Conductivity. Figure 3 shows the temperature dependence of the ionic conductivity for neat and binary electrolyte samples. All plots indicate the VFT-type temperature depen-
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Figure 4. Temperature dependence of the self-diffusion coefficients of ions in the [emim][FSA] ionic liquid (Demim and DFSA) and those in the [emim][TFSA] ionic liquid (Demim and DTFSA) upon cooling (80 to -20 °C).
Figure 2. (a) Temperature dependence of the viscosity (η) for the [emim][TFSA] and [emim][FSA] ionic liquids with and without Li salt (0.32 mol kg-1) upon cooling (80-10 °C). (b) Temperature dependence of the relative viscosity.
Figure 5. Temperature dependence of the self-diffusion coefficients of ions (a) Demim, DTFSA, and DLi in the Li-salt-doped [emim][TFSA] ionic liquid and (b) Demim, DFSA, and DLi in the Li-salt-doped [emim][FSA] ionic liquid upon cooling (80 to -20 °C). For comparison, the data of neat samples were added, represented by open marks.
Figure 3. Temperature dependence of the ionic conductivity (σ) for the [emim][TFSA] and [emim][FSA] ionic liquids with and without Li salt (0.32 mol kg-1) upon cooling (80 to -39 °C).
dence. The ionic conductivity for the [emim][FSA] and [emim][TFSA] ionic liquids at 30 °C are 17.7 and 10.6 × mS cm-1, respectively. The Li salt addition induced the decrease in the ionic conductivity to 14.9 and 6.86 × mS cm-1, respectively, at 30 °C. The decrease of the ionic conductivity for the [emim][FSA] ionic liquid is remarkably smaller than that for the [emim][TFSA] ionic liquid, which suggests that the FSA--based ionic liquids have advantage for the applications to electrolytes of electrochemical devices used at low temperature. The ionic conductivity of FSA--based ionic liquids was measured by several groups.14,17,19,22-29 The ionic conductivity of their Li salt mixtures was also reported.17,19,26,27,29 Although the temperature dependence of the conductivity of the ionic liquids composed of the pyrrolidinium cations and FSA- doped with Li salt was reported, the temperature dependence of the
conductivity of the [emim][FSA] ionic liquid doped with Li salt was not reported. Self-Diffusion Coefficients of Ions. The temperature dependence of the self-diffusion coefficients of ions (D) in the [emim][FSA] and [emim][TFSA] ionic liquids is shown in Figure 4. Clearly, the emim+ and FSA- in the [emim][FSA] ionic liquid diffuse faster than the emim+ and TFSA- in the [emim][TFSA] ionic liquid, which is consistent with the viscosity. In the present ionic liquids, Demim is larger than Danion, but the differences in Demim and DFSA are small in the whole temperature range. At 30 °C, Demim and DFSA were 8.40 and 7.62 × 10-11 m2 s-1, respectively, in the [emim][FSA] ionic liquid, and Demim and DTFSA were 6.00 and 3.54 × 10-11 m2 s-1, respectively, in the [emim][TFSA] ionic liquid. The selfdiffusion coefficients of ions in the binary samples are shown in Figure 5, where the data of neat samples were added for comparison. The order of D values is Demim> DFSA, DTFSA> DLi within the same samples and each value scattered in the Lisalt-doped [emim][TFSA], while the differences are smaller in the Li-salt-doped [emim][FSA]. The self-diffusion coefficients of ions in ionic liquids are important for understanding their transport properties such as viscosity and ionic conductivity.
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Figure 6. Atomic charge distributions calculated for FSA-. Figure 8. Optimized geometries and stabilization energies (Eform) calculated for the [emim][FSA] complex. Interaction energies (Eint) are shown in parentheses. Energy is in kcal/mol. The color codes of atoms are as follows: carbon (black), hydrogen (light blue), nitrogen (blue), oxygen (red), fluorine (light green) and sulfur (yellow).
Figure 9. Relative energy calculated for the trans and cis forms of FSA- at the MP2/cc-pVTZ//MP2/6-311G** level. The energy is in kcal/mol. Figure 7. Torsional potentials for the F-S-N-S bond of the FSAand the C-S-N-S bond of the TFSA- calculated at the MP2/ccpVTZ//MP2/6-311G** level.
Unfortunately, however, the temperature dependence of the selfdiffusion coefficients of ions in the FSA--based ionic liquids and their Li salt mixtures was not reported. Charge Distributions. The atomic charge distributions of the FSA- were calculated by electrostatic potential fitting using the Merz-Singh-Kollman scheme62,63 from the MP2/6-311G** wave functions of an isolated FSA-, as shown in Figure 6. The negative charges of the FSA- mainly locate on the oxygen and nitrogen atoms. The negative charges on the oxygen (-0.55 and -0.56 e) and nitrogen (-0.73 e) atoms of the FSA- are close to those on the oxygen (-0.53 and -0.54 e) and nitrogen (-0.73 e) atoms of the TFSA-.51 The negative charges on fluorine atoms of the FSA- (-0.30 e) are smaller than those on the oxygen and nitrogen atoms as in the case of the TFSA(-0.14 to -0.20 e). The positive charges on the sulfur atoms of the FSA- (1.27 e) are substantially larger than those on the sulfur atoms of the TFSA- (0.96 e). Torsional Potential. Torsional potentials for the FSA- and TFSA- were calculated by ab initio and DFT calculations (B3LYP/6-31G* and MP2/cc-pVTZ(-f)//MP2/6-31G* levels), which shows that the TFSA- has a higher torsional barrier compared with that of the FSA-.12,13 Our MP2/cc-pVTZ//MP2/ 6-311G** level calculations (Figure 7) also show that the torsional barrier for the F-S-N-S bond of the FSA- (3.8 kcal/ mol) is substantially lower than that for the C-S-N-S bond of the TFSA- (6.1 kcal/mol). The MP2/cc-pVTZ//MP2/6311G** level torsional potentials were close to the B3LYP/631G* and MP2/cc-pVTZ(-f)//MP2/6-31G* level potentials, as shown in Figure 1S in Supporting Information. Structures and Stabilization Energies for the [emim][FSA] Complex. The geometries of the [emim][FSA] complex were optimized from 54 initial geometries. The 29 geometries of the [emim][FSA] complex shown in Figures 8 and 2S (Supporting Information) were obtained. The FSA- has two stable rotamers (trans and cis).12,13 The MP2/cc-pVTZ//MP2/6-311G** level calculations show that the trans rotamer is 1.09 kcal/mol more stable than the cis rotamer, as shown in Figure 9. Fujii et al. reported a slightly smaller energy difference (0.60 kcal/mol) from the B3LYP/6-311+G(3df) calculations.12 They also reported that the two rotamers coexist in equilibrium in the [emim][FSA] ionic liquid. In this study, both the trans and cis
forms of FSA- were used for the geometry optimizations of the [emim][FSA] complex. The stabilization energies (Eform) for the formation of the complex from isolated ions are shown in Figures 8 and 1S (Supporting Information). The [emim][FSA] complex has a very large (negative) Eform. The Eform calculated for the most stable geometry (1a) was -77.0 kcal/mol. The FSA- has the trans form in 1a. Complex 1d is the most stable geometry for the [emim][FSA] complex in which the FSA- has the cis form. Although the Eint for 1d (-80.5 kcal/mol) is 1.2 kcal/mol larger (more negative) than that for 1a (-79.3 kcal/mol), the Eform for 1d (-76.4 kcal/mol) is 0.6 kcal/mol smaller than that for 1a (-77.0 kcal/mol). The larger Eint for 1d shows that the interaction of the cis form of FSA- with the emim+ is stronger than that of the trans one. The larger stability of 1a is attributed to the smaller Edef for 1a (2.3 kcal/mol) compare with that for 1d (4.1 kcal/mol). Large numbers of local minimum structures having nearly identical energies were found for the [emim][FSA] complex, as in the case of the [emim][TFSA] complex. The Eform values for 22 local minima (1a-1v) lie between -74.9 and -77.0 kcal/ mol. The differences are less than 2.1 kcal/mol. The C2-H of emim+ (Figure 8) has close contact with the oxygen or nitrogen atom of FSA- in these structures.64 The Eform values calculated for 1y-1cc, where the FSA- has close contact with the C4-H or C5-H (-66.9 to -70.1 kcal/mol), are substantially smaller than those for 1a-1v. The calculations show that the FSAprefers to locate near the C2-H of emim+, as in the case of other anions. The coordination sites of anions at imidazolium cations in ionic liquids were studied both by experimental and theoretical methods. X-ray analysis of crystals and neutron diffraction studies of ionic liquids show that anions prefer to have contact with the C2-H of the imidazolium cation.65-69 Molecular dynamics simulations also suggest that the C2-H prefers to have contact with an anion.70-74 Ab initio calculations of ion pairs showed that the imidazolium cations have several coordination sites of anions,25,39,40,51,75-79 in which anions (BF4-, PF6-, TFSA-, etc.) prefer to have close contact with the C2-H of imidazolium cations.51,78,79 It was pointed out that the center of the positive charge of imidazolium cations is close to the midpoint between the two nitrogen atoms of imidazolium, and therefore, the anions prefer to locate near the C2-H for increasing the stabilization by the electrostatic interaction.80
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TABLE 1: Interaction Energies for FSA- and TFSAComplexesa complex
Eintb
Edefc
Eformd
Eese
Eindf
Eotherg
[emim][FSA] 1a [emim][FSA] 1y [emim][TFSA]h Li[cis-FSA] 2a Li[trans-FSA] 2b Li[cis-TFSA]i Li[trans-TFSA]i
-79.3 -72.0 -80.5 -142.6 -141.9 -145.0 -144.7
2.3 0.8 1.7 8.2 9.8 9.4 7.5
-77.0 -70.1 -78.8 -134.3 -132.1 -135.7 -137.2
-75.2 -67.8 -75.3 -138.8 -138.1 -140.6 -140.3
-10.0 -8.4 -11.1 -43.6 -43.7 -46.3 -46.6
6.0 4.1 5.9 39.9 39.9 41.9 42.3
a Energy in kcal/mol. Geometries of complexes are shown in Figures 8 and 10. b BSSE-corrected interaction energies for complexes calculated at the MP2/6-311G** level. c Sum of increases of energies of ions (emim+, FSA-, and TFSA-) by the deformation of geometries associated with complex formation. See text. d Formation energy of the complex from isolated ions. Sum of Eint and Edef. e Electrostatic energy. See text. f Induction energy. See text. g Eother ) Eint - Ees - Eind. Eother is mainly exchange-repulsion and dispersion energies. h Reference 51. i Geometries were taken from ref 52.
The large electrostatic energies (Ees) for 1a and 1y (-75.2 and -67.8 kcal/mol, respectively, Table 1) show that the electrostatic interaction is the major source of the attraction in the [emim][FSA] complex. The induction interaction is not negligible, although the induction energy (Eind) is substantially smaller than Ees. The calculations show that the electrostatic interaction is the cause of the larger stability of 1a compared with that of 1y. Structure and Stabilization Energy of the Li[FSA] Complex. The geometries of the Li[FSA] complex were optimized from 14 initial geometries. The optimized geometries and Eform calculated for the optimized geometries (2a-2h) are shown in Figure 10. The Eform for the Li[FSA] complex is very large, and for the most stable structure (2a), it was -134.3 kcal/mol. The FSA- has the cis form in 2a. The FSA- has the trans form in 2b, 2c, 2d, and 2g. Although 2b is most stable among the four structures, it is 2.2 kcal/mol less stable than 2a.81 The Li+ has contact with two oxygen atoms belonging to different SO2 groups in 2a-2c. Other structures (2d-2h) are substantially less stable. The Eform for 2d-2h are -114.8 to -125.9 kcal/ mol. The FSA- has the cis form in the most stable geometry of the Li[FSA] complex, in contrast to an isolated stable transFSA-. The same level (MP2/6-311G**//HF/6-311G** level) calculations show that the trans form is 1.15 kcal/mol more stable than the cis one in the isolated FSA- ion. The stronger interaction energy (Eint) and smaller deformation energy (Edef) are the causes of the preference of the cis conformation of FSAin the Li[FSA] complex. The Eint values for 2a and 2b are -142.6 and -141.9 kcal/mol, respectively. The Edef values for 2a and 2b are 8.2 and 9.8 kcal/mol, respectively. Two oxygen atoms have contact with the Li+, and therefore, the two oxygen atoms and two sulfur atoms of FSA- are nearly coplanar in 2a and 2b. This planarity constraint is one of the causes of the large Edef for 2a and 2b. The effects of the planarity constraint on the Edef for the Li[cis-FSA] (2a) and Li[trans-FSA] (2b) complexes were evaluated. The geometries of the cis and trans forms of isolated FSA- were optimized with imposing the planarity constrains. The Edef calculated for the optimized cis and trans forms of FSA- were 1.2 and 3.9 kcal/mol, respectively, at the MP2/6-311G**//HF/6-311G** level. The larger Edef for the Li[trans-FSA] complex can be attributed to the planarity constraint associated with the binding with the Li+. The very large electrostatic energies (Ees) for 2a and 2b (-138.8 and -138.1 kcal/mol, respectively, Table 1) show that
the electrostatic interaction is the cause of the strong attraction between the Li+ and FSA-.82 The induction energies (Eind) for 2a and 2b (-43.6 and -43.7 kcal/mol, respectively) are significantly larger than that for the [emim][FSA] complex 1a (-10.0 kcal/mol). The Li+ has a strong electric field around it due to its small radius. Apparently, the strong electric field around the Li+ is responsible for the very large induction energies for the Li[FSA] complex. The Ees for the Li[cis-FSA] complex (2a) is larger than that for the Li[trans-FSA] complex (2b), while the Eind for 2a and 2b are nearly identical. These results show that the electrostatic interaction is the cause of the larger Eint for 2a compared with that for 2b. Comparison with TFSA- Complexes. The Eform calculated for the most stable [emim][FSA] complex (-77.0 kcal/mol) is smaller than that for the most stable [emim][TFSA] complex (-78.8 kcal/mol).51 However, the difference is only 1.8 kcal/ mol. The weaker attraction between the emim+ and FSA- can be one of the causes of the larger self-diffusion coefficients of ions and ionic conductivity and the smaller viscosity of the [emim][FSA] ionic liquid compared with the [emim][TFSA] ionic liquid. The transport properties of ionic liquids were determined by several factors. The comparison of the selfdiffusion coefficients of ions in ionic liquids and the magnitude of the stabilization energies by the formation of ion pairs suggests that at least three factors (size of ion, shape of ion, and magnitude of interaction energy) control the diffusion of ions in ionic liquids.83 The self-diffusion coefficients of ions in the [bmim][TFSA] ionic liquid are substantially larger than those in the [bmim][CF3SO3] (bmim is 1-buthyl-3-methylimidazolium) and [bmim][BF4] ionic liquids, although the TFSA- is significantly larger than the CF3SO3- and BF4-. The self-diffusion coefficients of the cation and anion in the [bmim][TFSA] ionic liquid measured at 30° are 3.4 and 2.6 ( × 10-7 cm2 s-1), respectively. Those in the [bmim][CF3SO3] ionic liquid are 2.1 and 1.6 ( × 10-7 cm2 s-1), respectively, and those in the [bmim][BF4] ionic liquids are 1.8 and 1.7 ( × 10-7 cm2 s-1), respectively.61 The Eform calculated for the [emim][TFSA] complex (-78.8 kcal/mol) is smaller (less negative) than those for the [emim][CF3SO3] and [emim][BF4] complexes (-82.6 and -85.2 kcal/mol, respectively).51 These results suggest that the weaker attraction in the [emim][FSA] complex compared with that in the [emim][TFSA] complex is one of the causes of the larger self-diffusion coefficients of ions in the [emim][FSA] ionic liquids. On the other hand, Ludwig et al. reported that strong specific interactions between ions in an ionic liquid decreases the viscosity and increases the conductivity by the formation of ion pairs in the condensed phase.84 It is likely that the conformational flexibility of ions also affects the diffusion of ions. Borodin et al. reported that an artificial increase of the torsional barrier of the TFSA- resulted in slowing down of ion transport in their molecular dynamics simulations of ionic liquids, while the increase of the torsional barrier of FSA- did not result in slowing down of ion transport.46 The torsional barrier of the FSA- is substantially lower than that of the TFSA-. The lower torsional barrier can be one of the causes of the faster diffusion of ions in the [emim][FSA] ionic liquid. The Eform for the most stable Li[FSA] complex (-134.3 kcal/ mol) is smaller than that for the most stable Li[TFSA] complex (-137.2 kcal/mol), as in the case of the emim+ complexes.52 The electrostatic and induction interactions are responsible for the smaller Eform for the Li[FSA] complex. The Ees and Eind for the most stable Li[FSA] complex are -138.8 and -43.6 kcal/ mol, while those for the most stable Li[TFSA] complex are -140.3 and -46.6 kcal/mol, respectively. The negative charges
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Figure 10. Optimized geometries and stabilization energies (Eform) calculated for the Li[FSA] complex. Interaction energies (Eint) are shown in parentheses. The energy is in kcal/mol.
on the oxygen and nitrogen atoms of the FSA- are nearly identical to that of the TFSA-, while the positive charges on the sulfur atoms of the FSA- (1.27 e) are substantially larger than those of the TFSA- (0.96 e). This difference is a cause of the smaller Ees for the Li[FSA] complex.85,86 Probably smaller polarizability of the FSA- compared with that of the TFSA- is the cause of the smaller Eind in the Li[FSA] complex. The Li+ solvation in the TFSA--based ionic liquids was studied extensively by experimental and theoretical methods.87-97 Raman spectroscopic measurements of the Li-salt-doped TFSA-based ionic liquid show that two TFSA- ions bind to the Li+.20,92,96 The remarkable increase of the viscosity of the TFSA--based ionic liquid by the addition of Li salt can be attributed to the formation of bulky clusters by the binding of the Li+ with TFSA anions. In ionic liquids, the breaking and formation of the binding occur associated with the diffusion of ions, which suggests that the magnitude of the interactions between the Li+ and anion is one of the important factors controlling the diffusion of ions in the Li-salt-dissolved RTILs. The smaller attraction between the Li+ and FSA- is one of the reasons why the addition of Li salt to FSA--based RTILs does not remarkably increases their viscosity. Previously, we have reported that the Eint for the Li[cis-TFSA] complex (-145.0 kcal/mol) is larger than that for the Li[transTFSA] complex (-144.7 kcal/mol), but the Eform for the Li[cisTFSA] complex (-135.7 kcal/mol) is smaller than that for the Li[trans-TFSA] complex (-137.2 kcal/mol). The smaller Eform for the Li[cis-TFSA] complex can be attributed to the larger Edef. The Edef for the Li[cis-TFSA] complex (9.4 kcal/mol) is larger than that for the Li[trans-TFSA] complex (7.5 kcal/mol). The Eform for the Li[cis-FSA] complex (-134.3 kcal/mol) is larger than that for the Li[trans-FSA] complex (-132.1 kcal/ mol). The larger Eform is attributed to the larger Eint. The Eint values for the Li[cis-FSA] and Li[trans-FSA] complexes are -142.6 and -141.9 kcal/mol, respectively. The geometries for the trans and cis forms of isolated TFSAwere optimized with imposing the planarity constraint, as in the case of the FSA-. The Edef values calculated for the cis and trans forms are 2.9 and 1.3 kcal/mol, respectively. The calculations show that the deformation energy associated with the planarity constraint in the cis-TFSA- is larger than that in the trans-TFSA-, in contrast to the FSA-. In the Li[cis-TFSA] complex, the two -CF3 groups have close contact. The nearest F · · · F distance in the HF/6-311G** level optimized geometry is 3.04 Å. Probably the steric repulsion between the -CF3 groups is a cause of the large Edef for the Li[cis-TFSA] complex. An important topic is how many FSA- or TFSA- molecules
can enter a lithium coordination sphere, and we are extending the calculations along this line. Conclusion In the neat [emim][FSA] and [emim][TFSA] ionic liquids, the temperature-dependent behavior of ionic conductivity (σ) and self-diffusion coefficients (D) correlates well with the viscosity 1/η, that is, the larger σ and D were obtained from the smaller η of the [emim][FSA] ionic liquid compared with those of the [emim][TFSA] ionic liquid. The Li salt addition effects on the σ and D for the two ionic liquids are similar, while smaller changes were observed for the [emim][FSA] ionic liquid than those for the [emim][TFSA] ionic liquid. The stabilization energies for the formation of the FSAcomplexes with emim+ and Li+ were calculated by high-level ab initio methods. The stabilization energies for the FSAcomplexes are smaller than those for the corresponding TFSAcomplexes. The weaker electrostatic and induction interactions in the FSA- complexes are the main causes of the smaller stabilization energies compared with those for the TFSAcomplexes. The lower viscosity of the [emim][FSA] ionic liquid compared with that of the [emim][TFSA] ionic liquid is attributed not only to the smaller size of the FSA-. The weaker interactions of the FSA- with emim+ can be one of the causes of the lower viscosity of the [emim][FSA] ionic liquid. The addition of the Li salt to the [emim][TFSA] ionic liquid significantly increases the viscosity, while the addition does not induce remarkable increase of the viscosity in the [emim][FSA] ionic liquid. The small increase of the viscosity of the [emim][FSA] ionic liquid by the addition of the Li salt can be attributed to the weaker interactions of the FSA- with Li+ compared with those of the TFSA-. The weaker interactions enable faster exchanges of the FSA- binding with Li+ and therefore increase the diffusion of ions. Although the trans form isolate FSA- is more stable than the cis form, the Li[cis-FSA] complex is more stable than the Li[trans-FSA] complex. The larger stability of the Li[cis-FSA] complex is attributed to the larger electrostatic interaction between ions and the small deformation energy of the FSA-. Acknowledgment. We thank Tsukuba Advanced Computing Center for the provision of the computational facilities. Supporting Information Available: Torsional potentials calculated for FSA- and TFSA-and 29 optimized geometries and stabilization energies of the [emim][FSA] complex. This
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(81) Complex 2c is slightly less stable than 2b. Complex 2b has C2 symmetry, while 2c does not have C2symmetry. (82) It was reported that the positive charge of emim+ is distributed not only to the carbon and nitrogen atoms of the imidazolium ring but also to the methyl and methylene groups attached to the imidazolium ring.51 The fact that a Li+ is a central charge and the emim+ has a dispersed charge is one of the causes of the stronger attraction in the Li[FSA] complex compared with that in the [emim][FSA] complex. (83) Tsuzuki, S.; Shinoda, W.; Saito, H.; Mikami, M.; Tokuda, H.; Watanabe, M. J. Phys. Chem. B 2009, 113, 10641. (84) Ludwig, R.; Paschek, D. Chem. Phys. Chem. 2009, 10, 516. (85) The relative viscosity of [emim][TFSA] (1.9 at 10°C) is significantly larger than that of [emim][FSA] (1.2 at 10°C). The increase of the relative viscosity is 4.5 time larger in the TFSA- case. The Li salt is added in units of moles (of Li salt) per kilogram of the ionic liquid. The molecular weight of [emim][TFSA] (391) is 34% larger than that of [emim][FSA] (291). Therefore, the molar ratio of Li salt to ionic liquid is larger in the TFSAcase than that in the FSA- case. This could be one of the causes of the larger effects of Li salt on the viscosity of the [emim][TFSA] ionic liquid compared with that of the [emim][FSA] ionic liquid shown in Figure 2. The effects of Li salt addition on the viscosity of ionic liquids combined with the FSA- and pyrrolidinium were reported (refs 26 and 29). The increase of relative viscosity is nearly proportional to the concentration of the Li salt. The dependence of the diffusion coefficients of ions in the [emim][TFSA] ionic liquid on the concentration of Li salt is similar to that in the [emim][FSA] ionic liquid. The ionic conductivity of the 1,2-dimethyl3-propylimidazolium bistrifluoromethylsulfonylimide also shows similar dependence on the concentration of Li salt.86 These results suggest that larger molar ratio of Li salt to ionic liquid in the TFSA- case is not the
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