Effect of Pressure on the Transport Properties of Ionic Liquids: 1-Alkyl

Jul 19, 2008 - Department of Molecular Science and Technology, Faculty of Engineering, Doshisha UniVersity,. Kyo-Tanabe, Kyoto 610-0321, Japan...
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J. Phys. Chem. B 2008, 112, 9830–9840

Effect of Pressure on the Transport Properties of Ionic Liquids: 1-Alkyl-3-methylimidazolium Salts Kenneth R. Harris,*,†,‡ Mitsuhiro Kanakubo,*,†,‡ Noriaki Tsuchihashi,§ Kazuyasu Ibuki,§ and Masakatsu Ueno§ School of Physical, EnVironmental, and Mathematical Sciences, UniVersity College, UniVersity of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia, National Institute of AdVanced Industrial Science and Technology (AIST), 4-2-1 Nigatake, Miyagino-ku, Sendai 983-8551, Japan, and Department of Molecular Science and Technology, Faculty of Engineering, Doshisha UniVersity, Kyo-Tanabe, Kyoto 610-0321, Japan ReceiVed: March 11, 2008; ReVised Manuscript ReceiVed: April 27, 2008

The self-diffusion coefficients (D) of the cation and anion in the ionic liquids 1-hexyl-3-methylimidazolium and 1-octyl-3-methylimidazolium hexafluorophosphates ([HMIM]PF6 and [OMIM]PF6) and 1-butyl-3methylimidazolium and 1-octyl-3-methylimidazolium tetrafluoroborates ([BMIM]BF4) and ([OMIM]BF4) have been determined together with the electrical conductivities (κ) of [HMIM]PF6 and [BMIM]BF4 under high pressure. The pressure effect on the transport coefficients is discussed in terms of velocity cross-correlation coefficients (VCCs or fij), the Nernst-Einstein equation (ionic diffusivity-conductivity), and the fractional form of the Stokes-Einstein relation (viscosity-conductivity and viscosity-diffusivity). The (mass-fixed frame of reference) VCCs for the cation-cation, anion-anion, and cation-anion pairs are all negative and strongly pressure dependent, increasing (becoming less negative) with increasing pressure. VCCs are the more positive for the stronger ion-velocity correlations; therefore, f+ - is least negative in each case. In general, f- - is less negative than f+ +, indicating a smaller correlation of velocities of distinct cations than that for distinct anions. However, for [OMIM]PF6, the like-ion fii are very similar to one another. Plots of the VCCs for a given ion-ion correlation against fluidity (reciprocal viscosity) show the fij to be strongly correlated with the viscosity as either temperature or pressure are varied, that is, fij ≈ fij(η). The Nernst-Einstein deviation parameter, ∆, is nearly constant for each salt under the conditions examined. It is emphasized that nonzero values of ∆ are not necessarily due to ion pairing but result from differences between the like-ion and unlikeion VCCs, because ∆ is proportional to (f+ + + f- - - 2f+ -). The diffusion and molar conductivity (Λ) data are found to fit fractional forms of the Stokes-Einstein relationship, (ΛT) ∝ (T/η)t and Di ∝ (T/η)t, with t ) (0.90 ( 0.05) for all these ionic liquids, independent of both temperature and pressure within the ranges studied. Introduction

f-- ≡

In a previous study, we reported ion self-diffusion coefficients (Di) and salt conductivities (κ) at high pressure for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM]PF6).1 These were used to determine ionic velocity cross-correlation coefficients (VCCs or fij) for like- and unlikeion interactions by using the formulas of Scho¨nert2 for a simple salt with two constituent ions in the mass-fixed frame of reference:

Aν+Bν- h ν+Az+ + ν-Bzf++ ≡

NAV 3

(

M

∫0∞ 〈V+R(0) V+β(t)〉 dt ) RTκ z-FcM

)

(1) 2

-

D+ ν+c (2)

* To whom correspondence should be addressed. E-mail k.harris@ adfa.edu.au and [email protected]. † University of New South Wales. ‡ National Institute of Advanced Industrial Science and Technology. § Doshisha University.

NAV 3

(

M

+ ∫0∞ 〈V-R(0) V-β(t)〉 dt ) RTκ z+FcM

)

2

-

Dν-c (3)

and

f+- ≡

NAV 3

M M

∫0∞ 〈V+R(0) V-β(t)〉 dt ) RTκ z+z-+(FcM )2

(4)

where NA is the Avogadro constant, V is the volume of the ensemble, Vi is the ion velocity relative to that of the center of mass of the system, R is the gas constant, T is the temperature, F is the Faraday constant, c is the amount concentration (molarity) of salt, ν+ and ν- are the stoichiometric numbers and z+ and z- the charges of the cation and anion, and M, M+, and M- are the molar masses of salt, cation, and anion, respectively. The VCCs are time integrals of the ensemble average of the velocity correlations of different ions as indicated by the subscripts R and β. The Nernst-Einstein parameter, ∆, is a measure of the deviations from the ideal Nernst-Einstein relation between the conductivity and ion self-diffusion coefficients for noninteracting charged species (with n being the number density (cNA), e the electronic charge, and k the Boltzmann constant),

10.1021/jp8021375 CCC: $40.75  2008 American Chemical Society Published on Web 07/19/2008

Effect of P on the Transport Properties of Ionic Liquids

ne2 2 (z D + z-2D-)(1 - ∆) kT + +

κ)

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9831 TABLE 1: Range of Diffusion Measurements

(5) T/°C

or, in terms of the molar conductivity, Λ,

Λ)

F2 2 (z D + z-2D-)(1 - ∆) RT + +

c(2f+- - f++ - f--) (D+ + D-)

anion p/MPa

T/°C

p/MPa

[HMIM]PF6

(6)

∆ is actually a function of the difference between the mean of the cation and anion fii and f+- for the cation-anion interaction,3

∆)

cation

(7)

For [BMIM]PF6, ∆ was found to be nearly constant, approximately 0.38, between 50 and 70 °C at pressures up to 200 MPa. VCCs were first introduced to the study of transport processes in solution by McCall and Douglass4 in an analysis of deviations from the Hartley-Crank equation relating mutual and self-diffusion coefficients in binary nonelectrolyte mixtures. As in eq 7, such deviations depend on differences between VCCs. Later, Hertz5 derived expressions for the VCCs in binary electrolyte solutions, relating these to the intra- and interdiffusion coefficients, the molar conductivity, and the transport number. This work included an expression equivalent to eq 7, and this equation has been given in various forms for electrolyte solutions and molten salts by a number of authors.6 Positive, nonzero values of ∆ are sometimes taken to indicate ion association where the experimental conductivities are less than those calculated from the ion self-diffusion coefficients.7 Such a simple model is incorrect. The shorttime velocity correlations present in dense fluids are sufficient in themselves to give nonzero ∆. These interactions include correlated collisions due to the high density of liquids, as well as caging, back-scattering, and the like.8 These effects may be seen in molecular dynamics simulations.9 Equation 7 shows this formally. The same conclusions concerning the effects of ionic interactions can be deduced from the frictional coefficient expressions due to Laity,10 which also relate intradiffusion coefficients and the conductivity of molten salts. Moreover, experimental measurements for unassociated molten salts yield small positive values of ∆ (e.g., 0.18 for NaCl),11 a result supported by molecular dynamics simulations for simple model systems.12,13 Ion association should only be considered if there is independent experimental evidence for the formation of long-lived molecular species. For [BMIM]PF6, the combination of the diffusion and molar conductivity (Λ) results with previously determined high-pressure viscosities14 showed that these quantities fit fractional forms15 of the Walden [(ΛT) ∝ (T/η)t ] and Stokes-Einstein [Di ∝ (T/η)t] relations, with t ) (0.91 ( 0.05). This single value fitted the three independently determined properties. Fractional fits for the Walden relation have been reported in the literature for some molten salts15 and, in slightly different form, for certain ternary 1-ethyl3-methylimidazolium metal chloride mixtures,16 but our study seems to be the first to confirm the validity of both equations for a molten salt at high pressure, with the exponent t being independent of both temperature and pressure within the ranges studied. This result has been supported by the subsequent work of Chung et al.17 who reported values of t between 0.7 and 1 at atmospheric pressure over a temperature range of approximately 100 K for the pair 1-methyl-3neopentylimidazolium tetrafluoroborate and 1-methyl-3-neo-

50 - 81 50 60 75

0.1 49 - 80 0.1 - 30 50 0.1 - 50 60 0.1 - 150 75 [OMIM]PF6

0.1 0.1 - 40 0.1 - 60 0.1 - 150

50 - 80 60 70 75 80

0.1 60 - 80 0.1 - 24 75 0.1 - 70 80 0.1 - 100 0.1 - 124 [BMIM]BF4

0.1 0.1 - 38 0.1 - 68

25 - 80 25 50 75

0.1 25 - 80 0.1 - 50 50 0.1 - 175 75 0.1 - 300 [OMIM]BF4

0.1 0.1 - 110 0.1 - 175

40 - 80 50 60 75

0.1 0.1 - 25 0.1 - 57 0.1 - 150

50 - 80 50 60 75

0.1 0.1 - 75 0.1 - 124 0.1 - 200

pentylimidazolium bis(trifluoromethylsulfonyl)amide and the silicon-substituted analogues 1-methyl-3-trimethylsilylimidazolium tetrafluoroborate and 1-methyl-3-trimethylsilylimidazolium bis(trifluoromethylsulfonyl)amide. Given that ionic liquids are fragile18 and readily form glasses, it is interesting that fractional Stokes-Einstein (FSE) behavior has also been suggested as indicating dynamic heterogeneities (regions of higher and lower mobilities) in strongly supercooled liquids,19 especially water.20 These differ from heterogeneities in liquid structure. However, this interpretation of FSE is not uniformly accepted. For example, Ngai,21 in interpreting FSE for translational relaxation time data22 for [BMIM]PF6, concluded that a coupling model based on different intermolecular cooperativities for different transport properties was sufficient to fit the experimental results. An analysis of high-pressure diffusion and viscosity data in the literature shows that a number of molecular liquids fit FSE well above their glass transition temperatures;23 therefore, a FSE fit appears to be a characteristic common to at least two liquid classes (salts and simple molecular liquids). It seems in itself, FSE is not necessarily indicative of dynamic heterogeneities. Here, we report new high-pressure diffusion coefficients for four further 1-alkyl-3-methyl imidazolium salts, 1-hexyl3-methylimidazolium and 1-methyl-3-octylimidazolium hexafluorophosphates([HMIM]PF6,CASRegistryNumber304680-35-1 and [OMIM]PF6, 304680-36-2) and 1-butyl-3-methylimidazolium and 1-methyl-3-octylimidazolium tetrafluoroborates ([BMIM]BF4, 174501-65-6 and [OMIM]BF4, 244193-52-0) together with high-pressure conductivities for [HMIM]PF6 and [BMIM]BF4. High-pressure conductivities for [OMIM]PF6 and [OMIM]BF4 have been published separately.24 By using these and the earlier results for [BMIM]PF6,1 together with literature data obtained at atmospheric pressure for other ionic liquids,7b,25 we examine the VCCs and apply the Nernst-Einstein and Stokes-Einstein relations in an analysis of the effect of pressure on the transport properties for these systems.

9832 J. Phys. Chem. B, Vol. 112, No. 32, 2008

Harris et al.

TABLE 2: Coefficients for Eq 8 (Litovitz) and 9 (VFT) Litovitz property

R′

D+/10-12 m2 · s-1 D-/10-12 m2 · s-1 κ/S · m-1 Λ/µS · m2 · mol-1

7.6347 7.6046 3.3254 8.8845

-1.6968 -1.7140 -1.6632 -1.6820

D+/10-12 m2 · s-1 D-/10-12 m2 · s-1

7.3894 7.7867

D+/10-12 m2 · s-1 D-/10-12 m2 · s-1 κ/S · m-1 Λ/µS · m2 · mol-1 D+/10-12 m2 · s-1 D-/10-12 m2 · s-1

108

3

VFT R′′

β′′/K

T0/K

st devn/%

2.7 9.4037 2.7 9.1648 2.7 5.2458 2.5 10.913 [OMIM]PF6

-975.21 -915.91 -1050.7 -1086.9

179.72 185.24 169.58 168.04

2.7 2.7 1.6 1.6

-1.7934 -1.8971

2.1 9.7000 1.0 10.171 [BMIM]BF4

-1174.2 -1221.7

169.16 170.57

2.1 1.0

7.5428 7.6117 3.4459 8.7537

-1.2784 -1.3191 -1.2099 -1.2282

1.4 1.2 3.6 3.4 [OMIM]BF4

9.8560 9.9447 4.3634 9.7561

-1064.0 -1077.7 -635.32 -663.19

148.86 150.61 181.63 179.90

1.2 1.0 2.0 2.0

7.3866 7.8077

-1.6087 -1.6790

2.9 2.5

9.5317 9.8825

-1079.1 -1070.8

167.01 171.28

2.9 2.6

β′/K

st devn/% [HMIM]PF6

Experimental Section The hydrophobic hexafluorophosphate salts were prepared and purified as for [BMIM]PF6.1,24,26 The hydrophilic tetrafluoroborates were prepared in a slightly different way, as described elsewhere.27 The water content as determined by Karl Fischer titration was as follows: (as mass fractions) [HMIM]PF6, 17 ×10-6; [OMIM]PF6, 27 ×10-6; [BMIM]BF4, 77 ×10-6; [OMIM]BF4, 54 ×10-6. The mass fractions of Cl- were determined with a Shimadzu EDX800HS energy dispersive X-ray fluorescence spectrometer (which became available toward the end of our experiments); the values were [HMIM]PF6, (0 ( 40) ×10-6; [BMIM]BF4, (91 ( 58) ×10-6; [OMIM]BF4, (93 ( 28) ×10-6. The molar masses of [HMIM]PF6, [OMIM]PF6, [BMIM]BF4, and [OMIM]BF4 were taken to be 312.232, 340.289, 226.021, and 282.129 g · mol-1, respectively. The ionic self-diffusion coefficients of [HMIM]PF6, [OMIM]PF6, [BMIM]BF4, and [OMIM]BF4 were determined by steadygradient spin-echo NMR, by using the 1H resonance for the cations and the 19F resonance for the anions, as described previously,1 water and benzene being used as calibrants; the precision is ( 3%. The conductivities of [HMIM]PF6 and [BMIM]BF4 were measured as described in earlier papers;1,24 the precision is also ( 3%. Viscosities and high-pressure densities required for the Stokes-Einstein and Nernst-Einstein calculations and molar conductivity and velocity correlation coefficients were taken from our earlier studies.14,27,28 New pVT results29 for [BMIM]PF6 and [BMIM]BF4 became available after our calculations were completed, but densities computed from these are not sufficiently different from our earlier estimates to warrant a full recalculation of the viscosities, molar conductivities, and velocity correlation coefficients. Results The range of pressures and temperatures for the ionic selfdiffusion coefficient measurements are given in Table 1. These are limited both by the lower limit of measurement of the apparatus, ∼ 10 ×10-12 m2 · s-1, and by the pressure and temperature dependence of the T2 relaxation time. Signal heights are reduced as the temperature is decreased or the pressure is increased and by the need to use longer 90-180° pulse spacings with smaller D. The electrical conductivities have been measured at atmospheric pressure from 0 to 80 °C and as a function of

pressure up to 200 MPa at 25, 50, and 75 °C. Numerical results are tabulated in the Supporting Information (Tables S1-S10). For comparison with the results of other workers, the analogue of the Litovitz equation that we have previously used for the viscosity of ionic liquids14,27,28 is convenient because it requires only two coefficients and can be quite useful for data extrapolation.

ln(Di,κ,Λ) ) R ′ + β ′ ⁄ T3

(8)

We have also used the flexible and commonly employed Vogel-Fulcher-Tammann (VFT) equation

ln(Di,κ,Λ) ) R ′′ + β ′′ ⁄ (T - T0)

(9)

Table 2 lists the coefficients and standard deviations of these fits. At high pressures, the results were fitted to modified Litovitz (ML) and VFT (MVFT1 and MVFT2) equations:1,14 the coefficients and standard deviations of these fits are given in Table 3.

ML:

2 3 (Di,κ,Λ)(T,p) ) exp(a + bp + (c + dp + ep ) ⁄ T )

(10) MVFT1: (Di,κ,Λ)(T,p) ) exp(a ′ + b ′ p + δ(p)T0 ⁄ (T - T0)) with δ(p) ) (c ′ + d ′ p + e ′ p2) ⁄ T0 (11) MVFT2: (Di,κ,Λ)(T,p) ) exp(a ′′ + b ′′ p + δT0(p) ⁄ (T - T0(p)) with T0(p) ) x + yp + zp2 (12)

The fitted coefficients are obtained by nonlinear regression. In the case of the viscosity, the (empirical) polynomial forms in these equations represent well the shape of ln(η) versus p curves found in high-pressure studies.30 A similar form has been used for single isotherms by To¨dheide’s group for the conductivity of liquid tetraalkylammonium tetraalkylborates to pressures of 500 MPa.31 δ is the analogue of the Angell strength parameter in the VFT expression for the viscosity (where it is usually represented by D). For MVFT1, δ is allowed to be pressure-dependent with T0 constant; for MVFT2, T0 is allowed to be pressure-dependent with δ constant. (For the viscosity, T0 can be related to the glass temperature, Tg,32 which is known to be pressure-dependent.33)

Effect of P on the Transport Properties of Ionic Liquids

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9833

TABLE 3: Coefficients of Best Fit for eqs 10, 11, and 12 for D+, D-, K, and Λa D+/10-12 m2 · s-1

[HMIM]PF6

a b/10-3 MPa-1 c/106 K3 d/106 K3 · MPa-1 e/K3 · MPa-2 standard uncertainty of fit (%)

7.634 (0.033) -8.68 (2.3) -169.62 (1.2) -0.028 (0.087) 300 (107) 2.4

a′ b′/10-3 MPa-1 c′/K d′/K · MPa-1 e′/10-5 K · MPa-2 T0/K standard uncertainty of fit (%)

9.478 (0.84) -8.64 (3.3) -999.7 (265) -0.125 (0.52) 124.4 (46) 177.7 (21) 2.4

a′′ b′′/10-3 MPa-1 δ x/K y/10-2 K · MPa-1 z/10-5 K · MPa-2 standard uncertainty of fit (%)

9.220 (0.82) -5.55 (2.0) -5.02 (1.9) 183.7 (20) 4.36 (2.9) 2.5

D–/10-12 m2 · s-1

[HMIM]PF6

a b/10-3 MPa-1 c/106 K3 d/106 K3 · MPa-1 e/K3 · MPa-2 standard uncertainty of fit (%)

7.610 (0.036) -5.65 (2.2) -171.41 (1.4) -0.133 (0.084) 128 (112) 2.4

a′ b′/10-3 MPa-1 c′/K d′/K · MPa-1 e′/10-5 K · MPa-2 T0/K standard uncertainty of fit (%)

9.78 (1.0)

a′′ b′′/10-3 MPa-1 δ x/K y/10-2 K · MPa-1 z/10-5 K · MPa-2 standard uncertainty of fit (%) κ/S · m-1 a b/10-3 MPa-1 c/106 K3 d/106 K3 · MPa-1 e/K3 · MPa-2 standard uncertainty of fit (%) a′ b′/10-3 MPa-1 c′/K d′/K · MPa-1 e′/10-5 K · MPa-2 T0/K standard uncertainty of fit (%) a′′ b′′/10-3 MPa-1 δ x/K y/10-2 K · MPa-1 z/10-5 K · MPa-2 standard uncertainty of fit (%)

-1112 (332) -1.500 (0.21) 169.6 (25) 2.4 9.269 (0.78)

[OMIM]PF6 ML, eq 10 7.531 (0.055) -184.61 (2.2) -0.369(0.005) 2.5 MVFT1, eq 11 9.854 (1.6) -1185 (551) -1.536(0.034) 171.2 (39) 2.5 MVFT2, eq 12 9.790 (1.4) -6.79 (4.1) 172.0 (34) 10.80 (2.1) 2.5 [OMIM]PF6 ML, eq 10 7.795 (0.058) -190.06 (2.3) -0.437 (0.009) 1.8 MVFT1, eq 11 10.12 (2.5) -1204 (866) -1.802 (0.63) 172.0 (61) 1.9 MVFT2, eq 12 9.92 (2.5)

-5.26 (1.9) 181.4 (19) 11.56 (1.2)

-6.44 (6.9) 176.6 (60) 13.03 (4.5)

2.7

1.9 [HMIM]PF6 ML, eq 10 3.3119 (0.016) -0.471 (0.39) -165.898 (0.48) -0.3393 (0.012) 80.0 (43) 2.5 MVFT1, eq 11 5.3450 (0.100) 5.000 (0.41) -1079.72 (28) -2.4210 (0.066) 0.365 (0.14) 167.63 (1.8) 1.9 MVFT2, eq 12 5.4128 (0.11) -0.544 (0.28) -6.606 (0.27) 166.38 (2.0) 0.1121 (0.32) -7.94 (0.92) 2.1

[BMIM]BF4 7.468 (0.016) -125.13 (0.53) -0.251 (0.003) 32 (14) 1.7

[OMIM]BF4 7.399 (0.027) -0.72 (1.7) -161.32 (1.0) -0.286 (0.072) 2.4

9.478 (0.26) 2.764 (0.56) -947.8 (85) -1.694 (0.13) 25.52 (8.8) 157.25 (7.2) 1.8

-1097 (206) -1.409 (0.13) 31.2 (40) 166.0 (16) 2.4

10.317 (0.18)

9.578 (0.60)

-9.255 (0.81) 134.12 (4.8) 8.756 (0.32) -4.828 (0.33) 1.1

-6.57 (1.8) 166.3 (15) 10.73 (1.1) -5.09 (3.0) 2.4

[BMIM]BF4

9.600 (0.62)

[OMIM]BF4

7.671 (0.029)

7.715 (0.049)

-133.91 (1.0) -0.2444 (0.003)

-164.27 (1.8) -0.3164 (0.009) 131.9 (56) 2.3

2.7 10.375 (0.60) 5.31(1.3) -1222 (221) -2.305 (0.35) 140.1 (17) 2.5 10.483 (0.63) 1.66 (1.1) -9.21 (2.9) 137.1 (17) 0.102 (1.4) -4.32 (2.0) 2.6

9.969 (1.3) -1108 (426) -1.437 (0.28) 0.974 (0.39) 167.8 (32) 2.2 10.338 (0.92) -7.97 (3.2) 156.5 (22) 9.942 (1.4) -8.215 (2.5) 2.3 [BMIM]BF4 3.4327 (0.022) 0.256 (0.36) -120.585 (0.67) -0.2271 (0.014) -36.0 (51) 3.7 4.2229 (0.081) 3.310 (0.26) -600 (20) -1.3667 (0.046) -3.672 (0.12) 185.05 (2.0) 2.1 4.2691 (0.073) -0.825 (0.15) -3.324 (0.13) 183.95 (1.8) 0.103 (0.29) -6.54 (1.2) 1.9

9834 J. Phys. Chem. B, Vol. 112, No. 32, 2008

Harris et al.

TABLE 3: Continued Λ/µS · m2 · mol-1

[HMIM]PF6 ML, eq 10 8.8713 (0.015) -0.8464 (0.38) -167.785 (0.46) -0.3417 (0.012) 104.8 (41) 2.5 MVFT1, eq 11 11.011(0.10) 4.6115 (0.42) -1115.8 (29) -2.4546 (0.067) 0.494 (0.15) 166.134 (1.8) 1.9 MVFT2, eq 12 11.041 (0.11) -0.888 (0.29) -6.790 (0.28) 165.57 (2.0) 11.1 (0.33) -8.35 (1.3) 2.1

a b/10-3 MPa-1 c/106 K3 d/106 K3 · MPa-1 e/K3 · MPa-2 standard uncertainty of fit (%) a′ b′/10-3 MPa-1 c′/K d′/K · MPa-1 e′/10-5 K · MPa-2 T0/K standard uncertainty of fit/% a′′ b′′/10-3 MPa-1 δ x/K y/10-2 K · MPa-1 z/10-5 K · MPa-2 standard uncertainty of fit (%) a

[BMIM]BF4 8.7412 (0.022) -0.134 (0.35) -122.438 (0.64) -0.2272 (0.013) -23.0 (48) 3.5 9.6119 (0.083) 2.965 (0.26) -626.6 (21) -1.3894 (0.047) 1.149 (0.12) 183.36 (2.0) 2.1 9.7886 (0.084) -1.032 (0.16) -3.747 (0.16) 179.08 (2.0) 10.0 (0.31) -6.31(1.2) 2.0

The standard uncertainties are given in parentheses.

TABLE 4: Stokes-Einstein Relation Exponents, t ln(ΛT) versus ln(D+ + D-) ln(ΛT) versus ln(D+) ln(ΛT) versus ln(D-) ln(D+) versus ln(T/η) ln(D-) versus ln(T/η) ln(ΛT) versus ln(T/η) a

[BMIM]BF4

[OMIM]BF4

[BMIM]PF6a

[HMIM]PF6

[OMIM]PF6

1.00 1.03 0.97 0.86 0.91 0.87

1.02 1.03 1.03 0.89 0.89 0.94

1.01 0.96 0.99 0.90 0.92 0.91

1.01 1.02 1.00 0.87 0.88 0.87

0.99 1.01 0.96 0.87 0.95 0.95

Reference 1.

our measurements by 33-84% between 0 and 80 °C; those of Vila et al.36 are also higher, by 31-18% between 25 and 80 °C. For [OMIM]BF4, the results of these groups are 33-47% and 86-18% higher than our previously published results.24 The diffusion data of Bagno et al.34 are scattered relative to ours. For [HMIM]PF6 and [BMIM]BF4, like [BMIM]PF6,1,25a D+ is larger than D-, despite the larger sizes of the cations. We note that of recent molecular dynamics simulations giving Di for 1-alkyl-3-methyl imidazolium salts, two37,38 are consistent with this experimental result, but that of Urahata and Ribeiro39 incorrectly predicts D+ to be greater than D- in the case of [OMIM]PF6. Discussion Figure 1. Deviations of literature conductivity and ion self-diffusion coefficient results from those of this work for [BMIM]BF4. Filled symbols, results of Watanabe et al.;25a open symbols, results of Bagno et al.;34 κ, triangles; D+, circles; D-, squares. The dashed lines indicate 95% confidence limits for the results of this work.

Of the ionic liquids studied here, only for [BMIM]BF4 have transport properties previously been reported.25a,34–36 Figure 1 shows deviations of the self-diffusion and conductivity results of Watanabe et al.,25a derived from their smoothed VFT fits, from eq 7. Generally, their data fall within the 95% confidence limits of our results, but the conductivities are higher at higher temperatures. This was also the case with [BMIM]PF6.1 The conductivities reported by Leys et al.35 are much higher than

Velocity Correlation Coefficients. The VCCs are a measure of the effects of the interactions between the ions on their mobilities. Although numerically dependent on the choice of the frame of reference,9 their determination does allow examination of cation-cation, anion-anion, and cation-anion interactions from a different perspective. We have confined our calculations to the mass-fixed frame, because that is the one normally used in molecular dynamics simulations, rather than the other possibility, the number-fixed frame. Figure 2 shows examples of the temperature and pressure dependence for the VCCs: (a) [BMIM]BF4 and [OMIM]PF6 at 0.1 MPa, as the least and most viscous liquids studied, (b) [BMIM]BF4 at 50 and 75 °C, and for comparison, (c) [OMIM]BF4 at 50 and 75 °C. (Numerical values are given in

Effect of P on the Transport Properties of Ionic Liquids

Figure 2. (a) VCCs, fij, as a function of temperature at 0.1 MPa pressure, for [BMIM]BF4 (filled) and [OMIM]PF6 (open). These were the least and most viscous salts examined. (b) VCCs, fij, for [BMIM]BF4 as a function of pressure at 50 °C (open) and 75 °C (filled). (c) VCCs, fij, for [OMIM]BF4 as a function of pressure at 50 °C (open) and 75 °C (filled). The f+ - at 25 °C in (b) and (c) are omitted for greater clarity. f+ + (diamonds), f- - (squares), f+ - (triangles).

Supporting Information Tables S11-S14.) The VCCs decrease (become more negative) with increasing temperature as the velocity cross-correlations become weaker and similarly decrease with decreasing pressure. For a given anion, the fij are less negative the larger the size of the cation, although the differences for the PF6- salts are much less marked than those for the BF4- salts. Thus, the VCCs appear to be made stronger by an increase in the length of the alkyl chain on the 1-alkyl3-methyl-imidazolium cation. It is instructive to examine the viscosity dependence of the VCCs. The VCCs decrease as the liquid is cooled and the

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Figure 3. VCCs, as a function of fluidity, φ, for [BMIM]BF4 and [OMIM]BF4 (offset by -5 units due to overlap). (a) Catiion-anion VCCs, f+ -: (0.1 MPa, 0-80 °C), filled circles; (25 °C, 0.1-200 MPa), squares; (50 °C, 0.1-200 MPa), triangles; (75 °C, 0.1-200 MPa), diamonds; calculated from the results of Watanabe et al., 25a (0.1 MPa, -10 to 90 °C), open circles. Error bars are about the size of the symbols at the highest fluidities. (b) Cation-cation VCCs, f+ +. [BMIM]BF4: (0.1 MPa, 25-80 °C), filled circles; (25 °C, 0.1-50 MPa), squares; (50 °C, 0.1-175 MPa), triangles; and (75 °C, 0.1-200 MPa), diamonds; calculated from the results of Watanable et al.,25a (0.1 MPa, -10 to 90 °C), open circles. [OMIM]BF4: (0.1 MPa, 0-80 °C), filled circles; (50 °C, 0.1-35 MPa), triangles; (75 °C, 0.1-150 MPa), diamonds. (c) Anion-anion VCCs, f- -. [BMIM]BF4: (0.1 MPa, 25-80 °C), filled circles; (50 °C, 0.1-100 MPa), triangles; (75 °C, 0.1-175 MPa), diamonds; calculated from the results of Watanabe et al.,25a (0.1 MPa, -10 to 90 °C), open circles. [OMIM]BF4: (0.1 MPa, 0-80 °C), filled circles; (50 °C, 0.1-125 MPa), triangles; (75 °C, 0.1-200 MPa), diamonds. The error bars in (b) and (c) correspond to ( 2% in the viscosity and ( 3% in the conductivity and self-diffusion coeffiecients.

conductivity and diffusion coefficients approach zero (or more properly, the much smaller values obtained in the solid or glass, if supercooled). When plotted against the fluidity (reciprocal

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viscosity), which behaves similarly, the VCC isotherms and isobars cluster together for a given salt; for example, the f+ values are grouped together, the f+ + form a second group, and the f- - form a third group. Figure 3 illustrates this for the tetrafluoroborates and Figure 4 for the hexafluorophosphates. VCCs at 0.1 MPa for [BMIM]BF4 and [BMIM]PF6 calculated from the data of Watanabe et al.25a are included because these span a larger temperature range than our results. (Numerical values are given in Supporting Information Tables S15-S16.) The plots suggest that the VCCs of a given liquid are simple functionals of the viscosity (fij ≈ fij(η)), for these ionic liquids within the ranges of temperature and pressure examined, although there is some scatter, particularly for the hightemperature isotherms for anion-anion interactions. Remarkably, the VCCs for the three hexafluorophosphates for a given interaction can be superposed upon one another; those for the tetrafluoroborates lie close together but diverge at higher fluidities. Watanabe et al.7b,25a,b have made other measurements at atmospheric pressure for tetrafluoroborates and bis(trifluorosulfonyl)imide (Tf2N-) salts. VCCs derived from these results are shown in Figures 5 and 6. Here, there is a greater spread at low viscosities, particularly for the salts with smaller cations, dimethylimidazolium and1-ethyl-3-methylimidazolium. In contrast to the BF4- and PF6- salts, the anion-anion VCCs are more negative than the cation-cation VCCs. An understanding of these results must await comparative molecular dynamics simulations on these liquids. However, the regularities that we have observed suggest that computation of velocity cross-correlation functions, as for metal halides, for example,9 may well be fruitful. Nernst-Einstein and Stokes-Einstein Relations. Figure 7 shows the temperature and pressure dependence of the Nernst-Einstein ∆ function for the BF4- and PF6- salts. In each case, ∆ is essentially independent of temperature and pressure within experimental error ((6%). For a given anion, ∆ becomes larger as the size of the cation increases, and for a given cation, it is larger for the BF4- salt than for the corresponding PF6- salt. As discussed previously for the example of [BMIM]PF6,1 we have fitted our results to fractional forms of the Stokes-Einstein and Walden relations:

ΛT ∝ D ∝

( ηT )

al.,15

t

(13)

We have followed Voronel et who used ionic melts resistivity and viscosity data extending over several orders of magnitude, obtaining a common exponent t ≈ 0.8 for a range of systems. (It should be noted that they made log(resistivity) - log(viscosity) plots (i.e ln(F/T) against ln(η/T)), neglecting the temperature-dependent concentration (density) term contained in Λ. The form of the Nernst-Einstein relation between Λ and the D, eq 6 (see also eqs 2 and 3 of ref 15a), nevertheless requires this to be included.1) The fits are summarized in Table 4. As an example, Figure 8 shows the relations between the quantities (ΛT) and (D+ + D-) for [BMIM]BF4. From eqs 5 and 13, one expects t ) 1; here, t ) (1.00 ( 0.05), with similar values for D+, and D-, 1.03 and 0.97 ( 0.05, respectively, and this pattern is repeated for the other ionic liquids. Consequently, we believe that our conductivities are to be preferred over those of Leys et al. 35 and Vila et al.36 Figures 9 and 10 show plots of ln(Di) and ln(ΛT), respectively, against ln(T/η), again for [BMIM]BF4 as an example. As illustrated in Table 4, t is independent of temperature and pressure for each ionic liquid, and within experimental error, it is identical for the three transport properties, cation and anion

Figure 4. VCCs, as a function of fluidity, φ, for [BMIM]PF6, [HMIM]PF6 (offset by -5 units) and [OMIM]6 (offset by -10 units). (a) Cation-anion VCCs, f+ -: (0.1 MPa, 0-80 °C), filled circles; (25 °C, 0.1-200 MPa), squares; (50 °C, 0.1-200 MPa), triangles; (75 °C, 0.1-200 MPa), diamonds; calculated from the results of Watanabe et al., 25a (0.1 MPa, -10 to 90 °C), open circles. (b) Cation-cation VCCs, f+ +. [BMIM]PF6: (0.1 MPa, 30-80 °C), filled circles; (50 °C, 0.1-125 MPa), triangles; (70 °C, 0.1-200 MPa), diamonds; calculated from the results of Watanable et al.,25a (0.1 MPa, -10 to 90 °C), open circles. [HMIM]PF6: (0.1 MPa, 50-80 °C), filled circles; (50 °C, 0.1-37.5 MPa), triangles; and (75 °C, 0.1-150 MPa), diamonds. [OMIM]PF6: (0.1 MPa, 50-80 °C), filled circles; (75 °C, 0.1-75 MPa), diamonds; (c) Anion-anion VCCs, f- -. [BMIM]PF6: (0.1 MPa, 40-80 °C), filled circles; (50 °C, 0.1-50 MPa), triangles; (70 °C, 0.1-150 MPa), diamonds; calculated from the results of Watanabe et al.,25a (0.1 MPa, -10 to 90 °C), open circles. [HMIM]PF6: (0.1 MPa, 50-80 °C), filled circles; (50 °C, 0.1-37.5 MPa), triangles; (75 °C, 0.1-150 MPa), diamonds. [OMIM]PF6: (0.1 MPa, 60-80 °C), filled circles; (75 °C, 0.1-37.5 MPa), diamonds; As for the tetrafluoroborates, the sets of data for each type of interaction are almost coincident.

diffusion coefficients, and molar conductivity. For these five salts, t ) 0.90 within the estimated experimental uncertainty, (0.05. Bielo´wka et al.40 have also found t to be independent of temperature and pressure for the conductivities (because of

Effect of P on the Transport Properties of Ionic Liquids

Figure 5. VCCs, as a function of fluidity, φ, calculated from the results of Watanabe et al.7b,25a for BF4- salts at 0.1 MPa and -10 to 90 °C: [EMIM]BF4, filled squares; [BMIM]BF4, filled triangles; BPBF4 (1butylpyridinium tetrafluoroborate), open diamonds. (a) Cation-anion velocity cross-correlation coefficients, f+ -. (b) Cation-cation velocity cross-correlation coefficients, f+ +. (c) Anion-anion velocity crosscorrelation coefficients, f- -. In (b) and (c), the BPBF4 lines may be affected by an apparent inconsistency in the self-diffusion coefficients as ln(ΛT) - ln(D plots for both ions have mean slopes of 1.13, rather than the expected values of 1. The plots are also nonlinear.

ionic impurities) and dielectric spectroscopic R-relaxation times, of two glass-forming liquids, N,N-diglycidyl-4-glycidyloxyaniline and N,N-diglycidylaniline. Therefore, this constancy of t with varying temperature and pressure may be a general property for some liquid types. Although the use of FSE relations is not newsin one form or another they date back to at least 197941,42sit is interesting

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9837

Figure 6. VCCs as a function of fluidity, φ, calculated from the results of Watanabe et al.25a,b for Tf2N- salts at 0.1 MPa and -10 to 90 °C: [MMIM]Tf2N, filled circles; [EMIM]Tf2N, filled squares; [BMIM]Tf2N, filled triangles; [HMIM]Tf2N, open circles; [OMIM]Tf2N, open squares. (a) Cation-anion VCCs, f+ -. (b) Cation-cation VCCs, f+ +. (c) Anion-anion VCCs, f- -. The [MMIM]Tf2N line in (c) may be affected by an apparent inconsistency in the anion self-diffusion coefficients because ln(ΛT) versus ln(D-) has a slope of 1.16 rather than the expected value of 1. The corresponding slope for the cation is 1.02.

that here, ionic liquids are shown to behave in a manner similar to both simple model systems and molecular liquids.23 Heyes et al.,44 for example, obtained t ) 0.975 for the hard sphere fluid (0.38 < n* < 0.96, where n* is the reduced number

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Figure 9. Plots of ln(Di) for the cation (closed symbols) and anion (open symbols) versus ln(T/η) for [BMIM]BF4. Symbols: circles, results at 0.1 MPa; inverted triangles, squares, and triangles, high-pressure isotherms for 25, 50, and 75 °C, respectively.

Figure 7. (a) Nernst-Einstein deviation function, ∆, as a function of temperature. Symbols: [BMIM]PF6, filled circles; [HMIM]PF6, filled triangles; [OMIM]PF6, filled squares, [BMIM]BF4, open circles; [OMIM]BF4, open squares. (b) Nernst-Einstein deviation function, ∆, as a function of pressure. Symbols: [BMIM]PF6, 50 °C, filled circles, 70 °C open circles; [HMIM]PF6, 50 °C, filled triangles, 75 °C, open triangles; [OMIM]PF6, 50 °C, filled diamonds; [BMIM]BF4, 50 °C, filled inverted triangles, 75 °C, open inverted triangles; [OMIM]BF4, 50 °C, filled squares, 75 °C open squares.

Figure 8. Plots of ln(ΛT) versus ln(D+ + D-) (filled symbols) and ln D+ (open symbols) for [BMIM]BF4. The anion plot, which overlaps that of the cation, has been omitted for clarity. Symbols: circles, results at 0.1 MPa; inverted triangles, squares, and triangles, high-pressure isotherms for 25, 50, and 75 °C, respectively.

density). By using the MD simulation results of Meier et al.45 for the Lennard-Jones fluid, one obtains t ) 0.95 (in the range 0.7 < T* < 2.5, 0.45 < n* < 1.05).23 Calculations based on literature high-pressure diffusion coefficients and viscosities for

Figure 10. Plot of ln(ΛT) for versus ln(T/η) for [BMIM]BF4. Symbols: circles, results at 0.1 MPa (0-80 °C); inverted triangles, squares, and triangles, high-pressure isotherms for 25, 50, and 75 °C, respectively.

the typical molecular liquids methane (above 2.3 times the critical density, where this strong fluid approximates Andrade (Arrhenius) behavior, with D and η varying as exp(const/T)), toluene, and acetonitrile yield values of 0.97, 0.96, and 0.83, respectively.23,46 Meckl and Zeidler47 have reported temperaturedependent t values in the range of 0.62 -0.74 for methanol, ethanol, and propan-1-ol. Even low-temperature water conforms to a first approximation,23 if one neglects some fine detail, with t(T) ≈ 0.66 -0.82 between -15 and 60 °C (the lowest value occurring at 5 °C).23,48 Therefore, it appears that t can be sensitive to strong structural effects like hydrogen bonding. Notwithstanding this apparent generality of FSE in different liquid classes, without a testable theory leading to FSE-like expressions, it is not clear what interpretation, if any, should be given to the parameter t. Most diffusion and viscosity results in the literature are for liquids well below the critical point and well above the glass temperature; therefore, the apparent FSE behavior observed in both ionic and molecular liquids may well be confined to a relatively small portion of the liquid phase space. For the present study, the constancy of t for each ionic liquid is better considered as a measure of the consistency of the experimental results.

Effect of P on the Transport Properties of Ionic Liquids Conclusions The self-diffusion coefficients (D) of the cation and anion in the ionic liquids 1-hexyl-3-methylimidazolium and 1-octyl-3methylimidazolium hexafluorophosphates ([HMIM]PF6 and [OMIM]PF6) and 1-butyl-3-methylimidazolium and 1-octyl-3methylimidazolium tetrafluoroborates ([BMIM]BF4) and ([OMIM]BF4) have been determined together with the electrical conductivities (κ) of [HMIM]PF6 and [BMIM]BF4 under high pressure. VCCs in the mass-fixed frame of reference for the cation-cation, anion-anion, and cation-anion pairs are all negative and strongly pressure-dependent, increasing (becoming less negative) with increasing pressure. VCCs are the most positive for the stronger ion-velocity correlations; therefore, f+ is the least negative in each case. In general, f- - is less negative than f++, indicating a smaller correlation of velocities between different cations than different anions. However, for [OMIM]PF6, the like-ion fii are very similar to one another. Plots of the VCCs for a given ion-ion correlation against fluidity (reciprocal viscosity) show the fij to be strongly correlated with the viscosity as either temperature or pressure are varied, that is, fij ≈ fij(η). The Nernst-Einstein deviation parameter, ∆, is essentially independent of temperature and pressure for each salt under the conditions examined. For a given anion, ∆ is larger the larger is the cation; but for a given cation, ∆ is larger for the tetrafluoroborate than for the hexafluorophosphate. It is emphasized that nonzero values of ∆ are not necessarily due to ion pairing but result from differences between the like-ion and unlike-ion VCCs, because ∆ is proportional to (f+ + + f- - 2f+ -). The diffusion and molar conductivity (Λ) data are found to fit fractional forms of the Stokes-Einstein relationship, (ΛT) ∝ (T/η)t and Di ∝ (T/η)t, with t ) (0.90 ( 0.05), for all these ionic liquids, independent of both temperature and pressure within the ranges studied. Acknowledgment. M.K. and K.R.H. would like to thank the Japan Society for the Promotion of Science (JSPS) and the Australian Academy of Science for JSPS Visiting Fellowships that permitted exchanges between our two laboratories. K.R.H. also thanks the National Institute of Advanced Industrial Science and Technology (AIST), Sendai, for their kind cooperation and hospitality during his visit. We thank Dr Lawrie Woolf (UNSW@ADFA) for many helpful discussions and Professor Richard L. Smith, Jr. and Mr H. Machida of Tohoku University, Sendai, for communication of their pVT data. Supporting Information Available: Numerical data for diffusion coefficients, conductivities, and velocity correlation coefficients are tabulated. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kanakubo, M.; Harris, K. R.; Tsuchihashi, N.; Ibuki, K.; Ueno, M. J. Phys. Chem. B 2007, 111, 2062. (2) Scho¨nert, H. J. Phys. Chem. 1984, 88, 3359. (3) Eq 5 was given incorrectly in ref 1 (eq 10) but was corrected in Kanakubo, M.; Harris, K. R.; Tsuchihashi, N.; Ibuki, K.; Ueno, M. J. Phys. Chem. B 2007, 111, 13867. (4) McCall, D. W.; Douglass, D. C. J. Phys. Chem. 1967, 71, 987. (5) Hertz, H.-G. Ber. Bunsenges. Phys. Chem. 1977, 81, 656. (6) (a) Woolf, L. A.; Harris, K. R. J. Chem. Soc., Faraday Trans.1 1978, 74, 733. (b) Geiger, A.; Hertz, H.-G. J. Chem. Soc., Faraday Trans.1 1980, 76, 135. (c) Weinga¨rtner, H.; Bertagnolli, H. Ber. Bunsenges. Phys. Chem. 1986, 90, 1167. (d) Padro´, J. A.; Trulla`s, J.; Sese´, G. Mol. Phys. 1991, 72, 1035. (7) For example: (a) Every, H.; Bishop, A. G.; Forsyth, M.; MacFarlane, D. R. Electrochim. Acta 2000, 45, 1279. (b) Noda, A.; Hayamizu, M.; Watanabe, M. J. Phys. Chem. B 2001, 105, 4603. (c) Shobukawa, H.;

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9839 Tokuda, H.; Tabata, S.-I.; Watanabe, M. Electrochim. Acta 2004, 50, 305. (d) Tokuda, H.; Tsuzuki, S.; Susan, M. A. B. H.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2006, 110, 19593. (8) Cohen, E. D. G. Physica A 1993, 194, 229. (9) Trulla`s, J.; Padro´, J. A. Phys. ReV. B 1997, 55, 12210. (10) (a) Laity, R. W. J. Chem. Phys. 1959, 30, 682. See also: (b) Morrison, G.; Lind, J. E., Jr. J. Phys. Chem. 1968, 72, 3001. (11) Rovere, M.; Tosi, M. P. Rep. Prog. Phys. 1986, 49, 1001. (12) (a) Hansen, J.-P.; McDonald, I. R. J. Phys. C: Solid State Phys. 1974, 7, L384. (b) Hansen, J.-P.; McDonald, I. R. Phys. ReV. A 1975, 11, 2111. (c) Ciccotti, G.; Jacucci, G.; McDonald, I. R. Phys. ReV. A 1976, 13, 426. (d) Sharma, R.; Tankeshwar, K. J. Chem. Phys. 1998, 108, 2601. (e) Koishi, T.; Tamaki, S. J. Non-Cryst. Solids 1999, 250-252, 501. (f) Koishi, T.; Tamaki, S. J. Chem. Phys. 2005, 123, 194501. (13) In this context, it should be noted that calculations for alkali chlorides and nitrates, based on high-temperature molten salt data in the standard NIST- National Standard Reference Data Series database (http:// www.nist.gov/srd/nsrds.htm), show inconsistencies when eq 5 is applied. Plots of ln(ΛT) versus ln(D+ + D-), although linear, have fractional slopes rather than the expected unit slope (and found for ionic liquids, as in this work and ref 1), which must cast some doubt on the experimental results in these examples. Therefore, numerical values for ∆ derived from the database for these systems may not be accurate. (14) Harris, K. R.; Woolf, L. A.; Kanakubo, M. J. Chem. Eng. Data 2005, 50, 1777. (15) (a) Voronel, A.; Veliyulin, E.; Machavariani, V. Sh.; Kisliuk, A.; Quitmann, D. Phys. ReV. Lett. 1998, 80, 2630. (b) Veliyulin, E.; Shasha, E.; Voronel, A.; Machavariani, V. Sh.; Seifer, Sh.; Rosenberg, Yu.; Shumsky, M. G. J. Phys.: Condens. Matter 1999, 11, 8773. (16) Elias, A. M.; Elias, M. E. Molten Salt Forum 1998, 5-6, 617. (17) Chung, S. H.; Lopato, R.; Greenbaum, S. G.; Shirota, H.; Castner, E. W., Jr.; Wishart, J. F. J. Phys. Chem. B 2007, 111, 4885. (18) Xu, W.; Cooper, E. I.; Angell, C. A. J. Phys. Chem. B 2003, 107, 6170. (19) (a) Douglas, J. F. Comput. Mater. Sci. 1995, 4, 292. (b) Douglas, J. F.; Leporini, D. J. Non-Cryst. Solids 1998, 235-237, 137. (c) Swallen, S. F.; Bonvallet, P. A.; McMahon, R. J.; Ediger, M. D. Phys. ReV. Lett. 2003, 90, 015901. (d) Jung, Y.-J.; Garrahan, J. P.; Chandler, D. Phys. ReV. E 2004, 69, 061205. (20) (a) Stillinger, F. H.; Hodgon, J. A. Phys. ReV. E 1994, 50, 2064. (b) Tarjus, G.; Kivelson, D. J. Chem. Phys. 1995, 103, 3071. (c) Eidiger, M. D. Annu. ReV. Phys. Chem. 2000, 51, 99. (21) Ngai, K. L. J. Phys. Chem. B 2006, 110, 26211. (22) Ito, N.; Huang, W.; Richert, R. J. Phys. Chem. B 2006, 110, 4371. (23) Harris, K. R., in preparation. (24) Kanakubo, M.; Harris, K. R.; Tsuchihashi, N.; Ibuki, K.; Ueno, M. Fluid Phase Equilib. 2007, 261, 414. (25) (a) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2004, 108, 16593. (b) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2005, 109, 6103. (c) Tokuda, H.; Ishii, K.; Susan, M. A. B. H.; Tsuzuki, S.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2006, 110, 2833. (26) Umecky, T.; Kanakubo, M.; Ikushima, Y. Fluid Phase Equilib. 2005, 228-229, 329. (27) Harris, K. R.; Woolf, L. A.; Kanakubo, M. J. Chem. Eng. Data 2007, 52, 2425. (28) (a) Harris, K. R.; Woolf, L. A.; Kanakubo, M. J. Chem. Eng. Data 2007, 52, 1080. (b) Harris, K. R.; Woolf, L. A.; Kanakubo, M. J. Chem. Eng. Data 2006, 51, 1161. (29) Machida, H.; Sato, Y.; Smith, R. L., Jr Fluid Phase Equilib. 2008, 264, 147. (30) (a) Bridgman, P. W. Proc. Roy. Soc. London, Ser. A 1950, 203, 1. (b) Bair, S. Tribol. Trans. 2004, 47, 356. (31) Mahiuddin, S.; Rohman, N.; Aich, R.; To¨dheide, K. Aust. J. Chem. 1999, 52, 373. (32) Angell, C. A. Science 1995, 267, 1924. (33) Drozd-Rzoska, A.; Rzoska, S. J.; Paluch, M.; Imre, A. R.; Roland, C. M. J. Chem. Phys. 2007, 126, 164504. (34) Bagno, A.; D’Amico, F.; Saielli, G. J. Mol. Liq. 2007, 131-132, 17. (35) Leys, J.; Wu¨bbenhorst, M.; Menon, C. P.; Rajesh, R.; Nockemann, P.; Thijs, B.; Binnemans, K.; Longuemart, S. J. Chem. Phys. 2008, 128, 064509. (36) Vila, J.; Varela, L. M.; Cabeza, O. Electrochim. Acta 2007, 52, 7413. (37) Prado, C. E. R.; Freitas, L. C. G. J. Mol. Structure: THEOCHEM 2007, 847, 93. (38) Pica´lek, J.; Kolafa, J. J. Mol. Liq. 2007, 134, 29. (39) Urahata, S. M.; Ribeiro, M. C. C. J. Chem. Phys. 2005, 122, 024511. (40) Bielo´wka, S. H.; Psurek, T.; Zioło, J.; Paluch, M. Phys. ReV. E 2001, 63, 062301.

9840 J. Phys. Chem. B, Vol. 112, No. 32, 2008 (41) (a) Hiss, T. G.; Cussler, E. L., Jr. AIChE J. 1973, 19, 698. (b) Evans, D. F.; Tominaga, T.; Chan, C. J. Soln. Chem. 1979, 8, 461. (c) Pollack, G. L.; Kennan, R. P.; Himm, J. F.; Stump, D. R. J. Chem. Phys. 1990, 92, 625. (42) Evans et al.41b defer to Steel, B. J.; Stokes, J. M.; Stokes, R. H. J. Phys. Chem. 1958, 62, 1514 as having first employed FSE, but although it is shown in the Steel paper that the Walden relation fails for ion transport in viscous solutions, a fractional exponent is not given explicitly. Hiss and Cussler41a seem to have been the first to do so with temperature as the variable and Wakai and Nakahara43 with pressure as the variable. (43) Wakai, C.; Nakahara, M. J. Chem. Phys. 1994, 100, 8347. (44) Heyes, D. M.; Cass, M. J.; Powles, J. G.; Evans, W. A. B. J. Phys. Chem. B 2007, 111, 1455. (45) Data: η (a) Meier, K.; Laesecke, A.; Kabelac, S. J. J. Chem. Phys. 2004, 121, 3671; D (b) Meier, K.; Laesecke, A.; Kabelac, S. J. J. Chem. Phys. 2004, 121, 9526.

Harris et al. (46) Data: methane, D (a) Oosting, P. H.; Trappeniers, N. J. Physica 1971, 51, 418. (b) Harris, K. R.; Trappeniers, N. J. Physica 1980, 104A, 262–108; η. (c) Haynes, W. M. Physica 1973, 70, 410; toluene, D: (d) Harris, K. R.; Alexander, J. A.; Goscinska, T.; Malhotra, R.; Woolf, L. A.; Dymond, J. H. Mol. Phys. 1993, 78, 235; η. (e) Harris, K. R. J. Chem. Eng. Data 2000, 45, 893; acetonitrile, D: (f) Hurle, R. L.; Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2921; η. (g) Dymond, J. H.; Awan, M. A.; Glen, N. F.; Isdale, J. D. Int. J. Thermophys. 1991, 12, 433. (47) Meckl, S.; Zeidler, M. J. Mol. Phys. 1988, 63, 85. (48) Data: D (a) Harris, K. R.; Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 377. (b) Harris, K. R.; Newitt, P. J. J. Chem. Eng. Data 1997, 42, 346; η. (c) Harris, K. R.; Woolf, L. A. J. Chem. Eng. Data 2004, 49, 1064. (d) Harris, K. R.; Woolf, L. A. J. Chem. Eng. Data 2004, 49, 1851.

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