Nuclear Magnetic Resonance Study of the Dynamics of Imidazolium

Department of Chemistry and Physics, William Paterson UniVersity of New Jersey, Wayne, New Jersey 07470,. Department of Physics, Hunter College, CUNY,...
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J. Phys. Chem. B 2007, 111, 4885-4893

4885

Nuclear Magnetic Resonance Study of the Dynamics of Imidazolium Ionic Liquids with -CH2Si(CH3)3 vs -CH2C(CH3)3 Substituents† Song H. Chung,*,‡ Richard Lopato,‡ Steven G. Greenbaum,§ Hideaki Shirota,|,# Edward W. Castner Jr.,| and James F. Wishart⊥ Department of Chemistry and Physics, William Paterson UniVersity of New Jersey, Wayne, New Jersey 07470, Department of Physics, Hunter College, CUNY, New York, New York 10021, Department of Chemistry and Chemical Biology, Rutgers, The State UniVersity of New Jersey, 610 Taylor Road, Piscataway, New Jersey 08854-8087, and Chemistry Department, BrookhaVen National Laboratory, Upton, New York 11973-5000 ReceiVed: March 4, 2007; In Final Form: April 4, 2007

Trimethylsilylmethyl (TMSiM)-substituted imidazolium bis(trifluoromethylsulfonyl)imide (NTf2-), and tetrafluoroborate (BF4-) ionic liquids (ILs) have lower room-temperature viscosities by factors of 1.6 and 7.4, respectively, than isostructural neopentylimidazolium ILs. In an attempt to account for the effects of silicon substitution in imidazolium RTILs and to investigate the ion dynamics, we report nuclear magnetic resonance (NMR) measurements of 1H (I ) 1/2) and 19F (I ) 1/2) spin-lattice relaxation times (T1) and self-diffusion coefficients (D) as a function of temperature for ILs containing the TMSiM group and, for comparison, the analogous neopentyl group. The 1H and 19F nuclei probe the dynamics of the cations and anions, respectively. The low-temperature line shapes were determined to be Gaussian, and the onset of the rigid lattice line width is correlated with the measured glass transition temperature. The spin-lattice relaxation data feature a broad T1 minimum as a function of inverse temperature for both nuclear species. The Arrhenius plots of the diffusion data for both nuclear species are found to exhibit Vogel-Tammann-Fulcher curvature. Analysis of the η and D data generally show fractional Stokes-Einstein behavior D ∝ (T/η)m. This is most prominent in the neopentylimidazolium BF4- IL with m ≈ 0.66.

Introduction There is wide interest in studying ionic liquids (ILs) as systems for research on mass transport in complex liquids as well as for possible industrial applications, including their use as replacements for volatile organic solvents in electrochemistry, enzyme catalysis, chemical synthesis, and radioactive material handling.1-9 Moreover, their physical properties can be easily varied over large ranges by changing the chemical composition. One goal in designing new ILs for laboratory use is to obtain lower ambient temperature viscosities, since ILs generally have relatively high viscosities (10∼105 cP)10 as compared with those of common organic solvents (0.2 ∼10 cP).11 Several groups12-15 have reported that precise control over viscosity can be obtained by designing cations with modest changes to their side groups. Recently, Shirota and Castner15 synthesized a new class of silicon-substituted imidazolium cation ILs whose viscosities are substantially reduced when the neopentyl group (NP) is replaced with the isostructural trimethylsilylmethyl (TMSiM) group (Figure 1). In particular, it was reported that TMSiM-substituted imidazolium ILs have roomtemperature viscosities that are reduced by factors of 1.6 and 7.4 relative to the neopentylimidazolium ILs for the bis†

Part of the special issue “Physical Chemistry of Ionic Liquids”. * Corresponding author. E-mail: [email protected]. ‡ William Paterson University of New Jersey. § Hunter College, CUNY. | Rutgers, The State University of New Jersey. ⊥ Brookhaven National Laboratory. # Present address: Division of Diversity and Fractal Science, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi, Inageku, Chiba 263-8522, Japan.

Figure 1. Structures of the ionic liquid components.

(trifluoromethylsulfonyl)imide (NTf2-) and tetrafluoroborate (BF4-) salts, respectively.15 Several systems of ILs have been studied by molecular dynamic simulations16,17 and by various other experimental techniques including conductivity,18,19 viscosity,18-20 optical Kerr effect spectroscopy,15,21-28 and nuclear magnetic resonance (NMR).18,19,29-34 The latter method is an excellent tool for probing microscopic processes and is complementary to many of the other experimental techniques. In particular, NMR has several advantages: its measurements are quick, accurate, and nondestructive, a specific nuclear species can be selected, it is sensitive to microscopic and macroscopic motions, and a wide range of temperature and frequencies can be covered. Although NMR relaxation methods require assumptions regarding the relaxation model that relates the correlation time τc to the translational motion of the probe species, pulsed gradient spinecho (PGSE) NMR technique provides a direct measurement of the self-diffusion coefficient D.35 An NMR investigation of silicon-substituted imidazolium cation ILs was conducted to study the ion dynamics and its relation to viscosity of these materials. In particular, we wish to know for a given reduction in viscosity whether there is a concomitant increase in the self-diffusion coefficient in accordance with the Stokes-Einstein relation36,37

10.1021/jp071755w CCC: $37.00 © 2007 American Chemical Society Published on Web 04/19/2007

4886 J. Phys. Chem. B, Vol. 111, No. 18, 2007

D)

kBT cπηr

Chung et al.

(1)

where T is the absolute temperature, η is the viscosity, r is the effective spherical radius of the diffusing species, and c is a constant with a value of 4 and 6 for the “slip” and “stick” hydrodynamic boundary conditions, respectively. A previous NMR study of the ion diffusion coefficients of N-butylpyridinium and 1-ethyl-3-methylimidazolium cation ILs with NTf2and BF4- anions indicated that the diffusion coefficients are well correlated with T/η.19 However, it has been empirically found that at temperatures T e 1.3Tg, where Tg is the glass transition temperature, a fractional Stokes-Einstein relation of the form

D ∝ (T/η)m

(2)

holds for a wide range of ionic melts and liquids,38-40 where 0.5 < m < 0.95. Recently, Ngai has used the coupling model to explain the fractional Stokes-Einstein equation for a supercooled ionic liquid41 based on the dielectric relaxation data of Ito and Richert.42 We report here the first measurements of 1H (I ) 1/2) and 19F (I ) 1/2) NMR relaxation times and self-diffusion measurements of this new class of ILs with the silicon-substituted imidazolium cation 1-methyl-3-trimethylsilylmethylimidazolium (Si-mim+) and its analogous alkylimidazolium cation, 1-methyl3-neopentylimidazolium (C-mim+) as NTf2- and BF4- salts. These NMR dynamical properties, together with the measured glass transition values, are used to investigate the ion dynamics and the effect of Si-substitution in imidazolium RTILs. Experimental Methods Materials. Synthesis of the novel silicon-containing ILs Si-mim+/NTf2- and Si-mim+/BF4-, and the ILs with the analogous alkyl group cation C-mim+/NTf2- and C-mim+/BF4-, is described elsewhere.15 The ILs studied were clear and colorless. To avoid uptake of moisture, the materials were handled and stored in an argon-filled dry box. The samples were dried at 343 K in a vacuum oven for about 15 h prior to the NMR experiments. The four samples were then placed in 5 mm diameter NMR tubes and flame sealed for the NMR measurements. Differential scanning calorimetry (DSC) was used to measure glass transition temperatures for the four ionic liquids, using a TA Instruments, Inc. Q100 DSC equipped with the LNCS liquid-nitrogen-cooling system. The DSC scanning rate was 5 K/min. Nuclear Magnetic Resonance. The NMR measurements were conducted on a Chemagnetics CMX-300 spectrometer equipped with a Japan Magnet Technology B0 ) 7.1 T widebore superconducting magnet. For this magnetic field strength, 1H and 19F resonances occur at ω /2π ) 301.0 and 283.2 MHz, 0 respectively. Spectra and Spin-Lattice Relaxation Times. The NMR spectra were obtained by collecting the free induction decay (FID) following a single π/2 pulse and Fourier transforming the data. Full widths were then determined from expanded spectral plots. The spin-lattice relaxation time, T1, was determined by sampling the amplitude of the FID following the π/2 pulse in the π-τ-π/2 sequence43 for about 15 values of τ. The time between the repetitions of the pulse sequence was always greater than 5T1. The uncertainty in the determination of the T1 is about 5%.

TABLE 1: Viscosities (295.2 K), Glass Transition Temperatures, and VTF Viscosity Fit Parameters liquid

ηa (cP)

Tg (K)

ln(η0)

ξ

T0 (K)

Si-mim+/NTf2C-mim+/NTf2Si-mim+/BF4C-mim+/BF4-

98 161 631 4638

201 203 216 221

-2.036 -2.264 -3.166 -5.914

4.430 4.979 5.886 10.226

176.5 175.8 183.1 172.1

a

Reference 15.

Self-Diffusion. The pulse gradient spin-echo experiments were performed using a 5 mm dual-frequency broadband gradient probe from Doty Scientific and a current amplifier provided by Nalorac. The NMR diffusion measurements use the Hahn spin-echo pulse35 π/2-τ-π with a pair of squareshaped gradient field pulses of magnitude g and duration δ. The first gradient pulse is applied between the two RF pulses, and a second identical gradient pulse is applied following the π pulse at a time ∆ after the first pulse. Appropriate gradient settings ∆ and δ were chosen to cause sufficient signal attenuation. This attenuation is dependent on how much the positions of the spins change as a result of self-diffusion in the time interval ∆. It has been shown35 that the attenuation of the echo amplitude A(g) is given by

A(g) ) exp[-D(γδg)2(∆-δ/3)]

(3)

where D is the self-diffusion coefficient and γ is the magnetogyric ratio of the spin. The diffusion coefficient was obtained by fitting this equation to the echo amplitudes for a series of 15 gradient strengths g ranging from ∼0.2 to 3 T m-1. Consistent with eq 3, the PGSE diffusion decays were observed to be single exponential. The typical reproducibility of the temperature-dependent diffusion coefficient measurements is within (5%. Measurements were obtained at 5-10 K intervals. Special care was taken to ensure that the samples were equilibrated for at least 30 min at a given temperature. An Oxford ITC533 temperature accessory was used with a stream of dry N2 gas to regulate the temperature to within (0.1 K. Results Differential Scanning Calorimetry and TemperatureDependent Viscometry. Measurement of the glass transition temperatures by DSC allows more detailed characterization of the variation of the viscosities with temperature according to the treatment of Angell.44 Table 1 shows the temperature of the onsets of the glass transitions for Si-mim+/NTf2-, C-mim+/ NTf2-, Si-mim+/BF4-, and C-mim+/BF4-. No freezing or melting transitions were observed for any of the ILs in this study when scanning in either the warming or cooling directions. The temperature dependences of the viscosities of the four ionic liquids were depicted in Figure 1 of ref 15. They show the non-Arrhenius behavior typical of ionic liquids, and the Vogel-Tammann-Fulcher (VTF) equation45-48 is usually employed to fit their temperature dependence. One form of the VTF equation for viscosity is given by

η(T) ) η0 exp

[ ] ξT0 T - T0

(4)

where η is the viscosity, T is the temperature, η0 is a reference viscosity at which the exponential term is 0 (high-temperature limit), ξ is the fragility parameter (equivalent to D in ref 44), and T0 is a characteristic temperature for which η diverges. Following the practice of Angell,44 an additional viscosity data

Dynamics of Imidazolium Ionic Liquids

J. Phys. Chem. B, Vol. 111, No. 18, 2007 4887 where K is related to the strength of the nuclear interaction and J(0) is the so-called adiabatic spectral density term. This term dominates at low temperatures, but when the fluctuation rate of the local fields becomes of the order of the resonance frequency, the nonadiabatic effects must be taken into account. At that point, the lifetimes of the spin states become important and consequently the additional line broadening term T1-1 must be considered. At sufficiently low temperatures, the crossover to a Gaussian line shape begins to occur. In the region where the line width was less than 6 kHz and the temperature is below that of the T1 minimum, the adiabatic term in the expression for the line width is dominant and there is a roughly Arrhenius temperature dependence given by

Figure 2. Plot of 19F NMR line width versus reciprocal temperature for Si-mim+/NTf2-.

point of 1013 cP was added at the glass transition temperature for each of the ILs. The resulting VTF fit parameters are given in Table 1. The viscosity behaviors of Si-mim+/NTf2- and C-mim+/NTf2- are very similar, whereas the BF4- salts are more viscous and show a larger difference between the trimethylsilylmethyl and neopentyl derivatives. The large value of the fragility parameter ξ for C-mim+/BF4- indicates that the viscosity behavior for this liquid is closer to Arrhenius and that C-mim+/BF4- is less fragile44 than the three other liquids studied here and most ionic liquids in general. Room Temperature 1H and 19F Spectra. Care was taken to ensure that the samples were not exposed to moisture for the NMR measurements. No 1H signals for H2O were detected after drying. The sample volumes were too small for accurate water content determination by Karl Fischer titration. The fluorine spectra for all samples show a single peak, whereas the proton NMR spectra exhibit several readily assigned peaks associated with the six chemically inequivalent protons present in the imidazolium cation. The most intense peak is attributed to the nine methyl protons of the TMSi group on the imidazolium cation. The next most intense peak is assigned to the methylene protons on the side group. The remaining two peaks are assigned to the protons on the imidazole ring. Temperature Dependence of the 19F Spectral Lineshapes. The linewidths of the fluorine spectra are generally observed to narrow with increasing temperature. Si-mim+/NTf2- was chosen as a representative system to measure the 19F spectra over the temperature range from 173 to 353 K. Figure 2 shows the full width at half-maximum ∆LW as a function of reciprocal temperature. The behavior of the 19F NMR line shape for this ionic liquid may be divided into two separate temperature regions. At elevated temperatures, a high-temperature plateau is observed that corresponds to the temperature region of the 19F T minimum. In this temperature regime the NMR spectra 1 exhibit a single line shape and are completely motionally narrowed lines. The Lorentzian line shape fits the data very well, and the ∆LW is a very well-defined parameter in terms of the spin-spin relaxation time (T2) since

∆LW )

1 πT2

(5)

The spin-spin relaxation rate is given by

1 1 ) K J(0) + T2 T1

(6)

∆LW ) A exp

( ) Ea kBT

(7)

where A is an amplitude factor and Ea is the activation energy associated with the slope of the linear temperature region. A fit of the relevant data to eq 7 yields an activation energy value for Si-mim+/NTf2- of about 0.76 eV. At low temperatures, the line width reached a rigid-lattice limiting value of ∆RL ) 12.9 kHz at 200 K and remained constant upon decreasing the temperature further. This is an indication that the overall translational motion of the 19F species has ceased. The temperature at which the onset of the rigid lattice line width occurs correlates well with the measured Tg of 201 K for this IL. As the temperature is increased above Tg, motional narrowing begins when the rate of the fluctuations (τc-1) of the local dipolar fields is comparable to their rigid lattice linewidths or when

τc-1 ≈ ∆RL

(8)

where τc is the motional correlation time. In the temperature regime of the T1 minimum for liquids, the T1 value is expected to be approximately equal to the T2 value. However, the T1 minimum has a value of 0.45 s whereas the calculated T2 value using eq 5 gives an anomalously small value that is 2 orders of magnitude different from the T1 minimum. 1H and 19F Spin-Lattice Relaxation Times. Relaxation in a heteronuclear spin I ) 1/2 system can lead to nonexponential spin-lattice relaxation behavior49 as observed in the present study for both nuclei. Consequently, it is difficult to define an unambiguous spin-lattice relaxation time that can be directly related to a motional model. Except at temperatures in the vicinity of where ωoτc ≈ 1, the magnetization recovery is exponential and a well-defined T1 can be obtained by fitting the data to the equation

[A0 - A(τ)]/A0 ) C exp(-τ/T1)

(9)

where A0 is the value of the integrated FID amplitude A(τ) approaches as τ f ∞, and C is a fitting constant. Figure 3 shows representative 1H and 19F magnetization recovery plots for Si-mim+/NTf2- at several temperatures. The influences of nonexponential effects are most marked at correlation times in the region of the reciprocal of the Larmor frequency ω0. At longer correlation times, the effects are less prominent. In the temperature regime where the magnetization recovery is significantly nonexponential, values of T1 were obtained by fitting the initial decay of the magnetization plots to an exponential function. For the purposes of this study this

4888 J. Phys. Chem. B, Vol. 111, No. 18, 2007

Figure 3. Typical 19F magnetization recovery plots for Si-mim+/NTf2at various temperatures.

approach50 provides values of T1’s which are independent of the inherent relaxation behavior (e.g., cross correlation effects) associated with closely coupled groups of spin I ) 1/2. The 1H and 19F spin-lattice relaxation time results for the ILs are shown in Figure 4 as a function of inverse temperature. The experimental values for the proton T1 are measured for the major component of the 1H NMR signal that is associated with the reorientation of the methyl groups on the cation. A welldefined minimum is seen for each liquid except for Si-mim+/ BF4-, for which the data were not obtained at lower temperatures. At the relaxation minimum, where ωoτc ≈ 1, the correlation time for the nuclear motion is ∼10-9 s. In Figure 4a, it is notable that the proton relaxation times for the TMSiM-substituted ILs differ from those of the NPsubstituted ILs by a nearly constant amount over the entire temperature range. Furthermore, there is a definite trend for the proton T1 minima to move to lower temperatures in the TMSiMsubstituted ILs in comparison to those with the neopentyl group. It is seen that replacement of the BF4- anion with the bulkier NTf2- anion affects not only the temperature at which the proton T1 minimum occurs, but also the depth of the minimum. For

Chung et al.

Figure 4. Plots of 1H and 19F NMR spin-lattice relaxation times as functions of inverse temperature for (a) 1H (cation) and (b) 19F (anion).

the Si-mim+/NTf2- sample a change in the slope of the proton T1 data occurs in the vicinity of the measured glass transition temperature for this IL. Figure 4b also shows the 19F relaxation time data for all of the liquids. However, only high-temperature data was obtained for Si-mim+/BF4- and C-mim+/BF4-. A definite but very broad asymmetric fluorine T1 minimum is observed for Si-mim+/ NTf2- and C-mim+/NTf2-. Unlike the proton T1 data, neither the depth of the 19F relaxation minimum nor the T1 temperature dependence appears to be affected to the same extent by the nature of the anion or Si-substitution on the imidazolium cation. In particular, the 19F data show that the T1 values for Si-mim+/ NTf2- and C-mim+/NTf2- ILs more or less overlap with one another. It has been argued in other studies of 19F spin-lattice relaxation that it is the time-dependent dipolar interactions that are the dominant relaxation mechanism.51,52 An approximate calculation indicates that the dipolar interactions with neighboring spins must be considered in any analysis of T1. An estimate of the spin-lattice relaxation rate can be obtained by using the

Dynamics of Imidazolium Ionic Liquids

J. Phys. Chem. B, Vol. 111, No. 18, 2007 4889

second moments of the static linewidths as a measure of the strength of the dipolar interaction. The estimated value of the T1 minimum is 0.54 s, whereas the experimental value is about 0.45 s. Estimates show that any contribution due to the 19F chemical shift anisotropy is small. The fluorine relaxation data reflects the anionic mobility associated with reorientational motion and ionic motion, with the latter becoming more important at higher temperatures. In ILs, the dynamics of the diffusing ions cause the fluctuations of the local fields. These fluctuations are described in terms of a correlation function g(t). The interpretation of the resulting correlation time τc depends on the form of the correlation function. Analysis of relaxation time data based on the Bloembergen-Purcell-Pound (BPP) model53 requires the use of a correlation function that decays as a single exponential

g(t) ) exp[-(t/τc)]

(10)

The spin-lattice relaxation rate is connected with the Fourier transform of the correlation function or the spectral density function

J(ω) )

τc 1 + ω2τc2

(11)

that is a single Lorentzian function of frequency ω. However, the data shown in Figure 4 clearly show an unexpected relaxation behavior for a liquid system, such as a very broad asymmetric minimum and lack of agreement between the T1 minima values and corresponding T2 values for that temperature. There have been a number of reports54 in the literature of NMR relaxation times in ionic conductors indicating similar non-BPP behavior. Typically this type of relaxation behavior is described by one of two explanations. One is that the relaxation results from correlated motions of the mobile ions. Another possible explanation is that different subgroups of the ion population have motions described by a BPP spectral density function J(ω) with each subgroup having a different correlation time.55 In particular, the stretched exponential (or Kohlrausch) form of the correlation function56

g(t) ) exp[-(t/τc)β]

(12)

has been shown to occur more commonly in amorphous materials than Debye behavior (β ) 1) does. The Kohlrausch function is also widely used to describe relaxation phenomena in supercooled liquids.41,42 1H and 19F Translational Self-Diffusion Coefficients. The range of temperatures over which the diffusion coefficient could be measured is limited by the short spin-spin relaxation time constants at low temperatures. Measurements of the selfdiffusion coefficients D for the cation and anion in each ionic liquid were made by using 1H and 19F nuclei, respectively. Given the high degree of ion association expected to occur in ILs, the measured D values represent an average of the diffusion of all single and associated species. Diffusion coefficients for each proton in the cations were determined to be very similar. Values obtained from the most intense methyl 1H peaks are the ones discussed in this paper. As shown in Figure 5, the diffusion coefficients D follow a VTF relationship45-48 over the temperature region investigated (253 to 353 K). However, the limited extents of the data preclude precise determination of the fit parameters D0, ξ and T0 as defined in eq 13, except in the case of Si-mim+/NTf2- (1H: D0

Figure 5. Semilog plots of 1H (cation) and 19F (anion) NMR selfdiffusion coefficients as functions of inverse temperature for (a) Si-mim+/NTf2-, (b) C-mim+/NTf2-, (c) Si-mim+/ BF4-, and (d) C-mim+/BF4-.

) 9.60 × 10-5 cm2 s-1, ξ ) 3.89 and T0 ) 186 K; 19F: D0 ) 1.56 × 10-4 cm2 s-1, ξ ) 4.51 and T0 ) 181 K).

D(T) ) D0 exp

[ ] -ξT0 T - T0

(13)

For Si-mim+/NTf2- and C-mim+/NTf2-, the diffusion coefficients of the cations are essentially the same as those of the anions at all temperatures, whereas for Si-mim+/BF4-, the cation diffusion coefficients vary between 0.8 and 1.0 times those of the anions. For C-mim+/BF4-, D(anion) > D(cation) at lower temperatures, but trends to D(anion) ≈ D(cation) at higher temperatures. Similar diffusion behavior was observed in an NMR study of other ILs.19 Figure 6 shows a composite of the fluorine and proton diffusion for all of the liquids. As can be seen, the trend for the 1H and 19F diffusion coefficients is as follows: Si-mim+/NTf 2 g C-mim+/NTf2- > Si-mim+/BF4- > C-mim+/BF4-. To determine whether the self-diffusion data follow the StokesEinstein behavior, extrapolated viscosity data from the VTF fit were used in Figure 7, which shows a linear plot of D vs T/η

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Figure 6. Semilog plots of NMR self-diffusion coefficients as functions of inverse temperature for (a) 1H (cation) and (b) 19F (anion).

for cations and anions. Although approximately linear behavior according to eq 1 is observed for Si-mim+/NTF2-, data for the other samples exhibit deviations from linearity by different amounts, with C-mim+/BF4- showing the greatest deviation. Each of the ILs exhibits a different initial slope, indicating that in the context of the Stokes-Einstein relationship36,37 the effective hydrodynamic radii follow the trend: Si-mim+/NTf2> C-mim+/NTf2- > Si-mim+/BF4-. Although Figure 5c shows that the diffusion coefficients are similar for the Si-mim+ cation and the BF4- anion, the molecular volumes for these ions differ by a factor of 6.15 The same is found to be true for the C-mim+ and BF4- ions where the anion is a factor of 5 smaller than that of the cation. Figure 8 is a log-log plot of the same data showing that the diffusion coefficient D for both cations and anions is a function of T/η. Deviations from nonlinearity noted in Figure 7 are evident in Figure 8. Although the IL Si-mim+/NTF2- shows an approximate log-log behavior consistent with eq 2 with m ≈ 1.0, the other ILs exhibit deviations of varying degree from the slope of m ) 1. The largest deviation in the slope is observed for the C-mim+/BF4- with m ) 0.66.

Figure 7. Diffusion coefficients D as functions of (T/η) for (a) 1H (cation) and (b) 19F (anion).

Discussion Cationic and Anionic Self-Diffusion Coefficients. The ion volumes estimated by the van der Waals increments method are 180.2 and 166.7 Å3 for the Si-mim+ and C-mim+ cations and 145.9 and 29.7 Å3 for the NTf2- and BF4- anions,15 respectively. The differences between the cation and anion radii imply that, if a Stokes-Einstein hydrodynamic model appropriately describes the liquid transport properties, the measured cationic and anionic diffusion coefficients should differ, particularly for the BF4- ionic liquids. Specifically, the StokesEinstein hydrodynamic model predicts that for a pair of spherical diffusing species, the ratio of diffusion coefficients Dcation/Danion should be equal to (Vanion/Vcation)1/3. Since the Si-mim+ and C-mim+ cations are only slightly larger than the NTf2- anion, the Stokes-Einstein model predicts Dcation/Danion ratios of 0.93 and 0.96, respectively. These ratios are consistent with diffusion coefficient measurements depicted in Figure 5, panels a and b, which show Danion ≈ Dcation over the entire temperature range

Dynamics of Imidazolium Ionic Liquids

Figure 8. log-log plots of diffusion coefficient D as a function of (T/η) for (a) 1H (cation) and (b) 19F (anion).

for Si-mim+/NTf2- and C-mim+/NTf2-. On the other hand, the BF4- anion is much smaller than its companion cations, leading to predicted Dcation/Danion ratios of 0.55 and 0.56, respectively, for Si-mim+/BF4- and C-mim+/BF4-. In the case of Si-mim+/ BF4-, Dcation is slightly smaller than Danion at some temperatures but never very significantly. In contrast, for C-mim+/BF4-, the cationic diffusion coefficient is clearly lower than that of the anion at low temperatures, approaching the ratio from the Stokes-Einstein model, but rises to parity with Danion at higher temperatures. This may be an indication of the presence of cooperative transport phenomena where cation and anion diffusion are coupled. Table 2 shows the self-diffusion coefficients calculated from the Stokes-Einstein equation [eq 1 with c ) 6] using the measured viscosity values at 295.2K. As can be seen from Figure 5, the measured diffusion coefficients for both 1H and 19F are nearly an order of magnitude faster than calculated from the Stokes-Einstein equation, using the measured shear viscosity and making only the minor assumption that the effective

J. Phys. Chem. B, Vol. 111, No. 18, 2007 4891 radii can be obtained from the molecular van der Waals volumes assuming spherical ions. Several factors are considered to be important in understanding the relation between viscosity, ionic size, and diffusion. Electrostatic interactions with neighboring ions are expected to be different for TMSiM vs NP groups, and the volume of the TMSiM side group is larger than that of the NP group. It is also probable that the torsional potentials are lower for the TMSiM group than the NP group, which may in turn lead to a greater multiplicity of orientations at a given temperature, further inhibiting ion packing in the liquid. The weaker interactions believed to be present in the Si-substituted ILs15 are correlated to the lower viscosity in the Si-substituted liquids relative to their neopentyl counterparts. The higher diffusion in Sisubstituted materials is related to the flexibility of the cations while similar cation and anion diffusion indicates strong attractive forces between the ions. Effect of Silicon Substitution. Introduction of a TMSiM side group to the IL reduces the viscosity and the glass transition temperature, which likely results because of a weaker cationanion electrostatic interaction for the Si-mim+ than for C-mim+. Si substitution also results in narrower spectral lines, higher diffusion coefficients, and shifts the proton T1 minimum to lower temperatures. These are NMR indications that indicate enhanced ionic motion associated with Si-substitution. Shirota and Castner showed previously that the intermolecular interactions are generally weaker for the Si-mim+ than for the C-mim+ ILs.15 The intermolecular vibrational spectra for Si-mim+ ILs have peak frequencies and first moments that are lower in frequency than the analogous C-mim+ ILs. The electrostatics are also different. Though a Si atom is substantially more electropositive than a C atom in an IL cation side chain, the excess bond lengths of Si-C vs the corresponding C-C bonds offset this effect. However, the increased polarization arising from the presence of the Si-substitution on Si-mim+ leads to a slightly larger effective dipole moment than for C-mim+. Although Si-substitution appears to affect the self-diffusion values, the diffusion results displayed in Figure 5 do not show changes that are commensurate with the reported changes in viscosities.15 For a given type of IL, the Si-substituted liquids generally have larger diffusion coefficients, but they differ only by a factor of about 1.2 at ambient temperatures from those of the NP cation regardless of the anion. This is in contrast to ILs consisting of TMSiM-substituted imidazolium cation, which have viscosities that are reduced by a factor of 1.6 and 7.4 relative to the neopentylylimidazolium ILs for the NTf2- and BF4- anions, respectively. The apparent lack of correlation between the diffusion coefficients with decreasing viscosity may be due to increases in the apparent hydrodynamic radii as indicated in Figure 7. The hydrodynamic radius estimated from the Stokes-Einstein equation for each ion follows the order Si-mim+/NTf2- > C-mim+/NTf2- > Si-mim+/BF4-, which is consistent with Shirota and Castner’s assertion15 that the Si-substituted ILs have a larger effective dipole moment than the neopentyl-substituted analogs and are more polarizable. The spin-lattice relaxation time is the sum of the rotational and translational parts

1 1 1 ) + T1 T1,rot T1,trans

(14)

where (T1,rot)-1 ∝ τc ∝ Vη and (T1,trans)-1 ∝ D-1. From Figure 4, it is seen that the 19F NMR T1 data for Si-mim+/NTf2- and C-mim+/NTf2- are similar. The similarity in 19F spin-lattice

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TABLE 2: Diffusion Coefficients Calculated from the Stokes-Einstein Equation at 295.2 K Vc (Å3)a

liquids +

-

Si-mim /NTf2 C-mim+/NTf2Si-mim+/BF4C-mim+/BF4a

180.2 166.8 180.2 166.8

Va (Å3)a 145.9 145.9 29.7 29.7

rc (Å)a 3.504 3.415 3.504 3.415

ra (Å)a 3.266 3.266 1.921 1.921

η (cP)b

DS-E,c (cm2/s)a

DS-E,a (cm2/s)a

98 161 631 4638

6.28 × 10 3.93 × 10-8 9.78 × 10-9 1.36 × 10-9

6.74 × 10-8 4.11 × 10-8 1.78 × 10-8 2.43 × 10-9

-8

a ) anion; c ) cation. b Reference 15.

relaxation behavior for the two liquids suggests that the measurements are sensitive to the dynamic processes experienced by the fluorine nuclei in a single species that is common to both ILs. Data for the other liquids are available only for temperatures above room temperature. At the high-temperature region, the trend for the T1 values is as follows: Si-mim+/NTf2> C-mim+/NTf2- > Si-mim+/BF4- > C-mim+/BF4-. This trend is consistent with the above relation and similar to the trend exhibited by the diffusion data. However it is clear from Figure 4 that the data for C-mim+/BF4- are quite different from the others, which is also consistent with the diffusion data shown in Figure 5. The proton T1 data, however, displays microscopic behavior that is sensitive to the changes in the Si substitution. The data represents the methyl rotations, however, the T1,min for Si-mim+/ NTf2- clearly occurs at a lower temperature, 278 K versus 304 K for the C-mim+/NTf2-. The motion of the protons in the NP group is reduced in the neopentylimidazolium ILs, with the result that the time scale of the nuclear motion is shifted to higher temperatures relative to the TMSiM-substituted imidazolium ILs and as a consequence, the T1,min shifts to higher temperatures. A similar trend is observed for the Si-mim+/BF4and C-mim+/BF4- liquids. The proton T1 minimum for the Si-mim+/NTf2- occurs at the lowest temperature, followed by C-mim+/NTf2- and C-mim+/BF4-. This trend correlates well with the viscosity of these liquids: Si-mim+/NTf2- < C-mim+/ NTf2- < Si-mim+/BF4- < C-mim+/BF4-. Effect of Different Anions on the IL Diffusion Coefficients. Replacement of different anions in the ILs is seen to affect the viscosity, and the various NMR dynamic parameters such as D, T1, and ∆LW presented in this paper. ILs with larger anions exhibit lower viscosity and Tg and larger diffusion coefficients. This effect is attributed to greater steric hindrance to ion packing resulting in a greater availability of free volume for transport of ions. For a given pair of ILs with the same cation (e.g., Si-mim+/NTf2- and Si-mim+/BF4-), different anions are observed to have a significant effect on viscosity and NMR parameters. For example at 295 K, Si-mim+/NTf2- and Si-mim+/BF4- differ in their viscosity by a factor of 6.4 and between C-mim+/NTf2- and C-mim+/BF4- the viscosity differs by a factor of 28.8. However, for both anions, the change in diffusion coefficient is only about 2.9, with the NTf2- anion exhibiting a larger diffusion coefficient. As discussed before, this discrepancy may be due to a reduction in the apparent hydrodynamic radii that offsets the increase in viscosity. The intermolecular interactions quantified by the intermolecular vibrational dynamics measured using Kerr spectroscopy methods show a more substantial change for the BF4- ILs than for NTf2- ILs.15 The 19F T1 data do not show a noticeable change either in the temperature dependence or the depth of the T1 minimum as before. However there is a definite trend for the 1H T1 minima to shift to lower temperatures in the C-mim+/BF4- and C-mim+/ NTf2- liquids. From Figure 4 it can be seen that the depth of the proton T1 minimum is also affected.

Summary In this study, we report an NMR and DSC characterization of a new class of silicon-substituted imidazolium cation ionic liquids. The temperature dependence of the NMR relaxation times and self-diffusion coefficients are reminiscent of glassforming materials. The T1 minima are very broad and the onset of the rigid lattice line width is correlated with the measured glass-transition temperature. Arrhenius diffusion plots for both nuclear species exhibit VTF-type curvature. Si-substitution results in narrower spectral lines, higher diffusion coefficients, and shifts the proton T1 minimum to lower temperatures. These NMR effects for Si-substituted ionic liquids correlate with the flexibility of the cations. Similar cation and anion diffusion indicates a strong degree of correlation between the ions in all liquids except for C-mim+/BF4-, where this trend is observed only at higher temperatures. At lower temperatures a decoupling of the ion motion is observed. The diffusion coefficient is found to be approximately proportional to T/η for Si-mim+/NTF2-. Other ILs exhibit fractional Stokes-Einstein behavior (T/η)m. This is most evident in the C-mim+/BF4- sample with m ≈ 0.7. To understand the Si-substitution effect on the viscosity of ILs, changes in the NMR dynamical properties have been correlated with the reported changes in viscosities. Acknowledgment. This work was supported by the Research Corporation- Cottrell College Science Award (WPUNJ), by the National Science Foundation and the Donors of the ACSPetroleum Research Fund (Rutgers), and by the U.S. Department of Energy (CUNY, and at BNL under Contract Number DE-AC02-98-CH10866). References and Notes (1) Welton, T. Chem. ReV. 1999, 99, 2071. (2) Earle, M. J.; Seddon, K. R. Pure Appl. Chem. 2000, 72, 1398. (3) Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3772. (4) Kitazume, T. J. Fluorine Chem. 2000, 105, 265. (5) Zhao, H.; Malhotra, S. V. Aldrichim. Acta 2002, 35, 75. (6) Wilkes, J. S. Green Chem. 2002, 4, 73. (7) Dupont, J.; de Souza, R. F.; Suarez, P. A. Z. Chem. ReV. 2002, 102, 3667. (8) Forsyth, S. A.; Pringle, J. M.; MacFarlane, D. R. Aust. J. Chem. 2004, 57, 113. (9) Davis, J. H., Jr. Chem. Lett. 2004, 33, 1072. (10) Bonhote, P.; Siaz, A.-P.; Papageorgiou, N.; Kalyanasundaram, K.; Gratzel, M. Inorg. Chem. 1996, 35, 1168. (11) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic SolVents, Physical Properties and Method of Purification, 4th ed.; John Wiley & Sons: New York, 1986. (12) Cooper, E. I.; Angell, C. A. Solid State Ionics 1983, 9&10, 617. (13) Matsumoto, H.; Yanagida, M.; Tanimoto, K.; Nomura, N.; Kitagawa, Y.; Miyazaki, Y. Chem. Lett. 2000, 922. (14) Funston, A. M.; Wishart, J. F. ACS Symp. Ser. 2005, 901, 102. (15) Shirota, H.; Castner, E. W., Jr. J. Phys. Chem. B 2005, 109, 21576. (16) Kobrak, M. N.; Znamenskiy, V. Chem. Phys. Lett. 2004, 395, 127. (17) Margulis, C. J. Mol. Phys. 2004, 102, 829. (18) Hayamizu, K.; Aihara, Y.; Nakagawa, H.; Nukuda, T.; Price, W. S. J. Phys. Chem. B 2004, 108, 19527. (19) Noda, A.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2001, 105, 4603. (20) Kanakubo, M.; Harris, K. R.; Tsuchihashi, N.; Ibuki, K.; Ueno, M. J. Phys. Chem. B 2007, 111, 2062. (21) Cang, H.; Li, J.; Fayer, M. D. J. Chem. Phys. 2003, 119, 13017.

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