J. Phys. Chem. B 2007, 111, 4669-4677
4669
Nanostructural Organization and Anion Effects on the Temperature Dependence of the Optical Kerr Effect Spectra of Ionic Liquids† Dong Xiao, Justin Rajesh Rajian, Amanda Cady,‡ Shengfu Li, Richard A. Bartsch, and Edward L. Quitevis* Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409-1061 ReceiVed: October 2, 2006; In Final Form: NoVember 9, 2006
The intermolecular spectra of three imidazolium ionic liquids were studied as a function of temperature by the use of optical heterodyne-detected Raman-induced Kerr effect spectroscopy. The ionic liquids comprise the 1,3-pentylmethylimidazolium cation ([C5mim]+), and the anions, bromide (Br-), hexafluorophosphate (PF6-), and bis(trifluoromethanesulfonyl)imide (NTf2-). Whereas the optical Kerr effect (OKE) spectrum of [C5mim][NTf2] is temperature-dependent, the OKE spectra of [C5mim]Br and [C5mim][PF6] are temperatureindependent. These results are surprising in light of the fact that the bulk densities of these room temperature ionic liquids (RTILs) are temperature-dependent. The temperature independence of the OKE spectra and the temperature dependence of the bulk density in [C5mim]Br and [C5mim][PF6] suggest that there are inhomogeneities in the densities of these liquids. The existence of density inhomogeneities is consistent with recent molecular dynamics simulations that show RTILs to be nanostructurally organized with nonpolar regions arising from clustering of the alkyl chains and ionic networks arising from charge ordering of the anions and imidazolium rings of the cations. Differences in the temperature dependences of the OKE spectra are rationalized on the basis of the degree of charge ordering in the polar regions of the RTILs.
Introduction Room temperature ionic liquids (RTILs) are salts composed of bulky organic cations and noncoordinating inorganic anions with melting points below 373 K. They have negligible vapor pressures and are, therefore, nonvolatile and nonflammable. Because of their nonvolatility, RTILs are being studied as potential green replacements for conventional volatile organic solvents. Because physicochemical properties can be adjusted through structural modification of the cation and choice of anion, an RTIL can be tailored for a particular application. Being able to tune their properties in this way has led to the use of RTILs as alternative solvents in chemical reactions, separation and extraction technology, and industrial processes.1,2 Recent molecular dynamics (MD) simulations3-7 have shown that RTILs based on the 1-alkyl-3-methylimidazolium cation ([Cnmim]+) with alkyl chains C4 and longer are spatially heterogeneous. Using a united-atom MD method, Urahata and Ribeiro3 showed that a low wave vector peak appears in the partial structure factor. They attributed this peak to the occurrence of an intermediate range order for C4 and C8 but not for shorter chains. Wang and Voth4 using a multiscale course-grain MD method showed that heterogeneous domains are formed by the aggregation of alkyl groups for C4 and longer, with the cation rings and anions homogeneously distributed. Lopes and Padua5 using an all-atom MD method showed by color coding the nonpolar and polar regions that the polar regions are not isolated, but are interconnected in such a way as to form a threedimensional, charge-ordered ionic network permeated by nonpolar regions in a manner not unlike that of a swollen gel. Lopes and Padua coined the phrase “nanostructural organization” to †
Part of the special issue “Physical Chemistry of Ionic Liquids”. * Corresponding author. E-mail:
[email protected]. ‡ Welch Summer Scholar.
describe this spatial heterogeneity in ionic liquids. The discovery that ionic liquids microphase segregate into stable nonpolar regions by aggregation of the tail groups of the cations and polar regions by charge-ordering of the anions and imidazolium rings of the cations is a promising development in the field of ionic liquids because it provides a framework for interpreting the dependence of the viscosity, diffusion, and conductivity on the alkyl chain length8 and the complex fluid behavior of mixtures containing ionic liquids.9,10 Another area in which nanostructural organization provides a conceptual framework is in the understanding of the intermolecular dynamics of RTILs. This was recently demonstrated by Xiao et al.11 Using femtosecond optical heterodyne-detected, Raman-induced, Kerr effect spectroscopy (OHD-RIKES), Xiao et al. found that the low-frequency (4 ps. The current apparatus and the analysis of OHD-RIKES data by the Fouriertransform-deconvolution procedure are described in detail in the Supporting Information. Results A. Time-Domain OHD-RIKES Responses. In OHDRIKES, the interaction of the femtosecond laser pulse with molecules of the liquid through the third-order nonlinear polarizability produces a transient birefringence in the liquid. The birefringent response of the liquid has an instantaneous component due to the electronic hyperpolarizability and a noninstantaneous nuclear component. The noninstantaneous component is directly related to the collective polarizability anisotropy correlation function. Typical normalized OHDRIKES responses for [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] at 295 K are shown in Figure 3. Near zero delay, the OHD-RIKES response for these RTILs is dominated by the instantaneous electronic response. The nuclear response appears as a shoulder on the electronic response that rapidly decays. At ≈15-20% of the peak height, the signal evolves into a shoulder, which is then followed after 0.5 ps by a nonexponential decay with a long time tail. Also present in the OHD-RIKES responses at ∼0.30 ps is a dip, which is a
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TABLE 1: Selected Physical Properties of Ionic Liquids at 298 K ionic liquid
molar mass, g mol-1
[C5mim]Br [C5mim][PF6] [C5mim][NTf2] c
viscosity, cP
density,a g cm-3
molar volume, cm3 mol-1
free volume,b cm3 mol-1
1.262 1.328 1.412
184.7 224.5 306.8
50.5 65.6 99.1
c
233.1 298.2 433.2
663 308d 59c
a Measured with vibrating tube density meter (Anton Paar DM 60 and DMA602). b free volume ) molar volume - molar van der Waals volume. Measured with a rheometer using cone-plate geometry (TA Instruments AR2000). d Ref 27.
Figure 2. Densities of [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] as a function of temperature. The solid lines are linear fits of the equation F ) F0 - aT to the data with fit parameters given in Table 2.
TABLE 2: Density Equation Parametersa ionic liquid
F0, g cm-3
a, 10-4 g cm-3 K-1
Rb
[C5mim]Br [C5mim][PF6] [C5mim][NTf2]
1.4561 1.5614 1.6755
6.4937 7.8265 9.1816
-0.9995 -0.9991 -0.9995
a Parameters corresponding to the linear least-squares fit of the equation F ) F0 - aT to the data in Figure 2 in the temperature range 280-330 K. b Correlation coefficient.
characteristic signature of a damped intermolecular mode. The underdamped high-frequency oscillations seen in [C5mim][NTf2] are assigned to intramolecular vibrations of NTf2- (see ref 22). The OHD-RIKES response in the time range 0.5 < t < 10 ps can be well fit by the empirical decay function
r(t) ) A1 exp(-t/τ1) + A2 exp(-t/τ2) + B
(1)
where B is a constant that accounts for the contribution to the orientational dynamics that relaxes on a time scale much longer than the time range of our measurements. The solid red curves in Figure 3 are fits of eq 1 to the data with the fit parameters given in Table 3. The relaxation times τ1 and τ2 obtained from these fits are within experimental error independent of temperature for all three ionic liquids, with τ1 ) 0.12 ( 0.06 ps, τ2 ) 0.67 ( 0.07 ps for [C5mim]Br; τ1 ) 0.22 ( 0.05 ps, τ2 ) 0.86 ( 0.13 ps for [C5mim][PF6]; and τ1 ) 0.35 ( 0.03 ps, τ2 ) 2.88 ( 0.40 ps for [C5mim][NTf2].32 The temperature independence of τ1 and τ2 is consistent with the temperature independence of the nonexponential relaxation observed for [C2mim][NO3] in the 0.5 < t < 500 ps time region.33 For simple molecular liquids, the τ1 component is associated with the nondiffusive (vibrational) part of the orientational response, whereas the slower components are associated with the diffusive part of the orientational response.16 Note that the values of τ1 are arbitrary and depend on where the fits are begun. Knowing the exact values of τ1, however, is not critical to obtaining RSDs from the time-domain data. Interestingly, the value of τ2 for these RTILs does not correlate with viscosity and temperature as one would predict
Figure 3. Typical OHD-RIKES time-domain data for [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] at 295 K. The solid red curves are nonlinear least-squares fits of a biexponential decay function (eq 1) to the data in the time range 0.5 < t < 10 ps. See Table 3 for biexponential fit parameters.
TABLE 3: Fit Parameters for OHD-RIKES Response for 0.5 < t < 10 ps at 295 Ka ionic liquid
A1
τ1, ps
A2
τ2, ps
B
[C5mim]Br [C5mim][PF6] [C5mim][NTf2]
0.1765 0.2039 0.1254
0.117 0.215 0.354
0.0137 0.0402 0.0130
0.672 0.862 2.88
0.0016 0.0073 0.0039
a
See eq 1 for definition of fit parameters.
for diffusive reorientation on the basis of the Debye-StokesEinstein (DSE) equation (τ ∝ η/T).34-36 Instead, the value of τ2 varies with the size of the anion: the smaller the anion, the shorter the relaxation time. The part of the orientational response that does not return to the baseline in the time range of our measurements, however, has been shown in similar RTILs to follow DSE behavior at longer times.23,25 B. Reduced Spectral Densities After the τ1 component is removed from eq 1, a response function associated with the nonvibrational dynamics is created
r(t) ) [1 - exp(-2t/β)][A2 exp(-t/τ2) + B]
(2)
where the β/2 risetime takes into account the fact that nuclear responses cannot follow the intensity profile of short pulses. In this study, β was set equal to 1/, where is the first moment of the spectral density. The response function associated with the nonvibrational dynamics is then convoluted with the pulse intensity autocorrelation. After “tail-matching” the convoluted response is subtracted from the OHD-RIKES signal, yielding the reduced OHD-RIKES response, which contains only electronic and vibrational contributions. The RSD is then obtained by applying the Fourier-transform-deconvolution procedure to this reduced response. The RSDs of [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] in the 0-200 cm-1 region are shown as a function of temperature in Figure 4. Whereas the RSD of [C5mim][NTf2] shifts to higher frequencies with decreasing temperature, the RSDs of [C5mim]Br and [C5mim][PF6] do not. There are slight variations in the RSDs of [C5mim]Br and [C5mim][PF6] with
4672 J. Phys. Chem. B, Vol. 111, No. 18, 2007
Figure 4. Reduced spectral densities of [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] as a function of temperature.
temperature, but these appear to be random. Within experimental error, the RSDs of [C5mim]Br and [C5mim][PF6] are temperature-independent. In Figure 5, we compare the RSDs of [C5mim]Br and [C5mim][PF6], which were obtained by averaging the RSDs measured at the different temperatures, and the RSD of [C5mim][NTf2] at 295 K. These RSDs are consistent with previously published RSDs for imidazolium RTILs.20-25 The RSD of [C5mim][NTf2] is highly structured with well-defined peaks. The intermolecular part is bimodal in character with a narrow low-frequency component and a broad high-frequency component. Superimposed on the intermolecular band are sharp peaks at ∼120, and ∼170 cm-1 corresponding to intramolecular vibrational modes of the NTf2- ion. In contrast, the RSDs of [C5mim]Br and [C5mim][PF6] are broad with few features. The absence of sharp intramolecular peaks indicates that the RSDs of [C5mim]Br and [C5mim][PF6] in this spectral region are mainly due to the intermolecular dynamics. Also worth noting is the increase in the relative intensity of the low-frequency shoulder compared to that of the highfrequency shoulder as the size of the anion increases. This increase in intensity of the low-frequency shoulder culminates in the appearance of the narrow low-frequency component in the OKE spectrum of [C5mim][NTf2]. This systematic variation of the OKE spectra with anion size suggests that the molecular motion associated with the low-frequency shoulder is different from the motion associated with the high-frequency shoulder. MD simulations on aromatic liquids, which also exhibit this
Xiao et al.
Figure 5. Reduced spectral densities for [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] at 295 K. The solid curves through the points are multicomponent fits of the reduced spectral densities. Also shown are the component bands obtained in the multicomponent analysis of the reduced spectral densities. See text for details and Tables 4 and 5 for spectral parameters of the component bands.
bimodal character, have shown that the high-frequency component is mainly attributed to the rotational motion of molecules, whereas the low-frequency component is attributed to cooperative, long-ranged, coupled, rotational/translational motion.37,38 C. Line Shape Analysis. To provide a quantitative description of the RSDs, multicomponent line shape analysis was performed on the RSDs, where the lowest frequency component is represented by the Bucaro-Litovitz line shape function,
IBL(ω) ) ABLωa exp(-ω /ωBL)
(3)
and the higher frequency components, by the antisymmetrized Gaussian line shape function,
IG(ω) ) AG { exp[-(ω - ωG)2/22] - exp[-(ω + ωG)2/22]} (4) The Bucaro-Litovitz function was first introduced to account for the contribution from collision-induced dynamics in the lightscattering spectrum of nonpolar molecular liquids.39 The antisymmetrized form of the Gaussian satisfies the requirement that the RSD goes to 0 at ω ) 0. Parameters from the analysis of the RSDs are given in the Supporting Information.
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TABLE 4: Spectral Parameters for OKE Spectra of [C5mim]Br and [C5mim][PF6]a intermolecular band
component 1
component 2
component 3
component 4
∆ω cm-1
cm-1
∆ω cm-1
area
cm-1
∆ω cm-1
area
cm-1
∆ω cm-1
area
cm-1
∆ω cm-1
area
ionic liquid
cm-1
[C5mim]Br [C5mim][PF6]
97.3 85.5
125 121
39.5 23.0
46.3 27.7
0.182 0.106
70.4 51.3
74.4 65.7
0.354 0.286
110 92.6
68 82
0.370 0.552
170 170
47.1 47.1
0.094 0.056
a
, first spectral moment (eq 5); ∆ω, full width at half-maximum; area, relative fractional area.
TABLE 5: Spectral Parameters for the Intermolecular Spectrum of [C5mim][NTf2] as a Function of Temperaturea intermolecular band
low-frequency component
high-frequency component
temp K
cm-1
∆ω cm-1
cm-1
∆ω cm-1
area
cm-1
∆ω cm-1
area
280 295 323 348 373 393
77.3 76.6 75.7 76.6 76.3 74.4
121 118 118 115 114 109
31.0 27.7 25.0 23.6 22.4 23.3
37.5 33.4 30.8 28.3 25.0 27.0
0.27 0.24 0.21 0.20 0.19 0.20
85.2 81.2 80.8 79.0 78.6 76.7
89.6 91.0 97.5 97.7 97.3 97.8
0.73 0.76 0.79 0.80 0.81 0.80
a , first spectral moment (eq 5); ∆ω, full width at halfmaximum; area, relative fractional area.
Because the line shapes of the RSDs are not simple, we will use the first spectral moment
≡
∫ωI(ω) dω ∫I(ω) dω
(5)
where I(ω) is an RSD or component band, to specify the frequency of the RSD or component band. Values of , the full width at half-maximum ∆ω, and relative areas for the component bands are given in Table 4 for [C5mim]Br and [C5mim] [PF6] and in Table 5 for [C5mim][NTf2]. In the 0-200 cm-1 region, the RSD of [C5mim]Br is composed of a low-frequency component at 39.5 cm-1, two intermediate-frequency components at 70.4 and 110 cm-1, and a high-frequency component at 170 cm-1 (Figure 5). Similarly, in this spectral region, the RSD of [C5mim][PF6] is composed of a low-frequency component at 23.0 cm-1, two intermediatefrequency components at 51.3 and 92.6 cm-1, and a highfrequency component at 170 cm-1. In contrast, in this spectral region, the intermolecular part of the RSD of [C5mim][NTf2] at 295 K can simply be fit by the sum of a narrow low-frequency component at 27.7 cm-1 and a broad high-frequency component at 81.2 cm-1. Values of and ∆ω for the intermolecular part of the RSDs are also given in Tables 4 and 5. These spectral parameters correspond to that of the RSD for [C5mim]Br and [C5mim][PF6] and to that of the RSD for [C5mim][NTf2] with the two intramolecular bands at 120 and 170 cm-1 removed. Comparison of the spectral parameters for the intermolecular part of the RSDs shown in Figure 5 reveals a systematic variation with the size of the anion: as the size of the anion increases from Br- to PF6- to NTf2-, decreases from 97 to 86 to 77 cm-1 while ∆ω decreases from 125 to 121 to 118 cm-1. Listed in Table 5 are values of the spectral parameters for the component bands in the RSD of [C5mim][NTf2] at different temperatures. In going from 280 to 393 K, the first spectral moment of the low-frequency component decreases from 31.0 to 23.3 cm-1, while that of the high-frequency component decreases from 85.2 to 76.7 cm-1. In contrast, the behavior of
∆ω with temperature is quite different for the two components. In the case of the low-frequency component, ∆ω decreases from 37.5 cm-1 at 280 K to 27.0 cm-1 at 393 K, while in the case of the high-frequency band, ∆ω increases from 89.6 cm-1 at 280 K to ∼97 cm-1 at 323 K and becomes constant above 323 K. The percent contribution of the high-frequency component to the intermolecular part of the RSD exhibits a similar trend. The contribution of this band increases from 73% at 280 K to 7980% at 348 K and becomes constant above 348 K. Discussion The above results indicate that the size of the anion has a dramatic effect on the temperature dependence of the OKE spectrum of an RTIL. To determine the origin of this sensitivity to anion size, we must first understand the basic mechanism that produces the OKE spectrum. In principle, the OKE spectrum will have contributions from a molecular term, an interactioninduced term, and a molecular-interaction-induced cross-term.37 The OKE spectrum for most liquids, however, tends to be dominated by the molecular term, which arises from the collective librational motion of the molecules in the liquid.37 For RTILs consisting of an organic cation and an inorganic anion, only the librational motion of the cation contributes to the OKE spectrum. This clearly is the case for RTILs with spherical anions, such as Br- and PF6-. To show this for RTILs with nonspherical anions, we make use of the dependence of the OKE spectrum on the square of the derivative of the polarizability anisotropy, (∂Πanis/∂q)2 , where q is a canonical coordinate associated with one of the modes of the liquid, to estimate the relative contributions of the various motions of liquid to the OKE spectrum.37 Giraud et al.21 showed that the value of (∂Πanis/∂q)2 for the imidazolium ring is a factor of ∼4.3 × 1013 times greater than that of the NTf2- ion. This difference in the polarizability derivatives simplifies the interpretation of the OKE spectra of these RTILs because the intermolecular part of the OKE spectrum can be viewed as being a reflection of the librational motion of the imidazolium ring. Librational motion in molecular liquids can be thought of as the pseudooscillatory orientational motion of the molecules within local potential minimums defined by their nearest neighbors (“rattling in cage”).40,41 The intermolecular potential governing librational dynamics to a large extent will be determined by cooperative packing and not by two-body interactions.37 In molecular liquids, the OKE spectrum tends to shift to higher frequency and broaden as the density increases. This behavior is ascribed to stiffening of the local potential due to an increase in the number density. As shown in Figure 6, the dependence of the OKE spectra of [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] at 295 K on the size of the anion at first glance is consistent with this density effect. Let us consider the isobaric expansion coefficient Rp ≡ [(1/F)(∂F/∂T)p] for these RTILs. Figure 7 shows that in the temperature range 280-330 K, Rp varies linearly with temperature (see Table 6 for fit parameters) and that the magnitude of Rp increases as the size of the anion increases in the order Br< PF6- < NTf2-, as observed previously.42 The temperature
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Figure 6. First spectral moment of the intermolecular part of OKE spectrum versus density at 295 K for [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2].
Figure 8. Thermal frequency coefficient ζωp of the intermolecular part of the RSD and the high-frequency component for [C5mim][NTf2] as a function of temperature. See eq 7 for definition of ζωp .
To explore further the implications of density inhomogeneities in the dynamics of RTILs, we define a parameter that is analogous to the isobaric expansion coefficient:
ζωp ≡ -[(1/)(∂/∂T)p]
Figure 7. Thermal expansion coefficient for [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] as a function of temperature. The solid lines are linear fits of the equation R ) R0 + bT to the data with fit parameters given in Table 6.
TABLE 6: Expansion Coefficient Parametersa ionic liquid
R0, 10-4 K-1
b, 10-7 K-2
Rb
[C5mim]Br [C5mim][PF6] [C5mim][NTf2]
4.3489 4.8483 5.2583
2.67 3.51 4.33
0.9995 0.9989 0.9994
a Parameters corresponding to the linear least-squares fit of the equation R ) R0 + bT to the data in Figure 7 in the temperature range 280-330 K. b Correlation coefficient.
independence of the OKE spectra in the case of [C5mim]Br and [C5mim][PF6] suggests that there are density heterogeneities in RTILs such that there are regions with different local densities that differ from the bulk density. The bulk expansion coefficient of the liquid will then be given by
Rp(T) )
∑i fi(T)Rip(T)
(6)
where Rip(T) is the local expansion coefficient in a given region in the liquid and fi(T) is the volume fraction of the region. For the OKE spectra of [C5mim]Br and [C5mim][PF6] to be temperature-independent, the expansion coefficients in regions where the librational motion is occurring must be much less than that of the bulk density.
(7)
This parameter has the same meaning as Rp in that it gives the fractional change in as temperature is changed. With values of in Table 5, eq 7 can be used to calculate ζωp for the intermolecular part and the high-frequency component band of the OKE spectrum of [C5mim][NTf2]. As discussed above, the high-frequency component is mainly associated with the librational motion of molecules in the liquids, so it is natural to consider this feature in determining the relationship between the intermolecular part of the OKE spectrum and the density of [C5mim][NTf2]. As can be seen in Figure 8, the value of ζωp for the high-frequency component varies from 7.4 × 10-4 to 8.0 × 10-4 K-1 in the temperature range 280-400 K, whereas the value of ζωp for the entire intermolecular spectrum in the temperature range is constant and equal to ∼2 × 10-4 K-1. The value of ζωp corresponding to the high-frequency band agrees well with the value of Rp, which varies from 6.5 × 10-4 to 6.7 × 10-4 K-1 in the temperature range 280-330 K. This agreement is not unreasonable if the high-frequency band is mainly associated with the librational motion of the imidazolium rings. That Rp and ζωp are not exactly equal to each other can be rationalized by the density of the local environment of the imidazolium rings not being the same as that of the bulk density. If the intermolecular part of the OKE spectra of these RTILs reflects the librational motion of the imidazolium rings and one assumes that these liquids phase separate into nonpolar and polar regions, then the OKE spectra must reflect the intermolecular dynamics in the polar regions. Figure 9 schematically shows the ionic liquid structure in [C5mim]Br and [C5mim][PF6]. The ionic network is depicted as a chain, with the anion represented by a spherical particle and the cation represented by a polar head group (the imidazolium ring) and a nonpolar tail (the C5 group). The tails point toward each other in such a way as to form the nonpolar regions. This admittedly is a simplistic picture in that we have depicted the ionic network as a single-stranded chain of ions, which would imply a nearest-neighbor coordination number of 2. The structure of an ionic network obviously is more complicated than this. Neutron diffraction experiments43-45 and MD simulations3,46,47 indicate that there are several anions in the first coordination shell around a given
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Figure 9. Schematic illustration of nanostructural organization in an ionic liquid showing how thermal expansion can occur without affecting the local structure of the domains in the ionic networks. See text for further details.
cation. The ionic network should, therefore, be thought of as a multistranded chain instead of a single-stranded chain of ions. Despite its simplicity, Figure 9 captures the elements of nanostructural organization that allow us to rationalize the observed behavior of the OKE spectra of the RTILs in this study, as we will now show. In explaining the additivity of the OKE spectra, Xiao, et al. postulated that block formation is driven by domains in [C5mim]Br that are more closely packed than in [C5mim][NTf2]. That ionic networks are more closely packed in [C5mim]Br and [C5mim][PF6] than in [C5mim][NTf2] is not unreasonable, given that there is ∼34-49% less free volume in [C5mim]Br and [C5mim][PF6] than in [C5mim][NTf2] (Table 1). Indeed, packing arguments are commonly used to rationalize the lower viscosities and melting points of ionic liquids with NTf2- as compared to ionic liquids with smaller inorganic anions.48 Because of this difference in packing, domains in [C5mim]Br are “solid-like”, whereas domains in [C5mim][NTf2] are “liquid-like”. The results reported here on the behavior of the OKE spectra with temperature are consistent with this characterization of the domains in RTILs: solid-like domains will result in temperatureindependent OKE spectra; liquid-like domains will result in temperature-dependent OKE spectra. This idea of solid-like versus liquid-like domains is also consistent with the charge ordering in RTILs, as evidenced by pronounced oscillations in cation-cation radial distribution functions (RDFs) and out-of-phase anion-cation RDFs derived from neutron diffraction measurements44,45 and MD simulations.3,46,47,49-51 Depending on the nature of the cation or anion, ionic liquids will exhibit varying degrees of charge order. Recent neutron diffraction measurements on ionic liquids with 1,3dimethylimidazolium ([dmim]+) as the cation confirm that there is significantly less charge ordering in salts with NTf2- in comparison to salts with PF6- and Cl-, as manifested by larger cation-cation and cation-anion separations.44,45,52 If the ionic networks in [C5mim]Br and [C5mim][PF6] are composed of domains with solid-like structure, defects must be present along the ionic network to allow thermal expansion to occur in the liquid. It is unlikely that the ionic networks in RTILs will be perfectly charge-ordered and that a certain degree of disorder is to be expected, with defects occurring along the
network. An obvious defect would be two ions of the same charge that are adjacent to each other. Although such defects are energetically unfavorable, we expect their formation to be entropically favored at higher temperatures. Because of electrostatic repulsion, defects will produce gaps in the ionic network. In Figure 9, we show sections of the ionic network corresponding to solid-like domains separated by defects. The presence of gaps facilitates thermal expansion without affecting the structure of the domains.53 Similarly, defects should also be present in ionic networks in [C5mim][NTf2]. Given the liquidlike structure of the domains in [C5mim][NTf2], the gaps will, however, not be as well-defined as they would be in [C5mim]Br and [C5mim][PF6]. One expects the ions in the ionic network to be more homogeneously distributed in [C5mim][NTf2] than in [C5mim]Br and [C5mim][PF6]. So from the point of view of density inhomogeneities, the expansion coefficient of the ionic network in [C5mim][NTf2] will be represented by a single term in the expression for the bulk expansion coefficient given in eq 6. Conclusion This study of the anion effect on the temperature dependence of the OKE spectra of ionic liquids, as well as our previous study of additivity in the OKE spectra of binary ionic liquid mixtures, has shown that valuable insights into the microscopic behavior of RTILs can be gained by using nanostructural organization as a conceptual framework for the interpretation of the data. First, the effect of the anion on the temperature dependence of the OKE spectra of [C5mim]Br, [C5mim][PF6], and [C5mim][NTf2] can be explained if we assume density inhomogeneities are present in RTILs, with local densities having different temperature dependences. This inhomogeneity in the density is consistent with MD simulations that show RTILs to be nanostructurally organized, with ionic networks permeated by nonpolar regions. Because the intermolecular spectrum arises from librational motion of imidazolium rings located in the ionic network, the temperature dependence of the OKE spectrum will be determined by the temperature dependence of the local densities within the network. Second, the temperature independence of the OKE spectra of [C5mim]Br and [C5mim][PF6] indicates that ionic networks
4676 J. Phys. Chem. B, Vol. 111, No. 18, 2007 in these RTILs are less prone to temperature changes than in [C5mim][NTf2]. We attribute this stability to charge ordering in the ionic networks of these RTILs. In contrast, the temperature dependence of the OKE spectrum of [C5mim][NTf2] is a manifestation of the ions in the network with significantly less charge ordering. We argued that because of this charge ordering, the ionic networks will be more closely packed or more solidlike and, hence, will have higher cohesive energy densities than in ionic liquids, in which there is less charge ordering in the ionic networks. If this argument is correct, then at high enough temperatures such that the thermal energy exceeds the local cohesive energy in the networks, the solid-like domains in the networks will melt, causing the OKE spectra of [C5mim]Br and [C5mim][PF6] to become temperature-dependent. Because RTILs have such a wide liquid range, it should be possible to test this idea. Interestingly, Wang and Voth6 recently showed in MD simulations on RTILs the existence of a calorimetric transition from solid-like nonpolar domains to liquid-like nonpolar domains. In a sense, going from a temperature-independent OKE spectrum to a temperature-dependent OKE spectrum can be explained by an analogous structural change involving a transition from solid-like domains to liquid-like domains, with the difference being that the domains are structural units of the ionic network. In principle, an understanding of this anion effect must ultimately come from MD simulations. Even for nonassociating liquids composed of simple symmetric top molecules, a fully molecular approach combining MD simulations and detailed theoretical analysis is needed to determine the exact microscopic origins of the OKE spectrum.14,37,38,54 One aspect of the intermolecular dynamics of RTILs that would greatly benefit from a fully molecular approach is the assignment of various features in their OKE spectra. Although we are able to fit OKE spectra empirically to a sum of component bands, there is no a priori reason to assume that these components correspond to actual intermolecular modes of the liquid. The increase in the relative intensity of the low-frequency shoulder compared that of high-frequency shoulder of the intermolecular part of the RSD as the size of the anion increases is so striking that it is difficult not to think of these features as being attributed to two different intermolecular modes. As we discussed above, the bimodal character of the OKE spectra in the case of simple aromatic liquids has been ascribed in MD simulations to a rotational mode at high frequencies and a coupled translational/rotational mode at low frequencies37,38 It would be interesting to see whether MD simulations result in a similar assignment of the OKE spectra of RTILs or whether these features are due to different intermolecular modes. Acknowledgment. This work was supported by the Welch Foundation under Grant D-1582 to E.L.Q. and Grant D-0775 to R.A.B. We thank S. Kohl of TA Instruments for help with the viscosity measurements. Supporting Information Available: Description of the OHD-RIKES apparatus and data analysis and fit parameters for multicomponent line shape analysis. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (2) (3) (4)
Rodgers, R. D.; Seddon, K. R. ACS Symp. Ser. 2005, 901, 334. Rodgers, R. D.; Seddon, K. R. ACS Symp. Ser. 2005, 902, 397. Urahata, S. M.; Ribeiro, M. C. C. J. Chem. Phys. 2004, 120, 1855. Wang, Y.; Voth, G. A. J. Am. Chem. Soc. 2005, 127, 12192.
Xiao et al. (5) Lopes, J. N. A. C.; Padua, A. A. H. J. Phys. Chem. B 2006, 110, 3330. (6) Wang, Y.; Voth, G. A. J. Phys. Chem. B 2006, 110, 18601. (7) Lopes, J. N. A. C.; Gomes, M. F. C.; Padua, A. A. H. J. Phys. Chem. B 2006, 110, 16816. (8) Tokuda, H.; Hayamizu, K.; Ishii, K.; Bin Hasan Susan, M.; Watanabe, M. J. Phys. Chem. B 2005, 109, 6103. (9) Anthony, J. L.; Anderson, J. L.; Maginn, E. J.; Brennecke, J. F. J. Phys. Chem. B 2004, 109, 6366. (10) Rebelo, L. P. N.; Najdanovic-Visak, V.; de Azevedo, R. G.; Esperanca, J. M. S. S.; da Ponte, M. N.; Guedes, H. J. R.; Visak, Z. P.; de Sousa, H. C.; Szydlowski, J.; Lopes, J. N. A. C.; Cordeiro, T. C. ACS Symp. Ser. 2005, 901, 270. (11) Xiao, D.; Rajian, J. R.; Li, S.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2006, 110, 16174. (12) Smith, N.; Meech, S. R. Int. ReV. Phys. Chem. 2002, 21, 75. (13) Rajian, J. R.; Hyun, B. R.; Quitevis, E. L. J. Phys. Chem. A 2004, 108, 10107. (14) Elola, M. D.; Ladanyi, B. M.; Scodinu, A.; Loughnane, B. J.; Fourkas, J. T. J. Phys. Chem. B 2005, 109, 24085. (15) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10. (16) Fourkas, J. T. In Ultrafast Infrared and Raman Spectroscopy; Fayer, M. D., Ed.; Marcel Dekker: Inc.: New York, 2001; pp 473-512. (17) McMorrow, D. Opt. Commun. 1991, 86, 236. (18) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. (19) Kinoshita, S.; Kai, Y.; Yamaguchi, M.; Yagi, T. Phys. ReV. Lett. 1995, 75, 148. (20) Hyun, B. R.; Dzyuba, S. V.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. A 2002, 106, 7579. (21) Giraud, G.; Gordon, C. M.; Dunkin, I. R.; Wynne, K. J. Chem. Phys. 2003, 119, 464. (22) Rajian, J. R.; Li, S.; Bartsch, R. A.; Quitevis, E. L. Chem. Phys. Lett. 2004, 393, 372. (23) Shirota, H.; Funston, A. M.; Wishart, J. F.; Castner, E. W., Jr. J. Chem. Phys. 2005, 122, 184512(1). (24) Shirota, H.; Castner, E. W., Jr. J. Phys. Chem. A 2005, 109, 9388. (25) Shirota, H.; Castner, E. W., Jr. J. Phys. Chem. B 2005, 109, 21576. (26) Dzyuba, S. V.; Bartsch, R. A. J. Heterocycl. Chem. 2001, 38, 265. (27) Dzyuba, S. V.; Bartsch, R. A. ChemPhysChem 2002, 3, 161. (28) Seddon, K. R.; Stark, S.; Torres, M.-J. ACS Symp. Ser. 2002, 819, 34. (29) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B.; Watanabe, M. J. Phys. Chem. B 2004, 108, 16593. (30) Zhiyong, G.; Brennecke, J. F. J. Chem. Eng. Data 2002, 47, 339. (31) Hyun, B. R.; Quitevis, E. L. Chem. Phys. Lett. 2003, 370, 725. (32) The value of τ1 for [C5mim][NTf2] reported here is the correct value and not the one reported in ref 22. (33) Cang, H.; Jie, L.; Fayer, M. D. J. Chem. Phys. 2003, 119, 13017. (34) Einstein, A. InVestigations on the Theory of Brownian Motion, 1st ed.; Dover: New York, 1956. (35) Debye, P. Polar Molecules, 1st ed.; Dover: New York, 1929. (36) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J. Phys. Chem. 1981, 85, 2169. (37) Ryu, S.; Stratt, R. M. J. Phys. Chem. B 2004, 108, 6782. (38) Tao, G.; Stratt, R. M. J. Phys. Chem. B 2006, 110, 976. (39) Bucaro, J. A.; Litovitz, T. A. J. Chem. Phys. 1970, 54, 3846. (40) Lynden-Bell, R. M.; Steele, W. A. J. Phys. Chem. 1984, 88, 6514. (41) Kohler, B.; Nelson, K. A. J. Phys. Chem. 1992, 96, 6532. (42) Gu, Z.; Brennecke, J. F. J. Chem. Eng. Data 2002, 47, 339. (43) de Andrade, J.; Boes, E. S.; Stassen, H. J. Phys. Chem. B 2002, 106, 3546. (44) Hardacre, C.; McMath, S. E. J.; Nieuwenhuyzen, M.; Bowron, D. T.; Soper, A. K. J. Phys. C 2003, 15, S159. (45) Hardacre, C.; Holbrey, J. D.; McMath, S. E. J.; Bowron, D. T.; Soper, A. K. J. Chem. Phys. 2003, 118, 273. (46) Morrow, T. I.; Maginn, E. J. J. Phys. Chem. B 2002, 106, 12807. (47) Del Popolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 1744. (48) Carmichael, A. J.; Hardacre, C.; Holbrey, J. D.; Seddon, K. R.; Nieuwenhuyzen, M. Proc. Electrochem. Soc. 2000, 99-41., 209. (49) Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M. Mol. Phys. 2001, 99, 801. (50) Margulis, C. J.; Stern, H. A.; Berne, B. J. J. Phys. Chem. B 2002, 106, 12017. (51) Margulis, C. J. Mol. Phys. 2004, 102, 829. (52) Deetlefs, M.; Hardacre, C.; Nieuwenhuyzen, M.; Padua, A. A. H.; Sheppard, O.; Soper, A. K. J. Phys. Chem. B 2006, 110, 1520. (53) Figure 9 exaggerates the structural change that occurs upon thermal expansion. At 300 K, the value of Rp varies from ∼5.2 × 10-4 K-1 in [C5mim]Br to 6.5 x 10-4 K-1 in [C5mim][NTf2]. For a temperature change of 10 K, there will be at most a fractional change in the volume of ∼0.50.7% in these ionic liquids. If we were to depict the actual structural change
Temperature Dependence of OKE Spectra corresponding to a ∼0.5-0.7% volume expansion, the final state would be hardly distinguishable from the initial state.
J. Phys. Chem. B, Vol. 111, No. 18, 2007 4677 (54) Elola, M. D.; Ladanyi, B. M. J. Phys. Chem. B 2006, 110, 15525.
