Low frequency modes
The low frequency mode, modelled with a Cole-Cole equation (fig. 3.15), is readily as-signed to the reorientation of the dipolar cations as extensively discussed previously (see section 3.2.1). This assignment is also in concordance with the MD simulations (fig. 3.14).
More importantly, the parameters of the low-frequency mode agree within the likely experi-mental errors with those obtained over the restricted frequency range at0.2.ν/GHz≤89 (section 3.2.1). Although significant differences between the present parameters for this mode and those derived from the more limited frequency range (section 3.2.1) are apparent for the more viscous compounds, the uncertainties in the determination of the relaxation parameters are also higher in these cases because of the location of the mode close to the low-frequency limit of the instrumentation (as discussed at length in section 3.2.1).
On the other hand, the origin of the Debye mode at ∼80GHz, which was already reported previously11,145,146(see also section 3.2.1), is not obvious. The simulated spectra (fig. 3.14) suggest indeed that there are considerable contributions of the translational modes (in-termolecular vibrations) and translational-rotational cross-correlation at these frequencies.
3.3. BROADBAND SPECTRA AT 0.2 GHZ ≤ν≤ 10 THZ AND 25◦C 79
Table3.6:Staticpermittivities,ε,relaxationtimes,τj,amplitudes,Sj,Cole-Coleparameter,α,resonancefrequenciesν0,j anddampingconstantsγjobtainedbyfittingasuperpositionofamodifiedCole-Cole,amodifiedDebyeandthreedamped harmonicoscillatorstotheexperimentalspectraofsevenRTILsat25◦ C.χ2 rrepresentsthereducederrorfunctionandn2 D thesquaredrefractiveindexatλ=589.6nm.TheinertialriseconstantoftheCole-ColeandDebyemodewasfixedto γlib=2THz.a RTILεS1τ1αS2τ2S3ν0,3γ3S4ν0,4γ4S5ν0,5γ5ε∞n2 Dχ2 r·105 [emim][BF4]14.778.9437.10.3870.7331.071.871.182.940.5981.952.150.6862.921.842.631.994b 386 [bmim][BF4]13.798.582250.4820.5761.591.541.032.290.5582.012.280.4082.951.752.542.016c 196 [hmim][BF4]12.207.664810.5250.2521.391.280.9522.070.6551.952.150.4412.921.622.352.027d 278 [emim][DCA]11.054.7031.80.1521.062.761.070.5621.161.392.434.290.3253.342.112.822.292e 163 [bmim][DCA]11.296.2062.70.3360.6211.930.5790.6981.311.252.444.360.2983.292.072.632.277e 72.5 [bmim][PF6]17.8113.215600.5420.4871.671.090.8791.750.7022.182.390.09052.871.082.381.985c 664 [bmim][CF3CO2]15.2410.31600.4810.2540.4810.8910.9622.170.5481.932.280.3083.262.032.662.079b 139 a Units:τjinps,γj,ν0,jinTHz;b Ref.206206;c Ref.207207;d Ref.208208;e Ref.209209.
However, due to the rather broad and featureless spectra of the present RTILs an unam-biguous splitting into rotational and translational contributions is not possible at this stage although consistent with the MD simulations (fig. 3.14), intermolecular vibrations appear to be the main contribution.
As can be seen in table 3.3.2, the damping constants of the higher-frequency DHO modes do not vary much. Therefore, assuming that mode 2 arises from intermolecular vibrations (i.e. a resonance phenomenon) the band-shape of mode 2 is expected to be close to a Debye band-shape if the damping constant has about the same value as for the other DHO modes observed, because of the similarity of the Debye equation and the DHO in the case of γ ν0. At such low frequencies (for vibrations) the differences between a Debye and DHO band-shape are too small to distinguish reliably between the two models. On the other hand, an interaction-induced rotation, as observed for many systems,184,210 would conform with the observed Debye shape.
THz modes
The high frequency (DHO) modes are mainly due to intermolecular vibrations and to some extent to librations, as indicated by MD simulations170 (see above). The presence of the three DHO modes for all investigated compounds at similar resonance frequencies suggests, that they are characteristic of cation-anion interactions rather than for the specific ions.
Although these modes are occasionally interpreted in terms of hydrogen bonding,200,201 the presence of far-infrared modes doesn’t prove the existence of a directional hydrogen-bond but is indicative of strong interactions in these RTILs. This assignment is in broad concordance withab initio calculations that yield several cation-anion bending and torsion modes at these frequencies.211
There are some studies that investigate fragments of the present frequency range (far-infrared200,201, THz26,143,144), but their limited ranges prevent the authors from more de-tailed conclusions.
A complementary technique, Optical-Kerr-Effect (OKE) spectroscopy, that is sensitive to the time correlations of the anisotropic part of the polarizability tensor, can access the same broad frequency range as the present measurements (see below). Due to the asymmetry of the cations (and some anions) and also because modes occurring at these frequencies are mainly interaction induced, the intermolecular modes of this study are expected to be OKE (Raman) active. Comparison with studies literature studies123,124,127,133 reveals that the DHOs observed in this study are in good agreement with the OKE results.124,127 The authors of these studies assume out-of-plane librations of the cation with different environments, caused by different positions of the closest counterions as molecular origin for these modes.
From fig. 3.17 it can be seen that there is no simple dependence ofSj orν0,j on the cation or anion. On the other hand if the cation is substituted, while the anion remains the same, the parameters vary smoothly with the alkyl chain length, n, of the side chain.
This observation is in accordance with the assignments to intermolecular vibrations, since the main cation-anion interaction side is at the C2-H position of the imidazolium ring.200 Accordingly, the side chain of the imidazolium ring has only a minor effect onto the
cation-3.3. BROADBAND SPECTRA AT 0.2 GHZ ≤ν≤ 10 THZ AND 25◦C 81
Figure 3.17: (a) Amplitudes, Sj and resonance frequencies, ν0,j, of the three DHO modes as a function of the alkyl side chain length of the cation, n (squares: j = 3, circles: j = 4, triangles: j = 5; closed and open symbols represent [BF4]− and [DCA]− containing RTILs, respectively).
anion interaction. Variation of the anion changes the resonance frequencies as well as the amplitudes considerably (fig. 3.17), meaning that the interaction energy is strongly affected by the nature of the anion.
The parameters defining mode 3 (S3 and ν0,3) are most sensitive to variation of the cation (fig. 3.17). Interestingly, ν0,3 decreases with increasing alkyl side-chain length for [BF4]− salts while it increases for RTILs with [DCA]− as the counterion. This suggests, that the interaction energy is affected differently by the alkyl chain length for the two anions. On the other hand modes 4 and 5 show only little variation with the side-chain length.