As already mentioned above, comparison with other experimental techniques can gain valuable insight into the dynamics of liquids.34,184 In the framework of the broadband di-electric studies the results were compared to optical Kerr effect (OKE) spectra. Where dielectric spectroscopy is sensitive to the time derivative of the correlation function of the macroscopic dipole moment (∝ dtdhµ(t)µ(0)i) OKE spectroscopy measures the time derivative of the correlation function of the anisotropic part of the polarizability tensor, Π, ((∝ dtdhΠ(t)Π(0)i)) Both techniques are sensitive to rotational motions and only weakly sensitive to translational motions.52,184 In principle, the two experiments are complemen-tary for intramolecular vibrations (OKE: Raman active; DR: IR-active). However, at
low (infrared) frequencies in the condensed phase, the modes arise from multiple parti-cle motions, and will be present in spectra obtained with both techniques. Consequently, comparison of DR and OKE spectra allows better resolution of the broad and overlapping bands.
Detailed discussion of the results from the comparison of OKE and DR spectra for three imidazolium-based RTILs ([emim][DCA], [emim][BF4] and [bmim][DCA]) can be found in the following publication:
David A. Turton, Johannes Hunger, Alexander Stoppa, Glenn Hefter, Andreas Thoman, Markus Walther, Richard Buchner, and Klaas Wynne “Dynamics of Imidazolium Ionic Liquids from a Combined Dielectric Relaxation and Optical Kerr Effect Study: Evidence for Mesoscopic Aggregation” J. Am. Chem. Soc. 2009,131, 11140-11146.
but some salient aspects will be presented here. Comparison of both spectra obtained with the two complementary techniques is exemplarily displayed for [emim][DCA] in fig. 3.18.
Results and Analysis
The great advantage of this concerted approach is the high signal to noise ratio of OKE spectroscopy at high frequencies and for DR at low frequencies (fig. 3.18). Although spectra obtained with both techniques are still rather broad and featureless at frequencies ranging from ca. 100 GHz to 6 THz, the OKE results allow a better resolution of the various modes at these frequencies. Thus, the OKE data show that four DHOs and one Gaussian oscillator are required to model the intermolecular modes. Consistent with computer simulations,170 these modes are dominated by many-particle interactions and are thus OKE and DR active.
At higher frequencies the intramolecular modes, which are OKE active but only weakly DR active, are described by another two underdamped DHOs. These modes are the [DCA]− bending vibration at∼5.5THz (184 cm−1) and intramolecular modes of the [emim]+cation at∼4.75THz and∼7.2THz (158 cm−1 and 240 cm−1).
Although the fitting model at THz frequencies is still somewhat uncertain due to the broad nature of the spectra, the combined analysis allows preclusion of inappropriate models.
The most surprising feature of these spectra is that the maximum in the OKE imaginary part is at lower frequencies than observed for the dielectric loss. Usually modes occurring at GHz frequencies arise from rotational relaxation. However, for single molecule rotational diffusion the relaxation time is determined by the macroscopic shear viscosity and the effective volume according to the SED equation (eq. 1.78, section 1.4.4). If the principal axis of the polarizability tensor,Π coincides with the dipole vector, µ, of the molecule the 2nd rank relaxation time of the OKE signal should be three times faster than the DR (1st rank) relaxation. In the case of the investigated RTILs qualitative comparison of the lower-frequency peak maxima would suggest that the OKE relaxation time is approximately five times slower than the DR relaxation time.
With no additional information it is not possible to fit the low frequency OKE mode unambiguously and studies of similar RTILs have employed a Cole-Davidson mode which is well established for the description of the so-called α relaxation in glass-forming and
3.3. BROADBAND SPECTRA AT 0.2 GHZ ≤ν≤ 10 THZ AND 25◦C 83
Figure 3.18: Spectra for [emim][DCA] at 25◦C showing the total fit (dashed) and its component parts (shaded areas): (a) OKE imaginary part with inset, a vertical expansion and (b) dielectric loss, ε00. Solid lines correspond to experimental spectra.
supercooled liquids.212,213 For several systems this mode resolves into a Debye and a Cole-Cole mode, when the glass transition is approached.212,213 For the present low frequency modes the combination of a Debye equation with a Cole-Cole mode modelled the low frequency OKE part excellently, and resulted in a meaningful physical interpretation.
The second interesting feature is that the OKE Cole-Cole mode occurs at similar frequencies to those of the DR spectra. In contrast to the previous fits (sections 3.2.1, 3.2.2 and 3.3;
Refs. 11,171) the low frequency Debye mode is also fitted to the DR spectra, although it is very weak in its amplitude. From DR spectra alone it is not possible to resolve this
weak mode, but with the concerted approach it is possible to model the spectra with this low-frequency Cole-Cole (α) and the sub-α (Debye) mode, with the latter terminating the α relaxation (this is necessary because the alpha mode cannot become slower than the sub-α relaxation (see section 1.3.2 and Ref. 52)).
Discussion
The most remarkable feature of the combined analysis is the large-amplitude mode ap-pearing in the OKE spectra at low frequencies (lower than the DR Cole-Cole mode). This is surprising because simple theories (see section 1.4.6) predict that OKE relaxation times should be faster than the DR relaxation time. Although the dipole vector and the principal axis of the polarizability tensor are very likely aligned differently in the dipolar cations, this can be eliminated on the basis of low frequency studies151 that this sub-α mode occurs at lower frequencies, not covered by the investigated frequency range of the DR experiment.
The large difference in intensity of the sub-αmode in OKE and DR spectra implies that this process must be due to a motion that corresponds to a considerable change in polarizability, while the macroscopic dipole moment is only weakly affected. Computer simulations198and a recent DR study of RTIL mixtures214suggest the formation ofπ-stacked cation clusters in the RTILs, especially for [emim][BF4]. On the other hand, cation dimers sandwiched by two anions, as found for [emim][AlCl4] by computer simulations198 and by NMR-spectroscopy for [emim]+ halides215 appear to be more likely for [emim][DCA].214 The position of the sub-α mode and its strong OKE activity suggests it is due to a motion of high symmetry such as a simple breathing mode of cation-stacked or micelle-like clusters. MD simulations also show strong contributions of translational modes at quite low frequencies,170,176,179
which might be a reflection of inhibited rotation by this clustering.
Recent MD simulations216 and a X-ray scattering study217 suggest a pronounced aggrega-tion of the alkyl substituents of the imidazolium ring with increasing chain-length. Due to bandwidth limitations RTILs with longer side-chains cannot be studied at present with OKE. However, the present results suggest considerable structuring already in RTILs with small cations, in accordance with the simulations.198 Such large scale aggregates have al-ready been postulated previously on the basis of dynamic light scattering (DLS) measure-ments, where time correlations of density fluctuations are recorded.218 The vast difference in timescales (DLS correlation time: ∼1s) can be explained by assuming that the present results involve infracluster motions.
The coincidence α Cole-Cole mode in the OKE and DR spectra can be explained by re-cent MD simulations,179 suggesting that the cations in [emim][PF6] reorient via large angle jumps. For jump reorientation the OKE/DR relaxation time ratio is less than 3 and for large angle jumps (> 109◦) DR relaxation time can even become faster than the corre-sponding 2nd rank (OKE) relaxation time. Indeed, the simulations179 predict that the 2nd rank correlation time can be up to two times slower than the 1st rank decay. Therefore jump orientation in combination with the asymmetry of the constituting ions of the RTILs can explain the observed similar relaxation times in the OKE and DR experiments. This relaxation mechanism can also explain the observation of the extraordinarily small volumes of rotation obtained with the Stokes-Einstein-Debye theory (see section 1.4.4) as observed