Importance of reorientational dynamics for the charge transport in ionic liquids

Most ionic liquids contain at least one rather complex ion species exhibiting a dipolar moment. In the present work, we provide a thorough evaluation of broadband dielectric spectra of 12 ionic liquids taking into account the often neglected reorientational dynamics of these ions. We confirm that this dynamics leads to a clear relaxational signature in the spectra, a fact that so far only was considered in few previous works. The obtained reorientational relaxation times are well consistent with earlier inelastic light-scattering and high-frequency dielectric investigations. Evaluating our dielectric spectra in terms of reorientational motions reveals a close coupling of the ion-rotation dynamics to the ionic charge transport in a broad temperature range from the low-viscosity liquid above room temperature deep into the high-viscosity supercooled state close to $T_g$. This coupling does not seem to be mediated by the viscosity but probably is of more direct nature, pointing to a revolving-door mechanism as also considered for plastic-crystalline ionic conductors. Our results show that the reorientational motion of the dipolar ions plays a significant and so far widely overlooked role for the ionic charge transport in ionic liquids.

Figure 1

Frequency dependence of ε${}^{\prime }$ (a), ε${}^{″}$ (b), and σ${}^{\prime }$ (c) of Bmim $\mathrm{P}{\mathrm{F}}_6$ at various temperatures. The solid lines are fits as described in the text. ε${}^{\prime }$(ν) and ε${}^{″}$(ν) were simultaneously fitted and the σ${}^{\prime }$ fit curve calculated from ε${}^{″}$. For 211 K, the dash-dotted lines show the dc, α-, and β-relaxation components of the fit curves. The inset shows a magnified view of ε${}^{\prime }$(ν) in the α-relaxation regime.

Figure 2

Frequency dependence of ε${}^{\prime }$ (a), ε" (b), and σ${}^{\prime }$ (c) of Bmim TFSI, measured at various temperatures. The solid lines are fits as described in the text. The inset shows a magnified view of ε${}^{\prime }$(ν) in the α-relaxation regime for three temperatures.

Figure 3

Frequency dependence of ε${}^{\prime }$ (a) and σ${}^{\prime }$ (b) of Bmim $\mathrm{P}{\mathrm{F}}_6$, measured at 223 K. The solid lines are fits assuming a CD function for the description of the reorientational α relaxation as already shown in Fig. 1. The dashed and dash-dotted lines represent alternative fits using the original [29] and modified [45] RBM, respectively. In all cases, the electrode polarization was taken into account by a distributed RC circuit [40]. The inset shows a magnified view of ε′(ν) in the α-relaxation regime. All fits were simultaneously performed for ε${}^{\prime }$ and σ${}^{\prime }$.

Figure 4

Temperature-dependent average reorientational α-relaxation times of Bmim $\mathrm{P}{\mathrm{F}}_6$ (a) and Bmim TFSI (b). Results detected by LS [11] (pluses) and dielectric spectroscopy (circles: present work; crosses: from Refs. [32, 34]) are shown. The lines are fits with the VFT formula.

Figure 5

Comparison of the temperature-dependent translational and reorientational ion dynamics of six ILs. ${\rho }_{\mathrm{dc}}$ (circles; first right scale) and average reorientational relaxation times from dielectric spectroscopy (crosses; left scale) are shown in Arrhenius representation. If available, in addition relaxation times from DSC (squares) and viscosity data [23, 65, 66, 67] (triangles; second right scale) are included. The different ordinates cover the same number of decades. Their starting values were chosen to achieve a good match of the ${\rho }_{\mathrm{dc}}$ and $\langle {\tau }_{\alpha }\rangle$ curves (for η, a match at high temperatures was intended). The lines are VFT fits of $\langle {\tau }_{\alpha }\rangle$.

Figure 6

Same plot as Fig. 5 for the other six investigated ILs.

Figure 7

Dc resistivity vs the average reorientational relaxation time of various ILs as determined from fits of the dielectric spectra. The line with slope one indicates approximately linear behavior, ${\rho }_{\mathrm{dc}}\propto \langle {\tau }_{\alpha }\rangle$.

Figure 8

(a) Temperature dependence of the normalized heat flow (HF) of five 10 K/min heating scans covering the glass-transition region of Bmim $\mathrm{P}{\mathrm{F}}_6$. Each heating scan was performed after a different precooling rate ranging from 1 to 100 K/min. (b) Difference in HF to the standard heating scan with 10 K/min. The inset shows the temperature-dependent relaxation times deduced from these DSC data using an Arrhenius representation.

Figure 9

Temperature dependence of the relaxation strength of the dipolar relaxation process of two ILs as determined from fits of the spectra as described in the main text.