Communication: Inflection in the pressure dependent conductivity of the protic ionic liquid C₈HIM NTf₂

In the past decade, the interest in researching ionic liquids (ILs) has risen tremendously. This can be ascribed to their many potential areas of application, including the usage as biosolvents, as a transport medium for electrodeposition, or as electrolytes in energy storage devices.¹ The base for this widespread potential can be found within the unique properties which many ILs have, like extremely high vapor pressure, good thermal, chemical, and voltage stability, or high solubility with many substances. Additionally, being salts with a low melting point, usually defined to be above room temperature¹ or 100 °C,² they have high ionic conductivity, which is essential for energy applications. Due to the mostly organic nature and thus the huge variability of possible cations and, to a lesser degree, anions, a vast amount of ILs exist.

On the other hand, from a physical point of view, many ILs are typical glass formers, i.e., they tend to supercool and form amorphous solids rather than crystals upon cooling. Like many glass formers, they exhibit super-Arrhenius like temperature dependence of the viscosity η, which is usually well described by the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation,^3–5 

where T is the absolute temperature, $η∞$ is the viscosity for very high T, and T_VF is the Vogel-Fulcher temperature. The strength parameter D quantifies fragility, i.e., the divergence from the ideal Arrhenius behavior. Similar expressions exist to describe the T-dependence of the dc-conductivity $σdc$ and the structural relaxation time. Many ILs seem to follow a fractional Walden rule, i.e., $Ληα=const.$ (with the molar conductivity Λ and the constant exponent $0<α<1$⁠).⁶ For so-called aprotic ILs, α usually is close to one and depends mainly on the degree of ion dissociation.^7,8 This implies that the inverse conductivity $1/σdc$ has the same temperature dependence as the viscosity. On the other hand, protic systems can exhibit pronounced deviations from this behavior, based on the presence of multiple conductivity mechanisms.⁹ 

Another way to generate a vitreous state is to increase the pressure p and therefore to limit free volume of the molecules. The relationship between the influences of pressure and temperature on the glass transition, and the differences therein, is an important aspect for the understanding of this process. A systematic analysis of both aspects allows us to separate the effects on local motion provided by molecular packing and by available energy.¹⁰ It is very interesting that compared to the temperature dependence of $σdc$ or η, the pressure evolution of these variables is much more complex. In general, the viscosity rises with pressure. Close to the glass transition, this increase is faster than exponential and can be described by a pressure equivalent of the VFTH-law,¹¹ 

where $η0$ is the viscosity for very low pressures, C_F is a pressure analog to D, and $p∞$ is the divergence pressure. By contrast, in the normal liquid state, i.e., for low pressures or high temperatures, a slower than exponential behavior is observed for many materials.¹² This leads to a clear deviation from the model presented above and a perturbation of the fitting parameters. To model $η(p)$ in this range, the McEwen equation

can be used.¹³ Here, q represents the McEwen exponent, while the McEwen parameter $α0$ determines the slope at p = 0. With a combination of both equations, as suggested by Bair,¹³ usually the whole pressure dependency of the viscosity is described rather well,

Interestingly, to our knowledge no reports of a slower than exponential behavior of the inverse conductivity have been published so far.

In this paper, we investigate the ion dynamics of the protic ionic liquid $C8HIM$ $NTf2$ over a wide T and p range. In the $σ(p)$ data, we observed a McEwen-like behavior of $1/σdc$ at low pressures, while at higher pressures a faster than exponential behavior is exhibited. The data were fitted according to the hybrid model (Eq. (4)) and analyzed with regard to the activation volume, illustrating the presence of an inflection point in the curves.

$C8HIM$ $NTf2$ (1-octylimidazolium bis(trifluoromethyl-sulfonyl)imide) was synthesized and purified at the QUILL Research Centre at Queen’s University Belfast. Details are available in the supplementary material. For the high pressure dielectric measurements, the sample was filled in a stainless steel plate capacitor with 100 $μm$ silica spacers. The capacitor was covered in a Teflon capsule, which was then placed in the high pressure chamber. Hydrostatic pressure was applied via a non-polar transmitting liquid (silicon oil). An Alpha-A analyzer (Novocontrol) was used to perform the dielectric measurements at a frequency range from 0.1 Hz to 1 MHz with an excitation voltage of 0.5 V, assuming a standard uncertainty of a conductivity of 1 mS/cm. The pressure was measured with a Nova Swiss tensometric pressure meter (resolution of 0.1 MPa). For the temperature control, a Weiss fridge was employed with an uncertainty of 0.1 K.

The real part of the conductivity $σ′$ of $C8HIM$ $NTf2$ is shown in Fig. 1 with dependence of the frequency ν for different values of the pressure p at a constant temperature of 273 K. The dc-conductivities can be observed at frequency-independent plateaus, e.g., for the 350 MPa curve between 100 Hz and approximately 10 kHz. At higher frequencies, the presence of intrinsic relaxations is suggested by a pronounced pressure dependence of sigma, visible for curves with $p≥$150 MPa. Frequencies below that of the observed plateau in $σ′$ exhibit a strong decrease of the conductivity with decreasing ν. This effect can be attributed to the well-known blocking electrode effect, i.e., the build-up of a thin, insulating layer at the electrodes. The compression of the sample leads to higher viscosity and thus to reduced ion mobility in the liquids. As an effect, both the intrinsic and the surface processes shift to lower frequencies with higher pressure. Additionally, it can be seen that $σdc$ is decreasing by more than two decades from $9×10−5S/cm$ to $3×10−7S/cm$ when p increases from 12 MPa to 400 MPa.

One method to evaluate dynamic processes is the dielectric modulus representation.¹⁴ Its significance is still controversially discussed; however, it allows for the identification of the charge transport connected with intrinsic relaxation processes, while the influence of electrode polarisation is suppressed leading to the frequent usage of this representation in the characterisation of ILs. From the maximum of the imaginary part of the dielectric modulus $M″$ (not shown), the so-called conductivity relaxation time $τσ=1/2πf(Mmax″)$ can be determined. For example, at 273 K and 400 MPa, $τσ$ reaches $6×10−6$ s and diminishes with pressurisation and with cooling.

To further examine the decrease of σ with pressure, the inverse dc-conductivity is presented as a function of p in Fig. 2 for different temperatures. It can clearly be seen that for $p<300$ MPa the 293 K curve is concave against the p-axis, i.e., $1/σdc$ develops slower than exponential with p. In contrast, a faster than exponential behavior is observed at higher pressures, indicated by the stronger increase in $1/σdc$⁠. This leads to an inflection in the curves. Whether this feature is reflected in the pressure dependent viscosity for $C8HIM$ $NTf2$ is not clear so far. However, a similar behavior can be seen in $η(p)$ for many molecular liquids^15,16 and some ionic liquids,¹⁷ even though the concave progression at low pressures is not necessarily incorporated in the models used in these reports. This inflection might arise from a non-linearity of the volume with a change of pressure.¹⁸ It has also been attributed to the pressure dependences of the compressibility and of the apparent activation energy at a constant volume.¹⁶ The hybrid model (Eq. (4)) is used to account for both the faster and the slower than exponential behavior and describes the measured data reasonably well (lines in Fig. 2), assuming a temperature independent pressure-related fragility (i.e., $CF=const.$⁠).¹⁹ Besides, it can be noted that due to improved ion mobility the conductivity rises when T is increasing, which is in agreement with Eq. (1). For example, at ambient pressure and T = 263 K, $σdc$ is approximately $4×10−5 S/cm$⁠, while at 373 K a value close to $10−2S/cm$ is reached. Extrapolation of the modulus data for T = 273 K and 293 K yields relaxation times on the order of 10⁻⁸ s at the inflection point (⁠$p≈200$ and 350 MPa, respectively).

The presence of the inflection point becomes more obvious when the $σdc(p)$ data are analyzed in terms of the activation volume parameter

as presented in Fig. 3, where R is the universal gas constant. $ΔV(p)$ is a measure of the local volume needed for the transversal ion movement and has a constant value for an Arrhenius like behavior. Consequently, a slower than exponential pressure dependence of $1/σdc$ is indicated by a negative slope, while a faster than exponential behavior correlates to a positive slope. Therefore the inflection point corresponds to the minimum in $ΔV$⁠, clearly visible, e.g., for the 273 K data at a pressure of approximately p_i = 200 MPa. With rising temperature, the point shifts to higher pressures. The shift is fast initially, but slows down significantly at high T. Measurements performed by Cook et al.¹⁵ show inflection points in the viscosity of glycerol and dibutyl phthalate (DBP) over a temperature range from 273 K to 398 K. While the temperature dependence of p_i for glycerol is similar to $C8HIM$$NTf2$⁠, DBP exhibits a more linear p_i(T)-behavior. It could be speculated that this observation is connected to the strong H-bonding in both glycerol and $C8HIM$$NTf2$⁠, which is absent in dibutyl phthalate. Besides, it should be noted that the inflection in glycerol is observed at higher pressure (e.g., 1.3 GPa at 296 K) than in DBP and $C8HIM$$NTf2$ (360, respectively, 352 MPa at similar T).

High pressure broadband dielectric spectroscopy was performed on the protic ionic liquid $C8HIM$ $NTf2$ for different temperatures. For the first time, we could observe a transition between slower than exponential and Vogel-Fulcher-like pressure dependence of the dc-conductivity, similar to the behavior reported in pressure dependent viscosity and relaxation times in other materials.^15–17 The measured data were fitted with the hybrid model suggested by Bair for $η(p)$ (Eq. (4)) over the whole pressure range. Since the conductivity is a key property for many potential applications of ionic liquids, e.g., for electrolytes in energy storage devices, the sighting of such a behavior in a protic IL is highly interesting, as it allows for a more thorough prediction. Additionally, this might help determine the physical mechanisms leading to the inflection in the pressure dependence of different properties.

See supplementary material for details of the synthesis and purification of $C8HIM$ $NTf2$⁠.

The authors thank J. Knapik-Kowalczuk and B. Blanchard for performing parts of the dielectric measurements. Z.W. and M.P. are deeply grateful for the financial support by the National Science Centre within the framework of the Opus 8 project (Grant No. DEC-2014/15/B/ST3/04246).