Dielectric study on mixtures of ionic liquids

Differential Scanning Calorimetry

Upon cooling, most ionic liquids can be solidified via a glass transition^{26, 29} as it was observed for all samples by DSC. Figure 1(a) and (b) show a magnified view of the step-like anomaly in the heat flow that is associated with the glass transition from the heating run for BPY_xBMIM_1−x BF₄ and BMIM Cl_xTFSI_1−x, respectively. The measurements were performed between 300 K and 100 K with a cooling and heating rate of 10 K/min. Prior to this measurements, all samples were dried under suitable conditions. The preparation of the samples, drying procedures and water contents are described in detail in the methods section. To determine the glass-transition temperature, the onset method is used, as depicted by the blue dotted straight lines in Fig. 1(a) and (b).

The glass-transition temperature for the pure component BPY BF₄ of the series of BPY_xBMIM_1−x BF₄ (Fig. 1(a)) is 191 K. When adding BMIM BF₄, T _g shifts continuously to lower temperatures as indicated by the arrows. Finally, for pure BMIM BF₄, T _g is 179 K. The inset in Fig. 1(a) illustrates the change of T _g as function of the mole fraction x of BPY_xBMIM_1−x BF₄. This change can be described by the line that represents the weighted average of T _g of the two pure ionic liquids, as the deviations are well below 1 K for all samples. Likewise, a glass-transition temperature between the two simple ionic liquids of a mixture has been reported in literature^{22, 30} and many ionic-liquid mixtures reveal a nearly linear trend of T _g with a change of concentration^{14, 15}.

The second mixing series of BMIM Cl_xTFSI_1−x is shown in Fig. 1(b). BMIM Cl exhibits a T _g of 234 K and again, T _g is lowered with decreasing x. For pure BMIM TFSI we report a T _g of 185 K. The black line in the inset of Fig. 1(b) is a linear extrapolation between the glass-transition temperatures of the two constituents. However, the measured transition temperatures of the samples with x = 0.25, 0.5 and 0.75 show a decrease of 7, 11 and 9 K with respect to this line. Previously it was shown²⁸ that residual water has a huge impact on T _g of BMIM Cl. Yet considering the careful sample preparation and the trend of T _g of BMIM Cl with amount of residual water²⁸, we assume that water impurities cannot explain this discrepancy. Notably all glass-transition temperatures of the mixtures are below the linear extrapolation, i.e., they are closer to T _g of BMIM TFSI. This points towards a dominant influence of BMIM TFSI on the glass temperature of this mixture. A possible explanation is that due to steric reasons the impact of the huge TFSI-anion is more significant for the glass transition, than the small chloride ion of BMIM Cl. Overall, the glass-transition temperatures are all between the parent compounds.

Dielectric Spectroscopy

We have measured the dielectric response of the two mixing series BPY_xBMIM_1−x BF₄ with x = 0/0.6/1.0 and BMIM Cl_xTFSI_1−x with x = 0/0.5/1.0 in a broad frequency-range from 1 Hz to 3 GHz (for BPyBF4 the spectrum was expanded to 40 GHz) and a wide temperature range from 170 to 373 K. This range allows a thorough analysis of the conductivity and the reorientational modes in the glassy and liquid phases of these systems. The samples were dried at about 373 K for at least 16 h inside a nitrogen gas cryostat until the dielectric properties reach time-dependent constant values (not shown). This is a typical sign for no further water removal²⁸, suggesting stable conditions with low values of water impurities. Subsequently, the samples were measured in the same cryostat to avoid a reabsorption of water prior to the measurement. The extended measurements above 3 GHz (c.f. Fig. 2(g–i)) had to be performed in ambient atmosphere and therefore previous drying in an oven in analogy to the calorimetry measurements were performed. Unfortunately, in all cases the sample size is too small for KFT, thus the exact water content cannot be determined after the dielectric measurements. However, no differences between the temperature-dependent cooling and heating runs were found, suggesting a constant and low amount of water impurity. Figure 2 displays the spectra of the cooling run of the BPY_xBMIM_1−x BF₄ series for selected temperatures. The real ((a), (d) and (g)) and imaginary ((b), (e) and (h)) parts of the dielectric permittivity (ε′ and ε′′, respectively) as well as the conductivity σ′ in (c), (f) and (i) are shown. The conductivity emphasizes the dc conductivity, although the information is already contained in ε′′ because of σ′ = ωε ₀ ε′′, where ε ₀ is the permittivity of free space. The rather controversially debated modulus representation (i.e., M* ∝ 1/ε*), sometimes used to characterize the ionic dynamics in ion conductors^31–35 is not presented, since permittivity and conductivity allow a more direct determination of the technically relevant dc conductivity.

The spectra of Fig. 2(a) are dominated by a huge increase of ε′(ν) above 10⁵ towards lower frequencies, which is typically found in many ion conductors, including ionic liquids^{36, 38}. This non-intrinsic effect of electrode polarization leads to a pseudo capacitance that is not an asset of the sample. It causes so-called colossal values³⁹ in the spectra of ε′ and superimposes the intrinsic sample properties. The electrode polarization shows up as a so-called Maxwell-Wagner (MW) relaxation step in ε′ (ν) that should lead to well-defined plateaus at low frequencies³⁷. However, as in many ion conducting materials, no distinct plateau is approached³⁶. This effect can be ascribed to the presence of several MW-relaxations or by a distribution of MW-relaxation times as discussed, e.g., in ref. 36. The MW-relaxation evolves as a step in ε′ and a local maximum in ε′′. It is observed in Fig. 2(b), e.g., at about 10⁵ Hz for the 348 K curve and is shifting towards lower frequencies with decreasing temperature. This temperature dependence originates from an increasing sample viscosity. The high-frequency flanks of these local maxima arise from the dc conductivity, which becomes more obvious in the conductivity representation (Fig. 2(c)) by the corresponding frequency-independent plateaus, e.g., from 1 kHz to 1 MHz for the 231 K curve. At lower frequencies, the electrode polarization leads to a decrease in conductivity, making it necessary to conduct ac-measurements to determine the dc conductivity.

At high frequencies, e.g., above 1 MHz for the 231 K curve, the conductivity in Fig. 2(c) has a pronounced frequency dependency. This indicates the presence of one or more intrinsic relaxations. The dielectric loss (Fig. 2(b)) shows signatures of a relaxational process indicated as peaks at the lowest temperatures and at elevated frequencies, e.g., around 5 MHz for the 171 K curve. The corresponding steps in the real part of the dielectric permittivity (Fig. 2(a)) are not visible at the current scaling of the spectra. Figure 2(a) reveals additional shoulders that are superimposed on the electrode polarization effect, indicating a further intrinsic relaxation with ε _s in the order of 10, e.g., above 1 kHz for the 252 K curve. The corresponding peaks in the dielectric loss (Fig. 2(b)) are covered by the dc conductivity but their high-frequency flank may cause the flattening of the spectra towards higher frequencies. This is also indicated by the increase of the conductivity at frequencies above the dc-plateau (Fig. 2(c)).

The processes described above can be analyzed in more detail by fitting the spectra simultaneously in ε′(ν) and ε′′(ν) with an equivalent-circuit^{37, 39}. To account for the strong MW-relaxations, we used two distributed RC circuits^{36, 40}, connected in series to the bulk response. The latter consists of a resistor representing the dc conductivity, connected in parallel to three complex capacitances that represent the intrinsic reorientational modes. In addition to the two relaxations mentioned above, at some temperatures a third process, allocated at frequencies in-between, improved the accuracy of the fit significantly. Although the whole equivalent-circuit represents the sample, only parts of the elements were needed for the fit at certain temperatures. The main reorientational mode, e.g., in Fig. 2(a) at 1 kHz for the 207 K curve, was modeled by a Cole-Davidson (CD) function⁴¹, as often employed in glassy matter^{42, 43}. It is most likely caused by the reorientation of the cations^{44, 45}. The other relaxations were modeled by Cole-Cole functions⁴⁶. For imidazole-based ionic liquids, a relaxation similar to the relaxational process at higher frequencies, e.g., around 5 MHz for the 171 K curve in Fig. 2(b), was discussed⁴⁴ in terms of a secondary Johari-Goldstein relaxation⁴⁷. The Cole-Cole function is known to provide a good description for such secondary relaxations⁴⁸. In summary, the found spectra are typical for ionic liquids and similar succession of dynamic processes were reported in several works^{26, 44, 45, 49–55}.

In general, the dielectric properties of BPY_0.6BMIM_0.4 BF₄ and BPY BF₄, shown in Fig. 2(d–i), are quite similar to the spectra of BMIM BF₄. Again, the equivalent-circuit described above was used to analyze the dielectric behavior. For BPY BF₄, the third intrinsic process was not required to describe the experimental data. The origin of this third intrinsic relaxation is still under debate. Our results are suggesting that it is only present in imidazole-based ionic liquids. However, the relaxation is rather weak (Δε ≈ 0.2) and superimposed by stronger relaxations for the most temperatures. Thus, we cannot exclude that the third relaxation is ubiquitous for all investigated ILs.

The dielectric properties of BMIM Cl_xTFSI_1−x (not shown) can be well described with the same equivalent-circuit. The third intrinsic relaxation was also found in all liquids of this series and it is most pronounced for BMIM TFSI leading to Δε ≈ 0.9. For BMIM TFSI, this relaxation was attributed in ref. 44 to an intrinsic Johari-Goldstein process arising from the presence of a nonsymmetrical anion. However, for ILs with symmetric anions, e.g. BF₄, this intrinsic relaxation emerges, too. A conventional Johari-Goldstein relaxation, as discussed for BPY_1−xBMIM_x BF₄, can explain the dielectric behavior.

For the BPY_1−xBMIM_x BF₄ series, the dc conductivity shows a dependence on the mixting ratio x, most notably at lower temperatures. At temperatures above 279 K (cf. Fig. 2(c,f,i)) σ _dc reveals almost the same value when changing x. In contrast, at lower temperatures the plateau significantly diverges, e.g., at 207 K in Fig. 2(c,f,i). This implies a change in the temperature dependence of the dc conductivity based on different glass-transition temperatures of these liquids. Naturally the local maximum in ε′′ (cf. Fig. 2(b,e,h)) of the MW-relaxation shifts towards lower frequencies for reduced conductivities. At lower temperatures (T < 235 K) the main reorientational mode (cf. Fig. 2(a) around 1 kHz for 207 K) is affected as well, which is shown in Fig. 2(d) and (g). All properties of the investigated mixture are located well between their two parent ionic liquids, which is also expected from the measurements of the glass-transition temperatures. The discussion focuses on the temperature dependence of the dc conductivity and the main reorientational mode determined from the fits of the dielectric properties for both mixing series.

Relaxation and conductivity dynamics

Fig. 3 shows the average relaxation time ⟨τ _α⟩ = βτ _α (where β is the broadening parameter of the CD function) of the main relaxation ((a) and (c)) and the dc conductivity ((b) and (d)) for both measurement series in an Arrhenius representation, as obtained by the fits described above. Both, the main relaxation time and the dc conductivity reveal the typical non-Arrhenius temperature dependence known from glass forming systems. Such behavior was reported for many ionic liquids^{26, 33, 35, 51, 54, 56–62}. Fits (solid lines) with the empirical Vogel-Fulcher-Tammann (VFT) law^63–66,

where τ ₀ is the inverse attempt frequency, T _VFT the divergence temperature and D the so-called strength parameter⁶⁶, are most suitable to describe the obtained data. For the dc conductivity, a modified form of eq. (1) with a negative exponent and σ ₀ as prefactor instead of τ ₀ was used. Most commonly, the fragility index m, which is defined as the slope at T _g in the Angell plot, log τ vs. T _g/T (ref. 67, is used to parameterize the deviation from Arrhenius behavior. Following Böhmer et al. (ref. 67), it can be calculated from the strength parameter via m = 16 + 590/D. The VFT-fits of ⟨τ _α⟩ allow to determine T _g using the empirical relation ⟨τ _α⟩(T_g) = 100 s. In many ionic liquids the glass-transition temperature of the ionic subsystem τ _σ(T_g) = 100 s, derived from the modulus relaxation, reasonably matches the temperature of σ _dc = 10⁻¹⁵ Ω⁻¹ cm⁻¹ (ref. 26). Here, we determined T _g of the ionic subsystem from the conductivity via this relation. These two temperatures are directly evaluated by the intersection of the VFT-fit and the upper ordinates and are indicated by the black arrows (cf. Fig. 3). Generally, the main relaxation time and the dc conductivity of both parent compounds comprise the behavior of their mixtures over the whole temperature range, as illustrated by Fig. 3.

For BPY_xBMIM_1−x BF₄ (Fig. 3(a) and (b)), the evolution of the dc conductivity and the relaxation times reveal almost identical values above 286 K (1000/T < 3.5). Due to their different glass-transition temperatures, the curves diverge upon further cooling. The glass-transition temperatures of the main relaxational mode for BPY BF₄, BPY_0.6BMIM_0.4 BF₄ and BMIM BF₄ are 197, 191 and 182 K, respectively. The temperatures deduced from the conductivity are slightly (about 2 K) below. The transition temperature of the mixture is at the weighted average of T _g of the two pure parent ionic liquids, which was also evidenced by the DSC measurements. However, the absolute values are slightly above the DSC results. The highest deviation is found for pure BPY BF₄. This indicates different water content for both experiments. Another explanation is a decoupling effect of the structural glass-transition temperature derived from DSC measurements and the ionic or rotational subsystems. The rather low deviations of the other samples indicate no significant decoupling in this series.We expect, based on our previous work (ref. 26), a change in fragility due to the similar dc-conductivities at room-temperature and different glass-transition temperatures. Indeed, the fragility index m, determined from the conductivity, is decreasing from 117 via 111 to 93 for lower glass-transition temperatures. This mixing series is close to ideal mixing as described by Clough et al. in ref. 14 for their ionic liquid mixtures.

The dielectric properties of the pure ionic liquids of BMIM Cl_xTFSI_1−x differ even at high temperatures, as shown in Fig. 3(c) and (d). BMIM Cl exhibits the highest T _g. Its dynamics are slower than those of BMIM TFSI and the mixture. The glass-transition temperatures determined from the main relaxational mode are 181, 195 and 232 K for BMIM TFSI, BMIM Cl_0.5TFSI_0.5 and BMIM Cl, respectively. The glass-transition temperatures deduced from the conductivity are 179, 191 and 228 K, which is slightly lower. These values are within measurement accuracy of the DSC results and there is no decoupling in this series as well. Corresponding to the results of the DSC measurement, the mixture exhibits a T _g which is about 10 K lower than the expected T _g using the weighted average of T _g of the pure ionic liquids. In this regard, this ionic liquid mixture deviates from the ideal mixing behavior. However, the fragility index m of BMIM Cl_0.5TFSI_0.5, determined from the VFT-fit of the dc conductivity, is about 107. Interestingly, this is close to the weighted average of fragility indices of the parent compounds BMIM TFSI and BMIM Cl, being 120 and 97, respectively.

Correlation of σ_dc with m and glass-transition temperature

Many aprotic ionic liquids exhibit a correlation of room-temperature conductivity with their T _g and fragility index²⁶. This correlation is deduced from the temperature dependent dc conductivity following a VFT-law, which is dominated by these two glass-parameters. The room temperature conductivity is calculated by inserting the relaxation time of the glass-transition temperature (τ(T _g) = 100 s) and the formula for the fragility index (m = 16 + 590/D) into the VFT-equation²⁶. The conductivity derived from that formula is shown as color-coded plane in the background of Fig. 4. This illustrates the trend of the room-temperature conductivity in correlation with T _g and m. As indicated by the red arrow the conductivity decreases with increasing T _g and decreasing fragility. T _g and the fragility of both mixing series were determined from the VFT-fit of the dc conductivity, as discussed above.

The circles in Fig. 4(a) represent the results of BPY_xBMIM_1−xBF₄. The colors of the symbols, which depicts the measured dc conductivity at room temperature, show almost identical values. The connecting black arrows that indicate variations of x, are almost parallel to a line of constant conductivity given by the σ(T _g,m) relation, following a trajectory of isoconductivity. That means, changes of the conductivity from the reduced T _g are compensated by the fragility, as it is expected from the Arrhenius plot in Fig. 3. The squares represent BMIM Cl_xTFSI_1−x, which shows an decreasing conductivity for increasing x. Both the decreased fragility index and the increased T _g diminish the conductivity. The variation of x results in conductivities almost parallel to the gradient of the colored plane. In summary, the trend of the dc-conductivities is well described by the colored plane, allowing to characterize the conductivity of the ionic liquids mixtures via the fragility index and T _g. Figure 4(b) and (c) show a plot of the room-temperature conductivity as a function of x. The line represents a linear change of the conductivity on a logarithmic scale, as expected for an ideal mixture⁴. For BPY_xBMIM_1−x BF₄ the mixture with x = 0.6 meets the line as predicted for an ideal mixture. Whereas, the dc conductivity at room temperature for BMIM Cl_0.5TFSI_0.5 is raised compared to this line. Most likely, this increase is based on the reduced glass temperature, as discussed above.

Sample preparation

The ILs were purchased from IoLiTec with a purity of 99%. The mixtures were prepared by blending the two neat ILs in the appropriate mass ratio. To minimize water content, all samples were dried in N₂-gas or vacuum at elevated temperatures for at least 16 hours prior to the measurements. The water content of BPY_xBMIM_1−x BF₄ was determined using coulometric KFT after drying but before to the DSC measurements. The mixing series exhibits less than 0.3 mol% residual water for all samples: BMIM BF₄ 0.23 mol%, BPY_0.6BMIM_0.4 BF₄ 0.25 mol% and BPY BF₄ 0.27 mol%. The high viscosity and hygroscopic nature of the samples of the BMIM Cl_xTFSI_1−x series hampered reliable KFT results. All samples of this mixing series were dried under identical conditions, i.e., for 24 h in nitrogen atmosphere at 373 K and for 48 h in reduced pressure at 353 K. Subsequently, the samples were sealed into the DSC aluminum pans in dried N₂-atmosphere. Comparing the measured T _g with previous results²⁷ the water content of these samples can be determined to be significant less than 1 mol%. For the dielectric measurements <3 GHz all samples were dried already in the employed cryostats, due to the small sample size no water content can be reported. The expanded spectra up to 40 GHz for BPY BF₄ was recorded in ambient atmosphere; thus the sample was dried separately, similarly as for the calorimetry measurements.

Thermal measurements

For the DSC measurements a DSC 8500 (Perkin Elmer) was used. The samples were cooled to 100 K and subsequently heated back to room temperature at 10 K/min. Aluminum pans, which were hermetically sealed after filling in the sample, were used for all measurements. The glass-transition temperatures were taken at the onset of the transition steps in the heating traces.

Dielectric measurements

The complex permittivity ε* = ε′ − iε′′ and the real part of the conductivity σ′ at frequencies 1 Hz ≤ ν ≤ 1 MHz were determined using a frequency-response analyzer (Novocontrol alpha-Analyzer) and at 1 MHz ≤ ν ≤ 3 GHz employing a coaxial reflection impedance analyzer (Agilent E4991A or Keysight E4991B). All samples were measured in steel-plate capacitors. For sample cooling between 170 and 370 K, a Novocontrol Quatro Cryosystem was utilized. For BPY BF₄, the spectrum was additionally expanded to 40 GHz using a coaxial reflection measurement with an open-ended sensor (Agilent E8363B PNA Series Network Analyzer with 85070E Dielecric Probe Kit). Sample heating from 300 to 370 K was done by an Eppendorf Thermomixer Comfort with an additional external temperature sensor.

Competing Interests

The authors declare that they have no competing interests.