Experimental Evidence for a State-Point-Independent Density-Scaling Exponent in Ionic Liquids

This Letter addresses a fundamental issue of condensed-matter physics, which is the validity of the density-scaling concept. For this purpose, the ambient and high-pressure conductivity measurements of two selected ionic liquids (ILs), with the different contribution of H-bonding interactions, were performed in the dynamic range of 13 orders of magnitude and corresponding to the density changes as large as 20%. All experimental data obtained within one compound are shown to superimpose each other when plotted as a function of ${\rho }^{\gamma }/T$. These results clearly show that for studied ILs the scaling exponent is a state-point-independent parameter that is in odds with the recent findings for van der Waals liquid [Sanz et al., Phys. Rev. Lett. 122, 055501 (2019)].

Figure 1

Structures of (a) [BMIm][OAc] and (b) $[\mathrm{BMMIm}][{\text{NTf}}_2]$ together with the exemplary hydrogen bonds formed between cation and anion.

Figure 2

The dielectric conductivity spectra of $[\mathrm{BMMIm}][{\text{NTf}}_2]$ recorded at ambient (a) and elevated pressure (b). (Inset) The Walden plot of $[\mathrm{BMMIm}][{\text{NTf}}_2]$ and [BMIm][OAc]. The viscosity data used to construct the Walden graph are presented in the Supplemental Material [28].

Figure 3

The isothermal and isobaric data of [BMIm][OAc] and $[\mathrm{BMMIm}][{\text{NTf}}_2]$ presented as a function of density. (Insets) Constructed by the horizontal crossing of the ${\log }_{10}{\sigma }_{\mathrm{dc}}(\rho )$ data at multiple isoconductivity conditions (${\log }_{10}{\sigma }_{\mathrm{dc}}$ taken every one decade). For [BMIm][OAc], we have started from $–{\log }_{10}{\sigma }_{\mathrm{dc}}=13$ and finished at $–{\log }_{10}{\sigma }_{\mathrm{dc}}=4$. Each of the ${\log }_{10}T$ vs ${\log }_{10}\rho$ dependence was analyzed separately by means of a linear fitting procedure (solid lines).

Figure 4

(a) Behavior of scaling exponent $\gamma$ for [BMIm][OAc] (open squares) and $[\mathrm{BMMIm}][{\text{NTf}}_2]$ (circles) as a function of density at ambient pressure. The exponents $\gamma$ were determined from the separate linear fitting of each $T(\rho )$ dependence presented in the inset of Fig. 3 (open symbols) and by means of Eq. (2) (closed symbols). The dashed lines denote the average value of $\gamma$ for each IL. (b) Scaling curves for [BMIm][OAc] and $[\mathrm{BMMIm}][{\text{NTf}}_2]$. Horizontal dashed lines denote the ${\log }_{10}{\sigma }_{\mathrm{dc}}$ at $T_b$.