Associating Imidazoles: Elucidating the Correlation between the Static Dielectric Permittivity and Proton Conductivity

Broadband dielectric spectroscopy is employed to investigate the impact of supramolecular structure on charge transport and dynamics in hydrogen-bonded 2-ethyl-4-methylimidazole and 4-methylimidazole. Detailed analyses reveal (i) an inverse relationship between the average supramolecular chain length and proton conductivity and (ii) no direct correlation between the static dielectric permittivity and proton conductivity in imidazoles. These findings raise fundamental questions regarding the widespread notion that extended supramolecular hydrogen-bonded networks facilitate proton conduction in hydrogen bonding materials.

Figure 1

Broadband dielectric spectra of 2-ethyl-4-methylimidazole. Real part of the complex dielectric function ${ϵ}^{\prime }$ and the derivative spectra ${ϵ}_{\mathrm{der}}^{\prime \prime }=[(-\pi )/2]\{(\partial {ϵ}^{\prime })/[\partial \ln (f)]\}$ of pure 2-ethyl-4-methylimidazole (2E4MIm) vs frequency. Solid lines represent fits using a combination of two Havriliak-Negami fitting functions. Shaded areas depict the contribution of the slow, Debye-like relaxation and dotted-dashed blue lines correspond to the structural $\alpha$ relaxation.

Figure 2

(a) Static dielectric permittivity ${ϵ}_s$ of pure 2-ethyl-4-methylimidazole (2E4MIm, closed squares) and 4-methylimidazole (4MIm, closed circles). The departure from the Onsager relation is captured by the Kirkwood correlation factor, $g_k$ (solid and dashed lines corresponding to 2E4MIm and 4MIm, respectively). (b) Relaxation rates of the structural, α relaxation (open squares) and slow, Debye-like relaxation (closed squares) of 2E4MIm. Solid lines represent fits by the Vogel-Fulcher-Tammann equation, $\omega ={\omega }_{\infty }\exp [B/(T-T_0)]$, see Supplemental Material [37]. Inset: Estimated number of molecules participating in a chain, chain length $\approx ({\omega }_{\alpha }/{\omega }_{\text{Debye}}{)}^{1/2}$.

Figure 3

Relaxation rate vs temperature for the slow, Debye-like relaxation (closed symbols) and structural, α relaxation (open symbols) of pure 2-ethyl-4-methylimidazole and low concentration (a) levulinic acid and (b) butyramide mixtures as obtained from the broadband dielectric spectra.

Figure 4

Static dielectric permittivity vs temperature of 2-ethyl-4-methylimidazole and its mixtures with (a) levulinic acid and (b) butyramide. Solid line is the static permittivity predicted for pure 2E4MIm by the Onsager relation.

Figure 5

Ionic conductivity ${\sigma }_0$ as a function of inverse temperature for (a) levulinic acid and (b) butyramide mixtures with 2-ethyl-4-methylimidazole. Minute amounts of levulinic acid substantially increase the ionic conductivity, while butyramide has no effect.