Low-frequency dynamics in ionic liquids: comparison of experiments and the random barrier model

By examining the fine features of dielectric spectra of ionic liquids, we show that the derivative of real permittivity progressively broadens at low frequencies when the glass transition is approached from above. This phenomenon, ubiquitous and yet difficult to ascertain in the widely used conductivity or modulus representations, is not captured by the popular analytical ac universality equations based on the random barrier model. Numerical simulations with the random barrier model reveal that the observed low-frequency broadening is associated with the contributions from high activation energy pathways, suggesting a direct connection between relaxation time distribution and barrier distribution. While the overall prediction of the random barrier model about ac conduction is insensitive to the distribution of activation energy in the extreme disorder limit, the fine features of the derivative spectra contain further information about the energy landscape. These results demonstrate the usefulness of derivative analysis of the dielectric spectra of ionic liquids and glasses at low frequencies, where materials exhibit individual characteristics despite apparent ac universality. The use of numerical solutions of the random barrier model improves the description of the dielectric spectra of the ionic materials studied herein, in some cases, eliminating the need of introducing ad hoc relaxation processes at low frequencies. Lastly, a new analytical equation is proposed to take into account the low-frequency spectrum broadening phenomenon while preserving the universal ac conductivity behavior predicted by the random barrier model.