Dielectric relaxation in ionic liquids: role of ion-ion and ion-dipole interactions, and effects of heterogeneity.

A semi-molecular theory for studying the dielectric relaxation (DR) dynamics in ionic liquids (ILs) has been developed here. The theory predicts triphasic relaxation of the generalized orientational correlation function in the collective limit. Relaxation process involves contributions from dipole-dipole, ion-dipole, and ion-ion interactions. While the dipole-dipole and ion-ion interactions dictate the predicted three relaxation time constants, the relaxation amplitudes are determined by dipole-dipole, ion-dipole, and ion-ion interactions. The ion-ion interaction produces a time constant in the range of 5-1000μs which parallels with the conductivity dominated dielectric loss peak observed in broadband dielectric measurements of ILs. Analytical expressions for two time constants originating from dipolar interactions in ILs match exactly with those derived earlier for dipolar solvents. The theory explores relations among single particle rotational time, collective rotational time, and DR time for ILs. Use of molecular volume for the rotating dipolar ion of a given IL leads to a predicted DR time constant much larger than the slowest DR time constant measured in experiments. In contrast, similar consideration for dipolar liquids produces semi-quantitative agreement between theory and experiments. This difference between ILs and common dipolar solvents has been understood in terms of extremely low effective rotational volume of dipolar ion, argued to arise from medium heterogeneity. Effective rotational volumes predicted by the present theory for ILs are in general agreement with estimates from experimental DR data and simulation results. Calculations at higher temperatures predict faster relaxation time constants reducing the difference between theory and experiments.