A Rayleighian approach for modeling kinetics of ionic transport in polymeric media

We report a theoretical approach for analyzing impedance of ionic liquids (ILs) and charged polymers such as polymerized ionic liquids (PolyILs) within linear response. The approach is based on the Rayleigh dissipation function formalism, which provides a computational framework for a systematic study of various factors, including polymer dynamics, in affecting the impedance. We present an analytical expression for the impedance within linear response by constructing a one-dimensional model for ionic transport in ILs/PolyILs. This expression is used to extract mutual diffusion constants, the length scale of mutual diffusion, and thicknesses of a low-dielectric layer on the electrodes from the broadband dielectric spectroscopy measurements done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and the PolyILs are determined. The extracted mutual diffusion constants are compared with the self-diffusion constants of ions measured using pulse field gradient (PFG) fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreement between the diffusivities extracted from the Electrode Polarization spectra (EPS) of IL/PolyILs and those measured using the PFG-NMR are found, which allows the use of the EPS and the PFG-NMR techniques in a complimentary manner for a general understanding of the ionic transport.