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

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The Journal of Chemical Physics
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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 pro-
vides a computational framework for a systematic study of various factors, including
polymer dynamics, in a ffecting 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 di ffusion
constants, the length scale of mutual di ffusion, and thicknesses of a low-dielectric layer
on the electrodes from the broadband dielectric spectroscopy (BDS) measurements
done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and
the PolyILs are determined. The extracted mutual di usion constants are compared
with the self di usion constants of ions measured using pulse field gradient (PFG)
fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreements
between the diff usivities 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.