Analytical Expression for the Impedance Response for a Lithium-Ion Cell

An analytical expression to predict the impedance response of a dual insertion electrode cell (insertion electrodes separated by an ionically conducting membrane) is presented. The expression accounts for the reaction kinetics and double-layer adsorption processes at the electrode-electrolyte interface, transport of electroactive species in the electrolyte phase, and insertion of species in the solid phase of the insertion electrodes. The accuracy of the analytical expression is validated by comparing the impedance response predicted by the expression to the corresponding numerical solution. The analytical expression is used to predict the impedance response of a lithium-ion cell consisting of a porous cathode and mesocarbon microbead anode. A qualitative graphical method to identify the co-existence of solid and solution phase transport limitations in the impedance spectra of insertion electrodes is also discussed in the paper.