Frumkin intercalation isotherm — a tool for the description of lithium insertion into host materials: a review

Abstract

This paper offers an integrated approach toward the elucidation of electroanalytical behavior of various Li-insertion anodes and cathodes. Specifically, the paper describes the application of a Frumkin adsorption/intercalation type isotherm as a tool for a quantitative description of electrochemical Li intercalation/deintercalation into various Li-insertion anodes and cathodes. Common and distinguished properties of such an intercalation process in a host material and adsorption of the same species on a metallic interface are compared and discussed, taking into account a pronounced difference in the corresponding potential profiles across the cells and possible kinetical rate-determining steps. The application of an equation combining the Frumkin isotherm with the conventional Butler–Volmer kinetics is exemplified by electrochemical Li insertion/deinsertion to/from a thin graphite and Li x CoO 2 electrodes. Four major electroanalytical techniques, SSCV, PITT, GITT and EIS, are frequently used for the determination of chemical diffusion characteristics of Li-ions. For these techniques, we have defined their characteristic time-invariant functions ( Iν −1/2, It 1/2, d E/d t 1/2 and A w, respectively) to present the diffusion time constant τ as a combination of one of these functions with the differential intercalation capacitance, C int. Such a presentation allows the above characteristic functions to be connected, and demonstrates the equivalence in application of the three differential techniques, PITT, GITT and EIS, for obtaining kinetic data. This conclusion was experimentally verified for a thin graphite anode and a Li x Ni 0.8Co 0.2O 2 cathode. This verification may have an important implication for the judicious utilization of GITT in distinguishing between possible rate-determining steps of a first-order phase transition. A common feature on the experimental plots of the chemical diffusion coefficient of Li +, D vs. the potential observed for a variety of Li-insertion compounds, appears in the form of a deep minima corresponding to the peak values of the differential intercalation capacitance. Taking into account a limitation due to Li transfer across the particle/solution interface and the intercalation process described by a Frumkin intercalation isotherm, log D vs. E curves could be simulated for Li insertion electrodes. We can explain the deviation of the experimental current vs. time plots during a PITT of Li insertion electrodes from the theoretical plots in the long-time domain, in terms of the distribution in their particle size.