Charge Transfer Kinetics in LiFePO4 Porous Electrodes: Butler-Volmer Equation Vs Marcus Theory

The local rates of charge transfer in carbon-coated LiFePO₄ porous electrodes are extracted from chronoamperometry experiments by a simple statistical theory,¹ which yield curved Tafel plots that cannot be explained by the standard Butler-Volmer (BV) model for lithium intercalation. The microscopic Marcus-Hush-Chidsey (MHC) model,²  however, accurately captures the deviation from the Tafel slope (α=0.5) at overpotentials larger than 150mV. The fitted reorganization energy is in excellent agreement with the Born solvation energy for electron transfer between the carbon coating and the Fe²⁺/Fe³⁺ redox site estimated from first principles dielectric properties, which implies that the kinetics are limited by electron transfer at the solid (carbon) – solid (Li_xFePO₄) interface, rather than by lithium ion transfer at the liquid (electrolyte) – solid interface, as previously assumed. This discovery suggests the need for a paradigm shift in mathematical modeling of electrochemical systems, replacing the BV equation with quantum mechanical theories of electron transfer³ and incorporating statistical effects of non-equilibrium thermodynamics.⁴ The proposed method of chronoamperometry and Tafel analysis generalizes Chidsey’s method for homogeneous monolayers and allows fundamental rate constants to be determined for phase-transforming particles and porous electrodes.

References

1.    Bai, P., Tian, G.Y. Statistical kinetics of phase-transforming nanoparticles in LiFePO4 porous electrodes. Electrochim. Acta 89, 644-651 (2013).

2.    Chidsey, C.E.D. Free-Energy and Temperature-Dependence of Electron-Transfer at the Metal-Electrolyte Interface. Science 251, 919-922 (1991).

3.    Marcus, R.A. Electron-Transfer Reactions in Chemistry - Theory and Experiment. Reviews of Modern Physics 65, 599-610 (1993).

4.    Bazant, M.Z. Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics. Acc. Chem. Res. 46, 1144-1160 (2013).

Figure

Tafel plot of the reaction rates extracted from chronoamperometry experiments, which deviate from the Butler-Volmer (BV) model, but can be captured by the Marcus-Hush Chidsey (MHC) model. Overpotentials are scaled to the thermal voltage k_BT/e≈25.7mV.