Reactive Flow in Large-deformation Electrodes of Lithium-ion Batteries

An electrode in a lithium-ion battery may undergo inelastic processes of two types: flow and reaction. Flow changes the shape of the electrode, preserves its composition and volume, and is driven by the deviatoric stress — a process similar to the plastic flow of a metal. By contrast, reaction changes the composition and volume of the electrode, and is driven by a combination of the mean stress and the chemical potential of lithium in the environment. Both flow and reaction are mediated by breaking and forming atomic bonds. Here we formulate a continuum theory of large-deformation electrodes by placing flow and reaction on the same footing. We treat flow and reaction as concurrent nonequilibrium processes, formulate a thermodynamic inequality and a rheological model, and couple the two processes through a chemomechanical flow rule. Within this theory, the driving force for reaction — the mean stress and the chemical potential — can stimulate flow in an electrode too brittle to flow under a mechanical load alone. For an electrode under vanishingly small stress and current, cyclic lithiation and delithiation can cause hysteresis in the voltage-concentration curve. For a thin-film electrode bonded on a substrate, cyclic lithiation and delithiation can cause hysteresis in both the voltage-concentration curve and the stress–concentration curve.