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. 

http://www.seas.harvard.edu/suo/papers/297.pdf International Journal of Applied Mechanics (In Press).