  We propose a weak solution theory for the sharp interface limit of the
Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An
essential feature of this model is the use of Butler-Volmer kinetics for
lithium-ion insertion, which arises as a Robin-type boundary condition relating
the flux of the chemical potential to the reaction rate, itself a nonlinear
function of the chemical potential and the ion concentration. To pass through
the nonlinearity as interface width vanishes, we introduce solution concepts at
the diffuse and sharp interface level describing dynamics principally in terms
of an optimal dissipation inequality. Using this functional framework and under
an energy convergence hypothesis, we show that solutions of the Cahn-Hilliard
reaction model converge to a Mullins-Sekerka type geometric evolution equation.
