Formulation of the coupled electrochemical–mechanical boundary-value problem, with applications to transport of multiple charged species

A framework is presented that treats the combined effects of nonlinear elastic deformation, lattice constraints, and electrochemical potentials. The electro-chemo-mechanical diffusion potential is derived, and the particular case where ionic species are subject to a crystal lattice constraint is also derived. By combining energy balance and local entropy production, the framework provides a consistent method to treat the evolution of charged species which also carry anelastic deformations in a crystal lattice. The framework is used to derive a finite element formulation that applies to general cases of interest for diffusion of active species in battery electrodes and in fuel cells. We demonstrate the application of the finite element formulation with two cases: ambipolar diffusion and kinetic demixing. The predicted system response demonstrates how mechanical effects cannot be disregarded, even in the presence of dominant electrostatic forces acting on ion transport. A cation rich surface layer is predicted when elastic forces, due to Vegard's stress, participate in the migration of defects in a multicomponent oxides. Simulations show how stress plays a central role in the cation segregation to interfaces, a phenomenon regarded as critical to power and durability of solid oxide fuel cells.

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