Currently existing theories and models to describe rechargeable lithium-ion batteries are based on the well-established porous electrode theory, which assumes a uniform mixture of reactive solid particles and ignores the geometrical details of the pores, particle segregation, and clustering, particle roughness, and crystallographic or microstructural anisotropy. Such descriptions are currently based on average measures of the transport and equilibrium properties of the underlying 
phases. Specifically, the tortuosity and porosity of currently used electrodes is described through the well-known Bruggeman relation for perfectly spherical particles. Experimentally, however, it has been found that material properties can greatly deviate from the perfect-sphere ideal. The current project has made contributions that extend the well-established porous electrode theory to overcome these deficiencies. We are developing theories that capture the average response of electrochemical systems, but will include the statistically rich spatial distribution of materials and associated microstructural properties.