Micro‐Macroscopic Coupled Modeling of Batteries and Fuel Cells: I. Model Development

A micro-macroscopic coupled model, aimed at incorporating solid-state physics of electrode materials and interface morphology and chemistry, has been developed for advanced batteries and fuel cells. Electrochemical cells considered consist of three phases: a solid matrix (electrode material or separator), an electrolyte (liquid or solid), and a gas phase. Macroscopic conservation equations are derived separately for each phase using the volume averaging technique and are shown to contain interfacial terms which allow for the incorporation of microscopic physical phenomena such as solid-state diffusion and ohmic drop, as well as interfacial phenomena such as phase transformation, precipitation, and passivation. Constitutive relations for these interfacial terms are developed and linked to the macroscopic conservation equations for species and charge transfer. A number of nonequilibrium effects encountered in high-energy-density and high-power-density power sources are assessed. Finally, conditions for interfacial chemical and electrical equilibrium are explored and their practical implications are discussed. Simplifications of the present model to previous macrohomogeneous models are examined. In a companion paper, illustrative calculations for nickel-cadmium and nickel-metal hydride batteries are carried out. The micro-macroscopic model can be used to explore material and interfacial properties for desired cell performance.