Effective Representation of Active Material and Carbon Binder in Porous Electrodes

Active cathode material and graphite anode material are routinely mixed with conductor and binder to improve the electric conductivity and mechanical stability of electrodes. Despite its benefits, this carbon binder domain (CBD) impedes ionic transport and reduces the active surface area, thus impacting the battery performance. We consider a composite spherical particle, whose active-material core is coated with CBD, and its homogeneous counterpart, for which we derived equivalent electrical conductivity, ionic diffusivity, and reaction parameters in the Butler-Volmer equation. These equivalent characteristics are defined to ensure that the same mass and charge enter the composite and homogenized spheres. They are expressed in terms of the volume fraction of the active material and transport properties of the active material and CBD. In general, the equivalent effective diffusion coefficient and reaction parameters are time-dependent and exhibit two-stage behavior characterized by the reaction delay time. At later times, these characteristics are time-independent and given explicitly by closed-form formulae. The simplicity of these expressions facilitates their use in single- and multi-particle representations of Li-ion and Li-metal batteries.