Reaction rate distribution across porous electrodes in Li-ion battery applications largely determines the overall battery performance. In the present work, expressions for the reaction rate distribution across porous electrodes are analytically derived and analyzed for small current and short time applications. The dependency on the effective ionic and electronic conductivities is systematically investigated and discussed. It is found that in the case of equal effective electronic and ionic conductivities, the reaction rate distribution is symmetric around the electrode mid-point. Small conductivities induce the charge-transfer reaction to preferentially occur at the interface of the current collector and separator, while high conductivities make the reaction rate distribution uniform across the electrode thickness. In the case of unequal conductivities, a decrease in the effective electronic conductivity shifts the reaction rate distribution towards the electrode/current collector interface. In contrast, a decrease in the effective ionic conductivity shifts the reaction rate distribution towards the electrode/separator interface. It is also found that the reaction rate distribution shows saturating behavior when the effective electronic or ionic conductivity grows infinitely. A further increase in the effective ionic or electronic conductivity does not lead to any further reaction rate distribution changes.
- Effective electronic conductivity
- Effective ionic conductivity
- Porous electrode
- Reaction rate distribution