where i0 denotes the exchange current density (SI unit: A/ m
2),
γ the reaction order (dimensionless),
αa the anodic charge transfer coefficient (dimensionless),
αc the cathodic charge transfer coefficient (dimensionless). The overpotential,
η, is according to the following equation:
During a discharge, the active surface area, av (SI unit: m
2/ m
3), is calculated using the equation below:
where ζ is a
morphology correction parameter (dimensionless). This surface area can also be used for side-reactions such as oxygen evolution and oxygen reduction and the non-faradaic double layer currents.
In the charging reactions, PbSO4 is a reactant but also an insulator, reducing the available active surface area. To account for this effect, the following expression can be used for the active surface area for the charging reactions:
