Three-dimensional conductivity model for porous electrodes in lead acid batteries

Abstract

In this paper, the critical volume fraction (CVF) of electrodes having porosity is predicted with the help of a three-dimensional (3D) conductivity model. The model consists of a 3D lattice of nodes; which in this paper, are assumed to be identical spheres, which are in electrical contact with their neighbors. The porosity that exists between these spheres is referred to as “micro-porosity” while the porosity that occurs from having missing spheres is referred to as “macro-porosity”. The critical volume fraction is the maximum utilization of an electrode's active material and occurs when the electrode's conductivity changes from being conductive to nonconductive. Previous 3D conductivity models used to determine the CVF did not account for porosity. The porosity is modeled from porosity size distribution previously determined experimentally by other researchers. The sphere size of the model is estimated from these porosity distributions and by assuming a simple cubic (SC) lattice structure as the sphere arrangement. Because the porosity between the spheres (i.e. “micro-porosity”) for such an arrangement is 48%, the sphere size can be estimated from the pore size where this value of electrode porosity occurs. Porosity smaller than this sphere size is assumed to be smaller than a single sphere, and to be counted as part of the 48% porosity that exists between the spheres. Porosity above the single sphere size is modeled with nonconductive additives having the same pore size as the porosity being modeled. This approach is therefore used to determine both the sphere size in the model as well as the influence of porosity on the critical volume fraction. The model provides reasonable estimates of the critical volume fraction of positive electrodes having porosity and agrees with experimental data.