Governing Equations in the Macro Scale

A Li-ion battery usually consists of a composite cathode, a separator and an anode. The outer ends of the batteries are connected to a current collector that channels the electrons produced out to the load circuit. 

The composite cathode usually consists of an inert conducting material, the polymer/salt electrolyte, and the solid active insertion particles. The key requirements for a material to be successfully used as a cathode in a rechargeable lithium battery are as follows  

LiCo02 is a standard candidate which has been successfully used in the portable electronics industry. 

Porous electrode theory assumes that medium is a superposition of continuous solid and electrolyte phases with a known vo-Inme fraction. The solid phase potential of the positive electrode is because of electronic conduction  

The solid phase current is related to the potential gradient as 

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