How lithium-ion batteries work conceptually: thermodynamics of Li bonding in idealized electrodes

A good explanation of lithium-ion batteries (LIBs) needs to convincingly account for the spontaneous, energy-releasing movement of lithium ions and electrons out of the negative and into the positive electrode, the defining characteristic of working LIBs. We analyze a discharging battery with a two-phase LiFePO₄/FePO₄ positive electrode (cathode) from a thermodynamic perspective and show that, compared to loosely-bound lithium in the negative electrode (anode), lithium in the ionic positive electrode is more strongly bonded, moves there in an energetically downhill irreversible process, and ends up trapped in the positive electrode. Only a sufficiently high charging voltage can drive it back to the other electrode. Since the stronger bonding in the positive electrode lowers the energy by ∼320 kJ mol^-1, a lot of energy is released. This explanation is quantitatively supported by an analysis of cohesive-energy differences of the electrode materials. Since electrons are only intermediates in the discharge reaction and the chemical potential of the electron cannot be measured, electrons do not need to be assigned a distinct energetic role. The incorporation of Li⁺ and an electron into the cathode is accompanied by the reduction of another ion or atom, usually a transition metal such as Fe or Co. The metal's ionization energy in the corresponding oxidation step correlates with the cell voltage, based on a decomposition of cohesive energy into electronic and ionic components. We relate the differences in cohesive energies to the chemical potential of lithium atoms, which is quantified, for instance for a two-phase electrode. The analysis is extended to a single-phase LiCoO₂ cathode, whose average voltage can be calculated from the cohesive-energy difference between LiCoO₂ and CoO₂.