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In order to more accurately reflect the electrode voltage of a lithium battery, it can be expressed by the change of Gibbs free energy ΔG, or by the lithium chemical potential difference (μCLi, μALi) between the positive and negative electrodes:

Formally, the chemical potential of lithium can be divided into two parts: the electrochemical potential Δμe and the ionic chemical potential ΔμLi+, which further describe the change of Gibbs free energy in the positive and negative electrodes, as well as its relationship with electron and ion exchange. It is generally believed that electrons play a dominant role, for example, by substituting transition metals in olivine materials to produce transition metal ions with higher ionization potentials, a higher average voltage can be obtained, which is supported by many reports (J. Electrochem. Soc., 144, 1188 (1997); J.Phys.Chem.B,108,16093(2004).). To gain insight into the fundamental processes of electron and ion exchange in electrodes and their associated effects on battery performance, Ceder et al. developed the first first-principles calculations (Phys. Rev. B, 56(3), 1354(1997).). However, until now, there has not been a single experiment that can clearly describe the effect of electron-ion interaction on battery voltage.

Voltage is a key parameter that determines the performance of lithium-ion batteries, and the higher the average voltage, the higher the energy and power density. Theoretically, the potential of the lithium intercalation electrode is very related to the chemical potential of the electrons and ions, as well as the difference in the voltage of the battery, but the precise contribution of the electrons and lithium ions to the voltage remains unclear because these quantities cannot be obtained experimentally.