Thermodynamics of Electrochemical Energy Storage

This intelligible equation is obtained rigorously when splitting the chemical potential of lithium into the contributions of the lithium ions and the electrons (//Li=fiLi + the difference of the first vanishes due to the presence of the electrolyte, and the difference of the second determines the voltage measured. 

The bracketed difference is the Gibbs energy of the reaction that would occur on direct contact. As the Gibbs energy differs from the reaction enthalpy by TAS (T thermodynamic temperature, AS reaction entropy), a positive AS would result in theoretical efficiencies greater than 100% (then the environment would cool). Usually, those efficiencies are approximately 100%, as AS is negligible. This high theoretical efficiency is another asset of electrochemical conversion devices. 

The second quantity besides cell voltage that is important here is the equilibrium storage capacity. This quantity follows from the defect chemistry and phase thermodynamics. 

Let us for simplicity assume the storage to solely occur through 

If the two defects on the right-hand side are dilute, an ideal mass action law can be formulated. The defect concentrations can be connected with the nonstoichiometry (8 = i- v i interstitial Lithium concentration v Lithium vacancy concentration), which is proportional to the storage capacity, while the lithium activity (see the 

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