Interaction between intercalation sites

Here g is measure of interaction between intercalation sites in the Frumkin isotherm, and X is the degree of occupation of intercalation sites. X can be expressed from the charge Q passed during intercalation as X = Q/Qmax, where is the maximum charge stored by the particular intercalation phase. In many cases, such as intercalation into graphite, multiple phases are present and therefore the entire intercalation region must be subdivided into subregions for analysis. 

Slow galvanostatic charging, SSCV, and one of the incremental titration techniques (PITT or GITT) provide valuable information on the experimental charge, Q, vs. potential, E, or differential intercalation capacitance, Cdif vs. potential, E, curves. These, in turn, are important for describing the occupation of the host lattice sites by inserted ions and (or) electrons in terms of intercalation isotherms. Short-range interactions between the inserted ions and lattice distortions affect greatly the shape of intercalation isotherms. 

In order to explore the thermodynamic properties, and especially the chemical potential ofthe intercalation compounds, a lattice gas model [10] has been adopted under the assumption that intercalated ions are localized at specific sites in the host lattice, with no more than one ion on any site, and that local and global electroneutrality is observed and there is no strong interaction between the electrons and the intercalated ions. It should be noted that, in solid-state chemistry, this model is often referred to as ideal solution approximation when used to describe the thermodynamics of nonstoichiometric compounds. According to this model, the chemical potential of A in A8MO2 in Equation (5.3) can be divided into two terms as... 

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