Thermodynamics of Intercalation and Deintercalation

In this respect, this chapter details the fundamentals and most important advances in the research activities on lithium intercalation into and deintercalation from transition metals oxides and carbonaceous materials, especially from thermodynamic and kinetic points of view, including methodological overviews. The thermodynamics of lithium intercalation/deintercalation is first introduced with respect to a lattice gas model with various approximations, after which the kinetics of lithium intercalation/deintercalation are described in terms of a cell-impedance-controlled model. Finally, some experimental methods which have been widely used to explore the thermodynamics and kinetics of lithium intercalation/deintercalation are briefly overviewed. 

Consider an electrochemical cell with a solid host MO2 as one electrode, an alkali metal A as the other electrode, and an electrolyte in which the monovalent cation A + is dissolved. The intercalation/deintercalation between the host MO2 and the guest ion A is given by Equation (5.1). On the other hand, the redox reaction between A and A may be written as 

As described previously, the main aspect of intercalation/deintercalation from a thermodynamic view point is that the concentration of the guest ion can change, without any change in the space group and lattice parameter of the host structure. Under electrochemical equilibrium conditions, therefore, the galvanic potential difference between two electrodes - that is, the cell voltage - can be derived as  

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 

The chemical potential - that is, the change in the Gibbs free energy G with the number of the intercalated ions (n) - can be divided into two parts related to the enthalpy (fi) and entropy (S) variations  

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Apart from the work toward practical lithium batteries, two new areas of theoretical electrochemistry research were initiated in this context. The first is the mechanism of passivation of highly active metals (such as lithium) in solutions involving organic solvents and strong inorganic oxidizers (such as thionyl chloride). The creation of lithium power sources has only been possible because of the specific character of lithium passivation. The second area is the thermodynamics, mechanism, and kinetics of electrochemical incorporation (intercalation and deintercalation) of various ions into matrix structures of various solid compounds. In most lithium power sources, such processes occur at the positive electrode, but in some of them they occur at the negative electrode as well. 

Another interesting thermodynamic phenomenon caused by the strong interaction of lithium ions is a two-phase coexistence during lithium intercalation and deintercalation that is, when intercalation/deintercalation proceeds in equilibrium between the Li-depleted and Li-rich phases (see Section 5.2.2). Pyun et al. also applied the Monte Carlo method to determine the mechanism of lithium intercalation into Lii I s[Ti5/3Li]y3 O4 in the two-phase domain [28]. For the cubic-spinel Lii+8 Ti5/3Lii/3]O4, both 8(a) and 16(c) sites are occupied by lithium ions each 8(a) site is adjacent to four first-nearest 16(c) and four second-nearest 8(a) sites, and each 16(c) site is surrounded by two first-nearest 8(a) and six second-nearest 16(c) sites. According to the model [28], the lattice Hamiltonian is defined as... 

In this chapter we have summarized the fundamentals and recent advances in thermodynamic and kinetic approaches to lithium intercalation into, and deintercalation from, transition metals oxides and carbonaceous materials, and have also provided an overview of the major experimental techniques. First, the thermodynamics oflithium intercalation/deintercalation based on the lattice gas model with various approximations was analyzed. Lithium intercalation/deintercalation involving phase transformations, such as order-disorder transition or two-phase coexistence caused by strong interaction oflithium ions in the solid electrode, was clearly explained based on the lattice gas model, with the aid of computational methods. 

Finally, a brief overview was presented of important experimental approaches, including GITT, EMF-temperature measurement, EIS and PCT, for investigating lithium intercalation/deintercalation. In this way, it is possible to determine - on an experimental basis - thermodynamic properties such as electrode potential, chemical potential, enthalpy and entropy, as well as kinetic parameters such as the diffusion coefficients of lithium ion in the solid electrode. The PCT technique, when aided by computational methods, represents the most powerful tool for determining the kinetics of lithium intercalation/deintercalation when lithium transport cannot be simply explained based on a conventional, diffusion-controlled model. 

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