Intercalate ion ordering

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... 

For most insertion compounds, the interaction of intercalated ions with each other in the host lattice is not negligible. In order to simply consider the contribution of ionic interaction in Equation (5.8), it is often assumed that each ion experiences a mean interaction or energy field from its neighboring ions, based on a mean-field theory [10]. According to this approximation, the contribution to the chemical potential is proportional to the fraction of sites occupied by the ions 5, and hence the interaction term is introduced into Equation (5.8) as... 

A glance at the structure of graphite, illustrated in Fig. 1, reveals the presence of voids between the planar, sp -hybridized, carbon sheets. Intercalation is the insertion of ions, atoms, or molecules into this space without the destruction of the host s layered, bonding network. Stacking order, bond distances, and, possibly, bond direction may be altered, but the characteristic, lamellar identity of the host must in some sense be preserved. 

In the intercalation reactions, ions (anions X or cations M+) penetrate into the van der Waals gaps between the ordered carbon layers resulting in the enlargement of their inter-layer distance [23,24]. The corresponding charges are conducted by carbon and accepted into the carbon host lattice. 

The electrons, if they are separated from the ions, will also contribute to the entropy, and one might naively expect an expression similar to Eqn (7.8). Then the chemical potential for an atom would be the sum of two terms like Eqn (7.10), one from ions and one from electrons, and so the entropy term would be doubled. This is not so, however, in metallic intercalation compounds. In metals, the entropy of electrons is small. Electrons added by intercalation do not have a choice of all the empty states in a band, but only those within kT of the Fermi energy. If the Fermi energy is expressed as a temperature Tp and is measured from the bottom of the band, the change in entropy with the number n of electrons, dS/dn, is of order kTfTj (Kittel, 1971), not of order k like Eqn (7.8) for... 

The inner structure of polyelectrolyte multilayer films has been studied by neutron and X-ray reflectivity experiments by intercalating deuterated PSS into a nondeut-erated PSS/PAH assembly [94, 99]. An important lesson from these experiments is that polyelectrolytes in PEMs do not present well-defined layers but are rather interpenetrated or fussy systems. As a consequence, polyelectrolyte chains deposited in an adsorption step are intertwined with those deposited in the three or four previous adsorption cycles. When polyelectrolyte mobility is increased by immersion in NaCl 0.8 M, the interpenetration increases with time as the system evolves towards a fully mixed state in order to maximize its entropy ]100]. From the point of view of redox PEMs, polyelectrolyte interpenetration is advantageous in the sense that two layers of a redox polyelectrolyte can be in electrochemical contact even if they are separated by one or more layers of an electroinactive poly ion. For example, electrical connectivity between a layer of a redox polymer and the electrode is maintained even when separated by up to 2.5 insulating bUayers [67, 101-103]. 

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