Gas Models of Chemisorbed Systems

As mentioned in Sect. I, even the simplest electrosorption systems are extremely complicated. This complexity means that a comprehensive theoretical description that enables predictions for phenomena on macroscopic scales of time and space is still generally impossible with present-day methods and technology. (Note that MD simulations, such as those presented in Sect. II, are only possible up to times of a few himdred nanoseconds.) Therefore, it is necessary to use a variety of analytical and computational methods and to study various simplified models of the solid-hquid interface. One such class of simpHfied models are LG models, in which chemisorbed particles (solutes or solvents) can only be located at specific adsorption sites, commensurate with the substrate s crystal structure. This can often be a very good approximation, for instance, for halides on the (100) surface of Ag, for which it can be shown that the adsorbates spend the vast majority of their time near the fourfold hollow surface sites. A LG approximation to such a continuum model, appropriate for chemisorption of small molecules or ions, ° is defined by the discrete, effective grand-canonical Hamiltonian, 

the lattice sites / are the preferred adsorption sites (the minima of the continuous corrugation potential), and c is a local occupation variable, with 1 corresponding to an adsorbed particle and 0 to a solvated site. The sums and run over all nth-neighbor pairs and over all adsorption sites, respectively, is the effective nth-neighbor pair interaction, and runs over the interaction 

To connect the electrochemical potentials to the concentrations in bulk solution of species X, [X], and the electrode potential, E, one has (in the dilute-solution approximation) 

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