Arbitrary Potential General Electrolytes

In the case of a charged plate immersed in a general electrolyte, the Poisson-Boltzmann equation (1.20), in terms of the scaled potential y(x) = eiff/kT, is rewritten as 

Note that as j 0,yij ) Exphcit expressions for/(y) for some simple cases are given below. 

The surface charge density-surface potential (cr-yo) relationship is obtained from Eqs. (1.23) and (1.55) and given in terms of/(yo) as 

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Voltammetric potential limits are an important special case of the general issue of background current. In the simplest case, an electrode will exhibit only capacitive current over some potential range, with no redox reactions of either the electrode surface or the electrolyte. As the potential is scanned away from this double-layer region, eventually the surface or the solvent will begin to oxidize or reduce, until the current exceeds that from the redox process under study. The potential limit for an electrode/electrolyte combination is usually considered to be the potential where the voltammetric background current exceeds some arbitrary value. This value depends on scan rate, electrode area, etc., but nevertheless provides a useful comparison of electrodes and solvents. 

An alternative description of a molecular solvent in contact with a solute of arbitrary shape is provided by the 3D generalization of the RfSM theory (3D-RISM) which yields the 3D correlation functions of interaction sites of solvent molecules near the solute. It was first proposed in a general form by Chandler, McCoy, and Singer [22] and recently developed by several authors for various systems by Cortis, Rossky, and Friesner [23] for a one-component dipolar molecular liquid, by Beglov and Roux [24, 25] for water and a number of organic molecules in water, and by Hirata and co-workers for water [26, 27], metal-water [26, 28] and metal oxide-water [31] interfaces, orientationally dependent potentials of mean force between molecular ions in a polar molecular solvent [29], ion pairs in aqueous electrolyte [30], and hydration of hydrophobic and hydrophilic solutes alkanes [32], polar molecule of carbon monoxide [33], simple ions [34], protein [35], amino acids and polypeptides [36, 37]. It should be noted that accurate calculation of the solvation thermodynamics for ionic and polar solutes in a polar molecular liquid requires special corrections to the 3D-RISM equations to eliminate the electrostatic artifacts of the supercell treatment employed in the 3D-RISM approach [30, 34]. 

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