Discrete Charge Effect

Potential Distribution Around a Nonuniformly Charged Surface and Discrete Charge Effects... 

Many attempts have been made to improve the classical Poisson-Boltzmann equation to include discrete charge effects, finite ion size, and so on (see, e.g., Refs. 35-37). At present some fundamental progress is being made on the basis of certain models in modem fluid-state theory, in which the hard-core repulsions of the ions are incorporated in a consistent way. " The Poisson-Boltzmann equation was found to be a limiting case of the hypernetted chain approximation at low densities. Also a computer simulation was reported." ... 

Nonspecific adsorption phenomena have often been discussed in terms of discrete charge effects. In order to describe the Stern type of adsorption of ions, the adsorption of a particular ion is considered to involve the rearrangement of the existing ions so as to form a hole for the ion to be adsorbed and then the adsorption of this ion at the hole, where the potential would be smaller than that calculated on the basis of a smeared surface charge. It has been shown that the rearrangement of ions to form a hole requires only a little energy so that the important problem is the calculation of the potential in the hole, known as the micropotential (local potential). 

J. C. Gil Montoro and J. L. F. Abascal, Molec. Phys., 89, 1071 (1996). Discrete Charge Effects on the Structure of Ions around Polyelectrolyte Models. 

Barlow, C. A., and J. R. MacDonald, Theory of discreteness of charge effects in the electrolyte compact double layer, AE, 6, 1 (1967). 

A. P. Winiski, A. C. McLaughlin, R. V. McDaniel, M. Eisenberg, and S. McLaughlin, An experimental test of the discreteness-of-charge effect in positive and negative lipid bilayers,... 

In XPS, on the other hand, photoelectrons, which are emitted when the sample surface is irradiated with a beam of x-rays, are analyzed. The emitted photoelectrons have discrete binding energies that are dependent on both the identity of the parent element and its chemical environment in the surface. Therefore, both the concentration and the chemical state of an element in the surface can be determined. Two advantages of XPS are that the incident x-ray beam is practically harmless to the surface and it also does not induce charging effects, so that the surface chemistry of adhesives and other insulators can readily be investigated 171 ... 

The influence of specific adsorption of nonreacting ions, chiefly anions, upon electrode kinetics at Hg electrodes is available from experiment and theory " . Equation (a) often proves to be approximately applicable, at least when the difference between the reaction plane and the outer Helmholtz plane are taken into account. However, marked discrepancies are noted that are attributed to local interactions between the reactant and the absorbing ions, including discreteness-of-charge effects - - . ... 

Additional alterations in the work terms with the electrode material for outer-sphere reactions may arise from discreteness-of-charge effects or from differences in the nature of the reactant-solvent interactions in the bulk solution and at the reaction plane. Thus metals that strongly chemisorb inner-layer solvent (e.g., HjO at Pt) also may alter the solvent structure in the vicinity of the outer plane, thereby influencing k bs variations in the stability of the outer-sphere precursor (and successor) states. Such an effect has been invoked to explain the substantial decreases (up to ca. 10 -fold) in the rate constants for some transition-metal aquo couples seen when changing the electrode materiaf from Hg to more hydrophilic metals such as Pt. Much milder substrate effects are observed for the electroreduction of more weakly solvated ammine complexes . 

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