Discreteness of charge

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

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,... 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

James, R. 0., and Mealy, T. W, Adsorption of hydrolyzable metal ions at the oxide-water interface III. A thermodynamic model of adsorption, J. Colloid Interface Sci. 40, 65-81(1972). Levine, Samuel, Remarks on Discreteness of charge and solvation effects in cation adsorption at the oxide/water interface, by Wiese, G. R., James, R. 0., and Mealy, T. W., Discussions of the Faraday Soc. 52, 41A-42A (1971). 

Wiese, G. R., James, R. 0., and Mealy, T. W. Remarks on Discreteness of charge and solvation effects in cation adsorption in the oxide/water interface, by Wiese, G. R., James,... 

The approximations involved in simplifications (i) and (li) are not too farfetched. Discreteness of charge, with the ensuing multi-imaging, tends to... 

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 . 

Estimation of the discreteness-of-charge potential requires a detailed model of the interfacial region which gives its dielectric properties and the location of images in the conducting metal phase. According to the model developed by... 

A Model of the Electric Double Layer at a Completely Ionized Monolayer with Discreteness-of-Charge Effect... 

Tphe discreteness-of-charge effect (discrete-ion effect) is a general char-acteristic of electric double layers in aqueous media (I) and therefore should manifest itself in ionized monolayers. In a number of papers (2,3,4,5), one of the authors and co-workers investigated the role of this... 

As the electrolyte concentration is low and the Debye radius many times exceeds this distance an identification of the potential in this zone with the potential of the adsorbing ions is reasonable. At high electrolyte concentration the diffuse layer thickness can be comparable to this distance. Even if the counterions are indifferent their distribution in this layer cannot be neglected because it decreases the electrostatic component of surfactant ion adsorption., i.e. enhance its adsorption. In this case we have to consider a discreteness of charges must, the formation of a counter ion atmosphere around the adsorbed ions and their overlap with the neighbour adsorbed ions. 

In addition, the GCS model involves average potentials in the vicinity of the electrode and ignores the discrete nature of charges in solution. Such discreteness of charge effects have been treated and invoked to account for failures in the usual double-layer corrections (67). 

Discreteness of Charge Charged colloidal species usually obtain their... 

In the simple GCSG model already described, the charge densities are assumed uniformly smeared over each plane rather than in the form of discrete ions. Levine and co-workers [8] modified the GCSG model by introducing the discreteness of charge effect to account for various phenomena, mostly relating to adsorption at the mercury/water and silver iodide/water interfaces. Their theory shows that the electrostatic work of adsorption at the IHP is not zet /p but... 

---