Surface charge diffusion

Charged surface plus diffuse double layer of ions —>... 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

This treatment assumes the surface charge to be diffused over a thickness 7... 

From the ion density profiles it is obvious that the surface charge is screened within less than 10 A. Thus, the thickness of the diffuse layer is of the same order of magnitude as the one derived from the Debye... 

In the polar pores, the diffusion coefficient of all ions is strongly reduced relative to the bulk values. No counterion dependence is observed for the SDC of CP. A more detailed analysis shows that the ion SDC depends on the ion s relative position in the pore [174]. In the case of the K ion, this dependence is particularly strong. K ions forming contact pairs with the surface charges are almost completely immobilized on the time scale of the simulations. The few remaining ions in the center of the pore are almost unaffected by the (screened) surface charges. The fact that most of the K ions form contact pairs substantially reduces the average value of the normalized K SDC to 0.2. The behavior of CP is similar to that of K. The SDC of sodium ions, which... 

If substrate diffusion becomes rate determining, only a small fraction of the film at the film/solution interface will be used. On the other hand, if charge diffusion becomes rate determining, the catalytic reaction can take place only in a film fraction close to the electrode surface. Each of these effects will render parts of the film superfluous, and it is obvious that there is no sense in designing very thick redox films, rather there is an optimal layer thickness to be expected depending on the individual system. 

Ohshima, H Kondo, T, Electrophoretic Mobility and Donnan Potential of a Large Colloidal Particle with a Surface Charge Layer, Journal of Colloid and Interface Science 116, 305, 1987. O Neil, GA Torkelson, JM, Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization, Macromolecules 32,411, 1999. 

FIG. 8 Inverse differential capacity at the zero surface charge vs. inverse capacity Cj of the diffuse double layer for the water-nitrobenzene (O) and water-1,2-dichloroethane (, ), interface. The diffuse layer capacity was evaluated by the GC ( ) or the MPB (0,)> theory. (From Ref. 22.)... 

As the membrane has a surface charge leading to formation of a diffuse electrical layer, the adsorption of ions on the BLM is affected by the potential difference in the diffuse layer on both outer sides of the membrane 02 (the term surface potential is often used for this value in biophysics). Figure 6.12 depicts the distribution of the electric potential in the membrane and its vicinity. It will be assumed that the concentration c of the transferred univalent cation is identical on both sides of the membrane and that adsorption obeys a linear isotherm. Its velocity on the p side of the membrane (see scheme 6.1.1) is then... 

The aqueous diffusivities of charged permeants are equivalent to those of uncharged species in a medium of sufficiently high ionic strength. The product DF(r/R) is the effective diffusion coefficient for the pore. It is implicit in k that adsorption of the cations does not occur, so that the fixed surface charges on the wall of the pore are not neutralized. Adsorption is more likely to occur with multivalent cations than with univalent ones. 

The experimental data bearing on the question of the effect of different metals and different crystal orientations on the properties of the metal-electrolyte interface have been discussed by Hamelin et al.27 The results of capacitance measurements for seven sp metals (Ag, Au, Cu, Zn, Pb, Sn, and Bi) in aqueous electrolytes are reviewed. The potential of zero charge is derived from the maximum of the capacitance. Subtracting the diffuse-layer capacitance, one derives the inner-layer capacitance, which, when plotted against surface charge, shows a maximum close to qM = 0. This maximum, which is almost independent of crystal orientation, is explained in terms of the reorientation of water molecules adjacent to the metal surface. Interaction of different faces of metal with water, ions, and organic molecules inside the outer Helmholtz plane are discussed, as well as adsorption. 

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