Diffuse electric layer region

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

At a semiconductor-electrolyte interface, if there is no specific interaction between the charge species and the surface an electrical double layer will form with a diffuse space-charge region on the semiconductor side and a plate-like counter ionic charge on the electrolyte side resulting in a potential difference (j) across the interface. The total potential difference across the interface can be given by... 

Since the diffusion coefficient of the dust particles is very small, the thickness of the diffusion boundary layer is small compared to the radius R of the collector. Therefore, the concentration distribution and the rate of deposition can be calculated by substituting for the velocity and electric fields the expressions valid for y/R 1. In that region, Eqs. (182) and (183) become... 

The electric field which actually affects the charge transfer kinetics is that between the electrode and the plane of closest approach of the solvated electroactive species ( outer Helmholtz plane ), as shown in Fig. 2.2. While the potential drop across this region generally corresponds to the major component of the polarization voltage, a further potential fall occurs in the diffuse double layer which extends from the outer Hemlholtz plane into the bulk of the solution. In addition, when ions are specifically absorbed at the electrode surface (Fig. 2.2c), the potential distribution in the inner part of the double layer is no longer a simple function of the polarization voltage. Under these circumstances, serious deviations from Tafel-like behaviour are common. 

It is postulated that one of the ions of the adsorbed 1 1 electrolyte is surface active and that it forms an ionized monolayer at the solid/liquid interface. All counterions are assumed located in the diffuse double layer (no specific adsorption). Similions are negatively adsorbed in the diffuse double layer. Since the surface-containing region must be electrically neutral, the total moles of electrolyte adsorbed, n2a, equals the total moles of counterions in the diffuse double layer which must be equal to the sum of the moles of similions in the diffuse double layer and the charged surface, A[Pg.158]

Figure 2 Conventional representation of micelles formed by an ionic surfactant, such as sodium dodecyl sulfate. The inner core region consists of the methylene tails of the surfactants. The Stem layer consists of surfactant headgroups and bound counterion species. The diffuse double layer consists of unbound counterions and coions which preserve the electrical neutrality of the overall solution. Also pictured are the transition moment vectors for the S-O stretching modes of sodium dodecyl sulfate.

At oxide semiconductor electrode-electrolyte interfaces, with no contribution from surface states, the electrical potential drop exhibits three components the potential drop across the space-charge region, sc, across the Helmholtz layer, diffuse double layer, d, the latter becoming negligible in concentrated electrolytes... 

The charged surface layer and the diffuse region together constitute the diffused electrical double layer (Fuerstenau, 1976). 

For the non-ideal behaviour of a system which contains a single component able to exist in different states, the rigorous thermodynamic expressions are far more complicated than those given above. The relevant mathematical formalism becomes yet more involved if the contributions of ionisation to the surface pressure of the adsorption layer and the chemical potentials of surface active ions located in the diffuse region of the double electric layer are taken into account. Therefore, to describe the adsorption behaviour of a protein/surfactant mixture, some assumptions have to be introduced which simplify the problem significantly. 

Simple diffusion from a flat surface through an unstirred layer 0.025 cm thick would result in a solute permeability 20-10 cm/s. Thus, the value of computed for this model, 5.5-10 cm/s, signifies that solute transport into an interspace bounded by a basement membrane retards its diffusion from the region adjacent to the cell membrane by a factor of four. The permeability can also be translated into an electrical resistance, R, by use of the formula... 

Additional issues arise when reduction of the size of a semiconductor is considered. In bulk semiconductors the valence and conduction bands bend. Because of the low carrier concentration, the electrical double layer in a bulk semiconductor/solution system extends into the interior of the semiconductor rather than into the solution. In terms of the Gouy Chapman model, the width of a diffuse double layer is inversely proportional to the square root of the carrier concentration for a typical semiconductor carrier concentration of 10 cm the band bending is calculated to occur over several hundred nanometers (in which region there is about one carrier). 

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