Gouy-Chapman profile

For two oppositely charged majority carriers with zq = z. s z the Gouy-Chapman-profile (see textbooks on electrochemistry) results which we write ( = x/A) here as... 

The solution of Eq. (5.220) for semiinfinite boundary conditions leads to the Gouy-Chapman profile [247]. Let us follow the treatment in Ref. [248] and change to the concentration as the variable. First, let us consider the case that only two equivalently (but oppositely) charged defects (subscripts + and -) are relevant (z+ = (z j = z). The bulk concentrations are equal for reasons of electroneutrality (c+oo = c oo = Coo). Oo combination with Eq. (5.215) we obtain the differential equation for the concentration enhancement ( + or C )... 

In Fig. 8 density profiles are presented for several values of charge density a on the wall and for the wall potential h = — and h= Fig. 9 contains the corresponding ionic charge density profiles. For the adsorptive wall potential h < 0) the profiles q z) in Fig. 9(a) and j (z) in Fig. 8(a) are monotonic, as in the Gouy-Chapman theory. For a wall which is neutral relative to the adsorption A = 0 the density profiles are monotonic with a maximum at the wall position. This maximum also appears on the charge... 

In the theoretical approaches of Poisson-Boltzmann, modified Gouy-Chapman (MGC), and integral equation theories such as HNC/MSA, concentration or density profiles of counterions and coions are calculated with consideration of the ion-waU and ion-ion in-... 

The potential of each channel may be composed of two potentials. One is an oxidation-reduction potential generating at the boundary surface between the Ag electrode and the lipid membrane. The other is a Donnan potential at the boundary between the lipid membrane and the aqueous medium or more generally a Gouy-Chapman electrical double-layer potential formed in the aqueous medium [24]. Figure 7 shows a potential profile near the lipid membrane. The oxidation-reduction potential would not be affected by the outer solution in short time, because the lipid membrane had low permeability for water. Then the measured potential change by application of the taste solution is mainly due to the change in the surface electrical potential. 

In the Gouy-Chapman diffuse layer the concentration-distance profile Is given by the Boltzmann distribution ... 

For a symmetric electrolyte near a neutral hard wall, there is no net charge and consequently no potential across the interface. In this case the mean field version of (28) that corresponds to the traditional Gouy-Chapman (GC) theory gives pi r) = poo and thus s(r) = 2poo = 00- Of course, for symmetrical ions we must have q(r) = 0 but there is a density profile. If we write, s(r) = Soo + Ss(r) and assume that Ss(r) and q(r) are small we may expand relation (29) in terms of these quantities and we obtain,... 

Figure 7. The effect of ion penetration (Fig. 6) coupled to smearing of the dielectric profile. Lines 1 and 2 correspond to the Gouy-Chapman behavior and Li = 0.3 nm from Fig. 6, respectively. Lines 3 and 4 are identical to line 2, except L3 is set to 0.02 nm and — 0.02 nm, respectively. (Reprinted with permission from Ref. 64 copyright 2001, Elsevier SA.)...

Figure 13.3.3 Potential profiles through the diffuse layer in the Gouy-Chapman model. Calculated for a 10 M aqueous solution of a 1 1 electrolyte at 25°C. 1/k = 30.4 A. See equations 13.3.14 to 13.3.16.

Figure 13.3.6 (a) A view of the differential capacitance in the Gouy-Chapman-Stem (GCS) model as a series network of Helmholtz-layer and diffuse-layer capacitances. (b) Potential profile through the solution side of the double layer, according to GCS theory. Calculated from (13.3.23) for 10 M 1 1 electrolyte in water at 25°C. 

Figure 21. A schematic diagram of the Stern adsorption layer (top) and the average potential profile of the Stern layer and Gouy-Chapman diffuse double layer.

FIGURE 6. The arrangement of water molecules and counterions near to a negatively charged membrane surface according to the Stern model. Within the Stern layer of polarized water molecules the electric potential falls linearly, and for distances further than this the potential profile follows that predicted by the Gouy-Chapman theory of electrical double layers. For ascites cells the potential drop between the surface potential and the zeta potential has been determined to be around... 

Figure 17.4 Charge profiles of acceptor dopants, oxygen vacancies, and electrons near a grain boundary interface with a space charge potential of + 0.44 V, according to both the Gouy-Chapman (dotted lines) and Mott-Schottky (solid lines) models.

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