Gouy region

Colloids The Thickness of the Double Layer and the Bulk Dimensions Are of the Same Order. The sizes of the phases forming the electrified interface have not quantitatively entered the picture so far. There has been a certain extravagance with dimensions. If, for instance, the metal in contact with the electrolyte was a sphere (e.g., a mercury drop), its radius was assumed to be infinitely large compared with any dimensions characteristic of the double layer, e.g., the thickness K-1 of the Gouy region. Such large metal spheres, dropped into a solution, sink to the bottom of the vessel and lie there stable and immobile. 

In Eq. (29), Rjn is the measurement resistor (across which the current or photocurrent is measured) and Rg is the electrolyte resistance. The term C is the capacitance, which, in the metal case, is the Helmholtz layer capacitance, Ch- (Once again, the Gouy region is ignored here.) For semiconductor-electrolyte interfaces, we have seen that two layers are involved in a series circuit configuration with corresponding capacitances of Csc and Ch (Fig. 6). Because Ch Csc, C Csc- This assumption is usually justified because Ch — 10 F cm and Csc = 1Q- — 10 F cm . If the composite resistance (/ m + R i) is 100 ohm, then tceii for metal electrodes is 10 s and that for the semiconductor case is... 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

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]. 

The classical model, as shown in Figure 1, assumes that the micelle adopts a spherical structure [2, 15-17], In aqueous solution the hydrocarbon chains or the hydrophobic part of the surfactants from the core of the micelle, while the ionic or polar groups face toward the exterior of the same, and together with a certain amount of counterions form what is known as the Stern layer. The remainder of the counterions, which are more or less associated with the micelle, make up the Gouy-Chapman layer. For the nonionic polyoxyethylene surfactants the structure is essentially the same except that the external region does not contain counterions but rather rings of hydrated polyoxyethylene chains. A micelle of... 

Similar considerations apply to situations in which substrate and micelle carry like charges. If the ionic substrate carries highly apolar groups, it should be bound at the micellar surface, but if it is hydrophilic so that it does not bind in the Stern layer, it may, nonetheless, be distributed in the diffuse Gouy-Chapman layer close to the micellar surface. In this case the distinction between sharply defined reaction regions would be lost, and there would be some probability of reactions across the micelle-water interface. 

The problem may be a semantic one because OH- does not bind very strongly to cationic micelles (Romsted, 1984) and competes ineffectively with other ions for the Stern layer. But it will populate the diffuse Gouy-Chap-man layer where interactions are assumed to be coulombic and non-specific, and be just as effective as other anions in this respect. Thus the reaction may involve OH- which is in this diffuse layer but adjacent to substrate at the micellar surface. The concentration of OH- in this region will increase with increasing total concentration. This question is considered further in Section 6. 

The surface concentrations c x and cjed differ from those in the bulk even if the surface region and the bulk are in equilibrium. Using the same arguments as in the Gouy-Chapman theory, the surface concentration cs of a species with charge number z is ... 

The most important result is the existence of an extended boundary region, where the structure of solution differs significantly from the bulk, and where the potential deviates from the predictions of the Gouy-Chapman theory. In this model the interfacial capacity can be... 

The electrostatic potential profile is rather complex. In the hydrophobic region, the features are similar to those discussed above for the pure DPPC layer cf. Figure 15. The electrostatic potential profile in the PE layer is parabolic, and outside the PE layer the potential is very low, but decays according to the classical Gouy-Chapmann theory, i.e. exponential decay towards zero. 

Figure 2. The distribution of ions around a charged particle, showing the tightly bound Stern layer and the diffuse Gouy-Chapman region. Reprinted from [45] Simkiss, K. and Taylor, M. G. Transport of metals across membranes . In Metal Speciation and Bioavailability in Aquatic Systems, eds. Tessier, A. and Turner, D. R., Vol. 3, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle J. and van Leeuwen, H. P. Copyright 1995 John Wiley Sons Limited. Reproduced with permission...

The description of the double layer reported in Figures 3 and 22 is only approximate the composition of the electrode/solution region is somewhat more complex. The double layer has been studied in most detail for a mercury electrode immersed in an aqueous solution. According to Gouy-Chapman-Stem there are several layers of solution in contact with the electrode, see Figure 25. 

The Gouy-Chapman model describes the properties of the diffuse region of the double-layer. This intuitive model assumes that counterions are point charges that obey a Boltzmann distribution, with highest concentration nearest the oppositely charged fiat surface. The polar solvent is assumed to have the same dielectric constant within the diffuse region. The effective surface... 

The Helmholtz model was found not to be able to give a satisfactory analysis of measured data. Later, another theory of the diffuse double layer was proposed by Gouy and Chapman. The interfacial region for a system with charged lipid, R-Na+, with NaCl, is shown in Figure 4.10. 

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