Gouy-Chapman region

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 surfaces being considered are not planar, and therefore instead of Helmholtz-Perrin parallel-plate condensers, one has concentric-sphere capacitors Gouy-Chapman regions show radial instead of planar symmetry. All such points complicate the mathematics, but lead to few new truths. Hence, such details will be ignored in this very simple account of the dominating role of double layers in colloid chemistry. 

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 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 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 next step is to determine the electrical charge and potential distribution in this diffuse region. This is done by using relevant electrostatic and statistical mechanical theories. For a charged planar surface, this problem was solved by Gouy (in 1910) and Chapman (in 1913) by solving the Poisson-Boltzmann equation, the so called Gouy-Chapman (G-C) model. 

Fig. 6.64. The Gouy-Chapman model, (a) The excess charge density on the OHP is smaller in magnitude than the charge on the metal. The remaining charge is distributed in the solution. The diffuse charge region, (b), can be simulated by a sheath of charge gd placed at a distance k 1 from the x = 0 plane, as depicted in (c).

However, even taking all these facts into account, this theory is not able to reproduce the capacitance-potential curves in the regions beyond the pzc proximity. The model seems, in fact, to be in sharp disagreement with the experimental behavior. The Gouy-Chapman theory might best be described as a brilliant failure. However, as will be seen, it represents an important contribution to a truer description of the double layer it also finds use in the understanding of the stability of colloids and, hence, of the stability of living systems (see Section 6.10.2.2). 

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