Chapman layer

Fig. 2. Schematic diagram of a suspended colloidal particle, showing relative locations of the Stem layer (thickness, 5) that consists of adsorbed ions and the Gouy-Chapman layer (1 /k) which dissipates the excess charge, not screened by the Stem layer, to 2ero ia the bulk solution (108). In the absence of a...

Stem layer, the Gouy-Chapman layer dissipates the surface charge. 

Layers of any molecule will form when the rate of production is controlled by photochemistry. These so-called Chapman layers can be described using all of... 

The rate of photolysis, J, depends on the absorption cross-section, a, the number density, the scale height and the angle, all of which are unique properties of a planetary atmosphere. For the Earth and the Chapman mechanism for ozone the O3 concentration maximum is 5 x 1012 molecules cm-3 and this occurs at 25 km, shown in Figure 7.12, and forms the Chapman layer structure. 

Radiative heating Scale height Chapman layers... 

Flabitable and continually habitable zone Variation of temperature and pressure with height Steady-state atmospheric networks leading to Chapman layers... 

The reflection spectrum of the atmosphere is a measure of the albedo of the planet (Figure 10.4) and, despite the strong methane absorption in the red, Titan s disc looks orange principally due to scatter from the surface of dense methane-hydrocarbon clouds. Scatter from aerosol particles within the thick clouds obscures the surface of the moon although the radar analysis reveals considerable Chapman layer structure within the atmosphere and some interesting surface features. 

Atmospheric structure Composition of N2 and CH4 with a complex hydrocarbon/Chapman layer structure... 

Chapman layers Layers of molecules forming in an atmosphere as a result of the balance between photolysis and the concentration of the reactants. 

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... 

It seems possible that a very hydrophilic anion such as OH- might not in fact penetrate the micellar surface (Scheme 1) so that its interaction with a cationic micelle would be non-specific, and it would exist in the diffuse, Gouy-Chapman layer adjacent to the micelle. In other words, OH" would not be bound in the Stem layer, although other less hydrophilic anions such as Br, CN or N 3 probably would bind specifically in this layer. In fact the distinction between micellar and aqueous pseudophases is partially lost for reactions of very hydrophilic anions. The distinction is, however, appropriate for micellar reactions of less hydrophilic ions. 

The problems of the constancy of a and the site of reaction are closely linked. It is very convenient to assume that the charge on the micellar head groups is extensively neutralized by counterions which bind specifically to the micellar surface. In this way micellar stability is associated with a balance between hydrophobic attractions between apolar groups and coulombic repulsions of the ionic head groups which will be reduced by favorable interactions with the counterions in both the Stem and the diffuse Gouy-Chapman layers. It is the behavior of the counterions which is important in considerations of their chemical reactivity. 

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. 

Beyond the IHP is a layer of charge bound at the surface by electrostatic forces only. This layer is known as the diffuse layer, or the Gouy-Chapman layer. The innermost plane of the diffuse layer is known as the outer Helmholtz plane (OHP). The relationship between the charge in the diffuse layer, o2, the electrolyte concentration in the bulk of solution, c, and potential at the OHP, 2> can be found from solving the Poisson-Boltzmann equation with appropriate boundary conditions (for 1 1 electrolytes (13))... 

For simplicity, we will consider the case in which surface charge and potential are positive, and that only anions adsorb. Furthermore, the potential drop in the Gouy-Chapman layer will be assumed to be small enough that its charge/potential relation can be linearized. The V o/oo/pH relationship can then be derived parametrically, with the charge in the Gouy-Chapman layer cr4 as the parameter. The potential at the plane of anion adsorption can then be calculated and substituted in Equation 28 to give ... 

Stern combined the ideas of Helmholtz and that of a diffuse layer [64], In Stern theory we take a pragmatic, though somewhat artificial, approach and divide the double layer into two parts an inner part, the Stern layer, and an outer part, the Gouy or diffuse layer. Essentially the Stern layer is a layer of ions which is directly adsorbed to the surface and which is immobile. In contrast, the Gouy-Chapman layer consists of mobile ions, which obey Poisson-Boltzmann statistics. The potential at the point where the bound Stern layer ends and the mobile diffuse layer begins is the zeta potential (C potential). The zeta potential will be discussed in detail in Section 5.4. 

Stern layers can be introduced at different levels of sophistication. In the simplest case we only consider the finite size effect of the counterions (Fig. 4.5). Due to their size, which in water might include their hydration shell, they cannot get infinitely close to the surface but always remain at a certain distance. This distance <5 between the surface and the centers of these counterions marks the so-called outer Helmholtz plane. It separates the Stern from the Gouy-Chapman layer. For a positively charged surface this is indicated in Fig. 4.5. 

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

In order to calculate the Gibbs free energy of a Gouy-Chapman layer we split its formation into three steps [66,67], In reality it is not possible to do these steps separately but we can do the Gedanken experiment without violating any physical principle. 

Most solid surfaces in water are charged. Reason Due to the high dielectric permittivity of water, ions are easily dissolved. The resulting electric double layer consist of an inner Stern or Helmholtz layer, which is in close contact with the solid surface, and a diffuse layer, also called the Gouy-Chapman layer. 

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