Layer Structure General Considerations

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts  

Assuming that the double layer is composed of two capacitors, the inner and the diffuse one, connected in series, which have the capacitanties C( and Cd, respectively, the measured total capacitance C can be ex-pressed  

According to this model, and in the absence of specific adsorption, the adsorbed solvent molecules are located in the inner Helmholtz plane, the thickness of which is determined by the radius of the molecule. At the same time, solvated ions define the location of the outer Helmholtz plane. Other ions, charged oppositely to the surface charge, are smeared out in the diffuse layer. 

The presence of the diffuse layer determines the shape of the capacitance-potential curves. For a majority of systems, models describing the double-layer structure are oversimplified because of taking into account only the charge of ions and neglecting their specific nature. Recently, these problems have been analyzed using new theories such as the modified Poisson-Boltzmann equation, later developed by Lamper-ski. The double-layer capacitanties calculated from these equations are 

The problem of influence of the electric field intensity on the permittivity of solvents has been discussed in many papers. The high permittivity of water results from the intermolecular forces and is a cumulative property. The electric field intensity is the lowest at the potential of zero charge (pzc), thus allowing water molecules to adsorb in clusters. When the electrode is polarized, the associated molecules, linked with hydrogen bonds, can dissociate due to a change in the energy of their interaction with the electrode. Moreover, the orientation of water molecules may also change when the potential is switched from one side of the pzc to the otha. 

---

In anthracene crystal as it follows from data collected in Table 3.1 the distance between a, b plane is large in comparison with distance between nearest molecules in this plane. As the result, as we already mentioned in Section 9.1, the interactions between molecules in different planes is smaller than interaction between molecules inside the same plane. This means that anthracene crystal the same as other crystals of the its family have layered structure which we explicitly take into account in microscopical theory of surface states. We will use the same Hamiltonian (2.2) as we used in consideration of bulk states in simplest Heitler-London approximation. However, now we have to take into account that translational symmetry exists only along the surface of crystal which we assume parallel to a, b plane. In an infinite crystal the diagonalization of Hamiltonian leads to two exciton bands Eit2(k), so that the general pattern of levels is the one shown schematically in Fig. 12.4b. 

Soil column experiments with conservative and reactive tracers are used for the development of reactive transport models in soil and groundwater and for the determination of model parameters. The influence of the real structure of the solid layers on the transport and reaction processes is very important and has to be taken into consideration for the development of mathematical transport models (Chin and Wang, 1992). Several methods exist for the investigation of layer structures (ultrasound and electrical tomography, computer tomography with X-rays) (Just et al., 1994 Meyer et al. 1994), but generally these methods give no information about the dynamic processes. 

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

---