Space-charge polarization

Samec et al. [15] used the AC polarographic method to study the potential dependence of the differential capacity of the ideally polarized water-nitrobenzene interface at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetra-phenylborate) electrolytes. The capacity showed a single minimum at an interfacial potential difference, which is close to that for the electrocapillary maximum. The experimental capacity was found to agree well with the capacity calculated from Eq. (28) for 1 /C,- = 0 and for the capacities of the space charge regions calculated using the GC theory,... 

FIG. 9 Simulated electrical potential and space charge density profiles at the water-1,2-DCE interface polarized at/= 5 in the absence (a) and in the presence (b) of zwitterionic phospholipids. The supporting electrolyte concentrations are c° = 20 mM and c = 1000 mM. The molecular area of the phospholipids is 150 A, and the corresponding surface charge density is a = 10.7 xC/cm. The distance between the planes of charge associated with the headgroups is d = 3 A. 

Figure 40. Energy diagrams illustrating the difference in values of external electric field of both polarities able to neutralize the internal electric field of asymmetric space charge.62...

We consider, now, an electron-depleted space charge layer that is gradually polarized in the anodic direction. As long as the Fermi level is located away from the surface state, the interfacial capacity is determined by the capacity of the depletion layer that obeys a Mott-Schottlsy relation as shown in Fig. 5-61. 

Fig. 8-28. Cathodic polarization curves for several redox reactions of hydrated redox particles at an n-type semiconductor electrode of zinc oxide in aqueous solutions (1) = 1x10- MCe at pH 1.5 (2) = 1x10 M Ag(NH3) atpH12 (3) = 1x10- M Fe(CN)6 at pH 3.8 (4)= 1x10- M Mn04- at pH 4.5 IE = thermal emission of electrons as a function of the potential barrier E-Et, of the space charge layer. [From Memming, 1987.]...

As anodic or cathodic polarization increases, the band level bending in a space charge layer (a depletion layer) becomes steeper, and the electron tunneling through the space charge layer is then ready to occur particularly in semiconductor electrodes of high concentrations of donors or acceptors where the space charge layer is thin. 

The entire set of molecules contained 782 bonds out of which 111 a-bonds were selected. The parameters were calculated by our methods to build a reactivity space with electronegativity difference, resonance effect parameter, bond polarizability, bond polarity, a-charge distribution, and bond dissociation energy as six coordinates. 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

The nature of bonding of the adsorbed species to the model cluster of metal surfaces can be analyzed in terms of the so-called constrained space orbital variation (CSOV) method. For halogen anions adsorbed on various silver surfaces, it has been found that Pauli repulsion, metal polarization, and charge transfer to the metal surface mainly contribute to the binding energy of the ions [104, 301]. 

We can further describe the polarization, P, according to the different types of dipoles that either already exist or are induced in the dielectric material. The polarization of a dielectric material may be caused by four major types of polarization electronic polarization, ionic (atomic) polarization, orientation polarization, and space-charge (interfacial) polarization. Each type of polarization is shown schematically in Figure 6.24 and will be described in succession. In these descriptions, it will be useful to introduce a new term called the polarizability, a, which is simply a measure of the ability of a material to undergo the specific type of polarization. 

The final type of polarization is space-charge polarization, sometimes called interfacial polarization, and results from the accumulation of charge at structural interfaces in heterogeneous materials. Such polarization occurs when one of the phases has a much higher resistivity than the other, and it is found in a variety of ceramic materials, especially at elevated temperatures. The space-charge polarization, P c, has a corresponding space-charge polarizability, The two are related via a relationship of the form for the other types of polarization. 

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