Space potential dependence

Figure 6. Scheme of microwave-electrochemical setup showing time-resolved, space-resolved and potential-dependent measurement techniques, as well as combinations of these. 

Relation (18) for the potential-dependent PMC signal is a reasonably good approximation only for the depletion region, where the space charge layer is controlled by the presence of fixed electron donors (Afo). It would become even more complicated if bimolecular or even more complicated kinetic reaction steps were considered. 

The Gartner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Gartner formula for the photocurrent /ph is... 

Between the space charge layer establishes the potential (j>2 and the magnitude of this potential depends on and the ionic strength of the solution. It will be apparent that 2 will determine the concentrations of charged electroactive species, while will determine the rate of the electron transfer step if... 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

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,... 

During the process, the solute diffuses into the intercellular space and, depending on the characteristics of the solute, it may pass through the membrane and enter the intracellular space. Differences in chemical potentials of water and solutes in the system result in fluxes of several components of the material and solution water drain and solute uptake are the two main simultaneous flows. Together with the changes in chemical composition of the food material, structural changes such as shrinkage, porosity reduction, and cell collapse take place and influence mass transfer behavior in the tissue. 

The general method for the determination of the flat band potential is based on the Mott-Schottky linear plot based on ca-pacitance/voltage relation. Starting from Eq. (9) the space charge distribution was calculated, and its potential dependence lead to the derivation of a model equivalent to a capacitance, given by ... 

In the interaction between two spherical bodies, if the potential depends only on the distance between the bodies, then there is spherical symmetry. The system is invariant to a rotation of the coordinate system about any axis. In this case, two components of angular momentum are conserved as the two bodies orbit around their common center of mass, the magnitude of their angular momentum is constanL while the plane of the orbit in space does not change. 

The measurement of ion activities assumes chemical equilibrium between the PVC membrane and the electrolyte bearing solutions. The time domain chemical and dielectric space charge changes that occur are minimized by membrane composition and sensor design and are considered negligible during the measurement period. Hence, the potential dependence of the ion activity is characterized by the Nemst equation. The following thermodynamic expressions describe the potentials of the... 

Occasionally, the impedance spectra of diamond electrodes are well described by the Randles equivalent circuit with a frequency-independent capacitance (in the 1 to 105 Hz range) [66], Shown in Fig. 11 is the potential dependence of the reciprocal of capacitance squared, a well-known Mott-Schottky plot. Physically, the plot reflects the potential dependence of the space charge region thickness in a semiconductor [6], The intercept on the potential axis is the flat-band potential E whereas the slope of the line gives the uncompensated acceptor concentration NA - Nd in what follows, we shall for brevity denote it as Na ... 

In the case of zinc oxide, Dev/ald (2) found that by measuring the capacity he could find the bias on the counter electrode that would correspond to zero electrostatic potential across the space-charge layer (the flat band potential). He could, of course, measure the electrolytic potential for this condition. He found that at low electron density this electrolytic potential depended linearly on the logarithm of the ratio of the electron or hole density to the intrinsic density with the right slope, i. e., (-pr). 

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