Potential distribution

Fig. 10.25 Longitudinal distribution potential on pipeline. Note Stations refer to points at which the potential is measured...

The nnmeric solution of Eq. (32.9) for the interface A" R+X with the common cation R+ is shown in Fig. 32.1. The expected Nemstian response of 59mV per decade is observed only in a limited range of the ratio of concentrations of electrolytes R+A and R X . When this ratio is too low or too high, the equilibrium potential approaches the distribution potential of the electrolyte that is present in excess. 

According to Eq. (32.10), the distribution potential corresponding to the equilibrium partition of the electrolyte RX is independent of the electrolyte concentration. On the other hand, when more than two ions are involved in the partition equilibrium, there always exists a thermodynamic relationship between the potential difference and the concentrations of ions present. More specifically, let us consider an ITIES with a different electrolyte in each phase. 

Koryta et al. (1977) have shown that the distribution potential for such an ITIES fulfills the inequality cp s+ 9 ix- 9 )r+> provided that RX consists of... 

The above equation allows the calculation of Galvani potentials at the interfaces of immiscible electrolyte solutions in the presence of any number of ions with any valence, also including the cases of association or complexing in one of the phases. Makrlik [26] described the cases of association and formation of complexes with participation of one of the ions but in both phases. In a later work [27] Le Hung extended his approach and also considered any mutual interaction of ions and molecules present in both phases. Buck and Vanysek performed the detailed analysis of various practical cases, including membrane equilibria, of multi-ion distribution potential equations [28,29]. 

The formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefficients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefficients are replaced by their mean values. A decrease of the difference in the activity coefficients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31 33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. 

For symmetrical electrolytes, of, e.g., type 1 1, such a liquid-liquid interface, in equilibrium, is described by the standard Galvani potential, usually called the distribution potential. This very important quantity can be expressed in the three equivalent forms, i.e., using the ionic standard potentials, or standard Gibbs energies of transfer, and employing the limiting ionic partition coefficients [3] ... 

According to Eq. (26), which directly ensues from Eq. (22), the distribution potential is the arithmetic mean of the Galvani potentials of cations and anions. These potentials are the ionic constituents of the distribution potential, and in fact, according to Eq. (5) they can be considered as electrical representations of the ionic transfer energies AG or limiting distribution coefficients of the ions, Bj [3]. Here, the reader is referred to the following equations ... 

In such cells, aqueous solutions contain electrolytes with a common cation. The EMF of this cell is equal to the difference of distribution potentials of both electrolytes and to the diffusion potential in the organic phase. Under appropriate conditions the EMF depends only on the difference of distribution potentials. It should be noted that cells of this type can also contain many and various ions in both phases. 

The distribution potential of this system, and the diffusion potential at the contact of nitrobenezene with many organic solvents, are close to zero [3,38 0]. The cell containing TEAPi-bridge can be represented by the following scheme ... 

Kakiuchi performed a very important analysis of the distribution potential in the small systems [14,31]. Using the general Le Hung approach, he discussed the behavior of Aj e at its extreme, when r 0 or oo. 

The distribution potential A 0distr is thus independent of the ion concentration. 

Concerning regularities of particle s motion in the electric and thermoelectric fields with distributed potential... 

Abstract. The subject of this research are the regularities of the particles motion in the electric and thermoelectric fields with distributed potential and the influence of temperature field to the particle motion trajectories in aggregate electric and thermal fields. The analytical solution of the problem of particle motion in thermoelectric field with distributed potential is produced. Common regularities of particle motion and trajectory changes in such fields are derived. It is shown that nonlinear curves give a nonconsiderable part of the trajectory within the macrostructures and so the trajectory shape doesn t considerably influence the electron flow transformation process. Conversely, the trajectory shape does influence the aforesaid processes in micro- and nanostructures defining the specific ways of transformation. 

We ll search for a solution of equation of motion in a stationary potential thermoelectric field with distributed potential. Such a field is generated in a plane-parallel structure (Fedulov, 2003) with distributed potential (fig. 1). The potential thermoelectric field in this structure can be described by the following independent expressions ... 

Then we can rewrite the equation of electron motion in thermal field with distributed potential as following ... 

The Eqs. (10) and (11) functionally connect thep parameter, the initial electron s velocity Vo and velocity s constituents Vqx and Voy in plane-parallel structure with distributed potential with the coordinate of its entry s point xo, on the electrode with distributed potential. Let us analyze Eq. (10) Under pxo < B the electron will lose the initial kinetic energy completely with generation of electromagnetic radiation (the kinetic energy is absorbed completely). Under these conditions the electron doesn t leave the structure. There is the partial selection of energy under px0 > B and the electron comes beyond the limits of structure. If electron enters the structure normally (Voy = Vo, Vox = Vo) the boundary condition after that electron leaves the structure can be written as ... 

Figure 2. The measurer macrostructure with distributed potential. 1 — the cathode (emitter), 2 — grids for a measured electrical signal, 3 — grid with a distributed potential and 4 — anode. 

While reviewing the operation of measuring and transformation devices based on distributed potential structures utilizing the decelerating (reflective) and accelerating field areas (fig. 4), the problem of its operation... 

Figure 5. A closed trajectory of electron s motion in structure with symmetric thermoelectric field. 1 — electrode with distributed potential, 2 — the pattern of electrical field, 3 — closed trajectory of the electron. 

The symmetric thermoelectric field can be created in structure, showed in fig. 5. The trajectories of an electron motion in a symmetric field with a distributed potential are represented there. 

The opportunity of creation of oscillating system in the structure with braking potential field, which were made by the distributed potentials and accelerating potential, is shown. The particle in such the field will make fourfold process of braking and accelerating. 

In practice of creation of measuring and transforming instruments on structures with a distributed potential there are tasks about research of trajectories of driving of a particle in a non-stationary thermoelectric field. This task arises in conditions, when a varying potential adds to one of electrodes of structure with a distributed potential. We considered the non-stationary task under condition of a linear dependence between coefficients in a stationary and non-stationary thermoelectric fields. The potential in such a field can be described by the equation... 

The equations of motion of charged particles are output at simultaneous operation of electrical and thermoelectric fields with distributed potentials, and analytical solutions of them are obtained. Essentially variations of a trajectory of charged particles motion under operation of an additional thermoelectric field with a distributed potential are detected. This one can be used to create a new type of measuring instruments and functional converters. 

Fedulov, V.I. Concerning Regularities of Particle s Driving in Potential Fields (on example of electron s movement in electrical field with distributed potential) in ARW977788 Emerging Applications of Vacuum-Arc-Produced Plasma, Ion and Electron Beams , edited by E.M. Oks and I.G. Brown (Kluwer Academic Publishers, Dordrecht, the Netherlands), 213, 2003. 

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Although the problem of the liquid membrane potential was solved in principle by Nemst, a discussion developed in the ensuing two decades between Bauer [6], who developed the adsorption theory of membrane potentials, and Beutner [10,11,12], who based his theories on Nernst s work. This problem was finaly solved by Bonhoeffer, Kahlweit and Strehlow [13], and by Karpfen and Randles [49]. The latter authors also introduced the concept of the distribution potential. 

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