Electrostatic potential, gradient

In most cases of practically useful ionic conductors one may assume a very large concentration of mobile ionic defects. As a result, the chemical potential of the mobile ions may be regarded as being essentially constant within the material. Thus, any ionic transport in such a material must be predominantly due to the influence of an internal electrostatic potential gradient,... 

If as a result of electrochemical processes, electrostatic potential gradients and electric currents can arise in different sections of a cell or whole organism, then conversely, currents or potential gradients applied from outside will produce certain changes in the cells and organisms. It is natural that these changes will depend on the electric field or current parameters. 

It follows from Eqn. 4—13 that the electron level o u/av) in the electrode is a function of the chemical potential p.(M) of electrons in the electrode, the interfacial potential (the inner potential difference) between the electrode and the electrolyte solution, and the surface potential Xs/v of the electrolyte solution. It appears that the electron level cx (ii/a/v) in the electrode depends on the interfacial potential of the electrode and the chemical potential of electron in the electrode but does not depend upon the chemical potential of electron in the electrolyte solution. Equation 4-13 is valid when no electrostatic potential gradient exists in the electrolyte solution. In the presence of a potential gradient, an additional electrostatic energy has to be included in Eqn. 4-13. 

In contrast to metal electrodes in which the electrostatic potential is constant, in semiconductor electrodes a space charge layer exists that creates an electrostatic potential gradient. The band edge levels and in the interior of semiconductor electrodes, thereby, differ from the analogous and at the electrode interface hence, the difference between the band edge level and the Fermi level in the interior of semiconductor electrodes is not the same as that at the electrode interface as shown in Fig. 8-14 and expressed in Eqn. 8—47 ... 

In order to estimate the order of magnitude of the internal electrical field, the two flux equations for the ions and electrons may be solved for the electrostatic potential gradient (rather than eliminating this quantity) as a function of the local difference in concentration (Weppner, 1985). 

FIGURE 4.6.2 Schematic diagram illustrating the directions of electric field, electrostatic potential gradients, electrochemical potential gradient, and emf for a representative cell under open circuit conditions, and set up in accord with Conventions 1 and 2, developed later. 

We next describe the operation of galvanic cells in mathematical terms, again taking the Daniell cell as our representative example. Consider Fig. 4.6.1 for electrons to flow through the external circuit left to right the electric field E points in the direction of the conventional positive current flow, i.e., to the left, whereas the electrostatic potential gradient Vfi = — points to the right. Under spontaneous... 

Fig. 4.6.1. Schematic diagram showing the direction of the emf, electrochemical potential gradient, electrostatic potential gradient, and electric field during spontaneous operation of a cell operating in conformity with Conventions 1 and 2, described below.

Discussion of non-equilibrium processes involving ions in terms of the micropotential is especially helpful because it focuses attention on the fact that major source of non-ideality in these systems is electrical in character. The arbitrary nature of the separation of the electrochemical potential into chemical and electrical contributions has often been pointed out in the literature. In fact, chemical interactions are fundamentally electrical in nature. However, the formal separation discussed here is conceptually important. Its usefulness becomes clear when one tackles problems related to the movement of ions in electrolyte solutions under the influence of concentration and electrostatic potential gradients. These problems are discussed in the following section. 

The solution must be electrically neutral (unless a large external electrostatic potential gradient is applied). If the molar polyelectrolyte concentration is m, and the average valence is z, there must be mz counterions (of unit valence) in solution, for instance Na+ ions for a polyacid. 

As explained above, the charges in the resin phase give rise to a difference in electrostatic potential between the external solution and the resin phase and also to electrostatic potential gradients within the resin phase. In the following discussion it is assumed that electrostatic effects are the only factors that contribute to changes in the activity coefficients. 

Another difference between an electrochemical reaction and a catalytic reaction is that a so-called electrical double layer will form as the appearance of electrostatic potential gradient in the interface of electrolyte solution and electrode (conductor). Graham summarized in more detail the electrical double layer in 1947. He considered that this electrostatic potential, i.e. the double layer potential, is different from the electrode potential. He also discussed and observed in detail the double layer potential of Hg-electrode-water solution system. He found that it could not observe such potential when electrode reaction occurred while the ideal polarization happened in a wide range of electrode potential if there was no electrode reaction. Hg is a liquid and it is thus easy to observe its surface tension and calculate the relationship between surface tension and double layer potential. Therefore, its structure is clearer. The structure of electrical double layer is composed of Helmholz layer and diffusion layer. The Helmohloz face is located between Helmholz layer and diffusion layer. The external of Helmohloz face is diffusion double layer. The model of Helmholz electrical double layer corresponds to simple parallel-plate capacitor. According to its equation, it can quantitatively describe the structure of diffusion double layer. 

Solution of Eq. (14.9) requires knowledge of the electrostatic potential gradient, which is provided by the Gauss equation ... 

With any lack of physical significance, Eq. (14.13) accounting for the electrostatic potential gradient can be rewritten by introducing the conductivity of each charged species (Eq. (14.3)) and the definition of the transport number, =... 

Introducing Eq. (14.16) into Eq. (14.15), the electrostatic potential gradient reads... 

Equation (14.23) can also be deduced from Eq. (14.14) by assuming a zero electrostatic potential gradient (i.e., v

[Pg.320]

All in all, the fuel cell principle explains how an electrostatic potential gradient or electromotive force is created and maintained by controlling the unequal composition of feed components. The current flowing through the load is uniquely determined by the coupled and balanced rates of reactant supply through diffusion media, rates of anode and cathode reactions at electrodes, and electron and proton fluxes through their respective conduction media. 

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