Electrochemical potential, generalized

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

The chemical potential pi, has been generalized to the electrochemical potential Hj since we will be dealing with phases whose charge may be varied. The problem that now arises is that one desires to deal with individual ionic species and that these are not independently variable. In the present treatment, the difficulty is handled by regarding the electrons of the metallic phase as the dependent component whose amount varies with the addition or removal of charged components in such a way that electroneutrality is preserved. One then writes, for the ith charged species. 

Derive a general equation for the electrochemical potential at the equivalence point for the titration of Fe + with Mn04 the reaction is... 

The most important class of redox indicators, however, are substances that do not participate in the redox titration, but whose oxidized and reduced forms differ in color. When added to a solution containing the analyte, the indicator imparts a color that depends on the solution s electrochemical potential. Since the indicator changes color in response to the electrochemical potential, and not to the presence or absence of a specific species, these compounds are called general redox indicators. 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Each of the respiratory chain complexes I, III, and IV (Figures 12-7 and 12-8) acts as a proton pump. The inner membrane is impermeable to ions in general but particularly to protons, which accumulate outside the membrane, creating an electrochemical potential difference across the membrane (A iH )-This consists of a chemical potential (difference in pH) and an electrical potential. 

A general discussion and attempts to clarify the definitions of electrochemical potential in light of recent theoretical results, as well as the surface and Volta potentials have been presented recently. 

Consider the case of a junction between two different metals a and p. Generally, they will have different values of the Fermi energy and work function. Between the two metals, a certain Volta potential will be set up. This implies that the outer potentials at points a and b, which are just outside the two metals, are different. However, it will be preferable to count the Fermi levels or electrochemical potentials from a common point of reference. This can be either point a or point b. Since these two points are located in the same phase, the potential difference between them (the Vofta potential) can be measured. Hence, values counted from one of the points of reference are readily converted to the other point of reference when required. 

The first controversial point in this mechanism is the nature of the reaction planes where the precursor formation and the ET reaction take place. Samec assumed that the ET step occurs across an ion-free layer composed of oriented solvent molecules [1]. By contrast, Girault and Schiffrin considered a mixed solvent region where electrochemical potentials are dependent on the position of the reactants at the interface [60]. From a general perspective, the phenomenological ET rate constant can be expressed in terms of... 

In general, the electrochemical potential cannot be separated into chemical and electrical components, as the chemical interaction of a species with its environment is also electric in nature. Nonetheless, the separation of the electrochemical potential is frequently made according to the equation... 

The electrochemical potential of an electron in a solid defines the Fermi energy (cf. Eq. 3.1.9). The Fermi energy of a semiconductor electrode (e ) and the electrolyte energy level (credox) are generally different before contact of both phases (Fig. 5.60a). After immersing the semiconductor electrode into the electrolyte, an equilibrium is attained ... 

A more general relation between potential and electronic pressure for a density-functional treatment of a metal-metal interface has been given.74) For two metals, 1 and 2, in contact, equilibrium with respect to electron transfer requires that the electrochemical potential of the electron be the same in each. Ignoring the contribution of chemical or short-range forces, this means that —e + (h2/ m)x (3n/7r)2/3 should be the same for both metals. In the Sommerfeld model for a metal38 (uniformly distributed electrons confined to the interior of the metal by a step-function potential), there is no surface potential, so the difference of outer potentials, which is the contact potential, is given by... 

Once electronic equilibrium is established, the surface and the volume of the semiconductor have a common Fermi level, i.e., the same electrochemical potential (depicted by the horizontal line FF in Fig. 22). However, owing to the bending of the bands the position of the Fermi level in the energy spectrum of the crystal (its position relative to the energy bands) will, generally speaking, depend on the distance from the surface. We shall characterize the position of the Fermi level by its distance from the top of the valence band, denoted by e+. Evidently, + = We intro-... 

Because CO2 is the final product of combustion, reactions of CO2 generally require a significant input of energy and result in the reduction of CO2. This energy requirement can be chemical energy stored in highly reactive bonds and intermediates, but of more relevance to this review are the reduction potentials required for electrochemical reactions. The electrochemical potentials required for the reduction of CO2 to a variety of one-carbon products are shown in reactions (1-5) [12]. These potentials are all within a couple of tenths of a volt of the potential required for the reduction of protons to hydrogen. 

It has been necessary to understand the relationship between molecular fine structure of cyanine dyes and important properties such as colour, dye aggregation, adsorption on silver halide and electrochemical potentials in order to design and prepare sensitizers with optimum performance. For general discussion of these topics and the mechanism of spectral sensitization, the reader is referred to recent surveys on the subject (B-77MI11401, 77HC(30)441). 

Though it is possible to conceive of experiments that do not exactly fit either, electrochemical methods generally fall into one of two categories those in which a potential is imposed on the cell, the current being monitored and those in which a current is applied, the potential being monitored. The first category is the more common. The term voltammetry is applied to both categories since each involves a study of how the potential and current are interrelated. 

For the sake of completeness, Figure 4-5 illustrates the more general situation of isothermal, isobaric matter transport in a multiphase system (e.g., Fe/Fe0/Fe304 / 02). A sequence of phases a, (3, y,... is bounded by two reservoirs which contain both neutral components (i) and electronic carriers (el). The boundary conditions imply that the buffered chemical potentials (u,(R)) and the electrochemical potentials (//el(R)) are predetermined in R] and Rr. Depending on the concentrations and mobilities (c/, b), c, 6 ) in the various phases v, metallic conduction, semiconduction, or ionic conduction will prevail. As long as the various phases are thermodynamically stable and no decomposition occurs, the transport equations (including the boundary conditions) are well defined and there is normally a unique solution to the transport problem. 

The potential that appears in the total force expression is the sum of the chemical potential and the electropotential of the charged ion. This total potential is generally called the electrochemical potential. 

Summary. We suggest a simple system of two electron droplets which should display two-channel Kondo behavior at experimentally-accessible temperatures. Stabilization of the two-channel Kondo fixed point requires fine control of the electrochemical potential in each droplet, which can be achieved by adjusting voltages on nearby gate electrodes. We study the conditions for obtaining this type of two-channel Kondo behavior, discuss the experimentally-observable consequences, and explore the generalization to the multi-channel Kondo case.1... 

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