Electrochemical potentials, interfacial

The metal ions Mz+, the atoms M, and the electrons at the interface are in equilibrium with the metal so we may use the electrochemical potentials of these species in the metal instead of the interfacial quantities, and split them into the chemical part and the electrostatic part ... 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

Fig. 9-1. Potential energy profile for transferring metal ions across an interface of metal electrode M/S py. = metal ion level (electrochemical potential) x = distance fiom an interface au. = real potential of interfacial metal ions = real potential of hydrated metal ions - compact layer (Helmholtz layer) V = outer potential of solution S, curve 1 = potential energy of interfadal metallic ions curve 2 = potential energy of hydrated metal ions.

The electronic properties of CNTs, and especially their band structure, in terms of DOS, is very important for the interfacial electron transfer between a redox system in solution and the carbon electrode. There should be a correlation between the density of electronic states and electron-transfer reactivity. As expected, the electron-transfer kinetics is faster when there is a high density of electronic states with energy values in the range of donor and acceptor levels in the redox system [2]. Conventional metals (Pt, Au, etc.) have a large DOS in the electrochemical potential... 

It is possible to find a range in which the electrode potential is changed and no steady state net current flows. An electrode is called ideally polarized when no charge flows accross the interface, regardless of the interfacial potential gradient. In real systems, this situation is observed only in a restricted potential range, either because electronic aceptors or donors in the electrolyte (redox systems) are absent or, even in their presence, when the electrode kinetics are far too slow in that potential range. This represents a non-equilibrium situation since the electrochemical potential of electrons is different in both phases. 

The first term refers to the electrolyte. Accordingly, the sum runs over all ion types present in the electrolyte. The second term contains the contribution of the electrons in the metal. T and Te are the interfacial excess concentrations of the ions in solution and of the electrons in the metal, respectively, /x is the chemical potential of the particle type i, Fa is Faradays constant, and /x is the electrochemical potential of the electrons. Substitution leads to... 

On the other hand, equilibrium at the polarized interface is described by the Gibbs-Lippmann equation (5.9). Here, the equilibrium potential eq, surface concentration Xj Fj of all adsorbing species, their bulk electrochemical potential fa, and the resulting interfacial charge Qi are linked rather less explicitly to surface tension y. 

The electrochemical potentials can be expanded and rearranged in the usual way (6.3), to yield the expression for the interfacial potential. 

Although the equilibrium principle was available (equality of electrochemical potential of each ion that reversibly equilibrates across an immiscible liquid/liquid interface), the elementary theory and consequences were not explored until recently (6). To develop an interfacial potential difference (pd) at a liquid interface, two ions M, X that partition are required. However,... 

The interfacial potential difference (pd) for the partition equilibrium interface is given by the equality of electrochemical potential in terms of all ions in equilibrium, equation (4). 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

It is assumed that deeply trapped holes, h+ff, are chemically equivalent to surface-bound hydroxyl radicals. Weakly trapped holes, on the other hand, that are readily detrapped apparently posses an electrochemical potential close to that of free holes and can therefore be considered to be chemically similar to the latter. Their shallow traps are probably created by surface imperfections of the semiconductor nanocrystals. From these traps the charge carriers recombine or they are transferred by interfacial charge transfer to suitable electron acceptors or donors adsorbed at the surface of the semiconductor. 

Thus, local corrosion (and the term local may imply a size of a few atoms up to that of a millimeter) occurs whenever a region of a material surface, a, is connected electrically (through a flow of electrons in the underlying metal region, p, at which there are interfacial reactions exhibiting an electrochemical potential different from that at a. The different constituents of an alloy would tend to provoke such a situation or, for example, S inclusions in steel. 

Adsorption and oil-water potentials. Dean, Gatty, and Rideal2 discuss the thermodynamics and the mechanism of the establishment of interfacial potential differences by the adsorption of ions, or by the adsorption or spreading of a film containing dipoles. They show that, provided that one or more of the charged components can pass the phase boundary and come into equilibrium on both sides, the adsorption of the interfacial film will not by itself change the phase boundary potential. For the electrochemical potentials of those charged components which can pass the boundary are equal, at equilibrium, in the two phases, i.e. 

Here, and p are the electric potentials in the metal, in the bulk solution and at the inner Helmholtz plane, x = / rw max is the surface concentration of the adsorbed water molecules in the absence of chemisorption and f(Fwmax - v/J) is their activity in the presence of chemisorption. In Eq. (24) the electrostatic contributions of the adsorbed molecules H2O and S to their electrochemical potentials also include the electrostatic potential energy of their dipoles in the interfacial electric field, -dftdx and are average values of the normal components of these dipoles, regarded as positive when their positive end is directed towards the solution. By substituting Eq. (24) into Eq. (23), rearranging terms, and differentiating jus with respect to [Pg.315]

Thus, product (D) should be in intimate contact with both the solid electrolyte (E) and working electrode (W) at (II) for a PEVD reaction to occur. If interfacial polarization is negligible, equilibria exist for both mass and charge transport across the interfaces at (II). Consequently, from Eqns. 9 and 10, the following electrochemical potential equilibrium equations at location (II) are valid ... 

In many experimental situations, a steady-state nonequilibrium condition between two phases (A and B) is sustained by electrical work being done on the system. For instance, the net interfacial electron flux Ja b is measured as a function of the difference in the electrochemical potential p Me,B- F " sufficiently small departure from equilibrium, it is observed that the net flux is proportional to the exchange flux and increases with increasing p A Me,B -... 

There is often a small region around equilibrium in which the net flux is proportional to and He A l e,B- Experimental investigation of the precise relationship between the net current flow and the deviation from equilibrium has been a major issue in interfacial science (Section 4.6). The measurement of the relationship between the interfacial electron flux and the electrochemical potential of the electrons in an electrode, and a fundamental interpretation of it, continue to be important issues in electrochemistry (Sections 4.7 to 4.9). 

An important subject in this chapter on Electron transfer at electrodes and interfaces is to draw an analogy between electrochemical and interfacial electron transfer between two solid phases. Any theory dealing with electron transfer has a thermodynamic and a kinetic basis. In Section 4.2, it was shown that electrons flow or tunnel in the direction of decreasing electrochemical potential the gradient of the electrochemical potential is the driving force behind a directed flow of electrons,... 

The chapter by Hill and Kelley addresses the interfacial electronic conductivity of DNA-based molecules controlled by the electrochemical potential. Binding of redox probes is a probe for electronic communication between the probe and the electrode through the DNA-molecular frame and therefore of the tunneling conductivity of the latter. This remains an intriguing issue as the redox-based electronic energies of the nucleobases are strongly off-rcsonance with the electrode Fermi energy and the redox level of the probe molecule. 

Experimental approaches to bioelectrochemical systems include other techniques which introduce new environments for interfacial bioelectrochemical function. Introduction of single-crystal, atomically planar electrode surfaces has opened a basis for the use of the scanning probe microscopies, STM and AFM, also for biological macromolecules. Importantly this extends to the electrochemical STM mode where electrochemical surfaces, adsorbate molecules, and now also biological macromolecules can be mapped directly in their natural aqueous environment, with full electrochemical potential control in situ STM and... 

The thermodynamic analyses used in this chapter make use of the electrochemical potential. In this way the electrical aspects of the interfacial equilibria are clearly defined. Earlier work on this problem, especially that by Volta and Nernst, had led to different conclusions regarding the source of the EMF in an electrochemical cell [12]. This problem was resolved by Frumkin, essentially, by writing out the interfacial equilibria using electrochemical potentials. In this regard, all interfaces in the cell must be considered including those between different metals at the terminals of the cell. This was shown in the discussion of the thermodynamic basis of the Nernst equation. 

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