Electrochemical potential interphases

The clearest introduction to the electrochemical potential (hat is given by its creator, in Chap. 8ofIv. A. Guggenheim, Thermodynamics, North-1 lollaiul, Amsterdam, 1967. [ lie issue of electric potentials near interfaces is discussed in detail in K. Faisons, Fquilihrium properties of electrified interphases. Modern Aspects Etectrochem. 1 103 (1954). 

Here, Ms and Ms,ads are the electrochemical potentials of S in the bulk solution and in the adsorbed state. Let us apply the Gibbs adsorption equation to the interphase between a pure metal M and an aqueous solution containing molecular and ionic species denoted by the subscript j, in addition to water w and the species S. Choosing the neutral metal atoms M and the electrons e in excess with respect to metal atoms as the constituents of the metal phase, we may formally write ... 

To show this, we express the condition of equilibrium at the interphase by setting the electrochemical potential of equal in the two phases ... 

Under electrochemical conditions and T, P = constant, adsorption isotherms can be derived using standard statistical considerations to calculate the Gibbs energy of the adsorbate in the interphase and the equilibrium condition for the electrochemical potentials of the adsorbed species i in the electrolyte and in the adsorbed state (eq. (8.15) in Section 8.2). A model for the statistical considerations consists of a 2D lattice of arbitrary geometry with Ns adsorption sites per unit area. In the case of a 1/1 adsorption, each adsorbed particle can occupy only one adsorption site so that the maximal number of adsorbed particles per unit area in the compact monolayer is determined by A ax = Ng. Then, this model corresponds to the simple Ising model. The number of adsorbed particles, A ads< and the number of unoccupied adsorption sites, No, per unit area are given by... 

The interphase boundaries between a semiconductor and a metal or electrolyte solution can also be conveniently represented using an energy diagram (Fig. 2). Here, energy and electrochemical potential levels are shown for all three phases making together the electrochemical cell, namely, the semiconductor photoelectrode, the metal counter-electrode, and the electrolyte solution in between, the latter containing a redox couple where an electrochemical reaction... 

In each case, the ion, species, or electron (boldface in Equation 19) that crosses or reacts at the interphase establishes the chemical equilibrium at the interface (equality of the electrochemical potential between solid or surface phase and solution) and thus determines (or influences) the interfacial potential difference. (The electron in Equations a and b may stand for a suitable reductant.) However, without further information the validity of the Nernst equation may not be inferred. 

Let us note that the influence of adsorption, whether specific or nonspecific, and that of surface coverage can be examined on safe grounds by our MD method because such effects enter automatically in the expressions for the chemical potentials through both their standard portions and their activity terms. In addition, the electric terms in the electrochemical potentials are affected by all the circumstances of the structure of the interphase and of the mechanism of the process, but as shown in the foregoing section, these terms are never handled separately from the corresponding chemical terms. Assumptions of a mechanistic or molecular nature can be introduced with a reasonable degree of safety when the thermodynamic treatment has been carried out as far as has been done above for a typical simple case. 

At the interphase equilibrium the electrochemical potentials of each substance in both phases are equal ... 

To consider the kinetics of chemical reactions in dynamical systems the idea of local properties of the reactants and products in local environment can be successfully used. At the interphase equilibrium the electrochemical potential of each substance (i) in each microphase (m) and volume phase (v) are the same ... 

It has been suggested that in practical non-aqueous lithium battery systems the anode (Li or graphite) is always covered by a surface layer named the solid electrolyte interphase (SEI), 1-3 run thick, which is instantly formed by the reaction of the metal with the electrolyte. This film, which acts as an interphase between the metal and the solution, has the properties of a solid electrolyte. This layer has a corrosive effect and grows with the cycling life of the battery [52], Thermodynamic stability of a lithium cell requires the electrochemical potentials of electrodes a and Ec located within the energetic window of the electrolyte, which contrains the cell voltage Eq of th electrochemical ceU to ... 

Every liquid interface is usually electrified by ion separation, dipole orientation, or both (Section II). It is convenient to distinguish two groups of immiscible liquid-liquid interfaces water-polar solvent, such as nitrobenzene and 1,2-dichloroethane, and water-nonpolar solvent, e.g., octane or decane interfaces. For the second group it is impossible to investigate the interphase electrochemical equilibria and the Galvani potentials, whereas it is normal practice for the first group (Section III). On the other hand, these systems are very important as parts of the voltaic cells. They make it possible to measure the surface potential differences and the adsorption potentials (Section IV). 

Double layer emersion continues to allow new ways of studying the electrochemical interphase. In some cases at least, the outer potential of the emersed electrode is nearly equal to the inner potential of the electrolyte. There is an intimate relation between the work function of emersed electrodes and absolute half-cell potentials. Emersion into UHV offers special insight into the emersion process and into double layer structure, partly because absolute work functions can be determined and are found to track the emersion potential with at most a constant shift. The data clearly call for answers to questions involving the most basic aspects of double layer theory, such as the role water plays in the structure and the change in of the electrode surface as the electrode goes frcm vacuum or air to solution. 

So, in general when two conducting phases are brought into contact, an interphase electric potential vill develop. The exploitation of this phenomenon is one of the subjects of electrochemistry and we can define electrochemical reactions as ones in which... 

Here we are interested in the potential difference across an interphase. Let us consider the interphase shown in Figure 5.1, where the potential of the solution is s and that of the metal is The potential difference across the interphase is A(f)(M,S) = < M (ks- This potential difference cannot be measured directly since instruments that measure potential difference require two terminals and we have only one terminal the metal M. Thus, to measure the potential difference of an interphase, one should connect it to another interphase and thus form an electrochemical cell. Potential difference across such an electrochemical cell can be measured. We discuss two types of electrode potentials metal/metal-ion and redox potentials. 

Let us consider the general electrochemical cell shown in Figure 5.2. The potential difference across the electrochemical cell, denoted , is a measurable quantity called the electromotive force (EMF) of the cell. The potential difference in Figure 5.2 is made up of four contributions since there are four phase boundaries in this cell two metal-solution interphases and two metal-metal interfaces. The cell in Figure 5.2 can be represented schematically as Pt/M7S/M/Pt. 

Eor an electrochemical reaction the rate of reaction v and the rate constant k depend on potential E specifically, the potential difference across electrode-solution interphase Acf) through the electrochemical activation energy AGf. Thus, the central problem here is to find the function... 

Since the advantage of using nonaqueous systems in electrochemistry lies in their wide electrochemical windows and low reactivity toward active electrodes, it is crucial to minimize atmospheric contaminants such as 02, H20, N2, C02, as well as possible protic contaminants such as alcoholic and acidic precursors of these solvents. In aprotic media, these contaminants may be electrochemically active on electrode surfaces, even at the ppm level. In particular, when the electrolytes comprise metallic cations (e.g., Li, Mg, Na), the reduction of all the above-mentioned atmospheric contaminants at low potentials may form surface films as the insoluble products precipitate on the electrode surfaces. In such cases, the metal-solution interface becomes much more complicated than their original design. Electron transfer, for instance, takes place through electrode-solution rate limiting interphase. Hence, the commonly distributed solvents and salts for usual R D in chemistry, even in an analytical grade, may not be sufficient for use as received in electrochemical systems. 

This equation is equivalent to Eq. 4H, considering that q is nothing but the surface excess of electrons on the metal side of the interphase, and the electrical potential E is the intensive variable determining the electrochemical free energy of electrons in the metal. 

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