Electrochemical potential, definition

The study clearly shows that the observed electrical signals are electrochemical in origin, and the first-order description of the process is consistent with that expected from atmospheric pressure behaviors. Nevertheless, the complications introduced by the shock compression do not permit definitive conclusions on values of electrochemical potentials without considerable additional work. 

Eq. (8)] represents by definition the zero point of the electrochemical potential scale (standard hydrogen electrode, often denoted SHE). 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

One might righteously ask why this close and preferential connection exists between the r vs and the r vs po dependencies. The answer is straightforward and has simply to do with the definitions of O and Fermi level EF (or electrochemical potential of electrons j (=EF))7 which are connected via ... 

Here is a summary of the definitions and conventions for working with electrochemical potentials ... 

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. 

Using the definition of the electrochemical potential this can be rewritten in the following forms ... 

Equation (3.1.2) and the definition of the chemical potential yield the equation for the electrochemical potential of species i with activity a,(j3) and charge z, in phase )8 in the form... 

Active transport. The definition of active transport has been a subject of discussion for a number of years. Here, active transport is defined as a membrane transport process with a source of energy other than the electrochemical potential gradient of the transported substance. This source of energy can be either a metabolic reaction (primary active transport) or an electrochemical potential gradient of a substance different from that which is actively transported (secondary active transport). 

For electrons in a metal the work function is defined as the minimum work required to take an electron from inside the metal to a place just outside (c.f. the preceding definition of the outer potential). In taking the electron across the metal surface, work is done against the surface dipole potential x So the work function contains a surface term, and it may hence be different for different surfaces of a single crystal. The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface. If the reference point for the Fermi level is taken to be the vacuum level instead, then Ep = —, since an extra work —eoV> is required to take the electron from the vacuum level to the surface of the metal. The relations of the electrochemical potential to the work function and the Fermi level are important because one may want to relate electrochemical and solid-state properties. 

The approach to the mathematical definition of the interface model is very simple. For every layer in the interface, the charge is defined once as a function of chemical parameters and once as a function of electrostatic parameters. The functions for charge are set equal to each other and solved for the unknown electrochemical potentials. Mathematical techniques for solving the equations have been worked out and described in detail (9). 

At the R/M interface there is electronic equilibrium, and their electrochemical potentials are the same. Therefore, = ]uR, and from the definition of n [seeEq. (6.34)],... 

The reader should be aware that considerable confusion exists with respect to names and definitions.176 For example, the AGH+ of Eq. 18-8 can also be called the proton electrochemical potential Ap,+, which is analogous to the chemical potential p of an ion (Eq. 6-24) and has units of kj/mol (Eq. 18-10). 

As a side remark, the most consistent form of the thermodynamic definition of the electrochemical potential is... 

Any surface (typically a piece of metal) on which an electrochemical reaction takes place will produce an electrochemical potential when in contact with an electrolyte (typically water containing dissolved ions). The unit of the electrochemical potential is volt (TV = 1JC1 s 1 in SI units).The metal, or strictly speaking the metal-electrolyte interface, is called an electrode and the electrochemical reaction taking place is called the electrode reaction. The electrochemical potential of a metal in a solution, or the electrode potential, cannot be determined absolutely. It is referred to as a potential relative to a fixed and known electrode potential set up by a reference electrode in the same electrolyte. In other words, an electrode potential is the potential of an electrode measured against a reference electrode. The standard hydrogen electrode (SHE) is universally adopted as the primary standard reference electrode with which all other electrodes are compared. By definition, the SHE potential is OV, i.e. the zero-point on the electrochemical potential scale. Electrode potentials may be more positive or more negative than the SHE. 

Although the calculation of Ece in the previous section appears satisfactory, it is not very rigorous. In this section we show how a rigorous thermodynamic argument4 leads to the same result. For this we need the concept of the electrochemical potential /i, that obeys the same criteria at equilibrium as the chemical potential ju. Its definition for component i in phase a is... 

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