Inner electric potentials

Gap energy (solid state) E, Inner electric potential 4>... 

In this equation, the second term describes purely electrostatic work, connected with an infinitely slow transfer of charge zF from infinity in a vacuum into the bulk of the second phase, i.e. to a point with electric potential 0. Here only electric charge is transferred, not a material species with which it might be connected. The ratio of this work to the transferred charge is equal to the inner electrical potential 0 of the given phase. 

The inner electrical potential 0 may consist of two components. Firstly, the phase may possess some excess electrical charge supplied from outside. This charge produces an outer electrical potential 0. This is defined as the limit of the ratio w/q for <7—>0, where w is the work expended for the infinitely slow transfer of charge q from an infinite distance to a point in the vacuum adjacent to the surface of the given phase and just outside the range of image forces. A particle transferred from this point further on in the... 

It should be recalled that the term surface potential is used quite often in membranology in rather a different sense, i.e. for the potential difference in a diffuse electric layer on the surface of a membrane, see page 443.) It holds that 0 = 0 + X (this equation is the definition of the inner electrical potential 0). Equation (3.1.2) can then be written in the form... 

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

Apparently no cell reaction can occur in this cell as the vacuum prevents movement of species between phases 1 and 3. The measured difference in the inner electric potentials of phases 5 and 1 is equal to the difference in outer electric potentials between phases 5 and 3,... 

The difference in inner electrical potentials between two electrolyte solutions separated by a membrane is termed the membrane potential, A m In th scheme... 

Finally, if the thickness of the electrical double layer (diffuse layer) in the droplet is comparable with r, the r dependence of kqbs will be dependent on the TBA+ concentration in the droplet since the spatial distribution of the inner electric potential of the droplet varies with [TBA+TPB ], However, since results analogous with those in Figure 14a ([TBA+TPB ] = 10 mM) have been obtained even at [TBA+TPB"] = 5mM (Aodiffuse layer effect does not contribute to the r effect on kobs at r > 1 /an. 

The macroscopic electric potential on the right side of Eq. s2.7 is known as an inner electric potential, and the potential difference on the right side of Eq. s2.9 is an example of a Galvani potential difference39... 

The effects of the crystallographic face and the difference between metals are evidence of the incorrectness of the classical representations of the interface with all the potential decay within the solution (Fig. 3.13a). In fact a discontinuity is physically improbable and experimental evidence mentioned above confirms that it is incorrect, the schematic representation of Fig. 3.136 being more correct. This corresponds to the chemical models (Section 3.3) and reflects the fact that the electrons from the solid penetrate a tiny distance into the solution (due to wave properties of the electron). In this treatment the Galvani (or inner electric) potential, (p, (associated with EF) and the Volta (or outer electric) potential, ip, that is the potential outside the electrode s electronic distribution (approximately at the IHP, 10 5cm from the surface) are distinguished from each other. The difference between these potentials is the surface potential x (see Fig. 3.14 and Section 4.6). 

Activation overpotential — When the activation energy of the - charge transfer reaction is high an -+ overpotential is needed to drive the reaction in the desirable direction with an appreciable rate. It is called activation overpotential (qac). The electric field (the -> inner electric potential, f) in the phase a determines the energy of the charged species this can be expressed by the -> electrochemical potential (pi). 

Charge transfer coefficient — Figure 2. Change of the energy barrier for the electron transfer and the effect of a change of electrode potential (for the sake of simplicity it is assumed that the inner electric potential of the solution phase remains unchanged)... 

Inner electric potential - potential, subentry - inner electric potential... 

Galvani potential difference — A

electrostatic component of the work term corresponding to the transfer of charge across the - interface between the phases a and f whose - inner electric potentials are (/>" and R, respectively, i.e., the Galvani potential difference is the difference of inner electric potentials of the contacting phases. The electrical potential drop can be measured only between the points which find themselves in the phases of one and the same chem-ical composition [i,ii]. Indeed, in this case p ( = p and... 

Verwey-Niessen model — Earliest theoretical model of the - interface between two immiscible electrolyte solutions (ITIES) assuming the existence of a diffuse double layer with one phase containing an excess of the positive space charge and the other phase an equal excess of the negative space charge [i] (Figure). The difference of - inner electric potentials, Afcj> = (f>w - [Pg.692]

Na is the Avogadro constant, Too is the electron energy at rest at infinite distance, Tp is the -> Fermi energy or the molar Fermi energy, respectively, T is the -> Faraday constant, fM and (pM are the outer electric and inner electric -> potentials of the metal phase (M), resp., and pf is the -> electrochemical potential of electrons in the metal phase. 

Distribution potential established when ionic species are partitioned in equilibrium between the aqueous and organic phases, W and O, is a fundamental quantity in electrochemistry at liquid-liquid interfaces, through which the equilibrium properties of the system are determined. In any system composed of two immiscible electrolyte solutions in contact with each other, the equilibrium is characterized by the equality of the electrochemical or chemical potentials for each ionic or neutral species, respectively, commonly distributed in the two phases [4]. It follows from the former equality that the distribution potential Aq aqueous phase, 0, with respect to the inner potential of the organic phase, 0°, is given by the Nernst equation [17,18],... 

Electric potential is the electric work necessary to transfer the unit charge in vacuum from the infinite distance to a position, the potential of which is to be established. If this position is situated inside of a phase (metal, solution, etc.), it is called the inner electric potential and is denoted by < ). The chemical potential of an ion in the presence of an electric potential is called its electrochemical potential, jl expressed as in Eq. (1) ... 

Inner Potential (Stern) In the diffuse electric double layer extending outward from a charged interface, the electrical potential at the boundary between the Stern and the diffuse layer is termed the inner electrical potential. Synonyms include the Stern layer potential or Stem potential. See also Electric Double Layer, Zeta Potential. 

Fig. 1.2.2 (a) Schematic situation at the border of a phase with vacuum. is the outer electric potential of phase a, i.e., the work that must be done when a unit charge is transferred from infinity (in the vacuum) to the surface of phase a. (The difference in the two outer electric potentials of two different phases is called the Volta potential difference.) x is the surface electric potential of phase a, i.e., the work to be done when a unit charge is transferred from the surface into phase a, and is the inner electric potential of phase a, i.e., the work to be done when a unit charge is transferred from infinity (in vacuum) into the inner of phase a. is a nonmeasurable quantity, whereas 1 can be calculated and measured. The three potentials are interrelated as follows (j> = + x -... 

Whereas a direct measurement of the inner electric potential of a single phase is impossible, the difference, i.e., the Galvani potential difference of two phases A

common interface, is accessible when a proper reference electrode is used, i.e., a metal/electfolyte system, which should guarantee that the chemical potential of the species i is the same in both electrolytes, i.e., the two electrolytes contacting the metal phases I and 11. In addition, the absence of a junction potential between the two electrolytes is required. Under such circumstances it is possible to measure a potential difference, AE, that is related to A(p however, it always includes the A4> of the reference electrode. The latter is set to zero for the Standard Hydrogen Electrode (see below). In fact, the standard chemical potential of the formation of solvated protons is zero by convention. 

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