Potential difference across the interface

It should be noted that the capacity as given by C, = a/E, where a is obtained from the current flow at the dropping electrode or from Eq. V-49, is an integral capacity (E is the potential relative to the electrocapillary maximum (ecm), and an assumption is involved here in identifying this with the potential difference across the interface). The differential capacity C given by Eq. V-50 is also then given by... 

Monolayers of distearoylphosphatidylcholine spread on the water-1,2-dichloro-ethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result... 

As will be described in detail below, solute distribution in biphasic systems can be modulated by application of a Galvani potential difference across the interface, thereby leading to the transfer of species from one phase to the other. Therefore, in electrochemical terms, passive transfer simply means the partition across an interface, mediated by a potential-driven process. 

This time, the boundary line is independent of the Galvani potential difference across the interface, and the corresponding pH value can be regarded as the effective dissociation constant, pK eff, which appears experimentally due to the partitioning of the neutral species. For a monoprotic substance, pK eff can thus be defined as ... 

In another notation, and supposing the metal appears for z -> -oo and the electrolyte for z -> oo, the potential difference across the interface may be written as... 

At a given potential or, more exactly, at a given potential difference across the interface, the variation of coverage of A with concentration of A constitutes the isotherm. The simplest commonly encountered isotherm is that due to Langmuir and arises if ... 

We can progress from here provided that we can find expressions for the partial derivatives of equation (2.99). Provided that the concentration of supporting electrolyte is sufficiently high that all the potential difference across the interface is accommodated within the Helmholtz layer, then transport of O and R near the electrode will only take place via diffusion (i.e. we can neglect migration). The equation of motion for either O or R is given by the differential form of Fick s equation, as discussed in chapter I ... 

A polarizable Interface is represented by a (polarizable) electrode where a potential difference across the double layer is applied externally, i.e., by applying between the electrode and a reference electrode using a potentiostat. At a reversible interface the change in electrostatic potential across the double layer results from a chemical interaction of solutes (potential determining species) with the solid. The characteristics of the two types of double layers are very similar and they differ primarily in the manner in which the potential difference across the interface is established. 

As is shown in Eqn. 4-3, the inner potential difference across the interface M/S consists of a chaise-induced potential and a dipole-induced potential =... 

At a semiconductor-electrolyte interface, if there is no specific interaction between the charge species and the surface an electrical double layer will form with a diffuse space-charge region on the semiconductor side and a plate-like counter ionic charge on the electrolyte side resulting in a potential difference (j) across the interface. The total potential difference across the interface can be given by... 

When charges are separated, a potential difference develops across the interface. The electrical forces that operate between the metal and the solution constitute the electrical field across the electrode/electrolyte phase boundary. It will be seen that although the potential differences across the interface are not large ( 1 V), the dimensions of the interphase region are very small (—0.1) and thus the field strength (gradient of potential) is enormous—it is on the order of 10 V cm. The effect of this enormous field at the electrode/electrolyte interface is, in a sense, the essence of electrochemistry. 

The argument for the formation of the double layer has proceeded simply. The existence of a boundary for the electrolyte necessarily implies a basic anisotropy in the forces operating on the particles in the intcrphase region. Owing to this anisotropy, there occurs a redistribution of the mobile charges and orientable dipoles (compared with their distribution in the bulk of the phases). This redistribution is the structural basis of the potential difference across the interface. 

There is a functional relationship between the charge on each phase (or the potential difference across the interface) and the structure of the interphase region. The fundamental problem of double-layer studies is to unravel this functional relationship. One has understood a particular electrified interface if, on the basis of a model (i.e., an assumed type of arrangement of the particles in the interphase), one can predict the distribution of charge (or variation of potential) across the interphase. 

The Measurement of Interfacial Tension as a Function of the Potential Difference across the Interface... 

The interfacial tension depends on the forces arising from the particles present in the interphase region. If the arrangement of these particles (Le., the composition of the interface) is altered by varying, for example, the potential difference across the interface, then the forces at the interface should change and thus cause a change in the interfacial tension. One would expect therefore that the surface tension y of the metal/solution interface will vary with the potential difference V supplied by the external source. 

A second implication and one that would allow one to evaluate the new model, is that the separation of charges and potential regions also produces a separation of differential capacities. One may start by differentiating the potential difference across the interface [Eq. (6.132)] with respect to the charge on the metal, qM,... 

However, it must not be imagined that the water molecules act by themselves and that they are unaffected by the presence of their neighbors. After all, dipoles interact with dipoles. Hence, the oriented water molecules also experience lateral interaction— a phenomenon that affects the net number of water molecules oriented in one direction and therefore the value of the dipole potential, gj-ipole (Section 6.7.6). Once the dipole potential is affected, the total potential difference across the interface gets affected, and consequently, the properties of the interface. 

Thus, according to the convention that the potential difference across the interface is the inner potential of the metal minus the inner potential of the solution, one has... 

Things are simple at the instant of immersion of a metal in an electrolytic solution. There is no field and no potential difference across the interface. Reactions (e.g., M+ + e — M) run for a very short while chemically. However, the very occurrence of a charge-transfer reaction across the interface in one direction creates an electric field, a fraction of which puts a brake on the reaction M+ + e — M. The same field, however, has an accelerating effect on the charge-transfer reaction in the opposite direction, M — M+ + e. 

Thus, the electronation and deelectronation reactions modify the electric field across the interface, and the field, in feedback style, alters the rates until the rates of M+ + e — M and M — M+ + e become equal. This is equilibrium. Underlying the condition of zero net current, an equilibrium exchange-current density Iq, flows across the interface in both directions. The potential difference across the interface at equilibrium depends upon the activity ratio of electron acceptor to electron donor in the solution. Alter the ratio, and the equilibrium potential changes.14... 

What, therefore, is the potential difference to be used Is it MzfraP< ), the potential difference from the metal to the contact adsorption plane, or IHP (inner Helmholtz plane, see Fig. 6.88), or is it MzfOHP<[>, the potential difference from the metal to the OHP (outer Helmholtz plane, see Fig. 6.88), or MzfSpotential difference from the bulk of the metal to the bulk of the electrolytic solution In respect to P, does one consider it to multiply the whole potential difference across the interface or only a fraction of this potential difference Similarly, what concentrations of electron acceptors and donors must be fed into the basic equation Bulk values or the values at the OHP or the values at the contact-adsorbed species (Fig. 6.88) ... 

Fig. 7.17. The potential difference across the interface can be divided into the linear portion of the layer extending to the OHP, at which the ions ready to discharge are located, and a portion in the diffuse part of the double layer, which is called the elec-trokinetic or potential.

Fig. 7.21. When a junction between a p-type and an n-type of semiconductor is established (a), a diffusion of holes and electrons in the opposite direction takes place (b). This results in a separation of charge (c) and the formation of an electrical potential difference across the interface (d).

Equilibrium is reached when the driving force for the diffusion (the concentration gradient) is compensated for by the electric field (the potential gradient). Under these equilibrium conditions, there is an equilibrium net charge on each side of the junction and an equilibrium potential difference d< >e. This process is analogous to the way charge transfer across a nonpolarizable electrode/solution interface results in the establishment of an equilibrium potential difference across the interface. 

Fig. 7.23. As the potential difference across the interface is lowered by superimposing an external field, the current starts flowing.

Any servicing difficulties and delays, such as preconditions that must be satisfied before electron tunneling occurs, lead to a queue of electrons on the electrode. In other words, the excess charge qM on the electrode becomes more negative, and thus the potential difference across the interface departs from the equilibrium value. The overpotential, therefore, is determined by the electron queue. 

Thus, when a constant current is imposed on an interface at which the rate of the electronation process is determined by diffusion (i.e., the other reaction steps, particularly electronation, in the overall reaction sequence are relatively fast), it is principally the interfacial concentration of M"+ that determines how the potential difference across the interface varies with time. The variation of with time must therefore be analyzed. 

This expression, known as Sand s equation, gives the variation of the interfacial concentration of M"+ with time after application of a constant current density. But one seeks also to know the time variation of the potential difference across the interface at which the electronation reaction M"+ + ne — M is occurring. To obtain this information, one recalls that the charge-transfer reaction across the interface is assumed in the present treatment to be virtually in equilibrium and therefore the Nenist equation (7.177) can be used to relate the potential difference to the concentration at the interface. That is, by substituting (7.181) in (7.177),... 

What is the quantitative relationship between the steady state, convection-with-diffusion current density and the potential difference across the interface How is the steady-state potential difference at a steady current density related to the zero-current, or equilibrium, potential difference These questions are the relevant ones for steady passage of current in convection-aided situations. 

Since the charge transfer is assumed to be virtually at equilibrium, one can again use the Nernst equation to express the potential difference across the interface. Thus, when the current is zero,... 

Fig. 9.12. When the potential difference across the interface is changed from zero to a value Aty, the Morse curve of the initial state is shifted vertically by the amount of electrical energy FA .

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