The electric potential

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

The electrochemical potentials pi, may now be expressed in terms of the chemical potentials pt, and the electrical potentials (see Section V-9) ... 

A special example of electrical work occurs when work is done on an electrochemical cell or by such a cell on the surroundings -w in the convention of this article). Themiodynamics applies to such a cell when it is at equilibrium with its surroundings, i.e. when the electrical potential (electromotive force emi) of the cell is... 

In these equations the electrostatic potential i might be thought to be the potential at the actual electrodes, the platinum on the left and the silver on the right. However, electrons are not the hypothetical test particles of physics, and the electrostatic potential difference at a junction between two metals is nnmeasurable. Wliat is measurable is the difference in the electrochemical potential p of the electron, which at equilibrium must be the same in any two wires that are in electrical contact. One assumes that the electrochemical potential can be written as the combination of two tenns, a chemical potential minus the electrical potential (- / because of the negative charge on the electron). Wlien two copper wires are connected to the two electrodes, the... 

I l. isson s equation relates the second derivative of the electric potential to the charge density ... 

For an ion traveling in a straight line in a complete vacuum, where there are no collisions, the velocity of the ion depends only on the electric potential difference through which it was accelerated, as shown by Equation 49.1 and Figure 49.4a. 

The selection of which ions can pass through the quadrupoles to reach the detector is made by varying the electric potentials and/or their frequency usually it is easier to keep the frequency constant and alter the voltage. 

Sodium and potassium ions are actively absorbed from the intestine. As a consequence of the electrical potential caused by transport of these ions, an equivalent quantity of Cf is absorbed. The resulting osmotic effect causes absorption of water (56). 

Galvanic Corrosion. Galvanic corrosion occurs when two dissimilar metals are in contact in a solution. The contact must be good enough to conduct electricity, and both metals must be exposed to the solution. The driving force for galvanic corrosion is the electric potential difference that develops between two metals. This difference increases as the distance between the metals in the galvanic series increases. 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

When concentration gradients in the solution can be ignored, equations 25 through 29 show that the electric potential is governed by Laplace s equation... 

Theory of Electrophoretic Motion. The study of the mechanics of electrophoresis focuses on the basis of electric potential on the surface of an object, and the relation of the electric potential to the velocity of the particle. Whereas research has been generally limited to nonmolecular particles of weU-defined geometry and is not strictly apphcable to molecules such as proteins and DNA fragments, this work is useful for understanding the physics of electrophoretic motion. 

The oxidation of another metal is limited by the outward flow of electrons through a uniform, unbroken oxide film. Assume that the electrical potential in the film immediately next to the metal is Vi, and the potential immediately next to the free surface is Vi, where Vj and Vi are constants. Use Ohm s Law to show that parabolic kinetics should apply in this case also. 

This handbook deals only with systems involving metallic materials and electrolytes. Both partners to the reaction are conductors. In corrosion reactions a partial electrochemical step occurs that is influenced by electrical variables. These include the electric current I flowing through the metal/electrolyte phase boundary, and the potential difference A( = 0, - arising at the interface. and represent the electric potentials of the partners to the reaction immediately at the interface. The potential difference A0 is not directly measurable. Therefore, instead the voltage U of the cell Me /metal/electrolyte/reference electrode/Me is measured as the conventional electrode potential of the metal. The connection to the voltmeter is made of the same conductor metal Me. The potential difference - 0 is negligibly small then since A0g = 0b - 0ei ... 

The driving force for the transport of all particles is a change in the electrochemical potential /i, which is related to the partial molar free enthalpy /i, and the electric potential 0 as follows ... 

The principle of the measurement is described with the help of Fig. 2-7 [50]. Potential measurement is not appropriate in pipelines due to defective connections or too distant connections and low accuracy. Measurements of potential difference are more effective. Figure 3-24 contains information on the details in the neighborhood of a local anode the positions of the cathodes and reference electrodes (Fig. 3-24a), a schematic representation of the potential variation (Fig. 3-24b), and the derived values (Fig. 3-24c). Figure 2-8 should be referred to in case of possible difficulties in interpreting the potential distribution and sign. The electrical potentials of the pipeline and the reference electrodes are designated by... 

The electrical potential field in the soil, taking into account the soil surface, is obtained by the image method, usually applied in potential theory, for the pipeline at the soil surface and superposition of the two fields. 

Figure 7 The electric potential relative to the hydrocarbon ( dipole potential) as a function of distance from the center of a fully hydrated DPPC bilayer.

Negative charge The electrical potential which an atom acquires when it gains one or more electrons a characteristic of an anion. 

Kelvin effect The electrical potential gradient caused by a temperature gradient along a conducting wire. Also known as the Thomson Effect. 

The basic reasons for grounding an electrical supply system are to limit the electrical potential difference (voltage) between all uninsulated conductive equipment in the area to provide isolation of faults in the system and to limit overvoltage on the system under various conditions. In the case of a grounded system it is essential to ground at each separately derived voltage level. 

Both entropic and coulombic contributions are bounded from below and it can be verified that the second variation of is positive definite so that the above equations correspond to a minimum [27]. Using conditions in the bulk we can eliminate //, from the equations. Then we get the Boltzmann equation in which the electric potential verifies the Poisson equation by construction. Hence is equivalent within MFA to the... 

FIGURE 10.2 The passive diffusion of a charged species across a membrane depends upon the concentration and also on the charge of the particle, Z, and the electrical potential difference across the membrane, Ai/<. 

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