Electrical potential, definition

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... 

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

In a similar way, electrochemistry may provide an atomic level control over the deposit, using electric potential (rather than temperature) to restrict deposition of elements. A surface electrochemical reaction limited in this manner is merely underpotential deposition (UPD see Sect. 4.3 for a detailed discussion). In ECALE, thin films of chemical compounds are formed, an atomic layer at a time, by using UPD, in a cycle thus, the formation of a binary compound involves the oxidative UPD of one element and the reductive UPD of another. The potential for the former should be negative of that used for the latter in order for the deposit to remain stable while the other component elements are being deposited. Practically, this sequential deposition is implemented by using a dual bath system or a flow cell, so as to alternately expose an electrode surface to different electrolytes. When conditions are well defined, the electrolytic layers are prone to grow two dimensionally rather than three dimensionally. ECALE requires the definition of precise experimental conditions, such as potentials, reactants, concentration, pH, charge-time, which are strictly dependent on the particular compound one wants to form, and the substrate as well. The problems with this technique are that the electrode is required to be rinsed after each UPD deposition, which may result in loss of potential control, deposit reproducibility problems, and waste of time and solution. Automated deposition systems have been developed as an attempt to overcome these problems. 

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... 

The outer electrical potential of a phase is the electrostatic potential given by the excess charge of the phase. Thus, if a unit electric charge is brought infinitely slowly from infinity to the surface of the conductor to a distance that is negligible compared with the dimensions of the conductor considered (for a conductor with dimensions of the order of centimetres, this distance equals about 10 4cm), work is done that, by definition, equals the outer electric potential ip. 

The expression for V(r), given as Eq. (3.1), follows from the definition of electrical potential, which will be reviewed here. Any distribution of electrical charge creates a potential V(r) in the surrounding space. For an assembly of point charges ). located at positions r, this electrical potential is simply a sum of Coulombic potentials, as given in Eq. (3.2). 

In a discussion of permeability it is important to recognize that we deal with operational definitions, since the act of measurement influences the state of the system. In your case, applying an electrical potential gradient and performing electrodialysis alter the distribution of ionophore within the membrane. I wonder whether you have attempted to measure permeability by isotopic tracer techniques In this method the distribution of ionophore would not be influenced. Furthermore, information can be obtained on the question of carriers versus channels or pores. It should not be difficult to determine the extent of possible isotope interaction between tracer species and abundant species in the membrane as discussed by Kedem and Essig [J. Gen. Physiol., 48, 1047 (1965)]. Positive isotope interaction would tend to suggest the presence of channels or pores, negative isotope interaction the presence of carriers. 

Hence, equilibrium constants of homogeneous electron-transfer reactions between (A) and B are evidently connected to the differences in reduction potentials of A and B. This connection reflects a definite physical phenomenon. Namely, if two redox systems are in the same solution, they react with each other until a unitary electric potential is reached. For the transfer of only one electron at room temperature, the following simplified equation can be employed ... 

We recognize from our previous experience that pt is a function of the entropy, volume, temperature, or pressure in appropriate combinations and the composition variables. The splitting of into these two terms is not an operational definition, but its justification is obtained from experiment. The quantity pt is the quantity that is measured experimentally, relative to some standard state, whereas the electrical potential of a phase cannot be determined. Neither can the difference between the electrical potentials of two phases alone at the same temperature and pressure generally be measured. Only if the two phases have identical composition can this be done. If the two phases are designated by primes,... 

When a chemical reaction is proceeding, it is, by definition, not at equilibrium and thus not reversible. Thus, entropy changes in chemical reactions cannot be obtained from heat effects in calorimetric experiments. Entropy changes can be obtained by studying chemical equilibrium (Chapter 7) or by opposing the tendency of the reaction to proceed with an applied electric potential (Chapter 10). 

Both of these quantities contain an arbitrary constant, the zero from which the potentials are measured, but differences of either the electrostatic potential or of the electrochemical potential, between two phases, are definite. The thermionic work function, x, the work required to extract electrons from the highest energy level within the phase, to a state of rest just outside the phase, is also definite and the relation between the three definite quantities fa, V, and x is given by (3.1), where is the electrochemical potential of electrons very widely separated from all other charges. The internal electric potential , and other expressions relating to the electrical part of the potential inside a phase containing dense matter, are undefined, and so are the differences of these quantities between two phases of different composition. This indefiniteness arises from the impossibility of separating the electrostatic part of the forces between particles, from the chemical, or more complex interactions between electrons and atomic nuclei, when both types of force are present. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

Volt — SI-derived measurement unit of the electric -> potential difference or voltage. Symbol V (named in honor of the Italian physicist Alessandro - Volta (1745— 1827)). Definition lvolt is the potential difference between two points of a homogeneous, linear conductor of constant temperature, when a current of one ampere converts one watt of power. 

Electric potential tp that causes a current at the point x, y, z lead to the definition of electric force Xe... 

The additive constant term fij in Equation 2.4 is the chemical potential of species j for a specific reference state. From the preceding definitions of the various quantities involved, this reference state is attained when the following conditions hold The activity of species j is 1 (RT In cij = 0) the hydrostatic pressure equals atmospheric pressure (VjP = 0) the species is uncharged or the electrical potential is zero (ZjFE = 0) we are at the zero level for the gravitational term (rrijgh = 0) and the temperature equals the temperature of the system under consideration. Under these conditions, fij equals fij (Eq. 2.4). 

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