Current density, definition

The only physical difference is that here the current, I, is not directly measurable and thus the dimensionless current density, J, is not directly computable. This difficulty can, however, be overcome if the ratio of the reactivities, A, of normally adsorbed and backspillover oxygen is known (e.g. from electrochemical promotion experiments, where A, as already noted, also expresses the Faradaic efficiency). Thus in this case upon combining the definition of A with equation (11.23) one obtains the following expression for J ... 

By definition a current of positive charge (an oxidation reaction) is taken as a positive current, a current of negative charge (a reduction reaction) is taken as a negative current. When the electrode is at equilibrium, the net current density j equals zero. This implies, that... 

By definition the partial current density ij is the number of charges that in unit time cross the unit cross-sectional area due to the migration of ions j that is,... 

It was demonstrated, however, in 1947 by John O M. Bockris that between the exchange current densities of the hydrogen reaction at different metals and the values of the electron work function (into vacuum), a definite correfation does exist. Many workers have confirmed this correlation. An example of this correlation is shown as a plot of log f vs. X° in Fig. 28.2. 

In electrorefining and in electroplating, where the same metal is used as a soluble anode, the theoretical cell voltage is zero or almost zero therefore, the energy efficiency, as per this definition, is expected to be zero or close to zero, whatever may be the current efficiency. The actual cell voltage depends on the current density, the temperature, the electrolyte... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The functional dependence of the activation energy of the anodic electrode reaction can be derived as follows. According to the definition of the rate of the electrode reaction, the partial current density... 

Assume that both the initial substances and the products of the electrode reaction are soluble either in the solution or in the electrode. The system will be restricted to two substances whose electrode reaction is described by Eq. (5.2.1). The solution will contain a sufficient concentration of indifferent electrolyte so that migration can be neglected. The surface of the electrode is identified with the reference plane, defined in Section 2.5.1. In this plane a definite amount of the oxidized component, corresponding to the material flux J0x and equivalent to the current density j, is formed or... 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

For a given hydrodynamic condition near the electrode in steady state, the maximum gradient is obtained when the concentration at the electrode is zero, or virtually zero. From the definition of limiting-current density, this situation corresponds to the limiting-current condition. 

Equation (7) is an exact analogue of the continuity equation (1.7) of hydrodynamics, and this allows definition of a probability current density... 

This definition suggests a reasonable formulation of entropy current density as... 

In contrast, current density is intrinsic and does not depend on the electrode area, since, by its definition, the current measured has been adjusted to compensate for differences in area. 

From the definition of current density i in equation (1.1), we obtain an area of 0.12 cm2. 

Figure 7. Top panels Schematic diagram of 3-D cylindrical battery arrays in parallel row (left) and alternating anode/cathode (right) configurations. Middle panels Isopotential lines between cathode (C) and anode (A) for unit battery cells. Bottom panel Current densities (in arbitrary units, a.u.) at the electrode surfaces as a function of the angle 9 (see middle panel for definition of 9). The area of the cathodes and anodes is equal throughout the diagram. (Reprinted with permission from ref 19. Copyright 2003 Elsevier.)...

Since the definition of current (density) in terms of moving charges is... 

The current density can, as a rule, be controlled by the plater. It determines the CE and/or whether deposition will take place at all. The definition of current density in terms of electrodeposition as given above yields an average figure of little use in most cases. A more accurate, useful, and immediate definition is given as... 

Figure 7.8 shows the current density of H2 evolution on Pt microcrystals [46]. It is intriguing that the activity increases as the particle size decreases, although the current is referred to unit real surface area. The excess increase in activity is definitely to be attributed to especially active surface atoms emerging in very small particles. 

Using the definition J = 1, the current density J can also be written as... 

Erdey-Gruz, 1048, 1306 1474 Erschler, 1133, 1134, 1425 Ethylene oxidation, anodic, 1052 1258 Exchange current density, 1049, 1066 correction of, 1069 definition, 1053 electrocatalysis and, 1278 impedance and, 1136 interfacial reaction, 1047 and partly polarizable interface, 1056 Excited states, lifetime, 1478 Exothermic reaction, 1041 Ex situ techniques, 785, 788, 1146... 

A simple idea is used to relate the current density across an interface to the rate at which electron acceptors (or electron donors) arrive at (or move away from) the interface. One starts off with the definition of steady state according to which the concentration of all the intermediates in the reaction must be constant with time. This condition can be achieved if the products of one step are used up in the succeeding step as fast as they are produced. If the first of two consecutive steps proceeded at a faster rate than the second, then the products of the first step would start accumulating (Fig. 7.83) and this would contradict the definition of steady state. 

Neutron flux density is the number of neutrons that enter a sphere of unit cross-sectional area per unit of time. This quantity is sometimes defined in terms of a unidirectional beam of neutrons incident perpendicularly upon a unit area, but this definition is less general. It is also sometimes called neutron current density. 

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