Total current density

The total current density flow in a dielectric material is given by Maxwell s equation  

The conduction current density is given by oE, where o is the conductivity of the ceramic material. 

For periodic waveforms, such as usually used for high frequency heating, equation 3 attains the following form  

Note that the total losses can quite easily be expressed in terms of an effective conductivity, defined as  

---

Equation (2-38) is valid for every region of the surface. In this case only weight loss corrosion is possible and not localized corrosion. Figure 2-5 shows total and partial current densities of a mixed electrode. In free corrosion 7 = 0. The free corrosion potential lies between the equilibrium potentials of the partial reactions and U Q, and corresponds in this case to the rest potential. Deviations from the rest potential are called polarization voltage or polarization. At the rest potential = ly l, which is the corrosion rate in free corrosion. With anodic polarization resulting from positive total current densities, the potential becomes more positive and the corrosion rate greater. This effect is known as anodic enhancement of corrosion. For a quantitative view, it is unfortunately often overlooked that neither the corrosion rate nor its increase corresponds to anodic total current density unless the cathodic partial current is negligibly small. Quantitative forecasts are possible only if the Jq U) curve is known. 

Fig. 2-5 Partial and total current densities in electrolytic corrosion of a homogeneous mixed electrode.

When cathodic polarization is a result of negative total current densities 7., the potential becomes more negative and the corrosion rate lower. Finally, at the equilibrium potential it becomes zero. In neutral water equilibrium potentials are undefined or not attainable. Instead, protective potentials are quoted at which the corrosion rate is negligibly low. This is the case when = 1 flA cm (w = lOjUm a ) which is described by the following criteria for cathodic protection ... 

In electrolyte solutions the positively and negatively charged ions will move in opposite directions when an electric field is applied. Therefore, outwardly the effect of motion of positive ions is exactly the same as that of the motion of negative ions, and the total current density is the sum of the partial currents due to hansport of each type of ion ... 

FIGURE 6.9 Plots of the total current density vs. (or K ) for (1) first-order and (2) zeroth-order reactions. 

Figure 6. pH dependence of (a) current density (on log scale) of oxygen ion incorporation into the oxide, at a constant total current density of 0.1 mA/cm2, and (b) the steady-state dissolution (aluminum ion) current density of oxide-covered aluminum at 4 V versus SCE.29... 

The total current density, J —Jx +J2> and a rather complicated formula may be obtained by straightforward algebra. In fact, for many practical purposes, the value of a>D is sufficiently large for us to neglect the effects of diffusion. This is equivalent to putting otl = ct2 = 1 in the formulae above,... 

By interpreting the term in brackets as the total current density the inhomogeneous Maxwell equation (2) is also written as... 

We assume that both reactions obey the Butler-Volmer equation, and denote the corresponding transfer coefficients by a and 2, the exchange current densities by jo,i and jo,2> and the equilibrium potentials by [Pg.150]

The enhancement in luminous efficiency achieved by inserting an ultrathin interlayer between the ITO and NPB is mainly due to the reduction of hole injection from ITO to NPB in OLEDs. For a simple approximation, luminous efficiency (rj) can be related directly to a ratio of the recombination current (/r) to the total current density of OLEDs (/tot). If one denotes the current contributions from holes and electrons in OLEDs as. /h and /e, respectively, then the sum of hole and electron currents, /tot. /h + /e, and tj can be expressed as... 

The assumption of electroneutrality implies that the diffuse double layer, where there is significant charge separation, is small compared to the volume of the domain, which is normally the case. Because there is no accumulation of charge and electroneutrality has been assumed, the divergence of the total current density is zero... 

Figure 10. Resistor-network representation of porous-electrode theory. The total current density, i, flows through the electrolyte phase (2) and the solid phase (1) at each respective end. Between, the current is apportioned on the basis of the resistances in each phase and the charge-transfer resistances. The charge-transfer resistances can be nonlinear because they are based on kinetic expressions.

Thus, the total current density, /totab is composed of two components. It is a result of the addition of current densities of the two partial processes. 

Electroless Deposition in the Presence of Interfering Reactions. According to the mixed-potential theory, the total current density, is a result of simple addition of current densities of the two partial reactions, 4 and However, in the presence of interfering (or side) reactions, 4 and/or may be composed of two or more components themselves, and verification of the mixed-potential theory in this case would involve superposition of current-potential curves for the electroless process investigated with those of the interfering reactions in order to correctly interpret the total i-E curve. Two important examples are discussed here. 

Figure 10.17. Total current density as a function of coumarin concentration constant-potential experiments -960 mV versus SCE, 980 rpm, pH 4. (From Ref. 33, with permission from Elsevier.)...

The total current density across the junction is therefore equal to the sum of the electron and hole current densities, just as the total ionic-migration current density in an... 

V is the voltage applied to the system. Unit activity coefficients and zero standard counterion potentials in both phases are assumed for the sake of simplicity. As was pointed out in 4.3, the solution of (4.4.15)-(4.4.22) with voltage V given corresponds to potentiostatic experimental conditions and yields the concentration, electric potential fields, and the ionic fluxes as functions of V. We could alternatively fix the total current density... 

Condition (5.2.3c) implies insulation, that is, vanishing of the total current density i, defined as we recall from the Introduction, as... 

Finally, recall that subtraction of (5.2.1b) from (5.2.1a) yields, taking into account (5.2.1c) and (5.2.5a), ix = 0 (this corresponds to solenoidality of the total current density vector in more than one dimension). 

It is an experimental fact that whenever mass transfer limitations are excluded, the rate of charge transfer for a given electrochemical reaction varies exponentially with the so-called overpotential rj, which is the potential difference between the equilibrium potential F0 and the actual electrode potential E (t) = E — Ed). Since for the electrode reaction Eq. (1) there exists a forward and back reaction, both of which are changed by the applied overpotential in exponential fashion but in an opposite sense, one obtains as the effective total current density the difference between anodic and cathodic partial current densities according to the generalized Butler-Volmer equation ... 

The total current density, J and a rather complicated formula... 

The two interfacial processes, charge transfer and double-layer charging, proceed in parallel and so the total current density is the sum of the faradaic and the charging (sometimes called non-faradaic) current densities... 

The total current density J is the sum of the individual current density charge carriers in the substance. 

The inhibiting effect of coumarin is shown in Figure 10.17. The total current density in this figure is the sum of the current densities for nickel deposition /Ni, hydrogen evolution, /H, and additive reduction /R. 

As the total current density is an invariant, comparison between equations 26 and 28 necessarily implies,... 

The integral part of Equation (2.59) represents the inverse average overpotential which is proportional to the inverse total current density at constant ASR. 

For this case of both diffusion and local mass transfer in the porous electrode, we define the dimensionless total current density as... 

Here, we define the dimensionless total current density as... 

---