Partial current densities

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. 

In this type of corrosion, metal ions arising as a result of the process in Eq. (2-21) migrate into the medium. Solid corrosion products formed in subsequent reactions have little effect on the corrosion rate. The anodic partial current-density-potential curve is a constant straight line (see Fig. 2.4). 

J/ = anodic partiai current density ). Jq= cathodic partial current density /g = total anodic current = total cathodic current... 

Fig. 4-3 Schematic representation of the partial current densities in corrosion in free corrosion (a-c) and with cell formation with foreign cathodic structures (d).

If, however, it is assumed from Eq. (2-40) that the protection current density corresponds to the cathodic partial current density for the oxygen reduction reaction, where oxygen diffusion and polarization current have the same spatial distribution, it follows from Eq. (2-47) with = A0/7 ... 

Besides the use of anodic polarization with impressed current to achieve passivation, raising the cathodic partial current density by special alloying elements and the use of oxidizing inhibitors (and/or passivators) to assist the formation of passive films can be included in the anodic protection method [1-3]. 

Passivating inhibitors act in two ways. First they can reduce the passivating current density by encouraging passive film formation, and second they raise the cathodic partial current density by their reduction. Inhibitors can have either both or only one of these properties. Passivating inhibitors belong to the group of so-called dangerous inhibitors because with incomplete inhibition, severe local active corrosion occurs. In this case, passivated cathodic surfaces are close to noninhibited anodic surfaces. 

The net current density is the difference between the two partial current densities, and the net anodic current density can be written in the form... 

If — during this process — the Cu2+-concentration decreases, the mixed potential will shift along the cathodic partial current density curve (like a polarographic curve in this example) toward the equilibrium potential of the zinc amalgam, in case the amalgam reservior is large enough. 

In addition to the exchange current density the transfer coefficient a is needed to describe the relationship between the electrode potential and the current flowing across the electrode/solution interface. From a formal point of view a can be obtained by calculating the partial current densities with respect to the electrode potential for the anodic reaction ... 

From a kinetic point of view a describes the influence of a change of the electrode potential on the energy of activation for the charge transfer reaction which in turn influences the partial current density. The transfer coefficients % for the anodic charge transfer reaction and for the cathodic reaction add up according to... 

II. Calculated current density and stoichiometry vs. deposition potential curves for parameter values representative of CdTe and with one partial current density diffusion limited. J Electrochem Soc 132 2910-2919... 

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 had been shown in Section 2.2 that at the equilibrium otential, the net (external) current density i is zero, but partial cimen densities i and i of the anodic and cathodic reaction exist for which the relation i =i = f holds where i° is the exchange current density. The value of i increases, that of i decreases, when the potential is made more positive but i decreases and i increases when the potential is made more negative. The net current density i is the difference of the partial current densities ... 

In the region of high polarization the kinetic equations for partial current densities i and i coincide with the equation for the net anodic or cathodic current density, respectively ... 

Different electrode reactions will occur independently, and their kinetic coefficients are unrelated. But for the forward and reverse process of a given reaction, such a correlation should exist, since at the equilibrium potential the corresponding partial current densities assume equal values. 

Thus, while the relation between the partial current densities and potential is exponential, in the region of low polarization a linear relation is obtained between polarization and the net CD, owing to a superposition of the currents of forward and reverse process. At A = 10 mV, the error introduced by the approximation above will be between 1 and 20%, depending on the relative values of a and p it becomes even smaller with decreasing polarization. Hence we can by convention consider the interval of polarization values between -10 and 10 mV as that of low polarization where the linear relation (6.6) is valid. 

FIGURE 63 Potential dependence of the anodic (i) and cathodic (i) partial current densities as well as of the anodic (i ) and cathodic (i ) net current densities. 

When the rate of the overall reaction is stated in electrical units [i.e., in terms of the current density (CD) i = nFv], it will be convenient to use the concept of partial current densities of the first and second steps, which are defined as q = l Fv and I2 = IqFvq. In the steady state, v = Vi = y2and i = + I2. With these parameters, Eq. (13.15) becomes... 

The net (external or overall) current density at an electrode is the algebraic sum of the partial current densities of all reactions ... 

FIGURE 13.2 Polarization curves for the partial current densities of reactions involving the metal and hydrogen, and the polarization curves for the overall current density. 

For large negative or positive overpotentials, i.e., for r)t P RT/nF, either the cathodic or the anodic partial current density predominates, so that according to eqn. 3.19... 

Thus, in the case of migration material fluxes (Eq. 2.3.11) it holds for the partial current density (the contribution of the ith ion to the overall current density) that... 

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... 

Fig. 5.2 Dependence of the relative current density j/j0 on the overpotential rj according to Eq. (5.2.28). Various values of the charge transfer coefficient a are indicated at each curve. Dashed curves indicate the partial current densities (Eqs 5.2.11 and 5.2.12 for a = 0.5). (According to K. Vetter)...

In general, for a larger number of electroactive substances, the partial current densities corresponding to the individual substances are additive. 

Figure 1 shows a generalized representation of an electroless deposition process obeying MPT [28]. Polarization curves are shown for the two partial reactions (full lines), and the curve expected for the full electroless solution (dashed curve). The polarization curve for anodic and cathodic partial reactions intersect the potential axis at their respective equilibrium potential values, denoted by / j]cd and respectively. At Emp, the anodic and cathodic partial current densities are equal, a... 

As discussed earlier, it is generally observed that reductant oxidation occurs under kinetic control at least over the potential range of interest to electroless deposition. This indicates that the kinetics, or more specifically, the equivalent partial current densities for this reaction, should be the same for any catalytically active feature. On the other hand, it is well established that the O2 electroreduction reaction may proceed under conditions of diffusion control at a few hundred millivolts potential cathodic of the EIX value for this reaction even for relatively smooth electrocatalysts. This is particularly true for the classic Pd initiation catalyst used for electroless deposition, and is probably also likely for freshly-electrolessly-deposited catalysts such as Ni-P, Co-P and Cu. Thus, when O2 reduction becomes diffusion controlled at a large feature, i.e., one whose dimensions exceed the O2 diffusion layer thickness, the transport of O2 occurs under planar diffusion conditions (except for feature edges). 

Here F is the Faraday constant C = concentration of dissolved O2, in air-saturated water C = 2.7 x 10-7 mol cm 3 (C will be appreciably less in relatively concentrated heated solutions) the diffusion coefficient D = 2 x 10-5 cm2/s t is the time (s) r is the radius (cm). Figure 16 shows various plots of zm(02) vs. log t for various values of the microdisk electrode radius r. For large values of r, the transport of O2 to the surface follows a linear type of profile for finite times in the absence of stirring. In the case of small values of r, however, steady-state type diffusion conditions apply at shorter times due to the nonplanar nature of the diffusion process involved. Thus, the partial current density for O2 reduction in electroless deposition will tend to be more governed by kinetic factors at small features, while it will tend to be determined by the diffusion layer thickness in the case of large features. 

At any time during the deposition, the mole fraction of Mn in the electrodeposit, Mft Mn, can be expressed as the ratio of the partial current densities,... 

Figure 32 is a graph showing the composition of alloys deposited onto copper substrates as a function of Ti2+ concentration and current density in 66.7 m/o AICI3-NaCl [177], Alloys were deposited under a range of current densities for several Ti2+ concentrations. At low Ti2+ concentrations, the alloy composition is dependent upon the applied current density. An alloy having a titanium concentration of 25 a/o is deposited only at low current densities. As the current density is increased, the Ti partial current density becomes limited by the diffusion of Ti2+, and the Ti content of the alloy drops. At a Ti2+ concentration of 150 mmol L 1. the current density... 

The equations for the two partial current densities derived above have a suggestive interpretation proposed by Gerischer [4]. In the expression for the anodic current density, the term p(e)[ 1 — /(e)] is the probability to find an empty state of energy e on the electrode surface. If one interprets ... 

For high anodic or cathodic overpotentials one of the partial current densities can be neglected ... 

Mass flux of the electrically charged component Ji is connected with charge transport and so with the partial current density /, defined as... 

Current-Potential Relationship for Partial Reactions, Partial i = /(A(/)) functions can be derived by joining equations expressing the rate of electrochemical reactions in terms of current [Eqs. (6.18) and (6.20)] and equations expressing the rate constant as a function of potential [Eqs. (6.31) and (6.32)]. Thus, the cathodic partial current density i is obtained from Eqs. (6.18) and (6.31) to yield... 

Exchange Current Density, When an electrode is at equilibrium, the equilibrium value of A(/> is A(/>eq and the equilibrium partial current densities i and i are equal ... 

Potential Difference A< Departs from Equilibrium Butler-Volmer Equation, When the interphase is not in equihbrium, a net current density i flows through the electrode (the double layer). It is given by the difference between the anodic partial current density i (a positive quantity) and the cathodic partial current density i (a negative quantity) ... 

This equation gives the relationship between the current density i and the charge-transfer overpotential rj in terms of two parameters, the exchange current density Iq and the transfer coefficient a. Eigure 6.7 depicts the variation of the partial current densities and the net current density with overpotential. It can be seen that for large... 

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