Current densities coefficients

Mobius, H.H. (1986). Oxygen Current Density Coefficient of Oxidic Materials as a Parameter for Selection and Development of Electrodes with Solid Electrolytes, Extended Abstracts of the 37th Meeting ISE, Int. Soc. of Electrochem., Vilnius, USSR, Vol. 1, p. 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

Hard plating is noted for its excellent hardness, wear resistance, and low coefficient of friction. Decorative plating retains its brilliance because air exposure immediately forms a thin, invisible protective oxide film. The chromium is not appHed directiy to the surface of the base metal but rather over a nickel (see Nickel and nickel alloys) plate, which in turn is laid over a copper (qv) plate. Because the chromium plate is not free of cracks, pores, and similar imperfections, the intermediate nickel layer must provide the basic protection. Indeed, optimum performance is obtained when a controlled but high density (40—80 microcrack intersections per linear millimeter) of microcracks is achieved in the chromium lea ding to reduced local galvanic current density at the imperfections and increased cathode polarization. A duplex nickel layer containing small amounts of sulfur is generally used. In addition to... 

From Fig. 10.40 it will be seen that contact between the electrolyte (soil or water) and the copper-rod electrode is by porous plug. The crystals of CUSO4 maintain the copper ion activity at a constant value should the halfcell become polarised during measurements. The temperature coefficient of such a cell is extremely low, being of the order of 1 x 10" V/°C and can thus be ignored for all practical purposes. To avoid errors due to polarisation effects, it is necessary to restrict the current density on the copper rod to a... 

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

Exchange current densities and transfer coefficients for evolution of gases at 20-25 C at different anodes... 

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... 

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. 

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. 

This Butler-Volmer6 equation allows the current density to be plotted against nFrjt/RT for different values of the transfer coefficient a the slope of the curves... 

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)...

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... 

The constants characterizing the electrode reaction can be found from this type of polarization curve in the following manner. The quantity k"e is determined directly from the half-wave potential value (Eq. 5.4.27) if E0r is known and the mass transfer coefficient kQx is determined from the limiting current density (Eq. 5.4.20). The charge transfer coefficient oc is determined from the slope of the dependence of In [(yd —/)//] on E. 

In the first case, the rate of deposition depends on the equilibrium concentration of ad-atoms, on their diffusion coefficient, on the exchange current density and on the overpotential. In the second case, the rate of deposition is a function, besides of the geometric factors of the surface, of the exchange current and the overpotential. This mechanism is valid, for example, in the deposition of silver from a AgN03 solution. 

Here ia is the exchange current density of the electrode reaction based on the bulk concentration aa and ac are the anodic and cathodic charge transfer coefficients, respectively and y is a dimensionless kinetic parameter. 

In the limiting-current method of measuring mass-transfer coefficients, the reacting-ion concentration at the electrode is made vanishingly small by applying a sufficiently large potential. In this case, therefore, only the current density and the bulk concentration need to be known. 

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