Despic and Bockris

Despic and Bockris considered an infinitesimal area of the electrode surface (Fig. 7.137). Then ... 

The surface diffusion problem can be considered in more detail by solving Pick s difiusion equations. The problem has been treated by a number of authors [2.24-2.29] (cf. Section 3.5) with almost identical results. The following description is based on those given by Despic and Bockris [2.25] and Vetter [2.27]. 

The first theoretical treatment of the metal deposition mechanism via surface diffusion was given by Lorenz [2.24], who adapted the theory of Burton, Cabrera and Frank [2.1] to the case of electrolytic metal deposition. Later the problem was treated by Vermilyea [2.29], Despic and Bockris [2.25], Fleischmann and Thirsk [2.28], and Damjanovic and Bockris [2.26], who brought the theory of surface diffusion to its present state. 

The expression derived by Despic and Bockris gives a potential dependence of especially when initial- and final-state profiles cross asymmetrically (see Fig. 15), i.e., when AFq is either a large exothermic or endothermic quantity, so that the transition state is, respectively, either close in configuration to the final state or to the initial state. The Tafel relation is consequently nonlinear simulated Tafel relations were calculated showing this behavior. 

Figure 15. Crossing of potential energy curves leading to potential dependence of p (after Despic and Bockris, ).

Finally, we note here that the representation of the potential dependence of P in the diagram in Despic and Bockris s paper (their Fig. 14) implies ultimately that activationless discharge will set in, as treated by Krishtalik. Then, of course, the process becomes entirely diffusion limited. Correspondingly, barrierless discharge would arise at the other extreme. 

On the basis of this treatment, Despic and Bockris showed that for the silver deposition reaction the assumption of a constant j3 is valid only at low overpotentials. At higher overpotentials, there is a considerable departure of the vs tjFID plot calculated assuming that )3 is a constant from that obtained with jS, calculated according to the above theory (Fig. 6). The experimental behavior for this reaction supports this theory. However, the silver deposition reaction is a... 

Figure 3. Adion concentration profiles, Cad(jc)/Cad, and current density distribution, i(x)/io, between two growth steps at different Xq/K and 17 values (Despic and Bockris). ...

Galvanostatic charging curves can also be used for that purpose, if Eq. (23) is extended to take into account the double-layer charging current, by the term Cj iidr /dt), where Cdl is the double-layer capacitance. The solution of the differential equation was given by Roiter, Juza, and Poluyan and rearranged by Despic and Bockris to give... 

An early example of an electrochemical rectifier based on polymers was reported by Lovrecek, Despic and Bockris (61) in 1959. The rectifier used polyvinyltoluenesulfonic acid and polyvinyltrimethylbenzyl-ammonium hydroxide to allow ion flow in one direction only. 

Some authors[86,87] consider that the concept of barrierless processes was introduced by Despic and Bockris[84]. As a matter of fact, however, in this paper, which appeared somewhat later than our publication[85], the authors discuss only a tendency to an activationless process and not the reverse case of a barrierless process. 

It seems to us that the conclusions drawn by Despic and Bockris are not entirely justified. In the first place, it cannot be asserted that the polarization curves must be strictly symmetric for an activationless discharge and ionization. For this purpose, it is necessary that the potential energy curve be completely symmetric in this case, i.e. the ideal heat of an elementary act be equal to zero at the equilibrium potential. Moreover, even if this condition is satisfied for a certain concentration of Ag" , it cannot be satisfied for another concentration which corresponds to a different value of the equilibrium potential. 

Secondly, the absolute values of the limiting currents for discharge and ionization are generally not equal. While the former is proportional to the concentration of the discharging cation, the latter is independent of it. However, Despic and Bockris[84] seem to have observed a symmetry of anodic and cathodic branches, and hence an equality of the limiting currents, over a wide interval of concentrations of Ag ions. 

Fig. 7.137. The model of the electrode surface. (Reprinted from A. R. Despic and J. O M. Bockris, J. Chem. Phys. 32 389, 1960 with the permission of the American Institute of Physics.)...

Fig. 12.22. Cell for partial H30+ discharge current (/H) measurements. A, Anodic compartment B, cathodic compartment C, capillary (diameter 0.3 mm) W, water jacket Fe, iron test electrodes E, reference electrode X, T, Z, Teflon taps G, taps for connection with Nichrome furnaces. (Reprinted from J. O M. Bockris, A. Despic, and D. M. Drazic, Electrochim Acta 32 p. 329, copyright 1961, Fig. 1 with permission from Elsevier Science).

J. O M. Bockris, B. T. Rubin, A. Despic, and B. I. ovrcccch, Elect rochim.. Acta 17 97 (1972). Cu-Ni alloy dissolution the dissolution rate of each alloying component is independent of its composition in the alloys. 

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