Butler-Volmer equation partial current densities

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) ... 

Large Cathodic Current We have seen from Figure 6.7 that for the large negative values of overpotential r], the partial cathodic current density i approaches i, i i. For these conditions the Butler-Volmer equation (6.45) can be simplified. Analysis of Eq. (6.45) shows that when rj becomes more negative, the first exponential term in the equation (corresponding to the anodic partial current) decreases, whereas the second exponential term (corresponding to the cathodic partial reaction) increases. Thus, under these conditions. 

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 ... 

For a given overpotential, the effective current density depends on the magnitude of the charge-transfer coefficient a as well as on the exchange current density iu. If the overpotential is high enough—that is, if either —(a Frj/RT) or (a Fr/)/RT > 1—then one of the partial current densities in the Butler-Volmer equation overrules the other ... 

When the rate is controlled by the - charge transfer step according to the - Butler-Volmer equation the anodic partial current density ( a) can be expressed as follows ... 

Charge transfer resistance — At low - overpotentials (q RT/nF) none of the -> partial current densities is negligible (see also activation overpotential, - charge-transfer overpotential, -> Butler-Volmer equation). 

The relationship between overpotential and current density of a single, activation-controlled electrochemical reaction is the Butler-Volmer equation, Eq. (10). As the equation shows, the rates of anodic and cathodic partial reactions are exponentially dependent on the overpotential. The net current is the sum of the anodic and cathodic partial currents. 

The only quantity in this equation that can be measured directly is the total current density. The partial current densities for each of the three reactions are obtained by weighing the deposit and analyzing its composition. Each of the current densities is calculated from the Butler-Volmer equation... 

Figure 12.33 shows the principle of cathodic protection for a system obeying Butler-Volmer kinetics. Because the anodic partial current density is negligible at the protection potential, iprot is equal to the cathodic partial current density at the potential E — ffprot- The Butler-Volmer equation thus yields for the protection current density ... 

Fig. 3.2a shows that the curves for the net current density coincide with the partial current density curves at large positive or large negative overpotentials. Under these conditions, one or other of the exponential terms in the Butler-Volmer equation dominates, and the limiting relationships become... 

Introducing the overpotential rj = E-Eo yields the Butler-Volmer equation. The total current density appears as the superposition of the anodic and the cathodic partial... 

Metal dissolution usually follows the Butler-Volmer equation (Eqs. (1-26) and (1-28)) independent from which surface position the transfer of the metal cation may occur. The relation for the exchange current density may contain the concentration of a catalyzing or complexing anion. The catalysis of iron dissolution by OH" ions is a typical example which has been studied in detail (Bonhoeffer and Heusler, 1956). Its mechanism includes a sequence of partial reactions of an electrode process and its in-... 

It should be noted that equation (1.36) retains a form which emphasizes that the measured current density at each overpotential is the sum of the partial cathodic and anodic current densities. Moreover, this indicates useful limiting forms. Thus, as the overpotential is made more negative, / increases while I decreases and quite rapidly — / >/. Then the first term in the Butler-Volmer equation has become negligible compared with the second and one can write ... 

---