Butler-Volmer relationship

This equation is known as the Butler-Volmer relationship. Figure 2.12 shows that the net current flowing at an electrode can be considered as the... 

This relationship may be inserted back into the general case of eqn. (40) to produce an alternative formulation of the Butler—Volmer relationship. 

As shown in Table 9.1, the typical timescale for the electrochemistry ( Cell Charging Time ) is on the order of 10-5 s. As a result, it is often that this transient is ignored in cell performance calculations, and the quasi-steady Butler-Volmer relationship is used alone (Qi et al., 2005). An example model for this particular type of dynamic cell behavior is given in Section 9.5. 

From Eqs. (16), (19), and the Butler-Volmer relationship, the following relation is obtained ... 

They have revealed that, under appropriate conditions, where charge transfer is rate controlling (with liquid metals or with solid ones at short time intervals, before other types of control take over), in the vicinity of the reversible potential, the kinetics obey the Butler-Volmer relationship ... 

The potential dependence of the apparent rate constant appears to follow a Butler-Volmer relationship, with a constant apparent charge transfer coefficient as described by Eq. (16). 

In 1990, Shao and Girault started a series of investigations based on the kinetic study of the transfer of acetylcholine Ac = CH3C02CH2CH2N (CH3)3 in which the physical properties of one of the solvents were varied. The experimental approach for the measurement of the kinetic parameters was chronocoulometry, a technique which, like convolution linear sweep voltammetry, does not impose any prerequisites on the potential dependence of the rate constants. To verify the suitability of the experimental method, they studied the potential dependence of the rate constant for Ac transfer from water to oil and from oil to water. As illustrated in Fig. 7, the results obtained show that the apparent rate constants obey the Butler-Volmer relationship, expressed by Eq. 10. Note that Fig. 7 has been obtained from two independent experiments. In the first experiment, acetylcholine was only present in the aqueous phase as a chloride salt and forced to cross to the organic phase, whereas in the second, acetylcholine was only present in the organic phase as a tetraphenylborate salt and forced to transfer to the aqueous phase. 

The second question one may ask is If the potential drop across the mixed solvent layer is very small, why do we observe a Butler-Volmer relationship for the potential dependence of the apparent rate constant ... 

The proportionality of n kf) to the applied potential difference (also called Tafel behavior) was observed back in 1975 by Gavach et al and has been corroborated ever since by many groups (e.g.. Ref. 53, 54, 56, 57). The results of Shao and Girault, illustrated in Fig. 7, show beyond any doubts that a Butler-Volmer relationship (as described by Eq. (10)) accounts very well for the experimental data. In the case of the metal-electrolyte solution interface, such an equation is rationalized by the fact that the applied potential difference, A, the driving force for the electron transfer reaction, is located at the interface and that the variation of the activation energy with A is a fraction of the variation of the electrical driving force. 

It can be seen in Fig. 16 that this type of facilitated ion transfer seems to follow a Butler-Volmer relationship as do normal ion transfer reactions. 

EfUmy assume a value at which O is converted to R at different rates. One has to keep in mind that this conversion occurs Umitedly to O species at the electrode, i.e., for x = 0 the concentration values that, in a way or another, are conditioned by Ef are those adjacent to the electrode surface. The expression in a way or another intends to distinguish between reversible and non-reversible charge transfers in the former case the Nemst s equation holds, in the latter a Butler-Volmer relationship is valid. 

Charge-transfer resistance represented in Eq. 5-24, is a non-linear element controlled by the Butler-Volmer relationship [1, pp. 45-48], with strong dependence on the electrochemical potential. External convection will enhance mass transport and minimize diffusion effects, keeping the assump-... 

Figure 7.18 shows that after subtraction of the bulk contribution the current-voltage situation at Ce02 can be described approximately by the Butler-Volmer relationship. As far as the symmetry factors are concerned, it has to be taken into account that z=2 (cf. Fig. 7.18 and footnote 66). The exchange current densities obtained by extrapolation to small values of ijt will now be discussed as a function of the control variables temperature, oxygen partial pressure and doping content (as was done in detail for the bulk conductivity in Chapter 5). 

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