Butler—Volmer relation

Combining Eqs. (18b.11) and (18b.12) one can write the familiar Butler-Volmer relation between current, potential, and the kinetic parameters... 

The extensive Butler-Volmer relation for charge transfer... 

In the following parts of this chapter, subsequently the remaining stages of the sequence (Equations 4.9 1.12) are supposed to be rate determining. Since the reasoning to come to a Butler-Volmer relation remains the same, a number of explanations from this part of the chapter will not be repeated further on. 

By expressing red in terms of the potential through the Butler-Volmer relation (kted = /i°e " ), it is easily deduced that under suitable conditions in which Eq. (3.40) is applicable, the potential varies linearly with ln / e - /plane //pli,nc ... 

If the substrate is an insulator Js — 0. If both tip and substrate reactions are electrochemical processes, the rate constants for oxidation (kf) and reduction (kb) are given by the Butler-Volmer relations... 

In the case of a current passing through a cell which represents a deviation from the equilibrium state, we can write the following Butler-Volmer relation between current and voltage for a single electrode ... 

For zF t] /RT 1, the term Vi ]) in the Butler-Volmer relation becomes a linear function of j/, i.e., V t]) = zFrj/RT, so that the propagation rate Vsd also becomes a linear function of overvoltage... 

A high-indexed surface zone with a high density of steps or growth sites (kink positions) would follow the same growth law as liquid metals, i.e., the Butler-Volmer relation. Vicinal faces, characterized by low-index surface zones separated by uniformly distributed monatomic steps show an intermediate behavior. 

Figure 4.20 Normalised cathodic and anodic rate coefficients andfc calculated from eqs. 4.63. 66, for T= 298 K and A, of (a) 0.2 eV (b) 0.5 eV (c) 1.0 eV. The dashed lines show the Butler-Volmer relation, eq. 4.66, for curve (a).

In traditional electrochemistry this equation is known as the Butler-Volmer relation in which /o is the exchange current. The latter is equal to the anodic and the cathodic partial currents at equilibrium (fj = 0) and are given by... 

The nondimensionalized cathode over potential, r], satisfies a Butler-Volmer relation... 

Here, r E) depends on the potential because the Butler-Volmer relation is not linear. The polarization resistance at the corrosion potential, is equal to ... 

The activation polarization represents the voltage loss due to the activation necessary for the charge-transfer reactions. The phenomenological Butler-Volmer relation is typically used to relate the activation polarization to the current density of the cell [23] ... 

For the oxidation reaction Ag - e Ag, it is assumed that an ion crosses the interface between electrode and electrolyte. As in the precee-dingly described case, an activation energy, depending on the electrode potential, is necessary and the current-potential relation is given by the Butler Volmer relation ... 

The I value being itself related to the applied overvoltage by the Butler Volmer relation (equation 2). 

Normalized steady-state tip current (/ = /-p/Z-poo) computed as a function of L for a quasi-reversible substrate reaction with different values of dimensionless rate constant (k = k°a/D) and dimensionless substrate potential = nFf]/RT) (67). The Butler-Volmer relations for the forward (reduction) and backward (oxidation) rate constants are = k txp(—aE ) exp [(1 — a)E ] where a is the transfer coefficient... 

For low voltage, the Tafel line deviates from the Butler-Volmer relation. A method given by Allen and Flickling (1957) allows plotting of i versus q, even at low voltages. The simple form of the BV equation (Equation 5.77) can be cast into the following form ... 

Boundaries 2 et 3 polarization behaviours which can be if possible described by the well-known Butler-Volmer relation or by empirical laws deduced from local probe techniques. 

The basic theory of ET in bulk liquid and at liquid/metal interfaces is well-developed ° but applications of that theory to ET at lES were slow to be adopted due to insufficient knowledge about the molecular structure of the liquid/liquid interface and due to experimental difficulties. ET rate constants under steady state conditions are typically obtained from current/voltage measurements. A potential difference V is established across the interface, and the current I is measured. If the basic theory of electron transfer at the solution/metal interface is applicable to the liquid/liquid interface, one then expects the following Butler-Volmer relation between the voltage and the current ... 

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