Overpotential current relation

The passage of a net current through an electrode implies that the electrode is no longer at equilibrium and that a certain amount of overpotential is present at the electrode-electrolyte interface. Since the overpotential represents a loss of energy and a source of heat production, a quantitative model of the relationship between current density and overpotential is required in design calculations. A fundamental model of the current-overpotential relationship would proceed from a detailed knowledge of the electrode reaction mechanism however, mechanistic studies are complicated even for the simplest reactions. In addition, kinetic measurements are strongly influenced by electrode surface preparation, microstructure, contamination, and other factors. As a consequence, a current-overpotential relation is usually determined experimentally, and the data are often fitted to standard models. 

Because the form of the current-overpotential relations is characteristic of a kinetically limited rate (see Fig. 34), Conway and Novak 341) proposed control by a step involving recombination of discharged Cl-atoms [Eq. (164)] and deduced a critical test-plot procedure for characterizing recombination-controlled kinetics. Expressing the current density for the recombination step as... 

We focus on the electronic conductivity of molecular monolayers and on single molecules enclosed between a pair of metallic electrodes. We address specifically in situ STM of redox (bio)molecules but concepts and formalisms carry over to other metallic nanogap configurations. Importantly, in addition to the substrate and tip, a third electrode serves as reference electrode [42-44] (Figure 2.2). This allows electrochemical potential control of both substrate and tip. The three-electrode configuration is the basis for two kinds of tunneling spectroscopy unique to electrochemical in situ STM. One is the current-bias voltage relation as for STM in air or vacuum, but with the notion that the substrate (over)potential is kept constant. The other is the current-overpotential relation at constant bias... 

This form discloses an immediate general implication in Eqs. 2.9)-(2.12), namely a pronounced ( spectroscopic ) maximum in the tunneling current-overpotential relation (at given bias voltage). For the symmetric configuration of Eq. (2.12), the maximum appears at the overpotential... 

Figure 8-9. Top Tunneling current/overpotential correlations of the two osmium complexes in Fig. 8-8. Constant bias voltage Vnas (= E,tp-Esubstrate) -015 V 0.1 M NaC104 and 0.1 M HCIO4. Bottom Effect of the bias voltage on the peak maximum (relative to the equilibrium potential of the surface-immobilized complexes, E ) of the tunneling current/overpotential relations, cf eqns. (8-21) and (8-22). Data from refs. 134 and 135.

Figure 9. Current-overpotential relations calculated for the Tafel-Volmer route, with (A) mo = 10, (B) 1, or (C) 10, with various values of Bq. Temkin isotherm with m = 5 and = 0.5 are assumed.

Insertion electrodes are MIECs that provide a source or sink for material as well as a conductive path for electric charge. For example, TiS2 serves as a cathode in Li batteries. It allows the intercalation of Li ions that arrive through a lithium-conducting SE. One expects that the charge transfer process across the SE/MIEC interface will exhibit a Butler-Volmer-type current-overpotential relation and that the diffusion in the MIEC electrode will yield a diflusion-limited current at high cnrrent densities. A detailed analysis confirms this mechanism. ... 

Equations (2.144) and (2.145) are extremely interesting as they show that the magnitude of the peak current is independent of the kinetics of the reaction. This is not surprising since from equations (2.139) and (2.141) it can be seen that kc can be increased to any value simply by increasing the potential. However, at a given scan rate, the position at which the peak current occurs is related to the kinetics Ep occurs beyond E° by an activation overpotential related to k°. 

The complete current-potential relation is shown in Fig. 6.3. For small overpotentials we observe Butler-Volmer behavior, for large overpotentials a limiting current. 

Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

Steady-state Current Overpotential Behaviour - For a simple single charge-transfer process equation (2.28) describes the closed-circuit behaviour. At low overpotentials, the current and overpotential are linearly related and the exchange current density can be evaluated from the gradient (see equation... 

Fig. 5.4 Current-potential relations for electrode reactions with (a) a large exchange current (small overpotential) and (b) a small exchange current (large overpotential).

Once the current is related with the overpotential, the rate of the electrochemical process can be related to the applied current (/ = /VI ) by (4.21), where F is the Faraday constant. This expression can be substituted in the mass balance and is used to characterize the generation (reaction) contribution. 

The analysis of the kinetics of alloy deposition is complicated by the fact that at least two reactions occur in parallel. Consequently, the current-potential relation observed represents a combination of the contributions of two processes, each having its own overpotential, rate constant and potential dependence of the current density. Thus, any information obtained from the current-potential relation observed is of questionable value in evaluating the mechanism of the formation of the alloy. 

FIGURE 1.14 Current density related to real surface area for the oxygen evolution reaction on perovskites at 0.30 V of overpotential versus the M-OH bond strength. The transition metals, M, of the perovskites are indicated in the plot. This plot is a simplified representation of that in [21]. 

One of the most important relations in mechanism determination is the current density-overpotential relation. At overpotentials greater than BT/aF, the rate of the reverse reaction may be neglected and the general expression for the overpotential-current density relation in the case of a cathodic reaction expressed by Eq. (41) reduces to... 

Stoichiometric numbers may be obtained from the current-potential relation at low overpotential, where... 

An additional advantage arises out of this dependence of rate on electric field. It gives an extra mechanism determining criteria for the reaction. The current density-overpotential relation is of utmost importance in electrocatalysis. 

Fio. 24. Effect of ultrasonic vibrations on the overpotential-current density relation for hydrogen evolution on a platinum electrode in 1 H28O4 at 26° 104). 

A theoretical analysis of the current distribution and overpotential-current density relations for two models of porous gas diffusion electrodes—the simple pore and thin film models—has been carried out (108,109). The results of the analysis for the simple pore model will be summarized here. The reactant gas diffuses through the pore to the gas-electrolyte interface at 2 = 0, where it dissolves in the electrolyte and the dissolved gas diffuses through the electrolyte to the various electrocatalytic sites along the pore at which the reaction occurs (Fig. 25). It is assumed that the first and second steps of diffusion of reactant gas through the electrolyte-free part of the pore (z < 0) and of dissolution of gas at the gas-electrolyte interface are fast. 

The current distribution relation in a single pore for certain values of exchange current density and overpotential are shown in Pig. 27. The analysis shows that, at medium and high overpotentials, catalysts can be placed in a small region of the pore only. 

Fig. 27. Current distribution relations for a case where all forms of polarization are considered. In curve (a) uniform current distribution in pore, for example, with exchange current density io = amp cm and overpotential (ij) less than 0.1 volt (b)...

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