Charge transfer overpotentials

Charge-transfer overpotential. The charge-transfer overpotential is caused by... 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

The use of these expressions is effectual only in cases where there is no extensive deviation in the system behavior due to charge transfer overpotential or other kinetic effects.(l) The calculated threshold or thermodynamic energy requirement (2 ) (AG in the previous equation) is often much lower than actually encountered, but is still useful in estimating an approximate or theoretical minimum energy required for electrolysis. Part of the difficulty in applying thermodynamics to many systems of industrial interest may reside in an inability to properly define the activities or nature of the various species involved in the... 

This equation gives the relationship between the current density i and the charge-transfer overpotential rj in terms of two parameters, the exchange current density Iq and the transfer coefficient a. Eigure 6.7 depicts the variation of the partial current densities and the net current density with overpotential. It can be seen that for large... 

The rate at which corrosion occurs is expressed as the current density (A m" ), i.e. the ionic flux across the electrical double layer of the metal and at equilibrium, it is termed the exchange current density. The Tafel equation relates the exchange current density to the charge transfer overpotential. 

Charge transfer resistance, 1056 Charge transfer overpotential, 1231 Charge transfer, partial. 922. 954 Charges in solution, 882 chemical interactions, 830 Charging current. 1056 Charging time, 1120 Chemical catalysis, 1252 Chemical and electrochemical reactions, differences, 937 Chemical equilibrium, 1459 Chemical kinetics, 1122 Chemical potential, 937, 1058 definition, 830 determination, 832 of ideal gas, 936 interactions, 835 of organic adsorption. 975 and work function, 835... 

Pure charge-transfer overpotential t]a exists only if the charge-transfer reaction is hindered and none of the other partial reactions is hindered. In this case the charge-transfer reaction is the rate-determining step. 

Fig. 9.21 Simulink electrochemical model with R-C model capacitance behavior. The BV Fen block is the quasi-steady Butler-Volmer overpotential equation giving current through the Ret charge transfer resistor as a function of charge transfer overpotential, r).

Charge-transfer overpotential — The essential step of an - electrode reaction is the charge (- electron or - ion) transfer across the phase boundary (- interface). In order to overcome the activation barrier related to this process and thus enhance the desirable reaction, an - overpotential is needed. It is called charge-transfer (or transfer or electron transfer) overpotential (f/ct). This overpotential is identical with the - activation overpotential. Both expressions are used in the literature [i-iv]. Refs. [i] Bard A], Faulkner LR (2001) Electrochemical methods. Wiley, New York, pp 87-124 [ii] Erdey-Gruz T (1972) Kinetics of electrode processes. Akademiai Kiadd, Budapest, pp 19-56 [Hi] Inzelt G (2002) Kinetics of electrochemical reactions. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 29-33 [iv] Hamann CH, Hamnett A, Viel-stich W (1998) Electrochemistry. Wiley VCH, Weinheim, p 145... 

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 dependence of the charge transfer overpotential rjet on the charge transfer current density jct can be described in semilogarithmic form... 

We first consider the case in which the charge transfer is the slow step. In this case, the rate of the electrode reaction is determined by the charge-transfer overpotential, rj = rjct. It is assumed here that... 

Work on the development of the modern theory of the charge-transfer overpotential started when Eyring and Wynne-Jones and Eyring formulated the absolute rate theory on the basis of statistical mechanics [3,4], This expresses the rate constant k of a chemical reaction in terms of the activation energy AG, Boltzmann s constant k% and Planck s constant h... 

Electrodes The AFCs use porous carbon electrodes. Platinum is a typical catalyst for both the anodic and cathodic reaction, but Ni and Ag are also used for the anodic and the cathodic reactions, respectively [6]. The kinetics of both reactions, but especially of oxygen reduction, is favorable in the basic environment. The charge-transfer overpotentials for the pure gases are less than 0.1 V for both electrode reactions. 

By combining the Nernst equation with the expressions for charge-transfer overpotential (r CT) and diffusion overpotential (r D), equations can be written for the total experimental polarization behavior, E(iex ox) and E(iex red), of a single half-cell reaction ... 

In this paper we describe a model of a cup plater with a peripheral continuous contact and passive elements that shape the potential field. The model takes into account the ohmic drop in the electrolyte, the charge-transfer overpotential at the electrode surface, the ohmic drop within the seed layer, and the transient effect of the growing metal film as it plates up (treated as a series of pseudo-steady time steps). Comparison of experimental plated thickness profiles with thickness profile evolution predicted by the model is shown. Tool scale-up for 300 mm wafers was also simulated and compared with results from a dimensionless analysis. 

Each value of current density, j, is driven by a certain overpotential, 17. This overpotential can be considered as a sum of terms associated with the different reaction steps r/mt (the mass-transfer overpotential), (the charge-transfer overpotential), (the overpotential associated with a preceding reaction), etc. The electrode reaction can then be represented by a resistance, R, composed of a series of resistances (or more exactly, impedances) representing the various steps R i, R, etc. (Figure 1.3.7). A fast reaction step is characterized by a small resistance (or impedance), while a slow step is represented by a high resistance. However, except for very small current or potential perturbations, these impedances are functions of E (or /), unlike the analogous actual electrical elements. 

Consider a cell composed of two ideal nonpolarizable electrodes, for example, two SCEs immersed in a potassium chloride solution SCE/KCl/SCE. The i-E characteristic of this cell would look like that of a pure resistance (Figure 1.3.8), because the only limitation on current flow is imposed by the resistance of the solution. In fact, these conditions (i.e., paired, nonpolarizable electrodes) are exactly those sought in measurements of solution conductivity. For any real electrodes (e.g., actual SCEs), mass-transfer and charge-transfer overpotentials would also become important at high enough current densities. 

Diffusion overpotential Charge transfer overpotential Galvani potential... 

The overpotentials at the anode qAnode (oxygen overpotential) and cathode qcathode (hydrogen overpotential), also referred to as charge transfer overpotentials, result from the inhibition of electron transport in the separate electrochemical reactions (see Fig. 11.2). In order for current to flow through the electrolysis cell, the resistance polarization must also be overcome. It is caused by the ohmic resistance of the ceU (electrolytes, separator and electrodes). The ohmic voltage drop can be calculated from the current density i in A cm and the surface-specific resistance R of the ceU in Q cm. ... 

In principle, the polarization at each electrode may have a contribution from charge transfer, mass transport, nucleation and passivation overpotentials. The major contribution will normally be from the charge transfer overpotential since mass transport control has a catastrophic effect on the battery voltage (see Fig. 10.3) and one would not normally design a battery to operate in such conditions. Examples of nucleation and passivation overpotentials do occur. The former occur when the electrode reaction requires the formation of a new phase although the nucleation overpotential is normally a transitory phenomenon since, once nuclei of the new phase are present in numbers, the overpotential will disappear. The... 

The radius of a nucleation exclusion zone can be calculated on the basis of the following discussion, taking into account the charge transfer overpotential also. If there is a half-spherical nucleus on a flat electrode, the extent of the deviation in the shape of the equipotential surfaces which occurs around it depends on the crystallization overpotential, current density, a resistivity of the solution and on the radius of the nucleus, r. If the distance from the flat part of the substrate surface to the equipotential surface which corresponds to the critical nucleation overpotential, rj, is /n, then this changes around defect to the extent where A is a number, as is presented in Fig. 2.18. 

It is obvious that a very small increase of current density in the limiting diffusion current density range causes a large increase in deposition overpotential. Hence, the charge transfer overpotential and the ohmic drop in the solution remain the same for all overpotentials belonging to the limiting diffusion current density plateau. 

In the case of a redox system out of equilibrium, the current density can be expressed as a function of the charge transfer overpotential Pc, according to the Butler-Volmer equation ... 

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