The activation overpotential

It is obvious that the net current density - a charge transfer per unit of time and surface -, quantifies 

Study of the electrode kinetics gives an expression of the form 

Butler and Volmer showed that for many reactions the following function can be used, 

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Seconday Current Distribution. When activation overvoltage alone is superimposed on the primary current distribution, the effect of secondary current distribution occurs. High overpotentials would be required for the primary current distribution to be achieved at the edge of the electrode. Because the electrode is essentially unipotential, this requires a redistribution of electrolyte potential. This, ia turn, redistributes the current. Therefore, the result of the influence of the activation overvoltage is that the primary current distribution tends to be evened out. The activation overpotential is exponential with current density. Thus the overall cell voltages are not ohmic, especially at low currents. 

The activation overpotential, and hence the activation energy, varies exponentially with the rate of charge transfer per unit area of electrode surface, as defined by the well-known Tafel equation... 

The activation overpotential Tiac,w is due to slow charge transfer reactions at the electrode-electrolyte interface and is related to current via the Butler-Volmer equation (4.7). A slow chemical reaction (e.g. adsorption, desorption, spillover) preceding or following the charge-transfer step can also contribute to the development of activation overpotential. 

The anode potential is so positive, due principally to the activation overpotential, that the majority of the impurity metals (Fe, Cu, Co, etc.) in the anode dissolve with the nickel sulfide. In addition, some oxygen is evolved (2 H20 = 02 + 4 H+ + 4 e ). The anodic current efficiency reduced to about 95% on account of this reaction. Small amounts of selenium and the precious metals remain undissolved in the anode slime along with sulfur. The anolyte contains impurities (Cu, Fe, Co) and, due to hydrogen ion (H+) liberation, it has a low pH of 1.9. The electrolyte of this type is highly unfit for nickel electrowinning. It is... 

The first two terms on the right-hand side of this equation express the proper overpotential of the electrode reaction rjr (also called the activation overpotential) while the last term, r)c, is the EMF of the concentration cell without transport, if the components of the redox system in one cell compartment have concentrations (cOx)x=0 and (cRed)x=0 and, in the other compartment, Cqx and cRcd. The overpotential given by this expression includes the excess work carried out as a result of concentration changes at the electrode. This type of overpotential was called the concentration overpotential by Nernst. The expression for a concentration cell without transport can be used here under the assumption that a sufficiently high concentration of the indifferent electrolyte suppresses migration. 

The other potential losses required to drive an electrode reaction are the activation overpotential, rja, and concentration overpotential, r]conc. The problem of current distribution is then governed Eq. (57) as well as by the following equations ... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

Since z act represents the real flux at the interface, it determines the activation overpotential, and provides the boundary condition for the electric field in solution. 

In a PEMFC, the power density and efficiency are limited by three major factors (1) the ohmic overpotential mainly due to the membrane resistance, (2) the activation overpotential due to slow oxygen reduchon reaction at the electrode/membrane interface, and (3) the concentration overpotential due to mass-transport limitations of oxygen to the electrode surfaced Studies of the solubility and concentration of oxygen in different perfluorinated membrane materials show that the oxygen solubility is enhanced in the fluorocarbon (hydrophobic)-rich zones and hence increases with the hydrophobicity of the membrane. The diffusion coefficient is directly related to the water content of the membrane and is thereby enhanced in membranes containing high water content the result indicates that the aqueous phase is predominantly involved in the diffusion pathway. ... 

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

Figure 6.14. Cell Voltage vs. Cell Current profile of a hydrogen - oxygen fuel cell under idealized (dotted-dashed curve) and real conditions. Under real conditions the cell voltage suffers from a severe potential loss (overpotential) mainly due to the activation overpotential associated with the electroreduction process of molecular oxygen at the cathode of the fuel cell. Smaller contributions to the total overpotential losses (resistance loss and mass transport) are indicated.

Since in cathodic reactions is always smaller than c°, the concentration polarization has a negative sign, which adds to the activation overpotential in causing the electrode to depart from the equilibrium potential in the negative direction for an electronation reaction. 

To keep the distinction clear, a suffix charge-transfer reaction an activation process is necessary. Hence, T)a is sometimes known as the activation overpotential. 

It must be mentioned here that the activation overpotential as given by the Butler-Volmer equation (7.24), contains implicit concentration terms hidden in i0 these concentration terms refer to the concentrations at the OHP and not to bulk values. Only in certain circumstances can the concentration at the OHP be placed equal to the bulk concentration, e.g., when OHPdS< ) = 0 and ric = 0. 

The link between the current density and the concentration overpotential under steady-state conditions for systems in which the exchange-current density is relatively large compared with the limiting current density (hence, the activation overpotential is negligible) was established through the concept of a limiting current iL arising from the fact that there is a maximum rate at which electron acceptors can move to an... 

Another feature of the spiral tip is that it has an abnormally high step and kink density and perhaps the tip has a higher exchange-current density for deposition than the corresponding planar surface. If this were so, the activation overpotential would be much less at the tip of the spiral than around its base. 

The form of the I vs. V relation (7.317) for a cell, which has just been derived, depends upon the assumption that the activation overpotentials Tij and ti2 at the two interfaces have pushed the i vs. T) curves into the exponential region. If, instead, the two interfaces are showing ohmic behavior, then one has from Eq. (7.308) and linear i vs. T) relations (7.25) ... 

Now the overpotentials Tjj and t 2 are the total overpotentials at the two interfaces. They must include the activation overpotentials Tja and concentration overpotentials Tlc. Thus, Eq. (7.321) can be written... 

In the case of very fast electrochemical reactions, it can be assumed that an overpotential is caused only by slow transport of reacting particles from the bulk of the solution toward the electrode surface and that the activation overpotential is negligible. What is the error of that approximation for the electrochemical... 

Charge transport is modeled by Ohm s law (Equation (3.10)) and the charge conservation equation (Equation (3.68)), while the current density distribution at the electrode/electrolyte interface is modeled through the Butler-Volmer equation (Equation (3.102)). It should be noted that, contrarily to Section 3.7, Equation (3.102) is here derived from Equation (3.37) rather than Equation (3.39), because the former allows for a better agreement between experimental and simulated results. Equations (3.40)-(3.42) are used to model, the exchange current density, the activation overpotential, and the ideal potential drop at the electrode/electrolyte interface, respectively. Heat transfer is modeled through Equation (3.6), and the appropriate heat terms for each domain. 

These relationships can be combined to give an expression for the net current density (j), which by definition is equal to j — jc in terms of the activation overpotential (substitute rj + AEe = AE), which is referred to as the Butler-Volmer equation ... 

At a current density (Fig. 13.6) sufficiently far below the limiting current density values [see Eq. (13.19)] and when the ohmic losses inside the cell are negligible, the activation-overpotential terms dominate the expression for the relation of current to potential, i.e.,... 

At higher current densities than those referred to in Eq. (13.20), the activation-overpotential terms in this equation change much less with current than the ohmic overpotential owing to the internal resistance of the cell. Under these conditions, when (I/A)/iL continues to remain negligible and the variation of Vand I (but not its absolute value) is dominated by the IRt term, one has (Fig. 13.7)... 

Fig. 13.7. Graphical representation of the influence of the internal resistance of an electrochemical energy converter on the cell potential when mass-transfer polarization is negligible. The early nonlinear part of the curve represents the effect of the activation overpotential on the cell potential before ohmic polarization has become important.

It is seen, therefore, that the cell potential V and consequently the efficiency of an electrochemical converter (Fig. 13.9) are determined by the activation overpotential, by the electrolyte conductance, and by mass transfer (i.e., the solubility of the reactants). The factors that dominate the way the efficiency of the conversion of energy changes with an increase in current density are at low current density, the activation... 

Note how, even in the region in which there is linear behavior of V with respect to /, the actual value of the potential that the generator could put out depends on the value of the so-called constant, i.e., on the activation overpotential and thus on the exchange current densities and the catalytic power of the electrodes. 

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