Overpotential concentration

Thus far, it was generally assumed that the concentration of electrochemically active species at the electrode surface and that in the solution bulk are the same. However, once an electrochemical reaction is initiated, the concentration of those species will commonly be higher or lower at the electrode/electrolyte interface than in the bulk of the solution. For example, considering copper deposition from an aqueous CuS04(aq) 

Roughly, the Nernst equation can be nsed to describe the overpotential due to the gradient of the concentration of the electrochemically active ions between the snr-face and the bulk. Let us define the concentration of the oxidized species in Reaction (6.5), respectively, at the surface and in bulk as and c. Then the overpotential due to the concentration difference is 

The general problem in using these equations is to estimate the surface concentration of the electrochemically active species and However, there is a way to avoid the problem, and the approach is presented in the following section. 

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As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

Charge Transport. Side reactions can occur if the current distribution (electrode potential) along an electrode is not uniform. The side reactions can take the form of unwanted by-product formation or localized corrosion of the electrode. The problem of current distribution is addressed by the analysis of charge transport ia cell design. The path of current flow ia a cell is dependent on cell geometry, activation overpotential, concentration overpotential, and conductivity of the electrolyte and electrodes. Three types of current distribution can be described (48) when these factors are analyzed, a nontrivial exercise even for simple geometries (11). 

The concentration overpotential T]C0nC)W is due to slow mass transfer of reactants and/or products involved in the charge-transfer reaction. There... 

This for the conditions of Fig. 5.2a gives at steady state Po2.nernst = 5-1015 bar. The answer is again nontrivial. If 11 is a purely concentration overpotential,9 10 then Eq. (5.5) is valid. But if r also contains an activation overpotential, this must be subtracted from T] and thus Po2,nernst can decrease substantially from this enormous value. A more rigorous analysis of and answer to this important question is given in Chapter 6. 

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. 

This is the basic relationship of electrode kinetics including the concentration overpotential. Equations (5.4.40) and (5.4.41) are valid for both steady-state and time-dependent currents. 

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. 

The Warburg impedance is related to the concentration overpotential and applied AC by... 

It is convenient to distinguish three components of the overpotential, r. Two of these are associated respectively with mass-transfer restrictions in the electrolyte near the electrode (concentration overpotential, f/c), and with kinetic limitations of the reaction taking place at the electrode surface (surface overpotential, rjs) the third one is related to ohmic resistance. 

The concentration overpotential i/c is the component of the overpotential due to concentration gradients in the electrolyte solution near the electrode, not including the electric double layer. The concentration overpotential is usually identified with the Nernst potential of the working electrode with respect to the reference electrode that is, the thermodynamic electromotive force (emf) of a concentration cell formed between the working electrode (immersed in electrolyte depleted of reacting species) and the reference electrode (of the same kind but immersed in bulk electrolyte solution) ... 

In rigorous treatments, e.g., Newman (N8a, Ch. 20), the concentration overpotential is defined as the potential difference (excluding ohmic poten-... 

The concentration overpotential rjc is the component directly responsible for the steep increase in potential observed as the current approaches the limiting current, since the Nemst potential difference (Eq. 6) becomes very large as the concentration of the reacting ion at the electrode approaches... 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

Greek Letters he t. Concentration overpotential (V) Surface overpotential (V)... 

The additional potential required to maintain a current flowing in a cell when the concentration of the electroactive species at the electrode surface is less than that in the bulk solution. In extreme cases, the cell current reaches a limiting value determined by the rate of transport of the electroactive species to the electrode surface from the bulk solution. The current is then independent of cell potential and the electrode or cell is said to be completely polarized. Concentration overpotential decreases with stirring and with increasing electrode area, temperature and ionic strength. 

Further increases in the applied potential do not increase the current and the cell is said to be completely polarized or operating under conditions of high concentration overpotential (p. 230). The diffusion current z d is hence directly proportional to the bulk concentration of the electroactive species. 

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 application of ultrasound to an electrolytic solution is beneficial in that it reduces the ohmic, activation and concentration overpotential thereby allowing discharge at lower applied voltage. 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

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