Potential concentration overpotential

As explained before, the open-circuit potential of the battery depends on concentration, temperature, and transport limitations. The real voltage delivered by a battery in a closed circuit is affected by ohmic limitations (ohmic potential), concentration limitations (concentration overpotential), and surface limitations (surface overpotential). The close circuit potential of the cell is given by the open-circuit potential of the cell minus the drop in potential due to ohmic potential, concentration overpotential, and surface overpotential. The ohmic potential is due to the ohmic potential drop in the solution. It is mostly affected by the applied charge/discharge current of the battery. The concentration overpotential is associated with the concentration variations in the solution near the electrodes. It is strongly affected by transport properties such as electrolyte conductivity, transference number, and diffusion coefficients. Finally, the surface overpotential is due to the limited rates of the electrode reactions. 

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 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 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). 

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. 

This means that the passage of the current has made the potential depart from the zero current value The zlinterfacial concentration of electron acceptors from the initial bulk value c° to anew value c°. Thus, d< ) — Zlpotential difference produced by a concentration change at the interface. This concentration-produced76 potential difference is often known as a concentration overpotential T c to distinguish it from the usual overpotential77 r a, which results from the charge-transfer reaction and was treated at length in Section 7.2.3. Hence, one writes... 

Overpotential Departure from equilibrium (reversible) potential due to passage of a net current. Concentration overpotential results from concentration gradients adjacent to an electrode surface. Surface overpotential results from irreversibilities of electrode kinetics. Supporting (inert or indifferent) electrolyte Compounds that increase the ionic conductivity of the electrolyte but do not participate in the electrode reaction. 

To obtain quantitative expressions for the corrosion current and the corrosion potential, one has to substitute the proper expression for the metal-dissolution- and electronation-current densities. If no oxide films form on the surface of the corroding metal and neither of the current densities is controlled by mass transport, i.e., there is no concentration overpotential, one can insert the Butler-Volmer expression for the deelectronation- and electronation-current densities. Thus,... 

Consider two half-cell reactions, one for an anodic and the other for a cathodic reaction. The exchange current densities for the anodic and the cathodic reactions are lO-6 A/cm2 and 1(T2 A/cm2, respectively, with transfer coefficients of 0.4 and 1, respectively. The equilibrium potential difference between the two reactions is 1.5 V. (a) Calculate the cell potential when the current density of 1CT5 A/cm2 flows through the self-driving cell, neglecting the concentration overpotentials. The solution resistance is 1000 Q cm2, (b) What is the cell potential when the current density is 10-4 A/cm2 (Kim)... 

The tertiary current distribution Ohmic factors, charge transfer controlled overpotential effects, and mass transport are considered. Concentration gradients can produce concentration overpotentials. The potential across the electrochemical interface can vary with position on the electrode. 

Concentration overpotential — The concentration overpotential of an electrode reaction at a given electrode current density is basically the difference in equilibrium potentials across the diffusion layer. More precisely, it is the potential of a reference electrode (of the same -> electrode reaction as the -> working electrode) with the interfacial concentrations which establish themselves under direct current flow, relative to the potential of an identical -> reference electrode with the concentrations of the bulk solution. From such a measured potential difference, with flowing direct current, one has to subtract the ohmic potential drop prevailing between the two electrodes. 

If net cathodic current flows then this potential is shifted negatively. Concentration polarization (alternatively called -> mass-transport polarization or - concentration overpotential) is encountered if the rate of transport of the redox reactant to the electrode surface is lower than that of the -> charge-transfer reaction. Together with the charge-transfer or -> activation polarization (overpotential), q3, and the polarization (overpotential) due to a preceding chemical reaction, qrxn> (see... 

Resistance overpotential p and activation overpotential p are characteristic of irreversible reactions and are, therefore, termed irreversible overpotentials . Since deviations from the equilibrium potential due to changes in the concentrations of the reactants are largely reversible, concentration overpotential p is known as a reversible polarization . Crystallization overpotential p is more complicated. It can be caused either by reversible polarization or irreversible polarization . The details will be discussed later. 

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