The concentration overpotential

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

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 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... 

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). 

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 concept of limiting current density permits a simple derivation of a relation between the steady-state concentration overpotential T]c and the current density i if the reaction is such that other forms of overpotential are negligible. One starts from the expression for the concentration overpotential T c [cf. Eq. (7.198)]... 

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... 

Suwanwarangkul R., Croiset E., Fowler M.W., Douglas P.L., Entchev E., Douglas M.A., 2003. Performance comparison of Fick s, dusty-gas and Stefan-Maxwell models to predict the concentration overpotential of a SOFC anode. Journal of Power Sources 122, 9-18. 

Further, the expression for the concentration overpotential can be substituted for Vcath,so anc Vcath,si- ey are... 

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 transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as... 

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. 

From the Nemst equation the concentration overpotential w is calculated to be... 

According to (14-6) the concentration overpotential is zero when the current is zero. ForO < i < the value ofnconc ° g tive, corresponding to cathodic polarization, and increases without limit as i approaches... 

The other component, the concentration overpotential, arises from depletion of the metal ion at the electrode surface. 

The concentration overpotential is not needed if the concentrations used in the kinetic expressions are those evaluated at the electrode surface. 

The thickness distribution of electrodeposits depends on the current distribution over the cathode, which determines the local current density on the surface. The current distribution is determined by the geometrical characteristics of the electrodes and the cell, the polarization at the electrode surface, and the mass transfer in the electrolyte. The primary current distribution depends only on the current and resistance of the electrolyte on the path from anode to cathode. The reaction overpotential (activation overpotential) and the concentration overpotential (diffusion overpotential) are neglected. The secondary... 

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. 

An electrode reaction always occurs in more than one elementary step, and there is an overpotential associated with each step. Even for the simplest case, the overpotential is the sum of the concentration overpotential and the activation overpotential. 

Overpotentials associated with concentration variations in the electrolyte are called concentration overpotentials (t) ) When the concentration near an electrode surface differs from that in the bulk, a concentration cell is established to equalize the two concentrations. Also, when there is diffusion of one ionic species (anion or cation) in the electrolyte due to a spatial variation in its concentration, a diffusion potential will be established to slow down the movement of the diffusing ion and speed up the movement of the oppositely charged ion so that electroneutrality in the solution is maintained. For the case where the electrolyte conductivity is assumed to be a weak function of concentration, the concentration overpotential can be expressed as the sum of a concentration cell potential and diffusion potential in the following way [4] ... 

We have already seen by way of Equation (26.77) that the electrode surface concentration of a reacting species is related to its bulk solution concentration, the applied current density, and the diffusion limiting current density. Substimtion of Equation (26.77) (which is applicable to an electro-active species that is consumed at the electrode) into Equation (26.95) gives a more useful form of the concentration overpotential, since it does not contain the surface concentration, which is often difQcult to measure ... 

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