Concentration polarization diffusion overpotential

Concentration Polarization (Diffusion Overpotential). If copper is made cathode in a solution of dilute CUSO4 in which the activity of cupric ion is represented by (Cu ), then the potential ( )i, in absence of external current, is given by the Nernst equation... 

The difference in concentration existing between the electrode surface and the bulk of the electrolyte results in a concentration polarization. According to the Nernst equation, the concentration polarization or overpotential produced from the change of concentration across the diffusion layer, may be written as... 

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... 

These relations are based on the fact that the potential loss due to charge-transfer reactions are negligible (the activation overpotential approaches zero). The diffusion overpotential is usually negative during cathodic processes and positive during anodic processes. The effects of concentration polarization are usually pronounced at high current densities, when a reaction species at the interface is consumed at a faster rate than it can be... 

If T ct Rd,c + Rd,a, we speak of concentration polarization, while if Ret > Rd,c + Rd,a, activation polarization prevails. This is meant to express that the overpotential is related either to the diffusion or to the activation processes. The diffusion overpotential can be given as... 

During the electrolytic process, current flows at a fine rate, but overpotential drop emerges due to connectors and wiring system, and electrolyte electrical resistance at the cathode-electrolyte interface. Also, overpotential may occur when concentration polarization is due to mass transfer by diffusion [1]. 

In this section, the variables related to oxygen and methanol are equipped with the subscripts ox and mt, respectively. Here, iox, imt are the ORR and MOR volumetric exchange current densities, Cox, cj are the local and reference (inlet) oxygen concentrations, Cmt, c t are the local and reference methanol concentrations, r]mt are the ORR and MOR polarization potentials (overpotentials), box, bmi are the ORR and MOR Tafel slopes, and Dox, Dmt are the oxygen and methanol diffusion coefficients, respectively. 

This gives the relation of concentration polarization and current for mass transfer by diffusion. Equation (2.40) indicates that as i approaches the limiting current i, theoretically the overpotential should increase to infinity. However, in a real process the potential will increase only to a point where another electrochemical reaction will occur, as illustrated in Fig. 2.16. Figure 2.17 shows the magnitude of the concentration over-potential as a function of iH[ with = 2 at 25°C, based on Eq. (2.40). 

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. 

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. 

The Eq. (2.78) describes the dependence of the overpotential on the deposition time from point b to point c. The overpotential changes due to the change of the surface concentration of adatoms from Co,a at the equilibrium potential to some critical value Ccr.a at the critical overpotential, rj, at which the new phase is formed. Hence, the concentration of adatoms increases above the equilibrium concentration during the cathode reaction, meaning that at potentials from point b to point c there is some supersaturation. The concentration of adatoms increases to the extent to which the boundary of the equilibrium existence of adatoms and crystals has been assumed to enable the formation of crystal nuclei. On the other hand, the polarization curve can be expressed by the equation of the charge transfer reaction, modified in relation to the crystallization process, if diffusion and the reaction overpotential are negligible, as given by Klapka [48] ... 

At high polarization concentration changes can no longer be ignored and concentration overpotential has to be included with activation overpotential. For the latter, only L (a characteristic length) had to be considered. For concentration overpotential not only has L to be considered but <5, the thickness of the diffusion boundary layer (see Section 2.3.1). Since we also have to consider concentration differences within the solution, the problem is formidable. More dimensionless parameters must be introduced to characterize behavior, but these serve only as a guide. 

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