Concentration overpotential transfer

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 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. 

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 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. 

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... 

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... 

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. 

Except for the need to take concentration overpotential into account in electroanalytical studies, it is an important factor for energy losses in electrochemical power sources (e.g., in -> batteries, fuel cells, etc.) and -> electrolysis (e.g., in electrochemical materials production, -> electroplating, etc.). Concentration overpotential is called also concentration polarization and mass transfer overpotential. 

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... 

Concentration overpotential arises due to external or internal mass transfer limitations. For typical cross-flow monoliths, Debenedetti (19) has shown that concentration overpotential is not important under conditions similar to those explored here. 

Chemical reactions can happen before or after the charge-transfer step. Any step can be rate determining, that is, the slowest one determines the total reaction rate. As the electrode polarizes, the resulting overpotential consists of several factors. The most important ones are activation, concentration, and resistance overpotentials. The activation overpotential results from the limited rate of a charge-transfer step, concentration overpotential from the mass-transfer step, and resistance overpotential is the result of ohmic resistances such as solution resistance. Depending on the nature of the slowest step, the reaction is activation, mass transfer, or resistance controlled. 

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. 

Charge-transfer (activation) overpotential (V) Concentration overpotential (V)... 

A mass transfer model has been developed for the pulse plating of copper into high aspect ratio sub-0.25 micron trenches and vias. Surface and concentration overpotentials coupled with the shape change due to the deposition on the sidewalls and the bottom of the tiench/via with time have been explicitly accounted for in the model. Important parameters have been identified and their physical significance described. The resulting model equations have been solved numerically as a coupled non-linear free boundary problem. A complete parametric analysis has been performed to study the effect of the important parameters on the step coverage and deposition rate. In addition, a linear analytical model has also been developed to obtain key physical trends in the system. 

Figure 1 is a cross-section of an electrolytic cell with a resistive electrode and a terminal for contact at one end of the electrode. The current lines in the cell are shown along with the corresponding potential drop. Within the electrolyte (point C-D) the potential drop is linear at the electrolyte/seed layer interface there is a sudden drop in potential, on one side there is the charge transfer and concentration overpotential while on the other side is the metal potential. Finally there is a non-linear drop through the seed layer (A-B). The current lines are closely spaced near the contact terminal both on the electrolyte side and within the seed layer. This effectively means that the local current density will be high next to the contact terminal where the current lines are closely spaced. 

The concentration overpotential is due to slow mass transfer of reactants and/or products involved in the charge-transfer reaction. For several electrode geometries there exist simple equations for computing its magnitude in terms of mass transfer coefficients or, more frequently, in terms of the limiting current II, which is the maximum current obtained when the charge-transfer reaction is completely mass-transfer controlled. Contrary to aqueous electrochemistry, where concentration overpotential is frequently important due to low reactant and/or product diffusivities in the aqueous phase, in solid... 

As in any heterogeneous reaction, two major controlling regimes are also possible in electrochemical reactions, surface reaction and external mass transfer, referred to specifically as surface overpotential (or charge transfer) and concentration overpotential, respectively, in electrochemical terminology. 

When the overvoltage is sufficiently low, then it can be divided into the sum of two terms which are frequently called the activation overpotential, ria, on the one hand, related to charge transfer kinetics and on the other hand the concentration overpotential, 7d, related to mass transport kinetics ... 

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