Current density-overpotential densities

The quadratic rate equation [Eq. (1)] of the continuum theory arises because it implicitly assumed the parabolic dependence of the free energy profile on the solvent coordinate q. One of the consequences of this quadratic equation is the generation of a maximum in the dependence of the rate of reaction on the free energy of reaction and also in current density-overpotential dependence. 

Figure 13 depicts the calculated current density, overpotential, and hydrogen concentration distribution in an assumed ideal (straight cylindrical) Raney-nickel pore of a pore diameter of 2 nm calculated with an exchange... 

According to a well-known current density/overpotential relationship in electrochemistry, we have... 

Figure 9 Comparison of normal current density, overpotential, metal voltage...

Figures 26.2 and 26.3 show typical current density-overpotential plots where i varies exponentially with r s, in accordance with the Butler-Volmer equation. In Figure 26.2, the effect of varying P on )-r 5 curves is shown (as P decreases, i increases at a given value of 1I5). The increase in current density at a given for increasing values of i is shown in Figure 26.3. From these two figures it can be concluded that electrochemical reactions that follow Butler-Volmer kinetics will be facile when the kinetic parameter p is small and the value of is large.

One of the most important relations in mechanism determination is the current density-overpotential relation. At overpotentials greater than BT/aF, the rate of the reverse reaction may be neglected and the general expression for the overpotential-current density relation in the case of a cathodic reaction expressed by Eq. (41) reduces to... 

An additional advantage arises out of this dependence of rate on electric field. It gives an extra mechanism determining criteria for the reaction. The current density-overpotential relation is of utmost importance in electrocatalysis. 

The space time yield is a measure of the rate of production per unit volume of reactor and is normally quoted in units such as mol dm h . The space time yield is proportional to the effective current through the cell per unit volume of reactor and hence on the current density (overpotential, concentration of electroactive species and the mass transport regime), current efficiency and the active surface area of electrode per unit volume. 

Figure 2.3 Current density—overpotential curves of 0 + n e R reaction at three different exchange current...

Figure 2.4 Current density—overpotential curves of 0 -i- nae <- / reaction at three different electron-transfer coefficients (a = 0.25, 0.5, and 0.75, respectively), calculated according Eqn (Z28a) using the parameter values of = / =8.314 J mol, T=298 K, F=96,487 CmoP, and /=1.0x 10 Acm . (For color version of this...

The general form of current density-overpotential relationship in electrodeposition of metals for the reaction... 

Using the current density-overpotential relationships and the procedure for the determination of the ohmic potential drop, the polarization curves for electrodeposition processes can be successfully simulated [9, 20]. 

The current density-overpotential curve equation (Eq. (1.20)), derived by taking the concentration dependence of io into account and the linear dependence of /q on the Cs/Cq ratio, can be rewritten in the form ... 

A ID anal3dical model of the SOFC sandwich (Pisani and Murgia, 2007) leads to implicit expressions for the electrode voltage-current relation in the limits of low and high current densities (overpotential). This model is designed to assist in the multidimensional CFD simulations of SOFC in the CFD environment the solution of implicit equations poses no problems. However, the relations (Pisani and Murgia, 2007) are not suitable for an analysis of the effect of hydrogen utilization on cell performance. 

The Equations for the Exchange Current Densities, Overpotentials, and Parameters... 

The reader is encouraged to practice employing the Tafel, Butler-Volmer, and generalized Butler-Volmer equations using a computer code such as Excel or Mathematica to better understand the current density-overpotential dependence. 

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

The overpotential is defined as the difference between the actual potential of an electrode at a given current density and the reversible electrode potential for the reaction. 

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

Seconday Current Distribution. When activation overvoltage alone is superimposed on the primary current distribution, the effect of secondary current distribution occurs. High overpotentials would be required for the primary current distribution to be achieved at the edge of the electrode. Because the electrode is essentially unipotential, this requires a redistribution of electrolyte potential. This, ia turn, redistributes the current. Therefore, the result of the influence of the activation overvoltage is that the primary current distribution tends to be evened out. The activation overpotential is exponential with current density. Thus the overall cell voltages are not ohmic, especially at low currents. 

Tertiay Current Distribution. The current distribution is again impacted when the overpotential influence is that of concentration. As the limiting current density takes effect, this impact occurs. The result is that the higher current density is distorted toward the entrance of the cell. Because of the nonuniform electrolyte resistance, secondary and tertiary current distribution are further compHcated when there is gas evolution along the cell track. Examples of iavestigations ia this area are available (50—52). 

It is evident from these expressions that since in the Tafel region / (the current density actually determined) must be greater than /(, (the equilibrium exchange current density), the signs of the overpotentials will conform to equations 1.60 and 1.61, i.e. will be negative and will be positive. 

Fig, 1.24 Tafel lines for a single exchange process. The following should be noted (a) linear f-log I curves are obtained only at overpotentials greater than 0-052 V (at less than 0-052 V E vs. i is linear) b) the extrapolated anodic and cathodic -log / curves intersect at tg the equilibrium exchange current density and (c) /, and the anodic and cathodic current densities... 

The relation between transport overpotential and current density for a cathodic reaction is given by... 

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