Overpotential-current density

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 ... 

Tills must be regarded as the fundamental equation of electrode kinetics, and it shows the way in which current density varies with exchange current density, overpotential, and the transfer coefficients. In the laboratory it is, however, more common to use one of the three limiting forms of Equation (1.31). The first two apply at high overpotentials. At high positive overpotentials / > /, and the second term may be ignored the anodic current density if then given by... 

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. 

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