Equilibrium exchange current

In this equation /g, is th equilibrium exchange current, and the arrow convention adopted is that / g represents the rate of cathodic reduction... 

If the areas of the electrodes are assumed to be 1 cm, and taking the equilibrium exchange current density /g for the Ag /Ag equilibrium to be 10 A cm", then /g will be 10 A, which is a very high rate of charge transfer. A similar situation will prevail at electrode II, and rates of exchange of silver ions and the potential will be the same as for electrode I. 

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 most significant parameter in the relationships given above is the equilibrium exchange current density io, which can be evaluated by extra-p>olating the linear t/ vs. log / curve to tj = 0, at which log / = log io. Alternatively, /q may be evaluated from the linear Ep vs. log / curve by extrapolating the curve to the equilibrium potential. ... 

Thus, the electronation and deelectronation reactions modify the electric field across the interface, and the field, in feedback style, alters the rates until the rates of M+ + e — M and M — M+ + e become equal. This is equilibrium. Underlying the condition of zero net current, an equilibrium exchange-current density Iq, flows across the interface in both directions. The potential difference across the interface at equilibrium depends upon the activity ratio of electron acceptor to electron donor in the solution. Alter the ratio, and the equilibrium potential changes.14... 

Since there is no net diffusion under equilibrium conditions, then- p hole current is equal to the p —> n hole current. These equilibrium currents are analogous to the equilibrium exchange currents at an electrode/solution interface. They represent the exchange of holes across the junction between the n- and p-types of material and will be designated by the symbol i0fl. This i0 will now be examined more carefully. 

The conductivity oof any step is determined largely by its equilibrium exchange-current density i0j. The smaller the i0 j is for the step, the lower is its conductivity. Thus one can say that the step with the smallest i0j generally determines the overall current.63... 

The procedure for correcting forthe departure from equilibrium to nonequilibrium surface coverage consists in (1) writing down the actual concentration in the Butler-Volmer equation or its relevant special case and (2) transforming this expression into one involving the equilibrium exchange-current density Iq, which contains the bulk concentration. 

When the cathodic current density (jc) is equal to the anodic current density (/a), the net current flowing across the electrode-solution interface is zero, and the net flux of O and R is zero. For this condition, the current densities represent the equilibrium-exchange current density (/0), given by ... 

Overpotentials" and Equilibrium Exchange Current Densities6 for Hydrogen Evolution and Overpotentials for Oxygen Evolution0 at Different Metals in... 

Now, to go to the experimental situation, what happens as we insert a metal electrode into an electrolyte solution without connecting it to an external electron source As we have discussed before (p. 22), an El is built up and hence a certain potential is established across the interface region. At this potential, charge transfer between electrode and electroactive species takes place, but, since no net current flows, the rates of electronation and de-electronation are identical. The system has reached the equilibrium potential at which the current density z for electronation is equal to the current density of de-electronation i. This current density is designated i0, the equilibrium exchange current density (cf. Table 6), given by the expression ... 

Figure 7 The current-voltage (I-V) behavior of an n-type semiconductor/metal junction in the dark. The shape of the I V curve is described by the diode equation (equation 17) thus, such a curve is referred to as a diode curve. The difference between curves 1 and 2 is that the equilibrium exchange current, 7o, is greater for curve 2...

Here the reaction rate r is defined per unit electrode area, moles per area per time, j0 is the equilibrium exchange current when E = eq, r 0M is the activation overpotential, and a is the transfer coefficient. For large activation overpotentials, the Tafel empirical equation applies ... 

Using Equation 18.14 to define the equilibrium exchange current density i al, we have... 

Diode equation the equation that describes the relationship between the applied bias and the resulting current of a semiconductor contact. It is generally of the form / = — 7o(exp(—gF/AT) —1) where /q is the equilibrium exchange current and Y is the applied bias... 

Depending on the relative rates of charge transfer, y o.Sch may be constrained by either solid-state or electrochemical limitations, and is respectively termed the saturation current or the equilibrium exchange current [17]- A single representation of either a pn or Schottky junction is schematized in the upper center of Fig. 2, by a junction generating a voltage V. 

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