Diffusion controlled current density

Equations 47-49 describe variations of parameters along the y coordinate of the catalyst layer (y = z/lc 1), where z is the catalyst layer thickness coordinate, y = 0 specifies the catalyst layer/gas interface, and y = 1 specifies the catalyst layer/ionomeric membrane interface (see Fig. 44), in which Rc (= /Ci/cr) is the protonic resistance through a unit cross-sectional area of the catalyst layer and 7d (=nFDC /lc ) is a characteristic diffusion-controlled current density in the catalyst layer. The thickness of the catalyst layer disappears from the equations by introducing Rc, ax, and I ). The experimental variables considered include the overpotential 1], the current density /, and the oxygen concentration C, when pox = 1 atm at the catalyst layer/gas interface. The O2 partial pressure, pox, at the catalyst layer/backing layer interface is determined, in turn, by the cathode inlet gas stream composition and stoichiometric flow rate and by the backing layer (GDL) transport characteristics. 

Many corrosion systems are controlled by diffusion limitations on oxygen because of its low solubility in aqueous solution (0.25 mM at room temperature). The diffusion-limited current density, iL, can be described mathematically by... 

The diffusion layer thickness is controlled by the hydrodynamics (fluid flow). Although more details on mass transfer effects are discussed in Chapter 5, it is worthwhile to point out here that the diffusion-limited current density is independent of the substrate material. 

Here im is the activation controlled current density occurring when transport to the interface is very fast. To clarify this equation, consider the two processes (activation and diffusion) to occur sequentially in the overall reaction sequence. Since they occur in series, the slowest rate will dominate the overall total rate. 

We stated earlier that for a diffusion-controlled process the diffusion layer thickness grows with t and hence the diffusion-limited current density declines with t. This might seem to be at... 

Typical potentiostatic transients are shown in Fig. 14K. Such data can be employed in two ways to evaluate the activation-controlled rate as a function of overpotential. We have already seen that the measured current density is related to the diffusion-limited current density by the equation... 

A rigorous analysis of the current-potential relation and current distribution in a single pore was carried out taking into account all forms of polarization considering a concentration gradient of only the reactant and in the axial direction of the pore (108). The assumption of a unidirectional concentration gradient is valid under the conditions that the local activation-controlled current density is considerably less than the limiting current density due to radial diffusion (i < iJlO). 

Distribution and intensity of corrosion is therefore usually determined by the access of oxygen to the various parts of the surface. Uneven oxygen access causes concentration cells (Section 7.5). Very often the corrosion is diffusion controlled, i.e. the diffusion-limiting current density is of special interest. Several examples of corrosion rate determined by the oxygen reduction rate are dealt with in Chapter 7. 

Oxygen reduction is a very important reaction for corrosion processes. Its kinetics have a relatively large overpotential, which causes a negative rest potential for most reactive metals. In a saturated aqueous solution of ca. 2 X10" M, oxygen reduction often occurs under diffusion control. The maximum diffusion limited current density is calculated according to Eq. (1-33) with the diffusion coefficient Do=10" cm s a Nemst diffusion layer thickness 5=2x 10 cm, and n = 4 for complete oxygen reduction to H2O or OH"... 

Thus, the diffusion-limited current density is proportional to therefore, employing fast transients can extend the range over which the activation controlled current density can be determined. 

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

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