Diffusion-limited current density

Example 6.2. Calculate the diffusion limiting current density for the deposition of a metal ion at a cathode in a quiescent (unstirred) solution assuming a diffusion layer thickness 8 of 0.05 cm. The concentration of ions in the bulk (cj,) is 10 moEL (10 moEcm ), the same as in Example 6.1. The diffusion coefficient D of in the unstirred solution is 2 X lO cm /s. Using Eq. (6.83), we calculate that the limiting diffusion current density for this case is... 

Limiting current density Maximum (diffusion-limited) current density at which a given electrode reaction can proceed. Above this limit another electrode reaction commences. 

Figure 24 Schematic polarization data for oxygen reduction reaction (ORR) in neutral (pH 7.2) solution. Diffusion-limited current density (i L) is present due to mass transport limitations on dissolved oxygen.

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. 

Figure 9 Polarization curve of carbon steel in deaerated, pH 13.5 solution at 65°C. Sample was initially held potentiostatically at —1.2 V(SCE) for 30 min before initiation of the potentiodynamic scan in the anodic direction at 0.5 m V/s. The cathodic loop results from the fact that the passive current density is only 1 pA/cm2, which is less than the diffusion-limited current density for oxygen reduction for the 0.5 ppm of dissolved oxygen present. (From Ref. 8.)...

Calculate the diffusion-limited current density that is expected for each rotation rate assuming a dissolved oxygen concentration of 6-8 ppm (see experimental data sheet for calculation procedure). 

Figure 39 Experimental and calculated diffusion-limited current densities for RDE experiment.

Consider the electrochemical oxidation of a crucial reaction in many types of fuel cells. The solubility of in aqueous solutions is rather low, (of the order of O.I mM), and the diffusion coefficient is D = 1.6x10 cm/s. The diffusion limited current density for this reaction, calculated from Eq. IK is shown in Fig. 3K, as a function of... 

The situation at a miniature disc microelectrode embedded in a flat insulator surface (such as an RDE of very small size) can be approximated by spherical symmetry, obtained for a small sphere situated at the center of a much larger (infinitely large, in the present context) spherical counter electrode. How will the change of geometry influence the diffusion-limited current density This is shown qualitatively in Fig. 18L. As time progresses, the diffusion layer thickness increases, causing, in the planar case, a proportional decrease in the diffusion current density. In the spherical configuration the electroactive... 

When an ultramicro electrode is used as an eleclroanalytical tool, the diffusion-limited current density is not affected by the rate of... 

We assumed here a solution of medium conductivity, and yet arrived at an ohmic potential drop of less than 1 mV at the very large current density of 0.8 A/cm. Thus, using an ultramicro electrode extends the range of measurable current densities because (a) the limiting current density is inversely proportional to the radius and (b) the resistivity is proportional to the radius. More concisely, we could say that both the diffusion-limited current density and the conductivity are inversely proportional to the radius. 

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... 

Thus, the diffusion-limited current density decreases with the square... 

As the diffusion-limited current density is reached, the concentration of reactant at the surface is reduced to zero, and therefore 0 = 0. Substituting in Eq. 36K we have... 

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... 

Owing to the finite electrolyte volume ofthe nanoliter droplet, the diffusion boundary layer reaches the dimensions of the droplet within seconds, assuming a diffusion coefficient of for example D = 110-5 cm2 s 1. A constant diffusion gradient can not be established because the bulk concentration is reduced. Thus, measurements of diffusion limited currents are not stable over time. The electron transfer reactions discussed below were carried out on anodic oxide layers with maximum current densities 3 to 4 orders of magnitude lower than the diffusion limited current densities, thus ensuring a stable support of consumables over the time of the measurement. In order to prevent evaporation of electrolyte, the ambient was saturated with water vapor. 

Of course, the influence of magnetic field appears to be restricted to the diffusion-limited regions. During electrolysis under parallel fields, the Lorentz force induces convective flow of the electrolyte close to electrode surface. A magnetically stimulated convection leads to a decrease of the diffusion layer thickness thus increasing the diffusion-limited current density.39 As a rule, it was adopted that the limiting diffusion current density depends on magnetic field, as z l oo 51/341 Anyway, the increase of the... 

We have already seen by way of Equation (26.77) that the electrode surface concentration of a reacting species is related to its bulk solution concentration, the applied current density, and the diffusion limiting current density. Substimtion of Equation (26.77) (which is applicable to an electro-active species that is consumed at the electrode) into Equation (26.95) gives a more useful form of the concentration overpotential, since it does not contain the surface concentration, which is often difQcult to measure ... 

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