Diffusion-limiting current density

Using the expression for the limiting diffusion current density, we can rewrite the surface concentration as... 

Together with the boundary condition (5.4.5) and relationship (5.4.6), this yields the partial differential equation (2.5.3) for linear diffusion and Eq. (2.7.16) for convective diffusion to a growing sphere, where D = D0x and = Cqx/[1 + A(D0x/T>Red)12]- As for linear diffusion, the limiting diffusion current density is given by the Cottrell equation... 

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... 

For a more complex (more usual) reaction involving surface intermediates, it is possible that their adjustment to steady-state value may lengthen the time at which the potentiostated current density reaches constancy, even at current densities well below the limiting diffusion-current density. 

What Is the Effect of Electrical Migration on the Limiting Diffusion Current Density ... 

Fig. 8.4. As the time increases, the limiting diffusion current density decreases in accordance with t V2. If the only objective is a high limiting current (with no need to reach steady state) it is best to work at the lowest practical times.

Current densities in the cathode are mainly determined by the respective value of oxide anion conductivity compared to the electronic conductivity (/Co" and ice", coupled to each other in Wagner diffusion). Equation (34) describes the current density limit for coupled transport of oxygen anions and electrons (777) ... 

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... 

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... 

The effect of hydrogen evolution on copper electrodeposition was examined at overpotentials of 550, 650, 800, and 1,000 mV For all examined solutions, overpotentials of 550 and 650 mV corresponded to the plateau of the limiting diffusion current density,... 

Anyway, there are two effects of hydrogen evolution on copper electrodeposition leading to the formation of the honeycomb-like structures. The first effect is a stirring of the solution in the nearelectrode layer caused by a vigorous hydrogen evolution leading to the decrease of the diffusion layer thickness and the increase of the limiting diffusion current density.10 The second effect concerns... 

It is clear from Fig. 38 that an overpotential of 550 mV belongs to the plateau of the limiting diffusion current density at all analyzed temperatures. An overpotential of 650 mV belongs to the plateau of the limiting diffusion current density only at a temperature of... 

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