Nemst diffusion layer thickness

The micro structured platelets, hold in a non-conducting housing, were realized by etching of metal foils and laser cutting techniques [69]. Owing to the small Nemst diffusion layer thickness, fast mass transfer between the electrodes is achievable. The electrode surface area normalized by cell volume amounts to 40 000 m m". This value clearly exceeds the specific surface areas of conventional mono- and bipolar cells of 10-100 m m. ... 

Note the similar expression at the rotating electrode [eqn. (27)]. A Nemst diffusion-layer thickness is defined as... 

In order to evaluate the conditions under which it is possible to achieve a stationary cyclic voltammogram, a key parameter is Nemst diffusion layer thickness, <5 , which was introduced in Sect. 2.2.1 for reversible processes when a single potential pulse is applied. It is possible to extend the definition of to a multipulse sequence, <5)f, as... 

In the case of spherical electrodes, Nemst diffusion layer thickness reaches the following limiting behaviors ... 

Fig. 5.10 Nemst diffusion layer thickness 5 le obtained in LSV (a) and Cyclic Voltammograms (b) corresponding to a spherical electrode. These curves have been calculated from Eq. (5.71)-(5.72) and (5.23) for A = 10 5mV and v = lOOrnVs-1. The values of the electrode radii appear on the curves. Reproduced with permission [29]...

If we set the condition of applicability of the equations for planar diffusion as r > 20(7iDt), if - in other words, we limit the Nemst diffusion layer thickness to 5% of the radius and introduce a typical value of D, we arrive at an inequality which is easy to remember, namely... 

The Nemst diffusion layer thickness is larger in a recessed area than at a crest, hence the local current density is smaller. As a result, recessed areas grow more slowly than crests, and the amplitude of roughness increases with time during plating. 

We can discuss this problem in terms of the ratio between the Nemst diffusion layer thickness 8, given by (nDt), and the radius of the electrode on the one hand, and between 5 and the distance between two electrodes, on the other. To do this, we shall list the various possibilities, and derive the corresponding behavior qualitatively. 

Figure 6.6 Schematic concentration profile at the cathode for pulse plating conditions [6.101] pulsating diffiision layer thickness stationary diffusion layer thickness iJn Nemst diffusion layer thickness.

To electrochemists this expression is clearly related to the diffusion length or Nemst diffusion layer thickness. So the potential step chronoabsorptometry experiment can be regarded as setting up an optical cell with the thickness equal to the Nemst diffusion layer. As time increases, not only does the diffiision layer thickness increase, but so does the amount of light-absorbing product generated in the layer. 

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"... 

If there is no convection. Equation 7.8 can be used with only the first term on the right-hand side. Under these conditions and when the potential is held constant, the current measurements can be used to define (1) the Nemst diffusion layer thickness, 5n, as a function of time and (2) the diffusion coefficient of the electrochemically active species. In the potentiostatic regime, the concentration of the electrochemi-caUy active species is a function of both distance from electrode, x, and time, t. Let us see how the equation for Pick s second law... 

If the solution flow is parallel to the electrode surface and perpendicular to the diffusion direction, the Prandtl layer thickness, 5pj, and the Nemst diffusion layer thickness, 5n, in a steady state are related as follows [2] ... 

The RDE allows defining the Nemst diffusion layer thickness, 8n, which depends on (1) the diffusion coefficient of the electrochemically active species, (2) kinematic viscosity of the solution, and (3) rotation rate of the electrode as follows ... 

Commonly, when there is a simple mixing (stirring) of solution, the Nemst diffusion layer thickness is not known. One of the systems where 6n can precisely be defined is the RDE. The main feature of the RDE is that it is equally accessible at any point of the electrode surface. 

The limiting current density on the RDE can be estimated if the Nemst diffusion layer thickness and the bulk concentration of the electrochemically active species are known. 

FIGURE 18.17 Depletion layer at an electrode surface in the absence (a) and presence (b) of external magnetic field applied perpendicular to the diffusional flux. J is the diffusional flux of the substrate, Cei is the substrate concentrations at the electrode surface, 5 and do are the Nemst diffusion layer thickness and hydrodynamic boundary layer thickness, respectively, and Uq, is the fluid velocity on the outer edge of the hydrodynamic boundary layer. (Adapted with permission from Ref. [118]. Copyright 2004, American Chemical Society.)... 

What is semi-infinite in this case How far is infiniiy, in the context of diffusion of a species in an aqueous solution It should be far enough from the surface for the concentration to have reached its value in the bulk. This applies when > 5 6). Employing Eq. (4.12) we find that 6 6 x 10 cm at 100 s, hence infiniiy lies less than 0.3 cm away from the surface. One does not even have to use a planar electrode in order to achieve one-dimensional (planar) diffusion. A cylindrical electrode (i.e., a wire) or a spherical electrode will also look planar as long as the Nemst diffusion layer thickness is small compared to the radius of curvature of the electrode. On the other hand, a miaoelectrode, typically having a radius of r < 10 fim will not follow the equations for semi-infinite linear diffusion, as discussed in Section 14.3 below. 

In alloy deposition the concentrations of the two alloying elements in solution could be different one maybe deposited at a rate controlled substantially by mass transport while the other may be essentially under conditions of activation control. The number of electrons needed to reduce each of the alloying elements should also be taken into account. For example, in deposition of a Au-Ni alloy from a solution containing AUCI4 and NiCk, at equal concentrations, the limiting current for Au would be 50% higher than that for Ni, (if the difference in the diffusion coefficient of the two ions is ignored). On the other hand, the hydrodynamic conditions, and, hence, the value of the Nemst diffusion-layer thickness are the same. 

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