Electrode Nemst diffusion layer, thickness

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

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... 

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]...

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. 

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. 

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. 

Voltammetry. Diffusional effects, as embodied in equation 1, can be avoided by simply stirring the solution or rotating the electrode, eg, using the rotating disk electrode (RDE) at high rpm (3,7). The resultant concentration profiles then appear as shown in Figure 5. A time-independent Nemst diffusion layer having a thickness dictated by the laws of hydrodynamics is established. For the RDE,... 

The concentration profiles are very sensitive to the kinetics of the electrode reaction. In this context, the determination of the diffusion layer thickness is of great importance in the study of non-reversible charge transfer processes. This magnitude can be defined as the thickness of the region adjacent to the electrode surface where the concentration of electro-active species differs from its bulk value, and it can be accurately calculated from the concentration profiles. In the previous chapter, the extensively used concept of Nemst diffusion layer (8), defined as the distance at which the linear concentration profile (obtained from the straight line tangent to the concentration profile curve at the electrode surface) takes its bulk value, has been explained. In this chapter, we will refer to it as linear diffusion layer since the term Nemst can be misunderstood when non-reversible processes... 

The diffusion-layer thickness S is defined by the Nemst diffusion layer model illustrated in Fig. 6. This model assumes that the concentration of M " " ions has a bulk concentration q, up to a distance 5 from the electrode surface and then falls off linearly to Cx= at the electrode surface. 

We have attempted to give supported results in a form appropriate for comparison with unsupported ones by considering full-cell conditions. The transition problems discussed above only occur for unstirred (liquid) electrolytes or for solid electrolytes. When a stirred solution or rotating electrode with lanfinar flow is employed, the I which appears in Z/> and Zw expressions is replaced by 5n, where 5n is the thickness of the Nemst diffusion layer. It decreases as the frequency of rotation of a rotating electrode increases and the experiment is always carried out for conditions where 5 1. 

According to Nemst, diffusion occurs in a stable layer of thickness 6 at the interface of the working electrode, i.e.. from the electrode surface to some distance into the solution (Fig. I). Within the Nemst diffusion layer, the decrease of analyte concentration in the sample solution to c at the electrode surface is linear and voltage dependent. Convection within the layer is negligible. 

Although many attempts have been made to establish spectroelectrochemical cells for spectral analysis in combination with electrode redox control, this method suffered from inadequate equilibration of the redox proteins with the electrode potential. This is mostly due to the Nemst diffusion layer with a thickness of some tens of micrometers which requires stirring for cells with longer optical pathlength. 

A comment about the relative sizes of the boundary layers discussed in ekctrochemistry is necessary. The dimentiQiu of the double layer may be 5 x I0 cm. In contrast, the Nemst diffusion layer may have a thickness of cm while the real layer effected by the electrode reaction may be an order of magnitude thicker ... 

RDEs provide well-controlled diffusion conditions (Figure 1.27). The flow of fhe electiolyfe gives access of fresh solution to the surface, whereas the electrochemical reaction at the electrode surface changes the electrolyte composition. Both effects compensate each other, leading to a constant thickness of fhe Nemst diffusion layer all over fhe disc with a laminar flow of the solution in vicinity of ifs surface. The analytical treatment of this convection and diffusion problem leads to Levich s equation ... 

When a steady-state of non-zero flux is to be reached, then non-planar diffusion and/or controlled convection of the electrolyte along the electrode surface are required. The term (TcDt) -, called the thickness of diffusion layer, can then be substituted by a constant value 3, Nemst thickness). The flux J is related to the faradic current I by the equation ... 

Cyclovoltammetry is typically performed by dipping a working electrode into a solution or suspension of the redox-active sample. Under these conditions, the electrode current is diffusion controlled and only a small fraction of the sample material that is in diffusional exchange with the electrode is involved in the reaction. The separation of the anodic peak (Ep a) and the cathodic peak (Ep c) depends on the scan speed, and the midpoint potential of a reversible electron transfer reaction is calculated as the average of Ep a and Ep c. Cyclovoltammograms for thin-layer OTTLE cells differ significantly. If the layer thickness is in the order of the Nemst layer (<100 pm), the entire cell volume is involved in the reactirai because of fast diffusional transport to the electrode. Consequently, the anodic and the cathodic peak are hardly separated, and are at identical potentials under ideal conditions. 

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