Nernst diffusion layer thickness

Fig. 2. Concentration profile of the reacting ion at an electrode. The so-called Nernst diffusion layer thickness is indicated by <5n. ...

Early investigators assumed that this so-called diffusion layer was stagnant (Nernst-Whitman model), and that the concentration profile of the reacting ion was linear, with the film thickness <5N chosen to give the actual concentration gradient at the electrode. In reality, however, the thin diffusion layer is not stagnant, and the fictitious t5N is always smaller than the real mass-transfer boundary-layer thickness (Fig. 2). However, since the actual concentration profile tapers off gradually to the bulk value of the concentration, the well-defined Nernst diffusion layer thickness has retained a certain convenience in practical calculations. 

The dependence of the limiting current density on the rate of stirring was first established in 1904 by Nernst (N2) and Brunner (Blla). They interpreted this dependence using the stagnant layer concept first proposed by Noyes and Whitney. The thickness of this layer ( Nernst diffusion layer thickness ) was correlated simply with the speed of the stirring impeller or rotated electrode tip. 

Fig. 7.95. The Nernst diffusion-layer thickness is obtained by extrapolating the linear portion of the concentration change to the bulk concentration value.

The equivalent Nernst diffusion layer thickness is T (4/3) times d. Eq. (3-1) becomes ... 

Consider the process of plating copper on a plane electrode. Near the electrode, copper ions are being discharged on the surface and their concentration decreases near the surface. At some point away from the electrode, the copper ion concentration reaches its bulk level, and we obtain a picture of the copper ion concentration distribution, shown in Fig. 6. The actual concentration profile resembles the curved line, but to simplify computations, we assume that the concentration profile is linear, as indicated by the dashed line. The distance from the electrode where the extrapolated initial slope meets the bulk concentration line is called the Nernst diffusion-layer thickness S. For order of magnitude estimates, S is approximately 0.05 cm in unstirred aqueous solution and 0.01 cm in lightly stirred solution. 

Here, c is the surface concentration of protons, S the Nernst diffusion layer thickness,... 

If the characteristic time is defined independently of the disk radius, and diffusion (12.26) results, the Nernst diffusion layer thickness is dependent only on the number of these time units. So if the characteristic time is r and the maximum duration of the experiment is Tmax (giving Tmax = Tmax/r), then the final diffusion layer thickness is 1JDrmax. Then, in dimensionless distance units (normalisation being division by the disk radius a), this becomes, after multiplying by 6 and noting (12.27),... 

We alluded to the Nernst diffusion layer thickness 5, in the first chapter. It relates to the mass-transport limited current density through the equation... 

The experimental data show that two electrons per O2 are transported through the Nernst layer in the rotating disk experiments. Consequently, reaction (LXIII) would need to proceed sufficiently fast to be essentially complete within a distance small compared to the Nernst diffusion layer thickness. Thermodynamics imposes an upper limit on the 2 concentration adjacent to the electrode, using the value of Enhe = -0.30 V for the 02-02 couple (see Figure 1). At a potential, for example, of jEnhe = —0.80 the upper... 

Looking again at Eq. (2.8), is identical with the Nernst diffusion layer thickness. Unfortunately, this quantity is often discussed and used as if it had physical reality when as we have seen from Fig. 2.5 it is a mathematical artifact arising from a particular mass transfer model. For this reason diffusion layer thickness is not normally found in design equations but Eq. (2.8) is written in the form ... 

FIGURE 2.26. Schematic representation of concentration profiles for the substrate and mediator expected for the Case C situation of the Andrieux-Sav ant scheme. These profiles are drawn for the mediated oxidation situation (the second wave) where the substrate is oxidized at the mass-transfer-limited rate. Arrowheads indicate current ratios approaching infinity tails denote current ratios approaching zero. The L and denote polymer layer thickness and the Nernst diffusion layer thickness, respectively. The latter dimensions are not drawn to scale. 

If the characteristic time is defined independently of the disk radius (as it is with LSV) and diffusion equation (12.27) results, the Nernst diffusion layer thickness is... 

Gonzalez Velasco, J. (2006) On the dependence of the Nernst diffusion layer thickness on potential and sweep... 

Absorption coefficient (cm ) (2) Transfer coefficient Nernst diffusion layer thickness (cm)... 

Nernst diffusion layer thickness 5n and shows why we have to consider a mixed convection-diffusion mass transport mode in this case. 

Note that an illustration of the Nernst diffusion layer thickness, 8n, is shown in Figure 6.9 for a case of nonstationary conditions when current density is constant. 

Here, we can conclude that (1) the Nernst diffusion layer thickness, 5, is a function of time as shown in Figure 7.1, (2) the dependence of the current density from time is given by Equation 7.13 and shown in Figures 7.2 and 7.3, (3) based on Equation 7.13, the diffusion coefficient of the electrolyte, D, can be found if the transport number, L, is known, and (4) from Equation 7.13, the surface concentration, c% can be obtained assuming that t and D are available. 

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