The Nemst diffusion layer

Examples of such irreversible species (12) include hydroxjiamine, hydroxide, and perchlorate. The electrochemistries of dichromate and thiosulfate are also irreversible. The presence of any of these agents may compromise an analysis by generating currents in excess of the analytically usehil values. This problem can be avoided if the chemical reaction is slow enough, or if the electrode can be rotated fast enough so that the reaction does not occur within the Nemst diffusion layer and therefore does not influence the current. 

From Fig. 2.1a, it can be observed that the Nemst diffusion layer, defined by the abscissa at which the concentration reaches the value r0 in the linear concentration profile, is independent of the potential in all the cases in spite of their having been obtained under transient conditions. This is in agreement with Eqs. (2.20) and... 

FromEq. (2.111), it can be deduced that the Nemst diffusion layer for a DME is... 

From these curves it can be seen that the Nemst diffusion layer, ffG, increases with time in all cases. Moreover, Fig. 2.20a shows how these curves are all coincident at short times and only small differences appear between the couples bands and cylinders and spheres and discs at times longer than 0.2 s. This indicates that for this electrode size and time below 0.2 s, the prevalent diffusion field is planar, so the electrode geometry becomes irrelevant. As the electrode size decreases (Fig. 2.20b and c), so does the temporal dependence of < , and the different curves begin to separate until they reach a steady state in the case of discs and spheres, or a pseudo-steady state in the case of bands and cylinders (Fig. 2.20c). Note that the ratio between the diffusion layers corresponding to small discs and spheres <5d clcro and <5(p[ )cro tends to the value ji/A (see also Sect. 2.7). 

Another example for the HMRRD electrode is given in Fig. 9 for Fe in alkaline solutions [12, 27]. The square wave modulation of the rotation frequency co causes the simultaneous oscillation of the analytical ring currents. They are caused by species of the bulk solution. Additional spikes refer to corrosion products dissolved at the Fe disc. This is a consequence of the change of the Nemst diffusion layer due to the changes of co. This pumping effect leads to transient analytical ring currents. Besides qualitative information, also quantitative information on soluble corrosion products may be obtained. The size of the spikes is proportional to the dissolution rate at the disc, as has been shown by a close relation of experimental results and calculations [28-30]. As seen in Fig. 7, soluble Fe(II) species are formed in the po-... 

An enlarged view of the two velocity components near the electrode surface is shown in Fig. 16D, for the same numerical parameters. The physical meaning of the Nemst diffusion layer becomes clear in this form of presentation. Thus, the perpendicular velocity component inside the Nemst diffusion layer is very small, not exceeding 2% of its value far away from the surface. This is the justification for the assumption that inside this diffusion layer the solution is practically stagnant, even though the solution as a whole is well stirred by rotating the electrode. 

Now consider the path of a chemical species formed at the rim of the disc electrode as it travels toward the inner edge of the ring electrode. There are two transport processes involved convective flow at a velocity v and diffusion. The species must diffuse a certain distance z into the solution, be transported across the gap at a velocity v, and diffuse back to the surface. The radial velocity at a distance of 10 pm from the surface (i.e., just outside the Nemst diffusion layer) is 3 cm/s. The time taken to cross the gap, which is... 

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... 

Plots of the dimensionless concentration C/Cf as a function of distance at different times are shown in Fig. IIK The gradual development of the Nemst diffusion layer with time can be clearly seen. The concentration profile near the surface is linear, but a deviation from linearity is observed farther away, as the concentration approaches its bulk value. 

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. 

In typical electrochemical measurements, the Nemst diffusion layer... 

How serious are these assumptions The concentration of the electroactive species in the Nemst diffusion layer can vary from zero (at... 

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. 

The current at any point in the voltammetry experiment described in Figure 23-5 is determined by a combination of (1) the rate of mass transport of A to the edge of the Nemst diffusion layer by convection and (2) the rate of transport of A from the outer edge of the diffusion layer to the electrode surface. Because the product of the electrolysis P diffuses away from the surface and i.s ultimately swept away by convection, a continuous current is required to maintain the surface concentrations demanded by the Nernst equation. Convection, however, maintains a constant supply of A at the outer edge of the diffusion layer. Thus, a steady-state cuirent results that is determined by the applied potential. 

We consider here a situation where the mass transport of the electroactive species may become rate determining, but all other processes which control the current-potential characteristics can still adjust rapidly. Thus, the concentration of the electroactive species, c, becomes time dependent. Since we allow only for diffusion, its temporal evolution is given by Pick s second law [i.e., in the case of a planar electrode, by dc/dt = D (d c/dz with the diffusion coefficient D, and z the spatial coordinate perpendicular to the electrode]. At the electrode (z = WE), the concentration obeys Pick s fust law, (dc/dz) z=we = Kuc i F). At a certain distance from the electrode, it is assumed that the concentration is at a constant value, c, its bulk value (constituting the second boundary condition). The concept of the Nemst diffusion layer underlies this idea. 

In the absence of the following reaction, we think of the concentration profile for R as decreasing linearly from a value Cr(x — 0) at the surface to the point where Cr = 0 at 5, the outer boundary of the Nemst diffusion layer. The coupled reaction adds a channel for disappearance of R, so the R profile in the presence of the reaction does not extend as far into the solution as 5. Thus, the added reaction steepens the profile and augments mass transfer away from the electrode surface. For steady-state behavior, such as at a rotating disk, we assume the rate at which R disappears from the surface to be the rate of diffusion in the absence of the reaction [(mRCR(x = 0) see (1.4.8)] plus an increment proportional to the rate of reaction [/jikCj (x = 0)]. Since the rate of formation of R, given by (1.4.6), equals its total rate of disappearance, we have... 

The scan rate, u = IdE/dtl, plays a very important role in sweep voltammetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for normal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diffusion and the peak-shaped response. When the scan rate is slow enough to maintain steady-state diffusion, the concentration profiles with time are linear within the Nemst diffusion layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diffusion layer cannot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

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