Nernst model

According to the Nernst model, the concentration gradient at the electrode is given by... 

FIGURE 6 Nernst diffusion-layer model. The solid line represents the actual concentration profile, and the dashed line for c0 the Nernst model concentration profile. 

In hydrodynamic systems Planar diffusion to a uniformly accessible electrode, e.g. for rotating disk electrodes (hypothetical Nernst model with S = diffusion layer thickness)... 

This can be illustrated in the example of a mechanical stirring device (forced convection) when used for homogenising the liquid electrolyte, mainly away from the zones that are next to the interfaces. The same case applies to analytical chemistry when a rotating disc electrode is involved or when a system is installed in industrial electrolysers in order to force the circulation of the electrolyte. By following a simplified model called the Nernst model one can define the thickness of the diffusion layer (often denoted by 5)... 

Section 4.3.1.4 describes in more detail the results produced by the Nernst model, which uses hydrodynamic calculations as laid out by Levk h. 

Figure 2.3 - Distribution of the conduction modes in an eiectroiyte when submitted to forced convection, according to the Nernst model...

Figure 4.20 in section 4.3.1.4 illustrates the differences between the actual concentration proFiles and those obtained when using the Nernst model. 

A steady state with a non-zero current is reached very quickly in these forced convection conditions. The interfacial slope is identical to that in the Nernst model as shown in figure 4.20. The Nernst layer thickness is lower than that of the diffusion layer since, at that distance from the electrode, the actual profile still has a significant slope with a relative concentration difference of 11% with respect to the initial concentration. The diffusion layer thickness is equal to 1.5 for a target accuracy of 1% and to 1.8 NERNsyfor a target accuracy of 0.1%. 

In this section we will first look at dihydrogen production in an acidic aqueous solution, whereby argon is continuously bubbled inside. Here, assuming unidirectional geometry, the steady states are described by the Nernst model due to convection, the composition remains homogeneous throughout the bulk of the electrolyte, i.e., in the area beyond the thickness layer <5. This composition is identical to the initial composition the pH is... 

The concept of forced convection is introduced here in simple terms. The steady state that emerges is defined by using the Nernst model (see section 4.3.1.4), and the corresponding concentration profiles are shown in figure A.27. 

Chronopotentiometry with diffusion-convection according to the Nernst model 311 Chronoamperometry with steady-state unidirectional diffusion. 312... 

In reality, as one moves away from the interface towards the bulk solution, the contribution of convection to transport increases while that of diffusion decreases. Rather than treating simultaneously transport by diffusion and convection, the Nernst model makes a clear separation between the two transport mechanisms a total absence of convection inside the Nernst diffusion layer (y < S), and an absence of diffusion outside the Nernst diffusion layer (y > S). The intensity of convection affects the flux at the electrode by fixing the thickness of the Nernst diffusion layer. For the remainder of this book, the Nernst diffusion layer will simply be called the diffusion layer. 

According to the Levich equation (4.105) the limiting current density for a rotating disk electrode is proportional to Cg. On the other hand, the Nernst model (equation 4.81) indicates that the limiting current is proportional to the product Cb Db- By combining these two equations we find that 5has a Db dependence. This result reveals the artificial character of the Nernst diffusion layer model. Every dissolved species that reacts in an electrochemical system has its own speeifie Nernst diffusion layer. 

Fig.l Diagram of the Nernst Boundary Layer (cone, of reacting species vs. distance from the electrode) 1. Nernst model concentration profile, 2. true concentration profile, 6 = Nernst diffusion layer, 6 = true diffusion layer... 

Despite the fact that the Nernst model is rather rough, it has been used in electrochemical kinetics up till now due to its simplicity and obviousness. It has been established by means of different methods that similar structures actually form in the conditions of natural convection. Their thickness makes up 0.01-0.03 cm however, it is rather difficult to strictly define because it depends on various factors, including the current density i. The empirical regularity const has been established experimentally under the steady-state conditions [1]. It should be mentioned that varies with the potential sweep rate v when a linear variation... 

Both the semi-infinite diffusion and Nernst s steady diffusion layer concept produce the same results when the diffusion front shift is not yet large as compared to In these conditions, the semi-infinite diffusion model, which is simpler from the mathematical point of view, is to be applied. However, the Nernst model is more general because the regularities of the first model follow from it at 5j.j oo. 

Though in the general case, mathematical expressions of the Nernst model are more complicated than of those semi-infinite diffusion, stationary mass transport is described by a rather simple Eq. (3.12). In this connection, there occurs an interesting possibility to use superposition of both models, which is convenient to apply when i is the periodic time function. Perturbation signals of this type are considered in the theory of electrochemical impedance spectroscopy. In this case, i(t)... 

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