Nemst thickness

The diffusion flux J, in mol/cm, is proportional to the concentration gradient and inversely proportional to the diffusion layer s effective thickness 5 (also called the Nemst thickness). The proportionality constant D is the diffusion constant hence,... 

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 ... 

Well-defined hydrodynamic conditions, with high rate of mass transport, are essential for successful use of electrochemical detectors. Based on the Nemst approximate approach, the thickness of the diffusion layer (<5) is empirically related to the solution flow rate (U) via... 

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. ... 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

The plots shown in Figure 6.3 show the variations of the concentrations of both reduced and oxidized forms ofTl (of reactant Tt in Figure 6.3(a) and product Tl in Figure 6.3(b)). Each concentration is depicted as a function of the distance from the electrode solution interface where oxidation is effected these curved traces are often termed concentration profiles. Each of the figures incorporate a series of concentration profiles, drawn as a function of time, to show how the Nemst layer increases in thickness during electrolysis, because the extent of electromodification has increased with time. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

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

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,... 

Fig. 6.24 Dependence of Nemst response of the thickness of the hydrated layer (adapted from Sandifer, 1998)...

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... 

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]...

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

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. 

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