Layers Nernst

Diffusion overpotential. When high current densities j exist at electrodes (at the boundary to the electrolyte), an impoverishment of the reacting substances is possible. In this case the reaction kinetics are determined only by diffusion processes through this zone, the so-called Nernst layer. Without dealing with the derivation in detail, the following formula is obtained for the diffusion overpotential that occurs (with as the maximum current density) ... 

Fig. 2.21 Prandtl and Nernst layer formation at the boundary between a solid plate and flowing liquid (c = 0)... 

The steady-state distribution of the concentration of the diffusing substance at the phase boundary is termed the Nernst layer.f For the material flux (cf. Eq. 2.5.18) we have... 

In a stagnant solution, free convection usually sets in as a density gradient develops at the electrode upon passing current. The resulting convective velocity, which is zero at the wall, enhances the transfer of ions toward the electrode. At a fixed applied current, the concentration difference between bulk and interface is reduced. For a given concentration difference, the concentration gradient of the reacting species at the electrode becomes steeper (equivalent to a decrease of the Nernst layer thickness), and the current is thereby increased. 

If instead of semi-infinite diffusion, some distance (5m acts as an effective diffusion layer thickness (Nernst layer approximation), then a modified expression of equation (63) applies where ro is substituted by 1 / (1 /Vo + 1 /<5m ) (see equation (38) above). For some hydrodynamic regimes, which for simplicity, are not dealt with here, the diffusion coefficient might need to be powered to some exponent [57,58],... 

Conversely, after the voltage is switched, Tl" ions will be oxidized to according to the reaction, Tl Tl + + 2e . Very soon, the electrode will be surrounded with a layer of solution that contains no Tl. It is said then to be depleted of T1+. The volume around the electrode, which now contains no Tl" ", is called the depletion region, the depletion layer or sometimes, the Nernst layer. Its thickness is often given the symbol 5. As the length of time increases following the potential being stepped, i.e. as the extent of electrolysis increases, so the thickness of the Nernst layer (5) increases. 

Nernst layer (Nernst depletion layer) (see Depletion region)... 

As follows from the hydrodynamic properties of systems involving phase boundaries (see e.g. [86a], chapter 2), the hydrodynamic, Prandtl or stagnant layer is formed during liquid movement along a boundary with a solid phase, i.e. also at the surface of an ISE with a solid or plastic membrane. The liquid velocity rapidly decreases in this layer as a result of viscosity forces. Very close to the interface, the liquid velocity decreases to such an extent that the material is virtually transported by diffusion alone in the Nernst layer (see fig. 4.13). It follows from the theory of diffusion transport toward a plane with characteristic length /, along which a liquid flows at velocity Vo, that the Nernst layer thickness, 5, is given approximately by the expression,... 

The solution to the time dependent Eq. (3-1) was derived by use of the method of Moments with the main assumption of the existence of a time dependent Nernst layer. 

Fig. 6-11. Scheme of the modified electrode (polymer film thickness 0) in contact with a solution containing a redox substrate. <5 is the Nernst layer thickness defined for a rotating disc electrode. From [85]. 

We think this example suffices to show that the use of neutral electrolyte solutions based on dipolar aprotic solvents may raise a lot of difficult questions with respect to both macroscopic and local, microscopic acidity or basicity. Adequate control experiments should be carried out, as correctly urged by Mayeda and Miller (1972), but these are not always easy to design. How difficult the problem can be is best shown by the fact that it was possible to effect transacetalization of benzaldehyde diethyl acetal in alkaline methanol solution by oxidizing hydrogen in the solution at a platinum anode (Schafer, 1974). In this experiment protons liberated at the anode must act catalytically in the inner part of the Nernst layer. 

Nernst layer -> Diffusion of electroactive species from the bulk solution to the -> electrode surface, or vice versa, takes place in a thin layer of stagnant solution close to the electrode/solution interface when the concentration of electroactive species at this interface, q (x = 0), deviates from the bulk concentration c (see Figure). The concentration gradient at the electrode/solution interface drives the diffusion flux of electroactive species. Generally, there is a linear concentration profile close to the electrode surface and at longer distances from the electrode surface the concentration asymptotically approaches the bulk concentration. The Nernst layer is ob-... 

The thickness of the Nernst layer increases with the square root of time until natural - convection sets in, after which it remains constant. In the presence of forced convection (stirring, electrode rotation) (see also Prandtl boundary layer), the Nernst-layer thickness depends on the degree of convection that can be controlled e.g., by controlling the rotation speed of a -> rotating disk electrode. See also - diffusion layer. See also Fick s law. 

Every solid catalyst in solution is surrounded by a "stagnant diffusion layer which reactants must cross in order to reach the surface. The resulting concentration profile is sketched in Fig. 6. The rate of the reactant s arrival at the solid/liquid interface is determined by its concentration gradient at that interface, (dc/dx)x=0. The diffusion layer therefore has the same effect on the rate as does the simplified layer shown by the dotted lines [63]. The thickness of this so-called Nernst layer is designated 5. It follows from Fick s first law of diffusion that the number of moles of reactant A, nA, that reach the surface in unit time is given by... 

The thicknesses of the Nernst layers are not necessarily the same for each solute, as will be made clear presently. 

Early workers in the field used paddle stirrers and similar devices to vary the Nernst layer thickness. Their results could be expressed by empirical relationships of the type... 

Further increase in anode potential gets into limiting current plateau range (El in Fig. 10.6). In this region, the potential is so high that the electrochemical reaction is faster than mass transport that is, Cu ions produced on the anode surface in a unit time are more than those that mass transport can remove from the anode surface into the bulk solution. As a result, a Cu ion concentrated layer is developed inside the Prandtl boundary layer [4]. The concentrated Cu layer is called Nernst layer or diffusion layer, which has a thickness of [13]... 

---