Electrode surfaces diffusion-convection layer

This section and the next are dedicated to the basics of the silicon-electrolyte contact with focus on the electrolyte side of the junction and the electrochemical reactions accompanying charge transfer. The current across a semiconductor-electrolyte junction may be limited by the mass transport in the electrolyte, by the kinetics of the chemical reaction at the interface, or by the charge supply from the electrode. The mass transport in the bulk of the electrolyte again depends on convection as well as diffusion. In a thin electrolyte layer of about a micrometer close to the electrode surface, diffusion becomes dominant The stoichiometry of the basic reactions at the silicon electrode will be presented first, followed by a detailed discussion of the reaction pathways as shown in Figs. 4.1-4.4. 

First, the different components of the bulk solution must be brought up to the electrode surface by the processes summarized under the heading mass transfer. Convection (movement of the solution relative to the electrode) takes molecules and ions to the boundary of the Nemst layer (Section 2), through which diffusion takes them up to the electrode surface. Diffusion occurs due to the... 

Diffusion—Convection Layer Near the Electrode Surface 173... 

The central part of the RDE theory and technique is the convection of electrolyte solution. Due to the solution convection, the reactant in the solution will move together with the convection at the same transport rate. Let s first consider the situation where the flow of electrolyte solution from the bottom of the electrode edge upward with a direction parallel to the electrode surface to see how the diffusion— convection layer can be formed and what is its mathematic expression. 

We assume that the concentration distribution within the diffusion—convection layer can be treated in the similar way to that described in Chapter 2, and then the concentration distribution of the oxidant near the electrode surface can be schematically expressed in Figure 5.2. Thus, the diffusion—convection current density (ioc.o) can be expressed in a similar form to those Eqns (2.57) and (2.58) ... 

In order to get the current—potential relationship on the RDE, particularly the expression of limiting current density as the function of the electrode rotating rate and the reactant concentration, Pick s second law has to be used to give the equations of reactant concentration change with time at the steady-state situation of diffusion—convection. When the surface concentration of oxidant reaches zero during the reaction at the steady-state situation, the concentration distribution within the diffusion—convection layer is not changing with time anymore, meaning that the diffusion rate is... 

It can be seen that this thickness of the diffusion—convection layer is not a function of the location on the electrode surface, which is different from that of Eqn (5.1), and therefore, the current density over the entire RDE surface is uniformly distributed. 

As we discussed above, the RDE theory is based on the convection kinetics of the electrolyte solution. If the electrode rotating rate is too small, meaning that the solution flow rate is too slow, it will be difficult to establish the meaningful diffusion-convection layer near the electrode surface. In order to make meaningful measurement, there is a rough formula that can be used to obtain the limit of electrode rotating rate (wiow) ... 

Mass transport phenomena taking place before or after charge transfer determine the concentration of the reactants and products at the electrode surface. The electrolyte layer contiguous to the surface, in which the concentration of the reactants or products differs from that in the bulk electrolyte is called the diffusion layer. The thickness of the diffusion layer depends on the prevailing convection conditions and is typically between 1 and 100 /tm. This is much more than that of the electric double layer, which is typically on the order of 0.2-10 nm only. 

Departing from the bulk solution towards the electrode surface, natural convection dies away due to the rigidity of the electrode surface and frictional forces, this is the diffusion layer, and since only concentration changes occur in this zone, dififu-sional transport is in operation. Note that in reality there is no real defined zones and these merge into one another, but it is a useful concept. Under experimental conditions, the diffusion layer is in the order of tens to hundreds of micrometers in size. 

Diffusion Layer the thin layer of solution adjacent to an electrode through which transport of species to or from the electrode surface occurs by diffusion rather than by convection. 

Convective diffusion to a growing sphere. In the polarographic method (see Section 5.5) a dropping mercury electrode is most often used. Transport to this electrode has the character of convective diffusion, which, however, does not proceed under steady-state conditions. Convection results from growth of the electrode, producing radial motion of the solution towards the electrode surface. It will be assumed that the thickness of the diffusion layer formed around the spherical surface is much smaller than the radius of the sphere (the drop is approximated as an ideal spherical surface). The spherical surface can then be replaced by a planar surface... 

During an electrode reaction in an unstirred solution, the thickness of the diffusion layer grows with time up to a limiting value of about 10- 4 m, beyond which, because of the Brownian motion, the charges become uniformely distributed. At ambient temperature the diffusion layer reaches such a limiting value in about 10 s. This implies that in an electrochemical experiment, the variation of concentration of a species close to the electrode surface can be attributed to diffusion only for about 10 s, then convection takes place. 

Convection (of the electrolyte liquid phase as a whole) can be natural (due to thermal effects or density gradients) or forced (principal mass transport mode in hydrodynamic techniques). Still, however, close to the electrode surface a diffusion layer develops. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

The two major causes of uneven current distribution are diffusion and ohmic resistance. Nonuniformity due to diffusion originates from variations in the effective thickness of the diffusion layer 8 over the electrode surface as shown in Figure 10.13. It is seen that 8 is larger at recesses than at peaks. Thus, if the mass-transport process controls the rate of deposition, the current density at peaks ip is larger than that at recesses since the rate of mass transport by convective diffusion is given by... 

Marken el al. concluded that microwave activation of electrochemical processes enables an increase in temperature at the electrode surface, a thermal gradient and a hot spot zone within the diffusion layer to be achieved and a convective flow to be induced146. 

Disc electrodes are commonly used in voltammetry as stationary and as rotating electrodes. The diffusion of electroactive species towards the surface of these electrodes is linear, as shown in Fig. 1.6a. The advantage of the second configuration is that rotation of the electrode causes convection in solution that compensates for the increase of the diffusion layer thickness with time after a period of about 200 ms. This results in a limiting current instead of a peak-shaped current (see also section 3.2) according to the Levich equation3 ... 

Note that the concept of transport tayer can be extended to other transport modes such as convection. Indeed, in the presence of convection, this concept is associated with the simpie idea that the solution can be divided into two parts, a thin layer close to the electrode surface with only diffusion, on the one hand, and the bulk solution where the stirring ensures a perfect mixing, and therefore uniform concentration, on the other [52]. 

Because the kinetic and mass-transport phenomena occur in a thin region adjacent to the electrode surface, this area is treated separately from the bulk solution region. Since kinetic effects are manifested within 100 A of the electrode surface, the resulting overpotential is invariably incorporated in the boundary conditions of the problem. Mass transport in the boundary layer is often treated by a separate solution of the convective diffusion equation in this region. Continuity of the current can then be imposed as a matching condition between the boundary layer solution and the solution in the bulk electrolyte. Frequently, Laplace s equation can be used to describe the potential distribution in the bulk electrolyte and provide the basis for determining the current distribution in the bulk electrolyte. 

Similar processes for producing conducting polymeric films of benzene and its derivatives had been studied earlier [2-4], Necessary conditions for the successful realization of these processes are the use of a platinum electrode and a polar solvent in the presence of catalysts (Lewis acids) and thermostatting of the reactor at -75°C. A poly(para)phenylene polymerizate of the linear structure H-(-C6FLr)n-H with the degree of polymerization n, which varies between 3 and 16, is formed. Forced convection of monomeric molecules facilitates the polymerization reaction in the diffusion layer near the electrode and the formation of a dense film on the electrode surface and prevents the formation of poly(para)phenylene in the bulk. 

Transport to the electrode surface as described in Chapter 5 assumes that this occurs solely and always by diffusion. In hydrodynamic systems, forced convection increases the flux of species that reach a point corresponding to the thickness of the diffusion layer from the electrode. The mass transfer coefficient kd describes the rate of diffusion within the diffusion layer and kc and ka are the rate constants of the electrode reaction for reduction and oxidation respectively. Thus for the simple electrode reaction O + ne-— R, without complications from adsorption,... 

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