Rotating disk electrode convection

The values of that can be realized experimentally vary between 5 X 10 " cm/s (natural convection) and 2 X 10 cm/s (rotating-disk electrode at/= 10,000 rpm). Therefore, reactions for which 10 cm/s will remain reversible whatever the stirring intensity. Such reactions are called completely reversible ( very fast ). Reactions with 10 cm/s will always be irreversible and are called completely irreversible ( very slow ). In the region of intermediate values of the constant, the character of the reaction will depend on stirring conditions. With other values of a and of ratios idfJid,on the boundaries between the various regions of electrode operation will shift slightly, but the overall picture of the phenomena remains the same. 

This value is based on Cu2+ diffusivities calculated Arvia et al. (A5) from limiting-current measurements at a rotating-disk electrode by, with CuS04 concentrations below 0.1 M. In practical applications (e.g., copper refining or electrowinning) higher Cu2+ concentrations are often required, as is also the case in free-convection limiting-current measurements. 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

The homogeneous catalysis method is suitable to measure rate constants over a very wide range, up to the diffusion limit. The lower limit is determined by interferences, such as convection, which occur at very slow scan rates. It is our experience that, unless special precautions are taken, scan rates below lOOmV/s result in significant deviations from a purely diffusion-controlled voltammetric wave. For small values of rate constants (down to 10 s ), other potentiostatic techniques are best suited, such as chronoamperometry at a rotating disk electrode UV dip probe and stopped-flow UV-vis techniques. ... 

The study of rotating disk electrode behavior provides a unique opportunity to develop a model that predicts the effect of diffusion and convection on the current. This is one of the few convective systems that have simple hydrodynamic equations that may be combined with the diffusion model developed herein to produce meaningful results. The effect of diffusion is modeled exactly as it has been done previously. The effect of convection is treated by integrating an approximate velocity equation to determine the extent of convective flow during a given At interval. Matter, then, is simply transferred from volume element to volume element in accord with this result to simulate convection. The whole process repeated results in a steady-state concentration profile and a steady-state representation of the current (the Levich equation). 

Convection terms commonly crop up with the dropping mercury electrode, rotating disk electrodes and in what has become known as hydrodynamic voltammetry, where the electrolyte is made to flow past an electrode in some reproducible way (e.g. the impinging jet, channel and tubular flows, vibrating electrodes, etc). This is discussed in Chap. 13. 

Convective diffusion — The electrochemical - mass transport controlled by both -> convection and - diffusion is called a process by convective diffusion [i]. Convection is caused by externally controlled force or spontaneous force. Convective diffusion has been conventionally used in a strict sense for well-controlled flow such as for -> rotating disk electrodes [ii], - channel elec-... 

Hydrodynamic boundary layer — is the region of fluid flow at or near a solid surface where the shear stresses are significantly different to those observed in bulk. The interaction between fluid and solid results in a retardation of the fluid flow which gives rise to a boundary layer of slower moving material. As the distance from the surface increases the fluid becomes less affected by these forces and the fluid velocity approaches the freestream velocity. The thickness of the boundary layer is commonly defined as the distance from the surface where the velocity is 99% of the freestream velocity. The hydrodynamic boundary layer is significant in electrochemical measurements whether the convection is forced or natural the effect of the size of the boundary layer has been studied using hydrodynamic measurements such as the rotating disk electrode [i] and - flow-cells [ii]. 

Hydrodynamic electrodes — are electrodes where a forced convection ensures a -> steady state -> mass transport to the electrode surface, and a -> finite diffusion (subentry of -> diffusion) regime applies. The most frequently used hydrodynamic electrodes are the -> rotating disk electrode, -> rotating ring disk electrode, -> wall-jet electrode, wall-tube electrode, channel electrode, etc. See also - flow-cells, -> hydrodynamic voltammetry, -> detectors. 

The characteristics of laminar flow can allow mathematical prediction of the solution velocity and this has led to a range of hydrodynamic devices which use forced convection as a transport component under laminar flow conditions, examples include, the -> rotating disk electrode [i],-> wall jet electrode [ii], and channel flow cell (see -> flow cell). 

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. 

Example 2.2 Convective Diffusion Equation The material balance equation near a rotating disk electrode in an electrolyte solution where the migration can be neglected can be written as... 

The classification of models for convective diffusion to a rotating disk electrode may be imderstood in the context of the solution to the steady-state equation (11.3). 

Graphical methods can be used to extract information concerning mass transfer if the data are collected under well-controlled hydrodynamic conditions. The systems described in Chapter 11 that are imiformly accessible with respect to convective diffusion would be appropriate. The analysis would apply to data collected on a rotating disk electrode as a function of disk rotation speed, or an impinging jet as a function of jet velocity. 

A Nemst stagnant-diffusion-layer model was used to accovmt for the diffusion impedance. This model is often used to account for mass transfer in convective systems, even though it is well known that this model caimot ac-coimt accurately for the convective diffusion associated with a rotating disk electrode. 

A refined process model was used that correctly accoimts for convective diffusion to a rotating disk electrode imder the assumption that the surface is uniformly accessible. This model also employs a constant-phase element to address complexities seen at high frequency. ... 

Figure 20.11 Normalized residual errors for the fit of the convective-diffusion models presented in Figure 20.12 to impedance data obtained for reduction of ferricyanide on a Pt rotating disk electrode a) real and b) imaginary.

The three-term convective-diffusion model provides the most accurate solution to the one-dimensional convective-diffusion equation for a rotating disk electrode. The one-dimensional convective-diffusion equation applies strictly, however, to the mass-transfer-limited plateau where the concentration of the mass-transfer-limiting species at the surface can be assumed to be both uniform and equal to zero. As described elsewhere, the concentration of reacting species is not uniform along the disk surface for currents below the mass-transfer-limited current, and the resulting nonuniform convective transport to the disk influences the impedance response. ... 

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