Rotating disk electrode hydrodynamic

Volt mmetiy. 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 Nernst diffusion layer having a thickness dictated by the laws of hydrodynamics is estabUshed. For the RDE,... 

At the rotating-disk electrode (RDE Fig. 4.6), it is the solid electrode and not the liqnid that is driven bnt from a hydrodynamic point of view this difference is nnim-portant. Liquid flows, which in the figure are shown by arrows, are generated in the solution when the electrode is rotated around its vertical axis. The liquid flow impinges on the electrode in the center of the rotating disk, then is diverted by centrifugal forces to the periphery. 

The constancy of the diffusion layer over the entire surface and thus the uniform current-density distribution are important features of rotating-disk electrodes. Electrodes of this kind are called electrodes with uniformly accessible surface. It is seen from the quantitative solution of the hydrodynamic problem (Levich, 1944) that for RDE to a first approximation... 

The most well-known hydrodynamic technique is the Rotating Disk Electrode (RDE) voltammetry, which, however, needs proper equipment. For information on this technique the reader is referred to specialized treatments.2"4 We prefer here to mention a simpler technique which can be carried out on the same equipment used for cyclic voltammetry. This technique is referred to as voltammetry at an... 

A rotating disk electrode (RDE) [7] is used to study electrode reactions, because the mass transfer to and from the electrode can be treated theoretically by hydrodynamics. At the RDE, the solution flows toward the electrode surface as shown in Fig. 5.22, bringing the substances dissolved in it. The current-potential curve at the RDE is S-shaped and has a potential-independent limiting current region, as in Fig. 5.6. The limiting current (A) is expressed by Eq. (5.33), if it is controlled by mass transfer ... 

Figure 3.39 (A) Rotating-disk electrode with hydrodynamic flow pattern. (B) Bottom view of rotating-disk electrode (RDE) and rotating ring-disk electrode (RRDE).

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). 

Hydrodynamic and stirred-solution electrodes. Certain advantages result when the electrode is moved past the solution or vice versa. The increased mass transport increases the current and often increases the sensitivity (although not necessarily the signal-to-noise ratio). In addition, hydrodynamic electrodes such as the rotated platinum electrode and rotated-disk electrode exhibit a current-potential behavior similar to that of the DME. That is, they give the familiar plateau when the current is limited by mass transport to the electrode surface and the current is proportional to the solution concentration of the electroactive species. 

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. 

The objective of the mass transport lab is to explore the effect of controlled hydrodynamics on the rate at which a mass transport controlled electrochemical reaction occurs on a steel electrode in aqueous sodium chloride solution. The experimental results will be compared to those predicted from the Levich equation. The system chosen for this experiment is the cathodic reduction of oxygen at a steel electrode in neutral 0.6 M NaCl solution. The diffusion-limited cathodic current density will be calculated at various rotating disk electrode rotation rates and compared to the cathodic polarization curve generated at the same rotation rate. 

Ef is the formal potential, c0x>buik> cRed,buik> c0x> =o and cRediX=0 are the bulk and surface concentrations of Ox and Red, F is Faraday s constant, R is the gas constant, T is the temperature (K), D0x and DRed are the diffusion coefficients of Ox and Red, and p = 1/2 for semi-infinite linear diffusion in the absence of hydrodynamics, p = 1 for steady-state at small electrodes in the absence of hydrodynamics, and p = 2/3 for steady-state at a rotating disk electrode (see - rotating disk 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. 

Hydrodynamic voltammetry — is a voltammetry technique featuring an electrolyte solution which is forced to flow at a constant speed to the electrode surface. -> mass transport of a redox species enhanced in this way results in higher current. The forced flow can be accomplished either by agitation of the solution (solution stirring, or channel flow), or the electrode (electrode rotation, see -> rotating disk electrode or vibration,... 

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). 

Refs. [i] Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs [ii] Opekar F, Beran P (1976) / Electroanal Chem 69 1 [iii] Pleskov YuV, Filinovski VYu (1976) 7he rotating disk electrode. Consultants Bureau, New York... 

These methods constitute the frame on which any particular method can be elaborated. Yet in practice, the experimental difficulty is that with standard apparatus, 5 /D cannot be varied over an extremely wide range. For example, with the rotating disk electrode (RDE), which is the most convenient steady-state method (with the exception of ultramicroelectrodes [109]), 8 depends on the rotation frequency w of the electrode (see Chapter 2). Yet to maintain correct hydrodynamic conditions w cannot be varied, with... 

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. 

Curve (b) of Figure 4 shows the same silent system as curve (a) but now upon a contracted current scale, while curve (c) shows the effect of ultrasonic irradiation upon curve (b), scanned at the same rate and in the oxidation direction only. Note that curves (b) and (c) are on the same current scale, both taken from ref. 31. Ultrasound has produced a 10-fold increase in maximum current. The plateau shape shows a limiting current at the extreme of oxidation potential reflecting hydrodynamic control independent of the voltammetric sweep rate. (This shape is also seen in other voltammetric procedures, e.g. when using rotating disk electrodes or microelectrodes.) In Figure 4 curve (c) this limiting current is found to be inde-... 

Another system of defined hydrodynamics is the rotating disk electrode [17], and here the limiting-current depends upon the rate of rotation of the disk as shown in Figure 8. Since ultrasound also produces a step-shaped trace to a limiting current it is possible by comparing silent and sonicated traces at a disk electrode to calculate a theoretical rotation speed at which the disk would have to rotate to achieve the same transport limit as is found under ultrasound. 

Consider hydrodynamics in a rotating disk electrode. [15] [24] The governing equations for velocity distributions are ... 

The hydrodynamic flow in convective solutions is difficult to treat theoretically to develop quantitative expressions for expected plateau-current values. An exception is the rotated-disk electrode (RDE). The RDE is a flat disk sealed onto an inert shaft that is rotated with minimum wobble in an otherwise quiet solution. From the hydrodynamics is derived the expression of the limiting plateau current, i ... 

The electrochemical aspects of mass transfer are examined here at the electrode-, or separator- solution interface. In certain cases, such as with rotating disk electrodes, precise hydrodynamic analyses are possible and thus the diffusion equations for these systems can be solved exactly. 

C. H. P. Bruins, D. A. Doombos, and K. Brunt, The Hydrodynamics of the Amperometric Detector Flow Cell with a Rotating Disk Electrode. AnaL Chim. Acta, 140 (1982) 39. 

To carry out theoretical studies of oxidation-reduction reactions, it is often of interest to know how kf. in Equation 2.5-6 is affected by the hydrodynamics of the system. A common method for obtaining a rigorous description of the hydrodynamic flow of stirred solution is based on measurements made with a rotating disk electrode (RDE). such as the one illustrated in Figure 25-21a and b. When Ihe disk electrode is rotated rapidly, the flow pattern shown by the arrows in the figure is set up. At the surface of the disk, the liquid moves out horizontally from the center of the de-% icc, which produces an upward axial flow to replenish Ihe displaced liquid. A rigorous treatment of the hydrodynamics is possible in this case and leads to the I.evich equation ... 

---