Analytical solution rotating disc electrode

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

Convection That form of mass transport in which the solution containing electroanalyte is moved natural convection occurs predominantly by heating of solution, while forced convection occurs by careful and deliberate movement of the solution, e.g. at a rotated disc electrode or by the controlled flow of analyte solution over a channel electrode. 

A rotating disc electrode (RDE) is a conductive disc of the material of interest embedded in an inert non-conductive polymer or resin that can be attached to an electric motor which has very fine control of the electrode s rotation rate. During the experiment, the electrode rotates in the solution under study, thus inducing a flux of redox analyte to the electrode [75]. 

Velocity (v) — is a vector measure of the rate of change of the position of a point with respect to time. For cartesian space the velocity of a point (x) can be written as v = dx/dt and has units of m s-1 using the SI system. In polar coordinates a two-dimensional velocity can be represented by an angular velocity (to) and the distance to the origin (r), v = cor. Velocity is found widely within electrochemical analysis, for example, within hydrodynamic devices such as the rotating disc electrode where the solution velocity may often be approximated analytically [i, ii], permitting, via further analysis, cur-rent/voltage characteristics to be calculated. 

The diffusion layer widtli is very much dependent on tire degree of agitation of tire electrolyte. Thus, via tire parameter 5, tire hydrodynamics of tire solution can be considered. Experimentally, defined hydrodynamic conditions are achieved by a rotating cylinder, disc or ring-disc electrodes, for which analytical solutions for tire diffusion equation are available [37, 4T, 42 and 43]. 

Movement of solution away from the disc in this way would cause a vacuum to form at the disc centre, and so more solution is drawn in, from the solution bulk towards the electrode face. In effect, the rotation of the disc induces a sort of pump action, with solution continually being drawn from the bulk, travelling toward the surface of the disc electrode, over the disc and hence back into the solution bulk. It is this pump action that we follow as the flux of analyte solution at the RDE. 

At heart, this titration method can be summarized as following the concentration of a reagent as a function of time Analyses with the RRDE are identical in concept. Analyte is formed at the central disc electrode, and because the disc rotates, such analyte is swept outward, past the ring electrode, and hence returned to the bulk solution. However, because the... 

The rotating ring—disc electrode (RRDE) is probably the most well-known and widely used double electrode. It was invented by Frumkin and Nekrasov [26] in 1959. The ring is concentric with the disc with an insulating gap between them. An approximate solution for the steady-state collection efficiency N0 was derived by Ivanov and Levich [27]. An exact analytical solution, making the assumption that radial diffusion can be neglected with respect to radial convection, was obtained by Albery and Bruckenstein [28, 29]. We follow a similar, but simplified, argument below. 

Rotated electrodes are used for studies of the character of electrode reactions and their kinetics and for the estimation of electroanalytical parameters. Convection provides a constant mass transport of the analyte to the electrode surface with changed diffusion characteristics compared to quiescent liquids. The effect is similar to a stirring of the solution, but the rotation of an electrode can be controlled much more precisely than of a solution. Rotating ring-disc electrodes are practically used only for elucidating electrochemical reaction mechanisms where oxidation or reduction on the disc creates (collection experiment) or consumes (shielding experiment) electroactive substances which are monitored with the ring electrode. 

Another example for the HMRRD electrode is given in Fig. 9 for Fe in alkaline solutions [12, 27]. The square wave modulation of the rotation frequency co causes the simultaneous oscillation of the analytical ring currents. They are caused by species of the bulk solution. Additional spikes refer to corrosion products dissolved at the Fe disc. This is a consequence of the change of the Nemst diffusion layer due to the changes of co. This pumping effect leads to transient analytical ring currents. Besides qualitative information, also quantitative information on soluble corrosion products may be obtained. The size of the spikes is proportional to the dissolution rate at the disc, as has been shown by a close relation of experimental results and calculations [28-30]. As seen in Fig. 7, soluble Fe(II) species are formed in the po-... 

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