Rotating disk electrode steady-state

Valdes, J. and B. Miller (1988). Thermal modulation of rotating disk electrodes steady-state response. The Journal of Physical Chemistry 92(1), 525-532. 

Fig. 3. Steady state concentration profiles of catalyst and substrate species in the film and diffusion layer for for various cases of redox catalysis at polymer-modified electrodes. Explanation of layers see bottom case (S + E) f film d diffusion layer b bulk solution i, limiting current at the rotating disk electrode other symbols have the same meaning as in Fig. 2 (from ref.

Electrode processes are often studied under steady-state conditions, for example at a rotating disk electrode or at a ultramicroelectrode. Polarog-raphy with dropping electrode where average currents during the droptime are often measured shows similar features as steady-state methods. The distribution of the concentrations of the oxidized and reduced forms at the surface of the electrode under steady-state conditions is shown in Fig. 5.12. For the current density we have (cf. Eq. (2.7.13))... 

Fig. 9. Logarithmic plot of apparent limiting-current density as a function of current increase rate at a rotating-disk electrode i — apparent limiting current density i, = true steady-state limiting current density di/dt = current increase rate (A cm-2 sec-1) (u = rotation rate (rad sec-1). [From Selman and Tobias (S10).]...

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). 

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 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. 

Fig. 18. Steady-state log j-E curves for H202 reduction and oxidation at a LaNi03 (1.2m2g 1) rotating disk electrode in 0.1 M KOH at 25°C after correction for mass transport in solution. H202 concentration = ImM [48],...

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... 

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). 

Another means of determining D, provided n is known, relies on the use of the rotating disk electrode (RDE). Based on the pioneering work of Levich [39], the steady state diffusion limiting current, measured at an RDE is given by ... 

For a rotating disk electrode, the treatment of steady-state, mass-transfer-controlled electrode reactions applies, where the mass-transfer coefficient is mo = 0.61Dq Here, Dq is the dif-... 

Sometimes one is interested only in the steady-state solution (e.g., with rotating disk electrodes or ultramicroelectrodes). Since dColdt = 0 in such a situation, the diffusion equation simply becomes... 

Although a major advantage of rotating disk electrode techniques, compared to stationary electrode methods, is the ability to make measurements at steady state without the need to consider the time of electrolysis, the observation of current transients at the disk or ring following a potential step can sometimes be of use in understanding an electrochemical system. For example the adsorption of a component. 

A number of experimental electrochemical methods are available. These include voltammetry under transient conditions (e.g. cyclic voltammetry) or under steady state conditions (e.g. rotating disk electrode), and spectroelectrochemistry (e.g. using UV-Vis spectroscopy to monitor an electrochemical process). We focus here on cyclic voltammetry. It is a readily available technique and information that can be gained includes ... 

Impedance may also be studied in the case of forced diffusion. The most important example of such a technique is a rotating disk electrode (RDE). In a RDE conditions a steady state is obtained and the observed current is time independent, leading to the Levich equation [17]. The general diffusion-convection equation written in cylindrical coordinates y, r, and q> is [17]... 

Figure 4.4.12. Steady state polarization curves for iron in NaS04-H2S04 solutions according to Keddam et al. [1981] (a) Simulated curves, b) Experimental data. Rotating disk electrode (rotating speed = 1600rpm, diameter = 3 mm), T = 25 0.2°C. (From M. Keddam, O. R. Mattos, and H. J. Takenouti, Reaction Model for Iron Dissolution Studied by Electrode Impedance Determination of the Reaction Model, J. Electrochem. Soc., 128, 257-274, [1981]. Reprinted by permission of the publisher. The Electrochemical Society, Inc.)...

To estimate ko or Xo quantitatively we must resort to an electrochemical technique that operates under steady-state conditions and for which the diffusion layer thickness is well-defined and quantifiable. The technique of choice is the rotating disk electrode (RDE) method. " Both of the aforementioned criteria are valid for the RDE. The solution hydrodynamics are well-defined, and the diffusion layer thickness can be estimated quantitatively in terms of the rotation speed... 

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