Double hydrodynamic electrodes

For a totally irreversible process, with significant overpotential, 

Double hydrodynamic electrodes have two working electrodes, the second (detector) placed following, i.e. downstream of, the first (gener- 

The most simple reaction scheme, in which all products are stable, is 

C can be equal to A. The fraction of B which reaches the detector electrode is always less than unity because a part, after diffusing from the electrode to distance 5, is transported by convection to bulk solution and does not reach the detector electrode. The fraction of B reaching the detector electrode under these conditions is called the steady-state collection efficiency, N0. 

Experimentally, the generator electrode current, /gen, is controlled (galvanostatic control), usually being slowly increased from zero in an anodic or cathodic direction depending on the electrode reaction, and the detector electrode is held at a potential such that all the B reaching it is converted into C, i.e. a potential in the limiting current region for B and C, and passes current /det. 

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Other more complex mechanistic schemes are studied by a variety of techniques. Double hydrodynamic electrodes are particularly useful for investigating schemes involving two electron transfer steps, such as ECE and DISP schemes. Some of the applications of the different electrochemical techniques in the elucidation of these reactions are described in the following chapters. 

A bipotentiostat controls the potential of two working electrodes independently, and measures the current that they pass. A typical circuit is shown in Fig. 7.8. Bipotentiostats are necessary in performing studies with double hydrodynamic electrodes (Sections 8.5-8.7). 

Fig. 7.10. Circuit for measuring collection efficiencies at double hydrodynamic electrodes. All resistances are equal except Rlt R2, and Rr, which are variable.

Figures 8.3, 8.4, 8.5, and 8.6 show typical designs of double hydrodynamic electrodes (two working electrodes)—rotating, wall-jet, tube, and channel. Using only one of the two working electrodes one obtains /L as in Table 8.1. Use of the two electrodes simultaneously is described in Sections 8.5-8.8.

Table 8.3. Values of a and / for some double hydrodynamic electrodes...

Fig. 8.11. Diffusion layer titration curve at a double hydrodynamic electrode (second order homogeneous reaction), (a) /det begins to rise when excess of B that did not react homogeneously reaches the detector electrode and A// /det = G(l/ar). (b) Assuming fast kinetics this is where linearity commences. From here...

In this last case the use of a double hydrodynamic electrode, generating R on the upstream electrode and detecting it on the downstream electrode, may be easier and more sensitive. The rotating disc electrode has also been used with success to distinguish similar mechanisms with coupled homogeneous reactions (ECE, DISP1, and DISP2)5. 

Applications of double hydrodynamic electrodes are particularly interesting because the change of phase in the current measured at the downstream electrode permits discrimination between the electron flow and the flux of electroactive species produced at the upstream electrode34. 

Amperometric titrations with double hydrodynamic electrodes... 

Titrations of non-electroactive compounds can be carried out by homogeneous reaction with titrants electrogenerated in situ. This can be done using double hydrodynamic electrodes in the diffusion layer microtitration technique described in Section 8.7. 

There are other equivalent ways of solving eqn. (17) for example, by double integration [3]. However, as will be shown in following sections, the approach outlined above is particularly valuable as it may be applied directly to other hydrodynamic electrodes. 

Figure 14.7 shows the technique of anodic stripping voltammetry with collection at a double hydrodynamic electrode30. The fact that it is possible to control the potentials of generator and detector electrodes independently is used to increase sensitivity. This procedure has been used with success at rotating and wall-jet electrodes4,27... 

The DigiSim program enables the user to simulate cyclic voltanunetric responses for most of the common electrode geometries (planar, full and hemispherical, and full and hemicylindrical) and modes of diffusion (semiinfinite, finite and hydrodynamic diffusion), with or without inclusion of IR drop and double-layer charging. 

Fig. 10.4. Equivalent circuit for the electrode with hydrodynamic modulation R. denotes the solution resistance, C0/. the double layer capacitance, RF the faradaic resistance and Z the impedance contributed by diffusional transport of the reactants to the surface. Hydrodynamic modulation is represented by the modulated current, JD and the resultant current in the external circuit represented by I,.

Helmholtz layer contains the second water molecule layer. From the Helmholtz double layer toward the bulk electrolyte are the diffusion layer and the hydrodynamic layer. In the diffusion layer, the concentration of species changes from that of the bulk electrolyte to that of the electrode surface. The diffusion layer does not move, but its thickness will decrease with increasing bulk electrolyte flow rate to allow higher reaction rates. The diffusion layer thickness is inversely proportional to the square root of the flow rate. The hydrodynamic layer or Prandtl layer has the same composition as the bulk electrolyte, but the flow of the electrolyte decreases from that of the bulk electrolyte to the stationary diffusion layer. 

The analysis of mass transfer in electrochemical cells requires the use of equations that describe the condition of electroneutrality (which applies for the entire elecnolyte outside the double layer at an electrode), species fluxes, mass conservation, current density, and fluid hydrodynamics. Often, mass transport events are rate limiting, as compared to kinetics processes at the electrode surface, in which case the overall electrode reaction rate is solely dependent on species mass transfer (e.g., during high-rate electroplating of some metals and for those elecnochemical reactions where the concentration of reactant in solution is low). 

The use of a second downstream electrode to monitor chemical fluxes at the working electrode is proving to be an important technique for the investigation of electrode mechanisms. This is particularly true for electrodes which have a more complicated structure than a simple metallic surface. Examples are modified electrodes, oxide electrodes, or enzyme electrodes. For these more complex systems, the separate measurement of the fluxes at the electrolyte-electrode interface provides unique and valuable information. Double electrodes can be constructed for all three hydrodynamic systems. A crucial parameter for such a double electrode is the collection efficiency, N, which, in the steady state, relates the flux of material detected as a limiting current on the downstream electrode to the flux of material generated on the upstream electrode. The collection efficiency is a function of the geometry of the electrode and is given for all three systems by [4, 9]... 

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