Double collection efficiency

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. 

In reactions involving gas evolution, the RRDE can be problematic in that bubbles may become trapped at the centre of the disc electrode. To obviate this, a rotating double ring electrode was suggested [34], The collection efficiency, N0, is given by eqn. (41) if we define... 

First-order collection efficiencies at the double channel electrode... 

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

The steady-state collection efficiency, N0, of the double electrode is given by... 

A small fraction of the reactant ions collide with Cm molecules, and product ions scattered into the forward hemisphere in the laboratory frame are collected by the octapole. Product and unscattered reactant ions are mass selected by a double focusing electric and magnetic sector mass spectrometer, and detected by an on-axis Daly detector [16]. In the following we give only relative cross sections, due to uncertainties in the absolute pressure of Cm, the product collection efficiency, and the alkali-metal ion beam intensities in the scattering cell. 

Figure 6.22. (A) Path length enhancement for a clear sample inside an integrating sphere. (B) Additional mirrors to provide a double laser pass through the sample and increased collection efficiency.

Theoretical calculations are not recommended for design, but Eq. (3.1-3) gives an indication of the effect of several variables, Increasing collection efficiency from 90 to 99% requires doubling the collector ares. 

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]... 

One advantage of the wall-jet system is that one can include a packed-bed electrode just upstream of the jet, thus making a packed bed wall-jet electrode (PBWJE) [5-7]. This is a valuable double electrode system in that a packed-bed electrode can achieve complete turnover of a reactant. We have verified that theory and experiment are in good agreement for the collection efficiency by the wall-jet electrode of material generated on the bed [6]. 

In this section, the discussion centres on the application of double channel electrodes in the study of electrode reaction mechanisms under conditions of laminar flow. (The modifications necessary to what follows when turbulent flow operates can be found in Sect. 6.2.) When employed in this way, the upstream (generator) electrode produces the species of interest, which is then detected on the downstream electrode. This procedure is illustrated schematically in Fig. 37. In general, the detector electrode is held at a potential at which the destruction of the species produced upstream is diffusion-controlled. Kinetic and mechanistic information about the electrogenerated species is then available from "collection efficiency , N, measurements, given by... 

Fig. 37. Principle behind double electrode operation under steady-state conditions. A proportion of the species B, electrogenerated upstream, can be lost before detection downstream via diffusion or reaction in solution. The collection efficiency, N, provides information about these two processes. Where the product of the homogeneous reaction, P, is electroactive, it too can be detected downstream.

Steady-state collection efficiencies as a function of double channel electrode geometry when the product of the generator electrode reaction is kinetically stable on the channel electrode timescale... 

The collection efficiency of the optical system increases with the square of the effective numerical aperture of the microscope objective lens. A good lens is therefore essential in order to obtain a high coincidence rate. If the sample is transparent the light can be collected from both sides, either by the condenser lens of the microscope or by a second microscope lens. Theoretically, the collection efficiency can be doubled and the coincidence rate increased by a factor of four. Moreover, in a microscope with two aligned microscope lenses exciting and detecting from both sides of the sample, the focal volume can be considerably decreased [64, 448]... 

Figure 10.7 Double-band assembly operating in generator/collector mode. (A) Relationship between feedback (l/ampl(f) = and collection efficiency (coU(t) = in absence of a chemical reaction. (B) Effect of a chemical reaction (EC mechanism) on the collection efficiency as a function of kg D. w/g = 2 and g/2(Df) = 0.005. k is the first-order rate constant of the chemical reaction.

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