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√3 1+x1/33 3 2x1/3 −1 1 31/2 +4 (3.16) (3.17) (3.18) G(x)= 4π ln 1+x y=r1 −1 +2πarctan r23 3.2. Cyclic voltammetry A second type of hydrodynamic voltammetry can be carried out using a rotation ring- disk electrode (RRDE). On an RRDE, the WE disk is surrounded by a second working electrode in the shape of a ring, separated from the disk by an insulating material (typ- ically the same as the shroud material). The two WEs are controlled separately, which makes it possible to hold or sweep the potential individually on the two WEs. Due to the rotation of the electrode, material is first pulled to the disk electrode where e.g. a reduction takes place. The material is then flung outwards, where it can be re-oxidised by the ring electrode if it is held at a potential higher than the redox potential. The situation is illustrated in Figure 3.6. r3 r2 r1 Ox Red Red Ox C Red Figure 3.6: Schematic cross-section of an RRDE tip and the reactions taking place at the disk and ring electrodes for a redox-active species initially in the oxidised state. Solid arrows denote reactions and dashed arrows denote movement. The reduced species is either re-oxidised at the ring, converted chemically to a new species C, or simply mixed with the bulk of the electrolyte. The electrode radii used for calculating the maximum collection efficiency are also indicated. Only a fraction of the redox-active species will be converted electrochemically at the ring electrode. The remaining fraction will mix with the bulk of the electrolyte, or if the reduced species is chemically unstable in the supporting electrolyte, undergo a (possibly) irreversible chemical reaction. The fraction collected at the ring, called the collection efficiency, is mainly controlled by the geometry of disk and ring electrodes. The maximum collection efficiency Nmax is defined as [62]: Nmax =1−G(y/z)+z2/3(1−G(y))−(1+y+z)2/3(1−G[(y/z)(1+y+z)]) (3.15) Ring ze- Disk ze- Ring r3 r3 z=3−2 r13 r13 where r1 is the radius of the disk, r2 is the inner radius of the ring, and r3 is the outer radius of the ring, as shown in Figure 3.6. Experimentally, the collection efficiency is 25PDF Image | Organic Redox Flow Batteries 2023
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