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Fig. 5.18 Potentiostatic methods: (A) single-pulse method, (B), (C) double-pulse methods (B for an electrocrystallization study and C for the study of products of electrolysis during the first pulse), (D) potential-sweep voltammetry, (E) triangular pulse voltammetry, (F) a series of pulses for electrode preparation, (G) cyclic voltammetry (the last pulse is recorded), (H) d.c. polarography (the electrode potential during the drop-time is considered constant; this fact is expressed by the step function of time actually the potential increases continuously), (I) a.c. polarography and (J) pulse polarography large-surface area calomel electrode or mercury sulphate electrode is used). The average current at the dropping mercury electrode ( / ) is given by the relationship Adt (5.5.8)
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where j is the instantaneous current density, tx is the drop-time and A is the instantaneous surface area of the electrode (see Eq. 4.4.4). If the approximate equation (5.4.9) is used, then the Ilkovic equation is obtained
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298 instead of the current density. The quantities ; and jd must be replaced by (/) and </ d ), KOX and icRed by KOX and KRed (kOx/kRed = (DOJDKed)V2) and k^ by the product k^(A), where (A) is the mean area of the electrode (in cm2): (A)=0.51m2l3,2/3,2/3 t (5.5.11)
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with m in g s l and tx in s. The theory of voltammetry with rotating disk electrode (RDE) was described in Sections 2.7.2 and 5.4.1. The properties of the voltammetric ultramicroelectrode {UME) were discussed in Sections 2.5.1 and 5.5.1 (Fig. 5.19). The steady-state limiting diffusion current to a spherical UME is Id = 4jtnFDrQc0 while to a hemispherical UME placed on an insulating support Id = 2jtnFDroco (5.5.13) (5.5.12)
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Fig. 5.19 Electrodes used in voltammetry. A dropping mercury electrode (DME). R denotes the reservoir filled with mercury and connected by a plastic tube to the glass capillary at the tip of which the mercury drop is formed. B ultramicroelectrode (UME). The actual electrode is the microdisk at the tip of a Wollaston wire (a material often used for UME) sealed in the glass tube
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299 For a disk UME situated in the plane of the insulating support Id = 4nFDroco (5.5.14)
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The non-steady state situation at UME represents a comparatively simple problem at a spherical electrode while it is very difficult to solve in the case of a disk electrode. When comparing these three voltammetric electrodes they show different performance with respect to the purpose of their use. 1. With a DME, clean surface is quite easy to achieve whereas with the other electrodes a special treatment of the surface is required in order to obtain reproducible results (page 307). Even in solutions containing surfactants, the amount adsorbed at DME can be controlled (cf. Section 364). 2. The mass transfer coefficient for both RDE and UME can be varied in a large interval while in the case of DME it is much smaller and also the possibility of changing it is rather restricted. 3. In contrast to DME, the charging of the electric double layer makes no problem with RDE and UME. 4. The work with both DME and RDE requires the use of a base (supporting or indifferent) electrolyte, the concentration of which is at least twenty times higher than that of the electroactive species. With UME it is possible to work even in the absence of a base electrolyte. The ohmic potential difference represents no problem with UME while in the case of both other electrodes it must be accounted for in not sufficiently conductive media. The situation is particularly difficult with DME. Usually no potentiostat is needed for the work with UME. 5. The area of the electrode can easily be measured with DME and RDE while in the case of very small UME it is often difficult to determine. 6. The high overpotential of hydrogen is an advantage of DME while this property can be exploited only with mercury-covered RDE and UME. On the other hand, the dissolution of mercury at rather low positive potentials is a disadvantage of DME which is not shared by RDE and UME made of nobler metals than mercury. In differential pulse polarography, the dropping mercury electrode is polarized by a sequence of pulses as shown in Fig. 5.18J. The difference between the currents flowing during several milliseconds before and at the end of a pulse is attenuated and recorded as function of the applied polarizing voltage, the charging current being thus eliminated. The resultant dependence of the current on the potential has the form of a peak, whose 'height' is proportional to the concentration. The high sensitivity of this method ensures it an important position in electroanalysis. The rotating ring disk electrode can be used to study the products of the electrode reaction (Fig. 5.20). The products of the electrode reaction at the disk are carried by convective diffusion to the ring where they undergo a
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