Mercury electrodes spheres

Convective diffusion to a growing sphere. In the polarographic method (see Section 5.5) a dropping mercury electrode is most often used. Transport to this electrode has the character of convective diffusion, which, however, does not proceed under steady-state conditions. Convection results from growth of the electrode, producing radial motion of the solution towards the electrode surface. It will be assumed that the thickness of the diffusion layer formed around the spherical surface is much smaller than the radius of the sphere (the drop is approximated as an ideal spherical surface). The spherical surface can then be replaced by a planar surface... 

Fig. 9. Types of rotating spherical electrodes reported in the literature, (a) Rotating micro-sphere electrode, (b, c) rotating hemisphere electodes (d) rotating ring-hemisphere electrodes (e) rotating dropping mercury electrode.

We carried out some measurements some years ago in order to measure the transfer coefficient in DMF for this couple at a mercury electrode [Hush, N. S. Dyke, J. M. J. Electroanal. Interfac. Electrochem. 1974, 53, 253]. The deviation from one-half for the value so obtained was consistent with reasonable values for the free energy of activation of ligand exchange in the inner-coordination spheres. 

The effect of ligands on the character and degree of the inner-sphere reorganization during electroreduction of aqua-, aquahydroxy-, hydroxy-, and ethylene-diamine tetraacetic acid (EDTA) complexes of Zn(II) [95] and electrochemical process of Zn(II) complexed by different ligands - glycinate [96], ethanol amine [97], azinyl methyl ketoximes [98], aspartame [99], glutathione [100, 101] and several cephalosporin antibiotics [102] -were studied at mercury electrodes in aqueous solutions. 

In general, because of non-uniform accessibility of the electrode, equations for current—voltage curves have to be solved either by using approximations or numerically. For historical reasons, the dropping mercury electrode was the first to be treated theoretically [146-149] and the equations obtained depend on whether the steady-state, expanding-plane, or expanding-sphere models are utilised [150]. 

When this equation is solved for r and the latter is substituted into the equation for the area of a sphere, an expression for the area of the dropping-mercury electrode drop as a function of the experimental parameters is obtained... 

Small t. The second term in (5.23) can be neglected, in other words the spherical nature of the electrode is unimportant. Diffusion at a sphere can be treated as linear diffusion. This is very important for the dropping mercury electrode (Section 8.3) for typical values of drop radius of 0.1 cm and D = 10 5 cm2 s-1, after t = 3 s there is only a 10 per cent error in using (5.19). 

The search for such curved Tafel plots has yielded some well-documented examples where essentially straight Tafel lines are observed, even when slight curvature is predicted from eqn. (37). In particular, this is the case for proton reduction [73] and the outer-sphere reduction of some Cr(III) aquo complexes [34] at mercury electrodes over wide overpotential ranges (> 600 mV). However, the former reaction is not an outer-sphere process with symmetrical reactant and product parabolae to which eqn. (37) should apply, but rather involves the formation of an adsorbed hydrogen atom intermediate. The influence of such a mechanistic feature upon the rate-potential behavior is unclear even now [74]. The Cr(III)/Cr(II) aquo couple at mercury has also been examined over wide ranges of anodic as well as cathodic over-potentials [75]. In contrast to the cathodic behavior, marked... 

This case arises, for example, when working with dropping or hanging mercury electrodes. Let us consider semi-infinite diffusion to a sphere of radius with both oxidized and reduced forms soluble in the solution. In this case Eq. (47) should be substituted by... 

Figure 3.6.1 Outer-sphere and inner-sphere reactions. The inner sphere homogeneous reaction produces, with loss of H2O, a ligand-bridged complex (shown above), which decomposes to CrCl(H20) + and Co(NH3)5(H20). In the heterogeneous reactions, the diagram shows a metal ion (M) surrounded by ligands. In the inner sphere reaction, a ligand that adsorbs on the electrode and bridges to the metal is indicated in a darker color. An example of the latter is the oxidation of Cr(H20)5 at a mercury electrode in the presence of Cl or Br .

In Fig.2, the potential ranges are given where a number of compounds topical to the explosives sphere are reduced/oxidized. The potential ranges are also given where carbon and mercury electrodes can be employed as working electrodes in Fig.2. The reactions that are thought to occur at the electrode and on which the method of analysis is based, are briefly discussed for the different components. 

Mechanisms for the electrochemical processes at mercury electrodes in solutions of [Ni(cyclam)] + and CO2 have been proposed (see Scheme 5.1 ). Scheme 5.1 shows the formation of a carbon-bonded Ni(II) complex by reaction of CO2 with Ni(cyclam)+. The formation of such a complex is considered to be a fundamental step in the mechanism of the [Ni(cyclam)] +-catalyzed electrochemical reaction. The overall process for the transformation of CO2 into CO also involves inner-sphere reorganization. Scheme 5.1 includes the formation of sparingly soluble complex containing Ni(0), cyclam and CO which is a product of the reduction of [Ni(cyclam)] + under CO. Depositation of a precipitate of the Ni(0) complex on the mercury electrodes inhibits catalysis and removes the catalyst from the cycle. The potential at which the [Ni L-C02H] + intermediate (see lower left hand of Scheme 5.1) accepts electrons from the electrode. This potential is not affected by substitution on the cyclam ring, as shown by comparison of [Ni(cyclam)] + and [Ni(TMC)] " (TMC = tefra-iV-methylcyclam)... 

These equations can be solved for semi-infinite external diffusion, where both Red and Ox forms are in the solution outside the sphere (diffusion to a spherical or hemispherical hanging mercury electrode, metallic solid spherical electrode), or they may diffuse inside the sphere (amalgam formation at mercury electrode, intercalation of Li into particles, hydrogen absorption into spherical hydrogenabsorbing particles). 

Other convective systems have been used in electroanalytical chemistry. The oldest one is the dropping mercury electrode [2, 3]. Convection here arises by virtue of the expansion of the growing mercury drop, and the transport equation is pleasantly simple and unidimensional for the simplified case, assuming a spherical drop that is not falling downwards, and assuming that the sphere is large compared... 

The active part of the working electrode normally consists of a small disk or sphere of platinum (depending on whether one wishes to work under conditions of planar or radial diffusion). Alternatively, one can use gold, mercury (as a gold-mercury amalgam), or carbon. 

It is clear that since the mercury drop approximates a sphere, the theory of spherical, and not linear, diffusion might have to be used. However, detailed considerations accessible in monographs show that if the electrodic reaction is driven for a sufficiently short time (/ < a few seconds) and if the mercury-drop radius is not too small (r > 0.05 cm), then the equations of linear diffusion can be used with validity. Thus, the partial differential equations for the diffusion of A and D are [see Fick s second law cf. Eq. (4.32)]... 

Specifically adsorbed thiocyanate also accelerates the kinetics of Cr(OH2)6+ oxidation on mercury with the incorporation of the anion ligand into the inner coordination sphere of the product. The oxidation of this cation is similarly enhanced by chloride ions [87] and the rate of the electrode reaction is proportional to the surface concentration of chloride ions which, like thyocyanate, are incorporated into the... 

The ohmic iR drop at the DME is that expected for a spherically symmetric radial current flux between the surface of an inner sphere of radius r, centimeters (mercury drop in this case) and the surface of an (imaginary) outer sphere of radius r2 (dashed circle of Figure 6.1 at the tip of the Luggin capillary). Using the model of concentric spherical electrodes of radii r, and r2... 

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