Electrode spherical effect

This is shown in Fig. 2.19. The relationships between A fJ, and nE v, and nIEE do not depend on electrode size [28-30]. So, if nE vi = 25 mV and nAF, = —5 mV, the relationship (2.21) is AWp = 0.465 + 0.45p [26]. If the frequency is high and a hanging mercury drop electrode is used, the spherical effect is usually negh-gible (p < 10 ). However, the influence of sphericity must be taken into consideration under most other conditions, and generally at microelectrodes. The net peak current is a linear function of the square-root of frequency Alp/nFAc QD I =... 

The electrokinetic effect is one of the few experimental methods for estimating double-layer potentials. If two electrodes are placed in a coUoidal suspension, and a voltage is impressed across them, the particles move toward the electrode of opposite charge. For nonconducting soHd spherical particles, the equation controlling this motion is presented below, where u = velocity of particles Tf = viscosity of medium V = applied field, F/cm ... 

Unlike solid electrodes, the shape of the ITIES can be varied by application of an external pressure to the pipette. The shape of the meniscus formed at the pipette tip was studied in situ by video microscopy under controlled pressure [19]. When a negative pressure was applied, the ITIES shape was concave. As expected from the theory [25a], the diffusion current to a recessed ITIES was lower than in absence of negative external pressure. When a positive pressure was applied to the pipette, the solution meniscus became convex, and the diffusion current increased. The diffusion-limiting current increased with increasing height of the spherical segment (up to the complete sphere), as the theory predicts [25b]. Importantly, with no external pressure applied to the pipette, the micro-ITIES was found to be essentially flat. This observation was corroborated by numerous experiments performed with different concentrations of dissolved species and different pipette radii [19]. The measured diffusion current to such an interface agrees quantitatively with Eq. (6) if the outer pipette wall is silanized (see next section). The effective radius of a pipette can be calculated from Eq. (6) and compared to the value found microscopically [19]. 

In electrochemistry, spherical and hemispherical electrodes have been commonly used in the laboratory investigations. The spherical geometry has the advantage that in the absence of mass transfer effect, its primary and secondary current distributions are uniform. However, the limiting current distribution on a rotating sphere is not uniform. The limiting current density is highest at the pole, and decreases with... 

Diffusion of electroactive species to the surface of conventional disk (macro-) electrodes is mainly planar. When the electrode diameter is decreased the edge effects of hemi-spherical diffusion become significant. In 1964 Lingane derived the corrective term bearing in mind the edge effects for the Cotrell equation [129, 130], confirmed later on analytically and by numerical calculation [131,132], In the case of ultramicroelectrodes this term becomes dominant, which makes steady-state current proportional to the electrode radius [133-135], Since capacitive and other diffusion-unrelated currents are proportional to the square of electrode radius, the signal-to-noise ratio is increased as the electrode radius is decreased. 

Electroanalytical application of hemispherical [35,36], cylindrical [37,38] and ring microelectrodes [39] has been described. A hemispherical iridium-based mercury ultramicroelectrode was formed by coulometric deposition at -0.2 V vs. SSCE in solution containing 8 x 10 M Hg(II) and 0.1M HCIO4 [35]. The radius of the iridium wire was 6.5 pm. The electrode was used for anodic stripping SWV determination of cadmium, lead and copper in unmodified drinking water, without any added electrolyte, deoxygenation, or forced convection. The effects of finite volume and sphericity of mercury drop elecPode in square-wave voltammetiy have been also studied [36]. 

A theory concerning the electrode kinetics of all these shapes has been given (Popov, 1996). It is quite complicated and involves interactions of differing growth rates, the co-deposition of H, and of course the effects of diffusion, which is sometimes planar but is also spherical if the radius of curvature to which the ions diffuse is less than -0.01 cm. Much more may be done to increase the variety of these shapes and to control them if electrical variables are introduced (e.g., pulsing, superimposed ac, etc.). The area is open for much fascinating research. 

Converting the small currents measured at ultramicro electrodes results in higher current densities compared with the values obtained at micro electrodes. This is also caused by the spherical diffusion path. This effect improves on the sensitivity and the detection limit for analytical purposes, and the small size of the electrodes in combination with application of high scan rates allow measurement to be performed in vivo and with a minimal (negligible) disturbance of the conditions of the system to be analysed. 

In Fig. 4.5 it can be seen the influence of t2 on the normalized RPV curves calculated from planar, spherical, and disc electrodes from Eqs. (4.67) and (4.36). From these curves, it can be observed that the decrease of t2 causes an increase of the anodic limiting current (with this increase being more noticeable in the case of planar electrodes), whereas it has no effect on the half-wave potential of the responses (marked as a vertical dotted line). 

In Fig. 4.8, the influence of the electrode radius of spherical electrodes on the peak potential can be seen. The DPV curves are normalized in order to show better the radius effect, i.e., v//)/) ),LPyeak. When y > la decrease of electrode radius... 

Fig. 4.25 Effect of the electrode radius and the chemical kinetics on the DDPV responses of a catalytic mechanism calculated from Eq. (4.229) for disc and spherical electrodes. A = 50mV, ti = 1 s, T2 = 0.050s, K = 1/ feq = 1> T= 298.15 K, and D= 1CT5 cm2 s I. The values of the electrode radius = rs and j = ( i + 2) 2 are indicated on the graphs. Dotted lines mark the potential values where the response equals to the half of the peak height...

From the analytical equation (6.105) obtained for CV, the study of the current-potential response in these techniques can be performed along with the analysis of the influence of the key variables. First, the effect of the parameter co (Eq. (6.98)) is shown in Fig. 6.15 where the curves are plotted for a spherical electrode of 50 pm radius. Note that large upvalues relate to the situation where the complexes of the reactant species A are more stable than those of species B, whereas the opposite situation is found for small negative potentials when co increases on account of the hindering of the electro-reduction reaction due to the stabilitization of the oxidized species with respect to the reduced ones. According to Eq. (3.289), an apparent formal potential can be defined as follows ... 

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