Current macroelectrode

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

So far we have discussed only the reversible case. The equivalence of the net Faradaic current at the NEE and at a macroelectrode of the same geometric area (Fig. 7) means that the flux at the individual elements of the NEE are many orders of magnitude larger than the flux at the macroelectrode. Indeed, the experimentally determined fractional electrode areas (Table 1) indicate that, for the reversible case, the flux at the elements of a... 

Cyclic voltammetry is generally considered to be of limited use in ultratrace electrochemical analysis. This is because the high double layercharging currents observed at a macroelectrode make the signal-to-back-ground ratio low. The voltammograms in Eig. 9B clearly show that at the NEEs, cyclic voltammetry can be a very powerful electroanalytical technique. There is, however, a caveat. Because the NEEs are more sensitive to electron transfer kinetics, the enhancement in detection limit that is, in principle, possible could be lost for couples with low values of the heterogeneous rate constant. This is because one effect of slow electron transfer kinetics at the NEE is to lower the measured Faradaic currents (e.g.. Fig. 8). 

There are other advantages of microelectrodes as compared to the macroelectrodes. Because the current is small, on the order of nA to pA, the voltage drop due to the electrical resistance of the medium is negligible. For this reason, it is possible to perform electrochemical experiments in media that would be otherwise unsuitable for macroelectrodes, such as resistive hydrocarbon solvents and solid electrolytes, without a potentiostat. Secondly, the double-layer capacitance is very small because the area of the electrode is small. This means that very fast modulation experiments... 

It is also possible to deduce the expression of /Plane for the case of different diffusion coefficients, since the surface concentrations c0 and are also constant at macroelectrodes when Do / /Jr (see Eq. (2.20)). Under these conditions the current is given by [20, 21] ... 

Eq. (4.61) and Table 2.3 of Sect. 2.6), whereas for the second potential pulse the amount of converted charge is much smaller than that obtained at a planar electrode (macroelectrode). Indeed, when the electrode radius becomes small enough the converted charge for the second potential pulse is constant and coincides with (for example, from Eq. (4.62) in the limit rs current-time curves. 

From Eq. (5.62) or (5.65) it is clear that when the electrode radius decreases the second term in the right-hand side of both equations becomes dominant and the current becomes stationary (see below). Thus, the typical peak-shaped signal of macroelectrodes evolves toward a sigmoidal or quasi-sigmoidal shape, indicative of stationary or quasi-stationary behavior, and therefore, under these conditions, the peak is no longer an important feature of the signal. 

From Eqs. (5.92)-(5.94), it is clear that K°phe ss < x°phe < xplane, that is, the maximum value of the dimensionless rate constant is that corresponding to a planar electrode (macroelectrode). For smaller electrodes, /c(sphc decreases until it becomes identical to the value corresponding to a stationary response, xpphe ss. In practice, this means that the decrease of the electrode size will lead to the decrease of the reversibility degree of the observed signal. It can be seen in the CV curves of Fig. 5.14, calculated for k ) = 10 eras 1 and v = 0.1 Vs-1, that the decrease of rs causes an increase and distortion of the dimensionless current similar to that observed for Nemstian processes (see Fig. 5.5), but there is also a shift of the curve toward more negative potentials (which can be clearly seen in Fig. 5.14b). 

As stated in Sect. 5.2.3.4, there is always a potential difference generated by the flow of faradaic current I through an electrochemical cell, which is related to the uncompensated resistance of the whole cell (Ru). This potential drop (equal to IRU) can greatly distort the voltammetric response. At microelectrodes, the ohmic drop of potential decreases strongly compared to macroelectrodes. The resistances for a disc or spherical microelectrode of radius rd or rs are given by (see Sect. 1.9 and references [43, 48-50]). 

Equation (6.41) for the current-potential response has been applied to the analysis of different experimental systems of interest. For example, the experimental SCV voltammograms of the two-electron reduction of anthraquinone-2-sulfonate (AQ) in different mixtures of alkylammonium salts obtained at a gold macroelectrode (radius = 0.9mm) with a scan rate v = lOOmVs 1 are shown in Fig. 6.3 when a staircase... 

The particular advantages of microelectrodes were discussed in Section 5.5. The current density at a microelectrode is larger than that at a spherical or planar electrode of larger dimensions owing to radial and perpendicular diffusion. Mass transport is greater, and we observe differences in the experimental results obtained by the various electrochemical techniques relative to macroelectrodes. 

To put HM methodology into the more general context of developments in techniques for electroanalysis, for a modulated macroelectrode the significant diminution in the charging current to the desired current signal contribution is comparable to that observed by decreasing the characteristic... 

One of the benefits of electrochemical batch injection analysis is that dilution of the sample with electrolyte is not necessary, see below. A sample of volume =sl00p.L is injected directly from a micropipette, tip diameter 0.5 mm, over the centre of a macroelectrode exactly as in a wall-jet system. This is equivalent to a flow injection system with zero dispersion. During the injection, and after a short initial period to reach steady-state, the hydrodynamics is wall-jet type and a time-independent current is registered. BIA was first devised using amperometric, e.g., [31], and potentiometric, e.g., [34], detection. A typical amperometric trace is shown in Fig. 16.5. By using a programmable, motorised electronic... 

Unlike macroelectrodes which operate under transient, semi-infinite linear diffusion conditions at all times, UMEs can operate in three diffusion regimes as shown in the Figure for an inlaid disk UME following a potential step to a diffusion-limited potential (i.e., the Cottrell experiment). At short times, where the diffusion-layer thickness is small compared to the diameter of the inlaid disc (left), the current follows the - Cottrell equation and semi-infinite linear diffusion applies. At long times, where the diffusion-layer thickness is large compared to the diameter of the inlaid disk (right), hemispherical diffusion dominates and the current approaches a steady-state value. 

Implicit in the above is the notation that current-voltage curves measured at macroelectrodes for all but fast voltage scan rates are characterized by a mass transport limited current plateau rather than a current peak as in linear sweep voltammetry at a planar electrode of larger than micro dimensions. 

Electrodes can be divided into four categories according to their characteristic dimensions 1) Macroelectrodes, such as parallel plates, 2) Microelectrodes, 3) Ultramicroelectrodes, and 4) Nanoelectrodes. The four types of electrodes are illustrated in Figure 11 together with their characteristic electrical properties important for their applicability resistance, R, double-layer capacitance, Cdi, and current, /. 

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