Microelectrodes diffusion-limited current

Diffusion at Microelectrodes The total diffusion-limited current is composed of the planar flux and radial flux diffusion components ... 

The diffusion-limited current at spherical and hemispherical microelectrodes follows directly from (5.23). We consider a hemispherical electrode as shown in Fig. 5.8. After a certain time, depending on the electrode size, a steady-state is reached, and the current is... 

The situation at a miniature disc microelectrode embedded in a flat insulator surface (such as an RDE of very small size) can be approximated by spherical symmetry, obtained for a small sphere situated at the center of a much larger (infinitely large, in the present context) spherical counter electrode. How will the change of geometry influence the diffusion-limited current density This is shown qualitatively in Fig. 18L. As time progresses, the diffusion layer thickness increases, causing, in the planar case, a proportional decrease in the diffusion current density. In the spherical configuration the electroactive... 

In electroanalysis, electrodes of millimeter dimensions are termed millielec-trodes, while the more recently developed very small area electrodes of micron dimensions are termed microelectrodes there are differences in properties beyond simply the change of dimension. Thus in millielectrode-scale experiments the enhancement of the diffusion-limited current plateau has been observed by a number of other workers—for example, in the reduction of methylviologen in aqueous acetonitrile [32], in the oxidation of bis(cyclopentadienyl) molybdenum dichloride in acetonitrile [33], as well as in several other studies on the aqueous ferrocyanide/ferricyanide couple using wire or disc millielectrodes to study diffu-sional phenomena [34—36], Typical values of the diffusion layer thickness of approximately 5 pm are found under ultrasound [35] in contrast to the normal value of approximately 500 pm in silent conditions. 

It is interesting to estimate the effective tip radius immersed in the water layer, which is responsible for a tip current of 1 pA at 1.5 V bias. As shown in Fig. 11, a polyurethane-coated W tip behaves as a microelectrode. A sigmoidal diffusion-limited current superimposed on the linear background current was obtained for the reduction of 1 mM Ru(NH3)g+ in 10 mM NaC104 solution. An effective radius estimated from the nearly steady-state current is 3 /xm. Also shown in Fig. 11 is the anodic background current due to the oxidation of W at potentials positive of 0.4 V versus SCE (curve b). From the data shown in curve c of Fig. 10 and curve b of Fig. 11, if one assumes that similar effective tip radius is responsible for both anodic and cathodic redox processes, an estimated effective contact radius of 3 nm can be obtained for a background current flow of 1 pA at a bias voltage of 1.5 V. 

Table 1. Steady state diffusion-limited currents at various shapes of microelectrodes. Adapted from [24, 25]...

The steady state diffusion-limited currents at microelectrodes are described by equations given in Table 1. The first three types of microelectrodes obey the same equation, namely... 

Much more accurate measurements of diffusion coefficients can be obtained with LSV or CV using UMEs. These measurements are much less dependent on the electrochemical reversibility of the redox couple. Measurement of the diffusion-limited current from a voltammogram recorded at a microelectrode is demonstrated in Figure 19.3c. The concept is identical to that already discussed for chronoamperometry at UMEs at slow scan rates (i.e., long times) the current becomes steady state as long as the potential is well past Ey2-The dependence of D on the steady-state current is given by equation (19.3) for a hemispherical UME and equation (19.4) for a disk UME. The time considerations for CV are the same as those discussed above for chronoamperometry, except that the time is estimated from the scan rate and the difference between the final potential and Ey . 

Amperometric sensors — A class of electrochemical sensors based on amperometry. A diffusion-limited current is measured which is proportional to the concentration of an electrochemically active analyte. Preferred technique for biosensors with or without immobilized enzymes (biocatalytic sensors). The diffusion layer thickness must be kept constant, either by continuous stirring or by means of an external diffusion barrier. Alternatively, microelectrodes can be... 

Myiand JC, Oldham KB (1990) Diffusion-limited currents at hemispheroidai microelectrode. J Electroanal Chem 288 1-14... 

Daniele S, Ciani I, Batistel D (2008) Effect of the insulating shield thickness on the steady-state diffusion-limiting current of sphere cap microelectrodes. Anal Chem 80 253-259... 

Owing to the steady-state nature of the spherical diffusion at the microelectrode, the limiting current should be independent of potential sweep rates at lower sweep rates. As the sweep rate increases, the contribution of planar diffusion increases. The value of sweep rate at which planar diffusion begins to significantly interfere depends on the size of microelectrode. 

When an ultra-microelectrode is used as an electroanalytical tool, the diffusion-limited current density is not affected by the rate of flow, which typically creates a diffusion layer thickness of the order of50-100 pm. This can be a great asset for online monitoring in industrial applications, where the flow rate may fluctuate and would otherwise have to be measured and corrected for. 

Most successful is a rotating Pt wire microelectrode as illustrated in Fig. 3.75 as a consequence of the rotation, which should be of a constant speed, the steady state is quickly attained and the diffusion layer thickness appreciably reduced, thus raising the limiting current (proportional to the rotation speed to the 1/3 power above 200 rpm140 and 15-20-fold in comparison with a dme) and as a result considerably improving the sensitivity of the amperometric- titration. 

In this section, both approaches will be compared in chronoamperometry under limiting current conditions at spherical electrodes and microelectrodes. As is well known, for spherical electrodes and taking into account the Butler-Volmer model, the value of the diffusion-controlled reduction current at large overpotentials, e B is given by the following expression (see Eq. (2.147) of Sect. 2.5.2) ... 

Compared to conventional (macroscopic) electrodes discussed hitherto, microelectrodes are known to possess several unique properties, including reduced IR drop, high mass transport rates and the ability to achieve steady-state conditions. Diamond microelectrodes were first described recently diamond was deposited on a tip of electrochemically etched tungsten wire. The wire is further sealed into glass capillary. The microelectrode has a radius of few pm [150]. Because of a nearly spherical diffusion mode, voltammograms for the microelectrodes in Ru(NHy)63 and Fe(CN)64- solutions are S-shaped, with a limiting current plateau (Fig. 33a), unlike those for macroscopic plane-plate electrodes that exhibit linear diffusion (see e.g. Fig. 18). The electrode function is linear over the micro- and submicromolar concentration ranges (Fig. 33b) [151]. 

The response of SECM is distance-dependent as shown in Fig. 16.8. At large distances from the substrate the current measured is that of the microelectrode tip. The tip is a disc microelectrode, so that far from a substrate in the steady state the diffusion-limited tip current, /T., will be measured. For a simple n-electron electrode reaction this is... 

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