# Theory

The cyclic voltammetry (CV) wave is shaped differently at a microelectrode, as illustrated in Figure 1, for the oxidation of ferrocene in acetonitrile. Not only is the magnitude of the current much less due to the smaller electrode area, but also the current goes to a steady-state value and is not peak-shaped. This steady-state current is explained by envisioning the microelectrode as a “dot” with the diffusion layer being hemispherical in shape and extending out into the solution. The amount of electroactive species diffusing to the electrode surface is defined by the volume enclosed by this expanding hemisphere, rather than a plane projecting into the solution as for a planar electrode. Only at very short times when the diffusion layer, δ, is still much smaller than the radius, ro, of the microelectrode, will the current be approximated by what is given by the Cottrell relationship [ref. 2] if the applied potential is a step function. At times when δ >> r, diffusion to the edge of the electrode becomes significant; i.e., the diffusion profile approximating a hemispherical shape. Under such a condition, the current goes to a steady-state value as given by [ref. 3]

$\mathrm{\mathit{i}_{ss} = 4nFDC^b\: r_o}\tag{1}$

where iss is the steady-state current in ampere, n is the number of electrons in the reaction, D is the diffusion coefficient of the electroactive species in cm2/s, Cb is the bulk concentration of the electroactive species in mole/cm3, and ro is the radius of the disk microelectrode in cm.

Figure 1. Oxidation of 3 mM ferrocene in 0.1 M NaCl04 with acetonitrile as the solvent. 10 μm Pt microelectrode with a gel-filled Ag/AgCl reference electrode. The scan rate is 100 mV/s.

The low level of current makes iR losses negligible even at high scan rates. This allows the determination of kinetic rates of electron transfer that are very fast by scanning at high rates. Also, the small area means that the background or capacitive current is low in comparison to the Faradaic current so that the signal to noise (S/N) is enhanced, allowing measurements at lower concentrations. Of course, one important feature of microelectrodes, particularly carbon fibers, is being able to make measurements in small volumes such as applications in biological cells and nerve synapse [ref. 4]. A 3-electrode potentiostat with capability to measure small currents at a wide range of scan rates is recommended for working with microelectrodes. Some have been developed specifically for in-vivo and in-vitro studies of neurotransmitters, such as dopamine and norepinephrine [ref. 5].

Another difference between CV at microelectrodes compared to larger ones is that the reverse current is not due to the redox of the product formed during the forward scan, but is the continuation of the forward scan reaction. Thus, the forward and reverse waves track each other in an “ideal” reversible electrode reaction. In this experiment, the CV for the reduction of ferricyanide is used to characterize what happens at a microelectrode.