Microelectrodes steady state current

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. 

As illustrated in Figure 3.2, when the microelectrode is distant from the surface by several electrode diameters, a steady-state current, ij., is observed at the tip. The magnitude of the current is the same as that observed for a microdisk in a conventional experiment. When the tip is near a surface, the tip current, ij, differs from ij.oc, and depends on both the distance between the surface and tip, and the chemical nature of the surface. If the interfacial assembly efficiently blocks electron transfer, i.e. it is an electronic insulator, the mediator will not be regenerated, thus causing to be less than unity. If the Red species becomes re-oxidized at... 

Large t. The spherical term dominates, which represents a steady-state current. However, due to the effects of natural convection this steady state is never reached at conventionally-sized electrodes. The smaller the electrode radius, the faster the steady state is achieved. It is possible to achieve a steady state at microelectrodes. These are described further in Section 5.5. 

The development of ultramicroelectrodes with characteristic physical dimensions below 25 pm has allowed the implementation of faster transients in recent years, as discussed in Section 2.4. For CA and DPSC this means that a smaller step time x can be employed, while there is no advantage to a larger t. Rather, steady-state currents are attained here, owing to the contribution from spherical diffusion for the small electrodes. However, by combination of the use of ultramicroelectrodes and microelectrodes, the useful time window of the techniques is widened considerably. Compared to scanning techniques such as linear sweep voltammetry and cyclic voltammetry, described in the following, the step techniques have the advantage that the responses are independent of heterogeneous kinetics if the potential is properly adjusted. The result is that fewer parameters need to be adjusted for the determination of rate constants. 

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. 

Figure 8 is a block diagram of a typical two-electrode configuration for making microelectrode measurements where the function generator and recorder could, of course, be replaced by a microcomputer with appropriate interfaces. To minimize noise, the cell is mounted in a Faraday cage and cables are kept as short as possible. Using a system of this type, noise-free measurements of steady-state currents as small as 10 12 A have been made... 

When sohd submicroelectrodes are used there is no need of stirring the solution between pulses. The initial conditions are easily regained due to steady state current which develops at the microelectrode surface after relatively short time, during the delay period r. 

H. P. Wu. Fabrication and characterization of a new class of microelectrode arrays exhibiting steady-state current behavior, Anal. Chem. 65, 1643-1646 (1993). 

It can be seen that at short times the spherical correction can be neglected. On the other hand, at large t values, a steady-state current will flow. The smaller the electrode radius, the faster the steady state is achieved. The steady state can easily be reached at microelectrodes however, at electrodes of ordinary size (To > 1 mm), steady-state current is seldom observed due to the effect of natural convection. 

The other extreme represents the situation at very small electrodes and a steady state current is predicted. The reason for this is that a very steep concentration gradient is created, which sucks in electroactive species this situation occurs for microelectrodes. 

When CV is conducted at stationary microelectrodes with slow V, in both forward and backward scans sigmoidal current-voltage curves are found which are usually coincident, except for processes involving coupled chemical reactions that display more or less marked hystereses. This sigmoidal shape (steady-state current) can be accounted for by considering the radial diffusion to the edges of ultramicroelectrode surfaces that is very important at slow v, so as to make the diffusion rate of analyte molecules to the electrode surface comparable with the charge transfer rate. 

One of the most remarkable features of microelectrode measurements is that one can observe steady state redox currents in relatively short time domains. When the current response at a microelectrode is in a steady state, a hemispherical diffusion region of the electrogenerated species is formed around the microelectrode probe (Fig. la). The size of the diffusion region largely relies on the probe radius and the steady state current is expressed by the following equation ... 

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