Diffusion at Microelectrodes

1 Diffusion at Microeiectrodes The total diffusion-lunited current is composed of the planar flux and radial flux diffiision components  

For disk, spherical, and hemispherical geometries, the general expression for the radial component m equation (4-14) is given by 

---

For the purposes of considering diffusion at microelectrodes, it is convenient to introduce two categories of electrodes those to which diffusion occurs in a linear fashion and those to which diffusion occurs in a nonlinear fashion. The former category consists of cylindrical and spherical electrodes. As shown schematically in Figure 12.2A, the lines of flux (i.e., the pathway followed by material diffusing to the electrode) are straight, and the current density is the same at all points on the electrode. Thus, the diffusion problem is one-dimensional (i.e., distance from the electrode surface) and involves solution of the appropriate form of Fick s second law, Equation 12.7 or 12.8, either by Laplace transform methods or by digital simulation (Chap. 20). 

Special attention should be paid to spherical geometry, since the mathematical treatment of spherical microelectrodes is the simplest and exemplifies very well the attainment of the steady state observed at microelectrodes of more complex shapes. Indeed, spherical or hemispherical microelectrodes, although difficult to manufacture, are the paragon of mathematical model for diffusion at microelectrodes, to the point that the behavior of other geometries is always compared against them. 

Table 6.4 gives the output of Program 5 under certain conditions. We see that for a layer thickness z/ = 2.5 x 10" cm, Program 5 finds a value of Hip close to that obtained by other techniques [Table 6.4(a)]. Orthogonal collocation is used to simulate rotating ring disk electrodes and cyclic voltammetry for CE and EC mechanisms. Furthermore orthogonal collocation is used to characterize diffusion at microelectrodes and microelectrode arrays. ... 

FIGURE 12.15 Lines of flux that predominate at different electrode dimensions (A) radial diffusion at microelectrodes and (B) linear diffusion at macroelectrodes. 

Amatore C, Svir I (2003) A new and powerful approach for simulation of diffusion at microelectrodes based on overlapping sub-domains application to chronoamperometry at the microdisk. J Electroanal Chem 557 75-90... 

The spherical diffusion at microelectrodes [494] with no supporting electrolyte is given by ... 

Radial diffusion — Diffusion converging to a point is called radial diffusion, and is applied for diffusion at small microelectrodes when the radius of the electrode is much larger than the diffusion layer thickness estimated from (Dtj1/2. Genuine radial diffusion occurs at a spherical electrode. However, radial diffusion is sometimes used for diffusion at an edge of a planar electrode, which is also called lateral diffusion. See also -> hemispherical diffusion. 

Several newer techniques, such as cyclic voltammetry (CV) are now used to identify a proper choice of an antioxidant. CV is an electrolytic method that uses microelectrodes and an unstirred solution, so that the measured current is limited by analyte diffusion at the electrode surface. The electrode potential is ramped linearly to a more negative potential, and then ramped in reverse back to the starting voltage. The forward scan produces a current peak for any analyte that can be reduced through the range of the potential scan. The current will increase as the potential reaches the reduction potential of the analyte, but then falls off as the concentration of the analyte is depleted close to the electrode surface. As the applied potential is reversed, it wiU reach a potential that will reoxidize the product formed in the first reduction reaction, and produce a current of reverse polarity from the forward scan. This oxidation peak will usually have a similar shape to the reduction peak. The peak current, ip, is described by the Randles-Sevcik equation ... 

Normally large electrodes are used for the common sensors. In our case we use 25 pm diameter microelectrode (see Figure IB) for two reasons The first reason is that we can directly combine the complete electrochemical setup, namely working, reference and counter electrode on top of a small tip. Because of the low currents (some nA) at microelectrode, counter and reference electrode can be combined and the potential of the counter/reference electrode is nearly stable and is not distorted by the small currents. The second positive effect of the use of microelectrodes is that the ratio between Faradayic and double layer current is increasing with decreasing active surface. The reason for that is the different diffusion mechanism compared with Targe electrodes. At microelectrodes the diffusion takes place in a spherical way like to the surface of a drop [2]. 

It is useful to investigate the effect of an experimental timescale on the iR drop observed at microelectrodes. In a subsequent section, we discuss in more detail how the diffusion field at microelectrodes depends on the characteristic time of the experiment. At short times, the dominant mass transport mechanism is planar diffusion and the microelectrode behaves like a macroelectrode. Therefore, at short times. 

Fig. 4 Diffusion fields observed at microelectrodes. (a) Linear diffusion observed at short times and (b) radial (convergent) diffusion observed at long times.

The possibility of nonlinear electroosmotic flow, varying as m oc E, seems to have been first described by Murtsovkin [1, 2], who showed that an alternating electric field can drive steady quadrupolar flow around a polarizable particle (Fig. la). This effect has recently been unified with other nonlinear electrokinetic phenomena in microfluidics [3], such as AC electro-osmotic flow (ACEO) at microelectrodes [4, 7, 8] (Fig. lb), DC electrokinetic jets at dielectric corners [5] (Fig. Ic), and nonlinear flows around metal posts [9] (Fig. Id-e). These are all cases of induced-charge electroosmosis (ICEO) - the nonlinear electroosmotic flow resulting firom the action of an electric field on its own induced diffuse charge near a polarizable surface. 

---