Steady-State Dual-Electrode Techniques

FIGURE 1.90. Variation of low-frequency resistance with electrode potential, same experimental conditions as in Fig. 1.88. 

This device has been employed by Faulkner et and Lyons and 

FIGURE 1.91. Schematic representation of the dual-electrode ring-disk (RD) geometry and the overcoated RRDE experiment illustrating concentration profiles of oxidized and reduced sites under steady-state conditions. 

The dual-electrode technique measures the steady-state amperomet-ric ring current response to a change in concentration of the oxidized form of the polymer bound redox-active group caused by a suitable potential step at the disk. Let us assume that an oxidation reaction occurs at the disk 

Now the current i driven through the polymer at any potential E can be equated to the flux of oxidized species at the disk electrode. Hence the lateral electron diffusion current is given by 

---

The simplest treatments of convective systems are based on a diffusion layer approach. In this model, it is assumed that convection maintains the concentrations of all species uniform and equal to the bulk values beyond a certain distance from the electrode, 8. Within the layer 0 x < 5, no solution movement occurs, and mass transfer takes place by diffusion. Thus, the convection problem is converted to a diffusional one, in which the adjustable parameter 8 is introduced. This is basically the approach that was used in Chapter 1 to deal with the steady-state mass transport problem. However, it does not yield equations that show how currents are related to flow rates, rotation rates, solution viscosity, and electrode dimensions. Nor can it be employed for dual-electrode techniques or for predicting relative mass-transfer rates of different substances. A more rigorous approach begins with the convective-diffusion equation and the velocity profiles in the solution. They are solved either analytically or, more frequently, numerically. In most cases, only the steady-state solution is desired. 

The characteristic current ip is directly related to the electronhopping diffusion coefficient Dp- This quantity can be obtained either by using dual-electrode steady-state techniques or transient techniques of chronoamperometry or chronocoulometry. These procedures are discussed in detail in Chapter 1. 

---