Electrode geometry problems

Charge Transport. Side reactions can occur if the current distribution (electrode potential) along an electrode is not uniform. The side reactions can take the form of unwanted by-product formation or localized corrosion of the electrode. The problem of current distribution is addressed by the analysis of charge transport ia cell design. The path of current flow ia a cell is dependent on cell geometry, activation overpotential, concentration overpotential, and conductivity of the electrolyte and electrodes. Three types of current distribution can be described (48) when these factors are analyzed, a nontrivial exercise even for simple geometries (11). 

As has been stated several times, the geometry problem in junctions is difficult. Several papers have utilized the differences in the IETS calculated spectrum at different trial geometries to compare with the experimental spectrum, and thereby to deduce the true geometry of the structure. Figure 10 shows some results by Troisi [107], in which he was able to deduce the angle between the molecular backbone and the electrode, based on agreement with the IETS spectrum. 

The solution of this simple problem leads to the following solution, independently of the electrode geometry (see below) ... 

Under these conditions (see Eqs. (4.199)-(4.202)), it can be easily demonstrated that the Superposition Principle can be applied and the diffusion differential equation and the boundary value problem of this process, independently of the electrode geometry, are simplified to... 

In Sect. 3.4.10, it was presented the solution to this reaction scheme when a single potential step is applied. Next the application of any succession of potential steps of the same duration t, is considered. The general solution corresponding to the pth applied potential can be easily obtained because this is a linear problem, and, therefore, any linear combination of solutions is also a solution of the problem, and also that the interfacial concentrations of all the participating species only depend on the potential and are independent of the history of the process regardless of the electrode geometry considered (see Sect. 5.2.1). The two above conditions imply that the superposition principle can be applied [38] in such a way that the solution for the current corresponding to the application of the pth potential can be written as follows ... 

For the simpler cases where a low (usually one) dimensional linear PDE may be solved in isolation, the system may be analytically tractable. For anything more than model problems at most practical electrode geometries, numerical methods are currently the only way by which the equation systems may be solved. 

One might naively conclude from this fact that in using nonaqueous solutions instead of aqueous solutions in an electrochemical system, the conductivity presents no problem. Unfortunately, this is not the case. The crucial quantity that often determines the feasibility of using nonaqueous solutions in practical electrochemical systems is the specific conductivity a at a finite concentration, not the equivalent conductivity /1° at infinite dilution. The point is that it is the specific conductivity which, in conjunction with the electrode geometry, determines the electrolyte resistance R in an electrochemical system. This elecdolyte resistance is an important factor in the operation of an electrochemical system because the extent to which useful power is diverted into the wasteful heating of the solution depends on fiR, where / is the current passing through the electrolyte hence, R must be reduced or the [Pg.545]

Studied electrode geometry, the essentials of the kinetic mechanisms are not totally settled. Each of the key steps (adsorption, surface mobility, charge transfer, and desorption) still constitutes a huge scientific problem involving the application of the macrohomogeneous concept. 

The examples provided above are for simple geometries. The potential distribution becomes complicated as the electrode geometry becomes more complex. Also, it is difficult to solve the Laplace equation and realize an analytical solution. This forces one to solve the problem numerically. 

This approach has some disadvantages resulting mainly from oxygen concentration dependence. The problem can be alleviated by designing the electrode geometry in such a way that oxygen can reach the electrode surface by both axial and radial diffusion while glucose is restricted to axial diffusion alone [127]. 

In electrochemistry, a wide variety of complex electrode geometries and flow patterns can be used, and few are amenable to quantitative treatment. Hence the normal approach to the convective diffusion problem is to treat the cell as a uniform or averaged entity, and to seek expressions in terms of space averaged quantities which permit some insight into mass transport conditions in the cell. 

---