Transport geometry

The present section is devoted to discussing each of these features and analyzing the various options. 

Determined by the shape of the electrode, the geometry of the space surrounding the electrode has an important effect on the transport problem. 

A semi-infinite transport geometry implies that, for the duration of the experiment, effects generated at the working electrode do not reach the other electrode or the cell walls, so that the transport coordinate behaves as if it were infinite in extent. The prefix semi reflects the fact that the geometry appears infinite in one direction (away from the electrode) but not in the other (towards the electrode). Because of the limited duration of most electrochemical experiments, cells may be tiny and yet be appropriately described as having a semi-infinite transport geometry. 

Transport geometries may be classified as simple or complex according to the number of spatial coordinates needed to describe the transport. Simple geometries involve only one coordinate, that directed normal to the electrode surface, whereas complex transport geometries require two or three coordinates for their description. 

Only three simple transport geometries are normally encountered planar, cylindrical, and spherical. These are shown in Fig. 13. In planar transport, the flux lines are parallel to each other and normal to the electrode. Cylindrical transport occurs with electrodes that are cylindrical, such as wires, or hemicyclindrical the flux lines converge in the plane which is normal to the cylinder axis but are parallel in planes which include the cylinder axis. Spherical transport is encountered with spherical or hemispherical electrodes, the flux lines being continuations of the radii 

---

Fig. 13. Simple transport geometries, (a) Planar (b) cylindrical (c) spherical. The arrows indicate flux lines to the electrode surface.

Of the many complex transport geometries, some of the most important are those encountered with inlaid electrodes (Fig. 14) [25— 30], in which the electrode is planar and embedded in an insulator whose surface is a continuation of the electrode plane. If such an electrode is large, it may be appropriate to treat it as a case of planar transport, with a correction for the edge effect [31, 32], For a small inlaid electrode, however, or for experiments of long duration, such an approximation is no longer valid. 

The most popular transport geometry is planar and semi-infinite more derivations deal with this situation than with any other. There are two reasons for this. First, it is usually the simplest. Second, more complex geometries (spherical, inlaid, etc.) can often be approximated by this geometry with suitable corrections. 

Constraints Mass Transport., Geometry, Conservation Energy, Mass), etc. 

Figure 12.2 A schematic of the transport geometry and reactant concentration between the well mixed gas phase outside of the boundary layer and the substrate surface where growth reactions occur. The behaviors are simplified and approximated as linear. In reality the behaviors are more complex but the result is the same.

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

The mathematical model most widely used for steady-state behavior of a reactor is diffusion theory, a simplification of transport theory which in turn is an adaptation of Boltzmann s kinetic theory of gases. By solving a differential equation, the flux distribution in space and time is found or the conditions on materials and geometry that give a steady-state system are determined. 

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). 

---