Other experiments with finite planar geometry

8 OTHER EXPERIMENTS WITH FINITE PLANAR GEOMETRY 

Constant-current experiments, such as that described in the preceding subsection, are not as popular as experiments in which the potential is the controlled variable. In this section, we shall address controlled-potential experiments in cells with finite planar geometry, even though such experiments do not lend themselves readily to kinetic studies. We shall assume, as in previous sections, that the anode reaction is the converse of the cathode reaction. 

In a controlled-potential experiment, it is not possible, without making an assumption about the electron-transfer process, to predict the faradaic current or to predict the concentration of M + at the surfaces of the cathode or anode. One can, however, write the simple equation 

The above equations are valid for any experiment in a cell with finite planar geometry. For example, they apply to the experiment described in Sect. 4.7 in fact, eqns. (116) can be derived from eqns. (123) and (124) by setting i(t) equal to the constant i and performing a Laplace inversion. The Laplace inversion is difficult in this derivation and the interested reader is referred to ref. 79 for guidance. 

For reasons already mentioned in Sect. 3.1, cells with finite planar geometry are usually thin cells (i.e. L is small, usually a fraction of a millimetre) and there are only two electrodes. A controlled-potential experiment thus usually involves fixing the potential between the two electrodes, though this does not necessarily mean fixing the potential across either electrode. That is, the way in which the applied potential divides itself between the anode and the cathode will, in general, change with time, even if the total applied potential remains constant. For this reason, the simplification that normally attends experiments carried out at constant applied potential is not achieved with finite planar cells. 

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