Kirja

In this chapter, we introduce a few of the most common experimental methods in electrochemistry. The salient problem of electrochemistry is that electric current, as easy as it is to measure accurately, appears as the boundary condition of the transport equation. The variable of the equation, concentration, is usually not of interest, only its gradient on the surface of the electrode, which is also time-dependent. Common (numerical) methods for solving partial differential equations therefore do not apply as such to electrochemistry.

There are both stationary (time-independent) and time-dependent methods. The former methods may seem simpler as only the Laplace equation $\nabla^2c=0$ is solved whereas a partial differential equation, Fick’s second law must be solved in the latter methods. That is not, however, the whole truth because stationary methods often make use of hydrodynamics that complicate mathematical analysis greatly. We will therefore begin with relatively simple time-dependent or transient methods that have closed-form (analytical) solutions which can be found using Laplace transforms.