Membrane Potentials and the Donnan Effect

The electrical aspects of membrane phenomena have long been of interest in science, and attracted the attention in the nineteenth century of famous physical chemists including Gibbs, Nernst, Planck, and Ostwald. Originally, this interest was connected to electrical phenomena in biological systems. In the present discussion attention is focused on membranes used in specific ion electrodes. 

A membrane can be either a liquid or a solid. Its electrical properties arise when it allows transport of an ion of one charge but not that of another. Membranes are usually sufficiently thick that one can distinguish an inside region and two outer boundary regions which are in contact with electrolyte solutions. Two types of membranes are considered here (1) membranes of solid and glassy materials (2) liquid membranes with dissolved ion-exchanging ions or neutral ion carriers (ionophores). In fact all of these membranes are involved in ion exchange. It is important to understand how this process affects the potentials which develop in the system at both sides of the membrane. 

The functioning of a membrane is illustrated for the case that it can exchange cations with solutions 1 and 2. On the other hand, anions cannot enter the membrane. Furthermore it is assumed that the solvent in the solutions, usually water, also does not enter the membrane. This situation is not always valid. Estimation of the membrane potential is more complex when the solvent enters the membrane due to osmotic effects. The cation involved in membrane transport is designated M and is assumed to be present in both solutions, so that the system can now be described as 

In general, the chemical potentials of the cation are not equal in a given solution and in the membrane. At equilibrium the electrochemical potentials of the cation must be equal in the two phases. As a result, a potential difference called the Donnan potential is established at each interface. Moreover, the concentration of the cation on the left-hand side of the membrane is not always the same as that on the right and the cation diffuses from the location of high concentration to the one where it is lower. The non-equilibrium diffusion process gives rises to a diffusion potential. 

Of course, there are many membranes into which anions may enter and cations are excluded. Some important examples will be discussed in the following presentation. It turns out that basic principles of the functioning of membranes in electro analysis can be illustrated very well using the example of the glass membrane which is involved in the pH electrode. This is discussed in detail in the following section. Then, the functioning of liquid membranes is considered in the next section. 

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