A closer look at the Nernst-Planck model for liquid junctions in galvanic cells and the concept of EMF

It is realized now that what is called the liquid-junction potential is given, in the classical theory of Nernst and Planck, by a line integral, which is path independent only in the case of a single independent concentration. Although previous model studies suggest that this integral is consistent with the potential calculated by the 1D version of Poisson's equation in the limit of long diffusion times, it is shown here, with a simple static model, that this may be true in the 3D space only at an infinitely large cross-section of the junction. At finite cross-sections, supposing that a charge separation exists, the potential difference across it is a function of the area of the cross-section and the distance across it, which is at variance with the properties of the integral. It is argued therefore that this integral cannot be interpreted in terms of electrostatics, but represents a quantity, the EMF, which is conceptually different from the potential.