Some Limitations of the Nernst-Einstein Relation

There were several aspeets of the Stokes-Einstein relation that reduced it to being only an approximate relation between the diffusion coefficient of an ionic species and the viscosity of the medium. In addition, there were fundamental questions regarding the extrapolation of a law derived for macroscopie spheres moving in an incompressible medium to asituation involving the movement ofions in an environment of solvent molecules and other ions. In the case of the Nernst-Einstein relation, the factors that limit its validity are more subtle. 

An implicit but principal requirement for the Nernst-Einstein equation to hold is that the species involved in diffusion must also be the species responsible for conduction. Suppose now that the species M exists not only as ions but also as ion pairs of the type described in Section 3.8.1. 

The diffusive transport of M proceeds through both ions and ion pairs. In the conduction process, however, the situation is different (Fig. 4.64). The applied electric field exerts a driving force on only the charged particles. An ion pair as a whole is electrically neutral it does not feel the electric field. Thus, ion pairs are not participants in the conduction process. This point is of considerable importance in conduction in nonaqueous media (see Section 4.7.12). 

In systems where ion-pair formation is possible, the mobility calculated from the diffusion coefficient =D/kT is not equal to the mobility calculated from the equivalent conductivity u yZieo = (A/ZjeQ)F and therefore the Nernst-Einstein equation, which is based on equating these two mobilities, may not be completely valid. In practice, one finds a degree of nonapplicability of up to 25%. 

Another important limitation on the Nernst-Einstein equation in electrolytic solutions may be approached through the following considerations. The diffusion coefficient is in general not a constant. This has been pointed out in Section 4.2.3, where the following expression was derived. 

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