Diffusivity, Mobility and Conductivity The Nernst-Einstein Relation

Diffusivity, Mobility and Conductivity The Nernst-Einstein Relation 

We have above introduced concentrations and relations between concentrations of species of interest The area-specific flux (flux density) of a species, i, resulting from a driving force, F, is proportional to its concentration and to its mechanical mobility (ease of movement) j j = Cj Bj Fj as we come back to in the next section. First we briefly recall from textbooks that for species with an activated diffusion, the self-diffusion coefficient, D, mechanical mobility, B, charge mobility, u, and conductivity, a, are linked through the Nemst-Einstein relation (1.14)  

For species that migrate by other mechanisms than diffusion (notably itinerant electrons and holes), the diffusion coefficient is undefined, and instead one uses mobilities with temperature dependences typical of band transport with phonon-, impurity-, or large polaron-Hmited transport [8]. 

Wagner Transport Theory for Dense Ceramic Hydrogen-Separation Membranes 1.4.1 

---