Nemst-Einstein relationship

Equation 11 gives the conductivity for a particular ion having a transference number, in a crystal, which is the Nemst-Einstein relationship. 

Equation (10.19) may be simplified for predominant electronic conduction, assuming that the classical Nemst-Einstein relationship can be represented as... 

Since the ionic conductivity and diffusivities are related by the Nemst-Einstein relationship, what governs one governs the other. Fast ionic conductors are a class of solids in which the ionic conductivity is much larger than the electronic conductivity. For a solid to exhibit fast ion conduction, the concentration and mobility of ionic defects must be quite large. The band gap of the material must also be quite high to minimize the electronic contribution to the overall conductivity. The electronic conductivity depends critically on the concentration of free electrons and holes. There are essentially three mechanisms by which mobile electronic carriers can be generated in a solid ... 

The most basic data that the Mott-Littleton and supercell methods provide are the energies and entropies of defect formation. Nevertheless, despite the fact that these techniques are essentially static approaches it can also be possible to deduce information on the dynamic processes of diffusion and conductivity. These two processes are related by the Nemst-Einstein relationship ... 

Wagner s theory is valid only for the growth of relatively thick films. The Nemst-Einstein relationship and the equation for transport by gradients of chemical and electrical potential (66) are valid only for small electric fields, whereas according to Eqs. (77 and 78) the voltage between the two interfaces of a film... 

An attempt has been made to analyse the results for membrane conductivity obtained in the presence of two counter-ions, the proton and an alkali ion. From the results of self-diffusion flux measurements by radiotracer techniques, Gavach et al. obtained a value for the individual mobility of Na ions in the membrane containing both Na" and counter-ions. By measuring the conductivity of the membrane containing only as the mobile ion and applying the Nemst-Einstein relationship, they determined the relative mobilities of these two counter-ions and concluded that the individual mobility of the proton increases by up to 150% as the number of Na" ions increases in the membrane. This increase with mole fraction of Na" " ions has been attributed to an increase of the proton hydration, Na" being less hydrated than H. ... 

This dilute-solution approach does not account for interaction between the solute molecules which could be dominant for many concentrated ionic solutions. Also, this approach will either use too many or too few transport coefficients depending on if the Nemst-Einstein relationship is used to relate mobility and diffusivity. 

At infinite dilution the ionic conductivity is related to the tracer diffusion coefficient of the ion (Z)°) through the well-known Nemst-Einstein relationship ... 

Ionic conductivity follows the Nemst-Einstein relationship, for hopping species, derived early in this chapter ... 

Much more recently Harris [271] examined the applicability of the Nemst-Einstein relationship between the molar conductivity A and the ionic diffusivities D ... 

Experimental results have been used to obtain averaged activity coefficients. Another approach toward characterization of degenerate semiconductors has been to include the nonidealities associated with degeneracy within a modified Nemst-Einstein relationship. " The modified Nemst-Einstein relationship is given by ... 

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