Conductivity prefactor relation

Fig. 7.3. Measured values of the conductivity prefactor a, versus the conductivity activation energy, showing the Meyer-Neldel relation. Data from sever different laboratories are shown (Tanielian 1982).

Fig. 7.7. Relation between the conductivity prefactor and activation energy for different conduction regimes described in the text.

Here Tq is — C2 and is a prefactor proportional to which is determined by the transport coefficient (in this case at the given reference temperature. The constant B has the dimensions of energy but is not related to any simple activation process (Ratner, 1987). Eqn (6.6) holds for many transport properties and, by making the assumption of a fully dissociated electrolyte, it can be related to the diffusion coefficient through the Stokes-Einstein equation giving the form to which the conductivity, <7, in polymer electrolytes is often fitted,... 

Therefore, within the linear approximation, the conductivity activation energy Eg measures the value of ( tr— )g and the prefactor contains the additional factor exp(y/k). The temperature dependence of the energies accounts for the Meyer-Neldel relation provided that... 

A more detailed analysis of the conductivity data is needed to explain the prefactor and to understand the Meyer-Neldel relation. The magnitudes of Yp and Yg depend on the location of the Fermi energy, the density of states distribution and the thermal state of the material. There are three situations which can be analyzed easily. 

Until now we have mainly treated electrons and holes analogously to the ionic defects. As far as the mobility is concerned, quantum mechanical eflfects cause severe differences. There is no energy of activation (AH = 0) in the case of perfect band conduction and, formally speaking, the temperature dependence of the mobility is effectively determined by the prefactor. The determining process for the finite mobility is scattering by lattice vibrations and/or imperfections. The T / relation for acoustic phonon scattering is a typical law in this context (see Chapter 3) (see Fig. 6.14). Unless the electronic charge concentration has been fixed by dop-... 

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