Nernst-Einstein equation correlation

In spite of the high ionic conductivity, there is no guarantee that the IL can transport the desired ions such as metal ions or protons. It is therefore important to analyze the ion transport properties in ILs. The ion conduction mechanism in ILs is different from that in molecular solvents. The ionic conductivity is generally coupled to carrier ion migration and ionic conductivity (a) correlates to diffusion coefficient (D) according to the Nernst-Einstein equation (see Eq. (3.10)) where n and q imply the number of carrier ions and electric charge, respectively. R, T, and F stand for the gas constant, the temperature in K, and the Faraday constant, respectively. 

The interpretation of the pre-factor as a conductivity as well as the correlation between defect diffusion coefficient Dk and mobility uk known as Nernst-Einstein equation follow directly from Table 3. 

In a number of articles, the Nernst-Einstein equation was used to correlate values of the electrical conductivity and the diffusion coefficients. The application of this equation to molten salts did not bring expected results as the electrical conductivity values calculated from the diffusion data are always higher than the experimental conductivity data. As a main reason for this difference, the presence of cavities in the melt is mentioned, which are sufficiently large so that both the cations and the anions could be placed in them. Such cavities are regarded as pair vacancies. If a pair jump of both kinds of ions using the pair vacancy takes place, both the atoms participate in the mass transfer and thus in the diffusion process, but not in the charge transfer. 

Under ideal conditions, activity a can be substituted with the concentration C. Furthermore, the conductivity of the defect species can be correlated with its concentration and diffusivity by the Nernst-Einstein equation ... 

The conductivity of defect can be correlated to its concentration and diffusivity, which is a measure of the random motion of the species i in the lattice, by the Nernst-Einstein equation ... 

Equation [3.7] correlates conductivity with ionic diffusion and electrolyte viscosity. Since the Nernst-Einstein equation [3.8] gives the relationship between conductivity and diffusion and since the right-hand side of equation [3.7] is obtained by combining equations [3.6] and [3.8], the decoupling index R, is basically a measure of the effect of viscosity on conductivity. 

Here at = [ciqf/kT], a and qt are, respectively, the concentration and charge of species i (anions and cations). Vi 0)Vi(t)) and AFf(t)) are, respectively, the velocity correlation function (VCF) and mean-squared displacement in time of species i. The steady current behavior at long times in the step-on experiment (see above) means that ABf t)) becomes linearly dependent on time, giving the Nernst-Einstein equation that connects the low-/" conductivity cr (O) (=diffusion coefficients A for the translational motions of the ions (9,10) ... 

Equation (5.56) relates the correlation factor fA with the cross coefficient LAA . From the Nernst-Einstein relation we know that LAA = bA-cA = DAcA/R T. For a tracer experiment with a negligible fraction of A, the jump conservation requires that Da = Dv-Nv, so that instead of Eqn. (5.56) we have... 

The term 1Tb (0 can be calculated directly using the probability theory or can be obtained by the correlation function of the velocity vectors of the ions. If the cross terms are neglected as in the approximation underlying the Nernst-Einstein (NE) equation, it is possible to write equation 6.15 (Funke, 1991) ... 

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