Week 2- The CAE
This week we dove into the original publication on the CAE by Matt Petrowsky. The problem addressed in this paper is that the simple Arrhenius expression did not accurately describe the conductivity of organic liquid electrolytes and amorphous polymer electrolytes. This non-Arrhenius behavior observed experimentally in these electrolytes was shown by Petrowsky to be due to the temperature dependence of the dielectric constant. In order to proof this idea, Petrowsky sought to prove the correlation between exponential prefactor and the dielectric constant (since the temperature dependence of the dielectric constant was already understood). In doing this they experimentally determined the activation energy and the conductivity in order to isolate the exponential prefactor such that;
σ/(e-Ea/RT) = σo
plotting the exponential prefactor against the dielectric see figure 5b. By doing this they proved the correlation between the exponential prefactor and the dielectric constant (which was already known to be temperature dependent). They were able to vary dielectric constant and exponential prefactor by taking ‘families’ of solvents (i.e. methanol, ethanol, propanol, butanol,… varying alkyl chain length with same organic functional groups), and using the same salt, TbaTf. Interpreting the exponential prefactor as being dependent on the dielectric constant (and therefore temperature) was not only verified but experimentally proven to be a more accurate expression for determining the dependency of conductivity on temperature with a correlation coefficient of 0.9991 in contrast to the simple Arrhenius expression which had a correlation coefficient of 0.974 for a hexanol solution, see figure 3.