Electrical conduction in solid polymer electrolytes: temperature dependence mechanism
It is generally accepted that the electrical conduction in solid polymer electrolytes (PE) is strongly temperature dependent: an Arrhenius dependence is observed at low temperatures, while a non-Arrhenius VogelTammanFulcher (VTF) behavior is seen at high temperatures. A theory is introduced, for the first time, for the electrical conduction of solid PE in the entire range of temperatures, by considering the fluctuation of the melting temperature and by the application of the statistical theory of gelation. The theory contains the expected Arrhenius and VTF dependence as the asymptotic limits at low and high temperatures, respectively. In addition, a critical transition temperature at which the electrical conductivity behavior changes from Arrhenius-like to VTF-like is determined analytically. This critical temperature is shown to increase linearly with the melting point of the PE. It is demonstrated that the theoretical results are in good agreement with the experimental evidence.
arrhenius vtf fluctuation critical temperature melting point