Moving Beyond the Arrhenius Law for Ion Hopping in Glassy Polymer Electrolytes

Polymer electrolytes usually show Arrhenius-like temperature dependence of the conductivity relaxation time (characteristic time of local ion rearrangements) at temperatures below their glass transition Tg. However, our recent analysis reveals that the Arrhenius fit of this regime leads to unphysically small prefactors, τ0 << 10^-13 s. Imposing a value of 10^-13 s for this parameter renders the fairly unexpected result that the activation barrier for charge transport in these polymers has strong temperature dependence even below Tg. Our study also revealed significant temperature variations of the dielectric permittivity and the instantaneous shear modulus in the glassy state of these polymers. Using the Anderson and Stuart model, we demonstrate that these variations provide strong justifications for variations of the free energy barrier for ion hopping. Most importantly, the proposed approach reveals that the free energy barrier controlling ion hopping in polymer electrolytes is significantly (~30-40%) lower than the estimated using traditional Arrhenius fit. These new insights call for revisions of many earlier results based on apparent Arrhenius fits, and the proposed new approach can provide more accurate guidance for the design of solid-state electrolytes with enhanced ionic conductivity.