Modeling electrode polarization in dielectric spectroscopy: Ion mobility and mobile ion concentration of single-ion polymer electrolytes

A novel method is presented whereby the parameters quantifying the conductivity of an ionomer can be extracted from the phenomenon of electrode polarization in the dielectric loss and tan δ planes. Mobile ion concentrations and ion mobilities were determined for a poly(ethylene oxide)-based sulfonated ionomer with Li+, Na+, and Cs+ cations. The validity of the model was confirmed by examining the effects of sample thickness and temperature. The Vogel-Fulcher-Tammann (VFT)-type temperature dependence of conductivity was found to arise from the Arrhenius dependence of ion concentration and VFT behavior of mobility. The ion concentration activation energy was found to be 25.2, 23.4, and 22.3±0.5 kJmol for ionomers containing Li+, Na+, and Cs+, respectively. The theoretical binding energies were also calculated and found to be ∼5 kJmol larger than the experimental activation energies, due to stabilization by coordination with polyethylene glycol segments. Surprisingly, the fraction of mobile ions was found to be very small, <0.004% of the cations in the Li+ ionomer at 20°C.