Frequency-dependent conductivity, relaxation times, and the conductivity/viscosity coupling problem, in polymer-electrolyte solutions: LiClO₄ and NaCF₃SO₃ in PPO 4000

This contribution seeks to rationalize the striking differences between conductivity/mechanical responses in the salt-polymer and superionic glass extremes of the amorphous solid electrolyte field. The decoupling index, R_τ, which is the ratio of structural to conductivity relaxation times and has values up to 10¹⁴ for superionic glasses, was shown by Torell and Angell to have very small values, of order 10^-3, for salt/polymer solutions, but no clear interpretation could be provided. In the present work, we use ac conductivity and viscosity-derived mechanical relaxation times measured over wide composition ranges in systems of known ion-pair content to investigate the composition dependence of R_τ, We observe systematic variations of R_τ with salt concentration which go in the opposite direction from that expected from the composition dependence of ion pairing. In dilute polymer solutions, diffusing ion apparently "see" a microviscosity considerably greater than that detected by the light scattering-based longitudinal mechanical relaxation, which is, however, found to give correctly the conductivity relaxation time in aqueous systems. With increasing salt concentration the decoupling index is found to increase exponentially such that values of unity are predicted for salt contents greater than one mole per six polymer repeat units (M:O=1:6) where less than a full coordination shell of ether oxygens is available for the cation. Crude extrapolations suggest the possibility of a continuous progression from anion mobility-dominated supercoupled polymer-salt solution to cation mobility dominated, highly decoupled superionic glass, as the cation solvation sheaths are stripped away.