Universal Relationship between Conductivity and Solvation-Site Connectivity in Ether-Based Polymer Electrolytes

We perform a joint experimental and computational study of ion transport properties in a systematic set of linear polyethers synthesized via acyclic diene metathesis (ADMET) polymerization. We measure ionic conductivity, σ, and glass transition temperature, T_g, in mixtures of polymer and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. While T_g is known to be an important factor in the ionic conductivity of polymer electrolytes, recent work indicates that the number and proximity of lithium ion solvation sites in the polymer also play an important role, but this effect has yet to be systematically investigated. Here, adding aliphatic linkers to a poly(ethylene oxide) (PEO) backbone lowers T_g and dilutes the polar groups; both factors influence ionic conductivity. To isolate these effects, we introduce a two-step normalization scheme. In the first step, Vogel–Tammann–Fulcher (VTF) fits are used to calculate a temperature-dependent reduced conductivity, σ_r(T), which is defined as the conductivity of the electrolyte at a fixed value of T – T_g. In the second step, we compute a nondimensional parameter f_(exp), defined as the ratio of the reduced molar conductivity of the electrolyte of interest to that of a reference polymer (PEO) at a fixed salt concentration. We find that f_(exp) depends only on oxygen mole fraction, x_0, and is to a good approximation independent of temperature and salt concentration. Molecular dynamics simulations are performed on neat polymers to quantify the occurrences of motifs that are similar to those obtained in the vicinity of isolated lithium ions. We show that f_(exp) is a linear function of the simulation-derived metric of connectivity between solvation sites. From the relationship between σ_r and f_(exp) we derive a universal equation that can be used to predict the conductivity of ether-based polymer electrolytes at any salt concentration and temperature.