## 2 Thermal and Electrochemical Parameters of Interest
### Ionic Conductivity  
Ionic conductivity is the movement of charged species in a material in response to an applied electric field [52]. Although solid polymer electrolytes, which are generally comprised of organic monomers, tend to have relatively low conductivities, the addition of ionic species like lithium salts has resulted in the fabrication of reasonably conductive materials (10\({}^{-8}\) to 10\({}^{-6}\) S/cm at room temperature) [18]. However, ionic conductivities on the order of 10\({}^{-4}\) to 10\({}^{-3}\) S/cm are necessary for polymer electrolytes to be competitive with their liquid counterparts [53]. The potential ionic conductivity of polymer electrolytes can be particularly high as the impedance of the electrolyte divided by the square of its thickness is the metric that is most commonly used to express ionic conductivity [52]. The superior thin-film forming abilities of most solid polymer electrolytes make them promising candidates in this regard. Ionic conductivity, measured as a function of sample temperature, can also be used to calculate activation energy for the ion transfer process. The activation energy is linked to many factors that impact ion transport including material properties, intermolecular and intramolecular interactions, local morphology and material interfaces [54]. Activation energies are calculated by plotting ionic conductivities measured at several temperatures via either the Arrhenius or the Vogel-Tammann-Fulcher (VTF) methods [54, 55]. The VTF method tends to be preferentially used in polymer electrolytes as it separates the effects of charge carrier concentration and polymer motion from the overall conductivity [55]. This generally results in more linear fits than with the Arrhenius equation as the pre-factor is related to charge carrier concentration [14, 55]. Activation energies for ion transfer processes in polymer electrolytes tend to be between 10 and 40 kJ/mol with lower activation energies being linked to less hindered ion transport [10, 17, 27, 38, 54]. The ionic conductivity of the samples presented in Table 1 was measured using electrochemical impedance spectroscopy (EIS) at ambient temperature (25 or 30 \({}^{\circ}\)C in most publications) as this is the temperature range that is most relevant to the operation of personal electronic devices. Additionally, reporting all conductivities in the same temperature range allows the polymer electrolytes to be more readily compared. The data presented in Table 1 show that adding an epoxide to a PEO-lithium salt polymer electrolyte can result in an order of magnitude increase in conductivity from \(10^{-7}\) to \(10^{-6}\) S/cm [18, 19]. However, increased ionic conductivity on the order of \(10^{-5}\) to \(10^{-4}\) S/cm was observed in some epoxide-based systems [7, 10, 14, 20]. Although the presence of epoxide-based monomers has resulted in increased ionic conductivity, practical conductivities for real-world battery systems (\(\sim\)\(10^{-3}\) S/cm) have only been achieved with the incorporation of liquid plasticizers [6, 36, 37]. This suggests that the additional crosslinking and/or functional groups that are produced by polymerization between epoxides and other reagents may limit polymer chain mobility or increase polymer salt interactions which are known to decrease ion mobility [53, 56, 44]. As for T\({}_{g}\), sample parameters that must be taken into account when evaluating these systems are lithium salt content and the possibility of adsorbed water or solvent (even in samples that were prepared using solvent-free methods) [57, 51]. Although the addition of lithium salt is the reason that these materials have appreciable ionic conductivity, high salt content can result in reduced lithium-ion motion as a result of increased affinity with the polymer and/or the formation of ion clusters [52, 53, 58, 59]. The presence of water, solvents or plasticizers increases polymer chain mobility and the resultant amorphous phase tends to conduct ions more readily [60].