Multiple Relaxations\nand Entanglement Behaviors of\nPolymerized Ionic Liquids with Various Anions/Cations

Polymerized ionic liquids (PILs)\nwith anions of bis(trifluoromethylsulfonyl)imide\n(TFSI<sup>–</sup>), hexafluorophosphate (PF<sub>6</sub><sup>–</sup>), and tetrafluoroborate (BF<sub>4</sub><sup>–</sup>) and cations of poly[1-(4-vinylbenzyl)-3-<i>alkyl</i>-imidazolium]\nP[VBC<sub><i>n</i></sub>IM]<sup>+</sup> with alkyl lengths\nC<sub>1</sub>, C<sub>2</sub>, and C<sub>4</sub> were successfully\nsynthesized and characterized. X-ray scattering showed an increase\nin backbone-to-backbone spacing (<i>d</i><sub>b</sub>) by\n0.8 Å per CH<sub>2</sub> added to the alkyl side chain. Rheological\nand dielectric measurements were used to measure rates of chain relaxation\nand ion dissociation/association. The glass transition temperatures <i>T</i><sub>g</sub> follow the trend: PC<sub>4</sub>-TFSI <\nPC<sub>2</sub>-TFSI < PC<sub>1</sub>-TFSI < PC<sub>1</sub>-BF<sub>4</sub> < PC<sub>1</sub>-PF<sub>6</sub>, which correlates well\nwith their dielectric behaviors. However, the fragility <i>m</i><sub>DR</sub> from dielectric relaxation increases with decreasing <i>T</i><sub>g</sub>, which is the opposite of the dependence of\nfragility <i>m</i><sub>Rheo</sub> from rheology for both\nour PILs and neutral polymers. The dielectric and rheological relaxations\nof our PILs are expected to be influenced by both their anion–cation\nbinding energies and their relative free volumes, while for neutral\npolymers, relaxations are primarily governed by free volume. The increase\nof fragility of <i>m</i><sub>DR</sub> with decreasing <i>T</i><sub>g</sub>, therefore, suggests that dielectric relaxation\nis influenced more by anion–cation binding energy than by free\nvolume, while the reverse is true for <i>m</i><sub>Rheo</sub>. The plateau modulus <i>G</i><sub>N</sub> and entanglement\nmolecular weight <i>M</i><sub>e</sub> estimated from rheological\nmeasurements agree with predictions of the packing model, using only\na small modification of the Flory characteristic ratio <i>C</i><sub>∞</sub> from that of a neutral polymer. Packing lengths\nof <i>p</i> = 6.0∼9.3 Å and tube diameters <i>d</i><sub>t</sub> = 11∼17 nm are found, depending on\nspecific cation and anion structures.