Theoretical study of the structure and thermodynamics of polymerized ionic liquids

We present a detailed study of ion-ion, ion-polymer and polymer-polymer real space pair correlations, their collective partial structure factor analogs, and the thermodynamic cohesive energy and bulk modulus of dense melts of polymerized ionic liquids (PILs) using PRISM integral equation theory with the modified-Verlet closure. Polymers are modeled as charged semiflexible chains, and mobile ions as spheres of sizes chosen to mimic Li, Na, Cs, Br, PF6 and TFSI. All species interact via a hard core repulsion plus variable strength screened Coulomb interactions. Rich interchain and collective correlations are predicted over a wide range of length scales with distinctive features such as ion-mediated bridging, intensity of monomer scale caging, Coulomb cage coordination number, and amplitude of longer length scale density fluctuations, which all depend on ion size, Coulomb interaction strength and packing fraction. Quantitative comparisons with the analogous neutral systems have also been determined. For some structural properties we find PILs fall in two qualitatively different classes of behavior corresponding to small and large ions. The results provide a foundation for creating microscopic theories of mobile ion diffusion, structural relaxation, and vitrification in PILs.