Polymer electrolytes are indispensable in numerous electrochemical systems. Existing polymer electrolytes rarely meet all technical demands by their applications (e.g., high ionic conductivity and good mechanical strength), and new types of polymer electrolytes continue to be developed. In this dissertation, the molecular structure and dynamics of three emerging types of polymer electrolytes featuring Coulombic liquids, i.e., polymerized ionic liquids (polyILs), nanoscale ionic materials (NIMs), and polymeric ion gels, were investigated using molecular dynamics (MD) simulations to help guide their rational design.

First, the molecular structure and dynamics of a prototypical polyILs, i.e., poly(1-butyl-3-vinylimidazolium hexafluorophosphate), supported on neutral and charged quartz substrates were investigated. It was found that the structure of the interfacial polyILs is affected by the surface charge on the substrate and deviates greatly from that in bulk. The mobile anions at the polyIL-substrate interfaces diffuse mainly by intra-chain hopping, similar to that in bulk polyILs. However, the diffusion rate of the interfacial mobile anions is much slower than that in bulk due to the slower decay of their association with neighboring polymerized cations.

Second, the structure and dynamics of polymeric canopies in the modeling NIMs where the canopy thickness is much smaller than their host nanoparticle were studied. Without added electrolyte ions, the polymeric canopies are strongly adsorbed on the solid substrate but maintain modest in-plane mobility. When electrolyte ion pairs are added, the added counter-ions exchange with the polymeric canopies adsorbed on the charged substrate. However, the number of the adsorbed electrolyte counter-ions exceeds the number of desorbed polymeric canopies, which leads to an overscreening of the substrate's charge. The desorbed polymers can rapidly exchange with the polymers grafted electrostatically on the substrate.

Finally, the molecular structure and dynamics of an ion gel consisting of PBDT polyanions and room-temperature ionic liquids (RTIL) were studied. First, a semi-coarse-grained model was developed to investigate the packing and dynamics of the ions in this ion gel. Ions in the interstitial space between polyanions exhibit distinct ordering, which suggests the formation of a long-range electrostatic network in the ion gel. The dynamics of ions slow down compared to that in bulk due to the association of the counter-ions with the polyanions' sulfonate groups. Next, the RTIL-mediated interactions between charged nanorods were studied. It was discovered that effective rod-rod interaction energy oscillates with rod-rod spacing due to the interference between the space charge near each rod as the two rods approach each other. To separate two rods initially positioned at the principal free energy minimum, a significant energy barrier (~several kBT per nanometer of the nanorod) must be overcome, which helps explain the large mechanical modulus of the PBDT ion gel reported experimentally.