This paper describes the development of a method of catalytic polymerization that was then applied to synthesize sulfate-based oligomers from sulfamide. Two molecules, copper triflate and copper acetate, catalyzed the formation of oligomers with diol monomers. Two oligomers were identified as products of the reactions. Oligomers with sulfate incorporated in the backbone proved to have an ability for ion diffusion. When the oligomers were doped with lithium salt, anion transportation was predominant, as shown by solid-state NMR. The lithium ion was found to be strongly bonded to the backbone, while the anion was highly mobile. To corroborate this finding, we conducted molecular dynamics (MD) simulations, which revealed the structural characteristics and static properties of two electrolytes containing LiTFSI and two different polyethylene oxide oligomers. Interactions between the anion and cation were analyzed through computation of the radial distribution function (RDF) and the spatial distribution function (SDF). Our findings indicate that while the anion presents weak interactions with the polymer chain, the cation interacts strongly with the oligomer backbone.