Molecular Dynamics simulations of the BAB type triblock copolymer lithium poly[(4-styrenesulfonyl) (trifluoromethylenesulfonyl) imide)]-block-poly(ethylene oxide)-block-lithium poly[(4-stryrenesylfonyl) (trifluoromethanesulfonyl) imide] (P(STFSILi)-b-PEO-b-P(STFSILi)) were carried out for different simulation temperatures and B-block lengths. By covalently binding the anion to the polymer backbone, it is immobilised and the cation transference number thereby raised significantly. It was found that the Li-ion diffusion decreases exponentially with growth of the B-block length. The poly(ethylene oxide) matrix dissolves Li-ions already during the equilibration stage of the simulation, and no Li-ion diffusion pathways were identified along the STFSI branches, which significantly influence the transport properties of the material.