Solvent-free block copolymers electrolytes are the strongest candidates for solid-state lithium metal batteries, as new polymers based on polyethylene oxide (PEO) and lithium bis(trifluoromethane)sulfonimide (LiTFSI) prevent the formation of lithium dendrites and ensure sufficient conductivity. Block copolymers based on PEO and either polystyrene (PS) or grafted PS-TFSI were compared to PEO by Nuclear Magnetic Resonance spectroscopy (NMR) in order to quantify and distinguish the transport and dynamics of Li+ and TFSI- and the effect of the polymer matrix. The self-diffusion coefficients of Li+ and TFSI- can be measured at various temperatures with pulsed-field-gradient (PFG) experiments and compared with electrical conductivity measurements, providing insights on lithium transport properties in each system. We measured 7Li NMR relaxation rates at various magnetic fields and temperatures, and we were able to extract complex correlation functions describing the fluctuations of the 7Li quadrupolar interaction inside the polymer matrix, yielding insights into cation dynamics with three different timescales. These results obtained from NMR can be compared to molecular dynamics or theoretical calculations.