Diblock copolymers of poly(styrene-b-ethylene oxide), PS-b-PEO, are employed together with lithium triflate (CF3SO3Li, LiTf) at several [EO]:[Li] ratios as solid polymer electrolytes. Their thermodynamic state, self-assembly, and viscoelastic properties are discussed in conjunction with the ionic conductivity. PS-b-PEO/LiTf differs from the well-investigated PS-b-PEO/LiTFSI system in that the electrolyte in the former binds intramolecularly to PEO chains. Microscopic and macroscopic parameters affecting ion transport are discussed. From a microscopic point of view different parameters were considered as potential regulators of ion transport: the characteristic domain spacing, d, the interfacial thickness, Delta, and the ratio of Delta/d. By comparing two block copolymer electrolytes (PS-b-PEO and PI-b-PEO) bearing the same conducting block (PEO) and the same electrolyte (LiTf) but in the presence of different interactions, among the microscopic parameters it is the domain spacing that appears to have the most decisive role in ionic conductivity. Ion conductivity in PS-b-PEO/LiTf exhibits a molecular weight dependence similar to that reported for the PS-b-PEO/LiTFSI system, however, with somewhat lower values reflecting anion size effects. Among the macroscopic factors that limit ionic conductivity, the possible preferential wetting of the electrodes by either of the constituent phases can lead to an orientation that effectively blocks ion transport. The viscoelastic properties of the block copolymer electrolytes differ substantially from the neat block copolymers. Li-ion coordination affects not only the PEO segments but also, surprisingly, the PS segments. An increase in PS glass temperature by similar to 10 K is reported. In addition, the viscoelastic properties suggest the formation of transient structures in the molten complex.