Nanostructured block copolymer electrolytes (BCE) are currently attracting widespread interest for applications in rechargeable lithium batteries. In order to investigate the influence of the composition, and therefore that of confinement, on the conductivity, a series of triblock PS-PEO-PS copolymers, with three linear PEO blocks of molecular weights 9, 10, or 35 kg mol(-1) and with PEO weight fractions varying from 36% to 75%, were synthesized and doped with LiTFSI. Measurements by impedance spectroscopy of the conductivity show that it increases with PEO molecular weight, which is quite counterintuitive. To explain this phenomenon, the conductivity of the BCE has been modeled using three factors: (1) the conductivity of bulk PEO, (2) the topology of the PEO percolating network, described by the tortuosity parameter, and (3) the influence on the tortuosity of the effective volume fraction of the PEO phase useful for the conduction, taking into account a "dead zone" excluded from ionic transport, at the PS/PEO interface. In this approach, by analogy with porous materials and in contrast with previous work, the tortuosity is not kept constant but depends on the PEO volume fraction effectively useful for charge transport. The thickness of the dead zone, 4-S EO units (similar to 1.6 nm), is the same as that of the exclusion zone for crystallization previously reported. This value does not depend either on the PEO molecular weight (from 9 to 35 kg mol(-1)) or on the EO/Li ratio (from 20 to 30). The absence of both conduction and crystallization in the excluded region could be due to the low mobility of the PEO chains in this zone. Consequently, the conductivity of BCE increases with PEO molecular weight because the proportion of the excluded zone becomes smaller as the PEO molecular weight increases. This model therefore provides a fairly precise description of the ionic conductivity of BCE used in lithium battery applications.