Single-ion-conducting block copolymers are of considerable interest as electrolytes for battery systems, as they eliminate overpotentials due to concentration gradients. In this study, we characterize a library of poly(ethylene oxide) (PEO)based diblock copolymers where the second block is poly (styrene-4-sulfonyltrifluor omethylsulfonyl) imi de with either cation: univalent lithium or divalent magnesium counterions (PEO-PSLiTFSI or PEO-P[(STFSI)(2)Mg]). The PEO chain length is held fixed in this study. Polymers were synthesized in matched pairs that were identical in all aspects except for the identity of the counterion. Using rheology, SAXS, DSC, and AC impedance spectroscopy, we show that the dependence of morphology, modulus, and conductivity on composition in these charged copolymer systems is fundamentally different from uncharged block copolymers. At a given frequency and temperature, the shear moduli of the magnesiated copolymer systems were approximately 3-4 orders of magnitude higher than those of the matched lithiated pair. The shear moduli of all of the lithiated copolymers showed liquid-like rheological features while the magnesiated copolymers did not. All of the lithiated copolymers were completely disordered (homogeneous), consistent with the observed rheological properties. As expected, the moduli of the lithiated copolymers increased with increasing volume fraction of the ion-containing block (phi(PSTFSI)), and the conductivity decreased with phi(PSTFSI) However, the magnesiated copolymers followed a distinct trend. We show that this was due to the presence of microphase separation in the regime 0.21 <= phi(PSTFSI) <= 0.36, and the tendency for microphase separation became weaker with increasing phi(PSTFSI). The magnesiated copolymer with phi(PSTFSI) = 0.38 was homogeneous. The morphological, rheological, and conductivity properties of these systems' are governed by the affinity of the cations for PEO chains; homogeneous systems are obtained when the cations migrate from the ion-containing block to PEO.