New polymer compositions based on poly(2,6-dimethyl-1,4-phenylene oxide) and other high-softening-temperature polymers are disclosed. These materials have a microphase domain structure that has an ionically-conductive phase and a phase with good mechanical strength and a high softening temperature. In one arrangement, the structural block has a softening temperature of about 210° C. These materials can be made with either homopolymers or with block copolymers.