Provided are compositions including a core moiety and a plurality of polymeric units, in which at least one of these can include an ionizable moiety or an ionic moiety. The core moiety may be a multivalent core moiety, trivalent core moiety, tetravalent core moiety, pentavalent core moiety, or multivalent arylene moiety. Materials, electrochemical cells, and methods using such compositions are also described.