A proton-conducting polymer comprises a plurality of repeating units of formula (I) for electrochemical reactions. The polymer may be synthesized from a super acid catalyzed polyhydroxyalkylation reaction of monomers Ar1', Ar2', and X1 (I) followed by a nucleophilic substitution reaction or a grafting reaction, and optionally an acidification reaction. Proton-exchange membranes and membrane electrode assemblies made from the polymer are also described.