NOVELTY - Polymer comprising at least one repeating unit containing at least one benzimidazolium-containing moiety (A) is new.    USE - The polymer is useful for incorporated into a catalyst layer of a fuel cell (claimed) electrolyzers.    ADVANTAGE - The polymer provides the fuel cell that exhibits high efficiency, low emission, and low cost energy converter and is soluble in methanol, isopropanol, and dimethylsulfoxide.    DETAILED DESCRIPTION - Polymer comprising at least one repeating unit containing at least one benzimidazolium-containing moiety of formulas (I)-(V) is new.    R1 = methyl, trifluoromethyl, alkyl, perfluoroalkyl, heteroalkyl, alkoxy, perfluoroalkoxy, halo, aryl, heteroaryl or polymer;    R2 = H, any group or polymer;    R3 = methyl, trifluoromethyl, alkyl, perfluoroalkyl, heteroalkyl, aryl, aralkyl, or polymer;    R5 = H, any group, and a polymer;    at least one of R1, R2, R3, R5 = polymer; and    X = alkylene, perfluoroalkylene, heteroalkylene, arylene, aralkylene, and no group.    INDEPENDENT CLAIMS are also included for:    (1) substituted benzimidazolium compounds of formula (VIII);    (2) ionic membrane comprising a cationic polymer;    (3) ionomer comprising the cationic polymer;    (4) post-functionalizing a polymer containing a benzimidazole moiety in a repeating unit to provide a neutral polymer containing a repeat unit of benzimidazolium formula (VI), comprising deprotonating the polymer containing the benzimidazole moiety with an alkali hydroxide by heating in a polar aprotic solvent and optionally an amount of water to provide a deprotonated benzimidazole containing polymer, optionally filtering and washing the deprotonated benzimidazole containing polymer, adding excess R-Y1 to the polymer solution and stirring to provide a neutral polymer containing a repeat unit (VI);    (5) post-functionalizing a neutral polymer containing a repeat unit of (VI) to a cationic polymer containing a benzimidazole-containing moiety of (I), (V), and (VI), comprising dissolving a neutral polymer containing a repeat unit of (VI) in an organic solvent to provide a polymer solution, and adding a known amount of R-Y1 to the polymer solution and stirring the polymer solution for a period of time to provide a cationic polymer containing (I), (V), and (VI); and    (6) forming polymer.    R11a-R11d, R21a-R21d, R31a-R31d = 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, or heteroaryl;    R12a-R12d, R22a-R22d, R32a-R32d = H, 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, or heteroaryl;    R13a, R13b, R14a, R14b, R23a, R23b, R24a, R24b = absent, 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, or heteroaryl;    R33a, R33b, R34a, R34b = 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, and heteroaryl;    R15a-R15f, R25a-R24f, R35a-R35f = H, 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, or heteroaryl;    X11, X21, X31 = absent, 1-6C alkylene, 1-6C haloalkylene, arylene, or heteroarylene, where A and B1 are point of attachments of the individual monomers and s, b, and c mole percentages;    s = 0-45 mol.%;    b+c = 55-100 mol.%;    b, c = more than 0 mol.%;    R = methyl, trifluoromethyl, alkyl, perfluoroalkyl, heteroalkyl, aryl, or aralkyl group; and    Y1 = anionic leaving group comprising iodide, bromide, chloride, or sulfonate ester.    Provided that: two of R13a, R13b, R14a, and R14b are absent, and the remaining two are present and are 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, or heteroaryl; and one of R23a, R23b, R24a and R24b is absent, and the remaining three are present and are 1-6C alkyl, 1-6C haloalkyl, 1-6C alkoxy, 1-6C haloalkoxy, halo, aryl, and heteroaryl.