Crosslinking of hydroxide stable, polybenzimidazoliums and polyimidazoliums membranes and ionomers

A crosslinked polymer comprising repeating units of the following Formulas (IV-A), (IV-B), (IV-C), and (IV-D)

• wherein
• R1a, R2a, R4a, and R5a are each independently selected from a bond, alkyl, perfluoroalkyl, heteroalkyl, aryl, aralkyl, and a crosslinking moiety, provided that two of R1a, R2a, R4a, and R5a is each independently selected from a crosslinking moiety and a bond, wherein the bond is configured to connect to a crosslinking moiety;
• and the remaining two of R1a, R2a, R4a, and R5a are each independently selected from alkyl, perfluoroalkyl, heteroalkyl, aryl, and aralkyl;
• R1b, R2b, R4b, and R5b are each independently absent or R1b, R2b, R1b, and R5b are each independently selected from a bond, alkyl, perfluoroalkyl, heteroalkyl, aryl, aralkyl, and a crosslinking moiety, provided that one of R1b, R2b, R4b, and R5b is selected from a crosslinking moiety and a bond, wherein the bond is configured to connect to a crosslinking moiety;
• when one of R1b, R2b, R4b, and R5b is absent, the imidazolyl group wherein one of R1b, R2b, R4b, and R5b is absent is neutral;
• and the remaining two of R1b, R2b, R4b, and R5b are each independently selected from alkyl, perfluoroalkyl, heteroalkyl, aryl, and aralkyl;
• R1c, R2c, R4c, and R5c are each independently selected from a bond, alkyl, perfluoroalkyl, heteroalkyl, aryl, aralkyl, and a crosslinking moiety, provided that one of R1c, R2c, R4c, and R5c is selected from a crosslinking moiety and a bond which is configured to connect to a crosslinking moiety and the remaining three of R1c, R2c, R4c, and R5c are each independently selected from alkyl, perfluoroalkyl, heteroalkyl, aryl, and aralkyl,
• R1d, R2d, R4d, and R5d are each independently selected from alkyl, perfluoroalkyl, heteroalkyl, aryl, and aralkyl;
• R3a, R6a, R3b, R6b, R3c, F6C, R3d, and R6d re each independently selected from alkyl, perfluoroalkyl, heteroalkyl, aryl, aralkyl, and heteroaryl;
• R7a, R10a, R11a, R14a, R7b, R10b, R11b, R14b, R7c, R10c, R11c, R14c, R7d, R10d, R11d, and R14d are each independently selected from alkyl, perfluoroalkyl, and heteroalkyl;
• and
• R8a, R12a, R8b, R12b, R8c, R12c, R8d, and R12d are each independently selected from hydrogen, alkyl, perfluoroalkyl, and heteroalkyl,
• wherein at least one of R1a, R2a, R4a, R5a, R1b, R2b, R4b, R5b, R1c, R2c, R4c, and R5c is a crosslinking moiety, and at least one of the remaining R1a, R2a, R4a, R5a, R1b, R2b, R4b, R5b, R1c, R2c, R4c, and R5c is a bond which is connected to the crosslinking moiety such that at least two repeating units of Formulas (IV-A), (IV-B), and (IV-C) are crosslinked,
• wherein the crosslinked polymer comprises r mole percentage repeating units of Formula (IV-A), s mole percentage repeating units of Formula (IV-B), t mole percentage of repeating units (IV-C), and u mole percentage of repeating units (IV-D), and
• r is from 1 mole percent to 95 mole percent,
• s is from 1 mole percent to 50 mole percent,
• t is from 1 mole percent to 95 mole percent,
• u is from 5 mole percent to 95 mole percent, and
• r+s+t+u=100 mole percent.