Arylene fluorinated sulfonimide polymers and membranes

1. A polymer comprising repeating units of Formula (I):

wherein Ar is a divalent group of Formula (III), (IV) or (V):

and is optionally substituted with one or more fluorine;

R f is a straight chain, branched or cyclic, perfluorinated alkylene group having from 1 to 20 carbon atoms and optionally substituted with one or more ether oxygens or halogens;

m is 1-6;

p indicates the average number of monomeric units;

M is one or more of monovalent cation;

and Q is S, SO 2 , CO, or CR 1 R 2 , wherein R 1 and R 2 are independently branched or cyclic perfluorinated alkyl groups having 1 to 10 carbon atoms, and wherein R 1 and R 2 can together form a ring.

2. The polymer of claim 1 wherein M is K, Na, Li, or H.

3. The polymer of claim 1 wherein R f is a perfluorinated alkylene group having from 2 to 10 carbon atoms.

4. The polymer of claim 3 wherein R f is a linear, perfluorinated alkylene group having from 2 to 4 carbon atoms.

5. The polymer of claim 1 wherein Ar is a divalent group of Formula (VII), (VIII), or (IX):

6. The polymer of claim 1 wherein m is 1.

7. The polymer of claim 1 wherein Q is SO 2 .

8. The polymer of claim 1 that is a homopolymer.

9. The polymer of claim 1 that is a copolymer.

10. The polymer of claim 1 comprising repeating units of Formula (X):

wherein Ar and Ar′ are independently divalent groups of Formula (III), (IV) or (V), and p and q indicate the average number of monomeric units for each block.

11. A membrane made from the polymer of claim 1 .

12. An electrochemical cell comprising the polymer of claim 1 .

13. A fuel cell comprising the electrochemical cell of claim 12 .