Hyper-branched polymer, electrode and electrolyte membrane including the hyper-branched polymer, and fuel cell including at least one of the electrode and the electrolyte membrane

A hyper-branched polymer, which is a product obtained by performing condensation polymerization reaction of a hyper-branched polymer composition comprising a diisocyanate compound represented by Formula 1 and a dihydroxyamine compound represented by Formula 2;

• N═C═O-A-N═C═O [Formula 1]
• wherein in Formula 1, A is a substituted or unsubstituted C1-C30 alkylene group, a substituted or unsubstituted C2-C30 alkenylene group, a substituted or unsubstituted C2-C30 alkynylene group, a substituted or unsubstituted C6-C30 arylene group, a substituted or unsubstituted C6-C30 heteroarylene group, a substituted or unsubstituted C4-C30 carbon ring group, or a substituted or unsubstituted C6-C30 condensed polycyclic group;
• HO—Ar1—NH—Ar2—OH Formula 2
• wherein in Formula 2, A1 and Ar2 are each independently a substituted or unsubstituted C2-C30 alkenylene group, a substituted or unsubstituted C2-C30 alkynylene group, a substituted or unsubstituted C6-C30 arylene group, a substituted or unsubstituted C6-C30 heteroarylene group, a substituted or unsubstituted C4-C30 carbon ring group, or a substituted or unsubstituted C6-C30 condensed polycyclic ring group.