A
polyimide, comprising 1-100 mol % of repeating units of formula (1), based on 100 mol % of total repeating units of the
polyimide, wherein each V is as defined herein; and each R1 is independently a
divalent group of formula (3), wherein A is anionic, and each A is independently —O, —S, —S(O)2, —S(O)2O, —OS(O)2O, —OP(O) (OR)dO, —P(O)(Re)O, —P(O)(ORf)O, or —OP(O)(Rg)O; and X is cationic, and each X is independently Li, Na, K, Cs, Mg, Ca, Sr, Cr, Mn, Fe, Co, Ni, Cu, Ag, Zn, Cd, B, Al, Ga, In, Ge, Sn, Pb, As, Sb,
phosphonium, imidazolium, guanidinium, or
pyridinium; and Rd, Re, Rf, and Rg are each independently
hydrogen, substituted or unsubstituted C1-8
alkyl, or substituted or unsubstituted C6-12
aryl.