A branched polyamine comprises about 8 to about 12 backbone tertiary amine groups, about 18 to about 24 backbone secondary amine groups, a positive number n&prime； greater than 0 of backbone terminating primary amine groups, and a positive number q greater than 0 of backbone terminating carbamate groups of formula (2): wherein (n&prime；+q) is a number equal to about 8 to about 12, the starred bond of formula (2) is linked to a backbone nitrogen of the branched polyamine, L&prime； is a divalent linking group comprising 3 to 30 carbons, and q/(n&prime；+q)×100% equals about 9% to about 40%.
