This invention discloses a rubbery polymer which is comprised of repeat units that are derived from (1) at least one conjugated diolefin monomer, and (2) at least one leaving group-bearing monomer having the structural formula: ##STR1##

wherein R represents an alkyl group containing from 1 to about 10 carbon atoms or a hydrogen atom, wherein R represents a methyl group or a hydrogen atom, with the proviso that if R represents an alkyl group then R represents a hydrogen atom, and wherein R¹ and R² can be the same or different, wherein R¹ represents an alkyl group that is functionalized with a leaving group, wherein R² represents a moiety selected from the group consisting of hydrogen atoms, alkyl groups containing from 1 to 18 carbon atoms, aryl groups containing from 6 to 18 carbon atoms, alkaryl groups containing from 7 to 18 carbon atoms, and alkyl groups that are functionalized with a leaving group.