The invention relates to a method for producing copolymers by
solution polymerization based on at least 1, 3-butadiene and at least one
hydrocarbon which is different from 1, 3-butadiene and contains at least one olefinic
double bond as monomers, using one or more
organolithium compounds as initiators, wherein the
polymerization is carried out at a temperature of the reaction mixture of 0 DEG C to 50 DEG C and a pressure of 0.2 MPa to 0.6 MPa, and wherein 55% to 65% by weight, based on the total
mass of monomers, of 1, 3-butadiene is added to the reaction mixture; a
copolymer comprising units derived from 1, 3-butadiene and units derived from, as monomers, at least one
hydrocarbon different from 1, 3-butadiene and comprising at least one olefinic
double bond wherein the
copolymer comprises
monomer units derived from 1, 3-butadiene of formulae (A), (B) and (C) wherein all of the units derived from 1, 3-butadiene present in the
copolymer are units derived from 1, 3-butadiene of formula (A), (B) and (C). The proportion of (A) is at least 80 mol% among monomeric units derived from 1, 3-butadiene present in the
polybutadiene, and wherein the sum of the proportions of (B) and (C) is not more than 20 mol% among all monomeric units derived from 1, 3-butadiene present in the
polybutadiene, and wherein the copolymer has a number average molecular weight Mn of from 2,000 g / mol to 5,400 g / mol and a
glass transition temperature TG of from-15 DEG C to 5 DEG C; and to the use of the copolymers according to the invention as reactive cross-linking agents.