Provided are polymers obtained by radical copolymerization of a mixture of (1) acrylic acid; (2) methacrylic acid; and (3) at least one allylcatechol selected from 4-allylbenzene-1,2-diol, 3-allylbenzene-1,2-diol and mixtures thereof. The polymers are especially useful for treating a metallic surface intended to be coated by a paint, a varnish or an adhesive. Also provided are methods of coatings making use of this polymer P, compositions comprising the polymer P and useful for these methods, and the obtained coated materials.