A polymer comprises randomly distributed units UA, UB, UC and UD and at least one unit bearing a subunit F according to the respective molar percentages m, n, o, p and f F pendant along the chain of the polymer and bearing an associative group comprising at least one nitrogen atom, R1 and R2, which are identical or different, denoting a hydrogen atom, a methyl radical or a phenyl radical which is unsubstituted or substituted in the ortho, meta or para position by a methyl radical, m≥50, n≥0, o≥0, f>0, 0