Provided are polymer modified substrates which comprise a) a substrate, b) a binding layer covalently attached to the surface of the substrate and covering at least a part of this surface; and c) a polymer brush formed by a plurality of polymer chains, each of which is covalently attached at one of its terminals to the binding layer. Moreover, methods are provided, for the preparation of the polymer modified substrates by polymerizing vinyl group containing monomers, such as vinylphosphonates, on a binding layer provided on a substrate.