Polymer Brushes on Flat and Curved Substrates: Scaling Concepts and Computer Simulations

The scaling concepts for isolated flexible macromolecules in good solvent grafted with one chain end to a flat surface (polymer mushrooms) as well as for layers of many overlapping end-grafted chain molecules (polymer brushes) are introduced. Monte Carlo attempts to test these concepts are briefly reviewed. Then the extension of these concepts to polymer brushes grafted to the interior of a cylinder surface is discussed. Molecular Dynamics results on chain average linear dimensions in the direction normal to the grafting surface and in axial direction are described, as well as distribution functions for the density of end monomers and of all monomers of the chains. It is argued that under typical conditions reachable in either simulation or experiment the data fall in a crossover regime, where no simple power-laws (as derived from the scaling description) hold. Moreover, extensions of the Daoud-Cotton blob picture to the cylinder geometry, implying that each chain in such a cylindrical brush is confined into a conical sector, are invalid; thus, chain ends in densely filled cylinders are not restricted to stay in the hemicylinder containing the grafting site of the chain.