Polymer adsorption and electron binding on rough and fractal surfaces

Mean-field theory is used to study the adsorption of polymer chains on a rough surface, both with and without excluded-volume interactions. In particular, the adsorption on a fractal surface generated from a hierarchy of small-amplitude sinusoidal perturbations is investigated. It is found that there is a simple scaling relation between the concentration of adsorbate on a fractal and on a plane boundary. Surface irregularity greatly enhances the adsorption of polymer. The probelm is mathematically equivalent to the binding of quantum mechanical particles by rough interfaces.