Polymer adsorption on surfactant monolayers and heterogeneous solid surfaces

We study polymer adsorption on a flat but heterogeneous surface, in both cases where the heterogeneity is quenched or annealed. We always find that the heterogeneity of the adsorbing surface enhances adsorption. As an example of surface with annealed heterogeneity we consider either soluble surfactant monolayers (at a fixed chemical potential) or insoluble (at a fixed concentration) for attractive interactions between polymer and surfactant. Even if the monolayer is on average neutral for polymer adsorption an isolated polymer chain adsorbs $via$ a local increase of the surfactant surface concentration. The adsorption of a polymer solution can induce phase transitions in an insoluble monolayer that phase separates into dense regions where the polymer adsorbs and dilute regions from which the polymer is depleted. Phase transitions induced by polymer adsorption can also occur for soluble monolayer. For a surface with periodic quenched heterogeneities we calculate the amount of adsorbed polymer as a function of the wavelength of the heterogeneity