Effect of surface undulation on polymer adsorption

Abstract

We study the adsorption of a long, flexible polymer (ideal or self-avoiding chain) interacting with a rough surface via a finite-range attraction. Within the Edwards equation approach, we develop a variational method to find the segmental distribution and the free energy of an adsorbed chain. As adsorption becomes strong, the segments tend to be localized within the valleys rather than above the hills of the undulating surface, resulting in a decrease of adsorption thickness. Consequently, the surface undulation enhances adsorption in the case of a strongly adsorbed chain whereas the undulation suppresses it for a weakly adsorbed one, since the enhanced entropic repulsion is dominant over the attraction from the surface. Considering the surface with undulation characterized by a Gaussian correlation as an example, we find an optimal correlation length at which the adsorption becomes the strongest and a critical correlation length below which desorption is induced.