Adhesion of membranes and filaments on rippled surfaces

Adhesion of membranes and filaments on periodic rippled surfaces is studied by means of a one-dimensional model. The adhesion behavior is found to depend crucially on the shape of the ripples. Fakir-carpet and sinusoidal patterns are studied in detail. Infinite staircases of periodic,ground states are found, with a periodicity diverging at a transition line. Moreover, the boundaries of the regions of existence of metastable states form a complex sequence on the fakir-carpet surface. This is inferred to lead to an unbinding transition by progressive stages when fluctuations are negligible. The occurrence of adhesion transitions for graphene, carbon nanotubes, and lipidic membranes is discussed quantitatively.