Thin membranes exhibit complex responses to external forces or geometrical
constraints. A familiar example is the wrinkling, exhibited by human skin,
plant leaves, and fabrics, resulting from the relative ease of bending versus
stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest
known membrane, deposited on a silica substrate decorated with silica
nanoparticles. At small nanoparticle density monolayer graphene adheres to the
substrate, detached only in small regions around the nanoparticles. With
increasing nanoparticle density, we observe the formation of wrinkles which
connect nanoparticles. Above a critical nanoparticle density, the wrinkles form
a percolating network through the sample. As the graphene membrane is made
thicker, global delamination from the substrate is observed. The observations
can be well understood within a continuum elastic model and have important
implications for strain-engineering the electronic properties of graphene.Comment: 11 pages, 8 figures. Accepted for publication in Physical Review
