Fabrication of gecko foot-hair like nano structures and adhesion to random rough surfaces∗

In this work the effect of substrate roughness on the adhesion of gecko foot-hair like nano structures as opposed to solid elastic materials is described and models of both synthetic nano-hairs and hair-substrate interaction are developed. First, by combining linear beam theory and geometric constraints, a nonlinear elastic model for the hair is derived. Then it is shown how for a given random surface, once its Zero Order Hold (ZOH) model is acquired through Atomic Force Microscopy, only the height distribution is needed to compute pull-off forces. In the effort of replicating gecko foot-hair adhesive properties, we synthesized arrays of nano hairs by casting polyurethane into a nano-pore array. Hairs of controlled size, in the range of 20-60 microns long and 200 nanometers thick, were thus fabricated, imaged via Scanning Electron Microscope (SEM). Elastic properties of polyurethane are measured and then fed into a model, based on cantilever beam theory, which, together with the height distribution of sample surfaces, provides a prediction for pull-off forces as well as a description of the hysteresis phenomena arising in push-in/pull-off cycles.