Shape insensitive optimal adhesion of nanoscale fibrillar structures

Gecko and many insects have adopted nanoscale fibrillar structures on their feet as adhesion devices. Here, we consider adhesion between a single fiber and a substrate by van der Waals or electrostatic interactions. For a given contact area A, the theoretical pull-off force of the fiber is sigma(th)A where sigma(th) is the theoretical strength of adhesion. We show that it is possible to design an optimal shape of the tip of the fiber to achieve the theoretical pull-off force. However, such design tends to be unreliable at the macroscopic scale because the pull-off force is sensitive to small variations in the tip shape. We find that a robust design of shape-insensitive optimal adhesion becomes possible only when the diameter of the fiber is reduced to length scales on the order of 100 nm. In general, optimal adhesion could be achieved by a combination of size reduction and shape optimization. The smaller the size, the less important the shape. At large contact sizes, optimal adhesion could still be achieved if the shape can be manufactured to a sufficiently high precision. The robust design of optimal adhesion at nanoscale provides a plausible explanation for the convergent evolution of hairy attachment systems in biology.