Topographical patterns are used to selectively tune the adhesion of polymers. Although nature has provided guidance, relatively little is known of how topographic patterns can be intelligently used not only to enhance adhesion but, more importantly, to tune adhesion. We demonstrate that properly designed, low-aspect-ratio posts can alter adhesion from 20% to 400% the value of conventional adhesion descriptors for nonpatterned interfaces. This control is not related to the magnitude of interfacial area but, rather, to altering the local separation processes at an interface by geometry. We establish general relationships that govern the interaction between material properties, pattern length scales, and the control of adhesion. These relationships provide insight into the mechanisms of adhesion for examples in nature, such as the gecko, while also providing concrete guidance for the future design of "smart" adhesives and coatings with nanoscale patterns.

A language-theoretic definition of word hyperbolic semigroup is given, which coincides with the original definition for a group. Word problems of semigroups are also considered.

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