Edge-defined metric buckling of temperature-responsive hydrogel ribbons and rings

We report the temperature-responsive buckling of ribbon-like hydrogel thin films based on photo-crosslinkable copolymers of poly(N-isopropyl acrylamide) (PNIPAM) with pendent benzophenone units. Due to the finite resolution of the photo-lithographic patterning method - here dominated by the convergence of light from the illumination source - nominally homogeneous layers are always surrounded by a more highly swelling border with a lateral size scale similar to the film thickness. As one of the in-plane dimensions of the gel sheet is reduced to only several times its thickness, this edge effect serves as a sufficiently large imperfection to drive buckling of the otherwise metrically flat ribbon. Due to the symmetric geometry, the resulting geometry has essentially constant curvature of the mid-line of the ribbon, with a radius of curvature defined by its thickness and width. In this manner, we prepare thermally responsive overcurved rings that buckle into more highly coiled configurations as they swell, due to the mismatch in metric curvature relative to the geometric shape of the object. We consider the conditions for unfrustrated coiling of both circular and polygonal rings in terms of the number of self-crossings made upon wrapping the surface of a sphere, and demonstrate the fabrication of 'self-cinching unknots', i.e. coiled ribbons that can fasten themselves onto other objects upon deswelling, due to topological constraints.