Swelling-driven rolling and anisotropic expansion of striped gel sheets

Swelling of spatially patterned gel films promises many new opportunities for understanding and exploiting differential growth as a means to define three-dimensional (3D) configurations of thin sheets. Here, we consider the swelling-driven deformation of sheets patterned with alternating parallel strips of material with high and low equilibrium extents of swelling, and the dependence of this process on film thickness, strip width, and swelling contrast. Temperature-responsive, photo-crosslinkable hydrogels are prepared from poly(N-isopropyl acrylamide) (PNIPAm) copolymers with pendent benzophenone groups that allow the degree of crosslinking to be programmed by the dose of UV light. Photo-patterned multi-strips deform by rolling around the axis perpendicular to the interface between high- and low-swelling regions, due to a balance between stretching energy in the transition region and bending of the entire sheet. However, when the strip width falls below a critical size proportional to the film thickness, the patterned sheets instead remain flat, undergoing greater expansion along the direction normal to the interfaces than in the direction parallel. This configuration suggests possibilities for patterning anisotropic growth, and also provides fruitful information on the contrast in modulus between the regions.