Self-actuating materials capable of transforming between three-dimensional shapes have applications in areas as diverse as biomedicine, robotics, and tunable micro-optics. We introduce a method of photopatterning polymer films that yields temperature-responsive gel sheets that can transform between a flat state and a prescribed three-dimensional shape. Our approach is based on poly(N-isopropylacrylamide) copolymers containing pendent benzophenone units that allow cross-linking to be tuned by irradiation dose. We describe a simple method of halftone gel lithography using only two photomasks, wherein highly cross-linked dots embedded in a lightly cross-linked matrix provide access to nearly continuous, and fully two-dimensional, patterns of swelling. This method is used to fabricate surfaces with constant Gaussian curvature (spherical caps, saddles, and cones) or zero mean curvature (Enneper's surfaces), as well as more complex and nearly closed shapes.

The process by which spatial variations in growth transform twodimensional elastic membranes into three-dimensional shapes is both a fundamentally interesting mechanism of shape selection and a powerful tool for the preparation of responsive materials. From the perspective of lithographic patterning of thin gel sheets, it is most straightforward to prepare materials consisting of discrete regions with different degrees of swelling. However, the sharp variations in swelling at the boundaries between such regions make it impossible for the sheet to adopt a configuration that is free of in-plane stresses everywhere. Thus, the deformation of such materials is not well understood. Here, we consider the geometrically simple case of a photo-crosslinkable poly(N-isopropylacrylamide) copolymer patterned into thin rectangular strips divided into one high-and one low-swelling region. When swelled in an aqueous medium at 22 C, the sheet rolls into a three-dimensional shape consisting of two nearly cylindrical regions connected by a transitional neck. Heating to 50 C leads to fully reversible de-swelling back to a flat configuration. We propose a scaling argument based on a balance between stretching and bending energies that relates the curvature of the 3D shape to the width and thickness of the strip, find good agreement with experimental data and numerical simulations, and further demonstrate how this simple geometry provides a powerful route for the fabrication of self-folding stimuli-responsive micro-devices.

In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts migration towards the flow centerline.

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.

We explore a surprising phenomenon in which an obstruction accelerates, rather than decelerates, a moving flexible object. It has been claimed that the right kind of discrete chain falling onto a table falls faster than a free-falling body. We confirm and quantify this effect, reveal its complicated dependence on angle of incidence, and identify multiple operative mechanisms. Prior theories for direct impact onto flat surfaces, which involve a single constitutive parameter, match our data well if we account for a characteristic delay length that must impinge before the onset of excess acceleration. Our measurements provide a robust determination of this parameter. This supports the possibility of modeling such discrete structures as continuous bodies with a complicated constitutive law of impact that includes angle of incidence as an input.