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.

Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds, highlighting a connection between mechanical metamaterials and programmable matter. Given origami's scale-free geometric character, this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.

Self-folding microscale origami patterns are demonstrated in polymer films with control over mountain/valley assignments and fold angles using trilayers of photo-crosslinkable copolymers with a temperature-sensitive hydrogel as the middle layer. The characteristic size scale of the folds W = 30 μm and figure of merit A/ W (2) ≈ 5000, demonstrated here represent substantial advances in the fabrication of self-folding origami.

Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.PACS numbers: 61.30. Dk, 61.30.St,61.46.Bc Entropy is a potent force in the theory of selfassembly. It can be argued, through entropic considerations alone, that hard spheres will self-assemble into the face-centered-cubic (fcc) lattice or any of its many variants related through stacking faults. As a result, when a material exhibits an fcc phase, it is often attributed to the optimality of the close-packed lattice. When less common or less dense lattices are formed, all sundry of explanations are invoked, ranging from quantum mechanics [1], lattice effects [2], partially filled Landau levels [3], and even soft interactions [4,5]. While there has been concerted effort to tailor the pair interaction to achieve a desired periodic arrangement [6] this must be done in the context of those packing motifs that arise from generic interactions. For instance, it would be no trick to tailor a potential to make an fcc lattice.With this in mind, here we consider a seemingly simple extension of the hard sphere model, namely a hard core interaction of radius σ with a soft shoulder of radius σ s and height ǫ (HCSS):When σ s /σ 1 this potential models hard spheres with a soft pair repulsion and was used to study isostructural transitions in Cs and Ce [7]. In generic repulsive potentials, it has been shown that as the range of the soft repulsion grows (corresponding to σ s /σ ≈ 2) a rich variety of density-modulated ground states appear [8, 9, 10] which can be characterized as periodic arrangements of regular sized clusters of the original spheres. In this Letter we establish a sufficient condition on the pair potential for clustering and the subsequent ordering of the clusters which generalizes results on soft potentials without hard cores [11]. We develop a self-consistent field theory for soft repulsion and use it to study the formation of striped phases. We corroborate our analytic treatment with numerical solutions that also predict the existence of hexagonal and inverted hexagonal phases with both fluid and crystalline order in the clusters, as shown in Fig. 1. We also present results from Monte Carlo simulations of the HCSS potential which both stimulate and support the more general results. In all cases, we find that over the range of stable aggregate structures the lattice constant remains fixed while the clusters change their size and morphology so as to maint...