Daily-life foldable items, such as popup tents, the curved origami sculptures exhibited in the Museum of Modern Art of New York, overstrained bicycle wheels, released bilayered microrings and strained cyclic macromolecules, are made of rings buckled or folded in tridimensional saddle shapes. Surprisingly, despite their popularity and their technological and artistic importance, the design of such rings remains essentially empirical. Here we study experimentally the tridimensional buckling of rings on folded paper rings, lithographically processed foldable microrings, human-size wood sculptures or closed arcs of Slinky springs. The general shape adopted by these rings can be described by a single continuous parameter, the overcurvature. An analytical model based on the minimization of the energy of overcurved rings reproduces quantitatively their shape and buckling behaviour. The model also provides guidelines on how to efficiently fold rings for the design of space-saving objects.

By confining discotic phthalocyanines in a network of crisscrossed nanogrooves, we obtain a uniaxial alignment of the columnar mesophase. The alignment process is based on the anisotropy of interface tension between the mesophase and the nanogrooves' walls. Preferential mesophase alignment results from this nonhomogeneity combined with the anisotropy of the network cell dimensions. A simple model is proposed to explain the experimental observations.

ÃÃ ] We thank D. Serban, A. Vlad, S. Faniel, L. Gence and B. Hackens for suggestions and discussions. We are grateful to the WINFAB technical team, P. Lipnik, P. Viville, P. Damman for help with experiments.

The stability of the polar Zn-terminated ZnO surface is probed by low-temperature scanning tunneling microscopy and scanning tunneling spectroscopy (STS). Surface states in the bandgap of ZnO are evidenced by STS and their presence is correlated with the local surface corrugation. Very defective surface regions are characterized by a bulk electronic structure showing a wide bandgap while nanometer-scale defect free regions exhibit a narrower bandgap and surface states. We also image atomically resolved (3×3)R30° reconstructions on the defect-free areas.