Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

An innovative self-healing polydimethylsiloxane (PDMS) elastomer, namely, PDMS-TFB, is reported by incorporating the reversibly dynamic imine bond as the self-healing points into the PDMS networks. The PDMS-TFB elastomer features good optical transmittance (80%) in full visible light region, high stretchability (≈700%), and excellent autonomous self-healing ability at room temperature. Surprisingly, the self-healing behavior can take place in water and even at a temperature as low as -20 °C in air, showing a promising outlook for broader applications. As a proof-of-concept, this study demonstrates the use of the PDMS-TFB elastomer for preparing anticorrosion coating and adhesive layer, and also the use of such an elastomer to be the platform for fabricating the flexible interconnector and chemical sensor. Remarkably, no significant difference is observed between the pristine and healed samples. Taking full advantage of these unique properties, it is anticipated that such a PDMS-TFB elastomer shows wide applications in the fields of materials science, electronics, biology, optics, etc.

The design of artificial receptors for sulfate ions is of great interest because of the importance of sulfate ions in environmental and biological systems.[1] One of the applications of sulfate ion receptors is extraction of the sulfate ion from nitrate-rich mixtures in the remediation of nuclear waste. [2] Based on liquid-liquid anion exchange technology, extraction of sulfate ions from an aqueous to an organic phase was realized by using macrocyclic receptors.[ ) of the receptor were needed in this case to ensure applicable extraction. Hence, the extraction efficiency has yet to be improved for sulfate ion extractants. This aim is quite challenging because of the extremely large hydration energy of the sulfate ion (DG h = À1080 kJ mol À1 for SO 4 2À compared to À300 kJ mol À1 for NO 3 À ) [3] according to the Hofmeister series, [4] as well as the high nitrate/sulfate ratios present in the crude waste. To overcome the Hofmeister bias, which disfavors the separation of the extremely hydrophilic sulfate ion from water, the receptor must have both excellent affinity and selectivity for sulfate ions.In recent years, some receptors for sulfate ions have been synthesized by employing different binding groups (mostly NH moieties), such as protonated Schiff base macrocycles, [5] diindolylureas, [6] and an M 4 L 6 cage containing a bipyridinefunctionalized monourea; [7] these receptors bind the anion in the 1:1, 3:1 and 6:1 (host/guest) mode, respectively. The trenbased tripodal trisurea backbone (L 1 ; tren = tris(2-aminoethyl)amine) has also been found to encapsulate the sulfate ion in a 2:1 (host/guest) ratio. [8] Although saturated coordination (12 hydrogen bonds) for sulfate and phosphate ions has been achieved by these receptors, the complementarity for the ions is not optimal in most cases. Calculations have demonstrated that the optimal saturated coordination mode for sulfate ions is binding in a tetrahedral cavity with 12 hydrogen bonds along the edges. [9] In this regard, the ideal sulfate ion receptor would possess a complementary tetrahedral cavity surrounded by 12 optimally arranged binding sites.The chelate effect may also play an important role in the host-guest binding affinity because of the favorable contributions from both entropy and enthalpy. As a typical example of the chelate effect, the Co 2+ complex of the bidentate ligand 1,2-diaminoethane is 10 8 times more stable than that of the unidentate ligand ammonia.[10] Moreover, the hexadentate ligand ethylenediaminetetraacetic acid (EDTA) displays extremely high binding affinities toward most metal ions (for example, 10 14.3 m À1 for Fe 2+ and 10 16.3 m À1 for Co 2+ ).[11]Given the similarities between anion coordination and classical transition-metal coordination chemistry, [12] increasing the number of binding sites to achieve high chelate effects should be an effective way to improve the extraction efficiency of sulfate ion extractants.We have devoted our efforts to the synthesis of selective anion receptors based on the urea functionality. [8a...