28. Simon, C. & Irvine, W. Robust long-distance entanglement and a loophole-free Bell test with ions andphotons. Phys. Rev. Lett. 91, 110405 (2003).29. Cabrillo, C., Cirac, J. I., Garcia-Fernandez, P. & Zoller, P. Creation of entangled states of distant atomsby interference. Phys. Rev. A 59, 1025–1033 (1999).30. Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement andquantum error correction. Phys. Rev. A 54, 3824–3851 (1996).Acknowledgements We acknowledge discussions with M. Madsen, P. Haljan, M. Acton andD. Wineland, and thank R. Miller for assistance in building the trap apparatus. This work wassupported by the National Security Agency, the Advanced Research and Development Activity,under Army Research Office contract, and the National Science Foundation InformationTechnology Research Division.Competing interests statement The authors declare that they have no competing financialinterests.Correspondence and requests for materials should be addressed to B.B. ([email protected])...............................................................Supramolecular dendriticliquid quasicrystalsXiangbing Zeng1, Goran Ungar1, Yongsong Liu1, Virgil Percec2,Andre´s E. Dulcey2& Jamie K. Hobbs31Department of Engineering Materials, University of Sheffield, SheffieldS1 3JD, UK2Roy & Diana Vagelos Laboratories, Department of Chemistry, University ofPennsylvania, Philadelphia, Pennsylvania 19104-6323, USA3H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK.............................................................................................................................................................................A large number of synthetic and natural compounds self-organize into bulk phases exhibiting periodicities on the 1028–1026metre scale1as a consequence of their molecular shape,degree of amphiphilic character and, often, the presence ofadditional non-covalent interactions. Such phases are found inlyotropic systems2(for example, lipid–water, soap–water), in arange of block copolymers3and in thermotropic (solvent-free)liquid crystals4. The resulting periodicity can be one-dimensional(lamellar phases), two-dimensional (columnar phases) or threedimensional (‘micellar’ or ‘bicontinuous’ phases). All such two-and three-dimensional structures identified to date obey therules of crystallography and their symmetry can be described,respectively, by one of the 17 plane groups or 230 spacegroups. The ‘micellar’ phases have crystallographic counterpartsin transition-metal alloys, where just one metal atom is equiva-lent to a 1032 104-atom micelle. However, some metal alloys areknown to defy the rules of crystallography and form so-calledquasicrystals, which have rotational symmetry other than theallowed two-, three-, four- or six-fold symmetry5. Here we showthat such quasiperiodic structures can also exist in the scaled-upmicellar phases, representing a new mode of organization in softmatter.Research on bulk nanoscale self-assembly of organic matter ispartly motivated by the fact that such complex structures may serveas scaffolds for photonic materials6and other nanoarrays, or asprecursors for mesoporous ceramics or elements for molecularelectronics. Larger biological objects, such as cylinder-like orsphere-like viruses, also pack on similar macrolattices7.Dendrons and dendrimers (tree-like molecules8) are provingparticularly versatile in generating periodic nanostructures(Fig. 1). Two micellar lattices, with space groups Im3¯m (body-centred cubic, b.c.c.)9, and Pm3¯n (refs 10, 11), have been estab-lished. An analogue of the Im3¯m phase has also been observed inblock copolymers12, and that of the Pm3¯n phase in lyotropic liquidcrystals13. Recently, a complex three-dimensional (3D) tetragonallattice (space group P42/mnm) was found, having 30 self-assembledmicelles in the unit cell (Fig. 1f)14.In many dendron systems, thermal transitions between thephases in Fig. 1 occur. The master sequence Colh! Pm 3n !P42=mnm ! Im 3m is obeyed with increasing temperature; in onlya handful of cases are all these phases displayed in the same material.In a number of compounds, however, an additional unidentifiedphase has been observed below any other 3D phase but above Colh.A small-angle X-ray powder diffractogram of this phase, recordedon dendron I (Fig. 1g), is shown in Fig. 2a. The synthesis of I isdescribed in ref. 15 and Supplementary Information, wherethis compound is labelled [3,4,5-(3,5)2]12G3CH2OH. Othercompounds that show the X-ray signature of this phase include(4-3,4,5-3,5)12G2CH2OH, [4-(3,4,5)2]12G2COOH, [3,4-(3,5)2]12G3COOH, [3,4-(3,5)2]12G3CH2OH, [3,4-(3,4,5)2]12G3CH2OH(ref. 15), polyoxazolines with tapered side groups containing alkylchains of different lengths16, as well as certain salts of 3,4,5-tris-(n-alkoxy)benzoic acid17.On heating, compound I shows the following phase sequence:room temperature !X ! 71 8C ! P42=mnm ! 728C! isotropicliquid, while on cooling phase X forms directly from the liquid(Supplementary Information). This allowed us to grow mono-domains of the unknown phase. That phase X is a quasicrystal isrevealed by the distinctive but crystallographically forbidden12-fold symmetry of the small-angle X-ray single-crystal pattern(Fig. 2b). When the sample is rotated around the 12-fold axis withthe incident beam perpendicular to the axis, the diffraction patternrepeats every 308. One such pattern is shown in Fig. 2c, wherethe Ewald sphere cuts through a pair of strong reflections in Fig. 2b.The structure of this liquid quasicrystal (LQC) is periodic in thedirection of the 12-fold axis, but quasiperiodic in the planeperpendicular to it.In contrast to normal 3D periodic structures, five instead of threebasis vectors are needed for indexing the diffraction peaks of adodecagonal quasicrystal18. Four of the vectors, q1, q2, q3and q4,Figure 1 Self-assembly of wedge-shaped molecules. a, Dendrons with fewer tetheredchains adopt a flat slice-like shape (X is a weakly binding group). b, The slices stack upand form cylindrical columns, which assemble on a two-dimensional hexagonal columnar(Colh) lattice (c). d, Dendrons with more end-chains assume a conical shape. e, The conesassemble into spheres, which pack on three different 3D lattices (f) with symmetriesIm3¯m, Pm3¯n and P42/mnm. g, Structure of compound I studied in this work.letters to natureNATURE |VOL 428 | 11 MARCH 2004 | www.nature.com/nature
View Full Document
Unlocking...