No abstract

We report a novel on-chip Rayleigh imaging technique using wide-field laser illumination to measure optical scattering from individual single-walled carbon nanotubes (SWNTs) on a solid substrate with high spatial and spectral resolution. This method in conjunction with calibrated AFM measurements accurately measures the resonance energies and diameters for a large number of SWNTs in parallel. We apply this technique for fast mapping of key SWNT parameters, including the electronic-types and chiral indices for individual SWNTs, position and frequency of chirality-changing events, and intertube interactions in both bundled and distant SWNTs.

The structures of eight related known intermetallic structure types are the impetus to this paper: Li21Si5, Mg44Rh7, Zn13(Fe,Ni)2, Mg6Pd, Na6Tl, Zn91Ir11, Li13Na29Ba19, and Al69Ta39. All belong to the F43m space group, have roughly 400 atoms in their cubic unit cells, are built up at least partially from the gamma-brass structure, and exhibit pseudo-tenfold symmetric diffraction patterns. These pseudo-tenfold axes lie in the {110} directions, and thus present a paradox. The {110} set is comprised of three pairs of perpendicular directions. Yet no 3D point group contains a single pair of perpendicular fivefold axes (by Friedel's Law, a fivefold axis leads to a tenfold diffraction pattern). The current work seeks to resolve this paradox. Its resolution is based on the largest of all 4D Platonic solids, the 600-cell. We first review the 600-cell, building an intuition discussing 4D polyhedroids (4D polytopes). We then show that the positions of common atoms in the F43m structures lie close to the positions of vertices in a 3D projection of the 600-cell. For this purpose, we develop a projection method that we call intermediate projection. The introduction of the 600-cell resolves the above paradox. This 4D Platonic solid contains numerous orthogonal fivefold rotations. The six fivefold directions that are best preserved after projection prove to lie along the {110} directions of the F43m structures. Finally, this paper shows that at certain ideal projected cluster sizes related to one another by the golden mean (tau=(1+ radical 5)/2), constructive interference leading to tenfold diffraction patterns is optimized. It is these optimal values that predominate in actual F43m structures. Explicit comparison of experimental cluster sizes and theoretically derived cluster sizes shows a clear correspondence, both for isolated and crystalline pairs of projected 600-cells.

Of the most common cubic intermetallic structure types, several (MgCu(2), Cu(5)Zn(8), Ti(2)Ni, and alpha-Mn) have superstructures with unusual symmetry properties. These superstructures (Be(5)Au, Li(21)Si(5), Sm(11)Cd(45), and Mg(44)Ir(7)) have the unusual property of pairs of perpendicular pseudo fivefold axes, most apparent in their X-ray diffraction patterns. The current work shows that an 8D to 3D projection method cleanly describes most (and in one case, all) of the atomic positions in the four superstructures mentioned above. This type of projection, which maps the E(8) lattice (a mathematically simple 8D crystal) into 3D space, combines the desired higher dimensional point group's perpendicular fivefold rotations with 3D translational symmetry-exactly what we see in the experimental crystal structures. The projection method successfully accounts for all heavy atom positions in the four superstructures, and at least 60-70 % of the light atom positions. The results suggest that all of these structures, previously known to be connected only by qualitative similarities in their atomic "clusters", are approximants of a single, as-yet unknown, class of quasicrystal.

Subcellular trafficking of neuronal receptors is known to play a key role in synaptic development, homeostasis, and plasticity. We have developed a ligand-targeted and photo-cleavable probe for delivering a synthetic fluorophore to AMPA receptors natively expressed in neurons. After a receptor is bound to the ligand portion of the probe molecule, a proteinaceous nucleophile reacts with an electrophile on the probe, covalently bonding the two species. The ligand may then be removed by photolysis, returning the receptor to its non-liganded state while leaving intact the new covalent bond between the receptor and the fluorophore. This strategy was used to label polyamine-sensitive receptors, including calcium-permeable AMPA receptors, in live hippocampal neurons from rats. Here, we describe experiments where we examined specificity, competition, and concentration on labeling efficacy as well as quantified receptor trafficking. Pharmacological competition during the labeling step with either a competitive or noncompetitive glutamate receptor antagonist prevented the majority of labeling observed without a blocker. In other experiments, labeled receptors were observed to alter their locations and we were able to track and quantify their movements.