Colossal C130 Fullertubes: Soluble [5,5] C130-D5h(1) Pristine Molecules with 70 Nanotube Carbons and Two 30-Atom Hemifullerene End-caps.

We report the seminal experimental isolation and DFT characterization of pristine [5,5] C130-D5h(1) fullertubes. This achievement represents the largest soluble carbon molecule obtained in its pristine form. The [5,5] C130 species is the highest aspect ratio fullertube purified to date and now surpasses the recent gigantic [5,5] C120-D5d(1). In contrast to C90, C100, and C120 fullertubes, the longer C130-D5h has more nanotubular carbons (70) than end-cap fullerenyl atoms (60). Starting from 39,393 possible C130 isolated pentagon rule (IPR) structures and after analyzing polarizability, retention time, and UV-vis spectra, these three layers of data remarkably predict a single candidate isomer and fullertube, [5,5] C130-D5h(1). This structural assignment is augmented by atomic resolution STEM data showing distinctive and tubular "pill-like" structures with diameters and aspect ratios consistent with [5,5] C130-D5h(1) fullertubes. The high selectivity of the aminopropanol reaction with spheroidal fullerenes permits facile separation and removal of fullertubes from soot extracts. Experimental analyses (HPLC retention time, UV-vis, and STEM) were synergistically used (with polarizability and DFT property calculations) to down select and confirm the C130 fullertube structure. Achieving the isolation of a new [5,5] C130-D5h fullertube opens the door to application development and fundamental studies of electron confinement, fluorescence, and metallic character for a fullertube series of molecules with systematic tubular elongation. This [5,5] fullertube family also invites comparative studies with single-walled carbon nanotubes (SWCNTs), nanohorns (SWCNHs), and fullerenes.

Gigantic C120 Fullertubes: Prediction and Experimental Evidence for Isomerically Purified Metallic [5,5] C120-D5d(1) and Nonmetallic [10,0] C120-D5h(10766).

We report the first experimental characterization of isomerically pure and pristine C120 fullertubes, [5,5] C120-D5d(1) and [10,0] C120-D5h(10766). These new molecules represent the highest aspect ratio fullertubes isolated to date; for example, the prior largest empty cage fullertube was [5,5] C100-D5d(1). This increase of 20 carbon atoms represents a gigantic leap in comparison to three decades of C60-C90 fullerene research. Moreover, the [10,0] C120-D5d(10766) fullertube has an end-cap derived from C80-Ih and is a new fullertube whose C40 end-cap has not yet been isolated experimentally. Theoretical and experimental analyses of anisotropic polarizability and UV-vis assign C120 isomer I as a [5,5] C120-D5d(1) fullertube. C120 isomer II matches a [10,0] C120-D5h(10766) fullertube. These structural assignments are further supported by Raman data showing metallic character for [5,5] C120-D5d(1) and nonmetallic character for C120-D5h(10766). STM imaging reveals a tubular structure with an aspect ratio consistent with a [5,5] C120-D5d(1) fullertube. With microgram quantities not amenable to crystallography, we demonstrate that DFT anisotropic polarizability, augmented by long-accepted experimental analyses (HPLC retention time, UV-vis, Raman, and STM) can be synergistically used (with DFT) to down select, predict, and assign C120 fullertube candidate structures. From 10 774 mathematically possible IPR C120 structures, this anisotropic polarizability paradigm is quite favorable to distinguish tubular structures from carbon soot. Identification of isomers I and II was surprisingly facile, i.e., two purified isomers for two possible structures of widely distinguishing features. These metallic and nonmetallic C120 fullertube isomers open the door to both fundamental research and application development.

The polytopes of the H3 group with 60 vertices and their orbit decompositions.

The goal of this article is to compare the geometrical structure of polytopes with 60 vertices, generated by the finite Coxeter group H3, i.e. an icosahedral group in three dimensions. The method of decorating a Coxeter-Dynkin diagram is used to easily read the structure of the reflection-generated polytopes. The decomposition of the vertices of the polytopes into a sum of orbits of subgroups of H3 is given and presented as a `pancake structure'.

Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.

This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 × A1. Thirteen of the A1 × A1 orbits are rectangles and four are line segments. The orbits form a stack of parallel layers centered on the axis of C60 passing through the centers of two opposite edges between two hexagons on the surface of C60. These two edges are the only two line segment layers to appear on the surface shell. Among the 24 convex polytopes with shell formed by hexagons and 12 pentagons, having 84 vertices [Fowler & Manolopoulos (1992). Nature (London), 355, 428-430; Fowler & Manolopoulos (2007). An Atlas of Fullerenes. Dover Publications Inc.; Zhang et al. (1993). J. Chem. Phys. 98, 3095-3102], there are only two that can be identified with breaking of the H3 symmetry to A1 × A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry.