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.
Exact icosahedral symmetry of C 60 is viewed as the union of 12 orbits of the symmetric subgroup of order 6 of the icosahedral group of order 120. Here, this subgroup is denoted by A 2 because it is isomorphic to the Weyl group of the simple Lie algebra A 2 . Eight of the A 2 orbits are hexagons and four are triangles. Only two of the hexagons appear as part of the C 60 surface shell. The orbits form a stack of parallel layers centered on the axis of C 60 passing through the centers of two opposite hexagons on the surface of C 60 . By inserting into the middle of the stack two A 2 orbits of six points each and two A 2 orbits of three points each, one can match the structure of C 78 . Repeating the insertion, one gets C 96 ; multiple such insertions generate nanotubes of any desired length. Five different polytopes with 78 carbon-like vertices are described; only two of them can be augmented to 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.
The goal of this article is to compare the geometrical structure of polytopes with 60 vertices, generated by the finite Coxeter group H 3 , 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 H 3 is given and presented as a 'pancake structure'.
The newly reported purification and isolation of pristine and unfunctionalized C90 and C100 fullertubes has generated excitement due to their unique “hybrid” structure of ½-fullerene endcaps, but with a single wall nanotubular belt and mid-section. Unique features of these fullertubes include a (1) defined molecular weight, (2) reproducible structure, (3) pristine tubular belt region, and (4) natural solubility into organic solvents without functionalization or polymer wrapping. Hence, the surface of the fullertube belt region would inherently be smooth and free from surface coatings, derivatization, or oxidation. These features provide a unique molecular architecture for investigating the true nature of electronic and photophysical properties of the fullertube's tubular belt. In this presentation, we will discuss our lab’s recent progress toward the isolation of segmentally longer fullertubes of higher aspect ratios as we seek to move from C120 fullertubes to C150 fullertubes and beyond. Figure 1
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