Read here about the general topic of the tensegrity structure of carbon allotropes including buckyballs, buckypaper and buckytubes.


Buckminsterfullerene or C60 was made in 1985 by Robert Curl, Harold Kroto and Richard Smalley at Rice University. The name was an homage to Richard Buckminster Fuller, whose geodesic domes it resembles. Fullerenes have since been found to occur (if rarely) in nature. A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and cylindrical ones are called carbon nanotubes or buckytubes. Fullerenes are similar in structure to graphite, which is composed of stacked graphene sheets of linked hexagonal rings; but they may also contain pentagonal (or sometimes heptagonal) rings.


Model of Buckminsterfullerene as a Tensegrity

Russell Z Chu in 2003 began to investigate a problem he saw in the conventional comprehension of this molecule. The truncated icosahedron is structurally unstable--if C60 was such a shape, it too would not persist. He decided to look at C60 for secondary structural elements that could stabilize its primary truncated icosahedron structure.
Using SpringDance, a Delphi-written version of de Jong's Elastic Interval Geometry rendering software, Chu generated a model of buckminsterfullerene as a tensegrity.
C60 as tensegrity by Chu, generated in SpringDance

In the image, the primary structure of C60 in red color is the truncated icosahedron, the typical description of C60.

Chu writes: The secondary structural elements are tensional elements. They are the yellow tension elements inside the pentagons and the aqua tensional elements inside the hexagons. These tensional elements are all the secondary connections from one carbon atom to the next nearest atom. The primary connections are the red truncated icosahedron. This tensegrity system is similar to the bicycle wheel, but instead of spokes it is a spherical tensional net. The bouncy property of C60 can be attributed to the tensegrity structural system.

Yue Li tackeld the same problem, applying his form-finding method, and generated the image below. He wrote, "Construction of Z-based Bucky ball tensegrity. (a) A hexagonal mesh. There are two
different modes of adding bars, which are coloured by cyan and magenta, respectively. (b) The topology of a C60 Bucky ball. (c) The form-finding result of the Bucky ball after adding bars." [2]

Buckyball (a) hexagonal mesh (b) C60 topology (c) tensegrity by Li, Feng, Cao and Gao

Carbon Nanotubes

Yue Li applied his form-finding method to nanotubes. He published the figure below, its caption read, "Construction of a Z-based tensegrity resembling a capped carbon nanotube. (a) The

topology of a capped (5,5) carbon nanotube. (b) The form-finding result of the capped carbon nanotube after adding bars." [2]

Capped (5,5) carbon nanotube (a) topology (b) tensegrity by Li, Feng, Cao and Gao

Nanotubes Form a Polymer-bound Tensegrity

Boris Yakobson and Luise Couchman propose that tensegrities can be constructed in nanoscale by combining mechanically stiff and flexible supramolecular units. The need arises due to the usual supramolecular interactions that dominate in nanotubes and C60 constructions. It does seem possible to connect rigid nanotubes by chemically attached polymer segments to keep them apart. This would harness the usual weak but always present attraction at large distances, nano-speaking (from tens of nanometers) resulting in a relatively shallow potential minimum at intermolecular vicinity of 0.2–0.5 nm spacing.
Needham, Wilson, and Yakobson published a 3 strut prism proposal. Three carbon nanotubes are covalently tensioned, or tethered, at their cap pentagons by polyethylene polymer chains.

Three carbon nanotubes are covalently tensioned, or tethered, at their cap pentagons by polyethylene polymer chains, by Needham, Wilson, and Yakobson.

Under compression, the nanotubes would deform in the following ways.

Nanotube compression simulation by Yakobson, Brabec, Bernholc

Tensegrity At Supramolecular Scale

Boris I. Yakobson of Rice University, Houston, Texas, and Luise S. Couchman of Naval Research Laboratory, Washington DC investigated the weak interactions between carbon nanotubes, naming these attractive potentials supramolecular forces. Their research indirectly lead to the discovery of the unusual role played by the forces between the nanotubes.

They wrote, "Usual supramolecular interactions possess the same generic properties as any other interatomic forces: weak but always present attraction at large distances (from tens of nanometers) results in a relatively shallow potential minimum at intermolecular vicinity of 0.2–0.5 nm spacing. Closer, it turns into a steep repulsive potential which, upon sufficient compression, can yield to a covalent bonding. Therefore supramolecular forces by themselves are unlikely to be able to support low-density assembly of molecules and nanotubes in particular: they would form aligned bundles or at least relatively dense random mats. In this context, it became of interest recently to explore transferability of certain ideas of macroengineering and to connect rigid nanotubes by chemically attached polymer segments to keep them apart. This seems at a first glance counterintuitive—how adding flexible links can prevent rigid beams from lumping together? However, at the macroscopic scale, the idea goes back to Fuller,[47] who has proposed and patented tensile–integrity structures, hence the terms tensegrity in the literature. Tensegrity is a design principle that describes how network structures achieve shape stability. The main point is that a disconnected set of rigid beams can be tethered by sparse series of tensile threads (each perfectly bendable and unsupportive to any compression) in such a way that global structure can become rigid, sustain compressive global load, and possess all-finite vibration eigenfrequencies. Such engineered structures can be found in architecture, furniture, entertainment, and aerospace applications (because of lightweight and ‘‘foldability’’). In cell biology, cytoskeleton is also suggested to possess tensegrity properties." [1]

The authors include a diagram of a t-prism of 3 struts, where the struts are carbon buckytubes and the tendons are polyethylene chains attached to the strut caps by covalent forces. See Needham, J.; Wilson, S.; Yakobson, B.I. Possibility of nanotube-based tensegrity structures.

Links and References


[1] Carbon Nanotubes: Supramolecular Mechanics, by Yakobson and Couchman. Dekker Encyclopedia of Nanoscience and Nanotechnology 587, DOI: 10.1081/E-ENN 120009130, p. 587.
[2] Constructing tensegrity structures from one-bar elementary cells by Yue Li, Xi-Qiao Feng, Yan-Ping Cao and Huajian Gao, Proc. R. Soc. A 2010 466, 45-61, doi: 10.1098/rspa.2009.0260