The NanoWorld of Buckminster Fuller
by Bonnie Goldstein DeVarco
VI. A Model for Nanoscale Architecture -- The Archetypal Fullerene
Buckminsterfullerene -- The "Rosetta Stone of Nanoscale Architecture"
In the 1996 issue of the "Chemical Intelligencer," E.J. Applewhite noted the appropriateness of the name "buckminsterfullerene" given to the carbon 60 molecule, whose stable configuration would not have been of the least surprise to Fuller.
Fuller's successful modeling of Nature's great technology left myriad artifacts demonstrating how to do more with less beautifully. Drawing his architecture from the fluid, ephemeral, aesthetically patterned designs of Nature, Fuller's dynamic and lightweight structures have demonstrated some of the most efficient uses of materials for large-scale design. Even in his final years, however, he was not able to take full advantage of the geodesic and tensegrity applications which could render his newest structures like the instruments he envisioned in the 1930s. The materials were not, and are still not available. But now, 14 years after his death, perhaps his insights into nature's design could be used for another type of architecture. Architecture on the nanoscale.
The burgeoning field of nanotechnology uses some of Fuller's earliest self-disciplines as its basis: learning design lessons from biological systems. In Richard Terra's article, "Progress Towards Molecular Nanotechnology," he describes the concept of molecular nanotechnology as the manipulation of matter at the atomic and molecular level in order to build micromachines. This field was initiated by Eric Drexler in the early 1980s and is explained in his classic text, Engines of Creation. Terra's words in 1996 echo some of Fuller's earliest assertions that nature is indeed, technology -- technology of the most functional sort and certainly the best model to follow.
It is interesting to note that the first models of nature's principles which were latched onto in the quest to mimic nature's design were the very molecules that were Buckminster Fuller's namesake. According to Richard Smalley, one of the discoverers of buckminsterfullerene in 1985 and the founder of the Center for Nanoscale Science and Technology, (CNST) at Rice University, buckminsterfullerene is the "archetypal fullerene" and the "Rosetta Stone of Nanoscale Architecture." In his 1996 lecture to the S. Texas Section of the American Institute of Chemical Engineers he noted,
Carbon 60, whose soccerball structure is composed of 20 hexagons and 12 pentagons, has a perfectly symmetrical three-dimensional shape. Smalley deemed C60 the "archetypal fullerene" because it is the most symmetrical member of the fullerene family, self-assembling into a form in which no strain of curvature is localized but rather spread around the entire molecule. This design property enables it to be exquisitely strong, flexible and durable with a complete absence of chemical reactivity. He attributed this unique quality to its mathematics:
Using what chemists now term "the pentagon road," wherein the introduction of 12 pentagons will cause closure of any size fullerene (the hexagons have no such limitations of number), no dangling atoms would be left to bond with other elements. Nanosized hexagonal graphene sheets in tubes grow to unmanageable lengths because their dangling atoms readily form new bonds on the ends. It is now possible, however, to attach pent-capped buckyball hemispheres on the ends of these growing "ropes" of carbon nanotubes to make them useful in various ways.
Reported most recently in February's 1997 issue of Scientific American, in a new development drawing from the lessons in the spontaneous self-assembly of buckyballs, Smalley and his crew of nanotechnicians are using buckytubes with buckyball tips to build the first nanosized "probes." These probes replace on a much smaller scale an already specialized tool of nanoengineering: the tips of a scanning force microscope (SF) which relies on such tips to nudge molecules.
Fuller offered a three-tiered exploration of the dynamic geometry of nature, exemplified in synergetics -- the tetrahedron, octahedron and icosahedron. Carbon loves to be bonded in a tetrahedral pattern and Fuller's geometry included many of structural permutations of this tetrahedral base. Not only do some exhibit perfect symmetry like the buckyball and his geodesic dome, but they can also twist and skew to contain the growth patterns of asymmetry as well. Fuller's structural explorations demonstrated a series of dynamic forms that were always in motion and spanned an oscillating continuum of symmetry and asymmetry. This has never been seen before in the earlier geometries of the Greeks or standard geometry as it is taught in the traditional classroom.
On a microscale, motion is an essential characteristic of structure. When chemists, physicists and biologists talk about cells, DNA, molecules and atoms, their reference to the structures themselves are always approximate. We must continue to view them these forms in their dynamic state. Buckyballs are molecules of 60 very mobile, oscillating atoms. Dr. R. Stanley Williams at U.C.L.A.'s department of chemistry describes the buckyballs in a blurry photograph made from the atomic force microscope as being "lined up like dancers on a stage... We cannot see the idividual atoms in the C60 molecules because they are whirling around over one million times per second." From his very first experiments with design, Fuller tried to understand the general principles behind moving, transforming structures. Synergetic geometry emerged as a system through which he could explain and model movement and transformation as well as self-regeneration, information coding and molecular structuring -- all essential characteristics of living systems. Fuller always treated these conditions as invisible, energetic "events" and behaviors of design itself rather than mere combinations of solid static parts.
Parallel Paths -- Viruses and Buckyballs
In February of 1962, virus experts first viewed pictures taken by electron microscope which magnified viruses between 200,000 and 500,000 times their normal size. To the scientists' surprise, reported the New York Herald Tribune, "They show the same kind of structure as the domes of Buckminster Fuller" Dr. [Robert] Horne, who took the first photos, explained, "We went along working out the mathematics of the viruses when somebody told us about Fuller's book . . . We opened it and there it was all worked out. It seems that both Fuller and nature have picked out the most rigid geometry they can find."43
Later that year, in the debut of the BBC's Horizons science series, Fuller was the first person to be featured in a special which concentrated on his geodesic domes and synergetics. This program showed Fuller discussing the icosahedral structure of virus' protein shells in Cavendish Laboratory with crystallographer Aaron Klug, and the tetrahedral structure of the enzyme, glutamic dehydroginase with electron microscopist Robert Horne.
Klug's discussions with Fuller centered around many models of viruses they had made since viewing the electron microscope photos -- models showing the spherical icosahedral shapes the viruses exhibited. Fuller emphasized that the symmetry of these virus structures were not necessarily the rule. Although his domes were based on geodesics which partially drew from the mathematics of spherical trigonometry, their icosahedral symmetry did not show exactly what the virologists were seeing. Asymmetrical properties even in the icosahedral shapes of the capsid layers would also be part of the virus structure. Fuller reasoned that "Nature puts things together in the simplest way. Then she tries to get more comfortable so she stretches into the spherical trig... because there is just enough oscillating differences there." Their discussion continued:
Later in 1962, in the first paper discussing virus structure after the new discovery, Klug and Donald Caspar outlined their "quasi-equivalence theory" which helped them map out and understand the many virus structures. They attributed their application of this theory to the inspiration of Fuller's geodesic structures but they forgot about his comments on asymmetry. Unfortunately the usefulness of Fuller's geometry, even with this early confirmation of microscale equivalents to his architecture, was discounted by virologists later in the 1970s and 80s. They had focused exclusively on his dome and had insisted that his artifacts only demonstrated perfect "symmetry." Many viruses exhibiting asymmetrical shapes were found after 1962. Caspar and Klug's quasi-equivalence theory was still valid, but Fuller's geometry was not. The conversations about asymmetry became irrelevant and so did synergetic geometry. Correspondence ensued between Klug, Horne and Fuller after their meeting as Fuller continued to clarify the relevance of his findings to theirs but the publicly recognized connection to synergetic geometry was short-lived.
Since Fuller's geometry was only known and recognized by the artifacts containing perfect symmetry, the relevance of synergetics was dismissed and dropped from the docket of historical reflection. Some of the reasons for this were explained in a 1990 article by Kirby Urner about synergetics and its underlying relevance to the rapidly emerging buckyball phenomenon, "The Invention Behind the Inventions - Synergetics in the 1990s" :
Fuller's approach to "Nature's geometry" at the time was seen as a simple extension of the works of D'Arcy Wentworth Thompson (who was first to apply mathematics to the biological world in his classic work, On Growth and Form). Yet a closer look will reveal synergetic geometry to be a much broader system of dynamic geometry from which only the symmetric artifacts came first. The geodesic dome, the most popular artifact in Fuller's repertoire, was just one demonstration of a system he had spent a lifetime developing. Fuller's geometry amply explored numerous conditions of asymmetrical patterning with a series of quanta modules, mites and couplers. These asymmetrical tetrahedra and octahedra would combine to form a broad range of structures and could model patterns of structural growth. Fuller's smaller primitive space fillers and his elaborations on the relevance of the tetrahelix and the open triangle may have added relevance when applied to the asymmetrical structures that chemists are now finding and making with buckytubes and nanotubes.
Models for Nanostructures -- Tensegrity, Buckyballs and DNA
Scientists are now speculating on the feasibility of making "tweezers" using two nanoprobes together. Thus, fullerenes may become the first microscale tools used in nanotechnology. Looking to various forms of carbon as a models of and models for nanoscale architecture in the world's the tiniest man-made machinery gives one of Fuller's assertions on architecture a prophetic twist: "the making of macrostructures out of microstructures." Richard Smalley's Introductory remarks on Chemistry on the Nanoscale at last Fall's 40th Conference on Chemical Research emphasized the central importance of these nanoprobes with buckyball tips as a new tool which will revolutionize nanotechnology.
Scientists' early efforts to combine the best structural characteristics of the varied molecular structures of carbon and use them in tandem may soon model some of Fuller's own juxtapositions of form in the medioscale. The octet truss and the geodesic dome begin to look like parts of a structural trio (tetrahedron, octahedron, icosahedron) exemplified on the microscale by the "golden triad of pure carbon," that is, graphite, diamond and fullerenes. In the thousands of articles that have already been written on buckminsterfullerene and its promise, however, the work and ideas of Buckminster Fuller have thus far been given only a passing nod. Fuller's explorations with tetrahelixes, the spiral helical structuring of tetrahedrons which for his structural analogue to DNA take more seriously the use of the tetrahedron as the basis of structure on the atomic and molecular level rather than permutations of the cube. Over and over these views seem to be mirrored in the newest findings with buckytubes and nanotechnology.
Fuller's commitment to being a comprehensivist which sometimes brought him into the domain of science has also led his work to be characterized by some as the work of a "pseudo-scientist." Although he recognized Fuller's architectural contributions, Hugh Aldersey Williams, in his excellent book on discovery of buckminsterfullerene, The Most Beautiful Molecule, criticized Fuller as a type of pseudo-scientist with "disciples," "acolytes" and "followers" who maintain that Fuller is a scientist. Aldersey-Williams explains that a pseudo-scientist is characterized by "the pointing out of spurious similarities, not least with the findings of mainstream science; explanation by scenario without the support of scientific law or theory; ....mak[ing] sure that your statements are so vague that criticism can never get a foothold; simply refus[ing] to acknowledge whatever criticism you receive."47
Fuller has rarely been referred to as a scientist, yet many would agree that some aspects of his work could have an important influence on the sciences. His work clearly benefitted from his application of various scientific principles to the discipline of architecture. Fuller never called himself a scientist. Instead, he often called himself a "Comprehensive Anticipatory Design Scientist" and urged hordes of students to merge the disciplines in unique and unprecedented ways. Fuller is not the only figure to have been characterized by such "religious" or "pseudo-scientific" terminology, however. Eric Drexler, the father of nanotechnology has been faced with similar criticisms. To counter such criticism, the Foresight Institute launched a vigorous online campaign to expose the errors in such criticisms in their Sci-Amer/Foresight Institute Debate page.48 In this lengthy point-by-point refutation, the Foresight Institute urged the journalist to retract his unfounded criticisms which characterize Drexler as "the avatar of nanotechnology" and various people his "disciples" or his "following."
With many promising new directions in nanotechnology and the notable proliferation of nanotechnology resources on the web, such criticisms may be soon be seen as both shortsighted and short-lived. Harvard University maintains that one of the most promising areas of nanotechnology is the work of Ned Seeman49 Seeman's 20-year explorations in molecular nanotechnology with DNA has confronted yet another scientist with limitations of the cubic frame of reference for structure on a nanoscale and validates the importance of Fuller's findings through his flexible "jitterbug."
As part of his research, Seeman took small strands of DNA and hooked them together into three-dimensional forms on a nanoscale. To do this, he applied a technique of attaching two links together to form a four-way junction called a "Holliday junction." He struggled to build these structures with DNA strands by starting out with the cube. Since the four-way "Holliday junctions" that form the vertices of these structures were floppy, his first models did not hold up well and had to be abandoned. According to Discover Magazine's online article on Seeman's work:
Other proposals in nanotechnology theoretically apply both geodesics and Fuller's octet truss system as the perfect designs to use to build more complex micromachines that can carry out numerous new functions. The book, Nanotechnology - Molecular Speculations on Global Abundance presents articles by a dozen different researchers applying nanotechnology in the field. In this book, Fuller's architectures are considered likely candidates for this new generation of machines.
Harry Chesley, software architect who has worked with Macromedia, Apple Computer and SRI international suggests the feasibility of building "a micron-scale geodesic structure built with carbon rod struts would form an extremely secure exoskeleton for housing nanomachinery. . . . A series of stucturally linked, concentric geodesics could easily form a secure shell for nanomechanisms, providing them with structures to push against."51
J. Storrs Hall, computer scientist at Rutgers University, postulates the use of a "utility fog" robot that acts like a cell, performing a particular function within a larger matrix in the same way that a functional pixel helps to make up an overall image on a screen. Tiny utility foglets which would contain about 5 trillion atoms can act as more ephemeral types of robots. These foglets could can add strength to materials as well as manipulate objects. Their overall design would be structured like Fuller's octet truss in its Isotropic Vector Matrix form.
Harvard Scientist Donald Ingber has been applying Fuller and Snelson's concept of tensegrity to the behaviors of the cytoskeleton and the cellular make-up for a number of years. Only this year however, has his work with his Harvard team of biotechnologists made breakthrough news. For many years Ingber has constructed three-dimensional tensegrity "cell models" of sticks and elastic string to model the behaviors of cells.
In the May 2, 1997 issue of Science, Ingber's studies have been hailed as a breakthrough in cell biology, "showing how mechanical forces on the cell can affect everything from the way proteins bind to DNA to whether malignant cell develops into a full blown tumor. And now a team of cell biologists -- inspired, in part, by Fuller's structural ideas -- has demonstrated that mammalian cells are densely 'hard-wired' with force-carrying connections that reach all the way from the membrane through the cytoskeleton to the genome." The article begins with the suggestion that Fuller's words, "Don't fight forces: use them" may turn out to be a motto for the living cell which "owes its shape and many of its properties to a 'tensegrity' structure."54 [Ingber's own article about tensegrity and the cytoskeleton, article "The Architecture of Life" appeared as the cover story for the January 1998 issue of Scientific American]. Neurophysiologist David Van Essen has also championed tensegrity in the body, applying its structural dynamics to the better understanding of the body's entire neurostructure.55
These breakthroughs on a microlevel require ways of computer-modeling the forces, structures and dynamics scientists are finding on a microscale. And now a new computer program has emerged which may be up to the task of modeling complex geodesic and tensegrity systems. Creating a new public domain Java applet, Gerald de Jong, a computer programmer from Rotterdam, has developed a way to model some of Fuller's many structures through a moving medium called "Elastic Interval Geometry." EIG is a programming language that is simple to learn, easy to download and easy to display on a web page in simple stereo visuals or animations.
De Jong has offered an entirely new tool to model dynamic structures on computer. This Java program can now be used by the scientists above to model microstructures and their behaviors. It can be combined with PovRay, QuickTime and the soon-to-be-released Java 3D, to make movies of structural dynamics with ease. His geometry program is based on Fuller's synergetics yet imbues it with the motion necessary to see the behaviors of these systems through time. Now a small number of java modelers on Gerald's Fluidiom listserv are exploring some of the many ways to model new versions of the geodesic, tensegrity and octet truss latticework structures based on the tetra-, octa- and icosahedron.
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copyright 1997, Bonnie DeVarco