Invisible Architecture

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.

He did not anticipate C60, but its discovery did validate his intuitions that geodesic design plays a more significant role in nature's arrangements than had hitherto been recognized. Fuller would have been less surprised than any of us to learn that the 60-atom array possessed an extraordinary property of stability. Although he regarded the hydrogen atom as the simplest--and hence the most beautiful--design in nature, Fuller had a lifelong interest in the carbon atom, and, in many of his writings and lectures, he celebrated J.H.van't Hoff's 1874 concept of the tetrahedral configuration of carbon bonds.38

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.

"One of the most compelling lines of evidence for the validity of the concept of molecular nanotechnology is that such machines already exist. Natural biological systems offer the best current proof that molecular machines are possible, and are capable of doing productive work. As such, the machinery of life stands as a sort of "existence proof" for the field... By studying biological systems, we learn about those basic principles. That evolutionary legacy also represents a reservoir of potential components that we might adapt for use in molecular machines of our own design." 39

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 has an incredible ability to spontaneously assemble to form these objects. That's what we really discovered. The more we think about that, and how neat these objects are, the more we are beginning to realize that we can find ways of tricking nature in to self assembling carbon into other fullerene-like shapes as well, and that these new materials may well have major practical as well as theoretical significance. "In fact, it emerges that buckyball was (and is) a sort of Rosetta Stone of what we now realize is an infinity of new structures made of carbon one way or another. . . And the deciphering of the C60 Rosetta Stone has led us to start dreaming of all sorts of new structures that truly are geodesic architecture on a nanometer scale, and to scheme about how to make them."40

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:

C60 is special because of all the structures made of pentagons and hexagons that can curl around and close, there is only one that can do it so smoothly that every atom has the same curvature as every other. This is a consequence of mathematics. Sixty is the most factorable of all integers. That's why the Babylonians used it as the base of their number system, that's why we still divide circles into 360 degrees, and why we have 60 minutes in an hour and 60 seconds in a minute. For reasons that so far seem obscure but probably are connected somehow to its high factorability, sixty is also the maximum finite number of ways you can rotate an object around a central point in 3 dimensional space so that when you finish rotating it looks exactly the same as before. Such an object has the symmetry of the icosahedron, the highest finite point group, which has 60 proper rotational symmetry elements. "It turns out that is all the information you need to select out of all the possible structures that you can imagine for 60 carbon atoms this one particular structure. When you start to think about how this works, you begin to realize that there must be an incentive for it curving, there must be an infinity of geodesic structures of carbon many of which are self-assembling in the condensing carbon vapor and, after all, these sort of things are really cool. 41

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.

Shaped like concentric cylinders of chicken wire, these multi-wall tubes can range between five and 20 nanometers thick, thus facilitating more atomic manipulation. When capped at one end with a hemispheric fullerene, the tip can serve as a chemical probe. What makes them even more appealing is their durability. Fellow researcher Daniel Colbert explains that although they tried to "crash" or damage the tubes, the inherent flexibility allows them to return to their original shape.42

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:

Klug: "I always thought of the icosahedron in the Greek sense as a perfect object. But when you see an edge, you actually see it as made of real rods and struts and things. This took some forgetting I can tell you, in fact one of the stumbling blocks that we had was we tried to think of structures as spherical bodies. We made this mistake... we always wanted to make the Greek ideal and never the real thing. But nature doesn't care less about ideals"

Fuller: "For instance I discovered that two lines couldn't go through the same point at the same time ... The very essence of this skewing is that things will not go through the same point at the same time" 44

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" :

"Caspar and Klug found that Fuller's [formula] did not account for all the capsomer counts they were getting. They needed to accommodate the so-called "skew" cases corresponding to what later came to be known as Class III geodesic structures."45

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.

This year's conference ends with a session devoted to perhaps the most important single problem in the development of chemistry on the nanometer scale: touching and "seeing" the individual objects that are made. This is the explosively developing field of proximate probes and their related spectroscopies. The most ambitious of these, as discussed by Dan Rugar, is the development of magnetic resonance with proximate probes, with the ultimate aim of being able to obtain the NMR image of a single protein molecule. Here too fullerene nanotubes may soon offer a major enabling technology as a molecularly perfect, direct probe from the macroscopic to the nanoscopic world. The current state of the art as exemplified by Phaedon Avouris, Alan Bard, and carlos Bustamante is already breathtaking.

In the end, chemistry on the nanometer scale may not be all that hard after all. Nanotechnologies that derive from this chemistry will certainly find their way into and perhaps even dominate the Annual Welch Conference Proceedings of this next century. Some of them may make even Eric Drexler blush. 46

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:

Seeman had actually learned that his junctions were floppy before he built the cube, but he decided to forge ahead anyway just to prove that he could build in three dimensions. Then he began to look for a way to make his structures more rigid. Now he thinks he's got it.

The solution comes in two parts. First Seeman has replaced rectangles with triangles as his basic building blocks. If the corners on a rectangle aren't rigid, the sides can move relative to one another. But if the corners on a triangle aren't rigid, it doesn't matter--as long as the sides of the triangle are rigid, nothing will move. . .

In three dimensions, Seeman has sketched out a number of rigid frameworks that could be assembled out of triangles. "It's pure Buckminster Fuller" he says, referring to the engineer whose famous geodesic dome depended on triangles for its structural strength. Like the geodesic dome, three-dimensional frameworks made from double-crossover molecules could be remarkable strong and rigid. 50

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.

"If the foglets are thought of as atoms, it is a face-centered cubic crystal formation, in which each atom touches twelve other atoms. If you imagine the foglets' arms as the girders of a trusswork bridge, they form alternate tetrahedrons and octahedrons, both of which are rigid three-dimensional shapes."52

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.

Subsequent experiments and analysis by Dr. Ingber and his associates suggest that the cytoskeleton -- the "scaffolding" in cells -- does take the form of a complex tensegrity with thousands of discontinuous compression members ordered and stabilized by continuous internal tension filaments. It seems likely that the nucleus is structured in the same way. Such a system maintains its integrity without relying on gravity. By (almost) instantly distributing applied loads, it can act as a transducer, a receptor, and carrier of information.53

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