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Other Dynamic Models
Topology and Phase
Physical Universe differentiates into three categories: liquid, crystalline, and gaseous phases. These distinct states of matter arise as a result of changing temperature or pressure, which induce different types of bonds. Fuller proposes a simple geometric analogy to make these invisible changes easy to comprehend. Appropriately, the model is completed with an exhaustive enumeration of the ways in which two tetrahedra can be connected to each other. The three arrangements of the minimum conceptual system model the three phases of physical matter.
First, two tetrahedra are triple-bonded, sharing one face between them (Fig. 11-8a). Because the relative positions of the two tetrahedra are completely fixed, the arrangement qualifies as a stable set of relationships and represents a crystalline structure: "The closestpacking, triple-bonded, fixed-end arrangement corresponds with rigid-structure molecular compounds" (931.60). Once again, the intention is not to create a large-scale duplicate of a particular "solid" compound, but rather to display the different characteristics of each chemical phase. The model is a kind of visual shorthand.
One of the three bonds is now released, leaving a double bond between two tetrahedra. The shared edge acts like a hinge (Fig. 11-8b); the tetrahedral pair can swing back and forth, but they cannot be moved doser together or farther apart. The configuration is thus noncompressibleone of the distinguishing characteristics of liquids. It bends any way you desiremalleable just like a liquidbut the double bond persists:
The medium-packed condition of a double-bonded, binged arrangement is still flexible, but sum-totally as an aggregate, all space-filling complex is noncompressibleas are liquids. (931.60)
Finally, we break another of the bonds. "Single-bonded" tetrahedra are joined by a vertex, and their behavior is analogous to that of a gas. The vertex bond acts as a universal joint; the two halves can swing freely with respect to each other, moving together and apart without disrupting the type of bond (Fig. 11-8c). The arrangement is compressible, expandable, and completely flexibleshort of dissociation. Perpetual connectedness indicates that both tetrahedra continue to participate in the same substance; they exhibit a consistent relationship, but lack structural definition:
Tetrahedra linked together entirely by...single-bonded universal jointing use lots of space, whicb is the openmost condition of flexibility and mutability characterizing the behavior of gases. (931.60)
The analogy is complete. All the while, Bucky holds the simple structures in his hands, and explains the different basic properties of solids, liquids, and gases. With any luck, a small child is present, forcing him to keep his discourse simple. How can the same type of molecule produce such radically different substances? Bucky offers a tangible explanation through geometry. This model is perhaps useful as a mnemonic devicean easy way to remember the chemistry lesson by relating the different characteristics to their analogous stage of the modelrather than as a true demonstration of phase changes in a substance.
It is worth noting that this model of interconnected tetrahedra is more appropriate, and, in fact, quite accurate, in connection with the bonding of carbon atoms within molecules. In conclusion, it is unfortunate that this and other polyhedral characteristics and relationships are generally overlooked in educational curricula.
Fuller developed many dynamic models, and readers who go on to further study will find a variety of examples in Synergetics. The transformations discussed in this chapter set the stage to explore other examples. Appropriate parallels in nature may well arise from such efforts.
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