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This draft article has been submitted to Nanotechnology for publication, and was presented at the Seventh Foresight Conference on Molecular Nanotechnology.
One of the fundamental requirements for positional assembly of molecular machines is the availability of molecular parts. One class of molecular parts might be characterized as molecular building blocks, or MBBs. With an atom count ranging anywhere from ten to ten thousand (and even more), such MBBs would be synthesized and positioned using existing (or soon to be developed) methods. Thus, in contrast to investigations of the longer term possibilities of molecular manufacturing (which often rely on mechanisms and systems that are likely to take many years or even decades to develop), investigations of MBBs focus on nearer term developmental pathways.
A more attractive approach as a target for near term experimental efforts is the use of molecular building blocks (MBBs) (Krummenacker, 1992; Merkle, 1999). Such building blocks would be made from dozens to thousands of atoms (or more). Such relatively large building blocks would reduce the positional accuracy required for their assembly. Linking groups less promiscuous than the radicals proposed for the synthesis of diamond would also reduce the rate of incorrect side reactions in the presence of contaminants.
The proposal to use molecular building blocks raises the obvious question: what do they look like?
Polymers are made from monomers, and each monomer reacts with two other monomers to form a linear chain. Synthetic polymers include nylon, dacron, and a host of others. Natural polymers include proteins and RNA (Watson et al., 1987) which, if the sequence of monomers forming the polymer is selected carefully, will fold into desired three dimensional shapes. While it is possible to make structures this way (as evidenced by the remarkable range of proteins found in biological systems), it is not the most intuitive approach (the protein folding problem is notoriously difficult).
A second drawback of this approach is the relative lack of stiffness of the resulting structure. The correct three dimensional shape is usually formed when many weak bonds combine to give the desired conformation greater stability and lower energy than the alternatives. However, this desired structure can usually be disrupted by changes in temperature, pressure, solvent, dissolved ions, or relatively modest mechanical force (e.g., when imaged by an AFM).
These limitations, caused in large measure by the restriction to two linking groups per monomer, motivates our investigation of MBBs with three or more linking groups.
There are two ways to assemble parts: self assembly and positional assembly. Self assembly is widely used at the molecular scale, and we find many examples of its use in biology (Watson, 1987). Positional assembly is widely used at the size scale of humans, and we find many examples of its use in manufacturing. Our inability to use positional assembly at the molecular scale with the same flexibility that we use it at the human scale seriously limits the range of structures that we can make.
By way of example, suppose we tried to make radios using self assembly. We would take the parts of the radio and put them into a bag, shake the bag, and pull out an assembled radio. This is a hard way to make a radio and if we demanded that all manufacturing take place using this approach our modern civilization would not exist.
By the same token, the range of things that can be made if we restrict ourselves to self assembly is much smaller than the range of things that can be made if we permit ourselves to add positional assembly to the other methods at our disposal. That this rather obvious point has not been more rapidly and generally understood with respect to the synthesis of molecular scale objects stems from the fact that we have never before been able to do positional assembly at the molecular scale. The idea of making a molecular structure by positionally assembling molecular parts is unfamiliar and different. Yet this capability, which has been demonstrated in nascent form by experimental work using the SPM (Scanning Probe Microscope) (Jung et al., 1996) is clearly going to revolutionize our ability to make molecular structures and molecular machines (Drexler, 1992; Feynman, 1960).
Positional assembly is done using positional devices. At the scale of human beings, the major problem in positional assembly is overcoming gravity. Parts will fall down in a heap unless they are held in place by some strong positional device. At the molecular scale, the major problem in positional assembly is overcoming thermal noise. Parts will wiggle and jiggle out of position unless they are held in place by some stiff positional device (Merkle, 1999).
The fundamental equation relating positional uncertainty, temperature and stiffness is:
s2 = kbT/ks
Where s is the mean error in position, kb is Boltzmann's constant, T is the temperature in Kelvins, and ks is the "spring constant" of the restoring force (Drexler, 1992). If ks is 10 N/m, the positional uncertainty s at room temperature is ~0.02 nm (nanometers). This is accurate enough to permit alignment of molecular parts to within a fraction of an atomic diameter.
A stiffness of 10 N/m is readily achievable with existing SPMs, but stiffness scales adversely with size. As we shrink a robotic arm, it gets less and less stiff and more and more compliant, and less and less able to position a part accurately in the face of thermal noise. To keep it stiff we have to make it from stiff parts. This is the fundamental driving force behind our desire to keep the MBB stiff.
In summary: stiffness is a fundamental design objective because we want to use positional assembly on molecular parts despite the positional uncertainty caused by thermal noise. This objective permeates our MBB design considerations.
MBBs with three linking groups could, like sp2 carbon, form planar structures with good in-plain strength and stiffness, but would be weak and compliant in the third dimension. While this problem could be reduced by forming tubular structures, stiff structures made using this approach would have to be made from many MBBs, as small numbers of MBBs (too few to form tubular structures) would lack stiffness.
MBBs with four linking groups not in a common plain are convenient for building three dimensional structures (much as the four bonds in a tetrahedral sp3 carbon atom allow it to form a stiff, polycyclic three-dimensional diamond lattice).
MBBs with three linking groups can be paired, each member of the pair sacrificing one linking group to form the pair. The pair of MBBs effectively has four linking groups (two available linking groups being provided by each member of the pair). Particularly if the four resulting linking groups are non-planar, the pair can be viewed as a single MBB with four linking groups. In this somewhat roundabout fashion, MBBs with three linking groups can form three dimensional structures much as MBBs with four linking groups.
MBBs with five linking groups can form three dimensional solids. For example, an MBB might have three in-plain linkage groups with inter-linkage-group angles of 120°; and have two out-of-plain linkage groups, both of which are normal to the plain (one linkage group pointing straight up, the other straight down). Such an MBB could form hexagonal sheets by using the three in-plain linkage groups, (each MBB corresponding to a single carbon atom in a sheet of graphite) but would also be able to link together adjacent sheets by using the two out-of-plain linking groups. The unit cell would have hexagonal symmetry.
MBBs with six linking groups can be connected together in a cubic structure, the six linking groups corresponding to the six sides of a cube or rhombohedron. MBBs with six linkage groups can naturally and easily form solid three dimensional structures in the same fashion that cubes or rhomboids can be stacked.
Buckyballs (C60) have now been functionalized with six functional groups (Hutchison et al., 1999; Quin and Rubin, 1999), opening up the possibility of using them as molecular building blocks for the construction of three dimensional structures.
An MBB with six in-plain linkage groups can form a particularly strong planar structure or sheet. The conformation of the sheet would depend only on the length of the inter-MBB links, and not on any ability of the MBB to maintain two linkage groups at some specific angle. As the distance between linked MBBs can often be controlled more effectively (the stretching stiffness of the link can be higher) than the angle between adjacent linkage groups (the bending stiffness is usually lower), this structure can be significantly stiffer in-plain than a planar structure formed from similar MBBs with three linkage groups.
Cubic or hexagonal close packed crystal structures are very stiff, involving 12 linking groups from each MBB. These structures can be described as follows: two very stiff sheets (six linkage groups in-plain) can be laid on top of each other. Each MBB in the upper sheet can be linked to three MBBs in the lower sheet (which form the vertices of a triangle). This arrangement can be repeated with a third, fourth, and more sheets. Six linkage groups connect each MBB to six in-plain neighbors, three linkage groups connect each MBB to three MBBs from the plain below, and three linkage groups connect each MBB to three MBBs from the plain above. The major advantage of this type of MBB is that the stiffness of the whole structure depends only on the stretching stiffness of the links between MBBs and not on the angular stiffness between adjacent linkage groups. This can be useful when the angular stiffness is poor, but the stretching stiffness is good.
MBBs with four linking groups can be paired, each member of the pair sacrificing one linking group to form the pair. The pair of MBBs effectively has six linking groups (three available linking groups being provided by each member of the pair). The pair can be viewed as a single MBB with six linking groups. This again leads naturally to unit cells that are cubic or rhomboid, but with each unit cell comprising two MBBs. This is similar to the primitive unit cell of diamond, which has two carbon atoms.
In summary, MBBs with two linking groups form three dimensional structures only with difficulty and only by using indirect and complex methods. MBBs with three linking groups readily form planar structures, which are strong and stiff in the plain but bend easily, like a sheet of paper, unless rolled into tubular structures to improve stiffness. They can also be used (although somewhat less naturally) to directly form three dimensional solids with a unit cell having four MBBs. MBBs with four linking groups quite naturally form strong, stiff three dimensional solids in which the unit cell is composed of two MBBs (as in diamond). MBBs with five linking groups can readily form strong, stiff three dimensional solids in which the unit cell is composed of six MBBs. MBBs with six linking groups readily form strong, stiff three dimensional solids in which the unit cell is composed of a single MBB. They can also form very stiff sheets if all linkage groups are in-plain, though this arrangement sacrifices stiffness out-of-plain. MBBs with twelve linking groups can form very strong and stiff three dimensional solids.
While MBBs can have any number of linkage groups, MBBs with fewer linkage groups are usually (though not always) more readily synthesized. If we seek an MBB with the least number of linkage groups that can still readily form strong, stiff three dimensional structures, then MBBs with four linkage groups are quite attractive. A high symmetry structure with four linkage groups will have tetrahedral symmetry (with an inter-linkage-group angle of approximately 109°). Much of the discussion in this paper is about specific tetrahedral MBBs.
In contrast, MBBs for positional assembly need not be soluble and do not even need a solvent: they can be used in vacuum. Like bricks, they can be picked up and moved to the desired location whether they are soluble or not.
If two MBBs can bond strongly to each other in two or more different configurations, then the self assembly process will randomly select from among these multiple configurations and produce a random clump of MBBs rather than any specific desired arrangement. For this reason, MBBs for self assembly often use multiple weak bonds, rather than a few strong bonds. Any particular weak bond can be broken by thermal noise. Only when the action of multiple weak bonds is combined does the resulting configuration of MBBs remain stable. Configurations that simultaneously enable multiple weak bonds are relatively rare, and so it is easier to design MBBs with multiple weak bonds that self assemble into a single desired structure.
By contrast, positional assembly can use MBBs that readily form a few very strong bonds. Inappropriate interactions between positionally assembled MBBs are prevented by the simple expedient of keeping them away from each other. When two MBBs are brought together, their orientations are controlled to prevent inappropriate bond formation. Thus, selective control over bond formation is achieved through positional control, rather than by designing the MBBs to be selective in bond formation. This approach permits the use of highly reactive MBBs that would be entirely inappropriate for self assembly.
The disadvantage of highly reactive MBBs is that they must be positionally controlled at all times. They cannot be allowed to mix randomly at any time, as this would cause them to rapidly form unusable clumps. While achievable, this imposes a number of constraints that are more difficult to meet with today's systems.
An alternative approach is to use protecting groups that cover or alter the highly reactive linkage groups. These protecting groups would then be removed when two positionally assembled MBBs were joined. The use of protecting groups is common in chemical synthesis, though the concept of selectively removing a protecting group from a single molecule by using positional control is still novel. Selective photoactivation of molecules within a region comparable in size to the wavelength of light is well known and used commercially. From the perspective of nanotechnology, regions that are hundreds of nanometers in size are very large, making optical approaches rather imprecise when viewed from the perspective of the desired long term objectives.
Positionally assembled MBBs must be held, while self assembled MBBs need not be held. This implies that positionally assembled MBBs must have "handles" by which they can be gripped. While it is possible in some cases to use the linkage groups of the MBB as handles, these linkage groups might well be intended to irreversibly form strong bonds. Because it is essential in positional assembly both to hold the MBB and to let go, such an MBB must be able to form reversible attachments to the positional device. Ideally, this would be done using a variable affinity binding site which has two states: bound and unbound. The tip of the positional device first binds to the MBB. Then it positions the MBB with respect to some workpiece under construction, to which the MBB bonds. Finally, the positional device releases the MBB. Tweezers serve this function: when closed they can grasp an object (high affinity), when open they release the object (low affinity). While there are many other designs for variable affinity binding sites (Merkle, 1997b), tweezers are widely applicable and illustrates the basic concept.
Pragmatically, the greatest advantage of self assembled MBBs is the extensive literature on self assembly and the extensive set of existing experimental techniques that have been used to self assemble some impressively complex structures. Positional assembly at the molecular scale, by contrast, is still in its infancy. For example, the self assembly of DNA into complex molecular structures has made remarkable strides (Seeman, 1994), and has been used to make a truncated octahedron (Zhang, 1994). To quote Seeman and coworkers (Seeman et al., 1997):
There are several advantages to using DNA for nanotechnological constructions. First, the ability to get sticky ends to associate makes DNA the molecule whose intermolecular interactions are the most readily programmed and reliably predicted: Sophisticated docking experiments needed for other systems reduce in DNA to the simple rules that A pairs with T and G pairs with C. In addition to the specificity of interaction, the local structure of the complex at the interface is also known: Sticky ends associate to form B-DNA. A second advantage of DNA is the availability of arbitrary sequences, due to convenient solid support synthesis. The needs of the biotechnology industry have also led to straightforward chemistry to produce modifications, such as biotin groups, fluorescent labels, and linking functions. The recent advent of parallel synthesis is likely to increase the availability of DNA molecules for nanotechnological purposes. DNA-based computing is another area driving the demand for DNA synthetic capabilities. Third, DNA can be manipulated and modified by a large battery of enzymes, including DNA ligase, restriction endonucleases, kinases and exonucleases. In addition, double helical DNA is a stiff polymer in 1-3 turn lengths, it is a stable molecule, and it has an external code that can be read by proteins and nucleic acids. [references omitted from this quote]The great drawback of self assembly, that it produces weak and compliant structures, can likely be adequately dealt with for transitional systems by careful design and post-modification of the self assembled structure to increase strength and stiffness. While the stiffness of DNA is good in comparison with most other polymers (Hagerman, 1988), it is still poor when compared with bucky tubes, graphite, diamond, silicon, and other "dry" nanotechnology materials.
First and foremost, the linkage groups will have particular properties. Of crucial concern are the conditions under which the links are made, and the extent to which inappropriate links are possible. If a specific functional group, call it R, bonds readily with other functional groups of type R (as is true for radicals), then the MBB cannot be kept in solution without rapidly forming undesired clumps. These limitations can be overcome by the use of protecting groups (or otherwise introducing some barrier to reaction) although this adds the additional requirement that the protecting groups be removed before an MBB is added to a growing workpiece.
A second type of linkage will involve two distinct functional groups, call them A and B. Functional groups of type A will readily bond with functional groups of type B, but A will not bond to A and B will not bond to B. The Diels-Alder reaction (Krummenacker, 1994) is a good illustration of this kind of functional group. The diene and dieneophile (corresponding to functional groups of type A and type B) will bond to each other, but not to themselves. They also bond to little else, and so can be used in most solvents (or in vacuum) and in the presence of impurities. As there are no leaving groups, the reaction itself does not introduce any possibly undesired contaminants.
A second advantage of the A-B functional groups is their increased tolerance of positional uncertainty. Consider two types of MBBs, type A and type B. Type A MBBs have four linkage groups of type A, while type B MBBs have four linkage groups of type B. Type As cannot link with other type As, nor can type Bs link with other type Bs. When type A and type Bs are combined in the diamond (or actually zinc-blende or wurtzite (hexagonal)) crystal lattice, they alternate. Each A is surrounded by four Bs, and each B is surrounded by four As.
In both the zinc-blende and wurtzite structures, there are no cycles of length five but many cycles of length six. That is, if we traverse a path from one MBB to another along the links between them, we will never find that we have completed a cycle and returned to the starting MBB without including at least six MBBs along the path. Clearly, a cycle with an odd length (such as five) would imply that either two As were linked or that two Bs were linked. This is forbidden by the nature of the A-B building blocks.
If, however, we were using MBBs of type R, which can readily link to each other, than a path of length five would be possible if the geometry of the MBBs was sufficiently distorted. Such a distortion might occur if the linking groups were insufficiently stiff, and permitted Rs near the edge of the crystal to come into contact with each other. This is exactly what happens on the diamond (100) surface, which forms strained dimers from adjacent carbon atoms which, if they were part of the bulk, would be separated by an additional carbon atom between them.
The use of A-B MBBs eliminates the possibility of odd cycles, and particularly cycles of length five. However, it does not eliminate cycles of length four, which could in principle occur if the geometry were sufficiently strained. As the strain required to achieve a cycle of length four is greater than the strain required to achieve a cycle of length five, R MBBs in a diamond lattice will more readily produce undesired cycles of length five than similar A-B MBBs will produce undesired cycles of length four.
This principle can be extended by introducing more types of functional groups, D, E, F, .... The more types of functional groups, the more strained the geometry must be before an incorrect link can be formed. In the limit, an arbitrary finite structure composed of a fixed number of MBBs arrayed in a regular lattice similar to diamond (or related structures) would have functional groups all of which were distinct and unique. Self assembly of such a structure would occur when the MBBs were mixed, and positional assembly would not be required at all. One method of providing a very large number of distinct types of functional groups is with DNA. There are many short DNA sequences that are selectively sticky, and which would bond only to the appropriate complementary sequence. Experimental work linking gold nanoparticles with DNA suggests this approach is experimentally accessible (Mirkin, 1996).
This illustrates a more general point: self assembly and positional assembly are endpoints on a continuum. As positional accuracy becomes poorer and poorer, "positional" assembly becomes more like self assembly. The techniques used in self assembly to ensure accurate assembly despite positional uncertainty can be gradually introduced into positional assembly as accuracy degrades.
This also illustrates the importance of stiffness in the linkage groups. The stiffer the linkage groups, the less likely that links will be formed where they shouldn't be. In the limit, sufficiently stiff linkage groups would entirely prevent strained (incorrect) structures from forming.
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This line of reasoning leads fairly directly to molecules like adamantane: a stiff tetrahedral molecule which can be readily functionalized. Composed of 10 carbon atoms the Beilstein database lists over 20,000 variants, supporting the idea that this family of molecular structures is large, contains many readily synthesized members, and has enough "design space" to provide solutions able to satisfy the multiple constraints imposed on a "good" molecular building block.
A few molecules in this class include adamantane; 1,3,5,7-tetrasila-adamantane; 1,3,5,7 tetrabora-adamantane (not yet synthesized, though 1-bora-adamantane has been synthesized); 1,3,5,7-tetraaza-adamantane (more commonly known as methenamine, readily synthesized and with a variety of commercial applications (Budavari et al., 1996)); 2,4,6,8,9,10-hexamethyl-2,4,6,8,9,10-hexabora-adamantane; and many others.
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Small pieces of "hexagonal diamond," such as iceane, have similar properties and could also be used as the basis for MBBs.
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If we use 1,3,5,7 tetrabora-adamantane and 1,3,5,7-tetraaza-adamantane as "B" and "N" building blocks, then each linking atom (N or B) is bonded to three other atoms in its MBB, thus providing a stiff support. The class of structures that can be formed includes the kind of structures typical of (for example) silicon carbide, where alternating silicon and carbon atoms are each bonded to four neighboring atoms of the other type. The B and N type adamantane-based MBBs are, in essence, larger versions of the same concept.
While 1,3,5,7 tetrabora-adamantane has not been synthesized, DFT calculations using a 6-311+G(2d,p) basis set show the molecule is a minima on the potential energy surface (Halls, 1999). While boron with three single bonds is normally planar, it is strained by the tetrahedral nature of the adamantane cage. Stabilization of the boron atoms in the tetrahedral (rather than planar) bonding pattern by suitable electron donor groups (e.g., NH3) should increase the stability of the building-block plus four-donor-groups complex.
One method of additive synthesis is to add invididual building blocks (rather than groups of building blocks) one at a time. Using positional assembly, this requires a method of grasping and releasing the individual building blocks. As the building blocks already have four sites designed to bind to the complementary building block, these sites could be used to "grip" the building blocks while they were positioned. The tip of the positional device would need to be specifically designed to bind to the building blocks strongly enough to hold them while they were being positioned and oriented, but weakly enough that they could be released when the positional device was withdrawn from the workpiece under construction (or, alternatively, the tip could undergo some change to reduce its binding affinity for the building blocks).
Using substractive synthesis, undesired building blocks could be removed by scraping them away. The major advantage of this approach is that the tip of the positional tool need not bind to the building blocks, and therefore a much wider range of tip structures would be acceptable. Orientation requirements for the tip would also be relaxed. Force applied to a single building block on the surface would break it free from the workpiece. Provided that the bonds holding the building block together were significantly stronger than the bonds between building blocks, whole building blocks would be removed from the workpiece (rather than fragmenting the building blocks).
Subtractive synthesis has another advantage: adding building blocks one by one will on occasion produce situations where the new building block is bound to the workpiece by a single bond (the first building block to be added on a (111) surface, for example). Because it is held by only a single bond, the building block will not be as well bound to the rest of the structure and would have a higher probability of falling off before further building blocks could be added. This is of particular concern when weak bonds are being used between building blocks.
By contrast, substractive synthesis can leave intact all bonds that will be present in the final (desired) structure. If the final structure has been designed so that each building block is held in place by at least two bonds, then at every point during synthesis every building block that will be kept will be held in place by at least two (and often three) bonds. As the probability that a building block will break away from the workpiece is an exponential function of the depth of the potential energy well in which the building block finds itself, and as the depth of this well is doubled when two bonds hold it in place as compared with only a single bond, this difference can be significant.
One of the intriguing aspects of subtractive synthesis is the remarkably wide range of potential building blocks that could be used. Virtually any large, reasonably stiff and reasonably compact organic molecule that remains crystalline at reasonably high temperatures could be used. Adamantane itself, for example, melts at 268°C. (Weast, 1989). Such building blocks would be held together primarily by van der Waals forces, which would increase as the size of the building blocks increased. Precise modification by an SPM in UHV (Ultra High Vacuum) would seem feasible provided the tip was sharp in comparison with the size of the building block. The primary concern would be that building blocks on the surface (rather than in the bulk) might be so weakly bound that they would leave the surface. This could in general be dealt with by lowering the temperature, but a more careful search through the space of possibilities for building blocks that remained bound to the surface at room temperature might prove simpler. It might also be possible to find building blocks that could be selectively removed without the use of UHV, further simplifying the experimental procedure.
Using two building blocks that alternate to form a crystal, a somewhat related but more structurally specific process (which we might call starburst crystals) would be to start with a single building block of type A and link it to as many building blocks of type B as possible (typically four or six). This might be done by adding a dilute solution of A to a concentrated solution of B, and then separating the ABn results. If the A building block is designated A0, then we might call the A building block surrounded by B building blocks A1.
This process can be repeated, the A1 building block can be mixed into a concentrated solution of A building blocks, adding an additional layer to the growing crystal and producing A2. A2 can be mixed into a concentrated solution of B building blocks, producing A3.
The critical difference between this process and the growth of a starburst dendrimer is that starburst crystalization adds building blocks only at those sites which extend the crystal structure. Thus, a new building block added in the Nth layer might bind to two or even three building blocks from layer N-1. Rather than exponential growth in the number of steps, this process has a growth rate that is cubic in the number of steps and the structure that results can be viewed as that part of a crystal that includes all crystal elements within a certain distance from some center.
If a building block added to layer N links to two building blocks from layer N-1, then it must link to the right two building blocks. If the links between building blocks are sufficiently stiff, this is not a problem. The new building block in layer N can only link appropriate pairs of building blocks from layer N-1. However, if the linkages are too floppy, the new building block might link to an incorrect pair of building blocks from layer N-1, producing an incorrect result. Preventing this requires either control over the geometry of growth (the bonds between building blocks cannot be too floppy) or selective control over linkage formation (different chemistries could be used for the formation of different links, even from the same building block; or linkage groups could be protected and de-protected).
A second obviously desirable structure would be a joint, which would provide one degree of rotational freedom and essentially no other degrees of freedom. The feasibility of sliding surface joints would depend in large part on the precise nature of the building blocks, but there is in general no problem in designing bearings with sliding surfaces (Merkle, 1993b). If the surfaces are not otherwise attractive to each other (e.g., hydrogen terminated carbon) then well designed bearings should have a small barrier to sliding motion. Bearings made from curved (strained) structures should be feasible at some scale, regardless of the building block, because some degree of strain is always tolerable.
Alternatively, multiple single-linkage-group bearings could be aligned. Two building blocks with intercalating layers could have single rotationally free linkage groups between facing layers. As the layers are molecularly precise, perfect alignment of such single-linkage-group bearings from successive layers would be feasible, thus permitting a molecular bearing of tolerable strength (at least at the molecular scale) to be built.
Finally, a more traditional door-hinge type of joint could be built by using intercalating layers from the two halves of the joint. Rather than attempting to strain the building blocks to provide smooth surfaces, relatively large holes (many building blocks in diameter) could be made which were aligned from layer to layer. A tubular pin (possibly made from strained building blocks, or possibly of some other type, such as buckytubes) could then be inserted through the holes, in the expecation that the smooth surface of the pin would be sufficient to support hinge rotation.
While the use of strained building blocks is feasible, it would also be possible to use building blocks that were "pre-strained." For example, if a single edge atom in adamantane were changed from C to Si, the resulting building block would no longer be exactly tetrahedrally symmetric. Appropriately "malformed" building blocks could be used on specific crystal surfaces to relieve strain of a particular type. In addition, dislocations could be introduced into the structure. Special building blocks, designed specifically to relieve strain at the core of the specific dislocation, could be used to insure the stability (and feasibility) of the dislocation structure.
Rotary joints are of major importance for positional devices. It is possible to make a Stewart platform using nothing but appropriate rotary joints between otherwise rigid blocks. The design is left as an exercise for the reader -- though we note here that each of the six struts in a Stewart platform must support two degrees of freedom at each end, much as a universal joint, and one degree of rotational freedom along the axis of the strut (Merkle, 1997c). Powering movement of the platform by moving the ends of the struts opposite the platform is a separate issue that is not dealt with by this design -- though almost any powered one-degree-of-freedom movement of the "free" end of the strut would be sufficient.
Adamantane, C10H16, is a tetrahedrally symmetric stiff hydrocarbon that provides obvious sites for either four, six or more functional groups. Over 20,000 variants of adamantane have been synthesized, providing a rich and well studied set of chemistries. Further research into this set of possibilities is worthwhile.