Abstract

Molecular manufacturing should let us synthesize most arrangements of atoms that are consistent with physical law. Assemblers have been proposed as a means for accomplishing this objective (see, for example, Merkle, 1996a). They would be able to build a wide range of useful products as well as copies of themselves. A simpler though less general proposal is a hydrocarbon assembler, restricted to manufacturing relatively stiff hydrocarbons. The design and analysis of such an assembler should be substantially simpler than that of a more general assembler. In this paper, we consider the "intermediary metabolism" of a hydrocarbon assembler, i.e., the set of reactions that permit processing of the feedstock molecules and their conversion into molecular tools (positionally controlled carbenes, radicals, and other reactive species). The specific feedstock molecule analyzed is butadiyne (a linear molecule, C₄H₂, also known as diacetylene; not to be confused with the more common but chemically distinct non-linear molecule butadiene: C₄H₆).

Introduction

Most members of the class of stiff hydrocarbons cannot be synthesized today, let alone economically synthesized. More broadly, almost none of the ways that physical law in principle allows us to arrange atoms can be economically achieved with present methods. The objective of the field of molecular nanotechnology is to develop methods which permit the economic synthesis of most structures permitted by physical law. As the direct attempt to achieve this objective might prove difficult, the problem is often broken down into subobjectives and subgoals. One approach is to assume that a general and inexpensive ability to manufacture complex structures with molecular precision can be achieved by using an assembler (Merkle, 1996a). The design of such a device is further broken down into subsystems, and the design and analysis of the subsystems carried out in greater detail. Various aspects of the over all system design can be considered (Drexler 1992, Merkle 1992, 1996a, 1997a, 1997b). This paper focuses on simplifying the set of molecular tools used, and the chemical reactions used to refresh those tools.

A complete analysis of the reactions by which an assembler converts incoming raw materials into reactive tools used to synthesize molecular structures is greatly simplified if we restrict ourselves to the elements hydrogen and carbon, and further restrict our attention to structures that are relatively stiff (excluding, for example, floppy polymers). The stiff hydrocarbons include a wide enough class of materials to be a very attractive goal (diamond, graphite, and structurally related materials are included in this class). Essentially all mechanical structures can be made from stiff hydrocarbons; including struts, bearings, gears, levers, etc. This can be most readily seen by noting that the strength-to-weight ratio of diamond is over 50 times that of steel or aluminium alloys -- a single part made of metal could be functionally replaced by a similarly shaped stiff hydrocarbon part. The resulting part would be lighter and stronger than the part it replaced, improving overall performance. The class of stiff hydrocarbons also includes molecular computers which, by today's standards, would be extraordinarily powerful (Drexler, 1992).

A more general assembler, able to manufacture structures which incorporate most of the elements of the periodic table, would be substantially more difficult to analyze. One approach to breaking down the task of building a relatively large and complex structure would be to consider a series of small incremental changes to an exposed surface, the cumulative effect of which would be to manufacture the whole. This implies we must analyze small changes to the exposed surface, presumably by considering small clusters of atoms on that surface. A very minimal cluster might be a single atom and the atoms to which it is bonded. If one atom is bonded to (say) three neighbors, and all four atoms can be any one of about 100 possibilities, then this gives us 100⁴ or ~100,000,000 possible clusters. This analysis is crude and likely too small because (a) atoms are often bonded to more than three other atoms and (b) understanding an incremental change to a small cluster often requires examination of atoms farther away than one bond length. Despite its shortcomings, this crude model tells us that we will need to analyze many types of incremental surface modifications before we can reasonably hope to synthesize the full range of structures accessible using this approach.

By contrast, if our structures contain only hydrogen and carbon then the design and analysis problems become much simpler. Hydrogen can only be bonded to one other atom which, if we exclude hydrogen gas, must be carbon. A carbon atom will usually be bonded to two, three, or four neighboring atoms, which can only be hydrogen or carbon. Our previous crude analysis would assign 2⁴ or 16 possible local clusters for carbon. While this can be reduced by considering isomers, it must also be increased to consider interactions that extend beyond a single bond length, e.g., aromatic rings and the like. In any event, the complexities of analyzing hydrocarbon structures with sufficient accuracy for the purposes discussed here is tractable with present capabilities. We cut short the combinatorial explosion before it begins.

While this rather drastic pruning makes the problems of designing and analyzing a hydrocarbon assembler more tractable, it does not directly address the feasibility of more general assemblers. Smalley in particular has argued (Smalley, 1997a) that a "completely universal" assembler is impossible, though he also said (Smalley, 1997b) "Most interesting structures that are at least substantial local minima on a potential energy surface can probably be made one way or another." He argues that a small set of molecular tools will be unable to catalyze all the reactions needed to synthesize the remarkably wide range of structures that are possible. Success will require the use of a great many custom-made catalytic structures.

Given the remarkable size of the combinatorial space of possible molecular structures it does indeed seem likely that at least some members of this space will resist direct synthesis by an assembler equipped with a relatively modest number of molecular tools. However, even if we assume that a substantial percentage of the space is inaccessible via this route (an assumption as yet lacking any clear support) the remaining "small" fraction would include structures of enormous value. Even the ability to manufacture only the highly restricted range of structures defined by the stiff hydrocarbons would usher in a revolution in manufacturing.

Further research aimed at clarifying the range of structures amenable to synthesis by positionally controlled molecular tools seems called for. Ideally, this would include not only the proposal and analysis of particular sets of molecular tools and the range of structures they could reasonably make, but also proposals of structures which could not be synthesized by the use of positionally controlled molecular tools.

One example of an "impossible" structure is a cubic meter of flawless diamond. Before it could be finished, background radiation would have introduced flaws. Drexler argued that it should be possible to define a structure which would be stable if complete but unstable when almost complete, a sort of molecular stone arch (Drexler, 1986, page 246). However, a specific, relatively small, stiff and stable structure that can reasonably be viewed as "impossible" to synthesize using positionally controlled tools has not yet been proposed. While it seems likely that at least some such structures must exist, our understanding of this issue would be greatly improved by specific examples.

An assembler operates in some external environment. While many environments are possible, we consider one specific environment in this paper: a feedstock solution made from the solvent acetone; butadiyne as a source of hydrogen and carbon; neon to support acoustic waves in the interior of the assembler while at the same time not reacting with the highly reactive molecular tools; and a "vitamin" which provides small amounts of elements such as silicon, tin, and one (or more) transition metals -- used basically for catalytic purposes.

Butadiyne (C₄H₂) seems attractive as a source of hydrogen and carbon for several reasons. The linear structure of butadiyne means that a simple tubular structure, such as a bucky tube, can serve as a suitable binding site to bind butadiyne from the feedstock solution (Merkle, 1997a). As bucky tubes are themselves made of hydrocarbons, a system which can synthesize most hydrocarbons should be able to synthesize the required binding sites. Second, as suggested by the following, relatively simple reactions can be used to convert butadiyne into useful molecular tools. Third, butadiyne has two carbons for every hydrogen. While it's difficult at present to make precise statements about the ratio of carbon to hydrogen in the structural elements of a hydrocarbon assembler, the presence of graphite and relatively thick diamond structures would make carbon significantly more common than hydrogen. As the present proposal uses a single molecule to provide both hydrogen and carbon, a molecule with a relatively high ratio of carbon to hydrogen is desirable (provided other constraints can be met).

By definition, an assembler can make another assembler: they are self replicating (Merkle, 1992, 1994, 1996a). To support self replication it is essential to achieve closure: it must be possible for the assembler to make everything it needs from the feedstock. In this paper, which focuses on the needed molecular tools, we must show that it is possible to generate a new set of molecular tools given only an existing set of molecular tools and a supply of butadiyne. It is not quite sufficient to show that it is possible to make each individual tool given the set of molecular tools and butadiyne. For example, if we could make one dimer deposition tool but used two hydrogen abstraction tools in the process, and we could make one hydrogen abstraction tool but required two dimer deposition tools in the process, then it would be impossible to make a new set of molecular tools from an existing set of molecular tools. The process would "run down hill" until we had exhausted our initial set of tools.

We will first consider how to make each molecular tool, and then consider "quantitative parts closure" in a later section to ensure that it is possible to manufacture a complete set of new tools without depleting an existing set.

Thermal noise

While we do not present an explicit analysis of the effects of thermal noise, some general observations seem in order. Classical positional uncertainty is described by the equation (Drexler, 1992):

(1) sigma² = kT/k_s

where:

• sigma is the mean positional uncertainty (meters, m)
• k is Boltzmann's constant (Joules/Kelvin, J/K)
• T is the absolute temperature (Kelvins, K)
• k_s is the stiffness (Newtons/meter, N/m)

Positional uncertainty can be reduced by increasing stiffness and lowering temperature. Obviously, we can reduce temperature if that should prove necessary. We can also increase stiffness: the stiffness of a structure scales favorably with size. If we have two positional devices (e.g., two robotic arms or two Stewart platforms) of otherwise similar design, the larger device will be stiffer. If the larger device is twice the size, and if all its components are scaled to be twice as large in all dimensions, then it will have twice the stiffness of the smaller device.

Once we know how much positional uncertainty we can tolerate -- and for specific molecular tools that are used to cause specific reactions to occur at specific sites, we can compute the maximum positional uncertainty that can be tolerated before something goes wrong -- then we can design a positional device with the required stiffness. This can be done either by scaling the device size, or by specifying the operating temperature. If we specify room temperature operation then we find that the device size is largely dictated to us. (Drexler, 1992) analyzed this problem and concluded that a robotic arm of about 100 nm (nanometers) in height and 30 nm in diameter and made of diamondoid materials would have a positional uncertainty at room temperature that was a modest fraction of an atomic diameter. (Merkle, 1997b) reached substantially the same conclusions. Stiff hydrocarbons should suffice to make both these and many other positional devices.

To provide a numerical example: if a positional device has a stiffness k_s of 10 N/m, then at room temperature (kT ~ 4 × 10^-21 J) equation (1) implies a positional uncertainty sigma of 0.02 nm (0.2 Å). The gaussian fall off implies that positional errors of even a few sigma are of very low probability. A properly designed diamondoid positional device should easily be able to achieve a stiffness much higher than 10 N/m. For comparison, the carbon-carbon bond has a stretching stiffness of about 440 N/m.

Put another way, the energy of a system is:

(2) E = 1/2 k_s x²

For our example k_s of 10 N/m, a 0.154 nm (1.54 Å) deviation (about the length of a carbon-carbon bond) increases the energy of the system by 1.18 × 10^-19 J (17 kcal/mol). Such a positional device is very unlikely to make an error as large as a bond length at room temperature.

The molecular tool itself cannot be scaled. A specific molecular tool operated at a particular temperature will have an upper bound on reliability that cannot be improved regardless of how stiff we make the supporting robotic arm. While the molecular tool cannot be scaled, it can be redesigned. The unmodified hydrogen abstraction tool has an estimated lateral stiffness at the carbon atom at its tip of about 6 N/m (Drexler, 1992, figure 8.2). (This tool is long and thin, which is adverse for stiffness). Drexler suggested buttressing the relatively flexible base of the hydrogen abstraction tool, and proposed one redesign which had an estimated stiffness of 65 N/m.

Ultimately, the room temperature reliability of molecular tools suitable for the synthesis of hydrocarbons depends on the achievable stiffness. Existing work suggests that reliable operation at room temperature can be achieved.

Butadiyne

Butadiyne, H-C#C-C#C-H, has a melting point of -36.4°C and a boiling point of 10.3°C. It dissolves readily in acetone. It can polymerize explosively under some conditions. The following information is from (Shostakovskii and Bogdanova, 1974), who provide rules for the safe handling of butadiyne. These include adequate dilution (less than about 30% by volume of butadiyne) and low temperatures (below about 0°C). Mixed 1:1 with butane, liquid butadiyne can be heated to a temperature of 220°C at a pressure of ~1.6 × 10⁷ Pascals (160 atmospheres) "without any danger of explosion." At 25°C and 500 mm Hg the gas showed no evidence of polymerization after 55 days. After three months in a sealed tube at room temperature, a 7.4% solution of butadiyne in acetone showed a "floculent polymer precipitate." Various inhibitors are recommended to prevent polymerization. The heat of solution of butadiyne in acetone is 10.3 Kcal/mole in the temperature range from -40°C to +15°C. Several other solvents could also be used, including butane.

While butadiyne was selected here as the primary feedstock molecule, this choice was motivated by considerations involving the simplicity and ease of analysis of the reactions and the simplicity of the binding site. Other hydrocarbon feedstocks will likely be advantageous when other criteria are used (e.g., ease of bulk production and handling of the feedstock).

A complete set of tools?

We assume that the following tools allow us to build all the stiff hydrocarbons that are needed in a hydrocarbon assembler. This assumption requires further investigation, but appears plausible at the present time. Our objective is therefore to synthesize and refresh the following molecular tools from butadiyne:

• The hydrogen abstraction tool:

  

• Two carbon, a silicon and a tin radical:

  

• Carbenes:

  

• The dimer deposition tool:

  

• Positionally controlled transition metal(s):

  

• The hydrogen deposition tool:

  

The hydrogen abstraction tool has been investigated using high order ab initio quantum chemistry by (Musgrave et al., 1991); and with molecular dynamics by (Sinnott et al., 1994) and (Brenner et al. 1996) using a potential energy function (Brenner, 1990) able to accurately model a wide range of hydrocarbon structures including transition states (e.g., bond formation and bond breaking). All support the conclusion that this tool should be able to abstract hydrogen from a wide range of hydrocarbons. The molecular dynamics simulations performed at 300 K support the idea that reliable room temperature operation should be feasible.

The elevation of the ethynyl radical to the status of "the" hydrogen abstraction tool is based on two main factors. First, it has a higher affinity than almost any other structure for hydrogen. While the H-F bond is stronger than the H-C bond in H-C#C-H, it is unclear how to hold and position a fluorine atom while retaining its high hydrogen affinity. Second, the ethynyl radical has desirable steric properties: it is unencumbered by bulky side groups and and can more easily abstract hydrogens from somewhat less accessible locations.

Many other radicals exist. The group IV radicals -- carbon, silicon, germanium, tin and lead -- seem particularly useful as they can be bonded to three supporting atoms in their radical state. This provides high stiffness and permits relatively large forces to be applied if desired. Group IV radicals also permit selection of radical properties -- the ethynyl radical is the strongest, the phenyl radical -- C₆H₅ -- is next, followed by the sp³ carbon radical; and then the silicon, germanium, tin and lead radicals in order. Radical properties can be fine tuned by modifying the supporting structures.

Many of the following reactions use one or more radicals. It is often unclear which radical would best serve a particular function. As a consequence, the specific radicals illustrated should be viewed as suggestions: substitution of alternative radicals, particularly other group IV radicals, might well prove advantageous.

Carbenes have proven remarkably useful in the synthesis of organic compounds. Positionally controlled carbenes should be equally if not more useful.

The ability to add two carbon atoms in a single operation using a dimer deposition tool provides more options in adding carbon to a growing structure. (A "dimer" is simply two of something joined together -- in this context, the "dimer" refers to two carbon atoms that are joined together by a triple bond: -C#C- ). While the addition of larger molecular fragments (e.g., polyyne strands, small segments of graphite, etc) will likely prove desirable in many circumstances, the short length of the present paper imposes limits on what we can consider. Future proposals will no doubt consider the advantages of adding larger moieties during the synthesis of hydrocarbons.

The remarkable utility of transition metal catalysts in chemical synthesis rather strongly suggests that positionally controlled transition metals can play a useful role in the synthesis of hydrocarbons. While the present paper uses only a single transition metal it seems likely that more than one will prove useful, particularly as we consider catalyzing a wider range of reactions than the specific ones considered here.

No single proposal is at present accepted as archetypal for the hydrogen deposition tool. Tin is a plausible candidate, as it forms a weak bond to hydrogen. Lead has an even weaker bond to hydrogen and so might prove superior.

We assume that synthesis takes place in an inert environment (vacuum or a noble gas) and that positional control is used throughout. (As the tools are often highly reactive, positional control is essential to prevent undesired reactions). These assumptions permit the use of novel and relatively simple reaction pathways. While the ability to achieve an inert environment using present methods might lead to an attractive implementation pathway, the primary point of the present discussion is to establish that, given a suitable environment, a relatively simple set of reactions and a relatively simple set of molecular tools should be sufficient to let us make the class of stiff hydrocarbons. This class of materials, with a few additions, should be sufficient to let us build some simple assemblers. This class would also let us build environments that would be inert, and in which reactive tools could be deployed with low error rates.

Binding and bonding to butadiyne

A bucky tube, such as the (9,0) bucky tube illustrated at the right, could serve as a binding site for a simple linear molecule like butadiyne (Merkle, 1997a). Such a binding site would serve to bind the butadiyne from the external feedstock solution, and would allow the transfer of the bound butadiyne to the interior of the assembler.

Free molecules inside the assembler must be avoided, as their uncontrolled collisions would produce undesired and unpredictable reactions. It is therefore most convenient to bond to butadiyne so that we can control its position and prevent it from uncontrolled encounters with, e.g., the reactive tools discussed here. As there are initially no bonds to the butadiyne it must be held in place by intermolecular forces (predominantly van der Waals and overlap repulsion forces) during the first bonding operation. This paper does not consider in any detail the structure of the site which both positions the butadiyne and makes it accessible to the appropriate molecular tools for the initial bonding operation. We do, however, point out that it is possible to completely surround the butadiyne with a custom-made structure specifically designed to position it during this operation. We also point out that this site will in general be very different from the binding site used to initially bind butadiyne from the feedstock solution.

As there are several tools, there are several candidates for the initial reaction. A carbene could be inserted into any of the bonds. As there are six atoms and five bonds, the carbene could potentially be inserted into any of five positions. There are three positions that are fundamentally distinct: one of the H-C bonds, one of the C#C triple bonds, or the central C-C single bond. Perhaps the most attractive possibility would be to insert a carbene into the H-C bond exposed when the butadiyne first enters the internal environment from its binding site. If the binding site is a bucky tube, then as the butadiyne first exits the bucky tube it could be met with a carbene. A detailed examination of such geometries is necessary to ensure that (1) the carbene will insert into the H-C bond, (2) the carbene will not insert into the adjacent C#C triple bond (despite the attractive electron density provided by the pi bonds) and (3) the butadiyne won't "slip by" and permit bonding in some other (undesired) location or fail to bond at all.

The use of radical additions might be a more attractive approach. As addition of a single radical would (a) permit the butadiyne considerable freedom (it could rotate around the newly formed bond) and (b) result in an open shelled (radical) structure, it would seem preferable to add to the butadiyne with two radicals and form two bonds to it. As we have several radicals to choose from and four carbons and two hydrogens as potential targets, there are many possible specific choices. One choice that seems particularly useful is two silicon radicals adding at the 1 and 4 positions. Following these additions the butadiyne moiety would be well controlled positionally, and we could remove the two hydrogens by applying two hydrogen abstraction tools. These reactions are illustrated below:

Reactions 1 and 2

If both radicals have the same spin then the obvious closed-shell electronic structure for the product requires an intersystem crossing. To ensure that this takes place rapidly and reliably, Drexler proposed that a "heavy" atom should be in the vicinity of the reaction.

Calculations at the 6-311+G(2d,p) Becke3LYP // 6-31G* Becke3LYP level show a barrier height for the addition of a single silicon radical (SiH₃) to a terminal carbon of the C₄H₂ of 14 × 10^-21 J (~ 2 kcal/mol). The geometry was optimized at the lower level of theory while a single point calculation at the optimized geometry was computed using the higher level of theory. Calculations were done using the Gaussian B3LYP keyword without zero-point vibrational correction. Details are available on the web at http://www.zyvex.com/nanotech/comp/. The "transition state" was not actually a stationary point on the potential energy surface as rotations of the SiH₃ moiety were blocked. (It is possible that the barrier to addition might be an artifact of this constraint). As the SiH₃ is supposed to be the tip of a larger tool (which would hinder any rotations), this better models the expected application.

The computed barrier is about three times thermal noise at room temperature, suggesting that the actual barrier for this radical addition is in any event small, and therefore that this reaction will be satisfactory in the present application (especially as activation energy could if necessary be provided by the use of mechanical force).

The use of silicon radicals in this first step permits us to use hydrocarbon structures to confine the butadiyne with less concern that surface hydrogens will be abstracted: the silicon-hydrogen bond is weaker than the carbon-silicon bond. As the radical will have to approach the butadiyne quite closely during the radical addition, and as the hydrocarbon structure confining the butadiyne will also have to be in close proximity to the butadiyne, allowing close proximity between the silicon radical and the confining structure relaxes a significant design constraint.

Another attractive possibility would be the use of two radicals but with different targets: one would attack a terminal hydrogen and the other would attack the adjacent carbon. If both radicals are appropriately positioned then this reaction could take place as the butadiyne emerged from a bucky tube. The result would be to transfer the hydrogen to one radical and the C₄H to the other radical.

Creating and extending the hydrogen abstraction tool

The next step is to create a hydrogen abstraction tool by transferring two carbon dimers to two carbon radicals (either sp² or sp³ radicals could be used in this step. While the illustrations are suggestive of an sp³ carbon, this is not necessary and might be undesirable in some cases). This is illustrated in the following figure:

Reactions 3 and 4

As we sometimes wish to use the dimer at the end of a polyyne as the source of carbon for some other reaction, we need a way to extend the polyyne. This is illustrated below:

Reaction 5

Reaction 6

Another useful reaction is the transfer of a dimer from one polyyne to another:

Reactions 7 and 8