A proposed "metabolism" for a hydrocarbon assembler

by

Ralph C. Merkle
Xerox PARC
3333 Coyote Hill Road
Palo Alto, CA 94304
merkle@xerox.com
www.merkle.com

Copyright 1997 by Xerox Corporation. All Rights Reserved.

This paper is available on the web at http://www.zyvex.com/nanotech/hydroCarbonMetabolism.html. It was published in Nanotechnology 8 (1997) pages 149-162. The published version may differ in some respects from this web page.

The author gave a talk based on this paper at the Fifth Foresight Conference on Molecular Nanotechnology.

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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/ks

where:

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 ks 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 ks x2

For our example ks 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 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

Refreshing the carbene insertion tool

Insertion of a carbene would usually be followed by withdrawal of the tool and detachment of the final carbon. It is therefore necessary to add a carbon to the end of the tool to refresh it. We can transfer a dimer from the end of a polyyne to the end of a cumulene using the following method. First, bond the end of the cumulene and the polyyne. The resulting structure is somewhat schizoid. The left end is a cumulene and the right a polyyne, but where the change takes place is not always clear. We can shift this point by using a silicon radical. We can also weaken the bond we wish to break by using an appropriate transition metal catalyst. Force applied to the ends will now cause the linear carbon sequence to break, presumably at the transition metal. This sequence of reactions is illustrated below:

Reactions 9 and 10

This sequence adds two carbons to the end of the carbene insertion tool, thus refreshing it. If we wish to increase the number of carbene insertion tools (note that we added carbons to a carbene insertion tool, but did not increase their number) we could take the lengthened carbene insertion tools and attach them to a diamond surface: the (100) surface seems particularly attractive for this purpose. Breaking the resulting cumulene would then produce two carbene insertion tools when before there was only one.

We will sometimes wish to transfer a single carbon atom from the end of one cumulene to another (rather than transferring a dimer consisting of two carbon atoms from a polyyne to a cumulene). Two cumulenes are joined, and then separated. The point of separation is different from the point where they were joined. The point of separation is controlled by the point at which two silicon radicals are applied to the cumulene strand. This is illustrated in the following sequence:

Reactions 11, 12 and 13

Reaction 14

A hydrogen deposition tool

Several of the preceding reactions used a hydrogen abstraction tool (the ethynyl radical). As a consequence, we must refresh this tool without using tools which require the hydrogen abstraction tool for their production. At the same time, we wish to create a hydrogen deposition tool -- a tool with a weakly bonded hydrogen. When used, the hydrogen deposition tool will transfer a hydrogen to a specific site. After use, the hydrogen deposition tool will have to be refreshed by transferring a hydrogen to it.

The obvious solution to both these problems is to transfer the hydrogen from the abstraction tool to the deposition tool.

As noted earlier, there are many possible structures that would serve as a hydrogen deposition tool. One candidate is tin, which forms a weak bond to hydrogen. One reaction to transfer a hydrogen from the abstraction tool to the depsosition tool is shown:

Reaction 15

This is similar to the proposal by (Drexler, 1992) and simultaneously refreshes both the hydrogen abstraction tool and the hydrogen deposition tool.

While this reaction is most useful, the tin radical is quite weak. While AM1 suggests that the H-C bond is weakened to 3 × 10-19 J (~45 kcal/mol) by the radical addition, there might still be a barrier to abstraction by tin (and the AM1 estimate might itself be seriously in error, see below). On the other hand, positional control can be used to weaken the H-C bond by, e.g., straightening the C#C-C angle; and can also be used to overcome any barrier by the use of an applied force. It will be necessary to examine this reaction more carefully to determine if transfer of the hydrogen to tin can be performed in one step. If not, the hydrogen could be transferred to a somewhat stronger radical as an intermediate step.

Dealing with excess hydrogen or carbon

As butadiyne provides both carbon and hydrogen in a fixed ratio, it is possible that either (a) there will be an excess of carbon or (b) there will be an excess of hydrogen.

If there is an excess of carbon, then we could build carbon-rich structures. The obvious candidate is graphite. As the present paper is focused on the synthesis of the molecular tools and assumes that it is possible to make diamondoid structures (including graphite) from them, we will not investigate the reactions needed for the synthesis of graphite here.

If we deal with an excess of carbon by building carbon-rich structures and keeping them within the assembler, then we need not design mechanisms for ejecting waste from the assembler. This "zero residue" design is attractive because of its simplicity.

The second possibility is that we have too much hydrogen. In this case, we could build hydrogen-rich structures. Such structures would need to have a higher ratio of hydrogen to carbon than our feedstock molecule, C4H2. Even a 1:1 ratio would suffice, as in hydrogenated graphite. A more attractive structure is polyethylene, which has a ratio of two hydrogens for every carbon. As our feedstock has four carbons for every two hydrogens, one of the four carbons would have to be used in polyethylene to absorb the waste hydrogen (if we assume that no hydrogen at all was used in the actual structures being built). If our assembler was pure carbon (with no hydrogen at all) we would still be able to use three out of every four carbon atoms. As this seems unlikely, we should be able to use more than 75% of the carbon from the feedstock molecule if waste hydrogen is converted to polyethylene.

Strictly speaking, the use of polyethylene violates our stiffness constraint: polyethylene is floppy. The use of hydrogenated graphite does not violate this constraint and still provides a 1:1 ratio of hydrogen to carbon, which is sufficient. It seems likely, however, that many floppy structures can be synthesized with the tools proposed here, and that in many instances this will be convenient. The use of stiff diamondoid "jigs" to constrain the motion of otherwise floppy structures is one approach to their synthesis. Bonding to structures to constrain their motion is another approach. The end of a growing polymer chain could be held in a fixed position with respect to the next monomer to be added, as is done by the ribosome. As polymers are routinely synthesized today, it seems likely that methods for synthesizing them in an assembler are feasible. While convenient, such an ability is not necessary in an appropriately designed assembler, nor in a wide range of useful products that such an assembler could make.

Again, we assume that the synthesis of hydrogen-rich structures is feasible but do not analyze methods for synthesizing specific structures in this paper.

Another approach -- more efficient when large amounts of excess hydrogen are present -- would be to make large bucky balls and store the excess hydrogen inside them as H2 gas. Especially for large spherical bags the ratio of hydrogen stored to carbon used would be very high, as the amount of stored hydrogen would increase as the cube of the size of the bag, while the surface area (and hence the amount of carbon) would increase only as the square. This would eventually be limited by the strength of graphite (a sufficiently large bucky ball made of a single layer of graphite would eventually burst from the pressure) but bucky balls able to contain hydrogen at a pressure of perhaps 108 Pascals (~1,000 atmospheres) with a radius of some hundreds of nm should be feasible.

A third approach would be to generate hydrogen gas and pump it out of the assembler. This seems less desirable, as the hydrogen might reenter through the binding sites designed to bring larger molecules into the assembler. This would require more complex systems (such as the multi-stage cascade proposed by (Drexler, 1992)) to ensure that the interior of the assembler was not contaminated with any H2.

As the production of hydrogen gas inside the assembler cannot be allowed (for example, it would react with the hydrogen abstraction tool and other reactive structures that assume an inert environment) its production would have to be isolated in some fashion from the rest of the assembler. The production of hydrogen gas, although it has advantages, makes the system design more complex. The incorporation of hydrogen into hydrogen-rich structures seems like a simpler approach.

Avoiding excess hydrogen or carbon

We could avoid excess hydrogen or carbon if instead of using a single feedstock molecule to provide both, we used two feedstock molecules -- one of which was hydrogen-rich and the other carbon-rich. Provided that the actual ratio of carbon to hydrogen in a hydrocarbon assembler was between the ratios of these two feedstock molecules, we could avoid any excess of either hydrogen or carbon.

The most hydrogen-rich feedstock molecule is hydrogen gas. For various reasons (discussed earlier) hydrogen gas might not be desirable as a feedstock molecule. An alternative hydrogen-rich feedstock molecule would be methane, which has a sufficiently high ratio of hydrogen to carbon that it seems unlikely that useful hydrocarbon structures would have a higher ratio.

The most carbon-rich feedstock molecule of relatively small size would be some type of buckyball. C60 is the best known. Polyynes terminated by hydrogen are smaller and have a good hydrogen to carbon ratio, but become increasingly unstable as they are made longer.

For the present proposals, we will assume that the 2:1 ratio of carbon to hydrogen in butadiyne is approximately the same as the ratio of these elements in a hydrocarbon assembler. Any excess of either element will be dealt with by building hydrogen-rich or carbon-rich structures, as appropriate, and retaining these structures in the assembler (zero residue).

Dimer Deposition Tools

While it's often useful to add a single carbon atom to a growing structure by using a carbene, it can sometimes be more convenient to add two carbon atoms at the same time. Such a dimer ( -C#C- )will usually bond readily to two radicals which are separated by an appropriate gap. If, for example, we remove two adjacent hydrogen atoms from the hydrogenated diamond (111) surface, we will have two radicals separated by ~0.25 nm. The use of a carbene to bridge a gap of this size is problematic, but a dimer should bond readily (Walch, 1996). Similar results for the edge of a graphite sheet are plausible.

There are many possible dimer deposition tools -- the primary requirement is that the dimer be bonded relatively weakly to the rest of the tool so that after the dimer bonds to the desired target structure removal of the tool results in separation of the dimer from the tool. The general structure of a dimer deposition tool is illustrated below:

The sequence to deposit the dimer would then proceed as follows. First, the dimer would attach to the surface:

Reaction 16

Following this, the tool would be withdrawn:

Reaction 17

leaving the dimer on the surface.

A more flexible approach would be to form two separately controlled weak bonds to the dimer, as illustrated below.

This allows the angle and strain of the C-Sn bond to be adjusted to suit the circumstances. The dimer would first be deposited on a suitably prepared site:

Reaction 18

After this, the first Sn moiety could be withdrawn:

Reaction 19

and then the second:

Reaction 20

resulting in deposition of the dimer on the surface, as desired.

A dimer deposition tool similar to a proposal by (Drexler, 1992), is illustrated at the left. This proposal has the useful property that separation of the dimer from its support causes a rearrangement of the bonding structure, thus eliminating any dangling bonds in the tool after the tool is withdrawn. However, it is possible that this dimer will rearrange to the undesired structure illustrated at the right. This issue needs to be investigated further.

Once the dimer has been deposited on a surface and the tool withdrawn, the tool has been discharged and must be reloaded. Because dimer deposition tools are selected to bind weakly to the dimer (and hence to readily release the dimer when desired), reloading them is energetically unfavorable. In the following sequence we first split a four carbon polyyne chain (as provided by an earlier reaction) into two dimers, bonded at both ends to silicon. We then bend the Si-C#C-Si so that the reaction between it and the discharged dimer deposition tool is energetically favored. The two silicons are then rotated so that they are pointing at each other and force is applied until the approaching silicons form a Si-Si bond and break the Si-C bonds.

Reaction 21

Reaction 22

Reaction 23

Not all proposals will work

Another proposal for a dimer deposition tool is illustrated at the left. Ab initio calculations at the 6-31G* MP2 level using Gaussian (Frisch, 1995) show all positive vibrational frequencies for the dimer deposition tool, thus implying that it is stable in vacuum at a sufficiently low temperature. AM1 calculations show a barrier between this proposed dimer deposition tool and the isomeric carbene (illustrated at the right) of about 4 × 10-19 J (~60 kcal/mol). Unfortunately, more accurate (and computationally intensive) calculations at the 6-31G* Becke3LYP level show the barrier is only ~6 × 10-20 J (~8 kcal/mol. This does not include zero-point correction), almost an order of magnitude smaller. As a consequence, this dimer deposition tool is unlikely to work reliably at room temperature.

While not all proposals for molecular tools will work as desired, it is important to bear in mind that the computational methods used to evaluate such tools can be made increasingly accurate by increasing the computational effort devoted to the analysis. Our confidence in the conclusions can be increased by having more researchers analyze the problem with multiple methods and greater computational power.

Quantitative parts closure

In this section we analyze the global use of the proposed molecular tools to make another set of tools. We do this to make sure we don't have a net negative production of some molecular tool, despite a superficial ability to synthesize that tool.

To start the analysis, we note that we can generate as many hydrogen abstraction tools (ethynl radicals) as desired. We start with a set of "spent" hydrogen abstraction tools (i.e., tools with a terminal hydrogen). We also require one functional hydrogen abstraction tool, one spent hydrogen deposition tool (the tin radical) and two silicon radicals. Using reaction 15, we transfer the hydrogen from the tip of the hydrogen abstraction tool to the hydrogen deposition tool. This consumes one hydrogen abstraction tool and one tin radical. We then use a reaction similar to reaction 8 to separate the two hydrogen abstraction tools. This produces two refreshed hydrogen abstraction tools, and leaves the two silicon radicals unchanged.

The net result of these reactions is to transfer a hydrogen from an abstraction tool to a deposition tool, while leaving the rest of the tool count unchanged. Of course, this reaction consumes a tin radical. As we are assuming that the hydrogen deposition tool will be discharged when we manufacture a structure which needs an additional hydrogen, and are further assuming that we can manufacture hydrogen rich structures if this is needed, we will not run out of tin radicals. Put another way, we can get rid of hydrogen by making hydrogen rich structures. When we do this, we remove hydrogens from hydrogen deposition tools. As these tools are simply hydrogen bonded to tin, removing the hydrogen creates tin radicals. This lets us produce as many tin radicals as might be desired.

As we can now refresh the hydrogen abstraction tool at will, we can freely use this tool in the manufacture of other tools. In particular, all other radicals can be generated from their hydrogenated precursors by applying the hydrogen abstraction tool.

Conversion of butadiyne into a bound polyyne (reaction 1 and 2) uses two hydrogen abstraction tools and two silicon radicals. Two additional silicon radicals are used in the production of two C#C dimers able to reload the dimer deposition tool (reaction 21). Loading of the dimer deposition tool results in the bonding together of two silicon radicals. However, these radicals can be regenerated simply by pulling them apart. As a consequence, the net effect of these reactions is to reload two dimer deposition tools with no net decrease in the number of silicon radicals. The two hydrogen abstraction tools used to remove the two hydrogens from butadiyne can be regenerated as discussed earlier.

Generation of carbenes from butadiyne uses only hydrogen abstraction tools, transition metals, and silicon radicals (reactions 9 through 14). The hydrogen abstraction tools are not limiting, and there is no net loss of silicon radicals in this process.

As a consequence, we can freely use all of these tools without concern that they cannot be refreshed. The manufacture of new hydrogen abstraction tools is shown in reactions 3 and 4, while creation of a new carbene insertion tool can be done by attaching a long cumulene to a diamond surface (such as the (100) surface) followed by severing the cumulene as in reactions 12 and 13.

We do not show the detailed synthesis of the positionally controlled transition metal(s), silicon radical or tin radical. As we now have an existing set of tools which we can freely use without concern that they will be irreversibly "used up," the synthesis of the other tools should be feasible. A detailed set of reactions for this process (which would require a specific proposal for the "vitamin" molecule) is needed, but is beyond the bounds of this paper.

Binding sites and feedstock composition

While we could assume a separate binding site for each of the low volume catalytic "vitamins" (e.g., Si, Sn, and the transition metal(s)), it would be easier to consolidate them into a single molecule which consisted of two regions: (1) a heterogenous region which included all required elements: Si, Sn, and the transition metal(s); and (2) a region which could be easily bound by a simple binding site. The latter region might be a simple rectangular planar molecule (as discussing in (Merkle, 1997a)). This single molecule would then be dissected by the molecular tools and converted into the needed positionally controlled catalytic agents. This approach reduces the number of binding sites required, and reduces the problem of designing many binding sites which bind uniquely to their own substrate and do not cross-bind to other substrates. On the other hand, it requires additional steps to convert the "vitamin" into useful structures. As the "vitamin" molecule can presumably be designed to simplify this process, and as it would be necessary to convert precursors into their active form in any event, this approach seems more attractive than the alternative of using a multitude of binding sites each tuned to a specific feedstock molecule.

This leaves us with a feedstock that consists of four main components:

  1. Acetone (the solvent)
  2. Butadiyne
  3. The "vitamin" molecule
  4. Neon
The vitamin need be present only in low concentration, which eases concerns about its solubility. Neon is small enough that solubility is not a significant issue. Butadiyne (like acetylene) is soluble in acetone.

We can view these four molecules as zero dimensional (neon), one dimensional (butadiyne), two dimensional (the 2-d tab on the vitamin), and three dimensional (acetone). This simplifies the interactions between the binding sites. Molecules of higher dimensionality cannot fit into binding sites of lower dimensionality, while molecules of lower dimensionality will have much lower affinity for binding sites of higher dimensionality. For example, almost nothing will fit into a snug binding site designed for neon. Impurities that can reasonably be expected to enter through a neon binding site are helium and H2. The former is harmless in small amounts, while the latter can be gettered from the external feedstock solution, thus insuring that the concentration of H2 in the feedstock solution is so small that it can be neglected.

In cases where a contaminant of lower dimension has a sufficient affinity for a binding site of higher dimension that it might be a problem, a specific method of eliminating the contaminant will be required. Most generally, the multi-staged cascade approach (Drexler, 1992) could be used. It is reasonable to expect that more special-purpose (and simpler) approaches will be sufficient for the present proposal (e.g., gettering of hydrogen).

Degrees of freedom

Several of the preceding reactions involve two, three and even four positionally controlled tools. While it would be possible to use four general purpose positional devices each having six degrees of freedom, the use of jigs or fixtures specialized for these reactions and which have substantially fewer degrees of freedom should reduce the need for general purpose manipulators. Human experience suggests that two six-degree-of-freedom positional devices along with appropriate supporting equipment should be sufficient. A single general purpose positional device would likely be enough if some thought were devoted to the design of appropriate fixtures.

Conclusions

The design of the complete intermediary metabolism of a simple hydrocarbon based assembler seems feasible. The proposals given here imply an assembler which (a) uses simple buckytubes as the binding sites for binding a simple linear feedstock molecule (butadiyne); (b) uses that feedstock molecule to renew the carbene insertion tools and dimer deposition tools; (c) recycles the hydrogen abstraction tools and the hydrogen deposition tools by transferring hydrogen from one to the other; (d) brings neon into the assembler using a binding site which is sufficiently small to exclude virtually all other molecules; (e) uses a rectangular binding site to bind to a rectangular tab on a "vitamin" molecule. The "vitamin" molecule serves as the precursor to all the positionally controlled catalysts and non-carbon radicals, including those made from Si, Sn and the transition metal(s). Note that only a few copies of the "vitamin" would be required, as the corresponding catalytic tools would be needed in very low volume (a few per assembler).

Further research (including ab initio quantum chemical modeling and molecular dynamics) is required to establish that the particular reactions suggested here will work as desired. The more general conclusion is that the design of a complete set of reactions which can convert simple feedstock molecules into a desired set of molecular tools is feasible and should be pursued. Given the wide range of possible molecular tools, the wide range of molecular feedstock molecules, and the even wider range of possible chemical reactions for synthesizing tools from feedstock molecules, it seems certain that better proposals will be advanced.

Acknowledgements

The author would like to thank Charles Bauschlicher, Eric Drexler, Al Globus, Creon Levit, Gustavo Scuseria, Jeffrey Soreff and Stephen Walch for their comments and suggestions. The author would also like to thank the NAS Computational Molecular Nanotechnology project at NASA Ames for providing computer time on an SGI cluster for many of the the Gaussian calculations used in this paper.

References



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