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).

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).

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.