Since many systems of interest to nanotechnology are not yet synthetically accessible, accurate simulation techniques are very important to this field. Simulations can help determine which structures are likely to perform well enough to justify attempts at fabrication.
Writing in [Nanotechnology 8:119-125 Sep97], D.W.Noid, R.E.Tuzun, and B.G.Sumpter describe numerical experiments which show that classical dynamics of nanomachines is in qualitative disagreement with the more accurate quantum mechanical analysis. The problem lies in the treatment of zero point motion. Each vibrational normal mode of a structure has a zero point energy of hf/2. In a classical analysis of the structure's vibration, this energy is free to move from mode to mode. When a classical system reaches thermal equilibrium, the energy is (on average) equally partitioned between modes. Unfortunately, this puts far too much energy into low frequency modes, precisely those modes that are important to the overall function of a nanomachine. The authors write: "It is the tremendous amount of energy in the high frequency modes that can be used [within the classical approximation] to generate the large amplitude motion in the low frequency modes." In the authors' simulation of a 100 unit polyethylene chain, a quantum mechanical analysis of the vibrations in the chain showed "distributions in the end-to-end distances had widths of the order of 0.1Å" while a classical simulation with only 25% of the zero point energy had widths of the order of 2Å and a simulation with the full zero point energy made such large nonlinear excursions that it folded up from the initial end-to-end distance of 125Å to around 20Å.
If this effect only limited the accuracy of classical simulations at very low temperatures it would not be a concern for simulating room temperature analysis of nanomachines. At sufficiently high temperatures, all of the normal modes in a structure are thermally excited and the thermal energy really can move from mode to mode. For stiff, light structures, however, the bulk of the high frequency modes are not excited at room temperature. For a cumulene (C=)n rod, for instance, the zero point energy in its vibrational modes corresponds to to an effective temperature of 1000 K.
Even in a classical simulation, if the system under study were purely harmonic, energy initially placed in one mode would remain in that mode, so the inaccurate large amplitude oscillations in the low order modes would not be generated from the energy in the high order modes. It is the nonlinear terms in the potential which transfer energy, particularly during chaotic motion. The authors found that "The instability in fullerene nanotubes was found to be due to a rapid energy transfer to low frequency modes which tend to retain the energy due to resonant transfer between the longitudinal and ring breathing modes, causing the onset of large-amplitude motion. ... large amplitude motion resulting from chaos and nonlinear resonances leads to positional instability."
The authors' quantum analyses of nanostructures' vibrations were done with a new technique, "internal coordinate quantum Monte Carlo (ICQMC)." With it, they were able "to compute ground-state energies and wavefunctions for polymer chains with up to 400 carbon atoms and carbon nanotubes with almost 300 atoms." This technique avoids the pessimism of the classical dynamics analysis, albeit at higher computational cost. Clearly, some hybrid technique is needed, perhaps some generalization of the united atom techniques used to lump together the atoms in small groups, but applied to larger parts of a structure, swallowing the zero point energy of modes within that part.
In the second paper reviewed in this section, [Nanotechnology 8:95-102 Sep97], J.Han, A.Globus, R.Jaffe, and G.Deardorff describe classical simulations of gears built from carbon nanotubes. Single walled tubes were used throughout these simulations. The gear teeth used were benzyne (C6H4) groups, bonded to what would ordinarily be a double bond in the nanotube with a 2+2 cycloaddition reaction, yielding a cyclobutane joint to the benzyne ring. Quantum chemical calculations for this structure have been done and "are in agreement with experiment for napthylene [sic] and buckyballs (C60) while experimental verification using nanotubes has not been reported." This structure is simpler than previous diamondoid and fullerene gears "and may be synthetically accessible." The authors suggest that "It may be practical to position molecular teeth in atomically precise precise positions required for gear design by, say, scanning tunneling microscopy (STM) techniques." The specific type of nanotube used in the bulk of the experiments is a "[14, 0] nanotube with a diameter of 11.0 Å." with seven teeth with adjacent pairs of teeth "separated by two six-membered rings around the nanotube."
Both adiabatic and isothermal simulations of the gears were done. During adiabatic simulation the temperature rose from a starting 200 K "to >1000K after 30 ps." The gears worked from 200 K to 600 K, but then started to slip. In isothermal runs a "Brendersen's thermostat was used to control the gear's temperature with a time constant of 0.4 ps," maintaining a steady temperature without requiring explicit simulation of heat bath atoms.
This study found gears of this type to be quite robust, functioning at rotation rates up to 100GHz, at temperatures up to 600-1000K, and failing by slipping rather than by gear breakage at the limits of these parameters. The simulations used Brenner's reactive potential within each gear. Three potentials were used for intergear interactions: a Lennard-Jones r-6-r-12 potential, a Buckingham exponential + r-6 + electrostatic potential, and a run with Brenner's reactive potential between the gears. During normal operation the faces of the teeth push on each other. The inter-tooth forces tilt the teeth, failing to mesh when they tilt enough to slide past each other. Even with a reactive potential included, slipping teeth were not found to react with each other, nor were they found to break off the tube. The three potentials yielded essentially the same limits on rotation rates, with 0.10 ~ 0.12 THz rotation rates found for all potentials.
Because the failure mode at high speeds is nondestructive, the authors suggest that "a trial and error procedure can be used to establish operation conditions for physical gears [emphasis in original] without needing to worry about destroying them."
Proximal probe techniques are a valuable enabling technology for nanotechnology because they permit experimenters to precisely control the 3D position of probes, both for analysis and fabrication.
Writing in [Science 277:1971-1975 26Sep97], E.W.Wong, P.E.Sheehan, and C.M.Lieber describe measurements of bending stiffness, buckling, and strength of silicon carbide nanorods and buckytubes using an atomic force microscope (AFM). This paper describes work on multiwall tubes, expecting that "it will be interesting to experimentally probe the diameter dependence of E in SWNTs [single wall nanotubes] as these materials become available."
The basic technique used to measure the properties of the tubes and rods was to deposit them on a MoS2 substrate, pin them down by evaporating SiO pads over them, and bend them with an AFM tip, measuring the lateral force on the AFM tip during the deflection. There is a term in the lateral force due to friction with the substrate, but it is small, and it can be eliminated from the analysis by looking at the derivative of the force with respect to the beam's deflection. When the normal load on the AFM tip is small, the measurement of one displacement vs. force curve ends when the tip pops up and over the rod or tube. When the normal load is large, the rod or tube may buckle or break when a sufficiently high lateral force is applied.
At low forces, this experiment measures the stiffness of the tubes or rods. The values found, 610 GPa for a 23.0 nm SiC nanorod and 660 GPa for for a 21.5 nm SiC rod "agree well with the 600 GPa value predicted theoretically for -oriented SiC (29) and the average values obtained previously for micrometer-diameter whiskers (6)." For multiwall carbon nanotubes "the average E [stiffness, Young's modulus] value from these experiments was 1.28±0.59 TPa with no dependence on tube diameter...[which is] similar to the in-plane modulus of graphite, 1.06 Tpa."
When subjected to large forces, the SiC rods and carbon tubes behave quite differently. The SiC rods fracture irreversibly, while the tubes buckle reversibly. The largest SiC bending strength observed was 53.4 GPa, considerably larger than the largest bending strength observed for the tubes, 28.5 GPa. The authors note that defects can reduce the strength of SiC rods, and suggest that their measurement technique can be used to optimize synthesis techniques to minimize these defects. The buckling of the tubes does not quite agree with simulations of this process. The simulation predicts that displacement after buckling occurs with nearly constant force, while the experimental results show force still increasing after buckling, albeit at a smaller rate. One of the possible explanations given is that the multiple tubes may slip with respect to each other, or may buckle at slightly different strains. Buckling data from well-characterized single wall tubes will avoid the ambiguities of partially known initial structures and will provide very good tests of our models of the mechanics of these structures. Even if we set aside the model refinements, these experiments have provided direct experimental tests of the mechanical qualities of valuable components for nanomachines.
In the second paper reviewed in this section, [Nanotechnology 8:A58-A62 Sep97], S.Hosaka et. al. demonstrate an AFM-based storage system that can store 1.25 Tbits/in2 and read them at a rate of 1.25 Mb/sec. They also demonstrate a scanning near-field optical microscope based recording technique, but this has lower density and the readout rate was calculated rather than demonstrated. The authors' readout mechanism is a normal optical deflection AFM technique, deflection of a tip in contact with the surface deflecting a silicon cantilever which in turn deflects a reflected laser beam. The data signal is detected from open-loop measurements of the sensor displacement, rather than from closed loop feedback through the piezoelectric actuator. The bandwidth limiting element of the system is thus the silicon cantilever, which had a resonant frequency of "2.2 MHz in contact condition." rather than the ~10kHz response of the piezo actuator. They also anticipate that "a readout speed of over 10 Mb s-1 will be possible by developing a cantilever with a higher resonant frequency."
The storage element sensed with their AFM are small pits "made by cold plastic deformation...by pushing the AFM tip into a polycarbonate disk with a piezo actuator." The authors were able to make "nanopit arrays with a 20 nm pitch in line and a 40 nm pitch in track...a fine bit array with a bit diameter of less than 10 nm and 25 nm pitch on the polycarbonate disk was formed." While these pits are well above the sizes needed for atomically precise fabrication, perhaps some hybrid technique might allow combining long range order from this technique with atomically precise pre-formed elements such as viruses. If this technique proves commercially viable, it would also provide a direct incentive to push a mass fabrication technique already at the 10 nm scale to finer geometries.
In the third paper reviewed in this section, [Nanotechnology 8:A10-A14 Sep97], D. Fujita et. al. describe a UHV apparatus for depositing Au dots on Si into a gap region between four macroscopic electrodes. Their goal "is to create single electron tunneling (SET) devices by applying the scanning tunneling microscope (STM) nanofabrication capabilities." Towards that end, they have built an apparatus with which they can deposit fine patterns with an STM, deposit a four-quadrant macroscopic electrode pattern for contacting the fine pattern and perform electrical measurements, and with which they can cool the experiment to 12 K. The cooling capabilities of their apparatus should let them use the conductivity of their Si substrates to help image and fabricate their structures while hopefully "the conductance of the Si substrate can be killed by lowering [the] temperature", so that SET operation can be observed on an effectively insulating substrate.
At present the authors can deposit gold dots, "typical sizes were about 5 nm across at the base and 0.5 nm high". Their STM uses an etched gold wire tip, finding that "atomically resolved images of the Si(111) surface were sometimes obtained even after the atom transfer of gold to the surface by application of voltage pulses to the tip."
Currently, the macroscopic electrode fabrication capability of their apparatus is a bit too coarse for their application, with an initial mask generating 25 micron gaps. They intend to reduce this to a 5 micron gap (within the 10 micron scanning range of their STM). Preliminary experiments in depositing dots on macroscopic electrodes were done with electrodes fabricated with an e-beam in another system. Using this substrate, they found that "gold dots could be deposited not only on the Si(111) surface but also on the gold electrodes and their boundary regions."
The ability to bring four connections to within a few nanometers of each other should allow a number of important experiments. For example, two of those connections might be used to make an electrostatic actuator, effectively adding another mechanical degree of freedom to the experiment in addition to the STM's degrees of freedom, perhaps allowing imaging of structures under adjustable local strain.
One route to the construction of nanometer scale structures is self-assembly. The selective binding of complementary DNA strands has proved to be a very effective tool in constructing such structures. The papers below describe structural work with this material.
Writing in [Molecular Nanotechnology: Biological Approaches and Novel Applications IBC Inc. 1997 pp 2.2.1-2.2.31] N.C.Seeman et. al. summarizes the construction of a wide variety of DNA nanostructures built in his lab from 1980 to the present day, describing both the usefulness of DNA as a nanoscale structural material and the difficulties encountered in building structures with it.
The typical structure for a DNA molecule is a linear double helix, but there are other forms that complexes of DNA strands can take. One example is a four-arm junction. In this junction each covalently bound strand is complementary, not to the entire length of another strand, but rather half of it is complementary to half of a second strand and another half is complementary to half of a third strand, thus joining the second and third strands together. Four properly chosen strands can be mixed together to yield a single stable complex. Not all types of DNA branches are this well behaved. Structures known as "parallel DNA double crossover molecules, or DNA mesojunctions" generate multimers of the simplest structure. For example "a molecule of strand 1 hydrogen bonds to a molecule of strand 2,which bonds to a molecule of strand 3,which bonds to a molecule of strand 4, which bonds to a different [emphasis in original] molecule of strand 1, and so on, to make an 8-molecule or 12-molecule complex." Nonetheless, stable branched junctions with as many as 6 arms have been made.
Back in 1980, Seeman noted that a 6 arm junction provided the right topology to link the junctions into an extended 3D crystal held together with complementary binding of the sticky ends of the DNA arms. This is a desirable way to build a crystal because "sticky ended association is the all-time grand champion molecular recognition event. It is reliable, and it is predictable." This is important because the structures of biological molecules can be found through x-ray diffraction, but only if they can be grown as crystals. About half the time, all of the tricks used to crystallize biological molecules fail. If they could be bound to a framework that was guaranteed to crystallize, this difficulty could be circumvented. Unfortunately, the original idea of forming a crystal from a single branched junction "is predicated on a rigid branched junction, but it does not work in this fashion, because they are not rigid."
One of the motivations for staying with DNA rather than modified compounds "is that, at some point, we would like to be able to make these objects biologically. It is not possible to clone or PCR a branch, but one can imagine making them in the form of one long strand and then getting them to fold up."
Quite a few isolated DNA topologies have been built in Seeman's lab: cubes, Borromean rings, truncated octahedra, dodecahedra. Some of the steps involved in the synthesises have low yields and the final yield of a structure can become rather small. Only 4 femtomoles of the cube were made, about 2.5 billion molecules. Diffraction requires around 100 billion molecules. One of the recent innovations has been to adapt solid phase support to these syntheses which "gives us control over a single edge at a time." This technology was used in the truncated octahedron synthesis.
Recently, work has started on a type of DNA joint, "the anti-parallel double crossover system", that shows more rigidity. It consists of "two branched junctions fused to each other in two physically adjacent arms." These joints are sufficiently rigid that they have been able to assemble 17 of them together without seeing them bend back to form cycles. The next step planned is to build a 2D triangular lattice.
In the second paper reviewed in this section, [Molecular Nanotechnology: Biological Approaches and Novel Applications IBC Inc. 1997 pp 2.5.1-2.5.26], D.E.Bergstrom, J.Shi, G.Lawrence, and M.Pingle describe a variety of modified nucleic acids which retain the specificity of DNA pairing while expanding the range of design options available for using them to construct structures. The authors' ideal target "framework would be one for which self-assembly would be coincident with precise placement of functional components in three-dimensional space." Three basic types of modifications to DNA are described: modifications to bases, modifications to the backbone, and modifications to the termini of the backbone.
The base modifications that the authors focus on are tethered bases, natural bases with additional bonds (typically replacing a C-H bond) to an additional group, notably "molecular signaling devices (e.g. fluorophors, haptens, spin labels)". They have found "the most interesting site for modification is C5 of C and T(U). In duplex DNA, C5 substituents project out from the major groove into the solvent surrounding the duplex. Unless the substituent is quite bulky near the C5 carbon, there is little interference with base pairing."
The authors describe three modifications of the DNA backbone which leave modified duplexes with stability equal to or better than that of natural DNA. The first modification is a slightly altered RNA. Natural RNA is hydrolytically unstable because of intermolecular attack on the phosphate backbone from a ribose hydroxyl. "Methylation of the 2'-OH to give 2'-OMe eliminates the hydrolysis problem without compromising duplex stability." A second modification to the sugar is to replace the 2'-deoxyribose with 2',3'-dideoxyhexose. This yields a linear, rather than helical, polymer. Duplexes "are more stable than the corresponding DNA duplexes of the same length." The most dramatic backbone modification replaces the sugar and phosphate groups altogether, replacing them with peptide bonds.
The authors' terminal modifications are the addition of pre-formed junctions to the DNA strands. The authors describe a number of strategies for attaching DNA strands to three-arm vertices. In one strategy, all three DNA arms can contain different sequences, maximizing the options for building structures with these vertices. In this strategy, one DNA arm is synthesized on a solid support, then the vertex is added with two different protecting groups on its remaining terminals, allowing the separate synthesis of two different strands. The authors current work centers "on characterization of the supramolecular structures formed when complementary three-arm oligonucleotide vertex conjugates are allowed to hybridize."
Electronic subsystems are a likely part of nanotechnology, for power distribution, for sensing, and for information processing. Understanding conduction on this length scale is necessary for the design and analysis of these subsystems.
Writing in [Science 278:252-253 10Oct97], M.A.Reed et. al. describe measuring the conduction through a single small molecule. The molecule measured is benzene-1,4-dithiol (HS-C6H4-SH) which they bound between two gold electrodes. Thiols form self-assembled monolayers on gold. In their experiment, they glued a notched gold wire to a flexible substrate, immersed it in a dilute solution (1 millimolar) of dithiol in tetrahydrofuran, and broke it by flexing the substrate. This left a monolayer of dithiol covering all exposed gold surfaces, including the break in the wire. They evaporated the THF solvent, flexed the substrate to adjust the gap between the pieces of the wire to ~8Å, forming a junction through a single dithiol molecule in the monolayer, then measured I(V) curves for their junctions.
The I(V) curves that they measured showed plateaus in the conductivity, with resistances of 22 megohms at a first plateau and 12.5 - 14.3 megohms at a second plateau. These values were reproducible on breaking and reforming the contact by flexing the substrate. "Measurements of an ensemble of similar molecules contacted to a gold nanocrystal" had given resistances of ~9 megohms and ~18 megohms per molecule in prior work, lending support to the interpretation of the I(V) curves as representing single molecule connections. Other evidence for this includes one observation where conductance plateaus were seen at twice the usual values, which "suggests a configuration of two noninteracting self-assembled molecules in parallel, substantiating the idea that the threshold resistance of a single molecule is ~22 megohms."
The conductance of this channel is low at biases of <0.7 volts. It appears when either a positive or negative bias of this magnitude is applied, as is consistent with the symmetrical structure of the dithiol. The authors suggest two models for the origin of the onset of conductivity. They suggest that it might either be due to a Coulomb blockade or due to a mismatch between the Fermi level in the electrodes and the level of "the lowest unoccupied molecular orbital (LUMO)"...essentially the conduction "band" for the bridge. Unfortunately "a definitive demonstration of Coulomb blockade would require a third gate electrode, which is problematic in the present configuration because a third proximal probe cannot be placed near the molecule." Frankly, I would like to see work on independently controlled dual probe STMs pursued in order to better probe systems like this one. Work is also needed to reconcile theoretical estimates of the device resistance, currently 100 kilohm, with the measured resistance. Setting aside dual probe STMs, perhaps measurements on a series of related compounds can illuminate these issues.
Jeffrey Soreff is a researcher at IBM with an interest in nanotechnology.