FIGURE 1
Schematic of a three-input, three-output rod, with logical description
Pgs 39-56 in MOLECULAR
ELECTRONIC DEVICES
F. L. Carter, R. E. Siatkowski, H. Wohltjen (Editors)
© Elsevier Science Publishers B.V. (North-Holland), 1988
The advent of molecular assemblers will eventually enable the construction of virtually any specified arrangement of atoms. Molecular mechanics-the modeling of molecular dynamics using newtonian mechanics and approximate force fields-allows estimation of the properties of assembler-built machines, including nanocomputers based on mechanical rod logic. The results of design efforts based on this approach include the specification of atomic arrangements for the gates and signal transmission elements of a rod logic system. Models based on molecular mechanics permit estimation of speed, volume, energy dissipation, thermal noise effects and other technical parameters of rod logic systems suitable for use in mechanical nanocomputers. These results help set lower bounds on the performance of future computers based on molecular components.
Molecular machinery and circuitry (save in their simpler instances) will be forms of nanotechnology, technology based on a general ability to build systems to complex, atomic specifications. Nanotechnology will be based on assemblers, molecular machines that guide chemical bonding operations by manipulating reactive molecules [2].
The concept of molecular machinery was latent in the earliest efforts to describe molecules as mechanical systems. The molecular theory of gases marked an early milestone; the recognition that biochemistry and molecular biology rest on molecular machines marked another [3]. Suggestions for building molecular machines, however, have been sparse, and the concept of using molecular assemblers to direct synthetic reactions [2] is apparently quite recent .
Richard Feynman's 1959 talk on miniaturization foreshadowed the concept of the assembler, though it lacked any clear discussion of molecular machinery, of directing chemical bonding, or of reliability in the face of thermal noise [4]. Feynman observed that 'The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom," and went on to remark: "But it is interesting that it would be, in principle, possible (I think) for a physicist to synthesize any chemical substance that the chemist writes down. Give the orders and the physicist synthesizes it. How? Put the atoms down where the chemist says, and so you make the substance."
The case for assemblers can be made most compactly through comparisons to existing biochemical machinery. Enzymes, ribosomes, and the genetic system demonstrate that molecular machines can exist, that they can position and manipulate reactive molecules, and that they can make and break specific chemical bonds under programmed control. These biochemical machines demonstrate lower bounds to the capabilities of more general molecular machines. These demonstrated capabilities indicate that protein engineering will offer a way to construct novel molecular machines, including devices resembling simple industrial robot arms-having perhaps two degrees of freedom-and able to position reactive molecules with respect to a molecular workpiece. These could serve as primitive assemblers.
The chief problems of synthetic chemistry are controlling reaction sites, providing activation energy, and providing free energy to drive otherwise unfavorable reactions. The use of even primitive assemblers to position reactive molecules will improve control of reaction sites, permitting the construction of molecular structures of a complexity well beyond reach of modern synthetic chemistry. Among these structures will be components for better molecular machines. Thus, however the first assembler may be built, we can expect to see an iterative process in which assemblers are used to build better assemblers. The use of strong, rigid materials in assemblers (as opposed to flexible polymers) will aid the use of mechanical energy to drive chemical reactions; other components will do likewise for the use of electrical energy. Together, these advances will make possible the synthesis of an extremely broad class of structures, which may be expected to include virtually all molecular structures of engineering interest (some limits are discussed in [5]). Protein engineering is already being pursued [6, 7]. Other paths to assemblers seem possible: these include further development of non-protein supramolecular chemistry [8] and the development of micromanipulators based on the positioning and sensing technologies demonstrated in scanning tunneling and atomic force microscopy [9, 10]. The nature of these steps is of only short-term importance: All paths lead ultimately to molecular machines able to build systems to complex, atomic specifications, including systems built from separately assembled parts. It is thus of interest to consider what sorts of computers can be built with this fabrication technology.
Work on this concept has produced schemes for signal transmission, logic gates, finite-state machines based on programmable logic arrays, data storage registers, power supplies, power transmission systems, and means for input and output of data to conventional microelectronics.
This paper focuses on the rod logic used to implement signal transmission and logic gates, describing its structure and dynamics with special attention to the problems posed by thermal noise.
A lock implements a conditional restraint on motion: the rod attached to the probe knob can be pulled in the direction indicated by the arrow if and only if the obstructing gate knob has been pulled from its path. If a gate knob is ordinarily out of the way, but can be pulled into a blocking position, the result is a logical not operation. (With this as a normal mode of operation, allowing free use of both default-open and default-closed gates, then the resulting rod logic will resemble CMOS logic more closely than it does NMOS.) Figure 1 shows a rod with three input locks and three output locks in an abstract representation.
FIGURE 1
Schematic of a three-input, three-output rod, with logical description
Rods slide through channels in a close-fitting matrix, forcing essentially longitudinal motion and thus allowing gate knobs to block probe knobs by blocking their channels. The relationship of knobs, rods, and the matrix is shown schematically in Figures 2 and 3.
In computation, the sequence of operations is as follows: First, the rod containing the gate knob rod is pulled; if it is in an unblocked (or "1") state, it moves; if it is in a blocked (or "0") state, it cannot. Second, the rod containing the probe knob is pulled; if it is not blocked elsewhere, then it will move if the gate knob is in a non-blocking position. Third, after a delay (during which gate knobs on the rod containing the probe knob can affect operations elsewhere) the pulling of the probe knob is reversed; if it had moved, it is reset. Fourth, the pulling of the gate knob is likewise reversed, restoring the initial conditions.
Key issues in rod logic include the design of the rods, knobs, and matrix,
the nature of logic states and transitions between them, and the effects
of friction and of thermal noise. These issues are interrelated. In particular,
the design of the rods, knobs, and matrix must meet constraints stemming
from friction and thermal noise. At one extreme, parts could contain many
atoms and move slowly, resembling familiar macroscopic machinery; this
possibility shows that rod logic can be made to work on some scale. The
design choices presented here are closer to the extreme of compactness
and speed, but are nonetheless selected from a large set of possible component
sizes, shapes, and arrangements. These choices result from several iterations
of analysis and redesign, trading off performance and ease of design and
analysis.
 |
 |
|
Schematic of lock components |
Lock components in channels |
For the inter-knob sections of rods, one choice seems outstanding: segments of carbyne, linear chains of carbon atoms linked by alternating triple and single bonds [14]. Since it is one atom wide, carbyne is at or near the limit of slimness; its diameter is about 0.30 nm (this radius, like others in this paper, is based on atomic separations yielding atom-atom contact forces of about 0.1 nN). Single-bonded carbon (i.e., diamond) is renowned for its strength, but the single bonds of carbyne are almost as short and strong as double bonds (0.1373 nm vs. 0.1337 for double bonds and 0.1541 for single; all bond parameters in this paper are from [15] or [16] unless otherwise noted). The strength of a rod will be well in excess of the 6 nN strength [17] of a C-C single bond. Further, the linear structure of carbyne allows bond bending to make no contribution to elongation under tension. Accordingly, carbyne is strong and stiff [14]. (Here, stiffness means elastic modulus in tension; rods are quite flexible in bending or in compression.)
The probe knob holds its fluorine atom 0.57 nm from the carbyne axis;
its total height is 0.97 nm. The gate knob holds its fluorine atoms 0.43
nm from the carbyne axis; its total height is also 0.97 nm. The gate knob's
length is important in thermal noise calculations (see Section
7.2): the F-F internuclear distance is 0.54 nm, and the length (measured
from 0.1 nN van der Waals surfaces) is 0.80 nm. (All van der Waals parameters
in this paper are derived from [15] and [18].)
 |
 |
| FIGURE 4
Probe knob structure (note carbyne segments) |
FIGURE 5
Gate knob structure (note carbyne segments) |
To reduce lateral vibrations, rods will operate under tension, here chosen to be 2.5 nN. As tension increases bond lengths, it reduces bond stiffnesses owing to nonlinearities in the interaction potential. These effects have been estimated by fitting a Morse potential to zero-tension bond length and stiffness data [22], and then evaluating bond lengths and spring constants at the given tension. The compliance of a benzene ring is dominated by bond bending [19] and bending interactions become stiffer with increasing displacement [18]; knobs have been modeled as linear springs and the expected increase in stiffness with tension neglected. Transverse vibrations of the rod reduce the effective modulus as described in Section 7.3; if all the above spring constants were infinite, rods at 300 K and 2.5 nN tension would have a finite modulus of about 1500 nN from vibrations alone. A major reason for tensioning rods is to reduce this effect.
The average rod modulus will be affected by the number of triple-bonded pairs per inter-knob segment; it seems that four pairs will suffice. With this rod configuration and the parameters and corrections just described, the rod modulus is about 89 nN. These calculations also yield the length of a tensioned subunit consisting of one knob and inter-knob segment, 1.50 nm. The associated mass per unit length is 3.0 ×10-16 kg /m for a series of probe knobs and 3.2 ×10-16 kg/m for a series of gate knobs. Taking the mean of these mass densities together with the given modulus, the speed of (longitudinal) sound in a rod is
[(89 ×10-9 N)/(3.1 ×10-11 kg/m)]1/2 » 17,000 m/s.
The volume per lock in a close-packed array is determined by the spacing of gate and probe knobs on their rods (1.50 nm) and on the total height of the lock assembly. Assuming that the fluorine atoms on the gate and probe knobs are aligned for a direct collision, and that one carbonatom diameter is allowed between the channels of stacked locks, the height of a lock is 1.81 nm. This yields a volume per lock of 4.1 cubic nanometers.
- Two springs. One is a stiff drive spring and the other an anchor
spring soft enough to apply an approximately constant tension of 2.5
nN to the gate segment over an extension of about 0.84 nm (see Section
5.2). (The value of 2.5 nN is chosen to satisfy thermal noise constraints;
see Sections 7.3 and 7.7.)
These springs can be fairly bulky yet add little to the volume per lock
in a long rod. Since it is easier to make molecular structures compliant
than to make them rigid, and since many designs are possible, no spring
design is specified here. Like knobs, springsegments can be covalently
bonded to rods.
Four locks viewed in section along two channels containing gate knobs.
Left to right top to bottom, the locks are in the states 1, 0, 0, 1.
FIGURE 7
Two locks viewed in section along the channel containing their probe
knobs.
Left to right, the locks are in the states 0, 1.
FIGURE 8
Schematic diagram of rod with additional moving parts
- An alignment knob. A proposed alignment knob structure is shown in Figure 9. This knob interacts with two barriers in its channel, the alignment stops (see Section 5.2).
- A displacement source. This provides properly timed displacements
at the far end of the drive spring; the nature of this mechanism (which
provides both power and timing for the rod logic system) is beyond the
scope of this paper.
Given that the matrix consists chiefly of elements near carbon on the periodic table, arranged with a structurally sound, three-dimensional pattern of bonding, the matrix as a whole will be strong and stiff. Its three-dimensional nature will make its compliance negligible compared to those of the long, slim rods. Accordingly, the matrix is treated as a fixed frame of reference in the thermal noise model of Section 7.
The matrix is assumed to contain no extraneous atoms. Gas molecules can be excluded by sealing the outer surface of the rod logic system.
Tracks consist of rows of atoms positioned as shown in cross section in Figure 10. A pair of rows lies on each side of the channel, with the members of the pair separated by about 0.3 nm and the pairs separated by about 0.45 nm. If the atoms in each row are 0.24 nm apart, then the number of track atoms per lock is about 50.
Track atoms have strong, repulsive van der Waals interactions with the atoms of the knob base rings and inter-knob segments. These interactions clamp the rod firmly, allowing only small lateral motions. A twisted track will couple longitudinal rod motion to rotation of knobs about the longitudinal axis; this is responsible for the varying cant of probe knobs shown in Figure 6.
FIGURE 10
Rod with (gate) knob and track, viewed in section across channel
A lock is in a 0 state if its gate knob, at equilibrium, blocks its probe channel. Thermal noise fluctuations cannot be allowed a significant chance of unblocking the channel even momentarily, since this would allow the probe knob to pass, causing an error in the logic system.
The lock configuration shown in Figure 6 reflects this asymmetry between 1 and 0 states. A small displacement can momentarily block the probe channel in the 1 state, but in the 0 state, the gate stops prevent small motions from unblocking the probe channel. Instead, the gate knob must move across the channel before it can cause an error state. The probability of this larger motion is analyzed in Section 7.
Logic systems may contain regular arrays of locks, as suggested by Figures 6 and 7, and by analogies to integrated circuit designs [23]. In such an array, a null lock may be constructed by omitting the tops of what would otherwise function as gate and probe knobs. In effect, these locks will always be in the 1 state.
A rod of the sort analyzed here is schematically illustrated in Figure 8. It consists of a series of probe knobs in a probe segment, each corresponding to one input lock. If all input locks are in the 1 state, the rod is in a I state, and is free to move when pulled. If a rod is in a 0 state or has not been pulled, its gates are in their resting position., as illustrated. If it is in a 1 state and has been pulled, its gates are in their extended position.
In any given cycle, first the input locks are set, then the displacement-source pulls the spring, then the output locks are probed. If one or more of the input locks is in a 0 state, then the rod beyond that lock cannot be pulled significantly: the probe knob for that lock lodges against the gate knob and the drive spring stretches to absorb the displacement. The gate segment remains in a resting position determined by the alignment knob and stop, together with a 0.5 nN net alignment force (2.5 nN applied by the anchor spring, minus 2.0 nN tension in the probe segment).
If all of the input locks are in the 1 state, then the displacement source can affect the entire rod. The stiff drive spring stretches only moderately, and hence transmits displacement. As the probe segment tension passes 2.5 nN, it begins to move the alignment knob and gate segment. Eventually, the probe segment tension reaches 3.0 nN, the alignment knob is lodged against the second alignment stop by a net force of 0.5 nN, and the gate knob segment is in its extended position. The distance traveled by the alignment knob and gate segment (determined by gate displacements needed to effect logic state transitions) is 0.84 nm. The probe segment tension varies by I nN, stretching it by about 1.1%, or 0.28 nm; since this sums with the alignment knob displacement, the drive spring must shift its end of the rod by about 1.12 nm. The gate segments tension remains constant, hence its length remains constant.
In the absence of detailed molecular mechanics calculations, rough approximations can indicate the magnitude of the dynamic variables in this motion. Assume a rod as described above, and assume that the drive spring imposes a smooth motion on its attachment point, amounting to a half-period of a sinusoid, taking a total of 50 ps. The peak speed is then:
In the rigid-body approximation (which is pessimistic in assuming that
all parts of the rod reach this maximum speed), the acceleration is
Since the speed of sound in the rod is about 17,000 m/s, mechanical signals will propagate from the displacement source to the alignment knob in less than 1.5 ps, and to the far end in less than 3 ps. These times are short compared to the 50 ps time for the overall motion, hence it is a fair approximation to neglect signal propagation time and the excitation of rod vibrations by the displacement source (collisions with the alignment stops are another matter; see Section 6.4). The maximum stretching of the rod due to signal delay is about 0.01 nm, and the associated elastic energy per output lock is about 0.001 kT.
Figure 11 shows the variation in van der Waals potential as one carbon atom moves past another along a series of straight lines with different distances of closest approach. Figure 11 also shows the variation in van der Waals potential as one carbon atom moves past a row of other atoms, at a fixed closest-approach distance of 0.3 nm, but with varying atomic spacings in the row. The dramatic smoothing of the potential as the effective row spacing approaches 0.1 nm can be explained in terms of a cutoff in the spatial frequency of the single-atom potential fields along the lines of travel. Figure 12 shows how the effect of short single-row spacings may be achieved using multiple rows.
FIGURE 11 Van der Waals interaction potentials between carbon atoms. Left, between two atoms, one fixed and one moving along lines with varying distances of closest approach. Right, between a similarly moving atom and rows of atoms, all with a 0.30 nm closest-approach distance, but with varying in-row spacings. Similar results are found at closer approach distances.
FIGURE 12
Effective spacing of stationary atoms equals one half their minimum
physical spacing
Each row of atoms in a track (see Section 4.2) has a spacing on the order of 0.24 nm. By staggering the rows properly on both sides of the rod, this can give the effect of a single row with a spacing of about 0.06 nm. The resulting potential is quite smooth, with residual longitudinal forces (for a uniform track) of less than 0.0001 nN /atom. Roughly equal numbers of atoms in the rod will experience forces of positive and negative sign, hence these forces to a first approximation will cancel.
This longitudinally smooth potential can be modified by rendering the track nonuniform: local changes in track spacing can create smooth, local potential barriers and wells. These nonunifor- can be created by building nonuniformities into the covalent structure supporting the rows of track atoms. Interactions with the bottom surface of the knob-base rings offer further opportunities to introduce controlled nonuniformities in potential.
Knobs will also interact with non-track portions of the matrix and with other knobs. By choosing knob-wall spacings near the smooth, 0.4 nm contour of Figure 11 and shaping the matrix properly, the many interactions between knob and wall atoms can be made to sum to a smooth potential. Longitudinal potential variations will remain, caused by electrostatic forces, crosschannels, and knob-knob interactions. Track nonuniformities can be designed to cancel these variations; in general, they need do so only when energies are summed over several adjacent locks. This may be called "tuning the track."
These considerations suggest that the maximum longitudinal force on the rod resulting from matrix and knob-knob interactions can be kept well under 0.1 nN. This force, which roughly corresponds to static friction, is acceptably low.
Acoustic radiation seems a minor loss. An elastic disturbance moving smoothly at subsonic speeds will radiate no sound; a knob moving along a track matches this description fairly well. Only oscillating force components will cause radiation. These forces are small (for the same reason that the track is smooth), and have frequencies on the order of (35 m /s)/(0.3 nm) » 1011 Hz. Since the speed of sound in the matrix will be on the order of 10,000 m/s, the entire rod length will be in the near field of any given disturbance. Under these circumstances, oscillating forces on an atomic scale will chiefly store and recover elastic energy, not radiate it; losses should be low.
A crude estimate of the energy dissipated through phonon scattering
(per lock, per operation) is P × f × A × Dt
× (v/c)2, where P = the power density of phonons in the
matrix (about 5 ×1011 W /m2 at 300 K [24]),
f = a correction factor reflecting the limited coupling between longitudinal
knob motion and matrix motions (0.1 or less), A = the area of the knobs
(10-18 m2), Dt = the time
of motion (50 ps), v = the speed of motion (35 m/s), and c = the speed
of sound in the matrix (10,000 m/s). The estimated loss per lock per operation
is then
When a probe knob presses against a closed gate knob, the resulting van der Waals interactions increase one constraining spring constant on the knobs by roughly fourfold, reducing typical excursions on that axis to about 0.015 nm. If we regard the moving knob as a moving gas parficle, that gas has undergone compression by a factor of 0.5. A variety of other events in the rod logic cycle will cause varying (generally lesser) degrees of compression. These events include moving a probe knob past an open gate knob and moving a gate knob toward a gate stop.
In an isothermal compression from volume V1 to V2, the work consumed would be ln(V2/V1)kT. For a ratio of 0.5, this has a magnitude of 0.7 kT. In an isothermal cycle of compression and expansion, the net work consumed would be zero, and the resulting time-average forces would be like those of a lossless nonlinear spring. In this approximation, compression effects simply add another position-dependent potential energy function in the description of rod motion, one which can be smoothed by track tuning (Section 6.1).
Deviations from isothermal compression cause what seem to be the dominant energy losses in the rod logic system. These deviations may be described in terms of the fractional change in volume per thermal coupling time. The resulting losses may be estimated by assuming that, during compression, the temperature is always that of an isothermal process that became adiabatic one thermal coupling time before the present moment.
Estimates of this coupling time can be made in different ways with similar results. If we assume coupling through collisions with walls during compression, then we get tens of collisions during compression (based on geometric considerations and the observation that the thermal speed is roughly 20 times the rod speed at which most compression occurs). Alternatively, we can note that knob vibrational modes couple strongly to transverse rod modes, which couple strongly to the thermal bath of the matrix. The pre-compression vibrational period of a knob will be about 0.5 ps, and frequency will increase during compression. Therefore, we expect some tens of cycles during a compression event lasting 5 ps. Assuming substantial equilibration of knob temperature per collision or vibration, the thermal coupling time will be on the order of one tenth the compression time, making compression significantly nonisothermal.
Assume a 10% change in volume during a thermal coupling time. Knob temperature (and work done) will then be roughly 5% too high during compression, and 5% too low during expansion, causing a loss per cycle of about 0.1 ln(V2/V1)kT, or 0.07 kT for a compression ratio of 0.5.
Overall compression losses per lock per cycle may be four times this value, or about 0.3 kT. This estimate is very rough, but should be of the right order.
Compression losses seem dominant, totaling (very roughly) 0.3 kT per lock. These losses depend on the ratio of the knob thermal coupling time to the compression time--a time inversely proportional to rod speed. In the speed range of interest these losses should scale roughly as the speed of the rod, or as the inverse of the cycle time.
| A | amplitude of mode (m) | L | distance, alignment knob to last gate (m) |
| b | rod bending stiffness (J-m) | M | modulus of rod (N) |
| c | track constraint (N/m2) | n | mode number |
| d | displacement | N | number of atoms in model rod |
| De | minimum displacement for error (m) | P(d) | probability of displacement ³ d |
| E | energy (J) | s | standard deviation of knob position |
| fx(X) | probability density function for X | st2 | variance due to transverse modes (m2) |
| F | fraction of energy in tension term | sl2 | variance due to longitudinal modes (m2) |
| f | net alignment force (N) | sr2 | variance due to rocking modes (m2) |
| G | average of F2 over all modes | T | temperature (K) |
| k | Boltzmann's constant (J/K) | t | rod tension (N) |
| K | spring constant for knob rocking (N/m) |
The problem of thermal noise is most acute at the gate knob farthest from the alignment knob, since it stores the least elastic energy for a given displacement. Estimates of De must reflect the tendency of gate knobs to deform under load and shed probe knobs toward whichever side of the central sulfur atom they fail on; in near-error conditions, though, this is countered by elastic forces pulling the gate knob toward its proper position. Calculations suggest that a reasonable threshold displacement is one that carries the gate knob from its reference position (with a fluorine atom squarely in front of the probe knob) to a position in which the sulfur atom has moved at least 0.07 nm past the probe knob: this yields a De of about 0.34 nm.
This tendency to shed probe knobs also has a favorable consequence. Probe knobs pressing against 0-state gate knobs push them toward their gate stops, increasing their resistance to displacement. In practical terms, a gate knob has only one chance per cycle to be misplaced.
The model used here considers displacements resulting
from transverse vibrations, longitudinal vibrations, knob rocking, and
shifting
of the rod as a whole caused by motion of the alignment
knob. Knob displacements are measured from a reference position, not from
mean knob positions. The model is classical, and hence overestimates contributions
from high-order vibrational modes. Description in terms of thermally excited
vibrational modes here entails no assumption of regular sinusoidal motions;
it can instead be regarded as simply an analytically tractible way to describe
small, arbitrary rod deformations, driven by entropic forces. The bulk
of the analysis ignores the effect of gate stops, but takes rough account
of them as a correction at the end.
and the fraction of this energy in the tension term is:
Given t = 2.5 nN, c = 1 N/rn-atom = 7.6x109 N/rn2 (a low value), and b = 4.8x10-29 J-m, the average over all the modes is:
The average total energy in the tension term is locally fitted by the linear expression:
Given the constant-tension boundary condition set by the anchor spring, the tension term in the average potential energy is reflected in a shortening of the average rod length by a distance ET/t. Greater tension tends to straighten the rod, implying a finite modulus even without bond stretching. This yields the 1500 nN modulus correction parameter used in Section 3.3.
Deviations from this average energy cause variations in rod length, contributing a thermal noise term. Each mode may be treated as a harmonic oscillator with (classically) an exponential probability density function (PDF) for energy. This yields a PDF for the change in rod length due to the average potential energy in the tension term of mode n:
(The average is taken because rod length responses are slow compared to transverse vibra tion times.) The variance in rod length due to mode n is then:
The variance in rod length due to fluctuations in the energy of all transverse modes is:
These individual exponential terms are small
and
numerous
enough to make the PDF of their sum
approximately
gaussian in the range of interest.
The PDF for the energy will be exponential, yielding a Rayleigh PDF for the vibrational amplitude and a gaussian PDF for the instantaneous displacement of the free end of the rod:
Summing over the modes yields the total variance in longitudinal vibrational displacement:
Design considerations make it desirable to minimize fsubject
to the error-rate constraint. This results in an exponential term too large
to treat by simply adding its variance to those above and treating the
sum as gaussian.
and the associated PDF is:
The effect of gate stops, which constrain several of these positional
displacements to be predominantly in a single direction, may be conservatively
approximated by doubling the probability density in the adverse tail of
the gaussian term. Including this factor of two, the probability of finding
the rod with a displacement greater than De is:
With f = 0.5 nN and the above values for other parameters, Pe equals 5 ×10-13, meeting the stated condition on errors. Satisfaction of the chosen error condition is a matter of design, not of chance. If better models, changed parameters, or a more stringent error condition should adversely affect this result, changes in parameters such as rod tension, alignment force, and gate knob length could be made, resulting in a generally similar design that again met the error condition.
Analysis reveals thermal noise as a major but acceptable constraint on logic element design. Operating delays for elements having 16 inputs and outputs are on the order of 50 ps, a time consistent with the implementation of mechanical nanocomputers having gigahertz clock rates. Rod logic elements have linear dimensions on the order of one ten-thousandth (and volumes on the order of one trillionth) of those of commercial VLSI circuit elements of the recent past. The volume per lock in a regular array is about 4.1 cubic nanometers, neglecting overhead for components roughly analogous to power, ground, and clock signal paths. The energy dissipated during lock operation is speed dependent; at the speed assumed here, it appears to be on the order of 0.4 kT per lock.
The design approach chosen is robust, in that the feasibility of devices of the sort described does not depend on the precise values of uncertain physical effects or parameters. A valuable contribution to the study of mechanical nanocomputers would be the use of existing molecular mechanics programs to model the dynamics of rods and locks in greater detail, to verify their gross behavior and to produce better estimates of energy losses.
By demonstrating a molecular mechanical technology able to implement
reliable logic systems, this work shows the possibility of molecular machines
able reliably to execute complex patterns of motion. This lends further
support to the concept of molecular assemblers able to build structures
to complex, atomic specifications [2], and
to the feasibility of a wide range of technologies relying on computer-directed
machinery with parts of molecular dimensions [10].
VOICE FROM AUDIENCE: I'm a chemist and my amicable criticism is that the cylindrical symmetry of the rods yoúve chosen would allow the perfect swiveling of the knobs and they'd avoid each other.
MR. DREXLER: Yes. In fact, one of the best ways of making a molecular bearing is to have an acetylene-like triple bond; this can give very, very low hindrance of rotation. That's avoided in this system by having each of the knobs slide in a channel that constrains it. This works not because of a torsional stiffness in the rod, which as you point out is essentially nonexistent, but instead by a mechanical constraint from the channel.
DR. MASTERS, TEXAS A. & M. U.: I have just one general comment. I think that the concepts here are decades down the road. Nevertheless, I think they're very important in bringing up the importance of the two-dimensionality of conventional machines.
MR. DREXLER: Yes. For example, the programmable logic array that I showed in my slides was drawn in two dimensions. There are two reasons for that. First of all, it's conceptually simpler, and that's something I'm driving for in this work, not to find the best way, but to find an adequate and analyzable way to do things. Second, it's easier to draw. Third, it corresponds to existing VLSI practice.
Actually, you decrease thermal noise problems and improve the packaging situation if you go to a more three-dimensional structure. One could use a rod that instead of being very long, instead has two parallel stacked segments that are constrained to move together. This would move the design in the direction yoúre outlining and might be desirable from a number of points of view.
DR. HAMEROFF, U. AZ. MED. CENTER: Molecular machines and nature
both utilize electrical and mechanical couplings. There exists a new technology
that utilizes electrical/mechanical coupling directly which may be a way
to bridge from the "macro" world to a submicroscopic realm. Scanning tunneling
microscopy (STM) can image and manipulate materials at the nanometer size
scale. STM technology, when optimally utilized such as in the "Nanotechnology
Workstation" presented here by Conrad Schneiker and myself, can interface
molecular scale devices in the near term rather than far in the future.
