Kinematic Self-Replicating Machines
© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.
Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.
B.4.1 Selection of Acoustic Frequency
Power and control signals are imported into the molecular assembler via externally generated high frequency acoustic signals. The need to provide sufficient coupling to the onboard transducer at reasonable power intensities dictates liquid phase, rather than gas phase, operations. Choice of frequency in liquid phase is driven by several offsetting considerations.
On the one hand, the highest feasible frequencies are preferred
because they permit control information to be imported at the fastest possible
rate, thus minimizing replication time for a design requiring a particular number
of steps for its manufacture. Also, at higher acoustic frequencies the onset
of harmful cavitation requires higher power intensities than are likely to be
necessary for normal manufacturing operations (Section
On the other hand, operating frequency must not be too high for several reasons. First, attenuation of acoustic signals increases exponentially with frequency – operation at 100 MHz could allow significant attenuation in organic solvent (Section B.3), producing substantial solvent heating, unless path lengths are very short. Second, acoustic signals must be transduced by pistons whose drag losses are proportional to the square of the speed of sliding interfaces . A 10 MHz piston that must travel ~10 nm/cycle moves at 0.1 m/sec dissipating a negligible ~0.001 kT/cycle, but at 100 MHz would move at 1 m/sec, a speed which can dissipate ~100 times more energy, up to ~0.1 kT/cycle (a significant loss) in sliding interfaces of these nanoscale dimensions . Third, the piston must be operated slowly enough (<<100 MHz) to remain in the viscous regime while displacing solvent molecules adsorbed at the piston cavity walls during each cycle of piston operation (Section B.220.127.116.11). Fourth, the time required for feedstock molecule binding at the acetylene binding site to occur with a high enough probability (qbinding = 1 - 10-12) to ensure full-cycle device replication with 99.99% certainty is tbinding = 92 x 10-9 sec, defining a maximum possible acetylene molecule import rate of ~11 MHz.
Acetylene (ethyne), the simplest alkyne and our carbon source in this design, can be used safely in the laboratory at atmospheric pressure without risk of flash decomposition up to 1000 K , though some decomposition in inert porcelain tubes is detected above 750 K . At room temperature, pure acetylene gas decomposes by deflagration above 2 atm and can detonate above 3.2 atm . (Deflagration is a slow-moving decomposition to the elements, producing fine carbon particles in the gas and gradual warming the tank as -54.34 kcal/mole heat of formation is slowly released, sometimes taking up to an hour before final detonation occurs.) Pure acetylene is shock sensitive and unlawful to ship under U.S. Department of Transportation regulations, but the gas dissolves readily in acetone, benzene, and other organic solvents; shipped as an acetone solution impregnating a porous solid inside the tank, C2H2 can safely tolerate pressures up to 17-20 atm before decomposition ensues. While butadiyne readily polymerizes in 7.4% acetone solution at room temperature during storage  or topochemically when heated or irradiated , acetylene does not polymerize under similar conditions and requires either chemical catalysis , IR laser irradiation at 107-108 W/m2 , or diamond-anvil compression into the solid state at >3-4 GPa at room temperature for tens of hours [3146-3149] for polymerization to occur. Thus for the present design, we choose acetylene as our hydrocarbon feedstock molecule.
Can acetylene tolerate without decomposition the passage of MHz acoustic pulses that will carry power and control signals to the proposed molecular assembler? Although acetylene is shock sensitive, Wang and Springer  have irradiated acetylene gas pressurized to 0.05-1 atm and heated to 300-900 K with 0.5-1 MHz ultrasound having a pulse duration of 20 msec without observing any decomposition reactions. Hart et al  observed sonolytic pyrolysis of acetylene in aqueous solution* at 20,000 W/m2 and 1 MHz, but peak pyrolytic activity occurred at a solution concentration of 0.002 M C2H2, falling essentially to zero for more concentrated solutions >0.01 M such as we are proposing to use. Sonolysis of liquid decane at 20 KHz and at acoustic intensities up to ~106 W/m2 evolves large amounts of C2H2, along with sonoluminescence, but there is no evidence of further decomposition of the acetylene. At the pressures (1-3 atm), frequencies (up to 10 MHz), C2H2 concentrations (0.15 M), and intensities (~6100 W/m2) contemplated here, solvated acetylene should be equally ultrasound-tolerant and cavitation (Section B.4.4.3) resistant, an expectation that should be verified experimentally up to acoustic frequencies of at least 10 MHz.
* Pyrolysis of acetylene  occurred in a 60 ml reaction vessel containing 37.5 ml of solution and 22.5 ml of argon gas, with acetylene added to this gas in varying small amounts. Sonolysis of acetylene has the character of combustion, producing a large number of reaction products including H2, CO, CH4, various hydrocarbons with intermediate C atom numbers (predominantly with even C numbers rather than odd) such as benzene and various C6H6 isomers, high C number products such as naphthalene, and a yellowish soot consisting of particles of which 50% were >0.45 micron in size. At the peak rate, all acetylene was consumed in a few minutes of run time. The combustion mechanism is thought to involve a gas nucleus in the liquid that grows slowly and isothermally in the ultrasonic field. The mechanism of growth is rectified diffusion  as the bubble oscillates. When the bubble reaches ~5 microns in size (at 1 MHz, in water), it undergoes a rapid adiabatic compression or collapse, momentarily creating temperatures of several thousand kelvins with pressures up to 100 atm. In contrast, a resonance bubble in n-octane at 10 MHz would be ~0.4 microns in diameter (Section B.4.4.3), larger than the assembler device and a substantial fraction of the ~2 micron reaction chamber width. Since the assembler solvent bath is an ultrapure liquid with no nucleation sites, and since the acoustic wavelength in n-octane at 10 MHz is ~100 microns >> 2-micron reaction chamber width (suggesting isotropic pressure throughout the chamber), cavitation bubbles should be difficult to initiate.
Additionally, pyrolytic activity of the acetylene appeared to depend upon the presence of the water, which supplied H and O for various reaction pathways, but more importantly upon the presence of the argon, which (when dissolved in water) readily produces cavitation bubbles, creating a gaseous reaction microvessel wherein acetylene sonolysis can occur. At low acetylene concentrations, the rate of pyrolysis increases with C2H2 concentration. But at higher acetylene concentrations, due to the lower specific heat of acetylene as compared to argon, the temperature reached in the adiabatic compression of the bubble becomes lower with increasing hydrocarbon content, leading to a maximum in the yield vs. hydrocarbon concentration curve. At C2H2 concentrations exceeding 0.01 M, the temperatures achieved inside the cavitation bubble apparently are insufficient to induce sonolytic pyrolysis. The assembler feedstock solvent bath is anticipated to be a 0.15 M solution of acetylene.
These considerations, along with past analyses by others [208, 217], lead us to adopt nacoustic = 10 MHz as a compromise operating frequency for the present design.
Last updated on 13 August 2005