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.3 Gas Phase vs. Solvent Phase Manufacturing
One simple extruding-brick assembler environment would employ a two-component gas phase system – hydrocarbon feedstock molecules and vitamin molecules – with the assembler replicating in gaseous suspension. Diamondoid particles <4 microns in diameter that are suspended in gas at STP have a thermal velocity exceeding their terminal sedimentation velocity , hence should not “settle out.”
However, the importation of acoustic control signals having sufficiently high frequency and of acoustic energy pulses having sufficiently high intensity to power the assembler (Section B.4.2) is facilitated by liquid phase, rather than gas phase, operation, for several reasons.
First, a plane acoustic wave of initial amplitude P0 (atm) and frequency n traversing a uniform medium of thickness X and absorption coefficient a is partially absorbed during transit, with transmitted amplitude Px = P0 e-aX. In the case of Ar gas atoms , which are incapable of either vibration or rotation, aAr = (1.7 x 10-11 sec2/m)n2 at 300 K and 1 atm, whereas for pure water awater = (2.5 x 10-14 sec2/m)n2 and typically aorganics = (3-600 x 10-14 sec2/m)n2 for organic fluids near STP . However, in acetylene gas at 300 K and 1 atm pressure, the absorption coefficient as a function of frequency between 1-10 MHz peaks out  as aacetylene ~ (3-5 x 10-4 sec/m)n – the vibrational relaxation time in acetylene gas at 300 K and 1 atm pressure, as measured by ultrasonic irradiation of the gas, is 7.4 x 10-8 sec, corresponding to ~13.5 MHz . For irradiation volumes having dimensions comparable to acoustic wavelength, e.g., X ~ 100 microns, absorption is far more severe in gas than in liquid. Absorption becomes less severe for shorter path lengths.
Second, the acoustic intensity Ifluid (W/m2) that must be applied to a fluid to obtain a given planar acoustic wave pressure amplitude Pfluid is given by Ifluid = Pfluid2 / (2 rfluid vsound), where rfluid is fluid density and vsound is the speed of sound in the fluid . For gaseous acetylene at STP, rfluid = 1.171 kg/m3 and vsound = 328 m/sec as estimated from the Newton-Laplace equation for gases; for liquid n-octane at 20 oC and 1 atm, rfluid = 702.5 kg/m3 and the speed of sound in liquid n-octane at 20 oC is vsound ~ 1194 m/sec . To produce a pressure amplitude of Pfluid = 1 atm within the fluid-filled reaction chamber, Ifluid = 1.3 x 107 W/m2 must be delivered to pure acetylene gas but only Ifluid = 6.1 x 103 W/m2 to pure liquid n-octane.
The thermal response to such power influx is readily, if crudely,
estimated as follows. A power flux Ifluid crossing a reaction chamber of linear
dimension Lchamber ~ 2 microns that is filled with fluid of thermal conductivity
Kfluid and heat capacity CV produces an equilibrium temperature differential
of DTchamber ~ Ifluid Lchamber / Kfluid in an equilibration time of tEQ ~ Lchamber2
CV / Kfluid . For pure acetylene gas
at STP, Kfluid = 2.11 x 10-2 W/m-K 
and CV ~ 1490 J/m3-K , so inserting
a 1 atm signal amplitude produces a decomposition-inducing temperature differential
of DTchamber ~ 1200 K in an equilibration time tEQ ~ 0.28 x 10-6 sec. For pure
n-octane liquid at 20 oC and 1 atm, K
A third important benefit of using a solvent is the significant elevation in the safe working pressure of highly sensitive carbon-rich feedstock molecules such as acetylene at room temperature – in the case of acetylene, from 2 atm as a pure gas to 17-20 atm as a gas dissolved in solvent (most commonly, acetone). This elevation applies as long as the acetylene remains in solution and does not effervesce or coalesce as micropockets of gas (e.g., during acoustic cavitation; Sections B.4.4.2 and B.4.4.3). A similar elevation of acetylene decomposition pressure threshold following solvation in liquid n-octane is anticipated but should be experimentally verified.
Last updated on 13 August 2005