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.4.4.1 Thermal Expansion in Diamond Walls
The proposed molecular assembler receives pdevice ~ 14.2 pW of continuous power when operated in single-band mode (e.g., from 1-2 atm or from 2-3 atm), or 56.8 pW when operated continuously in double-band mode (e.g., from 1-3 atm). Thus the device possesses a power density of pdevice / Vext = 6.89-27.6 x 109 W/m3. An acoustic power flux of Iacoustic ~ pdevice / Stransducer = 5070-20,300 W/m2 crossing an assembler of mean dimension Lassembler ~ 100 nm that is composed mostly of diamond having thermal conductivity Kdiamond = 2000 W/m-K and heat capacity CV ~ 1.82 x 106 J/m3-K produces a negligible equilibrium temperature differential of DT ~ Iacoustic Lassembler / Kdiamond = 0.25-1.0 x 10-6 K in an equilibration time of tEQ ~ Lassembler2 CV / Kdiamond = 9 x 10-12 sec . Across a reaction chamber of size Lchamber ~ 2 microns, the spatial thermal gradient of DTchamber / Lchamber ~ 3.9-15.7 x 104 K/m (taking Ifluid = Iacoustic in Section B.3) caused by differential acoustic heating of liquid n-octane solvent on opposite sides of the reaction chamber implies that the solvent temperature at either end of the assembler may differ by as much as DTsolvent,ends = (DTchamber / Lchamber) Xext ~ 0.01-0.05 K, producing a linear thermal expansion in the diamond walls (expansion coefficient adiamond = 8 x 10-7 K-1) that cannot be larger than Xext (adiamond DTsolvent,ends) ~ 0.4-1.5 x 10-14 m or >10-4 atomic diameters, which is negligible.
Last updated on 13 August 2005