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.184.108.40.206 Operational Regimes Defined
The interaction of the piston plate with the physisorbed n-octane monolayer during the piston return stroke will be governed by the characteristic diffusion time tdiffusion|| of the adsorbed n-octane molecules parallel to the surface. According to the well-known Einstein-Smoluchowski diffusion equation , tdiffusion|| ~ (Dx)2 / (2 Ddiffusion||) where Dx is the distance diffused in a fluid having lateral diffusion constant Ddiffusion||. For an adsorbed monolayer, Dx may be taken as the mean intermolecular separation distance within the monolayer, or Dx ~ aoctane1/2 ~ 0.77 nm for n-octane. tdiffusion|| is thus the mean time for a physisorbed molecule to diffuse one intermolecular separation distance. Although no studies of any kind have been done on the physisorption of n-octane on diamond surfaces, estimates from molecular dynamics and other theoretical investigations have found, for example, that Ddiffusion|| ~ 0.57 x 10-9 m2/sec for 1.3 monolayers coverage of liquid n-octane physisorbed on a-Al2O3(0001) at 300 K , Ddiffusion|| ~ 7.5 x 10-9 m2/sec for an n-octane monolayer on Cu(111) surface at 200 K , Ddiffusion|| ~ 1.7 x 10-9 m2/sec for butane at 149 K or hexane at 215 K adsorbed on graphite , Ddiffusion|| ~ 2.1 x 10-9 m2/sec for butane at 150 K on Pt(111) at close to monolayer coverage , Ddiffusion|| ~ 10 x 10-9 m2/sec for 1.0 monolayer coverage of liquid benzene on the basal plane of graphite at 250 K , and Ddiffusion|| ~ 2.8 x 10-9 m2/sec for the translational self-diffusion coefficient for liquid ethylene adsorbed on the basal plane of graphite at 75 K . Conservatively taking Ddiffusion|| ~ 1.0 x 10-9 m2/sec for liquid octane adsorbed on hydrogen terminated diamond at 300 K, then tdiffusion|| ~ 0.3 x 10-9 sec.
The characteristic time required for the piston plate to travel one intermolecular separation distance (Dx) is tpiston = Dx / vpiston. This defines three distinct operating regimes for the piston relative to the surface-adsorbed n-octane monolayer, as discussed further, below:
I. Desorption Regime: tpiston << tdiffusion|| (~ 0.3 x 10-9 sec)
II. Transitional Regime: tpiston ~ tdiffusion|| (~ 0.3 x 10-9 sec)
III. Viscous Regime: tpiston >> tdiffusion|| (~ 0.3 x 10-9 sec)
Last updated on 13 August 2005