© 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.4.3.3.3 Operation in the Desorption Regime

Assuming double-band piston operation for the rest of this discussion, the center of the transitional regime would occur at a piston frequency of n_transitional ~ Dx / (2 L_piston t_diffusion||) ~ 128 MHz, taking L_piston = 10 nm (Section B.4.2). If the piston is operated above this frequency, then there is insufficient time for adsorbed molecules to laterally diffuse and escape from the approaching piston plate, so the adsorbed molecules must be mechanically desorbed from the surface in order to allow the piston plate to pass.

Heat is evolved during the physical adsorption process [2987], so energy must be added to molecules physisorbed on a surface in order to desorb them. A laterally-moving tight-seal scraping plate that applies a mechanical energy greater than the bulk material energy of adsorption (aka. energy of desorption, heat of adsorption or enthalpy of adsorption) to an n-octane molecule physisorbed on a diamond surface is likely to desorb that molecule from the surface. Table B.1 shows desorption energies for even-numbered linear-chain hydrocarbons on different surfaces, at various temperatures. Graphite is considered a very weakly physisorbing “nonwetting” surface for hydrocarbons, gold is a moderately physisorbing surface, and mica is a strongly physisorbing surface [3173]. According to polymer adsorption theory [3240], adsorption or desorption from solution generally requires 0.2 kT to 4 kT per interacting polymer segment (e.g., ~0.8-17 zJ per carbon segment in a long-chain n-alkane at 300 K), depending on the chemistry of the repeat segments and of the solvent. Aside from one study [3189] of the physisorption of acetylene on the diamond (111) surface, the physical adsorption of alkanes and other hydrocarbons on diamond surfaces has yet to be systematically investigated. The range of desorption enthalpies appears to be 1-15 zJ per C unit for hydrocarbons on graphite and a few other hydrocarbon-nonwetting surfaces. In the absence of hard experimental data or reliable computational simulations, a value of ~1 kT/segment or ~4 zJ per CH_x unit for octane on diamond surface at 300 K appears reasonable, though the precise choice does not sensitively affect our conclusions.

Taking the enthalpy of desorption for physisorbed n-octane on diamond at 300 K as E_desorb ~ 32 zJ/molecule, then the power required for piston motion is p_desorb ~ 4 n_piston E_desorb (Y_int + Z_int) L_piston / a_octane. Taking L_piston = 10 nm, Y_int = 80 nm, Z_int = 40 nm, a_octane ~ 0.60 nm²/molecule, and n_piston > 128 MHz, then p_desorb > 33,000 pW >> p_assembler (= 56.8 pW; Section B.4.2), and so the piston becomes securely pinned by solvation forces and cannot move at this frequency.

Last updated on 13 August 2005