© 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.4.3.2 Confined-Fluid Density Layering Due to Near-Wall Solvation Forces

Despite laminar bulk-fluid flows throughout the center regions of the piston cavity, nanoscale density layering near the liquid-solid interface is a universal feature of liquids [3232] which has been demonstrated experimentally [3190, 3191, 3194] and in many simulations [3173-3177]. Layering is observed both in long chain fluids and in fluids of spherical molecules, and even in simulations of hard particles against hard walls [3168]. Layering is caused by the packing of molecules against the surface, which is partly an entropic effect due to the increase of free volume of individual molecules when the density is layered compared to that in a uniform density [3232].

The variations in density are most significant for fluids confined in very narrow spaces. It is believed that solvation forces are a signature of molecular ordering induced by the confining surfaces [3169]. In general [3194], low molecular weight fluids flowing between two walls separated by more than 5-10 molecular diameters (~2.5-5 nm for n-octane) experience a monotonically attractive van der Waals force as expected from continuum theories. But at smaller separations the force generally oscillates with distance, varying between attraction and repulsion, with a periodicity equal to the mean diameter of the liquid molecules. The oscillatory force law is a reflection of the tendency of simple molecules to order in layers near a smooth solid surface, and the enhancement of this ordering when two surfaces are in close proximity [3194]. Simulation studies have shown that symmetric molecules are absorbed into or squeezed out of the confined space in a stepwise fashion [3169], i.e., on a whole-layer basis [3180-3185], when the surface separation is changed. The confined film can undergo a series of pseudophase transitions between solidlike and liquidlike configurations [3184-3187].

Solvation force-driven density oscillations in confined liquids have been demonstrated for n-octane and related isomers in both theoretical [3175-3180] and experimental [3155, 3192-3194] studies, for non-octane alkanes both theoretically [3170-3172, 3185] and experimentally [3178, 3193-3200], and for various octane mixtures such as octane-butane [3232], octane-methanol [3155], or octane-water [3155, 3193]. The self-diffusion coefficient within the layers (which is related to the effective viscosity) has been shown [3204-3207] to drop abruptly when films of spherical molecules are confined below a given critical film thickness, indicating a rather sharp solidification process. Interestingly, octane shows among the fewest number of density oscillations (typically just two layers [3173, 3192-3194]) with distance from the confining surface, before resuming bulk density, of the common alkanes.

However, the space between adjacent walls in the piston cavity is ~Z_int = 40 nm >> 2.5-5.0 nm = 5-10 molecular diameters of the n-octane molecule. It has been found [3155] that liquid n-octane confined experimentally between two mica surfaces exhibits liquid behavior for gap thickness >5 molecular layers, and solidlike behavior for <5 molecular layers. In general, when two surfaces are farther apart than ~10 molecular diameters, a simple fluid in the gap retains its bulk Newtonian behavior and the shear plane remains coincident with the physical solid-liquid interface to within ~1 molecular diameter at shear rates up to 10⁵ sec^-1 [3208-3211], and with no change in thin-film viscosity from the bulk liquid for long-chain linear alkanes such as tetracosane (C₂₄H₅₀) for strain rates up to 10⁸-10¹¹ sec^-1 [3214]. While fluid strain rates found in a number of practical applications such as the lubrication of disk drives, micromachines, and camshaft lifters in automobile engines [3215] can reach ~10⁸ sec^-1, the shear rate inside our assembler piston cavity can only reach a maximum of ~v_piston / Z_int = 50 x 10⁵ sec^-1 for v_piston = 0.2 m/sec in double-band operation.

Surface force balances have also been used to probe the dynamic and structural properties of ultrathin films and suggest that, even when confined, liquids retain their bulk viscosity as long as the films are thicker than about ten molecular diameters, right up to the liquid-confining/solid interface (to within a single molecular layer) [3210-3213]. As Klein and Kumacheva [3203] explain: “The picture that emerges is that, as the [confining] surfaces approach each other from large separations, the confined liquids retain their bulk fluidity across the entire gap, until at a critical spacing the entire film undergoes a liquid-to-solid transition.”

For unconfined bulk liquids in contact with a single smooth solid surface, some layering of the molecules is induced, decaying over a few molecular diameters from the surface [3201-3204]. This layering is due to simple geometric packing. But theoretical molecular dynamics and Monte Carlo studies of liquid films of n-octane [3173, 3232], decane [3169], and hexadecane [3216] on various isolated surfaces near room temperature, and related experimental work [3210-3212], have confirmed that bulk simple liquid alkanes near a surface remain fluid right up to the solid-liquid interface.

The conclusion is that bulk viscosity flow conditions should prevail across the entire width of the piston chamber, except for piston interactions with physisorbed solvent molecules at the wall-fluid interface which is the subject of the following Section.

Last updated on 13 August 2005