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Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids

Power dissipation in sleeve bearings is dominated by phonon interactions, occurring chiefly through shear-reflection and band-stiffness-scattering mechanisms. A high-stiffness (1000 N/m) reference bearing with a radius and length of 2 nm dissipates energy at a rate PslidingDv2 W, where v is the interfacial sliding speed in m/s and D is estimated to be in the range 5.8 × 10−16 to 2.7 × 10−14, depending on interfacial parameters characterising fluctuations in stiffness due to differences in atomic alignment [1].

How does this compare with the power dissipated by the motion of a comparably sized object in a liquid medium? At low Reynolds numbers (which are characteristic of nanoscale systems), a sphere of radius R rotating at angular speed ω in a fluid of viscosity η will experience a viscous torque = −8πηR3ω [2], and hence will dissipate energy at a rate Pflow = 8πηRv2, where v is the linear speed at the “equator” of the sphere. For a sphere with R = 2 nm in water (η ≈ 10−3 Pa·s), Pflow ≈ 5 × 10−11v2 W. Relative to the reference bearing, an object rotating in a liquid thus dissipates energy at a rate about 2,000 to 100,000 times greater. A small fluid-lubricated bearing would likewise suffer from high power dissipation.

This comparison shows that mechanical systems based on well-ordered molecular structures can greatly outperform those based on disordered systems such as fluids. More generally, it illustrates why molecular machine systems operating in a machine-phase environment can be far more efficient than those operating in a liquid (note: transporting molecules by diffusion down a concentration gradient is not cost-free — it pays the same free-energy cost as any other way of driving the motion of molecules). While early systems can (and likely will) operate in fluids, considerations of efficiency will favor a move to well-ordered, fluid-free systems.

What are molecular sleeve bearings?

Link  A shaft in a sleeve can form a rotary bearing

[1] Drag mechanisms in symmetrical sleeve bearings:

Drexler, K. E. (1992) Nanosystems: Molecular Machinery, Manufacturing, and Computation. Wiley/Interscience, pp.290–293.

[2] Viscous torque on a sphere:

Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.