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 P_sliding ≈ Dv² 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 P_flow = 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), P_flow ≈ 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.