Most mechanical systems use bearings to support moving parts. Macromechanical systems frequently use liquid lubricants, but (as noted by Feynman, 1961), this poses problems on a small scale. The above scaling law ordinarily holds speeds and stresses constant, but reducing the thickness of the lubricant layer increases shear rates and hence viscous shear stresses:
In Newtonian fluids,
shear stress is proportional to shear rate. Molecular
simulations indicate that liquids can remain nearly
Newtonian at shear rates in excess of 100 m/s across a 1
nm layer (e.g., in the calculations of Ashurst and
Hoover, 1975), but they depart from bulk viscosity (or
even from liquid behavior) when film thicknesses are less
than 10 molecular diameters (Israelachvili, 1992; Schoen
et al., 1989), owing to interface-induced alterations in
liquid structure. Feynman suggested the use of
low-viscosity lubricants (such as kerosene) for
micromechanisms (Feynman, 1961); from the perspective of
a typical nanomechanism, however, kerosene is better
regarded as a collection of bulky molecular objects than
as a liquid. If one nonetheless applies the classical
approximation to a 1 nm film of low-viscosity fluid (
= 10 The problems of liquid lubrication motivate consideration of dry bearings (as suggested by Feynman, 1961). Assuming a constant coefficient of friction,
and both stresses and speeds are once again scale-independent. The frictional power,
is proportional to the total power, implying scale-independent mechanical efficiencies. In light of engineering experience, however, the use of dry bearings would seem to present problems (as it has in silicon micromachine research). Without lubrication, efficiencies may be low, and static friction often causes jamming and vibration. A yet more serious problem for unlubricated systems would seem to be wear. Assuming constant interfacial stresses and speeds (as implied by the above scaling relationships), the anticipated surface erosion rate is independent of scale. Assuming that wear life is determined by the time required to produce a certain fractional change in shape,
and a centimeter-scale part having a ten-year lifetime would be expected to have a 30 s lifetime if scaled to nanometer dimensions. Design and analysis have shown, however, that dry bearings with atomically precise surfaces need not suffer these problems. As shown in Chapters 6, 7, and 10, dynamic friction can be low, and both static friction and wear can be made negligible. The scaling laws applicable to such bearings are compatible with the constant-stress, constant-speed expressions derived previously. The above scaling relationships treat
matter as a continuum with bulk values of strength,
modulus, and so forth. They readily yield results for the
behavior of iron bars scaled to a length of 10 Aside from the molecular structure of matter, major corrections to the results suggested by these scaling laws include uncertainties in position and velocity resulting from statistical and quantum mechanics (examined in detail in Chapter 5). Thermal excitation superimposes random velocities on those intended by the designer. These random velocities depend on scale, such that
where the thermal energy
measures the characteristic energy in a single degree of
freedom, not in the object as a whole. For
=
3.5×10 Quantum mechanical uncertainties in
position and momentum are parallel to statistical
mechanical uncertainties in their effects on
nanomechanical systems. The importance of quantum
mechanical effects in vibrating systems depends on the
ratio of the characteristic quantum energy (
, the quantum of vibrational energy in a
°harmonic oscillator of
angular frequency
) and the characteristic thermal energy ( |

Copyright © 1998 by John Wiley & Sons, Inc.