Page 88 - Nanotechnology an introduction

Figure 7.22 A cantilever (from G. Galilei, Discorsi e Dimostrazioni Matematiche. Leyden, 1638).
Envisaged applications of nanoscale cantilevers are as logic devices; in effect ultraminiature versions of the interlocking between points and
signals developed for railway systems to prevent a signalman from selecting operationally incompatible combinations; and as sensors.
The advent of ultrastiff carbon-based materials (Chapter 9) has generated renewed interest in mechanical devices that can now be made at the
nanoscale (nanoelectromechanical systems, NEMS). Ultrasmall cantilevers (taking the cantilever as the prototypical mechanical device) have
extremely high resonant frequencies, effective stiffnesses and figures of merit Q and, evidently, very fast response times . It therefore
becomes conceivable that a new generation of relays, constructed at the nanoscale, could again contend with their solid-state (transistor-based)
rivals that have completely displaced them at the microscale and above. Relays have, of course, excellent isolation between input and output, which
makes them very attractive as components of logic gates.
Sensing applications can operate in either static or dynamic mode. For cantilevers (Figure 7.21) used as sensors, as the beam becomes very thin,
its surface characteristics begin to dominate its properties (cf. Section 2.2). Classically the adsorption of particles onto such a beam would
increase its mass, hence lower its resonant frequency. This effect would be countered if the adsorbed adlayer had a higher stiffness than the beam
material, thereby increasing its resonant frequency. In static sensing mode the adsorption of particles on one face of a beam breaks its symmetry
and causes it to bend.
Manufacturing variability may be problematical for ultrasensitive mass sensors; ideally they should be fabricated with atomic precision using a
bottom-to-bottom approach (Section 8.3); in practice nowadays they are fabricated using semiconductor processing technology.
7.9. Fluidic Devices
In gases, the dimensionless Knudsen number associated with the motion of the molecules is the ratio of the mean free path ℓ to some characteristic
size l:

(7.24)
The mean free path depends on the pressure and the simplest possible derivation assuming the gas molecules to be elastic objects with an
effective diameter σ yields

(7.25)
where n is the number per unit volume. Following similar reasoning to that of Section 7.4.1, one could take the nanoscale as the scale
corresponding to K = 1; it would therefore be pressure-dependent. At atmospheric pressure, the mean free path of a typical gas is several tens of
n
−3
nm. Given that even a moderate vacuum of say 10 mbar gives a mean free path of about 0.1 m, a low pressure nanodevice would seemingly
have no unique feature.
In fluids, we typically have molecules or particles of interest dissolved or suspended in the solvent. The particles (of radius r) undergo Brownian
motion, i.e., thermal collisions, and the mean free path is effectively the distance between successive collisions with the solvent molecules (formally,
it is the average distance from any origin that a particle travels before significantly changing direction) and is related to the diffusion coefficient D
and the thermal velocity c of the particle according to

(7.26)
the diffusivity depends on the friction coefficient according to the Stokes–Einstein law: