Page 24 - Nanotechnology an introduction

One consequence of these ideas is the impossibility of comminuting particles below a certain critical size d by crushing. Kendall [90] derives, in
crit
a rather simple way,
(2.24)
where F is the fracture energy; below this size crack propagation becomes impossible and the material becomes ductile.
Cracks can be arrested by interfaces, and it has long been realized that nature has solved the problem of creating strong (i.e., both stiff and tough)
structural materials such as bones, teeth and shells by assembling composite materials consisting of mineral platelets embedded in protein matrix.
The numerous interfaces prevent the propagation of cracks, and provided the stiff components of the composite are not bigger than the critical
Griffith length, optimal strength should be obtainable. This has recently been subjected to more careful quantitative scrutiny [87] yielding an
expression for the stiffness of the composite:

(2.25)

where G and Y are respectively the shear modulus of the protein and Young's modulus of the mineral, θ is the volume fraction of mineral, and a is
p
m
the aspect ratio of the platelets. It seems that the thickness of the platelets in natural materials (such as various kinds of seashells) roughly
corresponds to l . By assuming that the protein and the mineral fail at the same time, an expression for the optimal aspect ratio of the mineral
G
platelets can be derived, equal to , where τ is the shear strength of the protein matrix.
2.8. Quantum Smallness
In the preceding sections of this chapter, the various crossover lengths that demarcate the nanorealm from other realms have emerged as upper
limits of the nanorealm; above these lengths, the behavior is qualitatively indistinguishable from that of indefinitely large objects, and below them
novel properties are observable. But does the nanorealm have a lower limit? This has been implicit in, for example, the discussion of the
mesoscale at the beginning of this chapter, implying that the point where continuum mechanics breaks down and atoms have to be explicitly
simulated demarcates the lower limit of the nanoscale. On the other hand, discussion about the possible design of nanoscale assemblers can
hardly avoid the explicit consideration of individual atoms. Despite such challenges, it is probably fair to say that there has been considerably less
discussion about the lower limit of nanotechnology compared with the upper one.

The idea that nanotechnology embodies a qualitative difference occurring at a certain point when one has shrunk things sufficiently links
nanotechnology to Hegel, who first formulated the idea that a quantitative difference, if sufficiently large, can become a qualitative one in his
Wissenschaft der Logik. In essence nanotechnology is asserting that “less is different”. In order to defend condensed matter physics from the
criticism that it is somehow less fundamental than elementary particle physics, P.W. Anderson wrote a paper entitled “More is different” [7], in which
he developed the idea of qualitative changes emerging when a sufficient number of particles are aggregated together (in other words chemistry is
not simply applied physics, nor biology simply applied chemistry, but at each new level, implying simultaneous consideration of a larger number of
particles than in the preceding one, new phenomena emerge, the existence of which could not have been predicted even from complete knowledge
of the preceding level). Nanotechnology is a further example of the fundamental idea of the emergence of wholly new phenomena at a new level of
description, except that now we are not increasing the quantity, but decreasing it. The various examples gathered in the preceding sections, such
as the optical properties of semiconductor nanoparticles already mentioned, or the magnetic properties of nanoparticles, are all concrete
manifestations of Hegel's idea of a qualitative change emerging when a quantitative change becomes sufficiently large.
There is, however, an even more fundamental difference that appears when we enter the quantum realm—the world of the absolutely small, as
emphasized by Dirac: “It is usually assumed that, by being careful, we may cut down the disturbance accompanying our observations to any
desired extent. The concepts of big and small are then purely relative and refer to the gentleness of our means of observation as well as to the
object being described. In order to give an absolute meaning to size, such as is required for any theory of the ultimate structure of matter, we have
to assume that there is a limit to the fineness of our powers of observation and the smallness of the accompanying disturbance—a limit which is
inherent in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer. If the object under
observation is such that the unavoidable limiting disturbance is negligible, then the object is big in the absolute sense and we may apply classical
mechanics to it. If, on the other hand, the limiting disturbance is not negligible, then the object is small in the absolute sense and we require a new
theory for dealing with it”[42].
Another way in which the quantum realm is absolutely different from the classical one was elaborated upon by Weisskopf [165]. In classical physics,
laws predetermine only the general character of phenomena; the laws admit a continuous variety of realizations, and specific features are
determined by the initial conditions. On the other hand, in the quantum realm individual atoms have well-defined specific qualities. Furthermore their
identity is unique and immutable. “Two pieces of gold, mined at two different locations and treated in very different ways, cannot be distinguished
from one another. All the properties of each individual gold atom are fixed and completely independent of its previous history”[165] (gold has only
one stable isotope, it should be noted; this is not the case for all other elements, in which case the isotopic ratios could give clues to the
provenance of the samples). Similarly, all electrons have the same charge, spin and mass. The same identity extends to the crystal structure of a
substance (disregarding polymorphism), and indeed to other properties. This existence of well-defined specific qualities is alien to the spirit of
classical physics. Furthermore, these quantum “blocks” (atoms, electrons, etc.) are embodied in larger structures assembled from atoms, such as
chemical molecules, which also possess quality, specificity and individuality.
The divisibility of process is also a main feature of classical physics [165]: every process can be considered as a succession of partial processes.
Typically, a reversible change in thermodynamics is effected as a succession of infinitesimal steps. This gives rise to the Boltzmann paradox: since
all possible motions in a piece of matter should share in its thermal energy, if there were an endless regression of the kind molecules → atoms →
protons etc. → … then immense, indeed infinite energy would be needed to heat up matter, but this is evidently not the case. The existence of
quanta resolves the Boltzmann paradox: the notion of a succession of infinitesimal steps loses meaning in the quantum realm.
When it comes to the living world, classical features seem to be even more apparent than in the macroscopic inanimate world—human perceptions
such as the taste of a foodstuff depend on the recent history of what one has eaten, and the psychological circumstances at the time of eating, for