Page 18 - Nanotechnology an introduction

Element Symbol Atomic number Radius/nm [98]
Carbon C 6 0.077
Chlorine Cl 17 0.099
Gold Au 79 0.150
Hydrogen H 1 0.031
Silicon Si 14 0.117
Sodium Na 11 0.154
Zinc Zn 30 0.131
2.1. The Size of Atoms
An atom is important because it designates the ultimate (from a terrestrial viewpoint) particles in which matter exists. It was therefore very natural
for Richard Feynman to suggest atom-by-atom construction of objects as the lower limit of miniaturization of engineering [56]. It would be highly
impracticable to have to start with subatomic particles, such as protons, electrons, neutrons and so forth as building blocks, whereas atomically
precise construction, as Feynman rightly perceived and emphasized, is an engineering problem (hence solvable in principle), not a scientific one
(requiring the discovery of hitherto unknown laws). Table 2.1 gives the sizes of some atoms.
The scale of the individual atom might be considered as sufficient for a definition of the nanoscale, especially if nanotechnology were to be defined
solely in the context of atom-by-atom assembly of objects. But nanotechnology already seems to be much more than this. The definitions of
nanotechnology (Chapter 1) emphasize that novel, unique properties emerge at the nanoscale. This implies that merely assembling an otherwise
known macro-object atom-by-atom warrants the name of nanotechnology by virtue of the novelty of the assembly process.

2.2. Molecules and Surfaces
The dictionary definition of a molecule is typically “the smallest part of a substance that retains all the properties of the substance without losing its
chemical identity and is composed of one or more atoms”. This combines its etymological meaning as the diminutive of the Latin moles, mass
(which on its own would make the word essentially synonymous with “particle”) with Tyndall's definition as “a group of atoms drawn and held
together by what chemists term affinity”. This definition is readily applicable to typical covalent molecules such as most organic compounds; a
molecule of the carbohydrate called glucose is precisely the particle composed of 6 carbon atoms, 6 oxygen atoms and 12 hydrogen atoms
connected in such a way as to make what we know as glucose, and even a single such particle would taste sweet in the characteristic way of
glucose, but none of these atoms could be removed without destroying the “glucoseness”. Particles of other kinds of substances do not fit the
definition so well. A single atom of a metal such as gold, although chemically gold, has a different optical absorption spectrum from that of bulk
gold, and the same applies to numerous binary semiconducting compounds such as cadmium sulfide, CdS, which can be prepared as a vapor
containing isolated CdS molecules (in the chemical sense). In bulk material, the individual atoms are close enough for the wave functions of their
electrons to overlap, but to satisfy Pauli's exclusion principle, their energies must be slightly shifted, forming a band of states instead of a discrete
level as in the isolated atom or molecule; see also Section 2.5.
The surface of a particle is qualitatively different from the bulk because it is less connected; the smaller the radius, the greater the proportion of
underconnected atoms. Consider a “supersphere”, a spherical aggregate of spheres, which we can take to be atoms (Figure 2.1). By simple
geometric considerations, only one of the 19 atoms is not in contact with the surface. If the radii of the atom and the supersphere are r and R
3
respectively, then the proportion of atoms in the shell must be 1 − [(R − r)/R] . The mean connectivity, and hence cohesive energy, should vary
inversely with a fractional power of this quantity. If R is expressed in units of r, then the surface to volume ratio is equal to 3r/R: in other words, if R =
3r, equal numbers of atoms are in the bulk and at the surface. The nanoparticle is, therefore, one that is “all surface”. As a result, the melting point
T of small spheres is lowered relative to that of bulk material, according to
m
(2.1)
where C is a constant, and with the exponent n = 1 for metals as shown by experimental studies. In fact, melting is a rather complex phenomenon
and if an approach such as that of Lindemann's criterion is adopted, due account of the difference between the surface and the bulk atoms might
be important in determining the temperature of some practical process, such as sintering. Furthermore, it should be noted that if a nanoscale thin
film is investigated, rather than particles (i.e., a nanoplate), there is no depression of the melting point relative to the bulk [89].

Figure 2.1 Cross-section of a spherical nanoparticle consisting of 19 atoms.
As Wulff has pointed out, for a crystal growing in equilibrium with its vapor or solution, the ratio of the surface tension γ of the growing phase to the
distance from the center r should be constant. If the mechanical effect of the surface tension can be reduced to an isotropic pressure, then we have
the Laplace law