1206 28 The Structure of Solids, Liquids, and Polymers
The diameter of a C 60 buckyball is approximately 1 nanometer (1× 10 −^9 mor
10 Å), so it is called ananomaterial. Its interior cavity is able to contain a single atom
such as an argon atom. A variant of the C 60 buckyball is also the right size to fit into
the active site of the protease enzyme of the AIDS virus and thereby inhibit its action.
There are now numerous applications of nanomaterials, including automobile paints
with nanometer-size particles suspended in them. Nanocontainers and nanocorrals have
been created that have interior cavities capable of containing various sizes of atoms
or molecules.^50 Nanomotors and nanocars have been invented,^51 as well as a light-
triggered nanovalve.^52 Nanoparticles are used for polishing silicon surfaces, and a
means to produce spherical nanoparticles for this purpose has been developed.^53 Plati-
num nanoparticles with 24 facets have been created that have 200% to 400% greater
catalytic activity than spherical platinum nanoparticles.^54 Many other applications of
nanomaterials are being developed, and the field promises to become economically and
industrially important, as well as academically interesting. The field of nanomaterials
is so active that almost every issue ofChemical and Engineering Newscontains an
article about new advances in the field.Summary of the Chapter
In this chapter, we have discussed the structure of solids and liquids. Many solids
are crystalline, with molecular units arranged in a regular three-dimensional lattice.
There are two principal theories for the vibrations of lattices of atoms, the Einstein
and the Debye theories. In the Einstein theory the normal vibrational modes of the
lattice are assumed to vibrate with the same frequency. In the Debye model, the
normal modes of the lattice are assumed to vibrate with the same distribution of
frequencies as would a structureless solid. In each theory, the formula for the heat
capacity of the solid lattice conforms to the law of Dulong and Petit at high enough
temperature.
The band theory of the electronic structure of solids was discussed. In this the-
ory the electrons are assumed to occupy delocalized orbitals that comprise bands
of energy levels. The differences between conductors, semiconductors, and insulators
were discussed.
The structure of liquids is more difficult to discuss than is the structure of solids,
because the liquids are more disordered than solids, but not completely disordered
as are gases. Some elementary comments on the structure of liquids were presented,
including the definition of the radial distribution function, which gives the probability
of finding a second molecule at a given distance from another molecule.
The conformation of a simple polymer model, a freely jointed chain, was also
presented. The conformation of polymers in solution was introduced. A model system
to represent rubber elasticity was discussed, and a brief introduction to nanomaterials
was presented.(^50) X. Liuet al.,Angew. Chem. Int. Ed., 45 , 901 (2006).
(^51) B. L. Feringa,Nature, 437 , 1337 (2005),Proc. Natl. Acad. Sci., USA, 103 , 1178 (2006); R. Eelkema
et al.,Nature, 440 , 143 (2006).
(^52) A. Coseret al.,Science, 309 , 755 (2005).
(^53) X. Feng and Z. L. Wang,Science, 312 , 1504 (2006).
(^54) N. Tianet al.,Science, 316 , 732 (2007).