79
One- and Two-Dimensional Nanoparticles
5
5.1
Basic Considerations
One and two-dimensional nanoparticles, generally called nanotubes and nanorods
for the one-dimensional ones and nanoplates, the two-dimensional ones, are often
observed. These entities are interesting both from the standpoint of science and
for economic reasons, as these particles have a broad range of applications in many
fields of technology. Within this group there is a very special type of particle, the
fullerenes; fullerenes based on carbon or other inorganic compounds. As per definition, fullerenes are zero-dimensional particles, as they are simply spherical
entities; however, their geometry and the formation is understood only in connection to the related nanotubes or nanoplates.
One expects the shape of nanoparticles to represent a minimum of surface
energy. Therefore, in most cases, nanoparticles are spherical in shape, at least
facetted particles, which are close to a sphere. To understand the reason for nonspherical nanoparticles, one has to look at the crystalline structure and to the
method for synthesizing.
The surface energy depends on the crystallographic plane. For example, in
cubic structure, the planes describing a cube have the lowest surface energy.
The discussion is most important in noncubic systems. Depending on the surface energy of the different planes, noncubic substances may have a tendency to
crystallize in rods or plates. If the surface energy is modified by surface-active
substances, also in the case of cubic structures, rods or plates are obtainable.
Therefore, it is possible to produce rods of gold, even when gold crystallizes in a
cubic structure.
The dependency of the surface energy on the crystallographic plane has
consequences on the shape of nanoparticles: Assuming a prism with a quadratic
base with an edge length a, and a height c one obtains a rod-like prism in the
case that the surface energy of the base plane is large compared to that of
the side plane. In the other case, one obtains a plate-like prism. The ratio of the
sides of a tetragonal prism is equal to the ratio of the surface energies. This is
the rule for the formation of nanorods or nanoplates that can be derived from
thermodynamics.
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
One- and Two-Dimensional Nanoparticles
5
5.1
Basic Considerations
One and two-dimensional nanoparticles, generally called nanotubes and nanorods
for the one-dimensional ones and nanoplates, the two-dimensional ones, are often
observed. These entities are interesting both from the standpoint of science and
for economic reasons, as these particles have a broad range of applications in many
fields of technology. Within this group there is a very special type of particle, the
fullerenes; fullerenes based on carbon or other inorganic compounds. As per definition, fullerenes are zero-dimensional particles, as they are simply spherical
entities; however, their geometry and the formation is understood only in connection to the related nanotubes or nanoplates.
One expects the shape of nanoparticles to represent a minimum of surface
energy. Therefore, in most cases, nanoparticles are spherical in shape, at least
facetted particles, which are close to a sphere. To understand the reason for nonspherical nanoparticles, one has to look at the crystalline structure and to the
method for synthesizing.
The surface energy depends on the crystallographic plane. For example, in
cubic structure, the planes describing a cube have the lowest surface energy.
The discussion is most important in noncubic systems. Depending on the surface energy of the different planes, noncubic substances may have a tendency to
crystallize in rods or plates. If the surface energy is modified by surface-active
substances, also in the case of cubic structures, rods or plates are obtainable.
Therefore, it is possible to produce rods of gold, even when gold crystallizes in a
cubic structure.
The dependency of the surface energy on the crystallographic plane has
consequences on the shape of nanoparticles: Assuming a prism with a quadratic
base with an edge length a, and a height c one obtains a rod-like prism in the
case that the surface energy of the base plane is large compared to that of
the side plane. In the other case, one obtains a plate-like prism. The ratio of the
sides of a tetragonal prism is equal to the ratio of the surface energies. This is
the rule for the formation of nanorods or nanoplates that can be derived from
thermodynamics.
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.