properties. Therefore, surface science plays a central role in understanding nanomaterials.
1.4 DIMENSIONALITY AND ITS IMPLICATIONS
Nanosystems are principally defined by their size (spatial dimensionality). As established in the prior section, if a system has at least one
dimension in which the size is under 1000 nm, it is nanoscale. However,
nanosystems can be further divided by the number of dimensions that are
within the nanoscale (their spatial dimensionality). Silver nanoparticles
and buckyballs are both within the nanoscale along all dimensions. Since
none of their dimensions exceed 1000 nm, they are examples of zerodimensional (0D) nanomaterials. Correspondingly, a carbon nanotube (a
long tube composed of sp
2 hybridized carbon) is within the nanoscale
along two dimensions (the girth of the tube) but may exceed it along the
length of the tube; they are one-dimensional (1D) nanomaterials. A sheet
of graphene—an atomically thin layer of graphite composed entirely
of sp
2 hybridized carbon atoms—is within the nanoscale along a single
axis, but may stretch for distances large enough to be visible to the naked
eye along its other axes. This an example of a two-dimensional (2D)
nanomaterial.
By this definition, a three-dimensional (3D) material may seem impossible. How could a material have all of its dimensions exceeding the
nanoscale but still be considered within the realm of nanomaterials? This
contradiction can be resolved through the same mechanism by which
single molecules can be considered parts of nanomaterials. A 3D nanomaterial is a bulk material composed of other nanostructures arranged in
a regular pattern, where the distance between the components is within
the nanoscale. For example, a collection of nanoparticles linked together
by nanotubes or strands of DNA into a solid could be considered a 3D
nanomaterial. Examples of nanomaterials of different dimensionalities
are shown in Figure 1.4.
The concept of spatial dimensionality is related to the broader concept of
degrees of freedom, or ways in which a particle can move. The spatial
dimensionality of a system has a strong influence on its electronic
properties, as discussed in Chapter 4. However, in addition to spatial
dimensionality, nanomaterials can also be characterized by their internal
degrees of freedom. Translational degrees of freedom involve movement
through space; for example, an atom within a nanotube is only able to
CHAPTER 1: A Brief Introduction to Nanoscience
8
1.4 DIMENSIONALITY AND ITS IMPLICATIONS
Nanosystems are principally defined by their size (spatial dimensionality). As established in the prior section, if a system has at least one
dimension in which the size is under 1000 nm, it is nanoscale. However,
nanosystems can be further divided by the number of dimensions that are
within the nanoscale (their spatial dimensionality). Silver nanoparticles
and buckyballs are both within the nanoscale along all dimensions. Since
none of their dimensions exceed 1000 nm, they are examples of zerodimensional (0D) nanomaterials. Correspondingly, a carbon nanotube (a
long tube composed of sp
2 hybridized carbon) is within the nanoscale
along two dimensions (the girth of the tube) but may exceed it along the
length of the tube; they are one-dimensional (1D) nanomaterials. A sheet
of graphene—an atomically thin layer of graphite composed entirely
of sp
2 hybridized carbon atoms—is within the nanoscale along a single
axis, but may stretch for distances large enough to be visible to the naked
eye along its other axes. This an example of a two-dimensional (2D)
nanomaterial.
By this definition, a three-dimensional (3D) material may seem impossible. How could a material have all of its dimensions exceeding the
nanoscale but still be considered within the realm of nanomaterials? This
contradiction can be resolved through the same mechanism by which
single molecules can be considered parts of nanomaterials. A 3D nanomaterial is a bulk material composed of other nanostructures arranged in
a regular pattern, where the distance between the components is within
the nanoscale. For example, a collection of nanoparticles linked together
by nanotubes or strands of DNA into a solid could be considered a 3D
nanomaterial. Examples of nanomaterials of different dimensionalities
are shown in Figure 1.4.
The concept of spatial dimensionality is related to the broader concept of
degrees of freedom, or ways in which a particle can move. The spatial
dimensionality of a system has a strong influence on its electronic
properties, as discussed in Chapter 4. However, in addition to spatial
dimensionality, nanomaterials can also be characterized by their internal
degrees of freedom. Translational degrees of freedom involve movement
through space; for example, an atom within a nanotube is only able to
CHAPTER 1: A Brief Introduction to Nanoscience
8