At the end of the twentieth century, the existence of a certain size region of matter particles – the nanoscale region – finally became apparent. Physicists, specifying the definition of nanoobjects, argue that the upper limit of the nanoscale coincides, apparently, with the size of the manifestation of the so-called low-dimensional effects or dimensionality reduction effect.
Let’s try to translate the last statement from the language of physicists into human language.
We live in a three-dimensional world. All real objects surrounding us have some dimensions in all three dimensions, or, as physicists say, have dimension 3.
Let us conduct the following mental experiment. Choose a three-dimensional, volumetric, sample of some material, preferably a homogeneous crystal. Let it be a cube with edge length of 1 cm. This sample has certain physical properties that do not depend on its size. Near the outer surface of our sample, the properties may differ from those in the volume. However, the relative fraction of surface atoms is small, so the contribution of surface variation of properties can be neglected (this is the requirement that means, in physics language, that the sample is volumetric). Now let’s divide the cube in half – two of its characteristic dimensions will remain the same, and one, let it be the height d, will decrease by 2 times. What will happen to the properties of the sample? They will not change. Let’s repeat the experiment again and measure the property of interest. We will get the same result. Repeating the experiment many times, we finally reach a certain critical size d, below which the property we measure starts to depend on the size d. Why? At d ≤ d the fraction of contribution of surface atoms to the properties becomes significant and will continue to grow with further decrease of d.
Physicists say that at d ≤ d* in our sample there is a quantum-dimensional effect in one dimension. For them, our sample is no longer three-dimensional (which sounds absurd to any ordinary person, because our d, though small, is not equal to zero!), its dimensionality is reduced to two. And the pattern itself is called a quantum plane, or quantum well, by analogy with the term “potential well” often used in physics.
If in some sample d ≤ d* in two dimensions, it is called a one-dimensional quantum object, or a quantum thread, or a quantum wire. Zero-dimensional objects, or quantum dots, have d ≤ d* in all three dimensions.
Naturally, the critical dimension d* is not a constant for different materials and even for one material may vary significantly depending on which of the properties we measured in our experiment, or, in other words, which of the critical dimensional characteristics of physical phenomena determines a given property (free path of phonon electrons, de Broglie wavelength, diffusion length, penetration depth of an external electromagnetic field or acoustic waves, etc.).
However, it turns out that with all the variety of phenomena occurring in organic and inorganic materials in animate and inanimate nature, the value of d* lies approximately in the range of 1-100 nm. Thus, a “nano-object” (“nanostructure”, “nanoparticle”) is simply another variant of the term “quantum-dimensional structure”. It is an object with d ≤ d* in at least one dimension. They are particles of reduced dimensionality, particles with increased fraction of surface atoms. So, it is most logical to classify them by decreasing of dimensionality: 2D – quantum planes, 1D – quantum threads, 0D – quantum dots.
The whole range of reduced dimensions can be easily explained and, most importantly, observed experimentally on the example of carbon nanoparticles.
The discovery of carbon nanostructures was a very important milestone in the development of the nanoparticle concept.
Carbon is only the eleventh most common element in nature, but the unique ability of its atoms to combine with each other and form long molecules that include other elements as substituents has given rise to a huge number of organic compounds and Life itself. But even when combined only with itself, carbon is capable of generating a large set of different structures with very diverse properties – the so-called allotropic modifications.8 Diamond, for example, is a benchmark of transparency and hardness, a dielectric and insulator. However, graphite is an ideal “absorber” of light, a super-soft material (in a certain direction) and one of the best conductors of heat and electricity (in the plane perpendicular to the above mentioned direction). And yet both of these materials are composed only of carbon atoms!
But all this is at the macro level. But moving to the nanoscale opens up new unique properties of carbon. It turned out that the “love” of carbon atoms for each other is so great that they can form a whole set of nanostructures that differ from each other, including the dimensionality. These include fullerenes, graphene, nanotubes, nanocones, etc.
But let’s return to graphite itself. So, graphite is the most widespread and thermodynamically stable modification of elementary carbon with three-dimensional crystal structure, consisting of parallel atomic layers, each of which is a dense packing of hexagons. At the tops of any such hexagon is a carbon atom, and the sides of the hexagons graphically reflect the strong covalent bonds9 between the carbon atoms, which have a length of 0.142 nm. But the distance between the layers is quite large (0.334 nm), and therefore the bond between the layers is quite weak (in this case we speak of van der Waals interaction).
This crystal structure explains the peculiarities of the physical properties of graphite. First of all, it has low hardness and the ability to peel easily into tiny flakes. For example, pencil lead pencils with graphite flakes that peel off and remain on paper are written in this way. Secondly, the already mentioned pronounced anisotropy of the physical properties of graphite and, first of all, its electrical conductivity and thermal conductivity.
Any of the layers of the three-dimensional graphite structure can be considered as a giant planar structure having 2D dimensionality. Such a two-dimensional structure built only from carbon atoms is called “graphene”. It is “relatively” easy to get such a structure, at least in a mental experiment. Let’s take a graphite pencil lead and start writing. The height of the lead d will decrease. If we have enough patience, at some point the value of d will equal d*, and we will get a quantum plane (2D).
For a long time the problem of the stability of planar two-dimensional structures in the free state (without a substrate) in general and graphene in particular, as well as the electronic properties of graphene were the subject of only theoretical studies. More recently, in 2004, a group of physicists led by A. Geim and K. Novoselov obtained the first samples of graphene, which revolutionized this field, because such two-dimensional structures were, in particular, capable of exhibiting striking electronic properties, qualitatively different from all previously observed. That is why today hundreds of experimental groups are studying the electronic properties of graphene.
If we roll the graphene layer, monoatomic in thickness, into a cylinder so that the hexagonal mesh of carbon atoms closed without seams, we “construct” a single-walled carbon nanotube. Experimentally it is possible to obtain single-walled nanotubes with diameters from 0.43 to 5 nm. The characteristic features of the nanotube geometry are the record values of the specific surface area (on average ~1600 m2/g for single-wall tubes) and the length-to-diameter ratio (100,000 and above). Thus, nanotubes are 1D nanobjects – quantum filaments.
Multi-walled carbon nanotubes were also observed in the experiments. They consist of coaxial cylinders inserted one into another, with the walls at a distance (about 3.5 Å) close to the interplanar distance in graphite (0.334 nm). The number of walls can vary from 2 to 50.
If we place a piece of graphite in the atmosphere of an inert gas (helium or argon) and then illuminate it with a beam of a powerful pulsed laser or concentrated sunlight, the material of our graphite target can be vaporized (note that for this purpose the surface temperature of the target must be at least 2700°C). Under such conditions, a plasma is formed over the surface of the target, consisting of individual carbon atoms, which are entrained by a stream of cold gas, which leads to cooling of the plasma and formation of carbon clusters. So, it turns out that under certain conditions of clustering, the carbon atoms are locked together to form a framework spherical molecule C60 of dimension 0D (i.e., a quantum dot).
Such spontaneous formation of the C60 molecule in the carbon plasma was found in a joint experiment by G. Kroto, R. Curl and R. Smoley, carried out over ten days in September 1985. Let us refer the inquisitive reader to the book by E.A. We refer the inquisitive reader to the book “Fullerenes, Carbon Nanotubes and Nanoclusters: A Pedigree of Forms and Ideas” by E. A. Katz which describes in detail the fascinating history of this discovery and the events preceding it (with brief excursions into the history of science up to the Renaissance and even Antiquity) and also explains the motivation behind the strange at first sight (and only at first sight) name of the new molecule – buckminsterfullerene – after the architect R. Buckminster Fuller.
Subsequently, it was discovered that there is a whole family of carbon molecules – fullerenes – in the form of convex polyhedrons consisting only of hexagonal and pentagonal faces.
Examples of giant fullerenes with icosahedral symmetry: C140, C260, C960.
It was the discovery of fullerenes that was a kind of magic “golden key” to the new world of nanometer structures of pure carbon, causing an explosion of work in this field. To date, a large number of different carbon clusters with a fantastic (literally!) variety of structure and properties have been discovered.
But back to nanomaterials.
Nanomaterials are materials whose structural units are nanoobjects (nanoparticles). Figuratively speaking, the building of a nanomaterial is composed of bricks of nano-objects. Therefore, it is most productive to classify nanomaterials by the dimensionality of both the nanomaterial sample itself (external dimensions of the matrix) and the dimensionality of its constituent nanoobjects. The presented 36 classes of nanostructures describe the entire variety of nanomaterials, some of which (like the fullerenes or carbon nanorods mentioned above) have already been successfully synthesized, and some are still waiting for their experimental realization.
