. How nanoscale dimensions affect properties
Many properties are continuously modified as a function of system size. Often these are extrinsic properties, such as resistance, which depend on the exact size and shape of the specimen. Other properties depend critically on the microstructure of the material; for example, the Hall–Petch equation for yield strength, σ, of a material as a function of average grain size (d) is given by
where k and σ0 are constants. Intrinsic materials properties, such as resistivity, should be independent of specimen size, however, even many of the intrinsic properties of matter at the nanoscale are not necessarily predictable from those observed at larger scales.
As discussed above this is because totally new phenomena can emerge, such as:
- Quantum size confinement leading to changes in electronic structure
- The presence of wave-like transport processes
- The predominance of interfacial effects
1. Structural properties
The increase in surface area and surface free energy with decreasing particle size leads to changes in interatomic spacings. For Cu metallic clusters the interatomic spacing is observed to decrease with decreasing cluster size, as shown in Figure.
This effect can be explained by the compressive strain induced by the internal pressure arising from the small radius of curvature in the nanoparticle. Conversely, for semiconductors and metal oxides there is evidence that interatomic spacings increase with decreasing particle size. A further effect, is the apparent stability of metastable structures in small nanoparticles and clusters, such that all traces of the usual bulk atomic arrangement become lost. Metallic nanoparticles, such as gold, are known to adopt polyhedral shapes such as cube–octahedra, multiply twinned icosahedra and multiply twinned decahedra. These nanoparticles may be regarded as multiply twinned crystalline particles (MTPs) in which the shapes can be understood in terms of the surface energies of various crystallographic planes, the growth rates along various crystallographic directions and the energy required for the formation of defects such as twin boundaries. However, there is compelling evidence that such particles are not crystals but are quasiperiodic crystals or crystalloids. These icosahedral and decahedral quasicrystals form the basis for further growth of the nanocluster, up until a size where they will switch into more regular crystalline packing arrangements. Crystalline solids are distinct from amorphous solids in that they possess long-range periodic order and the patterns and symmetries which occur correspond to those of the 230 space groups. Quasiperiodic crystals do not possess such long-range periodic order and are distinct in that they exhibit fivefold symmetry, which is forbidden in the 230 space groups. In the cubic close-packed and hexagonal close-packed structures, exhibited by many metals, each atom is coordinated by 12 neighbouring atoms. All of the coordinating atoms are in contact, although not evenly distributed around the central atom. However, there is an alternative arrangement in which each coordinating atom is situated at the apex of an icosahedron and in contact only with the central atom. If however we relax this ‘rigid atomic sphere’ model and allow the central atom to reduce in diameter by 10%, the coordinating atoms come into contact and the body now has the shape and symmetry of a regular icosahedron with point group symmetry 235, indicating the presence of 30 twofold, 20 threefold and 12 fivefold axes of symmetry. This geometry represents the nucleus of a quasiperiodic crystal which may grow in the forms of icosahedra or pentagonal dodecahedra. These are dual solids with identical symmetry, the apices of one being replaced by the faces of the other. Such quasiperiodic crystals are known to exist in an increasing number of aluminium-based alloys and may be stable up to microcrystalline sizes. It should be noted that their symmetry is precisely the same as that of the fullerenes C20 (dodecahedrene with 12 pentagonal faces of a pentagonal dodecahedron, but unstable) and C60 (the well-known buckyball with 12 pentagonal faces and 20 hexagonal faces of a truncated icosahedron). Hence, like the fullerenes, quasiperiodic crystals are expected to have an important role to play in nanostructures.
2. Thermal properties
The large increase in surface energy and the change in interatomic spacing as a function of nanoparticle size mentioned above have a marked effect on material properties. For instance, the melting point of gold particles, which is really a bulk thermodynamic characteristic, has been observed to decrease rapidly for particle sizes less than 10 nm, as shown in Figure 1.14. There is evidence that for metallic nanocrystals embedded in a continuous matrix the opposite behaviour is true; i.e., smaller particles have higher melting points.3
3. Chemical properties
The ionization potential (the energy required to remove an electron) is generally higher for small atomic clusters than for the corresponding bulk material. Furthermore, the ionization potential exhibits marked fluctuations as a function of cluster size. Such effects appear to be linked to chemical reactivity. Nanoscale structures such as nanoparticles and nanolayers have very high surface area to volume ratios and potentially different crystallographic structures which may lead to a radical alteration in chemical reactivity. Catalysis using finely divided nanoscale systems can increase the rate, selectivity and efficiency of chemical reactions such as combustion or synthesis whilst simultaneously significantly reducing waste and pollution. Gold nanoparticles smaller than about 5nm in diameter are known to adopt icosahedral structures rather than the normal face centred cubic arrangement. This structural change is accompanied by an extraordinary increase in catalytic activity. Furthermore, nanoscale catalytic supports with controlled pore sizes can select the products and reactants of chemical reactions based on their physical size and thus ease of transport to and from internal reaction sites within the nanoporous structure. Additionally, nanoparticles often exhibit new chemistries as distinct from their larger particulate counterparts; for example, many new medicines are insoluble in water when in the form of micron-sized particles but will dissolve easily when in a nanostructured form.
4. Mechanical properties
Many mechanical properties, such as toughness, are highly dependent on the ease of formation or the presence of defects within a material. As the system size decreases, the ability to support such defects becomes increasingly more difficult and mechanical properties will be altered accordingly. Novel nanostructures, which are very different from bulk structures in terms of the atomic structural arrangement, will obviously show very different mechanical properties. For example, single- and multi-walled carbon nanotubes show high mechanical strengths and high elastic limits that lead to considerable mechanical flexibility and reversible deformation. As the structural scale reduces to the nanometre range, for example, in nanoayered composites, a different scale dependence from the usual Hall–Petch relationship for yield strength often becomes apparent with large increases in strength reported. In addition, the high interface to volume ratio of consolidated nanostructured materials appears to enhance interface-driven processes such as plasticity, ductility and strain to failure. Many nanostructured metals and ceramics are observed to be superplastic, in that they are able to undergo extensive deformation without necking or fracture. This is presumed to arise from grain boundary diffusion and sliding, which becomes increasingly significant in a fine-grained material. Overall these effects extend the current strength–ductility limit of conventional materials, where usually a gain in strength is offset by a corresponding loss in ductility.
5. Megnetic properties
Magnetic nanoparticles are used in a range of applications, including ferrofluids, colour imaging, bioprocessing, refrigeration as well as high storage density magnetic memory media. The large surface area to volume ratio results in a substantial proportion of atoms (those at the surface which have a different local environment) having a different magnetic coupling with neighbouring atoms, leading to differing magnetic properties. Figure 1.16 shows the magnetic moments of nickel nanoparticles as a function of cluster size. Whilst bulk ferromagnetic materials usually form multiple magnetic domains, small magnetic nanoparticles often consist of only one domain and exhibit a phenomenon known as superparamagnetism. In this case the overall magnetic coercivity is then lowered: the magnetizations of the various particles are randomly distributed due to thermal fluctuations and only become aligned in the presence of an applied magnetic field. Giant magnetoresistance (GMR) is a phenomenon observed in nanoscale multilayers consisting of a strong ferromagnet (e.g., Fe, Co) and a weaker magnetic or non-magnetic buffer (e.g., Cr, Cu); it is usually employed in data storage and sensing. In the absence of a magnetic field the spins in alternating layers are oppositely aligned through antiferromagnetic coupling, which gives maximum scattering from the interlayer interface and hence a high resistance parallel to the layers. In an oriented external magnetic field the spins align with each other and this decreases scattering at the interface and hence resistance of the device.
6. Optical properties
In small nanoclusters the effect of reduced dimensionality on electronic structure has the most profound effect on the energies of the highest occupied molecular orbital (HOMO), essentially the valence band, and the lowest unoccupied molecular orbital (LUMO), essentially the conduction band. Optical emission and absorption depend on transitions between these states; semiconductors and metals, in particular, show large changes in optical properties, such as colour, as a function of particle size. Colloidal solutions of gold nanoparticles have a deep red colour which becomes progressively more yellow as the particle size increases; indeed gold colloids have been used as a pigment for stained glass since the seventeenth century. Figure 1.17 shows optical absorption spectra for colloidal gold nanoparticles of varying sizes. Semiconductor nanocrystals in the form of quantum dots show similar size-dependent behaviour in the frequency and intensity of light emission as well as modified non-linear optical properties and enhanced gain for certain emission energies or wavelengths. Other properties which may be affected by reduced dimensionality include photocatalysis, photoconductivity, photoemission and electroluminescence.
7. Electronic properties
The changes which occur in electronic properties as the system length scale is reduced are related mainly to the increasing influence of the wave-like property of the electrons (quantum mechanical effects) and the scarcity of scattering centres. As the size of the system becomes comparable with the de Broglie wavelength of the electrons, the discrete nature of the energy states becomes apparent once again, although a fully discrete energy spectrum is only observed in systems that are confined in all three dimensions. In certain cases, conducting materials become insulators below a critical length scale, as the energy bands cease to overlap. Owing to their intrinsic wave-like nature, electrons can tunnel quantum mechanically between two closely adjacent nanostructures, and if a voltage is applied between two nanostructures which aligns the discrete energy levels in the DOS, resonant tunnelling occurs, which abruptly increases the tunnelling current. In macroscopic systems, electronic transport is determined primarily by scattering with phonons, impurities or other carriers or by scattering at rough interfaces. The path of each electron resembles a random walk, and transport is said to be diffusive. When the system dimensions are smaller than the electron mean free path for inelastic scattering, electrons can travel through the system without randomization of the phase of their wavefunctions. This gives rise to additional localization phenomena which are specifically related to phase interference. If the system is sufficiently small so that all scattering centres can be eliminated completely, and if the sample boundaries are smooth so that boundary reflections are purely specular, then electron transport becomes purely ballistic, with the sample acting as a waveguide for the electron wavefunction. Conduction in highly confined structures, such as quantum dots, is very sensitive to the presence of other charge carriers and hence the charge state of the dot. These Coulomb blockade effects result in conduction processes involving single electrons and as a result they require only a small amount of energy to operate a switch, transistor or memory element. All these phenomena can be utilised to produce radically different types of components for electronic, optoelectronic and information processing applications, such as resonant tunnelling transistors and single-electron transistors.
8. Biological systems
Biological systems contain many examples of nanophase materials and nanoscale systems. Biomineralization of nanocrystallites in a protein matrix is highly important for the formation of bone and teeth, and is also used for chemical storage and transport mechanisms within organs. Biomineralization involves the operation of delicate biological control mechanisms to produce materials with well-defined characteristics such as particle size, crystallographic structure, morphology and architecture. Generally complex biological molecules such as DNA have the ability to undergo highly controlled and hierarchical self-assembly, which makes them ideal for the assembling of nanosized building blocks. Methods for altering and controlling these interactions and building nanoscale building blocks and assembling nanoscale architectures are also discussed. Biological cells have dimensions within the range 1–10mm and contain many examples of extremely complex nano-assemblies, including molecular motors, which are complexes embedded within membranes that are powered by natural biochemical processes. Generally, naturally occurring biological nanomaterials have been refined by evolutionary processes over a long timescale and are therefore highly optimized. We can often use biological systems as a guide to producing synthetic nanomaterials or nanosystems, a process known as biomimicry.
