The optical properties of carbon nanotubes are highly relevant for materials science. The way carbon nanotubes interact with electromagnetic radiation is unique in many respects, as evidenced by their peculiar absorption, photoluminescence (fluorescence), and Raman spectra.
Carbon nanotubes are unique "one-dimensional" materials, whose hollow fibers (tubes) have a unique and highly ordered atomic and electronic structure, and can be made in a wide range of dimension. The diameter typically varies from 0.4 to 40 nm (i.e., a range of ~100 times). However, the length can reach , implying a length-to-diameter ratio as high as 132,000,000:1; which is unequaled by any other material. Consequently, all the electronic, optical, electrochemical and mechanical properties of the carbon nanotubes are extremely anisotropic (directionally dependent) and tunable.
Applications of carbon nanotubes in optics and photonics are still less developed than in other fields. Some properties that may lead to practical use include tuneability and wavelength selectivity. Potential applications that have been demonstrated include light emitting diodes (LEDs), bolometers and optoelectronic memory.
Apart from direct applications, the optical properties of carbon nanotubes can be very useful in their manufacture and application to other fields. Spectroscopic methods offer the possibility of quick and non-destructive characterization of relatively large amounts of carbon nanotubes, yielding detailed measurements of non-tubular carbon content, tube type and chirality, structural defects, and many other properties that are relevant to those other applications.
Geometric structure
Chiral angle A single-walled carbon nanotube (SWNT or SWCNT) can be envisioned as strip of a graphene molecule (a single sheet of graphite) rolled and joined into a cylinder. The structure of the nanotube can be characterized by the width of the diameter d of the tube and the angle (θ) of the strip relative to the main symmetry axes of the hexagonal graphene lattice. This angle, which varies from 0 to 30 degrees, is called the "chiral angle" of the tube and varies dependent on the conditions of nanotube growth.
(n, m) notation
The nanotube structure can be described by two integer indices (n,m) that describe the width and direction of that hypothetical strip as coordinates in a fundamental reference frame of the graphene lattice. If the atoms around any 6-member ring of the graphene are numbered sequentially from 1 to 6, the two vectors u and v of that frame are the displacements from atom 1 to atoms 3 and 5, respectively. Those two vectors have the same length, and their directions are 60 degrees apart. The vector is then interpreted as the circumference of the unrolled tube on the graphene lattice; it relates each point A1 on one edge of the strip to the point A2 on the other edge that will be identified with it as the strip is rolled up. The chiral angle α is then the angle between u and w.
The pairs that describe distinct tube structures are those with and . All geometric properties of the tube, such as diameter, chiral angle, and symmetries, can be computed from these indices.
The type also determines the electronic structure of the tube. Specifically, the tube behaves like a metal if is a multiple of 3, and like a semiconductor otherwise. Thus, across the available indices, one third of SWNTs are metallic, and two thirds are semiconducting. Truly metallic carbon nanotubes with minimal to nonexistent band gap have been defined only as those where .
Zigzag and armchair tubes Tubes of type with (chiral angle = 30°) are called "armchair" and those with (chiral angle = 0°) "zigzag". All other chiral angles produce what are known as chiral nanotubes.
Electronic structure The optical properties of carbon nanotubes are largely determined by their unique electronic structure. The rolling up of the graphene lattice affects that structure in ways that depend strongly on the geometric structure type .
Van Hove singularities
A characteristic feature of one-dimensional crystals is that their distribution of density of states (DOS) is not a continuous function of energy, but it descends gradually and then increases in a discontinuous spike. These sharp peaks are called Van Hove singularities. In contrast, three-dimensional (bulk) materials have continuous DOS.
Van Hove singularities result in the following optical properties of carbon nanotubes: Optical transitions occur between the v1 − c1, v2 − c2, etc., states of semiconducting or metallic nanotubes and are traditionally labeled as S11, S22, M11, etc., or, if the "conductivity" of the tube is unknown or unimportant, as E11, E22, etc. Crossover transitions , , etc., are dipole-forbidden and thus are extremely weak, but they were possibly observed using cross-polarized optical geometry. The energies between the Van Hove singularities depend on the nanotube structure. Thus by varying this structure, one can tune the optoelectronic properties of carbon nanotube. Such fine tuning has been experimentally demonstrated using UV illumination of polymer-dispersed CNTs.
Optical transitions are rather sharp (~10 meV) and strong. Consequently, it is relatively easy to selectively excite nanotubes having certain indices, as well as to detect optical signals from individual nanotubes.
Kataura plot
The band structure of carbon nanotubes having certain indexes can be calculated. A theoretical graph based on these calculations was designed in 1999 by Hiromichi Kataura to rationalize experimental findings. A Kataura plot relates the nanotube diameter and its bandgap energies for all nanotubes in a diameter range. The oscillating shape of every branch of the Kataura plot reflects the intrinsic strong dependence of the SWNT properties on the (n, m) index rather than on its diameter.
Optical properties Optical absorption
Optical absorption in carbon nanotubes differs from absorption in conventional 3D materials by presence of sharp peaks (1D nanotubes) instead of an absorption threshold followed by an absorption increase (most 3D solids). Absorption in nanotubes originates from electronic transitions from the v2 to c2 (energy E22) or v1 to c1 (E11) levels, etc. The transitions are relatively sharp and can be used to identify nanotube types. Note that the sharpness deteriorates with increasing energy, and that many nanotubes have very similar E22 or E11 energies, and thus significant overlap occurs in absorption spectra. This overlap is avoided in photoluminescence mapping measurements (see below), which instead of a combination of overlapped transitions identifies individual pairs.
Interactions between nanotubes, such as bundling, broaden optical lines. While bundling strongly affects photoluminescence, it has much weaker effect on optical absorption and Raman scattering. Consequently, sample preparation for the latter two techniques is relatively simple.
Optical absorption is routinely used to quantify quality of the carbon nanotube powders.
The spectrum is analyzed in terms of intensities of nanotube-related peaks, background and pi-carbon peak; the latter two mostly originate from non-nanotube carbon in contaminated samples. However, it has been recently shown that by aggregating nearly single chirality semiconducting nanotubes into closely packed Van der Waals bundles the absorption background can be attributed to free carrier transition originating from intertube charge transfer.
Carbon nanotubes as a black body An ideal black body should have emissivity or absorbance of 1.0, which is difficult to attain in practice, especially in a wide spectral range. Vertically aligned "forests" of single-wall carbon nanotubes can have absorbances of 0.98–0.99 from the far-ultraviolet (200 nm) to far-infrared (200 μm) wavelengths.
These SWNT forests (buckypaper) were grown by the super-growth CVD method to about 10 μm height. Two factors could contribute to strong light absorption by these structures: (i) a distribution of CNT chiralities resulted in various bandgaps for individual CNTs. Thus a compound material was formed with broadband absorption. (ii) Light might be trapped in those forests due to multiple reflections.
+ Reflectance measurements UV-to-near IR Near-to-mid IR Mid-to-far IR Wavelength, μm 0.2–2 2–20 25–200 Incident angle, ° 8 5 10 Reflection Hemispherical-directional Hemispherical-directional Specular Reference White reflectance standard Gold mirror Aluminum mirror Average reflectance 0.0160 0.0097 0.0017 Standard deviation 0.0048 0.0041 0.0027
Luminescence
Photoluminescence (fluorescence) Semiconducting single-walled carbon nanotubes emit near-infrared light upon photoexcitation, described interchangeably as fluorescence or photoluminescence (PL). The excitation of PL usually occurs as follows: an electron in a nanotube absorbs excitation light via S22 transition, creating an electron-hole pair (exciton). Both electron and hole rapidly relax (via phonon-assisted processes) from c2 to c1 and from v2 to v1 states, respectively. Then they recombine through a transition resulting in light emission.
No excitonic luminescence can be produced in metallic tubes. Their electrons can be excited, thus resulting in optical absorption, but the holes are immediately filled by other electrons out of the many available in the metal. Therefore, no excitons are produced.
Salient properties
Photoluminescence from SWNT, as well as optical absorption and Raman scattering, is linearly polarized along the tube axis. This allows monitoring of the SWNTs orientation without direct microscopic observation. PL is quick: relaxation typically occurs within 100 picoseconds. PL efficiency was first found to be low (~0.01%), but later studies measured much higher quantum yields. By improving the structural quality and isolation of nanotubes, emission efficiency increased. A quantum yield of 1% was reported in nanotubes sorted by diameter and length through gradient centrifugation, and it was further increased to 20% by optimizing the procedure of isolating individual nanotubes in solution. The spectral range of PL is rather wide. Emission wavelength can vary between 0.8 and 2.1 micrometers depending on the nanotube structure. Excitons are apparently delocalized over several nanotubes in single chirality bundles as the photoluminescence spectrum displays a splitting consistent with intertube exciton tunneling. Interaction between nanotubes or between a nanotube and another material may quench or increase PL. No PL is observed in multi-walled carbon nanotubes. PL from double-wall carbon nanotubes strongly depends on the preparation method: CVD grown DWCNTs show emission both from inner and outer shells. However, DWCNTs produced by encapsulating fullerenes into SWNTs and annealing show PL only from the outer shells. Isolated SWNTs lying on the substrate show extremely weak PL which has been detected in few studies only. Detachment of the tubes from the substrate drastically increases PL.
Position of the PL peaks depends slightly (within 2%) on the nanotube environment (air, dispersant, etc.). However, the shift depends on the index, and thus the whole PL map not only shifts, but also warps upon changing the CNT medium.
Raman scattering
Raman spectroscopy has good spatial resolution (~0.5 micrometers) and sensitivity (single nanotubes); it requires only minimal sample preparation and is rather informative. Consequently, Raman spectroscopy is probably the most popular technique of carbon nanotube characterization. Raman scattering in SWNTs is resonant, i.e., only those tubes are probed which have one of the bandgaps equal to the exciting laser energy. Several scattering modes dominate the SWNT spectrum, as discussed below.