Carbon peapods are the host-guest compounds (endohedral complexes) that consist of fullerenes encapsulated inside the single-walled carbon nanotubes.
Figure 1. The structures of peapods, based on C60 (top) and C20 (bottom) fullerenes.
We apply density functional theory at PBE/6-311G(d) level as well as nonorthogonal tight-binding model to study the Stone-Wales transformation in C36 fullerene embedded inside the (14,0) zigzag carbon nanotube. We optimize geometries of two different isomers with the D2d and the D6h symmetries and the transition state dividing them. The mechanism of Stone-Wales transformation from D2d to D6h symmetry for the encapsulated C36 is calculated to be the same as for the isolated one. It is found that the outer carbon wall significantly stabilizes the D6h isomer. However, carbon nanotube reduces the activation barrier of Stone-Wales rearrangement by 0.4eV compared with the corresponding value for the isolated C36.
Figure 2: Potential energies ΔE of endohedral complex C36@C224H28 (solid line) and isolated C36 fullerene (dashed line) during the SW transformation D2d-C36→D6h-C36. The insets show the C36 isomers with the D2d and the D6h symmetries and the transition state (TS). Rotation of C-C bond during the SW transformation is indicated in black. The atoms of carbon nanotube are not displayed for clarity.
We present a density functional study of the band structure and some elastic properties of semiconductor carbon nanotube endohedrally doped with the C36 fullerenes. We found that the electronic states belonging to C36s lied inside the band gap of the pristine tube (figure. 3). External strain applied along the tube axis results in decreasing of the semiconducting gap from 0.3 to 0 eV. Metallic behavior of the strained system is confirmed via the additional calculations of electronic transmission coefficients. Phonons influence is accounted with the molecular dynamics approach. Strain of about 0.04 corresponds to the linear part of stress-strain curve and is found to be sufficient to observe the semiconductor-to-metal transitions at room temperature (figure. 4). The encapsulated C36s do not affect the elastic properties of the host nanotube in the considered range of strains (figure. 5), in contrast to the embedded C60s.
Figure 3: Calculated band structures for the (14,0) carbon nanotube (a), D6h-C36 peapod (b), and D2d-C36 peapod (c).
Figure 4: Pristine semiconductor nanotube doped with the C36 fullerenes possesses metal or semiconductor behavior under uniaxial strain.
Figure 5: The stress-strain dependences for the (14,0) carbon nanotube (squares), D6h-C36 peapod (circles), and D2d-C36 peapod (triangles). Solid lines are the corresponding linear approximations obtained by the least-mean-square method.
The genetic algorithm is combined with the density functional theory to predict how the cylindrical spatial confinement affects the structural characteristics and optical adsorption spectra of the low energy Si18H12 and Si19H12 isomers. Retrieved ground states (minimum energy states) of Si18H12 and Si19H12 isomers significantly differ from the earlier proposed “ultrastable” aromatic molecular systems and prismanes. According to our calculations, they are represented by the almost spherical endohedral buckyballs. In contrast to pure silicic clusters (Si18 or Si19), the most of Si atoms in the low-energy Si18H12 and Si19H12 are four-coordinated. Spatial confinement results in more oblong structures with the different optical spectra. Prismanes under confinement get some energy advantages over the spherical structures, but despite this they do not become the most energetically favorable ones. Thus, the current results warrant however further research on the spatial confinement of silicic prismanes, as our study suggests challenges in devising the method of their synthesis without additional chemical techniques.
Figure 6: The atomic structures of the nine low-energy Si18H12 isomers. The internal energies (in eV) of the isomers are also presented. The energy of the Si18H12 prismane is assumed to be equal to zero.
Figure 7: The atomic structures of the nine low-energy Si19H12 isomers. The internal energies (in eV) of the isomers are also presented. The energy of the Si@Si18H12 endohedral prismane is assumed to be equal to zero.
Figure 8: The atomic structures of the nine low-energy Si18H12 isomers under the cylindrical constraint. The internal energies (in eV) of the isomers are also presented. The energy of the Si18H12 prismane is assumed to be equal to zero.
Figure 9: The atomic structures of the nine low-energy Si19H12 isomers under the cylindrical constraint. The internal energies (in eV) of the isomers are also presented. The energy of the Si@Si18H12 endohedral prismane is assumed to be equal to zero.
Within the framework of the coherent quantum-mechanical model, which is based on the solution of the time-dependent Schrödinger equation with exact open boundary conditions, we have numerically analyzed the behavior of the resonant-tunneling diode (RTD) in an alternating-current electric field in the presence of spacer layers. It is shown that the interaction of the energy levels in a quantum well of the RTD, and the same in a quantum well of the emitter spacer, leads to splitting of these levels, which sharply increases the active current of RTD. In this case, the value of the active current at the finite frequencies may exceed the active current within the low-frequency limits. For RTD, heterostructure considered active current at frequency 1.77 THz takes its maximum value at the thickness of the emitter spacer equals to 6.5 nm exceeding the corresponding value in the absence of the spacer by the factor of 32. The results obtained in this paper may be useful to improve the frequency characteristics of resonant-tunneling nanostructures.
Figure 10: LEFT: Dependence of the peak active current on the frequency of the ac electric field in case of the absence of the emitter spacer. RIGHT: Dependence of the maximum negative current Jcm on the frequency of the ac electric field in the presence of the emitter spacer.
For detailed information see the following publications:
1. K.S. Grishakov, K.P. Katin, M.M. Maslov. Strain-induced semiconductor-to-metal transitions in C36-based carbon peapods: Ab initio study // Diamond and Related Materials, Vol. 84, pp. 112–118, 2018. https://doi.org/10.1016/j.diamond.2018.03.023
2. M.V. Gordeychuk, K.P. Katin, K.S. Grishakov, M.M. Maslov. Silicon buckyballs versus prismanes: Influence of spatial confinement on the structural properties and optical spectra of the Si18H12 and Si19H12 clusters // International Journal of Quantum Chemistry, 2018. https://doi.org/10.1002/qua.25609
3. K.S. Grishakov, K.P. Katin, M.M. Maslov. Theoretical Studies of the Stone-Wales Defect in C36 Fullerene Embedded inside Zigzag Carbon Nanotube // Advances in Physical Chemistry, Vol. 2016, Article ID 1862959, 4 pages. http://dx.doi.org/10.1155/2016/1862959
4. K.S. Grishakov, V.F. Elesin. Emitter Spacer Layers Influence on the Dynamic Characteristics of Resonant-Tunneling Diode // IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 64, NO. 7, JULY 2017. https://doi.org/10.1109/TED.2017.2699693
5. K.S. Grishakov, V.F. Elesin, M.M. Maslov, K.P. Katin. Theoretical Study of High-Frequency Response of InGaAs/AlAs Double-Barrier Nanostructures // Advances in Materials Science and Engineering, Vol. 2017, Article ID 2031631, 7 pages. https://doi.org/10.1155/2017/2031631
The reported study was funded by RFBR according to the research Project no. 16-32-00588 mol_a.