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Effect of Peierls transition in armchair carbon nanotube on dynamical behaviour of encapsulated fullerene.

Poklonski NA, Vyrko SA, Kislyakov EF, Hieu NN, Bubel' ON, Popov AM, Lozovik YE, Knizhnik AA, Lebedeva IV, Viet NA - Nanoscale Res Lett (2011)

Bottom Line: The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory.It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude.The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physics Department, Belarusian State University, pr, Nezavisimosti 4, Minsk 220030, Belarus. poklonski@bsu.by.

ABSTRACT
The changes of dynamical behaviour of a single fullerene molecule inside an armchair carbon nanotube caused by the structural Peierls transition in the nanotube are considered. The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory. Significant changes of the barriers for motion along the nanotube axis and rotation of these fullerenes inside the (8,8) nanotube are found at the Peierls transition. It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude. The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.

No MeSH data available.


Related in: MedlinePlus

Interaction energy between the Fe@C20 endofullerene and (8,8) nanotube. Dependences of the interaction energy EWi between the Fe@C20 endofullerene and individual atoms of the (8,8) nanotube on the angle φ of rotation of the endofullerene about the nanotube axis are denoted by the thin lines. Dependence of the total interaction energy EW between the Fe@C20 endofullerene and the (8,8) nanotube on the angle φ is denoted by the thick line. (a) The (8,8) carbon nanotube with the Kekule structure; (b) the (8,8) carbon nanotube with the structure of metallic phase. All energies are given relative to the energy minima. Only dependences EWi with high values of the barriers ΔEri are shown.
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Figure 5: Interaction energy between the Fe@C20 endofullerene and (8,8) nanotube. Dependences of the interaction energy EWi between the Fe@C20 endofullerene and individual atoms of the (8,8) nanotube on the angle φ of rotation of the endofullerene about the nanotube axis are denoted by the thin lines. Dependence of the total interaction energy EW between the Fe@C20 endofullerene and the (8,8) nanotube on the angle φ is denoted by the thick line. (a) The (8,8) carbon nanotube with the Kekule structure; (b) the (8,8) carbon nanotube with the structure of metallic phase. All energies are given relative to the energy minima. Only dependences EWi with high values of the barriers ΔEri are shown.

Mentions: The potential surfaces of the interaction energy between the C20 fullerene and the nanotube, EW(φ, z), as functions of the relative displacement of the fullerene along the axis of the nanotube z and the angle of relative rotation of the fullerene about the axis of the nanotube φ are presented in Figure 3 for both the considered structures of the (8,8) nanotube. In the general case, diffusion of a fullerene along the nanotube axis is accompanied by rotation of the fullerene. Our calculations show that the barriers for rotation of both fullerenes about the axes which are perpendicular to the nanotube axis lie between 3 and 23 meV for any orientation of the fullerene and for both the considered structures of the (8,8) nanotube. These barriers are significantly greater than the barriers for rotation of the fullerenes about the axis of the nanotube (shown in Figure 3 for the C20 fullerene). Therefore, diffusion of the fullerenes along the nanotube axis is accompanied only by rotation about the nanotube axis. Thus, the minimal barrier ΔEd for diffusion of the fullerenes along the nanotube axis is the barrier between adjacent minima of the potential surface EW(φ, z). Figure 3 shows that the shapes of the potential surface EW(φ, z), corresponding to the Kekule structure of the (8,8) nanotube and to the structure of metallic phase are essentially different. For a case of the structure corresponding to the metallic phase of the (8,8) nanotube, all the barriers between adjacent minima of the potential surface EW(φ, z) are equivalent. In this case, the same barrier ΔEd = ΔEr should be overcome for diffusion of the fullerenes along the nanotube axis and for rotation of the fullerenes about this axis (see Figure 3b). For a case of the Kekule structure, two different barriers between the adjacent minima exist: the barrier ΔEd for diffusion of the fullerenes along the nanotube axis, and the barrier ΔEr to rotation of the fullerenes about this axis (see Figure 3a). For the Fe@C20 fullerene, the shapes of the potential surfaces EW(φ, z) are qualitatively the same as for C20 for both the considered structures of the nanotube. The calculated values of the barriers ΔEd and ΔEr are listed in Table 1 for both fullerenes. The dependences of the interaction energy between the C20 and Fe@C20 fullerenes and the nanotube on the relative displacement of the fullerene along the axis of the nanotube and the angle of its relative rotation about this axis, corresponding to both the considered structures of the (8,8) nanotube are compared as shown in Figure 4. Figure 4 is a vivid illustration of the significant changes of the barriers ΔEd and ΔEr. The most dramatic change corresponds to the rotation of the Fe@C20 fullerene about the nanotube axis. Let us discuss the reason of the significant changes of the barriers ΔEd and ΔEr at the Peierls transition by the example of the barrier ΔEr for rotation of the Fe@C20 endofullerene about the nanotube axis. Figure 5 presents the dependences EWi(φ) of the interaction energies between the endofullerene and individual atoms of the nanotube on the angle φ of rotation of the fullerene. Figure 5 shows that maxima of dependences EWi(φ) for individual atoms of the nanotube occur at different angles φmi and so the dependence EW(φ) of total energy on the angle of rotation is essentially smoothed. In other words, the barrier ΔEr in the dependence EW(φ) of the total interaction energy between the endofullerene and the nanotube is less by an order of magnitude than the barriers ΔEri in the dependences of the interaction energy between the endofullerene and only one of the nanotube atoms. Thus, the barrier ΔEr is very sensitive to the values of the barriers ΔEri and angles φmi. Therefore, the barrier ΔEr changes considerably at the found changes of the barriers ΔEri and angles φmi obtained from the Peierls distortions of the nanotube structure and the change of the nanotube symmetry at the transition. It should also be noted that small barriers to relative motion of nanoobjects resulting from the compensation of contributions of individual atoms to the barriers is a phenomenon well studied by the examples of such systems as double-shell carbon nanoparticles [13,14], double-walled carbon nanotubes [25,27-32] and a graphene flake in a graphite surface [33]. The considerable changes of barriers for relative rotation of shells at small changes of shell structure were found also for double-shell carbon nanoparticles [13,14].


Effect of Peierls transition in armchair carbon nanotube on dynamical behaviour of encapsulated fullerene.

Poklonski NA, Vyrko SA, Kislyakov EF, Hieu NN, Bubel' ON, Popov AM, Lozovik YE, Knizhnik AA, Lebedeva IV, Viet NA - Nanoscale Res Lett (2011)

Interaction energy between the Fe@C20 endofullerene and (8,8) nanotube. Dependences of the interaction energy EWi between the Fe@C20 endofullerene and individual atoms of the (8,8) nanotube on the angle φ of rotation of the endofullerene about the nanotube axis are denoted by the thin lines. Dependence of the total interaction energy EW between the Fe@C20 endofullerene and the (8,8) nanotube on the angle φ is denoted by the thick line. (a) The (8,8) carbon nanotube with the Kekule structure; (b) the (8,8) carbon nanotube with the structure of metallic phase. All energies are given relative to the energy minima. Only dependences EWi with high values of the barriers ΔEri are shown.
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Related In: Results  -  Collection

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Show All Figures
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Figure 5: Interaction energy between the Fe@C20 endofullerene and (8,8) nanotube. Dependences of the interaction energy EWi between the Fe@C20 endofullerene and individual atoms of the (8,8) nanotube on the angle φ of rotation of the endofullerene about the nanotube axis are denoted by the thin lines. Dependence of the total interaction energy EW between the Fe@C20 endofullerene and the (8,8) nanotube on the angle φ is denoted by the thick line. (a) The (8,8) carbon nanotube with the Kekule structure; (b) the (8,8) carbon nanotube with the structure of metallic phase. All energies are given relative to the energy minima. Only dependences EWi with high values of the barriers ΔEri are shown.
Mentions: The potential surfaces of the interaction energy between the C20 fullerene and the nanotube, EW(φ, z), as functions of the relative displacement of the fullerene along the axis of the nanotube z and the angle of relative rotation of the fullerene about the axis of the nanotube φ are presented in Figure 3 for both the considered structures of the (8,8) nanotube. In the general case, diffusion of a fullerene along the nanotube axis is accompanied by rotation of the fullerene. Our calculations show that the barriers for rotation of both fullerenes about the axes which are perpendicular to the nanotube axis lie between 3 and 23 meV for any orientation of the fullerene and for both the considered structures of the (8,8) nanotube. These barriers are significantly greater than the barriers for rotation of the fullerenes about the axis of the nanotube (shown in Figure 3 for the C20 fullerene). Therefore, diffusion of the fullerenes along the nanotube axis is accompanied only by rotation about the nanotube axis. Thus, the minimal barrier ΔEd for diffusion of the fullerenes along the nanotube axis is the barrier between adjacent minima of the potential surface EW(φ, z). Figure 3 shows that the shapes of the potential surface EW(φ, z), corresponding to the Kekule structure of the (8,8) nanotube and to the structure of metallic phase are essentially different. For a case of the structure corresponding to the metallic phase of the (8,8) nanotube, all the barriers between adjacent minima of the potential surface EW(φ, z) are equivalent. In this case, the same barrier ΔEd = ΔEr should be overcome for diffusion of the fullerenes along the nanotube axis and for rotation of the fullerenes about this axis (see Figure 3b). For a case of the Kekule structure, two different barriers between the adjacent minima exist: the barrier ΔEd for diffusion of the fullerenes along the nanotube axis, and the barrier ΔEr to rotation of the fullerenes about this axis (see Figure 3a). For the Fe@C20 fullerene, the shapes of the potential surfaces EW(φ, z) are qualitatively the same as for C20 for both the considered structures of the nanotube. The calculated values of the barriers ΔEd and ΔEr are listed in Table 1 for both fullerenes. The dependences of the interaction energy between the C20 and Fe@C20 fullerenes and the nanotube on the relative displacement of the fullerene along the axis of the nanotube and the angle of its relative rotation about this axis, corresponding to both the considered structures of the (8,8) nanotube are compared as shown in Figure 4. Figure 4 is a vivid illustration of the significant changes of the barriers ΔEd and ΔEr. The most dramatic change corresponds to the rotation of the Fe@C20 fullerene about the nanotube axis. Let us discuss the reason of the significant changes of the barriers ΔEd and ΔEr at the Peierls transition by the example of the barrier ΔEr for rotation of the Fe@C20 endofullerene about the nanotube axis. Figure 5 presents the dependences EWi(φ) of the interaction energies between the endofullerene and individual atoms of the nanotube on the angle φ of rotation of the fullerene. Figure 5 shows that maxima of dependences EWi(φ) for individual atoms of the nanotube occur at different angles φmi and so the dependence EW(φ) of total energy on the angle of rotation is essentially smoothed. In other words, the barrier ΔEr in the dependence EW(φ) of the total interaction energy between the endofullerene and the nanotube is less by an order of magnitude than the barriers ΔEri in the dependences of the interaction energy between the endofullerene and only one of the nanotube atoms. Thus, the barrier ΔEr is very sensitive to the values of the barriers ΔEri and angles φmi. Therefore, the barrier ΔEr changes considerably at the found changes of the barriers ΔEri and angles φmi obtained from the Peierls distortions of the nanotube structure and the change of the nanotube symmetry at the transition. It should also be noted that small barriers to relative motion of nanoobjects resulting from the compensation of contributions of individual atoms to the barriers is a phenomenon well studied by the examples of such systems as double-shell carbon nanoparticles [13,14], double-walled carbon nanotubes [25,27-32] and a graphene flake in a graphite surface [33]. The considerable changes of barriers for relative rotation of shells at small changes of shell structure were found also for double-shell carbon nanoparticles [13,14].

Bottom Line: The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory.It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude.The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physics Department, Belarusian State University, pr, Nezavisimosti 4, Minsk 220030, Belarus. poklonski@bsu.by.

ABSTRACT
The changes of dynamical behaviour of a single fullerene molecule inside an armchair carbon nanotube caused by the structural Peierls transition in the nanotube are considered. The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory. Significant changes of the barriers for motion along the nanotube axis and rotation of these fullerenes inside the (8,8) nanotube are found at the Peierls transition. It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude. The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.

No MeSH data available.


Related in: MedlinePlus