Density functional study of single-wall and double-wall platinum nanotubes

The electronic structure calculations are carried out within the density functional formalism for understanding the structure and energetics of platinum nanotubes. Various single-walled platinum nanotubes (both chiral and achiral) and double-walled platinum nanotubes (only achiral) are considered here. Our calculations reveal that among six row strand nanotubes, the relaxed Pt(6,4) is most stable while among the five row strand nanotubes, the relaxed Pt(5,3) is most stable. After complete relaxation, the atomic structures of both the Pt(6,4) and Pt(5,3) nanotubes remain tubular and chiral. However, the initial chirality is not retained in the final atomic structure. The double-walled platinum nanotubes, namely, the Pt(6,6)@(13,13), Pt(5,5)@(12,12), Pt(4,4)@(11,11), and Pt(1,1)@(7,7) are studied. The atomic structures of these double-walled nanotubes remain double walled and tubular after complete relaxation. It is interesting to note that most of our results agree with the existing experimental results.

Figure 1

The 2D triangular lattice network of Pt(111) sheet is shown here. The atomic structure of $\text{Pt}\left(n,m\right)$ is obtained by cylindrical folding of Pt(111) sheet. The circumference $\left(R\right)$ and unit cell length $\left(L\right)$ are shown for the Pt(5,5) nanotube.

Figure 2

Total energy per supercell is plotted as a function of the Pt-Pt bond length of the achiral Pt(6,6) nanotube. The optimal bond length turns out to be $2.66\text{Å}$.

Figure 3

Total energy per super cell is plotted as a function of the Pt-Pt bond length of the chiral Pt(6,5) nanotube. The optimal bond length turns out to be $2.60\text{Å}$.

Figure 4

This shows the variation in binding energy per atom with diameter for several single-walled platinum nanotubes. The dotted line corresponds to the binding energy per atom for 2D Pt(111) sheet. Notice that the binding energy per atom for single-walled nanotubes in the larger diameter regime approaches toward the value of the binding energy per atom for the 2D Pt(111) sheet.

Figure 5

The curvature energy per atom is plotted for single-walled platinum nanotubes as a function of $1/D^2$. Dotted line is the best fit for the curvature energy per atom versus $1/D^2$ plot.

Figure 6

(Color online) String tension values are plotted as a function of diameter of the single-walled and double-walled platinum nanotubes.

Figure 7

(Color online) String tension values are plotted as a function of diameter of the single-walled platinum nanotubes. Here, the PAW potential is used under the VASP.

Figure 8

(Color online) The total charge density plot of the Pt(6,4) nanotube on a plane perpendicular to the axis of the nanotube.

Figure 9

The relaxed atomic structure of the chiral Pt(6,4) nanotube within one unit cell is shown.

Figure 10

Electronic density of states (DOS) are plotted as a function of energy for the Pt(6,4) nanotube. The vertical line (dotted) indicates the fermi energy level.

Figure 11

(Color online) The total charge density of the Pt(5,3) nanotube is plotted on a plane perpendicular to the axis of the nanotube.

Figure 12

Electronic density of states versus energy plot of the Pt(5,3) nanotube. The vertical line (dotted) indicates the fermi energy level.

Figure 13

The relaxed atomic structure of the chiral Pt(5,3) nanotube within one unit cell is shown.

Figure 14

The relaxed atomic structure of the achiral Pt(10,10) nanotube within one unit cell is shown.

Figure 15

(Color online) The total charge density plot of the Pt(6,6)@(13,13) nanotube on a plane perpendicular to the axis of the nanotube. The charge density is negligible at the center of the tube.

Figure 16

The total charge density is plotted along a line between the two atoms, one in the inner shell and other in outer shell of the relaxed Pt(6,6)@(13,13) nanotube.

Figure 17

The band structure plot of the relaxed Pt(6,6)@(13,13) nanotube. The dotted line indicates the fermi energy level.