Density functional calculations of carbon nanotubes: Behavior of double-walled nanotubes compared to classical cylindrical capacitors

We present results from density functional theory calculations on the radial charge distribution of potassium-doped double-walled carbon nanotube (DWCNT) and double-walled nanotube with outer BN wall and inner carbon wall (BNCNT). We find that the curvature effect causes sizable charges on the inner tube in DWCNT with a small diameter inner tube. This behavior implies that small diameter DWCNTs may not behave like the classical cylindrical capacitor. More importantly, the charges are transferred mainly from potassium into the inner carbon nanotube in BNCNT despite the insulating characteristics of the outer tube. This unusual feature is due to strong Coulomb interactions in the BN nanotube and predominance of the inner-tube bands in the energy band of BNCNT. Moreover, the radial charge distribution in multiwalled carbon and BN/C nanotubes is discussed.

Figure 1

Electronic energy bands of zigzag $(n,0)@(n+9,0)$ DWCNTs: (a) $n=10$, (b) $n=9$, (c) $n=8$, (d) $n=7$, (e) $n=6$, and (f) $n=5$. The Fermi level is set to be zero.

Figure 2

Electronic energy bands of (a) undoped and (b) doped (5,0)@(14,0) DWCNTs and (c) undoped and (d) doped (5,0)@(14,0) BNCNTs. The Fermi level is set to zero.

Figure 3

The charge $n_k$ and the ratio $n_{\mathit{\text{inner}}}∕n_k$ as a function of the number of potassium atoms for doped (5,0)@(14,0) DWCNT.

Figure 4

(Color online) (a) Schematic diagram of graphite intercalation compounds used in our calculation. The bounding layer is replaced by (b) one, (c) two, and (d) three hexagonal BN layers. The black, red, green, and blue circles denote carbon, potassium, boron, and nitride atoms. The numbers on the right side of each layer represent the charge amount of this layer.