Energetics, structure, and long-range interaction of vacancy-type defects in carbon nanotubes: Atomistic simulations

The presence of vacancy clusters in carbon nanotubes has been assumed to explain the formation of carbon peapods and the difference between the experimentally measured and theoretical fracture strength of nanotubes. We use atomistic simulations at various levels of theory to study the characteristics of large vacancies formed by up to six missing atoms. We show that the formation of big “holes” on nanotube walls is energetically unfavorable as the vacancies tend to split into smaller defects due to the reconstruction of the nanotube atomic network. We also demonstrate that there is a weak but long-ranged interaction between the vacancies not only through strain fields but, surprisingly, also due to electronic effects, similar to those of adatoms on metal surfaces.

Figure 1

(Color online) Atomic structures of multivacancies on a (10,10) SWNT given by the DFTB method. Pentagons are colored in yellow (light gray), rings with more than six atoms in blue (slightly darker gray). Atoms with dangling bonds are represented as red (dark gray) balls. The atomic network of the pristine tube with the removed atoms is shown in the top right corner of each panel. The right part illustrates changes in the nanotube network.

Figure 2

Energies (in eV) gained by coalescing monovacancies $\left(V_1\right)$ to form higher-order defects $\left(V_i\right)$ on a (10,10) SWNT, as given by the DFTB method.

Figure 3

(Color online) Difference in the vacancy formation energy in a (5,5) nanotube (two single vacancies) as a function of separation between the defects for two orientations as calculated with the DFTB method. The insets show the energy at large separations as calculated with both the DFTB and EP models. The arrows visualize the correspondence between the plot points and the atomic structures.

Figure 4

(Color) (a) Strain fields near a single vacancy in graphene as given by the EP method. (b) Sketch illustrating the effect of vacancy orientation on the type of the interaction (repulsive or attractive) between two single vacancies in graphene.

Figure 5

(Color online) Isometric plot of the electron density near the Fermi level around a single vacancy in a (5,5) SWNT, as calculated by the plane wave DFT method. (a) Top view; (b) side view.