Atomic oxygen chemisorption on the sidewall of zigzag single-walled carbon nanotubes

A theoretical approach is developed to study the chemisorption of a single oxygen atom on the outer surface of zigzag single-walled carbon nanotubes (ZSWCNTs). The adatom Green’s function, the charge transfer between the nanotubes and the chemisorbed O atom, and the adsorption energy $\Delta E_{\mathrm{ads}}$ are calculated within the Anderson-Newns model, which takes account of Coulomb interaction between adsorbate electrons. Two different adsorption positions are considered, in which an oxygen atom forms a bridge between two nearest-neighbor carbon atoms: one is on top of an axial C-C bond (position I), and the other—on top of a zigzag C-C one (position II). According to our calculations carried out for a series of the ZSWCNTs $(p,0)$ with $p$ ranging from 9 to 18, the adsorption of a single O atom in both the above-mentioned positions is possible and equally probable from the energetic point of view as the corresponding adsorption energies, being negative, are almost identical. The absolute values of these energies generally fall into the range $1.1-2.7\mathrm{eV}$, larger $\mid \Delta E_{\mathrm{ads}}\mid$ values being associated with semiconducting tubes. For the latter ones, $\Delta E_{\mathrm{ads}}$ is found to be practically independent of the nanotube radius $R$, whereas for metallic tubes $\Delta E_{\mathrm{ads}}$ slightly decreases with increasing $R$, tending towards the “infinite” radius graphene case. The localized acceptor states created by the O adatom in the band gap of the semiconducting ZSWCNTs are found to be responsible for such a different behavior of $\Delta E_{\mathrm{ads}}$ as a function of $R$ for the two types of nanotubes (metallic and semiconducting), as well as for the lowering in $\Delta E_{\mathrm{ads}}$ (by about $0.5\mathrm{eV}$) for the semiconducting tubes as compared with the metallic ones. It is also shown that a fairly large charge transfer (of about 0.55 electron) to the O adatom occurs when it is chemisorbed on the outer surface of the ZSWCNTs, which suggests that their electronic transport properties can be significantly changed upon chemisorption of atomic oxygen.

Figure 1

Fragment of a two-dimensional graphite sheet which is rolled up in order to construct a ZSWCNT specified by an index $(p,0)$. The unit vectors denoted by ${\mathbf{e}}_x$ and ${\mathbf{e}}_y$ are directed along the circumference and the axis of the nanotube, respectively. Also shown a chiral vector $\mathbf{L}$ corresponding to the circumference of the tube and one of the primitive translation vectors of the lattice structure of a graphene plane, denoted by $\mathbf{a}$. The grey balls schematically show two possible stable adsorption positions of an oxygen atom on the surface of a SWCNT (for details, see the text). The vectors labeled ${\mathbf{R}}_i$ and ${\mathbf{R}}_{i+1}$ are the position vectors of two surface nearest neighbors of the adatom, which are connected by vector $\mathbf{d}$. The superscripts I and II refer to the two abovementioned positions of the adatom.

Figure 2

Plot of the chemisorption function ${\Delta }_a^{\left(\nu \right)}\left(\epsilon \right)$ defined in Eq. (19) for a semiconducting ZSWCNT (10,0) (a) and for a metallic one (12,0) (b). Dotted (full) curves correspond to bridge position I(II) of an adatom on the surface of the nanotubes. The dimensionless hopping parameter $B$ is 0.33.

Figure 3

Plot of the chemisorption function ${\Lambda }_a^{\left(\nu \right)}\left(E\right)$ defined in Eq. (22) for a semiconducting ZSWCNT (10,0). Dotted (full) curves correspond to bridge position I(II) of an adatom on the surface of the nanotube. Parameter $B$ is the same as in Fig. 2. The intersection with a slanting straight line $(\epsilon -E_{a\sigma })∕\eta$, marked with a solid dot gives the solution of Eq. (34) for the localized state energy ${\epsilon }_{l\sigma }$.

Figure 4

Localized state energies ${\epsilon }_{l\sigma }$ for several semiconducting ZSWCNTs as a function of the nanotube radius $R$. Open (solid) dots correspond to bridge position I (II) of an adatom on the surface of the nanotubes. These energies are calculated from Eq. (34) using the self-consistent values of $⟨n_{a\sigma }⟩$ obtained for each tube as explained in the text. The numbers in parenthesis stand for the tube chirality indices. The solid and dashed lines are intended as a guide to the eye.

Figure 5

Mean occupation numbers ${⟨n_{a\sigma }⟩}_l$ of the localized states, whose energies are presented in Fig. 4, versus the nanotube radius $R$. Open (solid) dots correspond to bridge position I (II) of an adatom on the surface of the nanotubes. The numbers in parenthesis stand for the tube chirality indices. The solid and dashed lines are intended as a guide to the eye.

Figure 6

Example of a graphical solution of Eq. (38) for the O adatom adsorbed in position II on the surface of a ZSWCNT (12, 0). The intersection points of curves 1 and 2 give a “nonmagnetic” root of Eq. (38) (marked with a heavy dot) and a pair of “magnetic” roots of the same equation (marked with crosses).

Figure 7

Adatom density of states ${\rho }_a^{\sigma }\left(\epsilon \right)$ defined in Eq. (32) for a semiconducting ZSWCNT (10,0) (a) and for a metallic one (12,0) (b). Dotted (full) curves correspond to bridge position I(II) of an adatom on the surface of the nanotubes.

Figure 8

Charge transfer $\Delta q∕e$ from the ZSWCNTs $(p,0)$ with $p=9–18$ to the O atom adsorbed in bridge position I (open symbols) and bridge position II (solid symbols) as a function of the nanotube radius $R$. The cutoff parameter ${\delta }_c$ is chosen to be equal to 0.15. The dots and the triangles refer to semiconducting and metallic ZSWCNTs, respectively. The numbers in parenthesis stand for the tube chirality indices. The solid and dashed lines are intended as a guide to the eye.

Figure 9

Charge transfer $\Delta q∕e$ from the ZSWCNTs $(p,0)$ with $p=9–18$ to the O atom adsorbed in bridge position II as a function of the nanotube radius $R$ for three different values of the cutoff parameter ${\delta }_c$: 0.1, 0.15, and 0.2. The solid, dashed, and dot-dashed lines are intended as a guide to the eye. Other notations are the same as in Fig. 8.

Figure 10

Chemisorption energies $\Delta E_{\mathrm{ads}}$ of a single O adatom on the surface of the ZSWCNTs $(p,0)$ with $p=9–18$ versus the nanotube radius $R$. The cutoff parameter ${\delta }_c$ is chosen to be equal to 0.15. The open (solid) dots as well as the open (solid) triangles refer to bridge position I (II). The dots and the triangles refer to semiconducting and metallic ZSWCNTs, respectively. The asterisks (*) and stars (⋆) show the results obtained for the O atom adsorbed directly on top of a surface carbon atom of semiconducting and metallic ZSWCNTs, respectively. The numbers in parenthesis stand for the tube chirality indices. The solid, dashed, and dot-dashed lines are intended as a guide to the eye.

Figure 11

Chemisorption energies $\Delta E_{\mathrm{ads}}$ of a single O adatom adsorbed on the surface of the ZSWCNTs $(p,0)$ with $p=9–18$ in bridge position II as a function of the nanotube radius $R$ for three different values of the cutoff parameter ${\delta }_c$: 0.1, 0.15, and 0.2. The dots and the triangles refer to semiconducting and metallic ZSWCNTs, respectively. The numbers in parenthesis stand for the tube chirality indices. The solid, dashed and dot-dashed lines are intended as a guide to the eye.