Ab initio study of K adsorption on graphene and carbon nanotubes: Role of long-range ionic forces

We present a first-principles study of potassium atom adsorption on graphene and carbon nanotubes. Our calculations are carried out using density functional theory combined with the pseudopotential approximation. This study is, in part, inspired by inconsistent results reported for this system in literature. The adsorption energy of potassium atom on graphene obtained in previous studies ranges from $0.44\text{to}2.0\mathrm{eV}$. We find that the reported disagreements can be explained by long-range electrostatic interactions between potassium and graphene. To illustrate this point, we present a simple classical model describing the interaction between the potassium atom and the graphene surface. The adsorption energies predicted by the model appear to be in good agreement with our first-principles calculations. In contrast, we find that the energy of potassium adsorption on carbon nanotubes depends on the nanotube surface curvature and chirality. This result suggests that the mechanism of interaction between potassium and carbon nanotubes may be different from that for the potassium-graphene system.

Figure 1

Periodic supercells used in SIESTA calculations: (a) $2\times 2$, (b) $4\times 2$, and (c) $4\times 4$. Supercell dimensions are given in terms of four-atom unit cells.

Figure 2

Structures of perimeter-passivated graphene clusters used in the study of K atom adsorption on graphene: (a) ${\mathrm{C}}_{24}{\mathrm{H}}_{12}\mathrm{K}$, (b) ${\mathrm{C}}_{42}{\mathrm{H}}_{18}\mathrm{K}$, and (c) ${\mathrm{C}}_{54}{\mathrm{H}}_{18}\mathrm{K}$.

Figure 3

Cylindrical nanotube fragments used in the study of K atom adsorption on carbon nanotubes: (a) fragments of the (3,3) nanotube and (b) fragments of the (5,0) nanotube. Bottom structures show larger fragments of the same (3,3) and (5,0) nanotubes.

Figure 4

Top, side, and front views of the charge density contour plots for the K atom attached to (a) the ${\mathrm{C}}_{54}{\mathrm{H}}_{18}$ cluster, (b) the ${\mathrm{C}}_{54}{\mathrm{H}}_{12}$ fragment of the (3,3) carbon nanotube and (c) the ${\mathrm{C}}_{60}{\mathrm{H}}_{10}$ fragment of the (5,0) nanotube. The maximum charge densities are equal to $1.87e∕a_o^3$, $1.40e∕a_o^3$, and $1.34e∕a_o^3$ for the systems (a), (b), and (c), respectively. Contour lines are drawn at $0.15e∕a_o^3$ intervals.

Figure 5

Adsorption energies of the K atom on graphene clusters. The energies are plotted as a function of the cluster radius. Continuous lines show the energies predicted by the classical model. The dashed and dotted horizontal lines correspond to the adsorption energies obtained by fitting the model to the results of LDA and GGA DFT calculations in the limit $R\to \infty$.