Calculating carbon nanotube–catalyst adhesion strengths

Density-functional theory is used to assess the validity of modeling metal clusters as single atoms or rings of atoms when determining adhesion strengths between clusters and single-walled carbon nanotubes (SWNTs). Representing a cluster by a single atom or ring gives the correct trends in SWNT-cluster adhesion strengths $(\mathrm{Fe}\approx \mathrm{Co}>\mathrm{Ni})$, but the single-atom model yields incorrect minimum-energy structures for all three metals. We have found that this is because of directional bonding between the SWNT end and the metal cluster, which is captured in the ring model but not by the single atom. Hence, pairwise potential models that do not describe directional bonding correctly, and which are commonly used to study these systems, are expected to give incorrect minimum-energy structures.

Figure 1

Adhesion energy of a single Ni atom bonded to different sites at the end of a (5,0) SWNT.

Figure 2

(Color online) Minimum-energy structures of a (5,0) SWNT bonded to (a) a Ni atom, (b) a ${\mathrm{Ni}}_5$ ring, and (c) a ${\mathrm{Ni}}_{13}$ cluster. The Ni atom (a) and ring (b) are constrained to the cylindrical plane of the SWNT wall.

Figure 3

Adhesion energy of a single Ni atom bonded to different sites at the end of a (5,5) SWNT.

Figure 4

(Color online) Structures of a (5,5) SWNT bonded to (a) a Ni atom, (b) the constrained ${\mathrm{Ni}}_{10}$ ring top site, (c) the constrained ${\mathrm{Ni}}_{10}$ ring middle site, and (d) a ${\mathrm{Ni}}_{55}$ cluster. Top views for the constrained and fully relaxed structures are shown in (e) and (f) for the ${\mathrm{Ni}}_{10}$ ring top site and in (g) and (h) for the ${\mathrm{Ni}}_{10}$ ring middle site.