The formation and stability of junctions in single-wall carbon nanotubes

The structure and stability of molecular junctions, which connect two single-wall carbon nanotubes (SWCNTs) of different diameters and chiral angles, (n ₁, m ₁)-(n ₂, m ₂), are systematically investigated by density functional tight binding calculations. More than 100 junctions, which connect well-aligned SWCNTs, were constructed and calculated. For a highly stable junction between two chiral (n ₁, m ₁) and (n ₂, m ₂) SWCNTs with opposite handedness, the number of pentagon–heptagon (5/7) pairs required to build the junction can be denoted as ∣∣n ₂ − n ₁∣ − ∣m ₂ − m ₁∣∣+min{∣n ₂ − n ₁∣, ∣m ₂ − m ₁∣} with (n ₂, m ₂) rotating π/3 angle or not. While for a junction connected by two zigzag, armchair or two chiral SWCNTs with the same handedness, the number of 5/7 pairs is equal to ∣n ₁ − n ₂∣ + ∣m ₁ − m ₂∣. Similar to the formation energies of grain boundaries in graphene, the curve of the formation energies vs. chiral angle difference present an 'M' shape indicating the preference of ∼30 degree junctions. Moreover, the formation energies of the zigzag-type and armchair-type junctions with zero misorientation angles are largely sensitive to the diameter difference of two sub-SWCNTs. (paper)