Interfacing carbon nanotubes of arbitrary chiralities into linear heterojunctions

Motivated by recent advances in synthesis and characterization of carbon nanotube (CNT) heterojunctions, we introduce a systematic approach for obtaining atomic geometries that connect two carbon nanotubes of different chiralities. Using our approach, it is straightforward to construct atomic interface geometries between two single-walled CNT’s of arbitrary chiralities arranged at different orientations and angles. Our method generalizes existing approaches and is readily applicable to joining domains of graphene nanoribbons as well. As an example, we focus on linear heterojunctions, and we postulate the minimum number of simple topological defects required at the interface, and the preferred spatial arrangements, to obtain maximally linear heterojunctions given any two arbitrary chiralities. We also provide a physical picture of the defect structure of the resultant interface geometries using the results of classical force-field simulations.

Figure 1

(a) Two CNT’s of similar radii but dissimilar chirality. (b) Characteristic triangles $\mathrm{ABC}$ and $A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}$ at the edges of the two graphene ribbons due to unwinding of the CNT’s. (c) Interface quadrangle ${\mathrm{ABA}}^{\text{'}}C$ formed by connecting the two characteristic triangles.

Figure 2

(i)(a)–(d) Heterojunctions with different numbers of topological defects with CNT $(10,8)$ on the left and CNT $(12,6)$ on the right. (ii)(a)–(d) Corresponding energy-minimized structures. (iii) The net strain energies for the four different heterojunctions. For reference, within the empirical force-field model (TB-EIP) used in this work, the strain energy to create a single pentagon-heptagon paired defect in a CNT of similar radii is about 5.4 eV.

Figure 3

The three basic quadrangles to be used as building blocks to tile the interface polygon.

Figure 4

HJ’s made of CNT segments of chiralities (6,6) and (5,7) shown in (a) requiring one $B$-type block, and chiralities (6,6) and (5,8) shown in (b) requiring one $C$-type block, in order for the HJ’s to be maximally linear.

Figure 5

Interface triangle $\mathrm{ABC}$ connecting CNT’s $(8,10)$ and $(16,0)$.

Figure 6

(a) HJ composed of CNT’s $(9,6)$ and $(9,3)$. (b) HJ composed of CNT’s $(14,8)$ and $(12,6)$.

Figure 7

(i)(a)–(h) Different arrangements of two defects at the interface of HJ $(8,10)-(12,6)$. (ii)(a)–(h) Histogram plots of bond lengths in the corresponding energy-minimized structures. (iii) Net strain energies computed with TB-EIP.

Figure 8

(i)(a)–(f) Interface quadrangle showing different arrangements of the four 5-7 defects connecting CNT’s $(10,8)$ and $(12,6)$. (ii)(a)–(f) Corresponding energy-minimized structures. (iii) Net strain energies computed with TB-EIP.