2.1. Winding of a BP Ribbon on a CNT with α = 0°
Table 1 and
Figure 1c indicate that when the CNT axis is parallel to the
z-axis, i.e., α = 0°, the BP ribbon can form into an ideal nanotube only upon the CNT (8, 8) when
Ly = 0 nm. On the CNTs (6, 6) and (7, 7) used, the BP nanotubes formed from the ribbon have defects at the tube ends (
Figure 1a,b). If the CNT (10, 10) is adopted, the BP ribbon can only wind upon the CNT, but fails to form into a nanotube. The reason is that the gap between the two oblique edges of the curly BP ribbon is too high and attraction between them is too weak to let the two edges move closer to each other for bonding (
Figure 1d).
When the CNT moves right, i.e.,
Ly > 0 nm, more atoms on the BP ribbon are closer to the CNT, and the final configurations of the four chiral BP nanotubes after assembly were different. The BP nanotube can be formed on both the CNTs (6, 6) and (7, 7) (inserts in
Figure 2). However, the BP ribbon still cannot form into a tube on the CNT (10, 10). Hence, we conclude that the value of
Ly is not the essential factor when the BP ribbon can only wind upon a CNT with a larger radius (
Table 1).
Winding of BP ribbon on CNTs with α = ±30°: The effect of correlation between the parameters, i.e.,
Ly and α, for determining the positions of the CNTs is necessarily demonstrated. As listed in
Table 2, for the CNTs with rotational angle α = 30°, they cannot capture the BP ribbon due to negligible attraction when
Ly ≤ 3 nm. In this condition, the ribbon escapes rather than winds upon the CNTs (
Figure 3). This is because the distance between the CNTs and the BP ribbon is too high and attraction upon the BP ribbon is too weak. Without getting closer to the CNTs, the ribbon has no chance to be curved and further forms into a tube. If
Ly = 6 or 9 nm, the distance between the two components is less than 1 nm (the cut-off of the L–J potential), and the BP ribbon can wind upon the CNTs to form the BP nanotube.
If α < 0°, e.g., −30°, the CNTs can attract the BP ribbon effectively even when
Ly = 0 nm. The ribbon does not escape any more. It can form into a tube with or without a defect, or forms into a scroll, or just winds upon a CNT with higher radius (
Table 3). For example, at
Ly = 6 nm, the distance between the CNTs and the BP ribbon reaches the minimum among the four cases. Only in this case, the ribbon becomes an ideal nanotube regardless of the CNTs’ radii. Therefore, the translation of CNT along the y-direction influences the final configuration of BP because of different initial distributions of attractive force on the BP ribbon (
Figure 4).
In
Table 3, the BP ribbon forms into a nanoscroll on the CNT (7, 7) when
Ly = 0 nm.
Figure 5 gives the representative snapshots to indicate the assembly process (
Movie S1 in Supplementary Materials). It can be found that the ribbon first winds upon the CNT (7, 7) and then winds upon itself (snapshot at 1000 ps in
Figure 5). The two oblique edges overlap rather than bond together well. According to the rest of the VPE curves of the system with respect to the CNTs (7, 7) (
Figure 6a) and (8, 8) (
Figure 6b), the system with
Ly > 0 nm becomes stable after no more than 180 ps, the ribbon forms into a tube, simultaneously. Hence, the state of the system after 200 ps does not change obviously. The sudden drop in each VPE curve tells the history of bonding between the two oblique edges on the BP ribbon.
When moving the oblique CNT (8, 8) from left to right (
Ly = 0, 3, 6, 9 nm), the self-assembly processes of the ribbon are illustrated by the snapshots of the BP during winding upon CNT between 0 and 150 ps, as shown in
Figure 7. The BP ribbon starts to curve at different locations (Loc), where most atoms are attracted by the CNT (e.g.,
Figure 4). For example, when the CNT is near the top left corner of the BP ribbon (
Ly = 0 nm), the BP begins to curve at this location due to the local strong attraction from the CNT. When
Ly = 9 nm, the BP nanotube has a defect after winding upon the CNT. Perfect BP nanotubes are only formed on the CNT with
Ly = 3 and 6 nm (
Figure 7b,c).
2.2. Effect of α on Self-Assembly of the BP Ribbon
To illustrate the influence of CNT’s rotation angle α on the self-assembly of the BP ribbon, the CNT (10, 10), which has a large radius, is first considered in simulations with the results listed in
Table 4. The ribbon’s behaviour depends on the initial conditions. For example, when
Ly = 0 nm, the BP ribbon escapes directly from the CNT if α > 3°. When
Ly = 3 nm (
Table 4), the state of the BP component as a different experience. For example, firstly, in the case of α = 0° and 3°, the BP ribbon just winds upon the CNT, but cannot form into a nanotube (Wind only). Secondly, for the cases of α = 6° and 9°, the state of the BP ribbon is between “Wind only” and “Tube”, i.e., “Wind only
Tube” (
Movie S2 in Supplementary Materials). In this case, the distance between the two oblique edges is smaller than that in “Wind only” (
Figure 1d), but still slightly longer than the bond length of P–P. Thirdly, for the CNT with α between 12° and 18°, it can trigger a successful self-assembly of the ribbon into a nanotube. When the ribbon is attracted and starts to wind on the CNT, the P atoms on the oblique edges move closer to each other and finally bond together (
Figure 8a,b). Finally, when the rotation angle is more than 30°, the distance between BP and CNT becomes higher, and the BP ribbon escapes due to the lack of attraction. The final configuration of the BP structure is sensitive to the value of α due to the zigzag potential barriers on the oblique edges of the BP ribbon.
Dividing the VPE of BP in the system with
Ly = 3 nm and α = 12° into two parts, i.e., new P–P bonds induced VPE, and the remaining part due to deformation together with the interaction between the two components (
Figure 8b), we find that the value of
PNew starts decreasing at 162 ps and keeps unchanged after 166 ps. During the bonding period, 23 new P–P bonds are generated between the two helical edges of the ribbon. In the same period, the value of
PDeform +
PInter jumps up. This is mainly caused by the deformation of the BP component from ribbon to tube.
As
Ly becomes higher (e.g., 6 or 9 nm), the BP ribbon has difficulty “escaping” from the CNT (
Table 4). If it does not escape, the ribbon can become a nanotube at a higher value of α, or between the “Wind only” and “Tube” at a lower value of α. However, the angle interval for forming a BP nanotube is difficult to obtain because random vibration of atoms on the ribbon may lead to failure of tube formation.
What would happen to the BP component if α < 0°? As α is negative, more atoms on the BP ribbon are closer to the CNT. If the CNT with
Ly = 0 nm can drive the self-assembly of the BP ribbon, so it does at
Ly > 0 nm. Hence, the self-assembly process of the ribbon on the CNTs with
Ly = 0 nm is considered, and the results are listed in
Table 5. The table indicates that the formation of a BP nanotube depends both on the value of α and the radius of CNT. For instance, the BP ribbon on the CNT (6, 6) could form into an ideal nanotube when α ≤ −9°; otherwise, the BP tube has a defect. On the CNT (7, 7), α ≤ −15° should be satisfied to form into a tube or a scroll. At a smaller angle of the CNT, the BP ribbon can easily form into a nanotube on the CNT (8, 8), but has difficulty at a larger angle of α. For example, the BP ribbon may become a nanotube with a defect or a scroll. If the CNT (10, 10) is used, the ribbon has difficulty becoming a nanotube. In most cases, the ribbon just winds upon the CNT. At a higher angle, the ribbon may form into a scroll or even half of the ribbon wind upon the tube; the remaining part does not curve (“1/2 scroll” in
Figure 9,
Movie S3 in the Supplementary Materials).