Structural evolution dynamics in fusion of sumanenes and corannulenes: defects formation and self-healing mechanism

The formation of carbon nanoribbons and CNTs have been studied at high temperatures (∼3000–4000 K) with a periodic boundary condition applied in one direction [63–66]. The shape of the transformed structure depends on the temperature, heating rate and the line density of carbon atoms along the direction in which periodic boundary conditions are applied. Most of the samples presented in this work end up forming GNRs at sufficiently prolonged heating at 3500 K, although in some cases the final structure is disintegrated or tubular (see figure 1). One of the main factors which affects the shape of the final structure is the line density (ρ_l) along the direction in which periodic boundary conditions are applied [64]. Most samples with a line density less than ∼4.9 atoms Å⁻¹ are disintegrated into unbound carbon molecules. Since a triangular lattice is more densely packed than a square lattice (for the same distance between the centers of the fragments), samples consisting of any type of monomer arranged on a triangular lattice end up forming GNRs after heating. If monomers are initially arranged on a square lattice, the ρ_l can be less than the critical value of 4.9 atoms Å⁻¹ under larger separation between monomers, resulting in an ensemble of decomposed structures. Three samples with the square unit cell containing two sumanenes as monomers are constructed with lattice constants of 15 (ρ_l = 5.29 atoms Å⁻¹, figure 1(a)), 16 (ρ_l = 4.96 atoms Å⁻¹, figure 1(b)) and 17 a.u. (ρ_l = 4.67 atoms Å⁻¹, figure 1(c)), which end up as a tubular structure, defragmented carbon molecules, and GNRs, respectively. If the line density is quite high (ρ_l = 5.29 atoms Å⁻¹, see figure 1(a)), then the transformation into a tubular structure occurs at relatively low temperatures of 1000 K. The initial geometry is favored to coalescence of the fragments by forming the additional hexagons (colored by blue). As has been discussed previously by DFT calculations, this configuration of two sumanenes is the most stable. The inherent curvature of the sumanenes leads to the rolling of the structure into the tube. The unsaturated edges of the curved nanoribbon are very active therefore they merge very fast preventing the structure to unroll back into a GNR at additional heating. The evolution of the potential energy profile of this process is represented in figure S1a, which is available online at stacks.iop.org/NANOF/2/025001/mmedia (supporting information) with the distinct feature between fast versus slow stages. In the case when the lattice constant is equal to 16 a.u. (ρ_l = 4.96 atoms Å⁻¹, figure 1(b)), the fragments can slightly tilt to promote the formation of pentagons. However, the bonding of two sumanenes through the pentagon is very unstable, and cannot be sustained at the high temperature. The structure is disintegrated at 3500 K. The potential energy profile of this process is represented in figure S1b (supporting information) showing the decrease at the beginning of formation of the preliminary GNR, and then increases when the sample disintegrates. In the case of the lattice constant of 17 a.u. (ρ_l = 4.67 atoms Å⁻¹, see figure 1(c)), two sumanenes form the covalently-bonded pair in the vertical direction with two hexagons in between. Note that the horizontal distance between them is sufficiently large, which allows the pairs to turn their orientation by forming a triangular lattice which is packed more densely than the square one (the thickness of the future GNR is decreasing). The structure is forming at a sufficiently high temperature when the edges fluctuate strongly enough, which hinders the joining between edges for making the CNT. Instead, the GNR is the favored product. The potential energy profile of the process is presented in figure S1c (supporting information), which exhibits multi-stage features reflecting fascinating structural re-organizations in the course of formation of the GNR [64, 66]. The details in the structural aspect will be analyzed in the next section.

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Here we consider the structural evolution of forming nanoribbon from sumanenes placed at the vertexes of a triangular lattice with the lattice constant of 17 a.u. (ρ_l = 4.67 atoms Å⁻¹ with periodic boundary conditions applied in the x-direction). At the initial stage, the sumanene fragments join together to form a local hexagon unit (see figure 2(a) at 200 K). With increasing temperature, a defected carbon nanoribbon with crooked edges is formed (see figure 2(a) at 300–2500 K) which contains pentagons, hexagons and heptagons. The edges of the nanoribbon gradually straighten out upon further heating (see figure 2(a) at 50–190 ps, T = 3500 K). However, this intermediate structure is very unstable. With prolonged heating at a higher temperature (see figure 2(a) at 3500 K after 200 ps), the nanoribbon structure begins to disintegrate. The carbon chains and individual atoms detach from the edges, while the holes inside the nanoribbon rapidly grow (see figure 2(a) at 210–230 ps). At 230 ps, the nanoribbon structure is almost completely defragmented: only one pentagon and two hexagons rings are left. Interestingly, the 'active' edge atoms react with defragmented carbon species in the form of atoms and chains to generate new bonds to rebuild a more energetically favorable sp² carbon network despite the presence of the substantial amount of defects (see figure 2(a) at 250 ps). To repair these defects, the migration of defects along large graphene network has been computed to unravel the effective defects propagation in the vicinity of other defects [67–69]. In contrast to infinite graphene sheets, the GNR is terminated by edges which provide another option to heal defects as observed experimentally in morphology and edge evolution of graphene domains [70]. This phenomenon is also observed in our simulation in the processes of 'edge-facilitated self-healing' defects due to the synergy of two edge-related effects: defects are effectively more mobile near edges; and structure reconstructions are more pronounced near edges. After 400 ps at 3500 K, the healing of the GNR is almost completed (see figure 2(a) at 400 ps), only with remaining pentagons at the edges due to the edges reconstruction. In summary, the GNR formation process exhibits three main stages: the first stage, a preliminary defective carbon nanoribbon is formed; the second stage, the nanoribbon is disintegrated to a large extent which is characterized by a minimal number of rings: pentagons, hexagons and heptagons; then the third stage, the structure rebuilds itself into a much more ordered GNR augmented by self-healing of defects facilitated by edges. The energy profile of the whole process drawn in figure S2 (see supporting information) represents clear features to characterize these stages [64, 66]. The process of the 'edge-facilitated self-healing' of the defects at the GNR edges will be analyzed in detail in the next section.

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The SW topological defect [71] is one of the most common defects in graphenes, CNTs, fullerenes, and other carbon nanostructures. It involves an in-plane 90° rotation of two carbon atoms with respect to the midpoint of the bond. In this transformation four adjacent hexagons are converted into two heptagon–pentagon pairs. The defected structure retains the same number of atoms as pristine graphene, thus no dangling bonds are introduced. Once the SW defect is formed, the high energy barrier (5 eV) [72] prevents the reverse transformation under normal conditions. To repair the SW defect, a stress field can be applied to promote inverse rotation of C–C bonds as shown in molecular dynamics studies [72, 73]. Additional computations show that the SW defect under stress conditions can split into two 5–7 pairs, which can further move apart [74, 75], as recently confirmed experimentally [76]. Interestingly, the SW defect can also be repaired by the planar reconstruction of zigzag edges in graphene [77, 78]. In the present work, the simulated self-healing of the SW defect located at the edge of the GNR provides desirable dynamic information to unravel detailed atomistic motions to heal the SW defect in this GNR structure. This process takes place at the last stage of the formation of the GNR described in the previous section between 380 and 400 ps (see figure 2(b)). For better visualization of the self-healing process, pentagons and heptagons of the SW defect are yellow- and pink-colored, respectively, while the hexagons appearing as a result of the self-healing process are blue-colored. In figure 2(b) two yellow atoms are connected by the bond, which is shared by the two adjacent heptagons of the SW defect. This bond will perform the critical rotation in the self-healing process. The edge rings adjacent to the SW defect (red-colored at the bottom of figure 2(b) at 383 ps) rearrange by forming chains connected to the SW defect from the left and right (see figure 2(b) at 383.5 ps). At the time of 384 ps, the pentagon and heptagon belonging to the SW defect (see the bottom yellow and pink rings in figure 2(b) at 384 ps) are destroyed, and transformed into a chain segment, which joins with the two previously formed chains. The C–C bond connecting the two yellow-colored atoms is now located at the edge of the hole formed by the atomic chain (see the red-colored atoms at the bottom of figure 2(b) at 384 ps). The edge reconstruction induces this C–C bond rotation (see figure 2(b) at 384.5 ps), transforming the pentagon–heptagon pair into a pair of the two adjacent hexagons (blue-colored). In the final step, the chain atoms join these hexagons closing the hole and forming another two hexagons located below the first pair (see figure 2(b) at 386 ps). Clearly, the edge of the GNR plays an important role in facilitating the reverse rotation of the C–C bond.

As discussed in the paragraph before section 2.1, covalently-bonded corannulenes–corannulenes, and corannulene–sumanene pairs have higher energy than the sumanene–sumanene pair. In this work, many of our initial structures containing corannulenes can also transform into a GNR upon heating. For example, the initial structure with two sumanenes and two corannulenes separated by 17 a.u. can be converted into a defected GNR at 2000–2500 K as shown in figure 3(a). Note that the formed hexagons in the junctions at the early stage of the structure transformation (blue-colored in figure 3(a) at 300 K) are not energetically favorable as covalently-bonded pairs involving corannulenes. In contrast to the sumanene–sumanene pair, the pair of corannulenes prefer to form with the pentagon in the junction. These intermediate structures with higher energies could lead to more dynamic yet effective atomic rearrangements as shown in figure 3(a) at 2000 K, which is believed to promote the further structure transformation into a GNR (figure 3(a) at 2500 K).

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Figure 3(b1) describes the process of the formation of a high quality GNR in the system with corannulenes separated by 17 a.u. Similar to the case of sumanenes, the dynamics exhibit stage-like features. At the first stage the corannulene species join together by formation of pentagons (yellow-colored on the figure 3(b1) at 300 K). These bonds are relatively easier to be broken than those in hexagon connecting two sumanenes (see figure 3(b1) at 48 ps at 3500 K). The bond breaking happens at 8 ps in this case, but at 180 ps in the case of the sumanenes (see section 2.2). At the second stage, the structure consists of only two pentagons and two hexagons joined by carbon chains. At the third stage at prolonged heating the system rebuilds itself into a defected nanoribbon (figure 3(b1) at 250–270 ps) followed by the gradual edge-facilitated self-healing process. The dynamics of the defect healing process is presented in figure 3(b2), which is similar to the process of the SW defect healing illustrated in figure 2(b). The bond between the pentagon–heptagon pair of the SW defect is broken to lead the formation of a hole. Now the bond between the two yellow-colored atoms (previously connecting the heptagon pair) is at the edge of the hole, and is free to rotate (figure 3(b2) at 59.65–59.9 ps), which promotes the transformation of the pentagon–heptagon pair to the hexagon–hexagon pair (blue-colored in figure 3(b2) at 60 ps). Finally, the hole closes after two additional hexagons are formed (figure 3(b2) at 60.1 ps) facilitated by dynamic motions of carbon atoms at the edge.

The 5-8-5 defect is frequently observed in the di-vacancy configuration in graphene samples [23–26, 79–82], which can be created either by coalescence of two single vacancies or by removing two neighboring atoms as sketched in figure 4(b). Previous simulations indicate that the formation energy of a di-vacancy is of the same order as that of a single vacancy (about 8 eV) [67, 68]. As two atoms are now missing, the energy per missing atom (4 eV per atom) is much lower than for a single vacancy. Hence, di-vacancies are thermodynamically favored over single vacancies. And the 5-8-5 defect is so stable that its shape can be sustained without any structural transformation for about 90 ps at 3000 K reported by Lee et al [25, 26]. The 5-8-5 defect is observed in the GNR structures studied in this work. The 5-8-5 defect presented in figure 4(a) is from the sample initially composing of two corannulenes and two sumanenes separated by 16 a.u. (figure 4(a) initial). The sumanenes and corannulenes join together by forming hexagons (blue-colored in figure 4(a) at 300 K) while the remaining unsaturated atoms in the two sumanenes form a bond with an octagon (brown-colored). Two yellow pentagons in the 5-8-5 defect belong to the two sumanenes. During the edge reconstruction (figure 4(a) at 3000–3500 K), additional polygons are formed at the edge to stabilize the 5-8-5 defect from the perturbation by dynamic motion of atoms at the edge. The 5-8-5 defect remains stable at 3500 K during 2 ns simulation. The understanding of forming the 5-8-5 defect in the GNR can provide a useful guide to analyze the interaction and evolution among assembled carbon fragments with a di-vacancy character.

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The coalescence of a set of 5-8-5 defects leads to forming an alternating line of pairs of pentagons separated by octagons [23, 24], as representative units in a degenerate grain boundary with a zero mis-orientation angle. In our simulations with four sumanenes per unit cell as initial structure, we observed the formation of two connected 5-8-5 defects in the GNR, which is presented in figure 5. At 300 K, the coalescence of sumanenes forms three hexagons (blue-colored in figure 5 at 300 K, 5 ps). At 2500 K, the atoms 1 and 2 (yellow- and orange-colored, respectively) form a bond to make a pentagon (see figure 5 at 2500 K, 30 ps). Subsequently, atom 2 connects to atom 4 (cyan-colored) to form a hexagon (containing atoms 1, 2 and 4, see figure 5 at 3000 K, 35 ps). At the same time, atom 3 (red-colored) in blue-colored hexagon (containing atoms 2, 3 and 6) makes one remarkable motion to connect to the atom below atom 2. Thus, the blue-colored hexagon changes to the pentagon, while the adjacent pentagon turns into a hexagon. The atoms 5 (purple-colored) and 6 (green-colored) are now located at the edges of a big hole at the center (see figure 5 at 3500 K, 36.5 ps). The reconstruction of the edges of the hole leads to bonding between atoms 5 and 6, and the formation of an octagon (brown-colored in figure 5 at 3500 K, 36.75 ps). Thereafter, atoms located at the top and bottom edges rearrange themselves to form two pentagons at the bottom (yellow-colored) and another octagon (brown-colored) at the top (figure 5 at 3500 K, 100 ps). The formation of polygons at the edges is very similar to the structural evolution discussed in section 3.1 where one 5-8-5 defect is generated. Note that one pentagon (yellow-colored) belonging to one sumanene remains intact in the whole course of simulation. Eventually, this pentagon becomes a part of the newly formed 8-5-5-8 grain boundary, which is oriented along the zigzag lattice direction and divides the nanoribbon into two grains with the same orientation (see figure 5 at 3500 K, 100 ps). The 8-5-5-8 domain boundary was also observed experimentally in graphene grown on a Ni surface (figure 5 bottom right) [83].

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The most common line defects in graphene separate domains of different crystal orientations. Surfaces with hexagonal symmetry, i.e. the cubic (111) surface or (0001) surface of hexagonal metals, are often chosen to grow graphene using the chemical vapor deposition method [31, 32, 43, 84]. The different lattice misfit between metal and graphene accounts for various orientations of grains. The coalescence of two graphene grains results in grain boundaries, which are often featured by a string of polygons, such as pentagon–octagon pairs [83] and pentagon–heptagon pairs [31, 32, 84–89]. The stability, thermodynamics and electronic properties of these grain boundaries have been computed extensively [20, 90, 91]. In this work, the intermediate structure experiences severe disintegration (for example figure 2 at 230–300 ps) followed by a remarkable re-building process to form GNRs with differently oriented grains. The fusion of these grains with different orientations form assorts of pentagon–heptagon grain boundaries, which are shown in figures 6(a)–(c) along with the experimental observed image of the grain boundary (figure 6(d)). All these grain boundaries meander instead of staying straight in the sp² carbon structure network, and the defects along the boundaries are aperiodic.

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In this section, we consider the structural repairing of a giant hole in GNRs. Barreiro et al [92] simulated the process of the healing of holes in graphene. They created holes with a 1 nm radius, and placed three a-C clusters on top of the holes. The holes were completely healed after 25–30 ps at 1800 K. The formed graphene contained at least one SW defect. In this work, the focus will be on edge-facilitated self-healing of the giant hole. The initial structure consisting of sumanenes on the triangular lattice was constructed with one sumanene fragment missing at the center (see figure 7(a) initial). In the process of energy minimization through structure optimization, these sumanenes join together by creating hexagons. During the first 40 ps of heating, the carbon atoms rearrange to heal small holes. However, the giant hole, due to missing fragments, remain at the center (figure 7(a) at 40 ps). Then, the upper bridge of carbon atoms which separate the hole from the outside breaks down (figure 7(a) at 100 ps). The remaining structure is the nanoribbon with a very crooked upper edge (figure 7(a) at 110 ps). This stage is similar to the severe structure disintegration one presented in figure 2 at 230 ps, which has the least number of rings and sp² hybridized atoms. Gradually, the edge on the top straightens out (figure 7(a) at 150 ps) accompanied by structural integration to a large extent facilitated by dynamic motions of atoms in the vicinity of a giant hole and edges. The structure (after 500 ps) is a GNR of quite good quality with only two representative defects: the inverse SW (ISW) defect, and the defect made of three pentagons and three heptagons.

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The former (on the top left corner of figure 7(a) at 500 ps) composes of two pentagons (yellow-colored) with a common side and two heptagons (pink-colored) [93–95]. The ISW defect can be created when an additional carbon dimer incorporates into the graphene at the expense of local curvature of the network. Because its formation energy is high (E_f ≈ 5 eV), the concentration of the ISW defects in the flat carbon nanostructure should be negligible, unless under extreme nonequilibrium structural treatment conditions [93–95]. The process of formation of the ISW defect in this work is illustrated in figure 7(b). The vicinity of the giant hole of the GNR formed in figure 7(a) can be clearly viewed in figure 7(b) (130 ps). Yellow-colored atoms are those between two pentagons in subsequently formed ISW defects (two adatoms). These atoms are initially located at the edges of the giant hole (figure 7(b) at 130 ps). Gradual rearrangement of the edges assisted with closing the giant hole brings the yellow-colored atoms close to each other (figure 7(b) at 137.5 ps). The two yellow-colored atoms eventually bond together, participating in the formation of pentagon (yellow-colored ring in figure 7(b) at 138.4 ps). Atom 1, which is adjacent to the yellow-colored atom, joins with atom 2 which belongs to one of the chains, to form the second pentagon in the ISW defect. Meanwhile atom 3 bonds with atom 4 to form a heptagon (pink-colored ring in figure 7(b) at 140 ps). So we have two edge-sharing pentagons (yellow-colored) bonded with one heptagon (pink-colored in figure 7(b) at 141.5 ps). Then atoms 5 and 6, belonging to the two different carbon outer 'tails', join together to form an octagon (brown-colored) adjacent to the pentagon pair (figure 7(b) at 142.5 ps). This octagon exists for the next 50 ps until it is converted into one heptagon (pink-colored) through local edge-facilitated structure reconstruction to bond atoms 5 and 7. While atoms 8 and 10, belonging to the outer chain, join the heptagon to form an outer hexagon (also containing atoms 5, 6 and 9). The subsequent formation of polygons from other carbon atoms and chains are also benefited from the dynamic atomic motions at the top edge (see figure 7(b) at 225 ps). Interestingly, the ISW is connected to one adjacent conventional SW defect consisting of a pentagon pair (yellow-colored) separated by a bonded heptagon pair (pink-colored). The ISW defect experiences tremendous structural deformation, which then generates a large strain field in its vicinity to lead the highly curved local structure (see the insert in figure 7(b) at 225 ps). This significant stress promotes the healing of the SW defect, i.e. two heptagons and two pentagons are converted into four hexagons (blue-colored in figure 7(b) at 500 ps), to release the stored large strain energy. This self-healing of the SW defect is achieved by rotating the bond between two heptagons facilitated by the stress field [72, 73].

The latter consisting of three pentagons and three heptagons can be observed in the structure presented in figure 7(a) at 500 ps. Interestingly, the same type of defect was reported recently by Meyer et al [96] on the characterization of graphene membranes with aberration-corrected, monochromated transmission electron microscopy. The defects include multiple five- and seven-membered carbon rings also presented at bottom-right part in figure 7(a). The formation of multiple pentagon–heptagon combinations could be one effective alternative option instead of introducing dislocations and disclinations. In this work, atoms near edges play an important role in the defective structure self-organization process to form this kind of collection of pentagon–heptagon pairs, which could be relevant to advance the understanding of the formation and transformation of sp² carbon network.