Stone-Wales Transformation Research Articles

Atomic-scale mutual integrals for mixed-mode fracture: Abnormal fracture toughness of grain boundaries in graphene

In this study, we developed a computational scheme based on the atomic-level J-based mutual integral (or two-state conservation integral) to analyze the mixed-mode fracture along grain boundaries (GB) in polycrystalline solids. Discrete atomic information, obtained from molecular dynamics simulation of crack propagation along GBs in polycrystalline solids, is incorporated with asymptotic singular fields near an interfacial crack tip between dissimilar materials in the atomic-level J-based mutual integral, to extract the individual stress intensity factors of modes I and II. As a model problem, crack propagation along GBs in polycrystalline graphene, an ordered array of non-hexagonal defects, is analyzed. In the model, GBs are considered to be the most favorable paths for crack propagation, as the carbon atoms along the GBs experience less-ordered interatomic interactions than those in pristine graphene. When a mixed-mode loading is applied to a crack running along a graphene GB, as the mode mixity increases, the fracture toughness of GBs in graphene gradually increases. However, if the mode mixity is greater than 8°, the fracture toughness gradually decreases, which can be considered a unique characteristic of GBs in graphene. This abnormally-low fracture toughness of GBs in graphene for high mode mixity, may be interpreted as the competition between bond-rotation and bond-breaking mechanisms of carbon atoms, in conjunction with the Stone–Wales transformation and nonagon structures at the crack tip along GBs in graphene.

Влияние адсорбции водорода на трансформацию Стоуна- Уэльса в углеродных нанотрубках малого диаметра

AbstractThe effect of hydrogenation of (4, 0) and (3, 0) carbon nanotubes on the Stone–Wales transformation is studied in the framework of the nonorthogonal tight-binding model. It is shown that the atomic hydrogen adsorption can lead to both a decrease and an increase in the barriers for the direct and inverse transformations depending on the orientation of a rotating C–C bond with respect to the nanotube axis. The characteristic times of formation and annealing the Stone–Wales defects have been estimated. The Young’s moduli have been calculated.

Theoretical Insight into Sc2C76: Carbide Clusterfullerene Sc2C2@C74 versus Dimetallofullerene Sc2@C76.

In terms of density functional theory in combination with a statistical thermodynamic method, we have investigated the Sc2C76 species including dimetallofullerenes Sc2@C76 and carbide clusterfullerenes Sc2C2@C74. Two dimetallofullerenes, Sc2@Cs(17490)-C76 and Sc2@Td(19151)-C76, possess the lowest relative energies but exhibit poor thermodynamic stability within the fullerene-formation region (500-3000 K). In contrast, four carbide clusterfullerene isomers, Sc2C2@D3h(14246)-C74, Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)-C74, and Sc2C2@C1(13334)-C74, have excellent thermodynamic stability when considering the temperature effect. The Sc2C2@D3h(14246)-C74 isomer, which satisfies the isolated-pentagon rule (IPR), was characterized by its crystallographic structure; however, the other three non-IPR structures with two pairs of pentagon adjacencies are predicted for the first time. In particular, Sc2C2@C2(13333)-C74 and Sc2C2@C1(13334)-C74 are linked by a single Stone-Wales transformation. Meanwhile, bonding critical points and Mayer bond orders in the four isomers were analyzed to disclose the unique interactions between the inner clusters and cages. Additionally, the structural characteristics, 13C and 45Sc NMR chemical shifts, and IR spectra of the four stable isomers are introduced to assist experimental identification and characterization in the future.

A Direct Observation of the Fine Aromatic Clusters and Molecular Structures of Biochars.

Biochar is a promising carbon material to improve soil quality and relieve global warming by adding it into soil. Though biochar has been used for millennia as a soil ingredient, fundamental studies on the structure of biochar have only recently attracted great interest, and molecular-level structures are being pursued. In this study, by applying solvent exfoliation, high-resolution transmission electron microscopy with Cs-correction and quadrupole time-of-flight mass spectroscopy, we report, for the first time, an atomic-level observation of the fine aromatic cluster and molecular structure of the exfoliated biochars. The observed aromatic clusters are generally smaller than 5 nm and decorate the graphene-like aggregates at different depths. The Stone-Wales transformation in the dispersed biochars was observed, which is critical to form carbon nanotubes, fullerenes, and other carbon nanostructures in the natural environment. In addition, the C-C bond length decreases as the pyrolysis temperature increases from 500 to 700 °C, indicating that aliphatic carbon transforms into aromatic carbon. The quaternary structure of biochar, including heterogeneous phases, graphene-like aggregates, nanosized aromatic clusters, and atomic arrangements, is conceptualized to enhance our knowledge of the biochar structure, which greatly aids in understanding the novel functions of biochar and offers a molecular guide for potential applications of biochar.

(Invited) Molecular-Scale Evidence Provides New Insights into Fullerene Formation Mechanism

It has been proposed that the fullerene formation mechanism involves either a top-down or bottom-up pathway. Despite of different starting points, either mechanism approved that particular fullerenes or metallofullerenes are formed through a consecutive stepwise process involving Stone-Wales transformations (SWTs) and C2 insertion or extrusion. However, the formation pathway has been seldom defined at the molecular level due to the missing link fullerenes. Herein, we present a series of previously missing species, including Sc2O@C2v(24107)-C78 and Sc2O@D3h(24109)-C78, Sc2O@C2(7892)-C70 and Sc2C2@D3h(14246)-C74. Each of them can be converted to other isomers or larger or smaller species via a simple conversion route involving Stone-Wales (SW) transformation and C2 insertion or extrusion. Thus, this study might provide molecular structural evidence for the less confirmed fullerene formation mechanism.

Sc2C2@D3h(14246)-C74: A Missing Piece of the Clusterfullerene Puzzle.

Clusterfullerenes with variable carbon cages have been extensively studied in recent years. However, despite all these efforts, C74 cage-based clusterfullerene remains a missing piece of the puzzle. Herein, we show that single-crystal X-ray crystallographic analysis unambiguously assigns the previously reported dimetallofullerene Sc2@C76 to a novel carbide clusterfullerene, Sc2C2@D3h(14246)-C74, the first experimentally proven clusterfullerene with a C74 cage. In addition, Sc2C2@D3h(14246)-C74 was charaterized by mass spectrometry, ultraviolet-visible-near-infrared absorption spectroscopy, 45Sc nuclear magnetic resonance, and cyclic voltammetry. Comparative studies of the motion of the carbide cluster in Sc2C2@D3h(14246)-C74 and Sc2C2@C2n (n = 40-44) revealed that a combination of factors, involving both the shape and size of the cage, is crucial in dictating the cluster motion. Moreover, structural studies of D3h(14246)-C74 revealed that it can be easily converted to Cs(10528)-C72 and Td(19151)-C76 cages via C2 desertion/insertion and Stone-Wales transformation. This suggests that D3h(14246)-C74 might play an important role in the growth pathway of clusterfullerenes.

Theoretical Studies of the Stone-Wales Defect in C36 Fullerene Embedded inside Zigzag Carbon Nanotube

We apply density functional theory at PBE/6-311G(d) level as well as nonorthogonal tight-binding model to study the Stone-Wales transformation in C36 fullerene embedded inside the (14,0) zigzag carbon nanotube. We optimize geometries of two different isomers with the D2d and the D6h symmetries and the transition state dividing them. The mechanism of Stone-Wales transformation from D2d to D6h symmetry for the encapsulated C36 is calculated to be the same as for the isolated one. It is found that the outer carbon wall significantly stabilizes the D6h isomer. However, carbon nanotube reduces the activation barrier of Stone-Wales rearrangement by 0.4 eV compared with the corresponding value for the isolated C36.

Isomeric Sc2O@C78 Related by a Single-Step Stone-Wales Transformation: Key Links in an Unprecedented Fullerene Formation Pathway.

It has been proposed that the fullerene formation mechanism involves either a top-down or bottom-up pathway. Despite different starting points, both mechanisms approve that particular fullerenes or metallofullerenes are formed through a consecutive stepwise process involving Stone-Wales transformations (SWTs) and C2 losses or additions. However, the formation pathway has seldomly been defined at the atomic level due to the missing-link fullerenes. Herein, we present the isolation and crystallographic characterization of two isomeric clusterfullerenes Sc2O@C2v(3)-C78 and Sc2O@D3h(5)-C78, which are closely related via a single-step Stone-Wales (SW) transformation. More importantly, these novel Sc2O@C78 isomers represent the key links in a well-defined formation pathway for the majority of solvent-extractable clusterfullerenes Sc2O@C2n (n = 38-41), providing molecular structural evidence for the less confirmed fullerene formation mechanism. Furthermore, DFT calculations reveal a SWT with a notably low activation barrier for these Sc2O@C78 isomers, which may rationalize the established fullerene formation pathway. Additional characterizations demonstrate that these Sc2O@C78 isomers feature different energy bandgaps and electrochemical behaviors, indicating the impact of SW defects on the energetic and electrochemical characteristics of metallofullerenes.

The Stone-Wales transformation: from fullerenes to graphite, from radiation damage to heat capacity.

The Stone-Wales (SW) transformation, or carbon-bond rotation, has been fundamental to understanding fullerene growth and stability, and ab initio calculations show it to be a high-energy process. The nature and topology of the fullerene energy landscape shows how the Ih-C60 must be the final product, if SW transformations are fast enough, and various mechanisms for their catalysis have been proposed. We review SW transformations in fullerenes and then discuss the analogous transformation in graphite, where they form the Dienes defect, originally posited to be a transition state in the direct exchange of a bonded atom pair. On the basis of density functional theory calculations in the local density approximation, we propose that non-equilibrium concentrations of the Dienes defect arising from displacing radiation are rapidly healed by point defects and that equilibrium concentrations of Dienes defects are responsible for the divergent ultra-high-temperature heat capacity of graphite.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.

Isomerization of sp2‐hybridized carbon nanomaterials: structural transformation and topological defects of fullerene, carbon nanotube, and graphene

The structural transformation of various carbon nanomaterials, such as fullerene, carbon nanotube (CNT), and graphene, has been extensively studied both experimentally and theoretically. It was broadly recognized that the isomerization of the sp2‐hybridized carbon network through the generalized Stone–Wales transformation (GSWT), which is equivalent to a CC bond's in‐plane rotation, is the key mechanism facilitating most structural revolutions in carbon materials. The GSWT process also plays a crucial role in the shape change, defect healing and the growth in these carbon materials and may greatly affect their mechanical, chemical, and electronic performances. In this review, we summarize the previous studies on the GSWT and topological defects in the sp2 carbon network as well as the consequent results of sp2‐hybridized carbon materials’ isomerization, including structural shrinkage of the giant fullerenes and CNTs at high temperature, plastic deformation of CNTs, coalescence of the fullerenes and carbon peapods, topological defects evolution under high energetic irradiation, and healing of the defects during the chemical vapor deposition growth of CNT and graphene. This review provides a clear picture of the isomerization of the sp2‐hybridized carbon materials, from single step process until the large‐scale structural transformation, and many examples for the readers to get into the topic deeply step by step. WIREs Comput Mol Sci 2017, 7:e1283. doi: 10.1002/wcms.1283This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Structure and Mechanism > Computational Materials Science

Stabilization of a Chlorinated (#4348)C66:C2v Cage by Encapsulating Monometal Species: Coordination between Metal and Double Hexagon-Condensed Pentalenes.

Carbon cages in endohedral and exohedral fullerene derivatives are usually different. A recent report suggested that chlorofullerene C66Cl10:Cs and endohedral metallofullerene (EMF) Sc2@C66 shared the same cage (#4348)C66:C2v, while it was denied by the definitive characterization of Sc2@C66, which actually possesses the (#4059)C66:C2v isomer. Here, we show that a (#4348)C66:C2v cage with a double hexagon-condensed pentalene (DHCP) moiety, which was captured by exohedral chlorination, is also capable of being stabilized by encapsulating tri- or divalent monometal (M) species. On the basis of density functional theory calculations combined with statistical mechanics analyses, (#4348)C66:C2v-based mono-EMFs M@C2v(4348)-C66 (M = Tb, La, Y, and Yb) were demonstrated to be the most stable and predominant isomers at the fullerene formation temperature region, while another chlorinated cage (#4169)C66:Cs, featured with triple sequentially fused pentagon (TSFP) moiety, is less favorable to be obtained in the form of EMFs, although these two cages can be interconverted by a simple Stone-Wales transformation. The superiority of M@C2v(4348)-C66 over M@Cs(4169)-C66 comes from the stronger interaction of M-DHCP over that of M-TSFP in both ionic and covalent bonding aspects. In addition, size-selective complexation of host [n]cycloparaphenylene ([n]CPP) and Tb@C2v(4348)-C66 was simulated, showing that [10]CPP exhibits the best affinity toward Tb@C66, which provides a new opportunity for isolation and characterization of C66-based mono-EMFs.

“W-X-M” transformations in isomerization of B39− borospherenes

The Stone-Wales transformation plays an important role in the isomerization of fullerenes and graphenic systems. The continuous conversions between neighboring six- and seven-membered rings in the borospherene (all-boron fullerene) B40 had been discovered (Martínez-Guajardo et al. Sci. Rep. 5, 11287 (2015)). In the first axially chiral borospherenes C3 B39− and C2 B39−, we identify three active boron atoms which are located at the center of three alternative sites involving five boron atoms denoted as “W”, “X”, and “M”, respectively. The concerted movements of these active boron atoms and their close neighbors between neighboring six- and seven-membered rings define the “W-X-M” transformation of borospherenes. Extensive first-principles molecular dynamics simulations and quadratic synchronous transit transition-state searches indicate that, via three transition states (TS1, TS2, and TS3) and two intermediate species (M1 and M2), the three-step “W-X-M” transformations convert the C3 B39− global minimum into its C2 isomer at room temperature (300 K) and vice versa. The maximum barriers are only 3.89 kcal/mol from C3 to C2 B39− and 2.1 kcal/mol from C2 to C3 B39−, rendering dynamic fluxionalities to these borospherenes. Therefore, the “W-X-M” transformation plays an important role in the borospherenes and borospherene-based nanostructures.

Diamond Nanothread as a New Reinforcement for Nanocomposites

This work explores the application of a new 1D carbon nanomaterial, the diamond nanothread (DNT), as a reinforcement for nanocomposites. Owing to the existence of Stone–Wales transformation defects, the DNT intrinsically possesses irregular surfaces, which is expected to enhance the noncovalent interfacial load transfer. Through a series of in silico pull‐out studies of the DNT in polyethylene (PE) matrix, it is found that the load transfer between DNT and PE matrix is dominated by the noncovalent interactions, in particular the van der Waals interactions. Although the hydrogenated surface of the DNT reduces the strength of the van der Waals interactions at the interface, the irregular surface of the DNT can compensate for the weak bonds. These factors lead to an interfacial shear strength of the DNT/PE interface comparable with that of the carbon nanotube/PE interface. The results show that the DNT/PE interfacial shear strength remains high even as the number of Stone–Wales transformation defects decreases. It can be enhanced further by increasing the PE density or introduction of functional groups to the DNT, both of which greatly increase the noncovalent interactions.

Reaction kinetics of bond rotations in graphene

The formation and healing processes of the fundamental topological defect in graphitic materials, the Stone-Wales (SW) defect, are brought into a chemical context by considering the rotation of a carbon–carbon bond as chemical reaction. We investigate the rates and mechanisms of these SW transformations in graphene at the atomic scale using transmission electron microscopy. We develop a statistical atomic kinetics formalism, using direct observations obtained under different conditions to determine key kinetic parameters of the reactions. Based on the obtained statistics we quantify thermally and irradiation induced routes, identifying a thermal process of healing with an activation energy consistent with predicted adatom catalysed mechanisms. We discover exceptionally high rates for irradiation induced SW healing, incompatible with the previously assumed mechanism of direct knock-on damage and indicating the presence of an efficient nonadiabatic coupling healing mechanism involving beam induced electronic excitations of the SW defect.

Single Step Stone-Wales Transformation Linking Two Thermodynamically Stable Sc2O@C78 Isomers.

Among the very recently reported dimetallic oxide fullerenes Sc2O@C2n (n = 35-47), a representative Sc2O@C78 still lacks of further characterizations. Herein, a systematical investigation on Sc2O@C78 has been performed by density functional theory combined with statistical thermodynamic studies. Two isolated pentagon rule (IPR) satisfying isomers, Sc2O@D3h(24109)-C78 and Sc2O@C2v(24107)-C78, are disclosed to possess prominent thermodynamic stabilities at the temperature region of fullerene formation. Significantly, these two structures are related by a single Stone-Wales transformation. Moreover, bonding critical points, bond orders, and delocalization indices have been analyzed to uncover covalent interactions in both isomers. In addition, (13)C NMR spectra and UV-vis-NIR adsorptions of the two stable structures are introduced to assist experimental identification and characterization in the future.

Sc3N@Cs(39715)–C82: a missing isomer linked to Sc3N@C2v(39718)–C82 by a single step Stone–Wales transformation

Density functional theory combined with statistical mechanics calculations indicate that Sc3N@C2v(39718)–C82 and Sc3N@Cs(39715)–C82 linked by a single Stone–Wales transformation can be obtained at the fullerene formation temperature region.

From brittle to ductile: a structure dependent ductility of diamond nanothread.

As a potential building block for the next generation of devices/multifunctional materials that are spreading in almost every technology sector, one-dimensional (1D) carbon nanomaterial has received intensive research interests. Recently, a new ultra-thin diamond nanothread (DNT) has joined this palette, which is a 1D structure with poly-benzene sections connected by Stone-Wales (SW) transformation defects. Using large-scale molecular dynamics simulations, we found that this sp(3) bonded DNT can transition from brittle to ductile behaviour by varying the length of the poly-benzene sections, suggesting that DNT possesses entirely different mechanical responses than other 1D carbon allotropes. Analogously, the SW defects behave like a grain boundary that interrupts the consistency of the poly-benzene sections. For a DNT with a fixed length, the yield strength fluctuates in the vicinity of a certain value and is independent of the "grain size". On the other hand, both yield strength and yield strain show a clear dependence on the total length of DNT, which is due to the fact that the failure of the DNT is dominated by the SW defects. Its highly tunable ductility together with its ultra-light density and high Young's modulus makes diamond nanothread ideal for the creation of extremely strong three-dimensional nano-architectures.

Molecular dynamics study of the tensile mechanical properties of polycrystalline graphene

Grain boundaries (GBs) are known to have an important influence on material properties, so understanding how GBs in graphene change its physical properties is important both scientifically and technologically. In this paper, we perform a series of molecular dynamics simulations to investigate the energies, mechanical properties and fracture process of 29 graphene GBs (symmetric and nonsymmetric) under tensile strains. With different arrangements of the pentagonal and heptagonal rings, the misorientation angle () ranges from 3.5 to 27.8. The GBs defects in graphene can produce a pre-strain that will lead to an increase of the energy of GBs. We study the atomic energy distribution around GBs and define a new parameter: single defect energy (Esingle) to calculate the average energy per GBs defect. It is found that Esingle shows a clear linear relation between and defect density (), because pre-strain filed can be cancelled out locally with the increase of defect density. And this pre-stain can reduce the strength of the C-C bond contained in GBs defects. Hence, with very few exceptions, mechanical failure always starts from the defective region. Furthermore, the energy of GBs can be used to reflect the strength of GBs indirectly. The simulated results show that the tensile strength of GBs is linearly related to the highest atomic energy (Emax), and it also depends on Esingle monotonically. Owing to the pre-strain, load distribution along GBs is uneven. Because some bonds are stretched while others are compressed, that is, the real number of bearing carbon bonds is less than the nominal number. Therefore, at the beginning of tension, the Young's modulus of polycrystalline graphene is significantly lower than that of the monocrystal one. But with the increase of strain, it becomes comparable to that of the monocrystal graphene at sufficiently large strain. The results of fracture process indicate that formation and propagation of crack are both dependent on strength GBs. For low GB strength, the fracture mechanism is transgranular fracture in the form of direct fracture of C-C bonds. When stress reaches a critical value, the weakest C-C bonds in GBs will breakdown and form a fracture site. Because of the uneven bearing condition, the C-C bonds in front of the crack possess considerable residual strength and could prevent crack from propagating. As a result, many other fracture sites in the GBs defect can be produced with the increase of strain, and finally, these sites emerge gradually along GBs and form a sawtooth crack. In contrast, the fracture process of high strength GBs is always accompanied with the variations of Stone-Wales (S-W) transformation and direct fracture of C-C bonds. Once the fracture site forms, the crack will propagate rapidly predominantly along armchair or zigzag direction and finally could cross GBs, this process can be called intergranular fracture. Our present work provides fundamental guidance for understanding how defects affect the mechanical behaviour, which is important for further research and application of graphene devices.

Effect of hydrogen adsorption on the formation and annealing of Stone–Wales defects in graphene

The heights of energy barriers preventing the formation and annealing of Stone–Wales defects in graphene with a hydrogen atom adsorbed on the defect or in its immediate vicinity have been calculated using the atomistic computer simulation. It has been shown that, in the presence of hydrogen, both barriers are significantly lower than those in the absence of hydrogen. Based on the analysis of the potential energy surface, the frequency factors have been calculated for two different paths of the Stone–Wales transformation, and the temperature dependences of the corresponding annealing times of the defects have been found. The results obtained have been compared with the first-principles calculations and molecular dynamics data.

Sm@C1(153491)-C94: A missing isomer from Sm@C94 mono-metallofullerenes

The Sm-containing endohedral metallofullerene (EMF) Sm@C94 has been investigated by quantum chemical and statistical thermodynamic methods. Sm@C1(153491)-C94 and Sm@C3v(153493)-C94 which both satisfy the isolated-pentagon rule (IPR) are exposed to possess considerable thermodynamic stabilities within the fullerene-formation temperature region (500⿿3000K). Sm@C3v(153493)-C94 has been indeed determined experimentally, and a novel structure, Sm@C1(153491)-C94, is reported for the first time. These two isomers are related by a single Stone⿿Wales transformation. Meanwhile, frontier molecular orbital, natural electron configuration, and Mayer bond order analyses were employed to uncover their electronic properties. In addition, their optical spectra were simulated to support experimental identification and characterization.