Pentagon-heptagon Defects Research Articles

Strength criterion of graphene GBs combining discrete bond strength and varied bond stretch

The strength criterion of graphene grain boundaries (GBs) under complex stress states plays an important role in guiding the design of high-performance graphene-related materials and devices under severe mechanical environments like ultrastrong structural materials or flexible electronics. However, finding a unified strength criterion that can adapt to different GB angles and loading states is still a challenge. In this work, we proposed a general method to construct the strength criterion of graphene GBs that includes the atomic details of defect. Firstly, systematic molecular dynamics (MD) simulations were carried out to explore the fracture behaviors of graphene GBs with different GB angles and loading states. Then, bond strength of heptagon ring σ t h R was obtained by projecting the applied stress field to the fractured bond direction, which gives the same value for the same type of C-C bond of same GB angle under different loading states. Besides, to further unify the bond strength of different GB angles, the residual stress caused by other pentagon–heptagon defects was considered by using the disclination dipole theory, in which the intrinsic bond strength σ t h 0 for different GB angles collapses to the same value. With this scenario, the strength criterion of graphene GBs is presented as the bond stretch stress generated by external load exceeds any bond strength of the hexagon–heptagon defect. Furthermore, a unified bond strength is found, linearly decreasing with the equilibrium bond length, which can further be applied to the strength criterion of other defective structures like two types of SW defects (without analytical solution of residual stress) and even pristine graphene. The present results provide a comprehensive understanding of the failure of graphene by considering the balance of bond strength of defective structure and bond stretch stress generated by external load, which may pave the way to construct the atomic structure based strength criterion of other two-dimensional materials.

Activation of Topological Defects Induces a Brittle-to-Ductile Transition in Epithelial Monolayers.

Epithelial monolayers are subjected to various mechanical forces, such as stretching, shearing, and compression. Thus, its mechanical response to external loadings is essential for its biological functions. However, the mechanism of the fracture failure of the epithelial monolayer remains poorly understood. Here, by introducing a new type of topological transition, i.e., detach transition or T4 transition, we develop a modified cellular vertex model to investigate the rupture of the cell monolayer. Interestingly, we find a brittle-to-ductile transition in epithelial monolayers, which is controlled by the mechanical properties of single cells and cell-cell contacts. We reveal that the external loadings can activate cell rearrangement in ductile cell monolayers. The plastic deformation results from the nucleation and propagation of "pentagon-heptagon defects" in analogy with the topological defects commonly seen in 2D materials. By using a simplified four-cell model, we further demonstrate that the brittle-to-ductile transition is induced by the competition between cell rearrangement and cell detachment. Our work provides a new theoretical framework to study the rupture of living tissues and may have important implications for many other biological processes, such as wound healing and tissue morphogenesis.

Reduce and concentrate graphene quantum dot size via scissors: vacancy, pentagon-heptagon and interstitial defects in graphite by gamma rays

Graphene quantum dots (GQDs) with ultrafine particle size and centralized distribution have advantages of small size, narrow size distribution and large specific surface area, which make it be better applied in bioimaging, drug delivery and so on. In our research, we used graphite irradiated by γ-rays to successfully prepare GQDs with ultrafine particle size, narrow size distribution and high quantum yields through solvothermal method. Vacancy defects, pentagon–heptagon defects and interstitial defects were introduced to graphite structure after irradiation, which caused the abundance and concentrated distribution of defects. The defects generated by irradiation could damage the lattice structure of graphite to make it easy for introduction of C–O–C inside graphite sheets. The oxygen-containing functional groups in graphene oxide (GO) increased and centrally distributed after irradiation in graphite, especially for C–O–C group, which were beneficial for cutting of GO and grafting of functional groups in GQDs. Therefore, average size of GQDs was successfully reduced to 1.43 nm and concentrated to 0.6–2.4 nm. After irradiation in graphite, the content of carbonyl and C–N in GQDs had a promotion, which suppressed non-radiative recombination and upgraded the quantum yields to 13.9%.

POOL BOILING ON DEFECTIVE GRAPHENE-COATED SURFACES: A MOLECULAR DYNAMICS STUDY

Proven to have superior mechanical and thermal properties, graphene has the potential to enhance the boiling heat transfer performance as a coating material. As defective graphene is inevitably produced together with pristine graphene, however, it is more practical to examine the impact of defective graphene. In the current work, a molecular dynamics simulation was adopted to investigate water pool boiling on copper substrate coated with five types of stable defective graphene monolayer. The results show that most of the cases coated with defective graphene have higher initial heat flux and reach equilibrium faster than the pristine graphene−coated case under the isothermal heating condition. Nevertheless, the percentage of pentagon-heptagon defect in the graphene unit cell does not have a clear correlation with its heat transfer performance. In particular, all the graphene coatings enhance the critical heat flux (CHF) value for water boiling by nearly two orders of magnitude, regardless of defectiveness. This is of practical significance to enable graphene thermal management applications.

Enhanced Bonding of Pentagon–Heptagon Defects in Graphene to Metal Surfaces: Insights from the Adsorption of Azulene and Naphthalene to Pt(111)

The performance of graphene-based (opto)electronic devices depends critically on the graphene/metal interface formed at the metal contacts. We show here that the interface properties may be control...

Molecular Dynamics of Chirality Definable Growth of Single-Walled Carbon Nanotubes.

In order to achieve the chirality-specific growth of single-walled carbon nanotubes (SWCNTs), it is crucial to understand the growth mechanism. Even though many molecular dynamics (MD) simulations have been employed to analyze the SWCNT growth mechanism, it has been difficult to discuss the chirality determining kinetics because of the defects remaining on the SWCNTs grown in simulations. In this study, we demonstrate MD simulations of defect-free SWCNTs, that is, chirality definable SWCNTs, under the optimized carbon supply rate and temperature. The chiralities of the SWCNTs were assigned as (14,1), (15,2), and (9,0), indicating the preference of near-zigzag and pure-zigzag SWCNTs. The SWCNTs contained at least one complete row of defect-free walls consisting of only hexagons. The near-zigzag SWCNTs grew via a kink-running process, in which bond formation between a carbon atom at a kink and a neighboring carbon chain led to formation of a hexagon with a new kink at the SWCNT edge. Defects including pentagons and heptagons were sometimes formed but effectively healed into hexagons on metal surfaces. The pure-zigzag SWCNTs grew by the kink-running and the hexagon nucleation processes. In addition, chirality change events along SWCNTs with incorporation of pentagon-heptagon pair defects were observed in the MD simulations. Here, pentagons and heptagons were frequently observed as adjacent pairs, resulting in ( n, m) chirality changes by (±1,0), (0,±1), (1,-1), or (-1,1).

The affection on the nature of percolation by concentration of pentagon–heptagon defects in graphene lattice

In this paper the percolation behavior with a specific concentration of the defects was discussed on the two-dimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice.

Unraveling the influence of grain boundaries on the mechanical properties of polycrystalline carbon nanotubes

The ability to produce homogeneous defect-free carbon nanotubes (CNTs) represents a major challenge in terms of utility and cost. Specifically, the existence of grain boundaries (GBs) are ubiquitous in large diameter CNTs obtained by various large-scale growth methods and their effects on the mechanical properties of CNTs are not fully explored. Understanding the influence of the grain size and the GB orientation upon the mechanical behavior of CNTs is crucial for their functional and structural applications. The significance and novelty of the current work lies in its ability to establish the mechanical properties and the fracture behavior of CNTs containing grain boundaries of varied size, orientation and structure to an applied uniaxial load using comprehensive molecular dynamics simulations. A specially developed program, using Voronoi tessellation method and Delaunay triangulation, was implemented to generate the atomistic descriptions of the considered polycrystalline CNTs with a variety of GB morphology. Our results reveal that the mechanical performance of CNTs is significantly affected by the orientations of the GBs, diameter and temperature. In terms of the fracture strength, the resulting failure patterns indicate that the polycrystalline CNTs fail in a brittle fashion and that pentagon-heptagon defects along the GBs serve as crack nucleation sites.

Mechanical properties of graphene grain boundary and hexagonal boron nitride lateral heterostructure with controlled domain size

In this paper, the mechanical properties of in-plane heterostructure with alternating stripes of graphene grain boundary (GB) and hexagonal boron nitride (h-BN) are investigated using classical Molecular Dynamics method. The graphene GB contains an array of pentagon-heptagon (5–7) defects, and has good interfacial continuity with the lateral BN domain. By studying the dynamic failure process of heterostructure with varying hybridization intervals and GB tilt angles, two different local failure types are noticed. Coupled effects of h-BN hybridization and GB tilt angle on the tensile strength of heterostructure are revealed. For heterostructure with graphene GBs of evenly spaced 5–7 defects, the tensile strength is insensitive to the h-BN hybridization and increases anomalously with the defect density. For heterostructure with graphene GB of unevenly spaced 5–7 defects, lateral h-BN hybridization enhanced the tensile strength of the heterostructure. Such strength enhancement effect is contributed to the bond length mismatch between graphene and h-BN, and deteriorates with the increase of hybridization interval. Our results give helpful insight into the strength characteristics of hybrid two-dimensional nanomaterials based electronic and optical devices.

Changing the chirality of single-wall carbon nanotubes during epitaxial growth : A density functional theory study

The energetic of the change in the chirality of single-wall carbon nanotubes (SWCNTs)during epitaxial growth from (n, m) to (n±Δ, mΔ)(Δ=1, 2) was investigated by density functional theory calculations. The calculated energies for changing the chirality of different SWCNTs show a nearly linear decrease with decreasing tube diameter. In the case ofΔ=1, more energy input is needed for near armchair (nAC) SWCNTs to change their chiralities than those for near zigzag (nZZ) SWCNTs with comparable diameters, due to the larger formation energies of pentagon-heptagon defects (5,7-defects) introduced in the nAC-SWCNTs. These larger formation energies for the nAC-SWCNTs come from the larger angles between the orientation of a 5,7-defect and the tube axis than those for nZZ-SWCNTs. The topological connection oftwo adjacent 5,7-defects, which is indispensable for changing the chirality during growth in the case of Δ=2, is found to be energetically most stable. The energies needed to change chirality in the case of Δ=2 are calculated to be less than twice those in the case of Δ=1 for SWCNTs with comparable diameters. These results may help us understand the change in chirality during the epitaxial growth of SWCNTs and guide the future synthesis of SWCNTs with a single-chirality .

Exploring pentagon-heptagon pair defects in the triangular graphene quantum dots: A computational study

We have applied density functional calculations to investigate Stone Wales (SW) and carbon ad-dimer (CD) defect formation in triangular graphene quantum dots (GQDs). According to our results, defect formation energies depend on the positions of SW defects, such that the rotation of the CC bond located near the vertex of triangular GQD is easier than the rotation of other CC bonds. Therefore, the multiply defective GQDs with isolated SW defect sites are the most favorable while the formation of pentalene like structures in the connected SW defect sites costs larger formation energies. Introducing of carbon dimer defects on a triangular GQD induces a curvature at the defective sites, which leads to a more complex defect configuration with cone-like structure in the CD defective GQD with three defective sites. Then, formation energies for CD defective GQDs are higher than those for SW defective ones. The electrophilicity values calculated for SW and CD defective GQDs are greater than those for pristine GQDs. Moreover, perturbation of strong sp2 bonding network of graphitic carbons on the GQD, leading to the formation of more localized CC bonds, results in further electron deficiency of multiply SW and CD defective GQDs with increasing of electrophilicity values.

Anomalous mechanical characteristics of graphene with tilt grain boundaries tuned by hydrogenation

Grain boundaries (GBs) as typical defective graphene structure have significant influence on its mechanical properties. The fracture strength of hydrogenated graphene with tilt GBs composed of pentagon–heptagon defects are systematically investigated using classical Molecular Dynamics (MD) method. Anomalous mechanical characteristics are revealed for graphene with hydrogenation either on or near the GBs. For graphene sheets with hydrogenation on tilt GBs under perpendicular pulling, the strength of hydrogenated GBs with large tilt angle is anomalously stronger than low-angle tilt boundary having fewer defects because of the interaction between polar stress fields of hydrogenated pentagon–heptagon defects. For graphene with hydrogenation near the GBs, the interaction between GBs and hydrogenated domains at different distance intervals is investigated. The strength is found to be governed by the peak normal stress in hydrogenated domain, and an exponential relationship between the normal strength and distance interval is revealed as a result of the stress field overlap between GB and hydrogenation interface. Our results gain meaningful insight into the effects of hydrogenation on the strength of graphene with tilt GBs, and provide guidelines for designing high-quality hydrogenated graphene-based nanodevices.

Migrations of pentagon-heptagon defects in hexagonal boron nitride monolayer: the first-principles study.

The first-principles calculations are employed to study the migrations of pentagon-heptagon (5-7) defects in hexagonal boron nitride monolayer (h-BN). A type of grain boundaries, consisted of 5-7 defects, is constructed on the basis of experimental observations. With the absorption of a pair of atoms, one 5-7 defect in the grain boundary migrates apart by one unit cell and afterward migrates again through the bond rotation. It is also found that the two migrations could be replaced by one single step when the pair of absorbed atoms is located at another specific site in the same heptagon. Energy barriers and reaction paths for the migrations of 5-7 defects in h-BN by the bond rotation are theoretically investigated by the standard nudged elastic band method and the generalized solid-state nudged elastic band method. To elucidate the difference between the bond rotation process of the 5-7 defects with N-N bonds and those with B-B bonds, a couple of typical 21.7° grain boundaries with either N-N or B-B bonds are investigated. It is shown that the energy barrier of the migration of defects with N-N bonds is lower than that with B-B bonds in this type of grain boundaries.

G0100205 格子力学モデルを用いたカーボンナノチューブの5-7欠陥対の相互作用に関する検討

Stone-Wales defects which often exist in carbon nanotubes (CNTs) and graphene sheets (GSs) can be broke down into pentagon-heptagon (5-7) defect pairs. Using the lattice mechanical model (Peierls-Nabarro model) which considering the effect of periodicity of defects, we will analyze the interaction of 5-7 defect pairs in CNTs. Compare the computational results in this work with the interaction between dislocations according to dislocation theory, and discuss the dependence of radials of CNTs in details. The results show that we can consider 5-7 defect pair as a dislocation and use dislocation theory to solve the problem of interaction between 5-7 defect pairs. The dislocation theory can simplify the simulation of defect pairs in CNTs, and give exactly solution at atomic scale. Based on one slip layer model, we will analyze the distribution of relative displacement on the slip plane and minimizing energy as a function of relative displacement. The minimum energy path will be found by nudged elastic band method. Meanwhile, we find that the interaction of defects plays an important role in the theoretical analysis of defect transformations which strongly effect the stability of CNTs.

Thermal rectification of heterojunction nanotubes

Using non-equilibrium molecular dynamics method, we have studied the thermal rectification of heterojunction nanotubes (HCNTs). All of these HCNTs, composed of two 4 nm long carbon nanotubes (CNTs), only have a pentagon-heptagon defects pair. Here the positive direction is defined as the direction where the heat flux flows from the large diameter CNTs to the small diameter CNTs. We have found that the thermal rectification depends on the diameter, the chirality and the temperature.#br#Diameter effect: We fix the diameter on one side and changed it on another side, i.e., the left side of the HCNTs is (3, 3) while the right side of the HCNTs is (n, n), in which n changes from 4 to 9. It is found that the thermal rectification efficiency of HCNTs increases with n (also with the diameter difference). If considering the temperature field of (3, 3)-(4, 4) HCNTs, one can find that there exists a region near the HCNT where the temperature changes sharply. This region when the flux is positive is similar to that when the flux is negative. However, if taking into consideration the (3, 3)-(9, 9) HCNTs, we find that the distribution of temperature field shows different behaviors when the directions of the heat flux are different, and the length of this region becomes longer than (3, 3)-(4, 4). It can be explained that the thermal rectification is caused by different temperature distributions in HCNTs.#br#Chirality effect: We keep the chirality unchanged on one side of HCNTs and change the chirality of the other side, namely, the chirality of the left side of HCNTs are (3, 3) and the right side are (9, 9), (11, 7), (13, 4) and (15, 1), all of their diameters are close to 4.1 Å. We can find that the intersection angle between two CNTs decreases when the right side of HCNTs changes from (9, 9) to (15, 1), and the thermal rectification efficiency will be enhanced. It can be explained that the phonon is scattered and absorbed more effectively at the hetero-junction as the intersection angle decreases.#br#Temperature effect: We have constructed a HCNT (3, 3)-(9, 9) and changed its average temperature from 200 to 400 K. Our results show that the thermal rectification efficiency will be weakened with the rise in average temperature because of increasing heat flux in the negative direction.#br#This research may be helpful to the research in nanoscale thermal diodes, thermal logical gates and controlling heat flux.

Wave propagation in carbon nanotube intramolecular junctions: finite element calculations

The dispersion of longitudinal and transverse waves in (n,0)–(2n,0) intramolecular junctions (IMJs) are investigated using an atomistic finite element method (FEM). The transient responses of IMJs with different connection types subjected to harmonic incident wave were modelled using three-dimensional elastic beams of carbon bonds and point masses. The linkage between the force-field constants of molecular mechanics and input parameters of beam and mass elements was established through the molecular structural mechanics approach. The wave dispersion simulated by FEM shows good agreement with that of the non-local elastic model in a wide frequency range up to the terahertz region. It is shown that both the microstructure of conical part (connection part) and the coupling of longitudinal vibration and transverse vibration brought by the conicity play important roles in the dispersion of longitudinal and transverse wave in a single-walled IMJ. The amplitude decay of longitudinal wave depended on the distance propagating; the wavelength and the structure in connection part are examined. The results show that the dispersion of the decay of the wave amplitude in IMJ with less pentagon–heptagon defects has a better agreement with analytical results of macroscopic conical shell.

Defect formation and transformation in graphene under electron irradiation: A molecular dynamics study

Molecular dynamics simulations were performed to study defect formation and transformation in graphene under electron irradiation. The single-vacancy was the most frequently formed defect and the number of defects did not depend on the defect formation energy for normal incidence. The single-vacancy transformed to other types of defects and migrated in graphene by heating. The recovery energies of adatom-vacancy and pentagon–heptagon defects were relatively small. The Stone–Wales defect was the most stable, and did not easily recover. In the single atomic chain formation process from graphene by electron irradiation, competition between defect formation by electron collision and the recovery by heating was observed.

Electronic and transport properties of monolayer graphene defected by one and two carbon ad-dimers

Using density functional theory combined with non-equilibrium Green’s function method, we have investigated the electronic and transport properties of graphenes defected by one and two carbon ad-dimers (CADs), placed parallel to the graphene lattice. Addition of these CADs to graphenes creates 3D paired pentagon–heptagon defects (3D-PPHDs). The band structure, density of states (DOS), quantum conductance, projected DOS, as well as the current–voltage characteristic per graphene super-cells containing each type of 3D-PPHD are calculated. The local strain introduced to graphene by 3D-PPHDs forces the C-bonds in the dimers to hybridize in sp 3-like rather than sp 2-like orbitals, creating localized states at the center of the corresponding defect below the Fermi energy. Simulations show that the zero-bias conductances per super-cells containing defects created by one and two CADs exhibit dip about ~0.579 and ~0.253 eV below their corresponding Fermi levels, respectively. These can be attributed to the localized states around the same energy levels. Simulations also show that the enhanced carriers scatterings within the graphenes defected by the 3D-PPHDs have increased their overall resistances, as compared with the pristine graphene. Moreover, the current–voltage characteristic calculated per super-cell for each case shows that the current for those containing one and two CADs, at an applied voltage of 0.5 V, is ~5 and 13 % less than the current calculated for the pristine super-cell of the same size.

Some Mechanical Properties of Carbon Nanotubes Heterojunctions

Some Mechanical Properties of Carbon Nanotubes Heterojunctions In the present research work, the structure of linear heterojunctions between two CNTs of different chirality’s, but similar radii, joined together through an interface that require more than one pentagon-heptagon defects have been studied. The elastic properties of carbon nanotube heterojunctions are investigated using secondgeneration improved reactive empirical bond order potential by Brenner and co-workers. In this study, the coordinates of carbon nanotube heterojunctions are generated. Each and every structure thus generated is allowed to relax till a minimum of energy is obtained. The requisite compressions, elongations and twists to the structures are applied and thus computed elastic moduli. Young’s Modulus increases with radius for small radii and attains a constant value of the order 1TPa. Poisson’s ratio and shear modulus have also been computed.

Role of 3D-paired pentagon–heptagon defects in electronic and transport properties of zigzag graphene nanoribbons

Electronic and transport properties of 11 zigzag graphene nanoribbons (11-z-GNRs) with two types of 3D-paired pentagon–heptagon defects (3D-PPHDs) are studied using density functional theory combined with non-equilibrium Green’s function method. The C ad-dimers that have been introduced to z-GNRs to form these 3D-PPHDs have induced local strains forcing the C-bonds in the ad-dimers to hybridize in sp3-like rather than sp2-like orbitals. Such transformations that cause extra electrons to accumulate around the 3D-PPHDs are responsible for the variations in the electronic and transport properties of the defected z-GNRs. Density of states (DOS) for 11-z-GNRs containing either type of 3D-PPHDs, compared with that of the pristine 11-z-GNR, exhibits a peak at a particular energy level below the Fermi level, within its first plateau. Each peak, corresponding to a dip in the related zero-bias conductance profile, is attributed to electrons trapped in the localized states around the same energy level. The current–voltage (I–V) characteristics are almost linear for 11-z-GNR defected by either type of 3D-PPHD. Presence of a 3D-PPHD, made by addition of a single C ad-dimer, above an 11-z-GNR super-cell decreases its average conductance by 10.7 %, while a 3D-PPHD made by addition of two C ad-dimers to the opposite sides of the same 11-z-GNR super-cell decreases its conductance by 23 %.