Nanoscopic imaging of oxidized graphene monolayer using tip-enhanced Raman scattering

Nano Research - Tip-enhanced Raman scattering (TERS) can be used for the structural and chemical characterization of materials with a nanoscale resolution, and offers numerous advantages compared...     

Recent development in 2D materials beyond graphene

Discovery of graphene and its astonishing properties have given birth to a new class of materials known as “2D materials”. Motivated by the success of graphene, alternative layered and non-layered 2D materials have become the focus of intense research due to their unique physical and chemical properties. Origin of these properties ascribed to the dimensionality effect and modulation in their band structure. This review highlights the recent progress of the state-of-the-art research on synthesis, characterization and isolation of single and few layer nanosheets and their assembly. Electronic, magnetic, optical and mechanical properties of 2D materials have also been reviewed for their emerging applications in the area of catalysis, electronic, optoelectronic and spintronic devices; sensors, high performance electrodes and nanocomposites. Finally this review concludes with a future prospective to guide this fast evolving class of 2D materials in next generation materials science.     

Atomistic simulations of J-integral in 2D graphene nanosystems

The J-integral is investigated in discrete atomic systems using molecular mechanics simulations. A method of calculating J-integral in specified atomic domains is developed. Two cases, a semiinfinite crack in an infinite domain under the remote K-field deformation and a finite crack length in a finite geometry under the tensile and shear deformation prescribed on the boundary, are studied in the two-dimensional graphene sheets and the values of J-integral are obtained under small-strain deformation. The comparison with energy release rates in Mode I and Mode II based on continuum theory of linear elastic fracture mechanics show good agreements. Meanwhile, the nonlinear strain and stress relation of a 2D graphene sheet is evaluated and is fitted with a power law curve. With necessary modifications on the Tersoff-Brenner potential, the critical values of J-integral of 2D graphene systems, which denoted as Jc, are eventually obtained. The results are then compared with those from the relevant references.     

Atomistic continuum modeling of graphene membranes

The paper deals with the modeling of thin, monolayer graphene membranes, which have significant electrical and physical properties used for nano- or micro-devices, such as resonators and nanotransistors. The membrane is considered as a homogenized graphene monolayer on the macroscopic scale, and a continuum–atomistic multiscale approach is exploited, focusing the Tersoff–Brenner (TB) potential for the interaction between the carbonic bonds. The associated Representative atomistic Unit Lattice (RUL) is thereby considered as a micro-scale quasi-continuum placed in context of computational homogenization. In this development, the Cauchy–Born rule (CBN) is extended by the atomic fluctuation to allow for relaxation in the RUL. The paper discusses the handling of the TB-potential, both in the context of macro–micro homogenization, and in the context of numerical implementation perspectives. In particular, explicit expressions of the homogenized membrane forces and stiffness are expressed in terms of the first and second gradient of the potential, with due consideration to the involved “non-local” pairwise interaction in the model. In addition, the detailed resulting macroscopic non-linear and linearized finite element response is formulated in terms of the relaxed lattice level atomistic response. Numerical results are provided for the lattice response in terms of the apparent anisotropic behavior induced by the graphene atomic structure. An assessment of the convergence of RULs with respect to different deformation states of the lattice membrane is also carried out. Finally, a validation of an experiment of a circular graphene membrane, using atomic force microscopy (AFM) measurements, is provided based on standard TB-parameters available in the literature.     

Elastic in-plane properties of 2D linearized models of graphene

Graphene is a monolayer of carbon atoms packed into a two-dimensional honeycomb lattice. This allotrope can be considered as mother of all graphitic forms of carbon. The elastic in-plane properties of graphene are studied and various existing linearized models of its elastic deformations are critically re-examined. Problems related to modelling of graphene by nonlinear multi-body potentials of interaction are also discussed. It is shown that experimental results for small deformations can be well described by both the two-parametric molecular mechanics model developed by Gillis in 1984, while some popular models have serious flaws and often the results obtained using these models do not have physical meaning. It is argued that in order to study elastic constants of linearized models of graphene layers, it is very convenient to use the four parameter molecular mechanics model. The advantages of this approach is demonstrated by its application to the Tersoff and Brenner nonlinear interaction potentials, and by its comparison with the Gillis two-parametric model.     

Flaw insensitive fracture in nanocrystalline graphene

We show from a series of molecular dynamics simulations that the tensile fracture behavior of a nanocrystalline graphene (nc-graphene) nanostrip can become insensitive to a pre-existing flaw (e.g., a hole or a notch) below a critical length scale in the sense that there exists no stress concentration near the flaw, the ultimate failure does not necessarily initiate at the flaw, and the normalized strength of the strip is independent of the size of the flaw. This study is a first direct atomistic simulation of flaw insensitive fracture in high-strength nanoscale materials and provides significant insights into the deformation and failure mechanisms of nc-graphene.     

Probabilistic fracture mechanics of 2D carbon-carbon composites

The fracture toughness of two types of carbon fabric reinforced carbon composite (KKARB^®, Types A and C) is evaluated, the mechanisms of crack propagation resistance are identified and both are related to microstructural differences.The two composites have the same constituents, i.e. fibers, yarns, fabric weaving and matrix precursor. However, different processing cycles result in apparent differences in microstructure (e.g. different number and length distribution of microcracks, crimp angle) and toughness.The crack diffusion model (CDM) is invoked to parameterize the fluctuating strength field of the composite in terms of an average fracture energy , a minimum fracture energy 179-1 and a shape parameter . The values of 179-1 are in direct correlation with the average size of microcracks in each composite, and is found to correlate with the scatter in fracture toughness.     

Hybrid lattice particle modeling: Theoretical considerations for a 2D elastic spring network for dynamic fracture simulations

A new hybrid lattice particle modeling (HLPM) scheme is proposed. The particle–particle interaction is derived from lattice modeling (LM) theory, whereas the computational scheme follows particle modeling (PM) technique. The newly proposed HLPM considers different particle interaction schemes, involving not only particles in the nearest neighborhood, but also the second nearest neighborhood. Different mesh structures with triangular or rectangular unit cells can be used. The current paper is concerned with the mathematical derivations of elastic interaction between contiguous particles in 2D lattice networks, accounting for different types of linkage mechanism and different shapes of lattice. Axial (α) and combined axial-angular (α − β) models are considered. Derivations are based on the equivalence of strain energy stored in a unit cell with its associated continuum structure in the case of in-plane elasticity. Conventional PM technique was restricted to a fixed Poisson’s ratio and had a strong bias in crack propagation direction, as a result of the geometry of the adopted lattice network. The current HLPM is free from the above-mentioned deficiencies and can be applied to a wide range of impact and dynamic fracture failure problems. Although the current analysis is based on the linear elastic spring model, inelastic considerations can be easily implemented, as HLPM has the same force interaction scheme as PM, based on the Lennard–Jones potential.     

Deformation and fracture in graphene nanosheets

Graphene nanosheets (GNSs) are flake-like materials composed of few-layer graphene sheets. GNSs are similar to multi-walled carbon nanotubes (CNTs) in graphene structures and in layer numbers. However, GNSs and CNTs behave very differently in deformation and fracture. In this study, natural graphite flakes were employed to make expanded graphite (EG), which is composed of partially connected GNSs. Both sonication and three-roll milling were used to separate the GNSs and to disperse them into an epoxy resin. By compacting EG, the GNSs inside were compressed and deformed. By breaking the GNS/epoxy composite, most GNSs on the cracked surfaces were fractured. Both SEM and TEM have been used for microscopic observations. The micrographs revealed that folding and wrinkling are the major modes of deformation, while tearing and peeling are the dominant modes of fracture. These modes are virtually non-existent in CNTs. The factors to cause the different behavior are discussed.     

Engineering graphene mechanical systems

We report a method to introduce direct bonding between graphene platelets that enables the transformation of a multilayer chemically modified graphene (CMG) film from a "paper mache-like" structure into a stiff, high strength material. On the basis of chemical/defect manipulation and recrystallization, this technique allows wide-range engineering of mechanical properties (stiffness, strength, density, and built-in stress) in ultrathin CMG films. A dramatic increase in the Young's modulus (up to 800 GPa) and enhanced strength (sustainable stress ≥1 GPa) due to cross-linking, in combination with high tensile stress, produced high-performance (quality factor of 31?000 at room temperature) radio frequency nanomechanical resonators. The ability to fine-tune intraplatelet mechanical properties through chemical modification and to locally activate direct carbon-carbon bonding within carbon-based nanomaterials will transform these systems into true "materials-by-design" for nanomechanics.     

Effects of graphene nanoplatelets and graphene nanosheets on fracture toughness of epoxy nanocomposites

The effects of graphene nanoplatelets (GPLs) and graphene nanosheets (GNSs) on fracture toughness and tensile properties of epoxy resin have been studied. A new technique for synthesis of GPLs based on changing magnetic field is developed. The transmission‐electron microscopy and the Raman spectroscopy were employed to characterize the size and chemical structure of the synthesized graphene platelets. The critical stress intensity factor and tensile properties of epoxy matrix filled with GPL and GNS particles were measured. Influence of filler content, filler size and dispersion state was examined. It was found that the GPLs have greater impact on both fracture toughness and tensile strength of nanocomposites compared with the GNSs. For instance, fracture toughness increased by 39% using 0.5 wt% GPLs and 16% for 0.5 wt% GNSs.     

Ductile fracture simulation of hydropiercing process based on various criteria in 3D modeling

Hydropiercing has been used widely in the past decade in the automotive industry. So far, the ductile fracture of hydropiercing process considering the effect of hydroforming has not been studied in detail due to the complicated deformation process. In order to simulate hydropiercing process accurately, a 3D model considering the effect of hydroforming process has been developed in this study. Six ductile criteria were implemented to predict crack initiation and propagation by means of the user subroutine VUMAT of ABAQUS. The comparative study among the results obtained by the simulations using the different ductile criteria and the experiments was explored. The model using the Rice and Tracey Criterion shows good agreement with the experiment at loading pressure of 60–60 MPa, however the others could not. Moreover, the simulation errors using the Rice and Tracey Criterion at different loading pressure and hydropiercing type are small enough too compared with experiments so that this criterion could be used to simulate the hydropiercing process. Finally, the deformation mechanism of hydropiercing process has been discussed on the bases of simulations with the Rice and Tracey Criterion and experiments.     

Thermoactivated fracture of graphene subjected to tensile strain

Graphene draws the attention of researchers due to its unique properties-in particular, record-high tensile strength. The time to fracture (TTF) of defect-free graphene strained by tension at a nonzero temperature has been studied by the method of molecular dynamics (MD). It is established that the time to thermoactivated fracture has a probabilistic character and obeys an exponential distribution. The mean TTF is proportional to the area of the graphene sheet and obeys the Arrhenius-Zhurkov law as a function of temperature and applied stress. The dependence of the activation energy for graphene fracture on the applied stress and sample area has been extrapolated to values of these parameters relevant for practical applications. The mechanism of graphene fracture has been analyzed.     

超级电容器用CeO_2-MnO/3D石墨烯复合材料的制备

以西瓜瓜瓤为碳源,采用两步碳化法制备三维石墨烯(3D-Fiberbased Graphene,3D G)材料,并使用水热法制备了CeO_2-MnO/3DG复合材料,以期获得比电容高,循环寿命好的石墨烯超级电容器电极材料。结果表明:3DG材料具有较高比表面积,最高可达到332m~2·g~(-1)。CeO_2-MnO/3DG复合材料具有三维导电网络结构,金属氧化物颗粒在石墨烯片层间生长均匀,粒径在10nm左右。电化学测试结果显示:在0.5 mol·L~(-1)的Na_2SO_4溶液中,电流密度1A·g~(-1),当摩尔比MnO∶CeO_2=4∶1,复合负载量在80%时得到的CeO_2-MnO/3D G复合材料拥有最高比电容,达308.5F·g~(-1),经过1 000次循环充放电测试比电容保持率为95.5%。CeO_2-MnO/3DG复合材料电化学性能的提高主要是因为两种金属氧化物复合负载与石墨烯的协同作用。     

Bending stiffening of graphene and other 2D materials via controlled rippling

In this paper, the effects of rippling on the bending stiffness of a monolayer graphene are studied. The initial rippling of the surface is modeled by cosine functions with a hierarchical topology. Considering both large displacement and small scale effect, the governing equilibrium equations are determined and solved. Then an equivalent bending stiffness is calculated for a rippled graphene and the effects of rippling, material discreteness, and structural dimension on its stiffness are discussed in details. The results quantify how the rippling strongly increases the effective bending stiffness of graphene and interacts with the discrete nature of the material not only because of increase in the moment of inertia. This approach can be applied to ripples design of 2D materials in order to achieve stiffening in bending as required in specific applications.     

Atomistic and continuum modelling of temperature-dependent fracture of graphene

This paper presents a comprehensive molecular dynamics study on the effects of nanocracks (a row of vacancies) on the fracture strength of graphene sheets at various temperatures. Comparison of the strength given by molecular dynamics simulations with Griffith’s criterion and quantized fracture mechanics theory demonstrates that quantized fracture mechanics is more accurate compared to Griffith’s criterion. A numerical model based on kinetic analysis and quantized fracture mechanics theory is proposed. The model is computationally very efficient and it quite accurately predicts the fracture strength of graphene with defects at various temperatures. Critical stress intensity factors in mode I fracture reduce as temperature increases. Molecular dynamics simulations are used to calculate the critical values of $J$ integral ( $J_\mathrm{IC}$ ) of armchair graphene at various crack lengths. Results show that $J_\mathrm{IC}$ depends on the crack length. This length dependency of $J_\mathrm{IC}$ can be used to explain the deviation of the strength from Griffith’s criterion. The paper provides an in-depth understanding of fracture of graphene, and the findings are important in the design of graphene based nanomechanical systems and composite materials     

Anomalous roughness of fracture surfaces in 2D fuse models

We study anomalous scaling and multiscaling of two-dimensional crack profiles in the random fuse model using both periodic and open boundary conditions. Our large scale and extensively sampled numerical results reveal the importance of crack branching and coalescence of microcracks, which induce jumps in the solid-on-solid crack profiles. Removal of overhangs (jumps) in the crack profiles eliminates the multiscaling observed in earlier studies and reduces anomalous scaling. We find that the probability density distribution ${p(\Delta h(\ell))}$ of the height differences ${\Delta h(\ell) = [h(x+\ell) - h(x)]}$ of the crack profile obtained after removing the jumps in the profiles has the scaling form ${p(\Delta h(\ell)) = \langle\Delta h^2(\ell)\rangle^{-1/2} ~f\left(\frac{\Delta h(\ell)}{\langle\Delta h^2(\ell)\rangle^{1/2}}\right)}$ , and follows a Gaussian distribution even for small bin sizes ?. The anomalous scaling can be summarized with the scaling relation ${\left[\frac{\langle\Delta h^2(\ell)\rangle^{1/2}}{\langle\Delta h^2(L/2)\rangle^{1/2}}\right]^{1/\zeta_{loc}} + \frac{(\ell-L/2)^2}{(L/2)^2} = 1}$ , where ${\langle\Delta h^2(L/2)\rangle^{1/2}\sim L^{\zeta}}$ and L is the system size.