Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

Hückel Molecular Orbital Analysis for Stability and Instability of Stacked Aromatic and Stacked Antiaromatic Systems

Face-to-face stacking of aromatic compounds leads to stacked antiaromaticity, while that of antiaromatic compounds leads to stacked aromaticity. This is a prediction with a long history; in the late 2000s, the prediction was confirmed by high-precision quantum chemical calculations, and finally, in 2016, a π-conjugated system with stacked aromaticity was synthesized. Several variations have since been reported, but essentially, they are all the same molecule. To realize stacked aromaticity in a completely new and different molecular system and to trigger an extension of the concept of stacked aromaticity, it is important to understand the origin of stacked aromaticity. The Hückel method, which has been successful in giving qualitatively correct results for π-conjugated systems despite its bold assumptions, is well suited for the analysis of stacked aromaticity. We use this method to model the face-to-face stacking systems of benzene and cyclobutadiene molecules and discuss their stacked antiaromaticity and stacked aromaticity on the basis of their π-electron energies. By further developing the discussion, we search for clues to realize stacked aromaticity in synthesizable molecular systems.

Evolution of the Electronic and Optical Properties of Meta-Stable Allotropic Forms of 2D Tellurium for Increasing Number of Layers

In this work, ab initio Density Functional Theory calculations are performed to investigate the evolution of the electronic and optical properties of 2D Tellurium—called Tellurene—for three different allotropic forms (α-, β- and γ-phase), as a function of the number of layers. We estimate the exciton binding energies and radii of the studied systems, using a 2D analytical model. Our results point out that these quantities are strongly dependent on the allotropic form, as well as on the number of layers. Remarkably, we show that the adopted method is suitable for reliably predicting, also in the case of Tellurene, the exciton binding energy, without the need of computationally demanding calculations, possibly suggesting interesting insights into the features of the system. Finally, we inspect the nature of the mechanisms ruling the interaction of neighbouring Tellurium atoms helical chains (characteristic of the bulk and α-phase crystal structures). We show that the interaction between helical chains is strong and cannot be explained by solely considering the van der Waals interaction.

Carbon Material With Ordered Sub-Nanometer Hole Defects

A holey carbon material with ordered sub-nanometer hole defects was synthesized from oxidative cyclodehydrogenation of a polyhexaphenylbenzene precursor. Band gap of around 2.2 eV is formed due to the narrow connection between the hexabenzocoronene subunits. It has weak interlayer interaction energy compared with graphene and shows easy dispersion in a wide range of solvents, surprisingly including water. Density functional theory calculations confirmd the excellent dispersion of this material in water. This new carbon material was then proved as effective support for various inorganic nanoparticles of small sizes. The supported iron nanoparticles showed enzyme-like catalysis behavior in nitrophenyl reduction reaction by NaBH4, exemplifying the great potential of this new material in catalysis.

In pursuit of accurate interlayer potentials for twisted bilayer graphynes

Recent explorations of twist in bilayer graphene and the discovery of superconducting phases at certain magic angles have laid the groundwork for a new branch in materials science called twistronics. However, theoretical studies on twisted layered materials are impeded due to the computational expense associated with first-principles calculations. Empirical force field approaches that include anisotropic terms to describe interlayer interactions have come to the fore as excellent alternatives to deal with such a stumbling block. Taking a cue from these formulations, herein, we describe our pursuit of capturing the interlayer interactions in bilayer graphynes with atomistic empirical potentials. The choice of the potentials, namely the improved Lennard-Jones potential and Hod's interlayer potential, is motivated by the objective of bringing out the role of anisotropy explicitly. Empirical parameters for both the potentials are calibrated against dispersion-corrected DFT calculations that are performed to incorporate the stacking, sliding and twisting features of the bilayer configurations. Although the isotropic improved Lennard-Jones potential is able to describe the interlayer stacking of graphynes, it is inadequate to account for the interlayer twist properties. The anisotropic Hod's interlayer potential portrays the interlayer twisting energy profiles of the benchmark DFT calculations with a reasonable accuracy. Our potential formulations can bestow impetus to the research on the homo- and hetero-bilayer structures of graphynes and other two-dimensional materials.

Step-Edge Epitaxy for Borophene Growth on Insulators

Borophene─a monatomic layer of boron atoms─stands out among two-dimensional (2D) materials, with its versatile properties tantalizing for physics exploration and next-generation devices. Yet its phases are all synthesized on and stay bound to metal substrates, hampering both characterization and use. Borophene growth on an inert insulator would allow postsynthesis exfoliation, but the weak adhesion to such a substrate results in a high 2D nucleation barrier, preventing clean borophene growth. This challenge can be circumvented in a strategy devised and demonstrated here with ab initio calculations. Naturally present 1D-defects, the step-edges on an h-BN substrate surface, enable boron epitaxial assembly, reduce the nucleation dimensionality, and lower the barrier by an order of magnitude (to 1.1 eV or less), yielding a v_1/9 phase. Weak borophene adhesion to the insulator makes it readily accessible for comprehensive property tests or transfer into the device setting.

Friction on incommensurate substrates: Role of anharmonicity and defects

We present molecular dynamics simulations of one- and two-dimensional bead-spring models sliding on incommensurate substrates after an initial kick, in the case where the coupling to the underlying substrate is weak, i.e., energy can dissipate only into the internal degrees of freedom of the sliding object, but not into the substrate below. We investigate how sliding friction is affected by structural defects and interaction anharmonicity. In their absence, we confirm earlier findings, namely, that at special resonance sliding velocities, friction is maximal. When sliding off-resonance, partially thermalized states are possible, whereby only a small number of vibrational modes becomes excited, but whose kinetic energies are already Maxwell-Boltzmann distributed. Anharmonicity and defects typically destroy partial thermalization and instead lead to full thermalization, implying much higher friction. For sliders with periodic boundaries, thermalization begins with vibrational modes whose spatial modulation is compatible with the incommensurate lattice. For a disk-shaped slider, modes corresponding to modulations compatible with the slider radius are initially the most dominant. By tuning the mechanical properties of the slider's edge, this effect can be controlled, resulting in significant changes in the sliding distance covered.

Theoretical investigation of lattice dynamics, infrared reflectivity, polarized Raman spectra and nature of interlayer coupling in two-dimensional layered gallium sulfide

Gallium sulfide (GaS) is a highly promising two-dimensional layered semiconductor owing to its remarkable thickness dependent electronic and physical properties. In this article, we perform a comprehensiveab initiostudy of lattice dynamics, mode symmetry assignments, polarized Raman and infrared (IR) reflectivity spectra of GaS system. Polarized Raman spectra are obtained for different light polarization set-ups of incoming and scattered light. The frequencies of all allowed vibrational modes at the zone-centre are calculated and symmetry labels are assigned. Furthermore, the variation of frequencies & intensities of Raman/IR active modes of ultrathin GaS films (few layers) as function of film thickness is studied. In addition, we also explore the nature of weak interlayer coupling in GaS. The weak forces between the GaS layers are usually assumed to be due to interlayer van der Waals (vdW) interaction. However, this assumption has not been reasonably explained in reported experimental studies. Our study strongly suggests that weak interlayer interactions in GaS may be primarily electrostatic (Coulomb) in nature and therefore the contribution of vdW interactions to layer-layer coupling and lattice dynamics may be significantly lower than that of electrostatic interaction. The suggested nature of interlayer coupling in GaS and related III-VI semiconductors may have important implications in determination of their various physical properties.

Computational Prediction of Superlubric Layered Heterojunctions

Structural superlubricity has attracted increasing interest in modern tribology. However, experimental identification of superlubric interfaces among the vast number of heterojunctions is a trial-and-error and time-consuming approach. In this work, based on the requirements on the in-plane stiffnesses of layered materials and the interfacial interactions at the sliding incommensurate interfaces of heterojunctions for structural superlubricity, we propose criteria for predicting structural superlubricity between heterojunctions. Based on these criteria, we identify 61 heterojunctions with potential superlubricity features from 208 candidates by screening the data of first-principles calculations. This work provides a universal route for accelerating the discovery of new superlubric heterojunctions.

Understanding the Role of Self-Adhesion in Crumpling Behaviors of Sheet Macromolecules

Understanding the crumpling behavior of two-dimensional (2D) macromolecular sheet materials is of fundamental importance in engineering and technological applications. Among the various properties of these sheets, interfacial adhesion critically contributes to the formation of crumpled structures. Here, we present a coarse-grained molecular dynamics (CG-MD) simulation study to explore the fundamental role of self-adhesion in the crumpling behaviors of macromolecular sheets having varying masses or sizes. By evaluating the potential energy evolution, our results show that the self-adhesion plays a dominant role in the crumpling behavior of the sheets compared to in-plane and out-of-plane stiffnesses. The macromolecular sheets with higher adhesion tend to form a self-folding planar structure at the quasi-equilibrium state of the crumpling and exhibit a lower packing efficiency as evaluated by the fractal dimension of the system. Notably, during the crumpling process, both the radius of gyration R_g and the hydrodynamic radius R_h of the macromolecular sheet can be quantitatively described by the power-law scaling relationships associated with adhesion. The evaluation of the shape descriptors indicates that the overall crumpling behavior of macromolecular sheets can be characterized by three regimes, i.e., the less bent, intermediate, and highly crumpled regimes, dominated by edge-bending, self-adhesion, and further compression, respectively. The internal structural analysis further reveals that the sheet transforms from the initially ordered state to the disordered glassy state upon crumpling, which can be facilitated by greater self-adhesion. Our study provides fundamental insights into the adhesion-dependent structural behavior of macromolecular sheets under crumpling, which is essential for establishing the structure-processing-property relationships for crumpled macromolecular sheets.

Computational design of graphitic carbon nitride photocatalysts for water splitting

A series of structures based on graphitic carbon nitride (g-C₃N₄), a layered material composed of linked carbon-nitrogen heterocycles arranged in a plane, were investigated by density functional theory calculations. g-C₃N₄ is a semiconductor that absorbs UV light and visible light at the blue end of the visible spectrum, and is widely studied as a photocatalyst for water splitting; however, its photocatalytic efficiency is limited by its poor light-harvesting ability and low charge mobilities. Modifications to the g-C₃N₄ structure could greatly improve its optical and electronic properties and its photocatalytic efficiency. In this work, the g-C₃N₄ structure was modified by replacing the nitrogen linker with heteroatoms (phosphorus, boron) or aromatic groups (benzene, s-triazine and substituted benzenes). Two-dimensional (2D) sheets and three-dimensional (3D) multilayer structures with different stacking types were modelled. Several new structures were predicted to have electronic properties superior to g-C₃N₄ for use as water splitting photocatalysts. In particular, introduction of phosphorus, benzene and s-triazine groups led to band gaps smaller than in the standard g-C₃N₄ (down to 2.4 eV, corresponding to green light). Doping with boron in the linker positions dramatically reduced the band gap (to 1.6 eV, corresponding to red light); the doped material has the valence band position suitable for water oxidation. Our computational study shows that chemical modification of g-C₃N₄ is a powerful method to tune this material's electronic properties and improve its photocatalytic activity.

Binding Free Energy Calculations of Bilayer Graphenes Using Molecular Dynamics

Bilayer graphenes are dimeric assemblies of single graphene layers bound together by π-complexation interactions. Controlling these assemblies can be complicated, as the layered compounds disperse in solvents or aggregate into higher columnar configurations and clusters. One way to assess the interactions that contribute to the stability of the layered compounds is to use molecular simulation. We perform pulling molecular dynamics on bilayer graphenes with different sizes and obtain the normal and shear force profiles of dissociation. We generate pathways of dissociation along the two directions and calculate the binding free energies of the structures with umbrella sampling simulations. We show that the dissociation process is direction-dependent. Along the shear direction, we compute the same free energy for the different samples, which validates the consistency of our simulations. We notice that the dissociation is less adiabatic on the normal than the shear direction, having an entropic contribution to the Gibbs energy. This contribution is more enhanced for the larger bilayer graphenes.

Tailoring nanocomposite interfaces with graphene to achieve high strength and toughness

The nanofiller reinforcing effect in nanocomposites is often far below the theoretically predicted values, largely because of the poor interfacial interaction between the nanofillers and matrix. Here, we report that graphene-wrapped B₄C nanowires (B₄C-NWs@graphene) empowered exceptional dispersion of nanowires in matrix and superlative nanowire-matrix bonding. The 0.2 volume % B₄C-NWs@graphene reinforced epoxy composite exhibited simultaneous enhancements in strength (144.2 MPa), elastic modulus (3.5 GPa), and ductility (15%). Tailoring the composite interfaces with graphene enabled effective utilization of the nanofillers, resulting in two times increase in load transfer efficiency. Molecular dynamics simulations unlocked the shear mixing graphene/nanowire self-assembly mechanism. This low-cost yet effective technique presents unprecedented opportunities for improving nanocomposite interfaces, enabling high load transfer efficiency, and opens up a new path for developing strong and tough nanocomposites.

Two-dimensional graphene-HfS2 van der Waals heterostructure as electrode material for alkali-ion batteries

Poor electrical conductivity and large volume expansion during repeated charge and discharge is what has characterized many battery electrode materials in current use. This has led to 2D materials, specifically multi-layered 2D systems, being considered as alternatives. Among these 2D multi-layered systems are the graphene-based van der Waals heterostructures with transition metal di-chalcogenides (TMDCs) as one of the layers. Thus in this study, the graphene–hafnium disulphide (Gr–HfS₂) system, has been investigated as a prototype Gr–TMDC system for application as a battery electrode. Density functional theory calculations indicate that Gr–HfS₂ van der Waals heterostructure formation is energetically favoured. In order to probe its battery electrode application capability, Li, Na and K intercalants were introduced between the layers of the heterostructure. Li and K were found to be good intercalants as they had low diffusion barriers as well as a positive open circuit voltage. A comparison of bilayer graphene and bilayer HfS₂ indicates that Gr–HfS₂ is a favourable battery electrode system.

A high rate capacity, moderate volume expansion and energetically stable alkali ion graphene–HfS₂ electrode material.

Strong influence of strain gradient on lithium diffusion: flexo-diffusion effect

Lithium ion batteries (LIBs) work under a sophisticated external force field and the electrochemical properties could be modulated by strain. Owing to electro-mechanical coupling, the change of micro local structures can greatly affect the lithium (Li) diffusion rate in solid state electrolytes and the electrode materials of LIBs. In this study, we found, through first-principles calculations, that the strain gradient in bilayer graphene (BLG) significantly affects the Li diffusion barrier, which is termed as the flexo-diffusion effect. The Li diffusion barrier substantially decreases/increases under a positive/negative strain gradient, leading to a change of Li diffusion coefficient of several orders of magnitude at 300 K. Interestingly, the regulation effect of strain gradient is much more significant than that of a uniform strain field, which can have a remarkable effect on the rate performance of batteries, with a considerable increase in the ionic conductivity and a slight change of the original material structure. Moreover, our ab initio molecular dynamics simulations (AIMD) show that the asymmetric distorted lattice structure provides a driving force for Li diffusion, resulting in oriented diffusion along the positive strain gradient direction. We predict the new phenomenon of a flexo-diffusion effect from a theoretical calculation aspect, these findings could extend present LIB technologies by introducing a novel strain gradient engineering.

Moiré Potential, Lattice Corrugation, and Band Gap Spatial Variation in a Twist-Free MoTe2/MoS2 Heterobilayer

To have a fully first-principles description of the moiré pattern in transition-metal dichalcogenide heterobilayers, we have carried out density functional theory calculations on a MoTe₂(9 × 9)/MoS₂(10 × 10) stacking, which has a superlattice larger than an exciton yet not large enough to justify a continuum model treatment. Lattice corrugation is found to be significant in both monolayers, yet its effect on the electronic properties is marginal. We reveal that the variation of the average local potential near Mo atoms in both MoTe₂ and MoS₂ layers displays a conspicuous moiré pattern. They are the intralayer moiré potentials correlating closely with the spatial variation of the valence band maximum and conduction band minimum. The interlayer moiré potential, defined as the difference between the two intralayer moiré potentials, changes roughly in proportion to the band gap variation in the moiré cell. This finding might be instructive in chemical engineering of van der Waals bilayers.

Two Phases with Different Domain Wall Networks and a Reentrant Phase Transition in Bilayer Graphene under Strain

The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of 3.0×10^{-3} is followed by the transition to another incommensurate phase with a striped network at the elongation of 3.7×10^{-3}. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation ∼10^{-2}.

Molecular dynamics simulation on the formation and development of interlayer dislocations in bilayer graphene

Molecular dynamics simulations are used to study the formation and development of interlayer dislocations in bilayer graphene (BLG) subjected to uniaxial tension. Two different BLGs are employed for the simulation: armchair (AC-BLG) and zigzag (ZZ-BLG). The atomic-level strains are calculated and the parameter 'dislocation intensity' is introduced to identify the dislocations. The interlayer dislocation is found to start at the edge and propagate to the center. For AC-BLG, the dislocations arise successively with the increase of applied strain, and all dislocations have the same width. For ZZ-BLG, the first dislocation arises alone. After that, two dislocations with different widths appear together every time. The simulated dislocation widths are in good agreement with existing experimental results. Across every dislocation, there is a transition from AB stacking to AC stacking, or vice versa. When temperature is taken into account, the dislocation boundaries become indistinct and the formation of dislocations is postponed due to the existence of dispersive small slippages. Due to the disturbance of temperature, dislocations present reciprocating movement. These findings contribute to the understanding of interlayer dislocations in two-dimensional materials, and will enable the exploration of many more strain related fundamental science problems and application challenges.

Effects of a graphene substrate on the structure and properties of atomically thin metal sheets

The production and use of atomically thin metal sheets are desirable but challenging. Here, density functional theory calculations indicate that the introduction of graphene as a support can play an unexpected role in the stability and function of Rh monolayer, as a representative of single-layer metal nanosheets. The graphene stabilizes the otherwise unstable Rh monolayer by the substrate interaction that not only impedes the out-of-plane movement of the Rh atoms but also decreases the surface energy. The Rh/graphene bilayer has good mechanical properties, comparable to those of emerging 2D graphene-based materials. The interfacial stress from the substrate interaction causes surface corrugations to form on the bilayer, exhibiting a degree of consistency in the direction and the area. Discrete magnetic units, compatible with the substrate interaction, are present in the corrugated Rh sheet. The visible magnetic anisotropy and spin-splitting of polarized carrier states of the corrugated Rh sheet dominate the spin-dependent transport in the bilayer film, which can be used as a building block for ultrathin electronic/spintronic devices.

Gapless van der Waals Heterostructures for Infrared Optoelectronic Devices

Mixed-dimensional van der Waals (vdW) heterostructures based on two-dimensional (2D) materials exhibit immense potential in infrared optoelectronic applications. However, the weak vdW coupling results in limiting performance of infrared optoelectronic device. Here, we exploit a gapless heterostructure that S dangling bonds of nonlayered PbS are connected to the bonding sites of MoS₂ (with factitious S vacancies) via strong orbital hybridization. The strong interface coupling leads to ultrahigh responsivity and photogain (G) exceeding 10⁵, and the detectivity (D*) is greater than 10¹⁴ Jones. More importantly, the gapless heterostructure shows fast rise and decay times about 47 and 49 μs, respectively, which is 5 orders of magnitude faster than that of transferred vdW heterostructures. Furthermore, an ultrahigh photon-triggered on/off ratio of 1.6 × 10⁶ is achieved, which is 4 orders of magnitude higher than that of transferred vdW heterostructures. This architecture can offer an effective approach for advanced infrared optoelectronic devices.

Graphether: a two-dimensional oxocarbon as a direct wide-band-gap semiconductor with high mechanical and electrical performances

Although many graphene derivatives have sizable band gaps, their electrical or mechanical properties are significantly degraded due to the low degree of π-conjugation. Besides the π-π conjugation, there exist hyperconjugative interactions arising from the delocalization of σ electrons. Inspired by the structural characteristics of a hyperconjugated molecule, dimethyl ether, we design a two-dimensional oxocarbon (named graphether) by the assembly of dimethyl ether molecules. Our first-principles calculations reveal the following findings: (1) monolayer graphether possesses excellent dynamic and thermal stabilities as demonstrated by its favourable cohesive energy, the absence of soft phonon modes, and high melting point. (2) It has a direct wide-band-gap energy of 2.39 eV, indicating its potential applications in ultraviolet optoelectronic devices. Interestingly, the direct band gap feature is rather robust against the external strains (-10% to 10%) and stacking configurations. (3) Due to the hyperconjugative effect, graphether has the high intrinsic electron mobility. More importantly, its in-plane stiffness (459.8 N m-1) is even larger than that of graphene. (4) The Pt(100) surface exhibits high catalytic activity for the dehydrogenation of dimethyl ether. The electrostatic repulsion serves as a driving force for the rotation and coalescence of two dehydrogenated precursors, which is favourable for the bottom-up growth of graphether. (5) Replacement of the C-C bond with an isoelectronic B-N bond can generate a stable Pmn21-BNO monolayer. Compared with monolayer hexagonal boron nitride, Pmn21-BNO has a moderate direct band gap energy (3.32 eV) and better mechanical property along the armchair direction.

Insights into the effect of the interlayer spacings of bilayer graphene on the desolvation of H+, Li+, Na+, and K+ ions with water as a solvent: a first-principles study

The desolvation effect of ions plays an important role in adjusting the capacity of supercapacitors and has attracted considerable attention after its discovery. Here, first-principles calculations were conducted to calculate the reaction energies of ions, water, and hydrated ions in bilayer graphene (BG) with different interlayer spacings (d) and to explore the desolvation behaviors of H+, Li+, Na+, and K+ ions. The calculated results showed that H+ can only exist in the state of H3O+ in AA-stacking BG, and desolvation exists only in the case of AB-stacking BG. The complete desolvation size for H+ ions in the AB-stacking system reached 5.6 Å, which was the largest desolvation size of the four ions studied. The critical desolvation sizes of Li+, Na+, and K+ in the BG layers of AA- and AB-stacking increased sharply as a consequence of the increasing ionic radius. However, the complete desolvation sizes of all three ions were in the range of 4-5 Å and with the increase in ionic radius, the complete desolvation sizes showed a reverse tendency. The complete desolvation size of Na+ in AB-stacking BG was slightly larger than that in AA-stacking BG. Further analysis presented that the ionic radii of H+, Li+, Na+, and K+ ions make a dominant contribution to the critical size of desolvation. Our present results provide useful information for improving the capacity of supercapacitors by precisely matching the pore structure and electrolyte through the adjustment of the pore structure of carbon materials.

Nanomechanics of graphene

The super-high strength of single-layer graphene has attracted great interest. In practice, defects resulting from thermodynamics or introduced by fabrication, naturally or artificially, play a pivotal role in the mechanical behaviors of graphene. More importantly, high strength is just one aspect of the magnificent mechanical properties of graphene: its atomic-thin geometry not only leads to ultra-low bending rigidity, but also brings in many other unique properties of graphene in terms of mechanics in contrast to other carbon allotropes, including fullerenes and carbon nanotubes. The out-of-plane deformation is of a 'soft' nature, which gives rise to rich morphology and is crucial for morphology control. In this review article, we aim to summarize current theoretical advances in describing the mechanics of defects in graphene and the theory to capture the out-of-plane deformation. The structure-mechanical property relationship in graphene, in terms of its elasticity, strength, bending and wrinkling, with or without the influence of imperfections, is presented.

Snap-through transition of buckled graphene membranes for memcapacitor applications

Using computational and theoretical approaches, we investigate the snap-through transition of buckled graphene membranes. Our main interest is related to the possibility of using the buckled membrane as a plate of capacitor with memory (memcapacitor). For this purpose, we performed molecular-dynamics (MD) simulations and elasticity theory calculations of the up-to-down and down-to-up snap-through transitions for membranes of several sizes. We have obtained expressions for the threshold switching forces for both up-to-down and down-to-up transitions. Moreover, the up-to-down threshold switching force was calculated using the density functional theory (DFT). Our DFT results are in general agreement with MD and analytical theory findings. Our systematic approach can be used for the description of other structures, including nanomechanical and biological ones, experiencing the snap-through transition.

Finding Stable Graphene Conformations from Pull and Release Experiments with Molecular Dynamics

Here, we demonstrate that stable conformations of graphene nanoribbons can be identified using pull and release experiments, when the stretching force applied to a single-layer graphene nanoribbon is suddenly removed. As it is follows from our numerical experiments performed by means of molecular dynamics simulations, in such experiments, favorable conditions for the creation of folded structures exist. Importantly, at finite temperatures, the process of folding is probabilistic. We have calculated the transition probabilities to folded conformations for a graphene nanoribbon of a selected size. Moreover, the ground state conformation has been identified and it is shown that its type is dependent on the nanoribbon length. We anticipate that the suggested pull and release approach to graphene folding may find applications in the theoretical studies and fabrication of emergent materials and their structures.

Structure and electronic properties of bilayer graphene functionalized with half-sandwiched transition metal-cyclopentadienyl complexes

Tuning the electronic and magnetic properties of graphene is a crucial problem in the design of practical on-off electronic devices. Using density functional theory calculations, we explore the electronic and magnetic properties of bilayer graphene functionalized by cyclopentadienyl (Cp = cyclopentadienyl, C5H5) based half-sandwich ligands, CpTM (TM = Sc-Ni). It is found that the adsorption of CpTM ligands can introduce high magnetic moments and open the band gap of bilayer graphene, due to the electron doping as well as the asymmetric charge distribution between two graphene layers. Furthermore, the p-n doping of bilayer graphene by co-binding F/NO2 and CpTM on two external sides of BLG can further widen the band gap up to 366.1 meV. This study proposes an effective way to the modulation of the electronic and magnetic properties of graphene.

High-coverage stable structures of 3d transition metal intercalated bilayer graphene

Alkali-metal intercalated graphite and graphene have been intensively studied for decades, where alkali-metal atoms are found to form ordered structures at the hollow sites of hexagonal carbon rings. Using first-principles calculations, we have predicted various stable structures of high-coverage 3d transition metal (TM) intercalated bilayer graphene (BLG) stabilized by the strain. Specifically, with reference to the bulk metal, Sc and Ti can form stable TM-intercalated BLG without strain, while the stabilization of Fe, Co, and Ni intercalated BLG requires the biaxial strain of over 7%. Under the biaxial strain ranging from 0% to 10%, there are four ordered sandwich structures for Sc with the coverage of 0.25, 0.571, 0.684, and 0.75, in which the Sc atoms are all distributed homogenously instead of locating at the hollow sites. According to the phase diagram, a homogenous configuration of C8Ti3C8 with the coverage of 0.75 and another inhomogeneous structure with the coverage of 0.692 were found. The electronic and magnetic properties as a function of strain were also analyzed to indicate that the strain was important for the stabilities of the high-coverage TM-intercalated BLG.

Critical length scales and strain localization govern the mechanical performance of multi-layer graphene assemblies

Multi-layer graphene assemblies (MLGs) or fibers with a staggered architecture exhibit high toughness and failure strain that surpass those of the constituent single sheets. However, how the architectural parameters such as the sheet overlap length affect these mechanical properties remains unknown due in part to the limitations of mechanical continuum models. By exploring the mechanics of MLG assemblies under tensile deformation using our established coarse-grained molecular modeling framework, we have identified three different critical interlayer overlap lengths controlling the strength, plastic stress, and toughness of MLGs, respectively. The shortest critical length scale L(C)(S) governs the strength of the assembly as predicted by the shear-lag model. The intermediate critical length L(C)(P) is associated with a dynamic frictional process that governs the strain localization propensity of the assembly, and hence the failure strain. The largest critical length scale L(C)(T) corresponds to the overlap length necessary to achieve 90% of the maximum theoretical toughness of the material. Our analyses provide the general guidelines for tuning the constitutive properties and toughness of multilayer 2D nanomaterials using elasticity, interlayer adhesion energy and geometry as molecular design parameters.

Interlayer interaction and related properties of bilayer hexagonal boron nitride: ab initio study

Properties of hexagonal boron nitride bilayer related to interlayer interaction (width and formation energy of dislocations, shear mode frequency, etc.) are estimated by approximation of potential energy surface by first Fourier harmonics.

Quantum Monte Carlo calculation of the binding energy of bilayer graphene

We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA-and AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9)  meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations.

Nitrogen Doping Enables Covalent-Like π-π Bonding between Graphenes

The neighboring layers in bilayer (and few-layer) graphenes of both AA and AB stacking motifs are known to be separated at a distance corresponding to van der Waals (vdW) interactions. In this Letter, we present for the first time a new aspect of graphene chemistry in terms of a special chemical bonding between the giant graphene "molecules". Through rigorous theoretical calculations, we demonstrate that the N-doped graphenes (NGPs) with various doping levels can form an unusual two-dimensional (2D) π-π bonding in bilayer NGPs bringing the neighboring NGPs to significantly reduced interlayer separations. The interlayer binding energies can be enhanced by up to 50% compared to the pristine graphene bilayers that are characterized by only vdW interactions. Such an unusual chemical bonding arises from the π-π overlap across the vdW gap while the individual layers maintain their in-plane π-conjugation and are accordingly planar. The existence of the resulting interlayer covalent-like bonding is corroborated by electronic structure calculations and crystal orbital overlap population (COOP) analyses. In NGP-based graphite with the optimal doping level, the NGP layers are uniformly stacked and the 3D bulk exhibits metallic characteristics both in the in-plane and along the stacking directions.

Oscillatory motion in layered materials: graphene, boron nitride, and molybdenum disulfide

Offset-driven self-retraction and oscillatory motion of bilayer graphene has been observed experimentally and is potentially relevant for nanoscale technological applications. In a previous article, we showed that friction between laterally offset graphene layers is controlled by roughness and proposed a simple reduced-order model based on density-functional theory (DFT) and molecular dynamics (MD) data, with which predictions on the experimental size-scale could be made. In this article, we extend our study to other layered materials, with emphasis on boron nitride (BN) and molybdenum disulfide (MoS2). Using MD and DFT simulations of these systems and a generalized version of the reduced-order model, we predict that BN will exhibit behavior similar to graphene (heavily-damped oscillation with a decay rate that increases with roughness) and that MoS2 shows no oscillatory behavior even in the absence of roughness. This is attributed to the higher energy barrier for sliding in MoS2 as well as the surface structure. Our generalized reduced-order model provides a guide to predicting and tuning experimental oscillation behavior using a few parameters that can be derived from simulation data.

Shear and friction between carbon nanotubes in bundles and yarns

We perform a detailed density functional theory assessment of the factors that determine shear interactions between carbon nanotubes (CNTs) within bundles and in related CNT and graphene structures including yarns, providing an explanation for the shear force measured in recent experiments (Filleter, T. etal. Nano Lett. 2012, 12, 73). The potential energy barriers separating AB stacked structures are found to be irrelevant to the shear analysis for bundles and yarns due to turbostratic stacking, and as a result, the tube-tube shear strength for pristine CNTs is estimated to be <0.24 MPa, that is, extremely small. Instead, it is pinning due to the presence of defects and functional groups at the tube ends that primarily cause resistance to shear when bundles are fractured in weak vacuum (∼10(-5) Torr). Such defects and groups are estimated to involve 0.55 eV interaction energies on average, which is much larger than single-atom vacancy defects (approximately 0.039 eV). Furthermore, because graphitic materials are stiff they have large coherence lengths, and this means that push-pull effects result in force cancellation for vacancy and other defects that are internal to the CNTs. Another important factor is the softness of cantilever structures relative to the stiff CNTs in the experiments, as this contributes to elastic instability transitions that account for significant dissipation during shear that has been observed. The application of these results to the mechanical behavior of yarns is discussed, providing general guidelines for the manufacture of strong yarns composed of CNTs.

The role of roughness-induced damping in the oscillatory motion of bilayer graphene

A multi-scale theoretical model is presented that is the first to offer quantitative agreement with experimental measurements of self-retraction and oscillation of bilayer graphene. The model integrates density-functional theory calculations of the energetics driving flake retraction and molecular-dynamics simulations capturing the dynamic response of laterally-offset rough surfaces. We demonstrate that nanoscale roughness explains self-retraction motion and propose a recipe for tuning that motion by controlling friction.

Interaction between graphene layers and the mechanisms of graphite's superlubricity and self-retraction

Graphene layer-layer interaction is explored as a function of the misorientation angle. A stepwise potential energy surface (PES), where the optimized commensurate configuration (AB stacking) corresponds to the global minimum and all incommensurate configurations correspond to nearly equal energies, is shown. The stepwise behavior is attributed to the alternating appearance of AB and AA stacking-like areas and the transition areas between them. Further, the PES of most incommensurate configurations is found to be ultra-smooth. Based on this, the puzzling experimental observation of graphite flake self-retraction is successfully explained.

Spin-polarized semiconductors: tuning the electronic structure of graphene by introducing a regular pattern of sp3 carbons on the graphene plane

First-principles calculations (generalized gradient approximation, density functional therory (DFT) with dispersion corrections, and DFT plus local atomic potential) are carried out on the stability and electronic structures of superlattice configurations of nitrophenyl diazonium functionalized graphene with different coverage. In the calculations, the stabilities of these structures are strengthened significantly since van der Waals interactions between nitrophenyl groups are taken into account. Furthermore, spin-polarized and wider-bandgap electronic structures are obtained when the nitrophenyl groups break the sublattice symmetry of the graphene. The unpaired quasi-localized p electrons are responsible for this itinerant magnetism. The results provide a novel approach to tune graphene's electronic structures as well as to form ferromagnetic semiconductive graphene.