Single-layer Sheets Research Articles

Nonlinear elastic behavior and anisotropic electronic properties of two-dimensional borophene

Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (β12, χ3, and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of β12, χ3, and striped phases over the strain ranges of −3.5%–3.5%, −4.5%–4.5%, and −2.5%–2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties.

Nanoscrolls Formed from Two-Dimensional Covalent Organic Frameworks

Two-dimensional (2D) covalent organic frameworks (COFs) represent an emerging class of nanomaterials with building blocks precisely connected in-plane through covalent bonds. Gaining insights into their structure and stabilities is critical to both their preparation and applications. Here, via atomistic molecular mechanics simulations and free-energy calculations, we investigate 2D COFs both under vacuum conditions and in solution, taking representative boronate ester-based and imine-based COFs as examples. Rather than remaining flat, single-layer 2D COF sheets with at least their length larger than ∼15–∼20 nm are found to preferably form nanoscrolls. These nanoscrolls display a finite number of configurations and represent open structures due to the large pores present in the 2D sheets; this feature distinguishes them from nanoscrolls formed by dense 2D materials such as graphene. Density functional theory calculations indicate that the intrasheet interactions in the nanoscrolls make their optical and el...

Fracture Toughnesses and Crack Growth Angles of Single-Layer Graphyne Sheets

Recently, Shang et al. (Angew Chem Int Ed 57(3):774–778, 2018) have developed a method to synthesize ultrathin (around 1.9 nm) graphyne nanosheets. We reported here the mixed-mode I–II fracture toughnesses and crack growth angles of single-layer graphyne sheets using molecular dynamics (MD) simulations and the finite element (FE) method based on the boundary layer model, respectively. The various carbon–carbon bonds of graphyne sheets in the FE method are equated with the nonlinear Timoshenko beams based on the Tersoff–Brenner potential, where all the parameters of the nonlinear beams are completely determined based on the continuum modeling. All the results from the present FE method are reasonable in comparison with those from our MD simulations using the REBO potential. The present results show that both the critical stress intensity factors (SIFs) and the crack growth angle strongly depend on the chirality and loading angle $$\varphi $$ ( $$\varphi =90^{\circ }$$ and $$\varphi =0^{\circ }$$ representing pure mode I and pure mode II, respectively). Meanwhile, the fracture properties of single-layer cyclicgraphene and supergraphene sheets are also studied in order to compare with those of the graphyne sheets. The critical equivalent SIFs are derived as $$1.55<K_{{\text {eq-cy}}}$$ (cyclic) $$<1.95$$ nN A $$^{-3/2}$$ , $$1.64<K_{{\text {eq-gy}}}$$ (graphyne) $$<2.64$$ nN A $$^{-3/2}$$ and $$0.61<K_{{\text {eq-su}}}$$ (super) $$<2.04$$ nN A $$^{-3/2}$$ in the corresponding zigzag and armchair sheets using the MD simulations, while the SIFs are $$0.32<K_{{\text {eq-cy}}}$$ (cyclic) $$<0.48$$ nN A $$^{-3/2}$$ , $$1.96<K_{{\text {eq-gy}}}$$ (graphyne) $$<2.49$$ nN A $$^{-3/2}$$ and $$1.42<K_{{\text {eq-su}}}$$ (super) $$<2.95$$ nN A $$^{-3/2}$$ using the FE method. These findings should be of great help for understanding the fracture properties of carbon allotropes and designing the carbon-based nanodevices.

General Self-Assembly Method for Deposition of Graphene Oxide into Uniform Close-Packed Monolayer Films.

Depositing a morphologically uniform monolayer film of graphene oxide (GO) single-layer sheets is an important step in the processing of many composites and devices. Conventional Langmuir-Blodgett (LB) deposition is often considered to give the highest degree of morphology control, but film microstructures still vary widely between GO samples. The main challenge is in the sensitive self-assembly of GO samples with different sheet sizes and degrees of oxidation. To overcome this drawback, here, we identify a general method that relies on robust assembly between GO and a cationic surfactant (cationic surfactant-assisted LB). We systematically compared conventional LB and cationic surfactant-assisted LB for three common GO samples of widely different sheet sizes and degrees of oxidation. Although conventional LB may occasionally provide satisfactory film morphology, cationic surfactant-assisted LB is general and allows deposition of films with tunable and uniform morphologies-ranging from close-packed to overlapping single layers-from all three types of GO samples investigated. Because cationic surfactant-assisted LB is robust and general, we expect this method to broaden and facilitate the use of GO in many applications where precise control over film morphology is crucial.

Molecular dynamics simulation on the buckling of single-layer MoS2 sheet with defects under uniaxial compression

The buckling behavior of a single layer MoS2 (SLMoS2) sheet with defects under uniaxial compression is investigated with molecular simulation in the present paper. Five typical defects are introduced to estimate the instability characteristics of defective MoS2 sheet. The buckling responses, including the critical strain and geometric morphology, influenced by defect type, stain rate, defect density and so on, are comprehensively explored. It is found that different type of defects results in reduction of the bending modulus to some different extent. Compared with the other three post-buckling morphologies, the first typical geometric morphology show the biggest difference between the defect-free and defective SLMoS2 sheets. It seems possible to realize our desired morphology in flexible electronics by proper preparing different kinds of defects. The finding in the present paper should be useful for the promising design of flexible optoelectronic devices and soft bioelectronics.

Spatially Precise Transfer of Patterned Monolayer WS2 and MoS2 with Features Larger than 104 μm2 Directly from Multilayer Sources

A current challenge in the processing of 2D materials, or “van der Waals (vdW) solids”, is the transfer of 2D layers from source crystals and growth substrates onto target substrates. Transfer—as opposed to direct growth and patterning on the target—enables low-temperature processing of the target as well as the use of diverse target materials. These two attributes will allow the assembly of vdW heterostructures to realize devices exploiting the unique properties of vdW materials. Until now, however, there has been no effective method for transferring regions of monolayer material of controlled shape from a multilayer source. We introduce such a method and demonstrate its use in the spatially controlled transfer of arrays of single-layer MoS2 and WS2 sheets from multilayer crystals onto SiO2 substrates. These sheets have lateral sizes exceeding 100 μm and are electronically continuous. The method offers a scalable route to parallel manufacturing of complex circuits and devices from vdW materials.

Mechanical characterization of phase-changed single-layer MoS2 sheets

Phase transitions in 2D materials, such as MoS2, result in drastic changes in the physical properties of the material. A change in the phase of MoS2 from 2H to 1T transforms it from a semiconductor to conductor, thus broadening its potential applications in electronics. The structural transformation associated with the phase change may significantly affect the mechanical properties. Here we statistically characterized the elastic modulus and fracture strength of phase-changed single-layer MoS2 sheets using the atomic force microscopy (AFM) nanoindentation technique. MoS2 sheets were subjected to lithium intercalation, which transformed them from the 2H phase to the 1T phase. The transformed sheets were again annealed to make a partially phase-changed sample. The elastic modulus and fracture strength of 1T phase MoS2 were about 50% lower than those of 2H phase MoS2. Annealing of the 1T phase MoS2 sheet resulted in a good recovery of the mechanical properties, up to 90% of those of the original 2H phase MoS2. This result was attributed to a mixture of phases in the annealed product, and the ratio of the phases was evaluated spectroscopically. Interestingly, while the fracture strengths differed for the three phases, their average fracture strains were quite similar, suggesting that the overall structure of the material maintained its integrity during the phase transition process.

Catalytic combustion of VOC on sandwich-structured Pt@ZSM-5 nanosheets prepared by controllable intercalation.

A sandwich-structured Pt@ZSM-5 nanosheets (Pt@PZN-2) was fabricated by controllable intercalating Pt nanoparticles between ZSM-5 single-layer sheets via electrostatic adsorption with ammonium ions in diquaternary ammonium surfactant, and the following calcinations. Pt clusters (ca. 4.3 nm) confined between nanosheet layers (thickness of ca. 2.9 nm) exhibits better dispersion and higher thermal stability even after high-temperature treatment, while the Pt clusters also served as pillars which well protected the inter-layers mesopores. Catalytic combustion of toluene (a model compound of large molecules VOCs) shows catalytic activity of Pt@PZN-2 is significant higher than that of Pt-loaded nanosheet ZSM-5 zeolite prepared by conventional impregnation (Pt/ZN-2). For example, the temperature at 98% toluene conversion of Pt@PZN-2 is only 176 °C which is 24 °C and 34 °C lower than that of Pt/ZN-2 and bulky ZSM-5 supported Pt by impregnation (Pt/CZ-500), respectively. Meanwhile, Pt@PZN-2 also gives 100% toluene conversion for more than 360 h at 230 °C with a higher metal stability. The good performance of Pt@PZN-2 was attributed to the high accessibility and enhanced diffusion of the bulky reactant to active site confined in the stable inter-layer mesopores resulting from the pillar of Pt nanoparticles.

Single point incremental forming of Cu-Al composite sheets: A comprehensive study on deformation behaviors

Compared with monolithic metal sheet, Single Point Incremental Forming (SPIF) of bimetal composite sheet has attracted increasing attention, as it takes advantages of materials with different superior properties, such as high strength, low density, and good corrosion resistance. However, deformation behaviors of bimetal composite sheet in SPIF may differ from the single-layer sheet, which depends on the layer arrangements and mechanical properties of each layer. In this regard, a comprehensive study was conducted to investigate the deformation behaviors of roll-bonded Cu-Al composite sheets in SPIF through predictive modeling, including analytical, empirical as well as numerical approaches, and extensive experimental work taking into consideration effects of key process parameters. It was demonstrated that overall, the formability, surface roughness, thickness variation and forming force in different layer arrangements, in terms of various process parameters, follow the similar trends to single-layer sheets. However, it was further revealed that deformation mode of layer-up sheet tends to a compression state and that of layer-down sheet tends to a stretching state. This leads to higher formability and larger forming force in Al/Cu layer arrangement compared to Cu/Al layer arrangement, as the exterior thinner but stronger Cu layer could endure more stretching deformation.

Metal/graphene heterobilayers as hydrogen evolution reaction cathodes: a first-principles study.

From the study of precious metal/graphene heterobilayers instead of commercial Pt/C catalysts, we propose a strategy for improving the performance/cost ratio of metals in electrocatalysis. Results from the Rh/graphene bilayer show that the Rh atoms that directly interact with graphene occupy most of the area of the supported metal sheet, and they exhibit better hydrogen evolution reaction (HER) activity than Rh and even than Pt. The interlayer charge transfer, rather than the intralayer charge transfer, leads to the downshift of the d-states of these Rh atoms in energy and weakens the H-Rh binding. This allows the HER process to be almost thermo-neutral. Support interactions determine whether the interlayer charge transfer or the intralayer charge transfer is dominant in the bilayer and surface corrugations on the two sheets. A different structure-activity relationship is present in two-dimensional systems. This study on the corrugation-sensitive HER activity and the activation mechanism of Rh/graphene heterobilayers is also helpful for the design of more ultrathin precious or non-precious metal/graphene heterostructures used as electrodes in water electrolysis.

Wrinkling and failure behavior of single-layer MoS2 sheets under in-plane shear.

In this paper, the wrinkling and failure behavior of single layer MoS2 (SLMoS2) sheets under in-plane shear is investigated using molecular simulations and the nonlocal model. Wrinkling and failure features, such as the stress-strain relation, the amplitude and the half-wavelength, are comprehensively explored. The effects of size, temperature and pre-existing cracks on the wrinkling and failure behavior are then taken into consideration. It is found that the whole process can be divided into three stages, i.e., the pre-buckling stage, the buckling stage and the failure stage. The classical continuum model is found to be limited in quantitatively analyzing the wrinkling behavior due to the lack of size effect. The nonlocal parameter, a key parameter to characterize the size effect, is first reported. What is more, compared with edge cracks, SLMoS2 sheets are more sensitive to pre-existing centre cracks. This work can provide a better understanding of the wrinkling and failure properties of SLMoS2 sheets under shear loads, and should be helpful for developing various flexible electronic devices.

Nonlinear vibrations of circular single-layer black phosphorus resonators

A strong nonlinear relationship between the displacement and the load in single-layer black phosphorus sheets (SLBPs) was observed under the large deflection by nanoindentation experiments. However, the nonlinear effect is rarely considered in the Nano-Electro-Mechanical-System (NEMS) resonators based on the SLBPs. In this letter, nonlinear static and dynamics behaviors of circular SLBPs (CSLBPs) are investigated using molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM), respectively, where the geometrical nonlinearity is systematically considered in the NOPM. Our results show that the response-frequency curves of forced vibrations in CSLBPs meet clear hardening-type nonlinearity. The damping ratios of CSLBPs are proportional to the square of the vibration amplitude. In particular, the NOPM together with the law of energy equipartition is further utilized to study the nonlinear thermal vibrations of the CSLBPs. Checking against present MD calculations shows that the solution of the present NOPM has high accuracy. The present study should be of great help for designing NEMS resonators based on two-dimensional (2D) orthotropic materials.

In Situ Optical Tracking of Electroablation in Two-Dimensional Transition-Metal Dichalcogenides.

Two-dimensional (2D) transition-metal dichalcogenides (TMDs) are a unique class of 2D materials possessing unique optoelectronic properties when exfoliated into mono- and few-layer sheets. Recently, electroablation (EA) has become of interest as a promising synthesis method for single-layer sheets of TMDs. Here, we introduce spectroelectrochemical micro-extinction spectroscopy (SE-MExS) as a high-throughput technique to study electrochemical thinning of TMDs as it occurs. This approach enables the parallel use of spectroscopy and imaging to nondestructively characterize 2D materials in situ. We unravel optoelectronics of the TMDs by observing changes in optical properties during EA. We find that the EA process for MoS2, WS2, MoSe2, and WSe2 occurs edge first, generating high density of edge sites. Our results show that stable monolayers of MoS2, WS2, and MoSe2 can be synthesized from bulk precursors by the EA process, while conversely, no WSe2 remains postablation.

Atomistic insights into mechanical and thermal properties of stanene with defects

Stanene, two-dimensional, graphene-like buckled honeycomb structure, has been deemed as a potential material for the next generation nano-electronics application. In electronic applications, the materials are subjected to both thermal and mechanical loadings. In addition, structural defects are inevitable during synthesis of nanomaterials. Therefore, it is essential to study the mechanical and thermal properties of stanene with various structural defects. We investigated the effects of point vacancy, bivacancy and Stone-Wales defects on tensile response and thermal transport of single-layer bulk stanene sheets using classical molecular dynamics (MD) simulations. MEAM potential is used to describe the inter-atomic forces in order to predict the properties of the stanene adequately. We probed the deformation process of defective bulk stanene by applying uniaxial tensile loading. Our study suggests that tensile strength and elastic modulus of stanene decrease with the increment of defect concentrations. Moreover, stanene sheet with Stone-Wales defect shows less in-plane stiffness to the loading. Using non-equilibrium molecular dynamics (NEMD) method, we found that, the phonon thermal conductivity of stanene is highly sensitive to defect concentrations. Only 0.1% of defect concentrations result in about 40% reduction in thermal conductivity. To elucidate the underlying mechanism responsible for this reduction, vibrational density of states (vDOS) are calculated. Overall, our reported results provide an insight into the effect of defects in mechanical and thermal properties of defective bulk stanene and will facilitate further tailoring of the design of stanene based nanoelectronics device.

Facile Synthesis of Graphene Oxide for Multicycle Adsorption of Aqueous Pb2+ in the Presence of Divalent Cations and Polyatomic Anions

This study reports a low-cost, NaNO3-free synthesis of graphene oxide (GO) at room temperature, for the purpose of Pb2+ adsorption in single, binary, and ternary association. The GO displays single layered sheets of ∼1 nm thickness with specific surface area of 195 m2/g. The removal of Pb2+ shows an equilibrium time of 15 min with maximum adsorption of 178.5 mg/g, which is best fitted to pseudo-second-order kinetic and Langmuir adsorption isotherm model. A reduction in adsorption efficiency of Pb2+ by 9.52% in Pb2+−Ni2+ and 10.88% in Pb2+−Cd2+ was observed with an increase in concentration of Ni2+ and Cd2+ from 10 to 50 mg/L. Similarly, 19.31% drop in overall efficiency of Pb2+ was observed with increase in the initial concentration of ternary solution (Pb2+ ̵ Ni2+ ̵ Cd2+) from 10 to 50 mg/L. The presence of SO42– and NO3– up to 800 mg/L has little effect on Pb2+ adsorption, compared to Ni2+ and Cd2+. The GO shows only 11.8% decrease in Pb2+ adsorption after five consecutive adsorption–desorption cycles. This study signifies the economic potential of GO toward selective removal of Pb2+ from wastewater in the presence of divalent cations and polyatomic anions on the basis of its multicycle performance.

Can an element form a two-dimensional nanosheet of type 15 pentagons?

Type 15 pentagon was recently discovered three decades since the 14th type of pentagon was reported in 1985. In contrast to such a long time span, the list of two-dimensional (2D) materials keeps growing longer on a monthly (if not daily) basis according to emerging experimental and theoretical reports. Combining these two seemingly irrelevant topics, we apply density functional theory (DFT) calculations to examine the possibility of forming a 2D nanosheet with the vertices of type 15 pentagons occupied by boron, carbon, silicon, phosphorous, sulfur, gallium, germanium, or tin atoms. We find that none of the optimized eight nanosheets remain the same initial structure filled with type 15 pentagons after the geometry optimizations by a DFT calculator. Instead, we obtain different rearranged structures for each nanosheet, most of which have not yet been reported before. For example, gallium atoms form a 2D nanosheet structure with a triangular pattern similar to single-layer boron sheet called borophene. These new 2D materials exhibit formation energies comparable to that of single-layer silicene, implying the feasibility of being grown on a substrate. The electronic structure shows that all the eight nanosheets are metallic (or semi-metallic for the carbon nanosheet), compensating for the dearth of metallic systems in existing 2D materials that are mostly semiconducting. Our work shows that linking a pentagonal geometry with DFT calculations yields both educational and scientific merits.

N-graphdiyne two-dimensional nanomaterials: Semiconductors with low thermal conductivity and high stretchability

Most recently, N-graphdiyne two-dimensional (2D) nanomaterials were successfully experimentally realized at the gas/liquid and liquid/liquid interfaces. We accordingly conducted density functional theory (DFT) and molecular dynamics simulations to explore the mechanical/failure, thermal conductivity and stability, electronic and optical properties of three N-graphdiyne nanomembranes. Our DFT results of uniaxial tensile simulations reveal that these monolayers can yield remarkably high stretchability or tensile strength depending on the atomic structure and loading direction. Studied N-graphdiyne nanomembranes were found to exhibit semiconducting electronic character, with band-gap values ranging from 0.98 eV to 3.33 eV, based on the HSE06 estimations. The first absorption peak suggests that these 2D structures can absorb visible, IR and NIR light. Ab initio molecular dynamics results reveal that N-graphdiyne 2D structures can withstand at high temperatures, like 2000 K. Thermal conductivities of suspended single-layer N-graphdiyne sheets were predicted to be almost temperature independent and about three orders of magnitude smaller than that of the graphene. The comprehensive insight provided by this work highlights the outstanding physics of N-graphdiyne 2D nanomaterials, and suggest them as highly promising candidates for the design of novel stretchable nanodevices.

Enhanced Magnetic Field Sensing Using Planar High-Temperature Superconductor Shields

Experimental and finite element model studies of magnetic shielding characteristics of one-side planar sheet structures of the second generation high-temperature superconducting (2GHTS) coated conductor tapes show that significant shielding can be achieved. The shields are shown to be useful for attenuating noise and enhancing the measurement accuracy of magnetic fields. The shields are particularly important for shielding the perpendicular component of the noise during the measurements. The location of the sensor with respect to the shield and the dimensions of the shield need to be designed appropriately to achieve the needed measurement accuracy. The number of superconducting layers in the shield is a design parameter that depends on the magnitude of the noise. The experimental results on shielding factor of a single layer sheet agree with the results of the finite element model.

The ionized graphene oxide membranes for water-ethanol separation

Nanoporous graphene oxide (GO) membranes have shown great promise in separating water and ethanol with high flux and selectivity. The current design of these membranes focuses on tuning the pore sizes in GO sheets to achieve superior selectivity. In this paper, using molecular dynamics simulations, we study the feasibility of achieving effective water-ethanol separation by tuning the ionization of the functional groups on the periphery of pores in single-layer GO sheets. For pores featuring neutral carboxyl (COOH) groups, the water-to-ethanol selectivity coefficient is ∼7 when the pore diameter is 0.68 nm but decays to ∼1.5 when the pore diameter increases to ∼1.12 nm. However, our simulations suggest that through the ionization (deprotonation) of the COOH groups of the 1.12 nm-wide pores, we can achieve a water-to-ethanol selectivity coefficient of ∼7 in these pores. This improvement is mainly attributed to the enhanced (suppressed) accessibility of water (ethanol) molecules to the pore induced by the ionization of the functional groups.

Molecular simulation of permeation behaviour of ethanol/water molecules with single-layer graphene oxide membranes

Graphene oxide (GO)-based materials have shown promise as water-permeating membranes in pervaporation separation. However, the feed permeation and surface affinity of single-layer nanoporous GO sheet for liquid mixtures remain unresolved. Here, the pressure-driven molecular transport of pure ethanol and pure water, as well ethanol-water mixtures, crossing through single-layer nanoporous GO sheet was studied by non-equilibrium molecular dynamics simulations. We show that single-layer GO sheet with controlled pore sizes can effectively reject ethanol and allow water permeation with high permeability. This means that porous GO sheets could act as an effective dehydration membrane, therefore providing the initial barrier for ethanol passage in GO-based membrane. The pore size effect was considered as the separation mechanism. Both ethanol and water molecules in the mixture show comparable affinity with GO surfaces. The hydrogen-bonding coupling interaction between mixture and surface functional groups provide addition influence on the molecular transport through GO pores.