Geometry, mechanics, and electronics of singular structures and wrinkles in graphene

Metal-Cation-Induced Tiny Ripple on Graphene

Ripples on graphene play a crucial role in manipulating its physical and chemical properties. However, producing ripples, especially at the nanoscale, remains challenging with current experimental methods. In this study, we report that tiny ripples in graphene can be generated by the adsorption of a single metal cation (Na+, K+, Mg2+, Ca2+, Cu2+, Fe3+) onto a graphene sheet, based on the density functional theory calculations. We attribute this to the cation-π interaction between the metal cation and the aromatic rings on the graphene surface, which makes the carbon atoms closer to metal ions, causing deformation of the graphene sheet, especially in the out-of-plane direction, thereby creating ripples. The equivalent pressures applied to graphene sheets in out-of-plane direction, generated by metal cation-π interactions, reach magnitudes on the order of gigapascals (GPa). More importantly, the electronic and mechanical properties of graphene sheets are modified by the adsorption of various metal cations, resulting in opened bandgaps and enhanced rigidity characterized by a higher elastic modulus. These findings show great potential for applications for producing ripples at the nanoscale in graphene through the regulation of metal cation adsorption.

Tuning instability in suspended monolayer 2D materials

Monolayer two-dimensional (2D) materials possess excellent in-plane mechanical strength yet extremely low bending stiffness, making them particularly susceptible to instability, which is anticipated to have a substantial impact on their physical functionalities such as 2D-based Micro/Nanoelectromechanical systems (M/NEMS), nanochannels, and proton transport membrane. In this work, we achieve quantitatively tuning instability in suspended 2D materials including monolayer graphene and MoS2 by employing a push-to-shear strategy. We comprehensively examine the dynamic wrinkling-splitting-smoothing process and find that monolayer 2D materials experience stepwise instabilities along with different recovery processes. These stepwise instabilities are governed by the materials' geometry, pretension, and the elastic nonlinearity. We attribute the different instability and recovery paths to the local stress redistribution in monolayer 2D materials. The tunable instability behavior of suspended monolayer 2D materials not only allows measuring their bending stiffness but also opens up new opportunities for programming the nanoscale instability pattern and even physical properties of atomically thin films.

Interplay of graphene-DNA interactions: Unveiling sensing potential of graphene materials

Graphene-based materials and DNA probes/nanostructures have emerged as building blocks for constructing powerful biosensors. Graphene-based materials possess exceptional properties, including two-dimensional atomically flat basal planes for biomolecule binding. DNA probes serve as excellent selective probes, exhibiting specific recognition capabilities toward diverse target analytes. Meanwhile, DNA nanostructures function as placement scaffolds, enabling the precise organization of molecular species at nanoscale and the positioning of complex biomolecular assays. The interplay of DNA probes/nanostructures and graphene-based materials has fostered the creation of intricate hybrid materials with user-defined architectures. This advancement has resulted in significant progress in developing novel biosensors for detecting DNA, RNA, small molecules, and proteins, as well as for DNA sequencing. Consequently, a profound understanding of the interactions between DNA and graphene-based materials is key to developing these biological devices. In this review, we systematically discussed the current comprehension of the interaction between DNA probes and graphene-based materials, and elucidated the latest advancements in DNA probe-graphene-based biosensors. Additionally, we concisely summarized recent research endeavors involving the deposition of DNA nanostructures on graphene-based materials and explored imminent biosensing applications by seamlessly integrating DNA nanostructures with graphene-based materials. Finally, we delineated the primary challenges and provided prospective insights into this rapidly developing field. We envision that this review will aid researchers in understanding the interactions between DNA and graphene-based materials, gaining deeper insight into the biosensing mechanisms of DNA-graphene-based biosensors, and designing novel biosensors for desired applications.

Conversion of chirality to twisting via sequential one-dimensional and two-dimensional growth of graphene spirals

The properties of two-dimensional (2D) van der Waals materials can be tuned through nanostructuring or controlled layer stacking, where interlayer hybridization induces exotic electronic states and transport phenomena. Here we describe a viable approach and underlying mechanism for the assisted self-assembly of twisted layer graphene. The process, which can be implemented in standard chemical vapour deposition growth, is best described by analogy to origami and kirigami with paper. It involves the controlled induction of wrinkle formation in single-layer graphene with subsequent wrinkle folding, tearing and re-growth. Inherent to the process is the formation of intertwined graphene spirals and conversion of the chiral angle of 1D wrinkles into a 2D twist angle of a 3D superlattice. The approach can be extended to other foldable 2D materials and facilitates the production of miniaturized electronic components, including capacitors, resistors, inductors and superconductors.

Dielectrophoretic force-induced wrinkling of graphene oxide: Enhancing electrical conductivity and expanding biosensing applications

Graphene oxide (GO) has many advantages, making it suitable for various applications. However, it has low electrical conductivity, restricting its applicability to electrochemical biosensors. This study used dielectrophoretic (DEP) force to control the movement and deformation of GO nanosheets to achieve high electrical conductivity without the chemical reduction of oxygen functional groups. Subjecting the DEP force to GO nanosheets induced physical deformation leading to the formation of wrinkled structures. A computational simulation was performed to set an appropriate electrical condition for operating a positive DEP force effect of at least 1019 v2/m3, and the interdigitated microelectrode structure was selected. The resulting wrinkled GO exhibited significantly improved electrical conductivity, reaching 21.721 μS while preserving the essential oxygen functional groups. Furthermore, a biosensor was fabricated using wrinkled GO deposited via DEP force. The biosensor demonstrated superior sensitivity, exhibiting a 9.6-fold enhancement compared with reduced GO (rGO) biosensors, as demonstrated through biological experiments targeting inducible nitric oxide synthase. This study highlights the potential of using DEP force to enhance electrical conductivity in GO-based biosensing applications, opening new avenues for high-performance diagnostics.

Domain convexification: A simple model for invasion processes

We propose an invasion model where domains grow up to their convex hulls and merge when they overlap. This model can be seen as a continuum and isotropic counterpart of bootstrap percolation models. From numerical investigations of the model starting with randomly deposited overlapping disks on a plane, we find an invasion transition that occurs via macroscopic avalanches. The disk concentration threshold and the width of the transition are found to decrease as the system size is increased. Our results are consistent with a vanishing threshold in the limit of infinitely large system sizes. However, this limit could not be investigated by simulations. For finite initial concentrations of disks, the cluster size distribution presents a power-law tail characterized by an exponent that varies approximately linearly with the initial concentration of disks. These results at finite initial concentration open novel directions for the understanding of the transition in systems of finite size. Furthermore, we find that the domain area distribution has oscillations with discontinuities. In addition, the deviation from circularity of large domains is constant. Finally, we compare our results to experimental observations on de-adhesion of graphene induced by the intercalation of nanoparticles.

Geometric, electronic and transport properties of bulged graphene: A theoretical study

Out-of-plane deformation in graphene is unavoidable during both synthesis and transfer procedures due to its special flexibility, which distorts the lattice and eventually imposes crucial effects on the physical features of graphene. Nowadays, however, little is known about this phenomenon, especially for zero-dimensional bulges formed in graphene. In this work, employing first-principles-based theoretical calculations, we systematically studied the bulge effect on the geometric, electronic, and transport properties of graphene. We demonstrate that the bulge formation can introduce mechanical strains (lower than 2%) to the graphene's lattice, which leads to a significant charge redistribution throughout the structure. More interestingly, a visible energy band splitting was observed with the occurrence of zero-dimensional bulges in graphene, which can be attributed to the interlayer coupling that stems from the bulged structure. In addition, it finds that the formed bulges in graphene increase the electron states near the Fermi level, which may account for the enhanced carrier concentration. However, the lowered carrier mobility and growing phonon scattering caused by the formed bulges diminish the transport of both electrons and heat in graphene. Finally, we indicate that bulges arising in graphene increase the possibility of intrinsic defect formation. Our work will evoke attention to the out-of-plane deformation in 2D materials and provide new light to tune their physical properties in the future.

A wrinkled nanosurface causes accelerated protein unfolding revealing its critical role in nanotoxicity

Wrinkles are often found to have a strong influence on the properties of nanomaterials and have attracted extensive research interest. However, the consequences of the use of wrinkled nanomaterials in biological systems remain largely unknown. Here, using molecular dynamics simulations, we studied the interactions of a wrinkled graphene with proteins, using the villin headpiece (HP35) as the representative model. Our results clearly revealed that the wrinkle, especially the wrinkle corner, showed stronger binding affinity to HP35 than the planar surface where HP35 experienced accelerated and more severe unfolding. This is because the transverse translocation of the aromatic residues of the protein is highly confined at the wrinkle corner. The movement of other parts of the protein causes unfolding of the protein secondary structure and releases hydrophobic residues to bind to graphene, causing complete denaturation. Further free energy analyses revealed that this is attributed to the stronger binding affinity of residues to the wrinkle corner than to the planar surface. The present findings provide a deeper understanding of the effect of graphene wrinkles on protein stability. This finding may be generalized to other types of biomolecules and may also guide the design of biomedical nanomaterials through surface structural engineering.

Wrinkled nanosurface can cause more severe protein distorsions than planar nanosurface because of stronger interactions.

The Ripple Effect of Graphite Nanofilm on Stretchable Polydimethylsiloxane for Optical Sensing

Graphene-based optical sensing devices have been widely studied for their broad band absorption, high carrier mobility, and mechanical flexibility. Due to graphene’s weak light absorption, studies on graphene-based optical sensing thus far have focused on hybrid heterostructure devices to enhance photo-absorption. Such hybrid devices need a complicated integration process and lead to deteriorating carrier mobility as a result of heterogeneous interfaces. Rippled or wrinkled graphene has been studied in electronic and optoelectronic devices. However, concrete demonstrations of the impact of the morphology of nanofilms (e.g., graphite and graphene) associated with light absorption in optical sensing devices have not been fully examined. This study explored the optical sensing potential of a graphite nanofilm surface with ripples induced by a stretchable polydimethylsiloxane (PDMS) supporting layer under different stretch:release ratios and then transferred onto silicon, both under experimental conditions and via simulation. The optical sensing potential of the rippled graphite nanofilm was significantly enhanced (260 mA/W at the stretch–release state of 30%), as compared to the pristine graphite/PDMS (20 mA/W at the stretch–release state of 0%) under laser illumination at a wavelength of 532 nm. In addition, the results of our simulated computation also confirmed the improved light absorption of rippled graphite nanofilm surface-based optical sensing devices, which was comparable with the results found in the experiment.

Phonon transport in graphene based materials

Graphene, due to its atomic layer structure, has the highest room temperature thermal conductivity k for all known materials. Thus, it is expected that graphene based materials are the best candidates for thermal management in next generation electronic devices. In this perspective, we first review the in-plane k of monolayer graphene and multilayer graphene obtained using experimental measurements, theoretical calculations and molecular dynamics (MD) simulations. Considering the importance of four-phonon scattering in graphene, we also compare the effects of three-phonon and four-phonon scattering on phonon transport in graphene. Then, we review phonon transport along the cross-plane direction of multilayer graphene and highlight that the cross-plane phonon mean free path is several hundreds of nanometers instead of a few nanometers as predicted using classical kinetic theory. Recently, hydrodynamic phonon transport has been observed experimentally in graphitic materials. The criteria for distinguishing the hydrodynamic from ballistic and diffusive regimes are discussed, from which we conclude that graphene based materials with a high Debye temperature and high anharmonicity (due to ZA modes) are excellent candidates to observe the hydrodynamic phonon transport. In the fourth part, we review how to actively control phonon transport in graphene. Graphene and graphite are often adopted as additives in thermal management materials such as polymer nanocomposites and thermal interface materials due to their high k. However, the enhancement of the composite's k is not so high as expected because of the large thermal resistance between graphene sheets as well as between the graphene sheet and matrix. In the fifth part, we discuss the interfacial thermal resistance and analyze its effect on the thermal conductivity of graphene based materials. In the sixth part, we give a brief introduction to the applications of graphene based materials in thermal management. Finally, we conclude our review with some perspectives for future research.

Advanced Optical Detection through the Use of a Deformably Transferred Nanofilm

Graphene has been extensively investigated in advanced photodetection devices for its broadband absorption, high carrier mobility, and mechanical flexibility. Due to graphene’s low optical absorptivity (2.3%), graphene-based photodetection research so far has focused on hybrid systems to increase photoabsorption. However, such hybrid systems require a complicated integration process and lead to reduced carrier mobility due to heterogeneous interfaces. Crumpled or deformed graphene has previously been reported in electronics and optoelectronics. However, a depth study on the influence of the morphology of nanofilms (e.g., graphite or graphene) related to light absorption in photodetection devices has not been demonstrated yet. Here, we present an interesting study in terms of the effect of the deformable surface and the smooth surface of a nanofilm transferred onto Si through two transfer strategies using isopropanol injection and nitrogen blowing (to form a deformable nanofilm surface) and deionized water injection and van der Waals interaction (to form a smooth nanofilm surface). As a result, optical detection in the case of the deformable nanofilm surface was enhanced significantly (~100%) compared with that of the smooth nanofilm surface in the visible laser wavelength (532 nm). In addition, evidence from the computational simulation also firmly affirms an advancement in the optical detection of deformed nanofilm-surface-based photodetection devices compatible with the experimental results.

Computational study of the water-driven graphene wrinkle life-cycle towards applications in flexible electronics

The ubiquitous presence of wrinkles in two-dimensional materials alters their properties significantly. It is observed that during the growth process of graphene, water molecules, sourced from ambient humidity or transferred method used, can get diffused in between graphene and the substrate. The water diffusion causes/assists wrinkle formation in graphene, which influences its properties. The diffused water eventually dries, altering the geometrical parameters and properties of wrinkled graphene nanoribbons. Our study reveals that the initially distributed wrinkles tend to coalesce to form a localized wrinkle whose configuration depends on the initial wrinkle geometry and the quantity of the diffused water. The movement of the localized wrinkle is categorized into three modes—bending, buckling, and sliding. The sliding mode is characterized in terms of velocity as a function of diffused water quantity. Direct bandgap increases linearly with the initial angle except the highest angle considered (21°), which can be attributed to the electron tunneling effect observed in the orbital analysis. The system becomes stable with an increase in the initial angle of wrinkle as observed from the potential energy plots extracted from MD trajectories and confirmed with the DOS plot. The maximum stress generated is less than the plastic limit of the graphene.

Critical Stable Length in Wrinkles of Two-Dimensional Materials

The emergent two-dimensional (2D) materials are atomically thin and ultraflexible, promising for a variety of miniaturized, high-performance, and flexible devices in applications. On one hand, the ultrahigh flexibility causes problems: the prevalent wrinkles in 2D materials may undermine the ideal properties and create barriers in fabrication, processing, and quality control of materials. On the other hand, in some cases the wrinkles are used for the architecturing of surface texture and the modulation of physical/chemical properties. Therefore, a thorough understanding of the mechanism and stability of wrinkles is highly needed. Herein, we report a critical length for stabilizing the wrinkles in 2D materials, observed in the wrinkling and wrinkle elimination processes upon thermal annealing as well as by our in situ TEM manipulations on individual wrinkles, which directly capture the evolving wrinkles with variable lengths. The experiments, mechanical modeling, and self-consistent charge density functional tight binding (SCC-DFTB) simulations reveal that a minimum critical length is required for stabilizing the wrinkles in 2D materials. Wrinkles with lengths below a critical value are unstable and removable by thermal annealing, while wrinkles with lengths above a critical value are self-stabilized by van der Waals interactions. It additionally confirms the pronounced frictional effects in wrinkles with lengths above critical value during dynamical movement or sliding.

Mechanisms of mechanical reinforcement by graphene and carbon nanotubes in polymer nanocomposites

Polymer nanocomposites reinforced with carbon-based nanofillers are gaining increasing interest for a number of applications due to their excellent properties. The understanding of the reinforcing mechanisms is, therefore, very important for the maximization of performance. This present review summarizes the current literature status on the mechanical properties of composites reinforced with graphene-related materials (GRMs) and carbon nanotubes (CNTs) and identifies the parameters that clearly affect the mechanical properties of the final materials. It is also shown how Raman spectroscopy can be utilized for the understanding of the stress transfer efficiency from the matrix to the reinforcement and it can even be used to map stress and strain in graphene. Importantly, it is demonstrated clearly that continuum micromechanics that was initially developed for fibre-reinforced composites is still applicable at the nanoscale for both GRMs and CNTs. Finally, current problems and future perspectives are discussed.

Wrinkling of two-dimensional materials: methods, properties and applications

Recently, two-dimensional (2D) materials, including graphene, its derivatives, metal films, MXenes and transition metal dichalcogenides (TMDs), have been widely studied because of their tunable electronic structures and special electrical and optical properties. However, during the fabrication of these 2D materials with atomic thickness, formation of wrinkles or folds is unavoidable to enable their stable existence. Meaningfully, it is found that wrinkled structures simultaneously impose positive changes on the 2D materials. Specifically, the architecture of wrinkled structures in 2D materials additionally induces excellent properties, which are of great importance for their practical applications. In this review, we provide an overview of categories of 2D materials, which contains formation and fabrication methods of wrinkled patterns and relevant mechanisms, as well as the induced mechanical, electrical, thermal and optical properties. Furthermore, these properties are modifiable by controlling the surface topography or even by dynamically stretching the 2D materials. Wrinkling offers a platform for 2D materials to be applied in some promising fields such as field emitters, energy containers and suppliers, field effect transistors, hydrophobic surfaces, sensors for flexible electronics and artificial intelligence. Finally, the opportunities and challenges of wrinkled 2D materials in the near future are discussed.

Structural reconfiguration and stress relaxation in twisted epitaxial graphene by annealing

The possibility to engineer the van der Waals interactions between graphene layers is crucial for controlling the electronic properties. Using epitaxial graphene with preferential orientations grown on the C-face 6H-SiC as a prototype, we have addressed the annealed structural reconfiguration of graphene layer in view of the evolutions of surface ripples and relative rotation angle (RRA) between lattices. It was found that the heat treatment of graphene layers under vacuum deformed the arcuate ripple surface and subsequently split one ripple into parallel twin pleats, which drastically increased the strains in the films. The originally oriented graphene layers, with small RRA between adjacent layers, were rearranged by the annealing resulting in disordered orientations and larger RRA. After a sufficient annealing, the compressive stress stored in the films was well released to give undistorted graphene lattices. The vacuum annealing is an effective treatment for irreversibly relaxing the graphene structure.

Structure of graphene and its disorders: a review

Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp3-defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.

Measuring and Manipulating the Adhesion of Graphene

We present a technique to precisely measure the surface energies between two-dimensional materials and substrates that is simple to implement and allows exploration of spatial and chemical control of adhesion at the nanoscale. As an example, we characterize the delamination of single-layer graphene from monolayers of pyrene tethered to glass in water and maximize the work of separation between these surfaces by varying the density of pyrene groups in the monolayer. Control of this energy scale enables high-fidelity graphene-transfer protocols that can resist failure under sonication. Additionally, we find that the work required for graphene peeling and readhesion exhibits a dramatic rate-independent hysteresis, differing by a factor of 100. This work establishes a rational means to control the adhesion of 2D materials and enables a systematic approach to engineer stimuli-responsive adhesives and mechanical technologies at the nanoscale.

Mechanically reconfigurable architectured graphene for tunable plasmonic resonances

Graphene nanostructures with complex geometries have been widely explored for plasmonic applications, as their plasmonic resonances exhibit high spatial confinement and gate tunability. However, edge effects in graphene and the narrow range over which plasmonic resonances can be tuned have limited the use of graphene in optical and optoelectronic applications. Here we present a novel approach to achieve mechanically reconfigurable and strongly resonant plasmonic structures based on crumpled graphene. Our calculations show that mechanical reconfiguration of crumpled graphene structures enables broad spectral tunability for plasmonic resonances from mid- to near-infrared, acting as a new tuning knob combined with conventional electrostatic gating. Furthermore, a continuous sheet of crumpled graphene shows strong confinement of plasmons, with a high near-field intensity enhancement of ~1 × 10⁴. Finally, decay rates for a dipole emitter are significantly enhanced in the proximity of finite-area biaxially crumpled graphene flakes. Our findings indicate that crumpled graphene provides a platform to engineer graphene-based plasmonics through broadband manipulation of strong plasmonic resonances.

Dimensionality-Dependent Electrochemical Kinetics at the Single-Layer Graphene-Electrolyte Interface

The theories to describe the rate at which electrochemical reactions proceed, to date, do not consider explicitly the dimensionality or the discreteness and occupancy of the energy levels of the electrodes. We show experimentally that such quantum mechanical aspects are important for dimensionally confined nanostructured materials and yield unusual variation of the kinetic rate constants with applied voltage in single-layer graphene. The observed divergence from conventional electrokinetics was ascribed to the linear energy dispersion as well as a nonzero density of states at the Dirac point in the graphene. The obtained results justify the use of density of states-based rate constants and considerably add to Marcus-Hush-Chidsey kinetics.

Mastering the Wrinkling of Self-supported Graphene

We present an approach that allows for the preparation of well-defined large arrays of graphene wrinkles with predictable geometry. Chemical vapor deposition grown graphene transferred onto hexagonal pillar arrays of SiO₂ with sufficiently small interpillar distance forms a complex network of two main types of wrinkle arrangements. The first type is composed of arrays of aligned equidistantly separated parallel wrinkles propagating over large distances, and originates from line interfaces in the graphene, such as thin, long wrinkles and graphene grain boundaries. The second type of wrinkle arrangement is composed of non-aligned short wrinkles, formed in areas without line interfaces. Besides the presented hybrid graphene topography with distinct wrinkle geometries induced by the pre-patterned substrate, the graphene layers are suspended and self-supporting, exhibiting large surface area and negligible doping effects from the substrate. All these properties make this wrinkled graphene a promising candidate for a material with enhanced chemical reactivity useful in nanoelectronic applications.

Edge Delamination of Monolayer Transition Metal Dichalcogenides

Delamination of thin films from the supportive substrates is a critical issue within the thin film industry. The emergent two-dimensional, atomic layered materials, including transition metal dichalcogenides, are highly flexible; thus buckles and wrinkles can be easily generated and play vital roles in the corresponding physical properties. Here we introduce one kind of patterned buckling behavior caused by the delamination from a substrate initiated at the edges of the chemical vapor deposition synthesized monolayer transition metal dichalcogenides, led by thermal expansion mismatch. The atomic force microscopy and optical characterizations clearly showed the puckered structures associated with the strain, whereas the transmission electron microscopy revealed the special sawtooth-shaped edges, which break the geometrical symmetry for the buckling behavior of hexagonal samples. The condition of the edge delamination is in accordance with the fracture behavior of thin film interfaces. This edge delamination and buckling process is universal for most ultrathin two-dimensional materials, which requires more attention in various future applications.

Mechanical and electronic coupling in few-layer graphene and hBN wrinkles: a first-principles study

Wrinkle engineering is an important pathway to develop novel functional devices of two-dimensional materials. By combining first-principles calculations and continuum mechanics modelling, we have investigated the wrinkling of few-layer graphene and hexagonal boron nitride (hBN) and provide a way to estimate their bending stiffness. For few-layer wrinkles under the same strain, the magnitude of structural deformation of each constituent layer gradually decreases from bottom to top layers, while interlayer interaction increases with increasing layer number. Comparing with monolayer wrinkles, the electronic properties of few-layer wrinkles are more sensitive to bending deformation as mechanical and electronic coupling induce charge redistribution at the wrinkles, making few-layer graphene and hBN wrinkles suitable for electromechanical system application.

Data mining graphene: correlative analysis of structure and electronic degrees of freedom in graphenic monolayers with defects

The link between changes in the material crystal structure and its mechanical, electronic, magnetic and optical functionalities-known as the structure-property relationship-is the cornerstone of modern materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the structure-property relationships of materials at the single-impurity and atomic-configuration levels. However, there are no statistics-based approaches for cross-correlation of structure and property variables obtained from the different information channels of STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window fast Fourier transform, Pearson correlation matrix and linear and kernel canonical correlation methods to study the relationship between lattice distortions and electron scattering from SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels, which can explain the coexistence of several quasiparticle interference patterns in nanoscale regions of interest. In addition, the application of kernel functions allowed us to extract a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. The outlined approach can be further used to analyze correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and generally has a complex multi-dimensional nature.

Wrinkled single-layer graphenes fabricated by silicon nanopillar arrays

The degree of crumpling affects the optoelectronic properties of graphene, which are very important for the performance of graphene-based devices and materials. In this article, we report an approach to tune the formation of wrinkles on single-layer graphene (SLG) by silicon nanopillar (SNP) arrays. By using gold nanoparticles as an etching mask, SNP arrays with different heights could be prepared by tuning the duration of etching. The formation of wrinkles on these SNP arrays was studied systematically. We found that thermal treatment could lead to a wrapping behavior of graphene around SNP arrays, which was accompanied by the emergence of many more wrinkles. Controllable wettability, conductivity and transmittance were demonstrated. This ability to tune wrinkles using SNP arrays can be employed to engineer the fabrication of graphene-related devices and other optoelectronic applications.

Analytical results for the wrinkling of graphene on nanoparticles

A continuum elastic model, describing the wrinkling instability of graphene on substrate-supported silica nanoparticles [M. Yamamoto et al., Phys. Rev. X 2, 041018 (2012)2160-330810.1103/PhysRevX.2.041018], is analytically studied, and an exact analytical expression of the critical nanoparticle separation or the maximum wrinkle length is derived. Our findings agree with the scaling property of Yamamoto et al. but improve their results. Moreover, from the elastic model we find a pseudomagnetic field as a function of the wrinkling deflection, leading to the conclusion that the middle of the wrinkled graphene may have a zero pseudomagnetic field, in marked contrast with previous results.

Tunable Plasmonic Reflection by Bound 1D Electron States in a 2D Dirac Metal

We show that the surface plasmons of a two-dimensional Dirac metal such as graphene can be reflected by linelike perturbations hosting one-dimensional electron states. The reflection originates from a strong enhancement of the local optical conductivity caused by optical transitions involving these bound states. We propose that the bound states can be systematically created, controlled, and liquidated by an ultranarrow electrostatic gate. Using infrared nanoimaging, we obtain experimental evidence for the locally enhanced conductivity of graphene induced by a carbon nanotube gate, which supports this theoretical concept.

Controllable Fabrication of Large-Area Wrinkled Graphene on a Solution Surface

It is unavoidable to form wrinkles, which are folds or creases in a material, in graphene, whenever the graphene is prepared by micromechanical exfoliation from graphite or chemical vapor deposition (CVD). However, the controllable formation and structures of graphene with nanoscale wrinkles remains a big challenge. Here, we report a liquid-phase shrink method to controllably fabricate large-area wrinkled graphene (WG). The CVD-prepared graphene self-shrinks into a WG on an ethanol solution surface. By modifying the concentration of the ethanol solution, we can easily and efficiently obtain WG with a uniform distribution of wrinkles with different heights. The WG shows high stretchability and can withstand more than 100% tensile strain and up to 720° twist. Furthermore, electromechanical response sensors based on double-layer stacking of WG show ultrahigh sensitivity. This simple, effective, and environmentally friendly liquid-phase shrink method will pave a way for the controllable formation of WG, which is an ideal candidate for application in highly stretchable and highly sensitive electronic devices.

Understanding geometric instabilities in thin films via a multi-layer model

When a thin stiff film adhered to a compliant substrate is subject to compressive stresses, the film will experience a geometric instability and buckle out of plane. For high film/substrate stiffness ratios with relatively low levels of strain, the primary mode of instability will either be wrinkling or buckling delamination depending on the material and geometric properties of the system. Previous works approach these systems by treating the film and substrate as homogenous layers, either consistently perfectly attached, or perfectly unattached at interfacial flaws. However, this approach neglects systems where the film and substrate are uniformly weakly attached or where interfacial layers due to surface modifications in either the film or substrate are present. Here we demonstrate a method for accounting for these additional thin surface layers via an analytical solution verified by numerical results. The main outcome of this work is an improved understanding of how these layers influence global behavior. We demonstrate the utility of our model with applications ranging from buckling based metrology in ultrathin films, to an improved understanding of the formation of a novel surface in carbon nanotube bio-interface films. Moving forward, this model can be used to interpret experimental results, particularly for systems which deviate from traditional behavior, and aid in the evaluation and design of future film/substrate systems.

Piezoresistive effects in controllable defective HFTCVD graphene-based flexible pressure sensor

In this work, the piezoresistive effects of defective graphene used on a flexible pressure sensor are demonstrated. The graphene used was deposited at substrate temperatures of 750, 850 and 1000 °C using the hot-filament thermal chemical vapor deposition method in which the resultant graphene had different defect densities. Incorporation of the graphene as the sensing materials in sensor device showed that a linear variation in the resistance change with the applied gas pressure was obtained in the range of 0 to 50 kPa. The deposition temperature of the graphene deposited on copper foil using this technique was shown to be capable of tuning the sensitivity of the flexible graphene-based pressure sensor. We found that the sensor performance is strongly dominated by the defect density in the graphene, where graphene with the highest defect density deposited at 750 °C exhibited an almost four-fold sensitivity as compared to that deposited at 1000 °C. This effect is believed to have been contributed by the scattering of charge carriers in the graphene networks through various forms such as from the defects in the graphene lattice itself, tunneling between graphene islands, and tunneling between defect-like structures.

Suspended monolayer graphene under true uniaxial deformation

2D crystals, such as graphene, exhibit the higher strength and stiffness of any other known man-made or natural material. So far, this assertion has been primarily based on modelling predictions and on bending experiments in combination with pertinent modelling. True uniaxial loading of suspended graphene is not easy to accomplish; however such an experiment is of paramount importance in order to assess the intrinsic properties of graphene without the influence of an underlying substrate. In this work we report on uniaxial tension of graphene up to moderate strains of ∼0.8%. This has been made possible by sandwiching the graphene flake between two polymethylmethacrylate (PMMA) layers and by suspending its central part by the removal of a section of PMMA with e-beam lithography. True uniaxial deformation is confirmed by the measured large phonon shifts with strain by Raman spectroscopy and the indication of lateral buckling (similar to what is observed for thin macroscopic membranes under tension). Finally, we also report on how the stress is transferred to the suspended specimen through the adhesive grips and determine the value of interfacial shear stress that is required for efficient axial loading in such a system.

Mechanical Control of Graphene on Engineered Pyramidal Strain Arrays

Strain can tune desirable electronic behavior in graphene, but there has been limited progress in controlling strain in graphene devices. In this paper, we study the mechanical response of graphene on substrates patterned with arrays of mesoscale pyramids. Using atomic force microscopy, we demonstrate that the morphology of graphene can be controlled from conformal to suspended depending on the arrangement of pyramids and the aspect ratio of the array. Nonuniform strains in graphene suspended across pyramids are revealed by Raman spectroscopy and supported by atomistic modeling, which also indicates strong pseudomagnetic fields in the graphene. Our results suggest that incorporating mesoscale pyramids in graphene devices is a viable route to achieving strain-engineering of graphene.

Tailored Crumpling and Unfolding of Spray-Dried Pristine Graphene and Graphene Oxide Sheets

For the first time, pristine graphene can be controllably crumpled and unfolded. The mechanism for graphene is radically different than that observed for graphene oxide; a multifaced crumpled, dimpled particle morphology is seen for pristine graphene in contrast to the wrinkled, compressed surface of graphene oxide particles, showing that surface chemistry dictates nanosheet interactions during the crumpling process. The process demonstrated here utilizes a spray-drying technique to produce droplets of aqueous graphene dispersions and induce crumpling through rapid droplet evaporation. For the first time, the gradual dimensional transition of 2D graphene nanosheets to a 3D crumpled morphology in droplets is directly observed; this is imaged by a novel sample collection device inside the spray dryer itself. The degree of folding can be tailored by altering the capillary forces on the dispersed sheets during evaporation. It is also shown that the morphology of redispersed crumpled graphene powder can be controlled by solvent selection. This process is scalable, with the ability to rapidly process graphene dispersions into powders suitable for a variety of engineering applications.

Formation of ripples in atomically thin MoS₂ and local strain engineering of electrostatic properties

Ripple is a common deformation in two-dimensional materials due to localized strain, which is expected to greatly influence the physical properties. The effects of the ripple deformation in the MoS2 layer on their physics, however, are rarely addressed experimentally. We here grow atomically thin MoS2 nanostructures by employing a vapor phase deposition method without any catalyst and observed the ripples in MoS2 nanostructures. The MoS2 ripples exhibit quasi-periodical ripple structures in the MoS2 surface. The heights of the ripples vary from several angstroms to tens of nanometers and the wavelength is in the range of several hundred nanometers. The growth mechanism of rippled MoS2 nanostructures is elucidated. We have also simultaneously investigated the electrostatic properties of MoS2 ripples by using Kelvin probe force microscopy, which shows inhomogeneous surface potential and charge distributions for MoS2 ripple nanostructures with different local strains.

Controlled folding of graphene: GraFold printing

We have used elastomeric stamps with periodically varying adhesive properties to introduce structure and print folded graphene films. The structure of the induced folds is investigated with scanning probe techniques, high-resolution electron-microscopy, and tip-enhanced Raman spectroscopy. Furthermore, a finite element model is developed to show the fold formation process. Terahertz spectroscopy reveals induced anisotropy of carrier mobility along, and perpendicular to, the graphene folds. Graphene fold printing is a new technique which allows for significant modification of the properties of 2D materials without damaging or chemically modifying them.

Study on wrinkling in graphene under gradient shear by molecular dynamics simulation

The formation and development mechanisms of wrinkles in a rectangular single layer graphene sheet (SLGS) subjected to in-plane gradient shear displacements are investigated through molecular dynamics (MD) simulations. The growth and propagation process of the SLGS wrinkling is elucidated by the developing atomic out-of-plane displacements of the key atoms. It reveals that the shape of SLGS and loading condition have a significant effect on the SLGS wrinkling deformation. The dependences of the wrinkling amplitude, wavelength, and out-of-plane displacements on the applied gradient shear displacements are obtained with MD simulations. The effects of aspect ratio, temperature, and loading grads on wrinkling in graphene are also studied.

Crumpled graphene: preparation and applications

This paper reviews the newest form of graphene (crumpled graphene) for energy storage applications.

On the crumpling of polycrystalline graphene by molecular dynamics simulation

By employing molecular dynamics simulation, this work unravels the crumpling process of polycrystalline graphene and its relevant mechanical properties.

Experimental realization of coexisting states of rolled-up and wrinkled nanomembranes by strain and etching control

Self-positioned nanomembranes, such as rolled-up tubes and wrinkled thin films, have been potential systems for a variety of applications and basic studies on elastic properties of nanometer-thick systems. Although there is a clear driving force towards elastic energy minimization in each system, the exploration of intermediate states, in which specific characteristics could be chosen by a slight modification of a processing parameter, have not been experimentally realized. In this work, arrays of freestanding III-V nanomembranes (NM) supported on one edge and presenting a coexistence of these two main behaviors were obtained by design of strain conditions in the NMs and controlled selective etching of patterned substrates. As the etching process continues, a mixture of wrinkled and rolled-up states is achieved. For very long etching times an onset of plastic cracks was observed in the points with localized stress. The well-defined morphological periodicity of the relaxed NMs was compared with finite element simulations of their elastic relaxation. The evolution of strain in the NMs with etching time was directly evaluated by X-ray diffraction, providing a comprehensive scenario of transitions among competing and coexisting strain states.

Strain superlattices and macroscale suspension of graphene induced by corrugated substrates

We investigate the organized formation of strain, ripples, and suspended features in macroscopic graphene sheets transferred onto corrugated substrates made of an ordered array of silica pillars with variable geometries. Depending on the pitch and sharpness of the corrugated array, graphene can conformally coat the surface, partially collapse, or lie fully suspended between pillars in a fakir-like fashion over tens of micrometers. With increasing pillar density, ripples in collapsed films display a transition from random oriented pleats emerging from pillars to organized domains of parallel ripples linking pillars, eventually leading to suspended tent-like features. Spatially resolved Raman spectroscopy, atomic force microscopy, and electronic microscopy reveal uniaxial strain domains in the transferred graphene, which are induced and controlled by the geometry. We propose a simple theoretical model to explain the structural transition between fully suspended and collapsed graphene. For the arrays of high density pillars, graphene membranes stay suspended over macroscopic distances with minimal interaction with the pillars' apexes. It offers a platform to tailor stress in graphene layers and opens perspectives for electron transport and nanomechanical applications.

Enhanced reactivity of graphene wrinkles and their function as nanosized gas inlets for reactions under graphene

Formation of wrinkles at graphene/Pt(111) surface was investigated by low energy electron microscopy (LEEM). Reversible wrinkling and unwrinkling of graphene sheets were observed upon cycled heating and cooling treatments, exhibiting a hysteresis effect with the temperature. In situ LEEM studies of graphene oxidation show preferential oxidation of the wrinkles than flat graphene sheets and graphene edges. The function of the wrinkles as one-dimensional (1D) nanosized gas inlets for oxygen and the strain at the distorted sp(2)-hybridized carbon atoms of the wrinkle sites can be attributed to the enhanced reactivity of wrinkles to the oxidation. Meanwhile, wrinkles also served as nanosized gas inlets for oxidation of CO intercalated between graphene and Pt(111). Considering that wrinkles are frequently present in graphene structures, the role of wrinkles as 1D reaction channels and their enhanced reactivity to reactions may have an important effect on graphene chemistry.

Electric-dipole-induced universality for Dirac fermions in graphene

We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.

Improved performance of graphene transistors by strain engineering

By means of numerical simulation, in this work we study the effects of uniaxial strain on the transport properties of strained graphene heterojunctions and explore the possibility of achieving good performance of graphene transistors using these hetero-channels. It is shown that a finite conduction gap can open in the strain junctions due to strain-induced deformation of the graphene bandstructure. These hetero-channels are then demonstrated to significantly improve the operation of graphene field-effect transistors (FETs). In particular, the ON/OFF current ratio can reach a value of over 10(5). In graphene normal FETs, the transconductance, although reduced compared to the case of unstrained devices, is still high, while good saturation of current can be obtained. This results in a high voltage gain and a high transition frequency of a few hundreds of GHz for a gate length of 80 nm. In graphene tunneling FETs, subthreshold swings lower than 30 mV /dec, strong nonlinear effects such as gate-controllable negative differential conductance, and current rectification are observed.

Reversibility of crumpling on compressed thin sheets: reversibility of crumpling

Compressing thin sheets usually yields the formation of singularities which focus curvature and stretching on points or lines. In particular, following the common experience of crumpled paper where a paper sheet is crushed in a paper ball, one might guess that elastic singularities should be the rule beyond some compression level. In contrast, we show here that, somewhat surprisingly, compressing a sheet between cylinders make singularities spontaneously disappear at large compression. This "stress defocusing" phenomenon is qualitatively explained from scale-invariance and further linked to a criterion based on a balance between stretching and curvature energies on defocused states. This criterion is made quantitative using the scalings relevant to sheet elasticity and compared to experiment. These results are synthesized in a phase diagram completed with plastic transitions and buckling saturation. They provide a renewed vision of elastic singularities as a thermodynamic condensed phase where stress is focused, in competition with a regular diluted phase where stress is defocused. The physical differences between phases is emphasized by determining experimentally the mechanical response when stress is focused or defocused and by recovering the corresponding scaling laws. In this phase diagram, different compression routes may be followed by constraining differently the two principal curvatures of a sheet. As evidenced here, this may provide an efficient way of compressing a sheet that avoids the occurrence of plastic damages by inducing a spontaneous regularization of geometry and stress.

Morphology control of surfactant-assisted graphene oxide films at the liquid-gas interface

Control of a two-dimensional (2D) structure of assembled graphene oxide (GO) sheets is highly desirable for fundamental research and potential applications of graphene devices. We show that an alkylamine surfactant, i.e., octadecylamine (ODA), Langmuir monolayer can be utilized as a template for adsorbing highly hydrophilic GO sheets in an aqueous subphase at the liquid-gas interface. The densely packed 2-D monolayer of such complex films was obtained on arbitrary substrates by applying Langmuir-Schaefer or Langmuir-Blodgett technique. Morphology control of GO sheets was also achieved upon compression by tuning the amount of spread ODA molecules. We found that ODA surfactant monolayers prevent GO sheets from sliding, resulting in formation of wrinkling rather than overlapping at the liquid-gas interface during the compression. The morphology structures did not change after a graphitization procedure of chemical hydrazine reduction and thermal annealing treatments. Since morphologies of graphene films are closely correlated to the performance of graphene-based materials, the technique employed in this study can provide a route for applications requiring wrinkled graphenes, ranging from nanoelectronic devices to energy storage materials, such as supercapacitors and fuel cell electrodes.