Mechanical properties of graphene cantilever from atomic force microscopy and density functional theory

Determining local modulus and strength of heterogeneous films by force-deflection mapping of microcantilevers

Estimating the elastic modulus and strength of heterogeneous films requires local measurement techniques. For local mechanical film testing, microcantilevers were cut into suspended many-layer graphene using a focused ion beam. An optical transmittance technique was used to map thickness near the cantilevers, and multipoint force-deflection mapping with an atomic force microscope was used to record the compliance of the cantilevers. These data were used to estimate the elastic modulus of the film by fitting the compliance at multiple locations along the cantilever to a fixed-free Euler-Bernoulli beam model. This method resulted in a lower uncertainty than is possible from analyzing only a single force-deflection. The breaking strength of the film was also found by deflecting cantilevers until fracture. The average modulus and strength of the many-layer graphene films are 300 and 12 GPa, respectively. The multipoint force-deflection method is well suited to analyze films that are heterogeneous in thickness or wrinkled.

Multiscale numerical simulation of in-plane mechanical properties of two-dimensional monolayers

Many applications of two dimensional (2D) materials are often achieved through strain engineering, which is directly dependent on their in-plane mechanical characteristics. Therefore, understanding the in-plane mechanical characteristics of the 2D monolayers becomes imperative. Nevertheless, direct experimental measurements of in-plane mechanical properties of 2D monolayers face great difficulties due to the issues related to the availability of high-quality 2D materials and sophisticated facilities. As an alternative, numerical simulation has the potential to theoretically predict such properties. This review presents some recent progress in numerically exploring the in-plane mechanical properties of 2D materials, including first-principles density functional theory, force-field based classical molecular dynamics, and the finite-element method. The relevant case studies are provided to describe the applications of these methods along with their pros and cons. We hope that the multiscale simulation methods discussed in this review will inspire new ideas and boost further advances of the computational study on the in-plane mechanical properties of 2D materials.

The recent progress of multiscale numeric methods for investigating in-plane mechanical properties of 2D monolayers is reviewed.

Manufacture and characterization of graphene membranes with suspended silicon proof masses for MEMS and NEMS applications

Graphene's unparalleled strength, chemical stability, ultimate surface-to-volume ratio and excellent electronic properties make it an ideal candidate as a material for membranes in micro- and nanoelectromechanical systems (MEMS and NEMS). However, the integration of graphene into MEMS or NEMS devices and suspended structures such as proof masses on graphene membranes raises several technological challenges, including collapse and rupture of the graphene. We have developed a robust route for realizing membranes made of double-layer CVD graphene and suspending large silicon proof masses on membranes with high yields. We have demonstrated the manufacture of square graphene membranes with side lengths from 7 µm to 110 µm, and suspended proof masses consisting of solid silicon cubes that are from 5 µm × 5 µm × 16.4 µm to 100 µm × 100 µm × 16.4 µm in size. Our approach is compatible with wafer-scale MEMS and semiconductor manufacturing technologies, and the manufacturing yields of the graphene membranes with suspended proof masses were >90%, with >70% of the graphene membranes having >90% graphene area without visible defects. The measured resonance frequencies of the realized structures ranged from tens to hundreds of kHz, with quality factors ranging from 63 to 148. The graphene membranes with suspended proof masses were extremely robust, and were able to withstand indentation forces from an atomic force microscope (AFM) tip of up to ~7000 nN. The proposed approach for the reliable and large-scale manufacture of graphene membranes with suspended proof masses will enable the development and study of innovative NEMS devices with new functionalities and improved performances.

3D patient-specific numerical modeling of the soft palate considering adhesion from the tongue

Collapse of the soft palate in the upper airway contributes to obstructive sleeping apnea (OSA). In this study, we investigate the influence of the adhesion from the tongue on the soft palate global response. This is achieved using a cohesive zone finite element approach. A traction-separation law is determined to describe the adhesion effect from the surface tension of the lining liquid between the soft palate and the tongue. According to pull-off experimental tests of human lining liquid from the oral surface of the soft palate, the corresponding cohesive properties, including the critical normal traction stress and the failure separation displacement, are obtained. The 3D patient-specific soft palate geometry is accounted for, based on one specific patient's computed tomography (CT) images. The calculation results show that influence of the adhesion from the tongue surface on the global response of the soft palate depends on the length ratio between the cohesive length and the soft palate length. When the length of the cohesive zone is smaller than half of the soft palate length, the adhesion's influence is negligible. When the adhesion length is larger than 70 percent of soft palate length, the adhesion force contributes to preventing the soft palate from collapsing towards to the pharynx wall, i.e. the closing pressure is more negative than in the no adhesion case. These results may provide useful information to the clinical treatment of OSA patients.

Investigation of the dynamic bending properties of MoS2 thin films by interference colours

A non-contact method for the observation of the elastic deformation of 2D molybdenum disulfide (MoS2) thin films using an ordinary optical microscope is reported. A pulsed laser is used to rapidly increase the bending deformation of the MoS2 thin films via heating. The bending angle of the MoS2 thin films shows high stability, changing only 5% in forty days without external forces. However, the bending angle of the MoS2 thin films substantially decreases after being wetted with the volatile polar solvent tetrahydrofuran (THF), because of its low surface tension. By removing the nano-Newton scale forces on the MoS2 thin films, the bending angle increases significantly within 4 minutes, and this feature of the thin films shows great potential for use in the fabrication of micro-force sensors. This is the first attempt to study the mechanical properties of 2D materials by optical methods. Further utilization of industrially manufactured MoS2 thin films for detecting micro-force qualitatively on the basis of their excellent bending properties would significantly reduce the production costs of micro-force sensors.

Effect of Ultrahigh Stiffness of Defective Graphene from Atomistic Point of View

Well-known effects of mechanical stiffness degradation under the influence of point defects in macroscopic solids can be controversially reversed in the case of low-dimensional materials. Using atomistic simulation, we showed here that a single-layered graphene film can be sufficiently stiffened by monovacancy defects at a tiny concentration. Our results correspond well with recent experimental data and suggest that the effect of mechanical stiffness augmentation is mainly originated from specific bonds distribution in the surrounded monovacancy defects regions. We showed that such unusual mechanical response is the feature of presence of specifically monovacancies, whereas other types of point defects such as divacancy, 555-777 and Stone-Wales defects, lead to the ordinary degradation of the graphene mechanical stiffness.

Structures, stabilities, and electronic properties of defects in monolayer black phosphorus

The structures, stabilities, and electronic properties of monolayer black phosphorus (M-BP) with different kinds of defects are investigated within the frame of density-functional theory. All the possible configurations of defects in M-BP are explored, and the calculated results suggest that the stabilities of the configurations with different kinds of defects are greatly related to broken bonds, structural deformation and the character of the bonding. The configurations with two or three vacancies are energetically more favorable than the ones with a single vacancy. Meanwhile, the doping of two foreign atoms, such as sulfur, silicon or aluminum, is more stable than that of the corresponding single dopant. The electronic properties of M-BP are greatly affected by the types of defects. The single S-doped M-BP not only retains the character of a direct semiconductor, but it also can enlarge the band gap by 0.24 eV relative to the perfect one. Such results reveal that the defects not only greatly affect the electronic properties, but they also can be used as an effective way to modulate the band gap for the different applications of M-BP in electronic devices.

Accurate calibration and uncertainty estimation of the normal spring constant of various AFM cantilevers

Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke's law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%.

Detection of long and short DNA using nanopores with graphitic polyhedral edges

Graphene is a unique material with a thickness as low as a single atom, high in-plane conductivity and a robust lattice that is self-supporting over large length scales. Schematically, graphene is an ideal solid-state material for tuning the properties of a nanopore because self-supported sheets, ranging from single to multiple atomic layers, can create pores with near-arbitrary dimensions which can provide exquisite control of the electric field drop within the pore. In this study, we characterize the drilling kinetics of nanopores using a thermionic electron source and various electron beam fluxes to minimize secondary hole formation. Once established, we investigated the use of multilayer graphene to create highly tailored nanostructures including nanopores with graphite polyhedral crystals formed around the nanopore edge. Finally, we report on the translocation of double stranded and single stranded DNA through such graphene pores and show that the single stranded DNA translocates much slower allowing detection of extremely short fragments (25 nucleotides in length). Our findings suggest that the kinetic and controllable properties of graphene nanopores under sculpting conditions can be used to further enhance the detection of DNA analytes.