We calculate bending moduli along the principal directions for thirty-two select atomic monolayers using ab initio Density Functional Theory (DFT). Specifically, considering representative materials from each of Groups IV, V, III-V monolayers, transition metal dichalcogenides, Group III monochalcogenides, Group IV monochalcogenides, and transition metal trichalcogenides, we utilize the recently developed Cyclic DFT method to calculate the bending moduli in the practically relevant but previously intractable low-curvature limit. We find that the moduli generally increase with thickness of the monolayer and that structures with a rectangular lattice are prone to a higher degree of anisotropy relative to those with a honeycomb lattice. We also find that exceptions to these trends are generally a consequence of unusually strong/weak bonding and/or significant structural relxation related effects.
A new formula for elastic bending modulus of monolayer graphene is derived analytically from an empirical potential for solid-state carbon-carbon bonds. Two physical origins are identified for the non-vanishing bending modulus of the atomically thin graphene sheet, one due to the bond angle effect and the other resulting from the bond order term associated with dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers are simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tange…
We study the bending of rectangular atomic monolayers along different directions from first principles. Specifically, choosing the phosphorene, GeS, TiS$_3$, and As$_2$S$_3$ monolayers as representative examples, we perform Kohn-Sham density functional theory calculations to determine the variation in transverse flexoelectric coefficient and bending modulus with the direction of bending. We find that while the flexoelectric coefficient is nearly isotropic, there is significant and complex anisotropy in bending modulus that also differs between the monolayers, with extremal values not necessari…
The mechanical and electronic properties of transition metal dichalcogenide (TMD) monolayers corresponding to transition groups IV, VI, and X are explored under mechanical bending from first principles calculations using the strongly constrained and appropriately normed (SCAN) meta-GGA (MGGA). SCAN provides an accurate description of the phase stability of the TMD monolayers. Our calculated lattice parameters and other structural parameters agree well with experiment. We find that bending stiffness (or flexural rigidity) increases as the transition metal group goes from IV to X to VI, with the…
We report on the optoelectronic properties of GaN$(0001)$ and $(1\bar{1}00)$ surfaces after their functionalization with phosphonic acid derivatives. To analyze the possible correlation between the acid's electronegativity and the GaN surface band bending, two types of phosphonic acids, n-octylphosphonic acid (OPA) and 1H,1H,2H,2H-perfluorooctanephosphonic acid (PFOPA), are grafted on oxidized GaN$(0001)$ and GaN$(1\bar{1}00)$ layers as well as on GaN nanowires. The resulting hybrid inorganic/organic heterostructures are investigated by X-ray photoemission and photoluminescence spectroscopy. T…
We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory…
We calculate transversal flexoelectric coefficients along the principal directions for fifty select atomic monolayers using ab initio Density Functional Theory (DFT). Specifically, considering representative materials from each of Groups IV, III-V, V monolayers, transition metal dichalcogenides (TMDs), Group III monochalcogenides, Group IV monochalcogenides, transition metal trichalcogenides (TMTs), and Group V chalcogenides, we perform symmetry-adapted DFT simulations to calculate the flexoelectric coefficients at practically relevant bending curvatures. We find that the materials demonstrate…
Recently, a new type of two-dimensional layered material, i.e. C3N, has been fabricated by polymerization of 2,3-diaminophenazine and used to fabricate a field-effect transistor device with an on/off current ratio reaching 5.5E10 (Adv. Mater. 2017, 1605625). Here we have performed a comprehensive first-principles study mechanical and electronic properties of C3N and related derivatives. Ab inito molecular dynamics simulation shows that C3N monolayer can withstand high temperature up to 2000K. Besides high stability, C3N is predicted to be a superior stiff material with high Young's modulus (10…
Flexoelectricity is a form of electromechanical coupling that has recently emerged because, unlike piezoelectricity, it is theoretically possible in any dielectric material. Two-dimensional (2D) materials have also garnered significant interest because of their unusual electromechanical properties and high flexibility, but the intrinsic flexoelectric properties of these materials remain unresolved. In this work, using atomistic modeling accounting for charge-dipole interactions, we report the intrinsic flexoelectric constants for a range of two-dimensional materials, including graphene allotro…
Intrinsic characteristic radius drives phonon anomalies in Janus transition metal dichalcogenide nanotubes
School of Mechatronic Engineering and Automation, Shanghai University（上海大学机电工程与自动化学院）；Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Frontier Science Center of Mechanoinformatics, School of Mechanics and Engineering Science, Shanghai University（上海大学力学与工程科学学院）
It is shown that for monolayer graphene electrons are confined on a perfect two dimensional surface. The implications for the electronic properties of corrugated graphene are discussed in view of a derivation of the constrained relativistic dynamics for the massless carriers in two dimensions. Surface curvature is related to a series of phenomena with practical applications such as curvature induced p-n junctions, band gap opening and decoherence. We also establish a bending free energy by treating graphene as a soft electronic membrane.
We present a novel formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of \emph{radial polarization} to make the coefficient a well-defined quantity for uniform bending deformations. We use the framework to calculate the flexoelectric coefficient for group IV atomic monolayers using density functional theory. We find that graphene's coefficient is significantly larger than previously reported, with a charge transfer mechanism that differs from other members of its group.
Bond stretching and angle bending force fields, appropriate to describe in-plane motion of graphene sheets, are derived using first principles' methods. The obtained force fields are fitted by analytical anharmonic energy potential functions, providing efficient means of calculations in molecular mechanics simulations. Numerical results regarding the mechanical behavior of graphene monolayers under various loads, like uniaxial tension, hydrostatic tension, and shear stress, are presented, using both molecular dynamics simulations and first principles' methods. Stress-strain curves and elastic …
Atomic modulations of two-dimensional materials using scanning tunneling microscope (STM) tip-induced forces modifies their mechanical and electrical properties. In situ topographic and spectroscopic probing through electrical tunneling has been used for straining sheets of graphite, monolayer graphene and NbSe2. The findings also resolve a thirty-five-year-old controversy involving numerous proposed models to explain the source of anomalously high measured atomic amplitudes (of up to 24 Angstroms, expected 0.2 Angstroms) from atomic corrugation on graphite surfaces. Our findings attributes th…
Flexoelectricity is the polar response of an insulator to strain gradients such as bending. While the size dependence of this effect makes it weak in bulk systems in comparison to piezoelectricity, it suggests that it plays a bigger role in nanoscale systems such as thin films and nanotubes (NTs). In this paper we demonstrate using first-principles calculations that the walls of carbon nanotubes (CNTs) and transition metal dichalcogenide nanotubes (TMD NTs) are polarized in the radial direction, the strength of the polarization increasing as the size of the NT decreases. For CNTs and TMD NTs w…
By using first-principles calculations, we investigated the effects of graphene/boron nitride (BN) encapsulation, surface functionalization by metallic elements (K, Al, Mg and typical transition metals) and molecules (tetracyanoquinodimethane (TCNQ) and tetracyanoethylene (TCNE)) on the electronic properties of layered indium selenide (InSe). It was found that an opposite trend of charge transfer is possible for graphene (donor) and BN (acceptor), which is dramatically different from phosphorene where both graphene and BN play the same role (donor). For InSe/BN heterostructure, a change of the…
