Interlayer interaction, shear vibrational mode, and tribological properties of two-dimensional bilayers with a commensurate moir\'e pattern

The potential energy surface (PES) of interlayer interaction of infinite twisted bilayer graphene is calculated for a set of commensurate moir\'e patterns using the registry-dependent Kolmogorov-Crespi empirical potential. The calculated PESs have the same shape for all considered moir\'e patterns with the unit cell size of the PES which is inversely related to the unit cell size of the moir\'e pattern. The amplitude of PES corrugations is found to decrease exponentially upon increasing the size of the moir\'e pattern unit cell. An analytical expression for such a PES including the first Fourier harmonics compatible with the symmetries of both layers is derived. It is shown that the calculated PESs can be approximated by the derived expression with the accuracy within 1%. This means that different physical properties associated with relative in-plane motion of graphene layers are interrelated and can be expressed analytically as functions of the amplitude of PES corrugations. In this way, we obtain the shear mode frequency, shear modulus, shear strength and barrier for relative rotation of the commensurate twisted layers to a fully incommensurate state for the considered moir\'e patterns. This barrier may possibly lead to the macroscopic robust superlubricity for twisted graphene bilayer with a commensurate moir\'e pattern. The conclusions made should be valid for diverse 2D systems of twisted commensurate layers.Comment: 9 pages, 3 figures; Supplemental Material: 2 pages, 1 figur

Synthesis of Novel Iono- and Photochromic Spiropyrans Derived from 6,7-Dihydroxy-8-Formyl-4-Methyl-2H-Chromene-2-One

Novel photochromic spiropyrans (SPPs) containing 6′-hydroxy group were synthesized and their spectral properties as well as abilities for complexation with metal ions studied. In solutions they exist as equilibrium mixture of spirocyclic (A) and merocyanine (B) isomers. The largest content of merocyanine form was found for the derivative with an electron-donating methyl group in position 5 of hetaryl fragment. The irradiation of SPPs in acetonitrile shifts the equilibrium to the B form. Similar effect causes the addition of metal cations due to formation of colored complexes with merocyanine isomers

Atomic-scale defects restricting structural superlubricity: Ab initio study on the example of the twisted graphene bilayer

The potential energy surface (PES) of interlayer interaction of twisted bilayer graphene with vacancies in one of the layers is investigated via density functional theory (DFT) calculations with van der Waals corrections. These calculations give a non-negligible magnitude of PES corrugation of 28 meV per vacancy and barriers for relative sliding of the layers of 7-8 meV per vacancy for the moiré pattern with coprime indices (2,1) (twist angle 21.8). At the same time, using the semiempirical potential fitted to the DFT results, we confirm that twisted bilayer graphene without defects exhibits superlubricity for the same moiré pattern and the magnitude of PES corrugation for the infinite bilayer is below the calculation accuracy. Our results imply that atomic-scale defects restrict the superlubricity of two-dimensional layers and can determine static and dynamic tribological properties of these layers in a superlubric state. We also analyze computationally cheap approaches that can be used for modeling of tribological behavior of large-scale systems with defects. The adequacy of using state-of-the-art semiempirical potentials for interlayer interaction and approximations based on the first spatial Fourier harmonics for the description of interaction between graphene layers with defects is discussed.A.S.M., A.A.K., and A.M.P. acknowledge support by the Russian Foundation for Basic Research (Grant No. 18-52-00002). I.V.L. acknowledges the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143)

Elastic constants of graphene: Comparison of empirical potentials and DFT calculations

The capacity of popular classical interatomic potentials to describe elastic properties of graphene is tested. The Tersoff potential, Brenner reactive bond-order potentials REBO-1990, REBO-2000, REBO-2002 and AIREBO as well as LCBOP, PPBE-G, ReaxFF-CHO and ReaxFF-C2013 are considered. Linear and non-linear elastic response of graphene under uniaxial stretching is investigated by static energy calculations. The Young's modulus, Poisson's ratio and high-order elastic moduli are verified against the reference data available from experimental measurements and ab initio studies. The density functional theory calculations are performed to complement the reference data on the effective Young's modulus and Poisson's ratio at small but finite elongations. It is observed that for all the potentials considered, the elastic energy deviates remarkably from the simple quadratic dependence already at elongations of several percent. Nevertheless, LCBOP provides the results consistent with the reference data and thus realistically describes in-plane deformations of graphene. Reasonable agreement is also observed for the computationally cheap PPBE-G potential. REBO-2000, AIREBO and REBO-2002 give a strongly non-linear elastic response with a wrong sign of the third-order elastic modulus and the corresponding results are very far from the reference data. The ReaxFF potentials drastically overestimate the Poisson's ratio. Furthermore, ReaxFF-C2013 shows a number of numerical artefacts at finite elongations. The bending rigidity of graphene is also obtained by static energy calculations for large-diameter carbon nanotubes. The best agreement with the experimental and ab initio data in this case is achieved using the REBO-2000, REBO-2002 and ReaxFF potentials. Therefore, none of the considered potentials adequately describes both in-plane and out-of-plane deformations of graphene.AMP and AAK acknowledge the Russian Foundation for Basic Research, Russia (Grant 18-02-00985). IVL acknowledges Grupos Consolidados del Gobierno Vasco (IT-578-13).Peer reviewe

Simulation of Tribological Properties of a Graphene Bilayer with Twisted Layers

The effect of atomic structural defects on the tribological properties of a system with structural superlubricity based on a graphene bilayer with twisted layers is studied using the density functional theory (DFT) method and the Kolmogorov–Crespi and Lebedev a semiempirical interatomic-interaction potentials. The amplitudes of corrugation the potential energy surface of the interlayer interaction and the barriers of relative motion of ideal graphene layers and layers with vacancies are estimated. Macroscopic ultralow friction is revealed for a graphene bilayer with ideal twisted layers. The DFT calculations show that the presence of vacancies in this graphene bilayer gives rise to a static friction force of 12–16 pN per vacancy. The adequacy of using semiempirical potentials of the interaction between graphene layers to study the tribological properties of a graphene bilayer with atomic structural defects is evaluated.The work of I.V. Lebedeva was supported by the European Union MaX Center of Excellence (grant EU-H2020 no. 824143)

Synthesis and Photo- and Ionochromic and Spectral-Luminescent Properties of 5-Phenylpyrazolidin-3-one Azomethine Imines

Photochromic 5-phenylpyrazolidin-3-one-based azomethine imines containing 2-((1H-imidazol-2-yl)methylene) 1, 2-(pyridin-2-ylmethylene) 2, 2-(quinolin-2-ylmethylene) 3, and 2-((8-hydroxyquinolin-2-yl)methylene) 4 substituents were synthesized. All the compounds exist in the ring-opened O forms. Under irradiation with light of 365 nm, compounds 1–4 undergo thermally reversible isomerization into ring-closed bicyclic diaziridine isomers C. Azomethine imines 1–3 exhibit properties of ion-active molecular “off-on” switches of fluorescence when interacting with F− or AcO− anions. Compound 4 represents a bifunctional chemosensor demonstrating a colorimetric “naked-eye” effect for Ni2+ cation and complete fluorescence quenching in the presence of H+, F−, and CN− ions