Abstract: Intrinsic ripples in freestanding graphene have been exceedingly difficult to study. Individual ripple geometry was recently imaged using scanning tunnelling microscopy, but these measurements are limited to static configurations. Thermally-activated flexural phonon modes should generate dynamic changes in curvature. Here we show how to track the vertical movement of a one-square-angstrom region of freestanding graphene using scanning tunnelling microscopy, thereby allowing measurement of the out-of-plane time trajectory and fluctuations over long time periods. We also present a model from elasticity theory to explain the very-low-frequency oscillations. Unexpectedly, we sometimes detect a sudden colossal jump, which we interpret as due to mirror buckling. This innovative technique provides a much needed atomic-scale probe for the time-dependent behaviours of intrinsic ripples. The discovery of this novel progenitor represents a fundamental advance in the use of scanning tunnelling microscopy, which together with the application of a thermal load provides a low-frequency nano-resonator.

Abstract: Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one angstrom even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures(1-5). Here, we show that van der Waals gaps between atomic planes of layered crystals provide angstrom-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher barrier than deuterons when entering van der Waals gaps in hexagonal boron nitride and molybdenum disulfide. This is attributed to the difference in the de Broglie wavelengths of the isotopes. Once inside the crystals, transport of both isotopes can be described by classical diffusion, albeit with unexpectedly fast rates comparable to that of protons in water. The demonstrated angstrom-size channels can be exploited for further studies of atomistic quantum confinement and, if the technology can be scaled up, for sieving hydrogen isotopes.

Abstract: When confined between graphene layers, water behaves differently from the bulk and exhibits unusual properties such as fast water flow and ordering into a crystal. The hydrogen-bonded network is affected by the limited space and by the characteristics of the confining walls. The presence of an extraordinary number of hydronium and hydroxide ions in narrow channels has the following effects: (i) they affect water permeation through the channel, (ii) they may interact with functional groups on the graphene oxide surface and on the edges, and (iii) they change the thermochemistry of water, which are fundamentally important to understand, especially when confined water is subjected to an external electric field. Here we study the physical properties of water when confined between two graphene sheets and containing hydronium and hydroxide. We found that: (i) there is a disruption in the solvation structure of the ions, which is also affected by the layered structure of confined water, (ii) hydronium and hydroxide occupy specific regions inside the nanochannel, with a prevalence of hydronium (hydroxide) ions at the edges (interior), and (iii) ions recombine more slowly in confined systems than in bulk water, with the recombination process depending on the channel height and commensurability between the size of the molecules and the nanochannel height – a decay of 20% (40%) in the number of ions in 8 ps is observed for a channel height of h = 7 angstrom (bulk water). Our work reveals distinctive properties of water confined in a nanocapillary in the presence of additional hydronium and hydroxide ions.

Abstract: Atomistic simulations are used to study the bending of rectangular graphene nanoribbons subjected to axial stress both for free boundary and supported boundary conditions. The shapes of the deformations of the buckled graphene nanoribbons, for small values of the stress, are sine waves where the number of nodal lines depend on the longitudinal size of the system and the applied boundary condition. The buckling strain for the supported boundary condition is found to be independent of the longitudinal size and estimated to be 0.86%. From a calculation of the free energy at finite temperature we find that the equilibrium projected two-dimensional area of the graphene nanoribbon is less than the area of a flat sheet. At the optimum length the boundary strain for the supported boundary condition is 0.48%.

Abstract: The electronic properties of boron nitride nanoribbons (BNNRs) doped with a line of carbon atoms are investigated using density functional calculations. By replacing a line of alternating B and N atoms with carbons, three different configurations are possible depending on the type of the atoms which bond to the carbons. We found very different electronic properties for these configurations: (i) the NCB arrangement is strongly polarized with a large dipole moment having an unexpected direction, (ii) the BCB and NCN arrangements are nonpolar with zero dipole moment, (iii) the doping by a carbon line reduces the band gap regardless of the local arrangement of the borons and the nitrogens around the carbon line, and (iv) the polarization and energy gap of the carbon-doped BNNRs can be tuned by an electric field applied parallel to the carbon line. Similar effects were found when either an armchair or zigzag line of carbon was introduced.

Abstract: Twisted graphene layers produce a moire pattern (MP) structure with a predetermined wavelength for a given twist angle. However, predicting the membrane corrugation amplitude for any angle other than pure AB-stacked or AA-stacked graphene is impossible using first-principles density functional theory (DFT) due to the large supercell. Here, within elasticity theory, we define the MP structure as the minimum-energy configuration, thereby leaving the height amplitude as the only unknown parameter. The latter is determined from DFT calculations for AB-and AA-stacked bilayer graphene in order to eliminate all fitting parameters. Excellent agreement with scanning tunneling microscopy results across multiple substrates is reported as a function of twist angle.

Abstract: Nanoindentation of bilayer graphene is studied using molecular-dynamics simulations. We compared our simulation results with those from elasticity theory as based on the nonlinear Föppl-Hencky equations with rigid boundary condition. The force-deflection values of bilayer graphene are compared to those of monolayer graphene. Youngs modulus of bilayer graphene is estimated to be 0.8 TPa which is close to the value for graphite. Moreover, an almost flat bilayer membrane at low temperature under central load has a 14% smaller Youngs modulus as compared to the one at room temperature.

Abstract: The instability of a free-standing one-sided hydrogenated/fluorinated graphene nanoribbon, i.e., graphone/fluorographene, is studied using ab initio, semiempirical, and large-scale molecular dynamics simulations. Free-standing semi-infinite armchairlike hydrogenated/fluorinated graphene (AC-GH/AC-GF) and boatlike hydrogenated/fluorinated graphene (B-GH/B-GF) (nanoribbons which are periodic along the zigzag direction) are unstable and spontaneously transform into spiral structures. We find that rolled, spiral B-GH and B-GF are energetically more favorable than spiral AC-GH and AC-GF which is opposite to the double-sided flat hydrogenated/fluorinated graphene, i.e., graphane/fluorographene. We found that the packed, spiral structures exhibit an unexpected localized highest occupied molecular orbital and lowest occupied molecular orbital at the edges with increasing energy gap during rolling. These rolled hydrocarbon structures are stable beyond room temperature up to at least T = 1000 K within our simulation time of 1 ns. DOI: 10.1103/PhysRevB.87.075448

Abstract: Using atomistic simulations we investigate the morphological properties of graphene deposited on top of a nanostructured substrate. Sinusoidally corrugated surfaces, steps, elongated trenches, one-dimensional and cubic barriers, spherical bubbles, Gaussian bumps, and Gaussian depressions are considered as support structures for graphene. The graphene-substrate interaction is governed by van der Waals forces and the profile of the graphene layer is determined by minimizing the energy using molecular dynamics simulations. Based on the obtained optimum configurations, we found that (i) for graphene placed over sinusoidally corrugated substrates with corrugation wavelengths longer than 2 nm, the graphene sheet follows the substrate pattern while for supported graphene it is always suspended across the peaks of the substrate, (ii) the conformation of graphene to the substrate topography is enhanced when increasing the energy parameter in the van der Waals model, (iii) the adhesion of graphene into the trenches depends on the width of the trench and on the graphene's orientation, i. e., in contrast to a small-width (3 nm) nanoribbon with armchair edges, the one with zigzag edges follows the substrate profile, (iv) atomic-scale graphene follows a Gaussian bump substrate but not the substrate with a Gaussian depression, and (v) the adhesion energy due to van der Waals interaction varies in the range [0.1-0.4] J/m(2).

Abstract: Large-scale atomistic simulations using the reactive force field approach are implemented to investigate the thermomechanical properties of fluorinated graphene (FG). A set of parameters for the reactive force field potential optimized to reproduce key quantum mechanical properties of relevant carbon-fluorine cluster systems are presented. Molecular dynamics simulations are used to investigate the thermal rippling behavior of FG and its mechanical properties and compare them with graphene, graphane and a sheet of boron nitride. The mean square value of the height fluctuations < h(2)> and the height-height correlation function H(q) for different system sizes and temperatures show that FG is an unrippled system in contrast to the thermal rippling behavior of graphene. The effective Young's modulus of a flake of fluorinated graphene is obtained to be 273 N/m and 250 N/m for a flake of FG under uniaxial strain along armchair and zigzag directions, respectively. DOI: 10.1103/PhysRevB.87.104114

Abstract: Using atomistic simulations we investigate the thermodynamical properties of a single atomic layer of hexagonal boron nitride (h-BN). The thermal induced ripples, heat capacity, and thermal lattice expansion of large scale h-BN sheets are determined and compared to those found for graphene (GE) for temperatures up to 1000 K. By analyzing the mean-square height fluctuations < h(2)> and the height-height correlation function H(q) we found that the h-BN sheet is a less stiff material as compared to graphene. The bending rigidity of h-BN (i) is about 16% smaller than the one of GE at room temperature (300 K), and (ii) increases with temperature as in GE. The difference in stiffness between h-BN and GE results in unequal responses to external uniaxial and shear stress and different buckling transitions. In contrast to a GE sheet, the buckling transition of a h-BN sheet depends strongly on the direction of the applied compression. The molar heat capacity, thermal-expansion coefficient, and Gruneisen parameter are estimated to be 25.2 J mol(-1) K-1, 7.2 x 10(-6) K-1, and 0.89, respectively.

Abstract: Using first-principles calculations and reactive force field molecular dynamics simulations, we study the structural properties and dynamics of a fluorine (F) atom, either adsorbed on the surface of single layer graphene (F/GE) or between the layers of AB stacked bilayer graphene (F@ bilayer graphene). It is found that the diffusion of the F atom is very different in those cases, and that the mobility of the F atom increases by about an order of magnitude when inserted between two graphene layers. The obtained diffusion constant for F/GE is twice larger than that experimentally found for gold adatom and theoretically found for C-60 molecule on graphene. Our study provides important physical insights into the dynamics of fluorine atoms between and on graphene layers and explains the mechanism behind the separation of graphite layers due to intercalation of F atoms.

Abstract: The report on square ice sandwiched between two graphene layers by Algara-Siller et al. [Nature (London) 519, 443 (2015)] has generated a large interest in this system. By applying high lateral pressure on nanoconfined water, we found that monolayer ice is transformed to bilayer ice when the two graphene layers are separated by H = 6,7 angstrom. It was also found that three layers of a denser phase of ice with smaller lattice constant are formed if we start from bilayer ice and apply a lateral pressure of about 0.7 GPa with H = 8,9 angstrom. The lattice constant (2.5-2.6 angstrom) in both transitions is found to be smaller than those typical for the known phases of ice and water, i.e., 2.8 angstrom. We validate these results using ab initio calculations and find good agreement between ab initio O-O distance and those obtained from classical molecular dynamics simulations. The reversibility of the mentioned transitions is confirmed by decompressing the systems.