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While graphene oxide (GO) is representative of a disordered phase of oxocarbons with lackluster electronic properties, the coexistence of ordered, stoichiometric solid-state carbon oxides with graphene brings renewed momentum to the exploration of two-dimensional crystalline oxocarbons. This enduring subject, spanning decades, has recently witnessed significant advancements. In this context, our study delves into a novel material class, COF-66, notable for its meticulously ordered two-dimensional crystalline structure and intrinsic porosity. Employing a global optimization algorithm alongside density-functional calculations, our investigation highlights a standout member within the COF-66 family exceptional quasi-flat oxocarbon (C6O6)exhibiting an unconventional oxygen-decorated pore configuration. This pioneering study introduces C6O6 as an innovative entrant into the crystalline carbon oxide arena, augmenting the established understanding alongside the well-recognized graphene oxide and two graphene monoxide, i.e. \alpha-GMO and e̱ta-GMO. Expanding the exploration, the COF-66 series encompasses 2D-porous carbon nitride (C6N6) and the recently synthesized 2D-porous boroxine (B6O6), adhering to a generalized stoichiometry of X6Y6, where X = B, C, and Y = B, N, O, with X 6= Y. Remarkably, the entire COF-66 ensemble adopts a 2D-crystalline framework, with the exception of C6B6, which assumes a distinct 3D-crystalline arrangement. Employing the PBE (HSE06) level of theory, our electronic structure calculations yield band gap values of 0.01 (0.05) eV, 3.68 (5.29) eV, 0.00 (0.23) eV, and 1.53 (3.09) eV for B6N6, B6O6, C6B6, and C6N6, respectively, reinforcing and aligning with prior investigations.

Ion-selective channels play a key role in physiological processes and are used in many technologies. While biological channels can efficiently separate same-charge ions with similar hydration shells, it remains a challenge to mimic such exquisite selectivity using artificial solid-state channels. Although, there are several nanoporous membranes that show high selectivity with respect to certain ions, the underlying mechanisms are based on the hydrated ion size and/or charge. There is a need to rationalize the design of artificial channels to make them capable of selecting between similar-size same-charge ions, which in turn requires understanding of why and how such selectivity can occur. To address this issue, we study angstrom-scale artificial channels made by van der Waals assembly, which are comparable in size with typical ions and carry little residual charge on channel walls. This allows us to exclude the first-order effects of steric and Coulomb-based exclusion. We show that the studied two-dimensional angstrom-scale capillaries can distinguish between same-charge ions with similar hydrated diameters. The selectivity is attributed to different positions occupied by ions within the layered structure of nanoconfined water, which depend on the ion-core size and differ for anions and cations. The revealed mechanism points at possibilities of ion separation beyond the simple steric sieving.

Recently, Bafekry et al. [J. Appl. Phys. 130, 114301(2021)] reported their density functional theory (DFT) results on the structural, phonon dispersion, elastic constants and electronic properties of a BCN monolayer. The aforementioned theoretical work however includes erroneous results and discussions, as will be explained in the following.

The intercalated water into nanopores exhibits anomalous properties such as ultralow dielectric constant.~Multi-scale modeling and simulations are used to investigate the dielectric properties of various crystalline two-dimensional ices and bulk ices. Although, the structural properties of two-dimensional (2D-) ices have been extensively studied, much less is known about their electronic and optical properties. First, by using density functional theory (DFT) and density functional perturbation theory (DFPT), we calculate the key electronic, optical and dielectric properties of 2D-ices. Performing DFPT calculations, both the ionic and electronic contributions of the dielectric constant are computed. The in-plane electronic dielectric constant is found to be larger than the out-of-plane dielectric constant for all the studied 2D-ices. The in-plane dielectric constant of the electronic response is found to be isotropic for all the studied ices. Secondly, we determined the dipolar dielectric constant of 2D-ices using molecular dynamics simulations (MDS) at finite temperature. The total out-of-plane dielectric constant is found to be larger than 2 for all the studied 2D-ices. Within the framework of the random-phase approximation (RPA), the absorption energy ranges for 2D-ices are found to be in the ultraviolet spectra. For the comparison purposes, we also elucidate the electronic, dielectric and optical properties of four crystalline ices (ice VIII, ice XI, ice Ic and ice Ih) and bulk water.

Water inside a nanocapillary becomes ordered, resulting in unconventional behavior. A profound enhancement of water flow inside nanometer thin capillaries made of graphene has been observed [B. Radha et.al., Nature (London) 538, 222 (2016)]. Here we explain this enhancement as due to the large density and the extraordinary viscosity of water inside the graphene nanocapillaries. Using the Hagen-Poiseuille theory with slippage-boundary condition and incorporating disjoining pressure term in combination with results from molecular dynamics (MD) simulations, we present an analytical theory that elucidates the origin of the enhancement of water flow inside hydrophobic nanocapillaries. Our work reveals a distinctive dependence of water flow in a nanocapillary on the structural properties of nanoconfined water in agreement with experiment, which opens a new avenue in nanofluidics.

Developing 'smart' membranes that allow precise and reversible control of molecular permeation using external stimuli would be of intense interest for many areas of science: from physics and chemistry to life-sciences. In particular, electrical control of water permeation through membranes is a long-sought objective and is of crucial importance for healthcare and related areas. Currently, such adjustable membranes are limited to the modulation of wetting of the membranes and controlled ion transport, but not the controlled mass flow of water. Despite intensive theoretical work yielding conflicting results, the experimental realisation of electrically controlled water permeation has not yet been achieved. Here we report electrically controlled water permeation through micrometre-thick graphene oxide (GO) membranes. By controllable electric breakdown, conductive filaments are created in the GO membrane. The electric field concentrated around such current carrying filaments leads to controllable ionisation of water molecules in graphene capillaries, allowing precise control of water permeation: from ultrafast permeation to complete blocking. Our work opens up an avenue for developing smart membrane technologies and can revolutionize the field of artificial biological systems, tissue engineering and filtration.

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. 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 de Broglie wavelength 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.

We report subnanometer, high-bandwidth measurements of the out-of-plane (vertical) motion of atoms in freestanding graphene using scanning tunneling microscopy. By tracking the vertical position over a long time period, a 1000-fold increase in the ability to measure space-time dynamics of atomically thin membranes is achieved over the current state-of-the-art imaging technologies. We observe that the vertical motion of a graphene membrane exhibits rare long-scale excursions characterized by both anomalous mean-squared displacements and Cauchy-Lorentz power law jump distributions.

Van der Waals assembly of two-dimensional (2D) crystals continue attract intense interest due to the prospect of designing novel materials with on-demand properties. One of the unique features of this technology is the possibility of trapping molecules or compounds between 2D crystals. The trapped molecules are predicted to experience pressures as high as 1 GPa. Here we report measurements of this interfacial pressure by capturing pressure-sensitive molecules and studying their structural and conformational changes. Pressures of 1.2 +/- 0.3 GPa are found using Raman spectrometry for molecular layers of one nanometer in thickness. We further show that this pressure can induce chemical reactions and several trapped salts or compounds are found to react with water at room temperature, leading to 2D crystals of the corresponding oxides. This pressure and its effect should be taken into account in studies of van der Waals heterostructures and can also be exploited to modify materials confined at the atomic interfaces.

An external electric field changes the physical properties of polar-liquids due to the reorientation of their permanent dipoles. For example it should affect significantly the physical properties of water confined in a nanochannel. The latter effect is profoundly enhanced, if the field is applied along the nanochannel. Using molecular dynamics simulations, we predict that an in-plane electric field applied parallel to the channel polarizes water molecules which are confined between two graphene layers, resulting in distinct-ferroelectricity and electrical hysteresis. We found that electric fields alter the in-plane order of the hydrogen bonds: reversing the electric field does not restore the system to the non-polar initial state, instead a residual dipole moment remains in the system. Our study provides insights into the ferroelectric state of water when confined in nanochannels and shows how this can be tuned by an electric field.

The rate of water flow through hydrophobic nanocapillaries is greatly enhanced as compared to that expected from macroscopic hydrodynamics. This phenomenon is usually described in terms of a relatively large slip length, which is in turn defined by such microscopic properties as the friction between water and capillary surfaces, and the viscosity of water. We show that the viscosity of water and, therefore, its flow rate are profoundly affected by the layered structure of confined water if the capillary size becomes less than 2 nm. To this end we study the structure and dynamics of water confined between two parallel graphene layers using equilibrium molecular dynamics simulations. We find that the shear viscosity is not only greatly enhanced for subnanometer capillaries, but also exhibits large oscillations that originate from commensurability between the capillary size and the size of water molecules. Such oscillating behavior of viscosity and, consequently, the slip length should be taken into account in designing and studying graphene-based and similar membranes for desalination and filtration.

Water confined between two layers with separation of a few Angstrom forms layered two- dimensional ice structure. Using large scale molecular dynamics simulations with the adoptable ReaxFF interatomic potential we found that flat monolayer ice with a rhombic-square structure nucleates between graphene layers which is non-polar and non-ferroelectric. Two layers of water are found to crystallize into a square lattice close to the experimental found AA-stacking [G. Algara- Siller et al. Nature 519, 443445 (2015)]. Each layer has a net dipole moment which are in opposite direction. Bilayer ice is also non-polar and non-ferroelectric. For three layer ice we found that each layer has a crystal structure similar to monolayer ice.

Ripples in pristine freestanding graphene naturally orient themselves in an array that is alternately curved-up and curved-down; maintaining an average height of zero. Using scanning tunneling microscopy (STM) to apply a local force, the graphene sheet will reversibly rise and fall in height until the height reaches 60-70 percent of its maximum at which point a sudden, permanent jump occurs. We successfully model the ripples as a spin-half Ising magnetic system, where the height of the graphene is the spin. The permanent jump in height, controlled by the tunneling current, is found to be equivalent to an antiferromagnetic-to-ferromagnetic phase transition. The thermal load underneath the STM tip alters the local tension and is identified as the responsible mechanism for the phase transition. Four universal critical exponents are measured from our STM data, and the model provides insight into the statistical role of graphenes unusual negative thermal expansion coefficient.

Epitaxial graphene is grown on a non-polar n+ 6H-SiC m-plane substrate and studied using atomic scale scanning tunneling microscopy. Multilayer graphene is found throughout the surface and exhibits rotational disorder. Moiré patterns of different spatial periodicities are found, and we found that as the wavelength increases, so does the amplitude of the modulations. This relationship reveals information about the interplay between the energy required to bend graphene and the interaction energy, i.e. van der Waals energy, with the graphene layer below. Our experiments are supported by theoretical calculations which predict that the membrane topographical amplitude scales with the Moiré pattern wavelength, L as L^-1 + \alpha L^-2.

Knowledge of and control over the curvature of ripples in freestanding graphene are desirable for fabricating and designing flexible electronic devices, and recent progress in these pursuits has been achieved using several advanced techniques such as scanning tunneling microscopy. The electrostatic forces induced through a bias voltage (or gate voltage) were used to manipulate the interaction of freestanding graphene with a tip (substrate). Such forces can cause large movements and sudden changes in curvature through mirror buckling. Here we explore an alternative mechanism, thermal load, to control the curvature of graphene. We demonstrate thermal mirror buckling of graphene by scanning tunneling microscopy and large-scale molecular dynamic simulations. The negative thermal expansion coefficient of graphene is an essential ingredient in explaining the observed effects. This new control mechanism represents a fundamental advance in understanding the influence of temperature gradients on the dynamics of freestanding graphene and future applications with electro-thermal-mechanical nanodevices.

Intrinsic ripples in freestanding graphene have been exceedingly difficult to study. Individual ripple geometry was recently imaged using scanning tunneling 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 tunneling 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 behavior of intrinsic ripples. The discovery of this novel progenitor represents a fundamental advance in the use of scanning tunneling microscopy, which together with the application of a thermal load provides a low-frequency nano-resonator.

Freestanding graphene membranes were successfully functionalized with platinum nanoparticles (Pt NPs). High-resolution transmission electron microscopy revealed a homogeneous distribution of single-crystal Pt NPs that tend to exhibit a preferred orientation. Unexpectedly, the NPs were also found to be partially exposed to the vacuum with the top Pt surface raised above the graphene substrate, as deduced from atomic-scale scanning tunneling microscopy images and detailed molecular dynamics simulations. Local strain accumulation during the growth process is thought to be the origin of the NP self-organization. These findings are expected to shape future approaches in developing Pt NP catalysts for fuel cells as well as NP-functionalized graphene based high-performance electronics.

Large-scale atomistic simulations using the reactive empirical bond order force field approach is implemented to investigate thermal and mechanical properties of single-layer (SL) and multi-layer (ML) molybdenum disulfide (MoS$_2$). The amplitude of the intrinsic ripples of SL-MoS$_2$ are found to be smaller than those exhibited by graphene (GE). Furthermore, because of the van der Waals interaction between layers, the out-of-plane thermal fluctuations of ML-MoS$_2$ decreases rapidly with increasing number of layers. This trend is confirmed by the buckling transition due to uniaxial stress which occurs for a significantly larger applied tension as compared to graphene. For SL-MoS$_2$, the melting temperature is estimated to be 3700~K which occurs through dimerization followed by the formation of small molecules consisting of 2 to 5 atoms. When different types of vacancies are inserted in the SL-MoS$_2$ it results in a decrease of both the melting temperature as well as the stiffness.

Moir'e patterns in the pseudo-magnetic field and in the strain profile of graphene (GE) when put on top of a hexagonal lattice substrate are predicted from elasticity theory. %which are confirmed by atomistic simulations. The van der Waals (vdW) interaction between GE and the substrate induces out-of-plane deformations in graphene which results in a strain field, and consequently in a pseudo-magnetic field. When the misorientation angle is about 0.5 deg. a three-fold symmetric strain field is realized that results in a pseudo-magnetic field very similar to the one proposed by F. Guinea, M. I. Katsnelson, and A. K. Geim [Nat. Phys. 6, 30 (2010)]. Our results show that the periodicity and length of the pseudo-magnetic field can be tuned in GE by changing the misorientation angle and substrate adhesion parameters and a considerable energy gap (23 meV) can be obtained due to out-of-plane deformation of graphene which is in the range of recent experimental measurements (20-30 meV).

Twisted graphene layers produce a moiré pattern (MP) structure with a predetermined wavelength for 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 (STM) results across multiple substrates is reported as function of twist angle.

The electronic properties of a triaxially strained hexagonal graphene flake with either armchair or zig-zag edges are investigated using molecular dynamics simulations and tight-binding calculations. We found that: i) the pseudo-magnetic field in the strained graphene flakes is not uniform neither in the center nor at the edge of zig-zag terminated flakes, ii) the pseudo-magnetic field is almost zero in the center of armchair terminated flakes but increases dramatically near the edges, iii) the pseudo-magnetic field increases linearly with strain, for strains lower than 15$%$ while growing non-linearly beyond this threshold, iv) the local density of states in the center of the zig-zag hexagon exhibits pseudo-Landau levels with broken sub-lattice symmetry in the zero'th pseudo-Landau level, and in addition there is a shift in the Dirac cone due to strain induced scalar potentials. This study provides a realistic model of the electronic properties of inhomogeneously strained graphene where the relaxation of the atomic positions is correctly included together with strain induced modifications of the hopping terms up to next-nearest neighbors.

The available synthesized silicene-like structures have been only realized on metallic substrates which are very different from the standalone buckled silicene, e.g. the Dirac cone of silicene is destroyed due to lattice distortion and the interaction with the substrate. Using graphene bilayer as a scaffold a novel route is proposed to synthesize silicene with electronic properties decoupled from the substrate. The buckled hexagonal arrangement of silicene between the graphene layers is found to be very similar to the theoretically predicted standalone buckled silicene which is only very weakly van der Waals coupled to the graphene layers with a graphite-like interlayer distance of 3.42\u2009Å and without only lattice distortion. We found that these stacked layers are stable well above room temperature.

The spatial dependence of the van der Waals (vdW) energy between graphene and hexagonal boron-nitride (h-BN) is investigated using atomistic simulations. The van der Waals energy between graphene and h-BN shows a hexagonal superlattice structure identical to the observed Moiré pattern in the local density of states (LDOS) which depends on the lattice mismatch and misorientation angle between graphene and h-BN. Our results provide atomistic features of the weak van der Waals interaction between graphene and BN which are in agreement with experiment and provide an analytical expression for the size of the spatial variation of the weak van der Waals interaction. We also found that the A-B-lattice symmetry of graphene is broken a long the armchair direction.

The electronic properties of graphene nano-flakes (GNFs) with different edge passivation is investigated by using density functional theory. Passivation with F and H atoms are considered: C$_{N_c}$ X$_{N_x}$ (X=F or H). We studied GNFs with $10<N_c<56$ and limit ourselves to the lowest energy configurations. We found that: i) the energy difference $\Delta$ between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) decreases with $N_c$, ii) topological defects (pentagon and heptagon) break the symmetry of the GNFs and enhance the electric polarization, iii) the mutual interaction of bilayer GNFs can be understood by dipole-dipole interaction which were found sensitive to the relative orientation of the GNFs, iv) the permanent dipoles depend on the edge terminated atom, while the energy gap is independent of it, and v) the presence of heptagon and pentagon defects in the GNFs results in the largest difference between the energy of the spin-up and spin-down electrons which is larger for the H-passivated GNFs as compared to F-passivated GNFs. Our study shows clearly the effect of geometry, size, termination and bilayer on the electronic properties of small GNFs.This study reveals important features of graphene nano-flakes which can be detected using Raman spectroscopy.

Free standing silicene is predicted to display comparable electronic properties as graphene. However, the yet synthesized silicene-like structures have been only realized on different substrates which turned out to exhibit versatile crystallographic structures that are very different from the theoretically predicted buckled phase of freestanding silicene. This calls for a different approach where silicene is stabilized using very weakly interacting surfaces. We propose here a novel route by using graphene bilayer as a scaffold. The confinement between the flat graphene layers results in a planar clustering of Si atoms with small buckling, which is energetically unfavorable in vacuum. Buckled hexagonal arrangement of Si atoms similar to free-standing silicene is observed for large clusters, which, in contrast to Si atoms on metallic surfaces, is only very weakly van der Waals coupled to the graphene layers. These clusters are found to be stable well above room temperature. Our findings, which are supported by density functional tight-binding calculations, show that intercalating bilayer graphene with Si is a favorable route to realize silicene.

The melting of fluorographene is very unusual and depends strongly on the degree of fluorination. For temperatures below 1000 K, fully fluorinated graphene (FFG) is thermo-mechanically more stable than graphene but at T$_m\approx$2800 K FFG transits to random coils which is almost twice lower than the melting temperature of graphene, i.e. 5300 K. For fluorinated graphene (PFG) up to 30 % ripples causes detachment of individual F-atoms around 2000 K while for 40-60 % fluorination, large defects are formed beyond 1500 K and beyond 60% of fluorination F-atoms remain bonded to graphene until melting. The results agree with recent experiments on the dependence of the reversibility of the fluorination process on the percentage of fluorination.

The influence of triaxial in-plane strain on the electronic properties of a hexagonal boron-nitride sheet is investigated using density functional theory. Different from graphene, the triaxial strain localizes the molecular orbitals of the boron-nitride flake in its center depending on the direction of the applied strain. The proposed technique for localizing the molecular orbitals that are close to the Fermi level in the center of boron nitride flakes can be used to actualize engineered nanosensors, for instance, to selectively detect gas molecules. We show that the central part of the strained flake adsorbs polar molecules more strongly as compared with an unstrained sheet.

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 the Gruneisen parameter are estimated to be 25.2 J\u2009mol$^{-1}$\u2009K$^{-1}$, 7.2$\times10^{-6}$K$^{-1}$ and 0.89, respectively.

Density-functional tight-binding and classical molecular dynamics simulations are used to investigate the structural deformations and melting of planar carbon nano-clusters $C_{N}$ with N=2-55. The minimum energy configurations for different clusters are used as starting configuration for the study of the temperature effects on the bond breaking/rotation in carbon lines (N$<$6), carbon rings (5$<$N$<$19) and graphene nano-flakes. The larger the rings (graphene nano-flake) the higher the transition temperature (melting point) with ring-to-line (perfect-to-defective) transition structures. The melting point was obtained by using the bond energy, the Lindemann criteria, and the specific heat. We found that hydrogen-passivated graphene nano-flakes (C$_{N}$H$_M$) have a larger melting temperature with a much smaller dependence on its size. The edges in the graphene nano-flakes exhibit several different meta-stable configurations (isomers) during heating before melting occurs.

Large scale atomistic simulations using the reactive force field approach (ReaxFF) are implemented to investigate the thermomechanical properties of fluorinated graphene (FG). A new set of parameters for the reactive force field potential (ReaxFF) optimized to reproduce key quantum mechanical properties of relevant carbon-fluor cluster systems are presented. Molecular dynamics (MD) simulations are used to investigate the thermal rippling behavior of FG and its mechanical properties and compare them with graphene (GE), graphane (GA) and a sheet of BN. 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 un-rippled system in contrast to the thermal rippling behavior of graphene (GE). 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 arm-chair and zig-zag direction, respectively.

The instability of a free-standing one sided hydrogenated/fluorinated graphene nano-ribbon, i.e. graphone/fluorographene, is studied using ab-initio, semiempirical and large scale molecular dynamics simulations. Free standing semi-infinite arm-chair like hydrogenated/fluorinated graphene (AC-GO/AC-GF) and boat like hydrogenated/fluorinated graphene (B-GO/B-GF) (nano-ribbons which are periodic along the zig-zag direction) are unstable and spontaneously transform into spiral structures. We find that rolled, spiral B-GO and B-GF are energetically more favorable than spiral AC-GO 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 unexpected localized HOMO-LUMO at the edges with increasing energy gap during rolling. These rolled hydrocarbon structures are stable beyond room temperature up to at least $T$=1000\u2009K.

Thermal fluctuations of single layer hydrogenated graphene (graphane) are investigated using large scale atomistic simulations. By analyzing the mean square value of the height fluctuations $<h^2>$ and the height-height correlation function $H(q)$ for different system sizes and temperatures we show that hydrogenated graphene is an un-rippled system in contrast to graphene. The height fluctuations are bounded, which is confirmed by a $ H(q) $ tending to a constant in the long wavelength limit instead of showing the characteristic scaling law $ q^{4-\eta} (\eta \simeq 0.85)$ predicted by membrane theory. This unexpected behaviour persists up to temperatures of at least 900 K and is a consequence of the fact that in graphane the thermal energy can be accommodated by in-plane bending modes, i.e. modes involving C-C-C bond angles in the buckled carbon layer, instead of leading to significant out-of-plane fluctuations that occur in graphene.

The strain induced pseudo-magnetic field in supported graphene deposited on top of a nanostructured substrate is investigated by using atomistic simulations. Step, elongated trench, one dimensional barrier, spherical bubbles, Gaussian bump and Gaussian depression are considered as support structures for graphene. From the obtained optimum configurations we found very strong induced pseudo-magnetic fields which can reach up to $\sim$ 1000\u2009T due to the strain-induced deformations in the supported graphene. Different magnetic confinements with controllable geometries are found by tuning the pattern of the substrate. The resulting induced magnetic fields for graphene on top of a step, barrier and trench are calculated. In contrast to the step and trench the middle part of graphene on top of a barrier has zero pseudo-magnetic field. This study provides a theoretical background for designing magnetic structures in graphene by nanostructuring substrates. We found that altering the radial symmetry of the deformation, changes the six-fold symmetry of the induced pseudo-magnetic field.

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 bump and Gaussian depression 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 wave lengths longer than 2\u2009nm, 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 graphene's orientation, i.e. in contrast to a small width (3 nm) nanoribbon with armchair edges, the one with zig-zag 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.

Recent experiments showed that non-uniform strain can be produced by depositing graphene over pillars. We employed atomistic calculations to study the non-uniform strain and the induced pseudo-magnetic field up to 5000 Tesla in graphene on top of nano-pillars. By decreasing the distance between the nano-pillars a complex distribution for the pseudo-magnetic field can be generated. Furthermore, we performed tight-binding calculations of the local density of states (LDOS) by using the relaxed graphene configuration obtained from the atomistic calculations. We find that the quasiparticle LDOS are strongly modified near the pillars, both at low energies showing sub-lattice polarization, and at high energies showing shifts of the van Hove singularity. Our study shows that changing the specific pattern of the nano-pillars allows us to create a desired shape of the pseudo-magnetic field profile while the LDOS maps provide an input for experimental verifications by scanning tunneling microscopy.

The electronic properties of boron-nitride nanoribbons (BNNRs) doped with a line of carbon atoms are investigated by using density functional calculations. Three different configurations are possible: the carbon atoms may replace a line of boron or nitrogen atoms or a line of alternating B and N atoms which results in very different electronic properties. We found that: i) the NCB arrangement is strongly polarized with a large dipole moment having an unexpected direction, ii) the BCB and NCN arrangement are non-polar with zero dipole moment, iii) the doping by a carbon line reduces the band gap independent of the local arrangement of boron and nitrogen around the carbon line, iv) an electric field parallel to the carbon line polarizes the BN sheet and is found to be sensitive to the presence of carbon dopants, and v) the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital decreases linearly with increasing applied electric field directed parallel to the carbon line. We show that the polarization and energy gap of carbon doped BNNRs can be tuned by an electric field applied parallel along the carbon line.

The buckling of graphene nano-ribbons containing a grain boundary is studied using atomistic simulations where free and supported boundary conditions are invoked. We found that when graphene contains a small angle grain boundary the buckling strains are larger when the ribbons with free (supported) boundary condition are subjected to compressive tension parallel (perpendicular) to the grain boundary. The shape of the deformations of the buckled graphene nanoribbons depends on the boundary conditions and the presence of the grain boundary and the direction of applied in-plane compressive tension. Large angle grain boundary results in smaller buckling strains as compared to perfect graphene or to a small angle grain boundary.

Using the valence force field model of Perebeinos and Tersoff [Phys. Rev. B \bf79, 241409(R) (2009)], different energy modes of suspended graphene subjected to tensile or compressive strain are studied. By carrying out Monte Carlo simulations it is found that: i) only for small strains ($|\varepsilon| \lessapprox 0.02$) the total energy is symmetrical in the strain, while it behaves completely different beyond this threshold; ii) the important energy contributions in stretching experiments are stretching, angle bending, out-of-plane term and a term that provides repulsion against $\pi-\pi$ misalignment; iii) in compressing experiments the two latter terms increase rapidly and beyond the buckling transition stretching and bending energies are found to be constant; iv) from stretching-compressing simulations we calculated the Young modulus at room temperature 350$\pm3.15$\u2009N/m, which is in good agreement with experimental results (340$\pm50$\u2009N/m) and with ab-initio results [322-353]\u2009N/m; v) molar heat capacity is estimated to be 24.64\u2009J/mol$^{-1}$K$^{-1}$ which is comparable with the Dulong-Petit value, i.e. 24.94\u2009J/mol$^{-1}$K$^{-1}$ and is almost independent of the strain; vi) non-linear scaling properties are obtained from height-height correlations at finite temperature; vii) the used valence force field model results in a temperature independent bending modulus for graphene, and viii) the Gruneisen parameter is estimated to be 0.64.

Nonequilibrium molecular dynamics simulations is used to study the motion of a C60 molecule on a graphene sheet subjected to a temperature gradient. The C60 molecule is actuated and moves along the system while it just randomly dances along the perpendicular direction. Increasing the temperature gradient increases the directed velocity of C60. It is found that the free energy decreases as the C60 molecule moves toward the cold end. The driving mechanism based on the temperature gradient suggests the construction of nanoscale graphene-based motors.

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 compered to those of monolayer graphene. Young's 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 Young's modulus as compared to the one at room temperature.

Using atomistic simulations we determine the roughness and the thermal properties of a suspended graphane sheet. As compared to graphene we found that hydrogenated graphene has: 1) a larger thermal contraction, 2) the roughness exponent at room temperature is smaller, i.e. $\simeq$ 1.0 versus $\simeq$ 1.2 for graphene, 3) the wave lengths of the induced ripples in graphane cover a wide range corresponding to length scales in the range (30-125)\u2009Å at room temperature, and 4) the heat capacity of graphane is estimated to be 29.32$\pm$0.23\u2009J/molK which is 14.8% larger than the one for graphene, i.e. 24.98$\pm$0.14\u2009J/molK. Above 1500\u2009K we found that graphane buckles when its edges are supported in the $x-y$ plane.

The van der Walls interaction between a carbon nanotubes sheet (CNTS) and a rare gas atom, is studied using both atomistic and continuum approaches. We present analytical expressions for the van der Waals energy of continuous nanotubes interacting with a rare gas atom. It is found that the continuum approach dose not properly treat the effect of atomistic configurations on the energy surfaces. The energy barriers are small as compared to the thermal energy, which implies the free motion above the CNTS in heights about one nanometer. In contrast to the energy surface of a graphene sheet, the honeycomb lattice structure in the energy surface of a CNTS is imperceivable. Defects alter the energy surface which therefore influence the gas absorbtion mechanism. (Corresponding author:neekamal@srttu.edu)

Atomistic simulations are used to study the bending of rectangular graphene nano ribbons subjected to axial stress both for free boundary and supported boundary conditions. The shape of the deformations of the buckled graphene nano ribbons, 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 nano ribbon is less than the area of a flat sheet. At the optimum length the boundary strain for the supported boundary condition is 0.48$%$.

We investigate the stability of circular monolayer graphene subjected to a radial load using non-equilibrium molecular dynamics simulations. When monolayer graphene is radially stressed, after some small circular strain ($\sim 0.4%$) it buckles and bends into a new bowl like shape. Young's modulus is calculated from the linear relation between stress and strain before the buckling threshold, which is in agreement with experimental results. The prediction of elasticity theory for the buckling threshold of a radially stressed plate is presented and its results are compared to the one of our atomistic simulation. Jarzynski equality is used to estimate the difference between the free energy of the non-compressed states and the buckled states. From a calculation of the free energy we obtain the optimum radius for which the system feels the minimum boundary stress.

In the letter "Phys. Rev. Lett 104, 196804 (2010)" the compression-relaxation mechanism (CRM) for a graphene sheet (GS) was reported to be irreversible and resulted in static ripples on GS, such that for T <Tc the free-energy of the rippled GS is smaller than that of roughened GS. We will point out several technical difficulties, such as the use of the relation Delta A=<W> for the free energy calculations and the definition of the rough state, with their simulations. We show that (at T <Tc) their introduced rough state suffer boundary stress, thus is a rippled state and their obtained inequality A_ripple<A_rough is no longer valid. Therefore the introduced mechanism is reversible. Furthermore, from theoretical point of view for an infinitely slow rate of CRM, the relation Delta A=<W> (in common non-equilibrium simulations) is allowed. In this case authors of Ref. [1] must report the used infinitely small rate and justify how it is in practice valid. We show Delta A <> <W> for the system that was used in [1].

The motion of a C60 molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a C60 molecule near a graphene sheet is found to be diffusive in the lateral directions. While, in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the C60 molecule. We also examine the rotational diffusion of C60 and show that its motion over the graphene sheet is not a rolling motion.

Nano-indentation of circular graphene flakes are studied by using Molecular Dynamics simulation. We show that the theory of continuum elasticity based on nonlinear Föpple-Hencky equations is applicable on a circular suspended graphene flake. Our simulation results are plenty compatible to those results calculated by the nonlinear elasticity theory. We find the force-displacement curves in good agreement with the recent experimental measurements and conclude they are temperature independent. In addition, we find the vibration frequency for such a system and monitor that it behaves as a sinusoidal manner at small circular graphene size.

The formation of atomic nanoclusters on suspended graphene sheets have been investigated by employing a Molecular dynamics simulation at finite temperature. Our systematic study is based on temperature dependent Molecular dynamics simulations of some transition and alkali atoms on suspended graphene sheets. We find that the transition atoms aggregate and make various size nanoclusters distributed randomly on graphene surface. We also report that most alkali atoms make one atomic layer on graphene sheets. Interestingly, the potassium atoms almost deposit regularly on the surface at low temperature. We expect from this behavior that the electrical conductivity of a suspended graphene doped by potassium atoms would be much higher than the case doped by the other atoms at low temperature.

Ground state energies for confined hydrogen (H) and helium (He) atoms, inside a penetrable/impenetrable compartment have been calculated using Diffusion Monte Carlo (DMC) method. Specifically, we have investigated spherical and ellipsoidal encompassing compartments of a few nanometer size. The potential is held fixed at a constant value on the surface of the compartment and beyond. The dependence of ground state energy on the geometrical characteristics of the compartment as well as the potential value on its surface has been thoroughly explored. In addition, we have investigated the cases where the nucleus location is off the geometrical centre of the compartment.

The behavior of lipid membranes in the presence of an external electric field is studied and used to examine the influence of such fields on membrane parameters such as roughness and show that for a micro sized membrane, roughness grows as the field increases. The dependence of bending rigidity on the electric field is also studied and an estimation of thickness of the accumulated charges around lipid membranes in a free-salt solution is presented.

We present both numerical and analytical study of graphene roughness with a crystal structure including $500 \times 500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of $ 0.6 < \chi < 0.7 $. The correlation function of height fluctuations depends upon temperature with characteristic length scale of $ \approx 90 {\AA}$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about $\simeq 2-3 {\AA}$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.

We numerically study the ground state properties of endohedrally confined hydrogen (H) or helium (He) atom by a molecule of C$_{60}$. Our study is based on Diffusion Monte Carlo method. We calculate the effects of centered and small off-centered H- or He-atom on the ground state properties of the systems and describe the variation of ground state energies due to the C$_{60}$ parameters and the confined atomic nuclei positions. Finally, we calculate the electron distributions in $x-z$ plane in a wide range of C$_{60}$ parameters.

A model based on microcanonical Monte Carlo method is used to study the application of the temperature gradient along a two-dimensional (2D) Ising system. We estimate the system size effects on thermal conductivity, $K$, for a nano-scale Ising layer with variable size. It is shown that $K$ scales with size as $ K=cL^\alpha$ where $\alpha$ varies with temperature. Both the Metropolis and Cruetz algorithms have been used to establish the temperature gradient. Further results show that the average demon energy in the presence of an external magnetic field is zero for low temperatures.