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The interaction between graphene layers is analyzed combining local orbital DFT and second order perturbation theory. For this purpose we use the linear combination of atomic orbitals-orbital occupancy (LCAO-OO) formalism, that allows us to separate the interaction energy as the sum of a weak chemical interaction between graphene layers plus the va...
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... analyze how dynamical processes affect the vdW interaction by means of the simple model shown in figure 9. Here, atoms 1 and 2, each represented by a two-level model, are coupled by means of the J interaction (J can represent, for example, the particular transition associated with the virtual transitions between orbitals, say s 1 → p 1 in atom 1 and s 2 → p 2 in atom 2). ...
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Citations
... In our work, the non-bonding interlayer interaction energy between the layers of the BLG is considered, where the dopant atoms play an essential role [46]. The interaction energy between the dopant atoms in graphene can be determined or obtained from the total energy of the system using DFT calculation. ...
We model bilayer graphene-like materials with Si$_2$C$_{14}$ and BC$_{14}$N stoichiometry, where the interlayer interactions play important roles shaping the physical properties of the systems. We find the interlayer interaction in Si$_2$C$_{14}$ to be repulsive due to the interaction of Si-Si atoms, and in BC$_{14}$N it is attractive due to B and N atoms for both the AA- and the AB-stacking. The repulsive interlayer interaction opens up a bandgap in Si$_2$C$_{14}$ while the attractive interlayer interaction in BC$_{14}$N induces a small indirect bandgap or overlaping of the valence conduction bands. Furthermore, the repulsive interaction decreases the Young modulus while the attractive interaction does not influence the Young modulus much. The stress-strain curves of both the AA- and the AB-stackings are suppressed compared to pure graphine bilayers. The optical response of Si$_2$C$_{14}$ is very sensitive to an applied electric field and an enrichment in the optical spectra is found at low energy. The enrichment is attributed to the bandgap opening and increased energy spacing between the $\pi{\text -}\pi^*$ bands. In BC$_{14}$N, the optical spectra are reduced due to the indirect bandgap or the overlapping of the $\pi{\text -}\pi^* $ bands. Last, a high Seebeck coefficient is observed due to the presence of a direct bandgap in Si$_2$C$_{14}$, while it is not much enhanced in BC$_{14}$N.
... where, [43][44][45][46][47][48][49] indicated that the interlayer binding energies in AB and AA stacked bilayer graphene are 17.7 ∼ 70 and 10.4 ∼ 31.1 meV/atom depending on calculation methods, respectively. The binding energy in 30 • TBG is 1.6 meV/atom smaller than that in the AB stacked bilayer graphene 9 . ...
In this paper, the electronic properties of several multilayer graphene quasicrystals are studied by means of the tight-binding method. The multilayer graphene quasicrystals are stacked in AA, AB or their combined orders, and the quasi-periodicity is introduced by rotating at least one layer by 30 degree. The periodic approximants of several multilayer graphene quasicrystals are proposed, and their effective band structures are derived by unfolding the band structures of approximants. The 30 degree twisted interface separates the system into subsystems, and our results show that these subsystems are coupled by the interlayer interactions crossing the interface but will retain their own band structures at low-energies. The band structures of all the subsystems with the same orientation are combined at the corners of the Brillouin zone, and scattered into their mirror-symmetric points inside the Brillouin zone, with weak and anisotropic spectral functions. Such mirror symmetry and combination effects are robust even if an external electric field is applied. Our results suggest that the 30 degree twisted quasicrystal interface can be used to engineer the band structures of multilayer graphene or other layered two-dimensional materials.
... The DFT-D method and its derivatives have been broadly employed to capture the physics and mechanics of multi-layer graphene [199][200][201][202] and the interaction of graphene with metal substrate [203]. It should be noted that the superlubricity in graphite [204] and weak shear strength [205] in graphene ought to be connected with the vdW characteristics between carbon layers. ...
The super-high strength of single-layer graphene has attracted great interest. In practice, defects resulting from thermodynamics or introduced by fabrication, naturally or artificially, play a pivotal role in the mechanical behaviors of graphene. More importantly, high strength is just one aspect of the magnificent mechanical properties of graphene: its atomic-thin geometry not only leads to ultra-low bending rigidity, but also brings in many other unique properties of graphene in terms of mechanics in contrast to other carbon allotropes, including fullerenes and carbon nanotubes. The out-of-plane deformation is of a ‘soft’ nature, which gives rise to rich morphology and is crucial for morphology control. In this review article, we aim to summarize current theoretical advances in describing the mechanics of defects in graphene and the theory to capture the out-of-plane deformation. The structure–mechanical property relationship in graphene, in terms of its elasticity, strength, bending and wrinkling, with or without the influence of imperfections, is presented.
... For example, the importance of the relative orientation of CNTs for application as field-emitters in flat panel displays has been underlined by Fan et al. 15 Dappe and co-workers used density functional theory to determine the interactions between flat graphene layers as a sum of weak-chemical interactions (arising from overlapping orbitals) and van der Waals interactions. [16][17][18] However, for the case of graphene dispersions in aqueous media, it is important to understand the interactions between curved graphene sheets for the determination of the dispersion stability of graphene involving curved interfaces. In this context, molecular dynamics simulations of planar hydrophobic solutes in water (representing planar graphene) have elucidated the role of weak solute-solvent interactions on the hydration behavior of hydrophobic solutes. ...
The effect of curvature and relative orientation between two curved graphene sheets in aqueous media is quantified by calculating the potential of mean force using molecular dynamics simulations and thermodynamic perturbation. The potential of mean force between two curved graphene sheets is found to scale as, UCG ~ R0.5 d-4.5, where R is the sheet radius of curvature and d is the inter-sheet distance. Further, a simple analytical calculation based on classical Hamaker theory and the Derjaguin approximation also arrives at the same scaling of interaction energy with respect to R and d. For the case where a misorientation, θ, exists between the two curved graphene sheets, the simulation results strongly suggest an inverse dependence of the potential of mean force on sin θ for θ > 30°. This result is very similar to the scaling predicted by the Derjaguin approximation for two cylinders crossed at an angle, θ, with respect to each other.
... The resulting value of E bind = 55 meV/atom is in reasonable agreement with experiment and almost identical to the D2 value. A similar tendency has been reported very recently in the work of Dappe et al., 66 who used a local-orbital DFT combined with second-order many-body perturbation theory and found that additional inclusion of dynamical screening effects reduced the dispersion interaction between graphene layers by 27 meV/atom. In spite of this improvement, the cohesion energy reported in Ref. 66 remained still too large. ...
... A similar tendency has been reported very recently in the work of Dappe et al., 66 who used a local-orbital DFT combined with second-order many-body perturbation theory and found that additional inclusion of dynamical screening effects reduced the dispersion interaction between graphene layers by 27 meV/atom. In spite of this improvement, the cohesion energy reported in Ref. 66 remained still too large. The bulk modulus of 43 GPa computed using TS + SCS compares well with the available experimental value. ...
The method proposed by Tkatchenko and Scheffler [ Phys. Rev. Lett. 102 073005 (2009)] to correct density functional calculations for the missing van der Waals interactions is implemented in the Vienna ab initio simulation package (vasp) code and tested on a wide range of solids, including noble-gas crystals, molecular crystals (α-N2, sulfur dioxide, benzene, naphthalene, cytosine), layered solids (graphite, hexagonal boron nitride, vanadium pentoxide, MoS2, NbSe2), chain-like structures (selenium, tellurium, cellulose I), ionic crystals (NaCl, KI), and metals (nickel, zinc, cadmium). In addition to the original formulation expressing the van der Waals (vdW) corrections as pairwise potentials whose strength is derived from the rescaled polarizabilities of the neutral free atoms, the self-consistently screened (TS+SCS) [ Phys. Rev. Lett. 108 236402 (2012)] variant of the method involving electrodynamic response effects has been examined. Analytical expressions for the forces acting on the atoms and for the components of the stress tensor needed for the relaxation of the volume and shape of the unit cell using the TS+SCS method are derived. While the calculated structures are reasonably close to experiment, the van der Waals corrections to the binding energies are often found to be overestimated in comparison with experimental data. The TS+SCS approach leads to significantly better results in some problematic cases, such as the binding energy of graphite. However, there is room for further improvements, in particular for strongly ionic systems.
We model bilayer graphene-like materials with Si2C14 and BC14N stoichiometry, where the interlayer interactions play important roles shaping the physical properties of the systems. We find the interlayer interaction in Si2C14 to be repulsive due to the interaction of Si-Si atoms, and in BC14N it is attractive due to B and N atoms. The repulsive interlayer interaction opens up a bandgap in Si2C14 while the attractive interlayer interaction in BC14N induces a small indirect bandgap. Furthermore, the repulsive interaction decreases the Young modulus while the attractive interaction does not influence the Young modulus much. The stress-strain curves of both the AA- and the AB-stackings are suppressed compared to pure graphene bilayers. The optical response of Si2C14 is very sensitive to an applied electric field and an enrichment in the optical spectra is found at low energy. The enrichment is attributed to the bandgap opening and increased energy spacing between the π-π* bands. In BC14N, the optical spectra are reduced due to the indirect bandgap or the overlapping of the π-π* bands. Last, a high Seebeck coefficient is observed due to the presence of a direct bandgap in Si2C14, while it is not much enhanced in BC14N.
Die besonderen Eigenschaften von Graphen ermöglichen das Design von elektronischen Bauteilen im Nanometerbereich. Graphen kann auf der Oberfläche von Siliziumkarbonat (SiC) durch das Ausdampfen von Si epitaktisch gewachsen werden. Ein detailliertes Verständnis der atomaren und elektronischen Struktur der Grenzschicht zwischen Graphen und SiC ist ein wichtiger Schritt um die Wachstumsqualität zu verbessern. Wir nutzen Dichtefunktionaltheorie um das Hybridsystem Graphen-SiC auf atomarer Ebene zu beschreiben. Experimentelle Arbeiten auf der Si Seite von SiC haben gezeigt, dass die Grenzschicht (ZLG) durch eine teilweise kovalent gebundene Kohlenstofflage wächst; darüber bildet sich die erste Graphenlage (MLG). Durch das Konstruieren eines ab initio Oberflächenphasendiagrams zeigen wir, dass sowohl ZLG als auch MLG Gleichgewichtsphasen sind. Unsere Ergebnisse implizieren, dass Temperatur- und Druckbedingungen für den selbstbegrenzenden Graphenwachstum existieren. Wir zeigen, dass sich das Doping und die Riffellung von epitaktischem Graphene durch H-Interkalation reduzieren. Im Experiment unterscheidet sich das Graphenwachstum auf der C Seite qualitativ von der Si Seite. Zu Beginn des Graphenwachstums wird eine Mischung verschiedener Oberflächenphasen beobachtet. Wir diskutieren die Stabilität dieser konkurierenden Phasen. Die atomaren Strukturen von einigen dieser Phasen, inklusive der Graphen-SiC Grenzschicht, sind nicht bekannt wodurch die theoretische Beschreibung erschwert wird. Wir präsentieren ein neues Model für die bisher unbekannte (3x3) Rekonstruktion, das Si Twist Model. Die Oberflächenenergie vom Si Twist Model und von der bekannten (2x2)c Phase schneiden sich direkt an der Grenze zur Graphitbildung. Dies erklärt die experimentell beobachtete Phasenkoexistenz zu Beginn des Graphenwachstums. Wir schlussfolgern, dass auf der C Seite der kontrollierte Graphenewachstum durch Si-reiche Oberflächenphasen blockiert wird.
The neighboring layers in bi-layer (and few-layer) graphenes of both AA and AB stacking motifs are known to be separated at a distance corresponding to van der Waals (vdW) interactions. In this Letter, we present for the first time a new aspect of graphene chemistry in terms of a special chemical bonding between the giant graphene "molecules". Through rigorous theoretical calculations, we demonstrate that the N-doped graphenes (NGPs) with various doping levels can form an unusual two-dimensional (2D) π-π bonding in bi-layer NGPs bringing the neighboring NGPs to significantly reduced interlayer separations. The interlayer binding energies can be enhanced by up to 50% compared to the pristine graphene bilayers that are characterized by only vdW interactions. Such an unusual chemical bonding arises from the π-π overlap across the vdW gap while the individual layers maintain their in-plane π-conjugation and are accordingly planar. The existence of the resulting interlayer covalent-like bonding is corroborated by electronic structure calculations and crystal orbital overlap population (COOP) analyses. In NGP-based graphite with the optimal doping level, the NGP layers are uniformly stacked and the 3D bulk exhibits metallic characteristics both in the in-plane and along the stacking directions.
We report diffusion quantum Monte Carlo calculations of the interlayer
binding energy of bilayer graphene. We find the binding energies of the AA- and
AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9)
meV/atom, respectively. The out-of-plane zone-center optical phonon frequency
predicted by our binding-energy curve is consistent with available experimental
results. As well as assisting the modeling of interactions between graphene
layers, our results will facilitate the development of van der Waals
exchange-correlation functionals for density functional theory calculations.
