Interlayer vdW Interaction Research Articles

Limits of Coherency and Strain Transfer in Flexible 2D van der Waals Heterostructures: Formation of Strain Solitons and Interlayer Debonding.

In flexible 2D-devices, strain transfer between different van-der Waals stacked layers is expected to play an important role in determining their optoelectronic performances and mechanical stability. Using a 2D non-linear shear-lag model, we demonstrate that only 1-2% strain can be transferred between adjacent layers of different 2d-materials, depending on the strength of the interlayer vdW interaction and the elastic modulus of the individual layers. Beyond this critical strain, layers begin to slip with respect to each other. We further show that due to the symmetry of the periodic interlayer shear potential, stacked structures form strain solitons with alternating AB/BA or AB/AB stacking which are separated by incommensurate domain walls. The extent and the separation distance of these commensurate domains are found to be determined by the degree of the applied strain, and their magnitudes are calculated for several 2D heterostructures and bilayers including MoS2/WS2, MoSe2/WSe2, Graphene/Graphene and MoS2/MoS2 using a multiscale method. As bilayer structures have been shown to exhibit stacking-dependent electronic bandgap and quantum transport properties, the predictions of our study will not only be crucial in determining the mechanical stability of flexible 2D devices but will also help to better understand optoelectronic response of flexible devices.

Multiphonon Raman spectroscopy properties and Raman mapping of 2D van der Waals solids: graphene and beyond

Strong in‐plane bonding (covalent) and weak van der Waals (vdW) interplanar interactions characterize a number of layered solids, as epitomized by graphite. The advent of graphene (Gr), individual atomic two‐dimensional (2D) layers, isolated from mineral graphite via micromechanical exfoliation enabled the ability to pick, place and stack of arbitrary compositions. Moreover, this discovery implicated an access to other 2D vdW solids beyond graphene and artificially stacking atomic layers forming heterostructures/superlattices. Raman spectroscopy (RS) is a fast reliable non‐destructive analytical tool and an integral part for lattice dynamical structural characterization of crystalline solids at nanoscale, revealing not only the collective atomic/molecular motions but also localized vibrations/modes and specifically used to determine the number of graphene layers and of other 2D vdW solids. We present Raman spectroscopy in first‐, second‐ and higher‐order vibrational modes involving 3 and 4 phonons (overtones and combination) and mapping of graphene (mono‐, bi‐, tri‐ and few‐) layers, semiconducting transition metal dichalcogenides (TMDs) [molybdenum disulfide (MoS2) and tungsten disulfide (WS2)] and wide bandgap hexagonal boron nitride (h‐BN) dispersed monolayers, revealing various molecular vibrations and structural quality/disorder. First‐ and higher‐order phonon modes are observed and analyzed in terms of Raman intensity (spatial inhomogeneity or thickness variation), band position (intrinsic mechanical strain) and intensity ratio (structural disorder) as a function of graphene layer (n). An empirical relation for G band position with n is corroborated. All of the higher order modes are observed to upshift almost linearly with n, betraying the underlying interlayer vdW interactions. These findings exemplify the evolution of structural parameters in layered materials in changing from 3‐ to 2‐ or low‐dimensional regime. The results are presented in view of applications of graphene by itself and in combination that help better understanding of physical and electronic properties for nano‐/optoelectronics. Copyright © 2015 John Wiley & Sons, Ltd.

Indirect-Direct Band Gap Transition by Van Der Waals Interaction Engineering in MoS<sub>2</sub>/WS<sub>2</sub> Bilayer Heterojunction

First principles calculations based on the density functional theory (DFT) are employed to estimate the electronic structures of bilayer heterostructure of MoS2/WS2. The dependences of the band structures on external electric field and interlayer separation are evaluated. The external electric filed induces a semiconductor-metal transition. At the same time, a larger interlayer separation, corresponding to a weaker interlayer interaction, makes an indirect-direct band gap transition happen for the heterojunction. Our results demonstrate that electronic structure tailoring of two-dimensional layered materials should include both spatial symmetry control and interlayer vdW interactions engineering.

Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory

Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nano-scaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become stronger. Also, it is found that the small scale and polymer substrate have noticeable effects on the buckling loads of embedded MLGS.

Effect of van der Waals interaction on the structural and cohesive properties of black phosphorus

We investigated the structural and the binding properties of black phosphorus (black-P) by employing density functional theory (DFT) calculations in combination with various implementations of the van der Waals (vdW) interaction. Both the binding energy curve of the two isolated puckered layers and the equation of states of the bulk black-P suggest that the conventional generalized gradient approximation (GGA) functional is incapable of describing the interlayer vdW interaction. From the comparison of the seven different vdW implementations, the appropriate vdW schemes in describing layer-structured black-P are found to be either the Grimme’s dispersion correction (DFT-D2) or the optB86b vdW denisty-functional approach.

The Environmental Effect on the Dynamical Behaviors of Single-Walled Carbon Nanotube in Water

The paper investigates the dynamical behaviors of single-walled carbon nanotube (SWCNT) in water, focusing on the effect of external environment (i.e., water) on SWCNT. The SWCNT-water system comprises three constituent parts, that is, the SWCNT, the absorbed layer of water molecules, and the water flow around the water layer. The SWCNT and the absorbed layer of water are modeled as two-layer thin shells coupled via the interlayer vdW interaction, and the water surrounding the absorbed water layer is considered as the potential flow. The numerical simulations show that the vdW interaction is responsible for an upshift in the frequency of the SWCNT and preserving the stability of system. Flow velocity has almost no effect on the natural frequency of SWCNT, while being quite significant for destabilizing of the CNT-fluid system. In addition, the effect of wavenumber on the coupled system is also considered. The study not only greatly reduces simulation time but also provides a new model to explain the experimental observation available in particular cases.

Dynamic behavior of triple-walled carbon nanotubes conveying fluid

In this study, the instability of triple-walled carbon nanotubes (TWCNTs) conveying fluid is studied based on an Euler–Bernoulli beam model. The van der Waals (vdW) interactions between different carbon nanotubes (CNTs) are taken into account in the analysis, and the Galerkin discretization approach is used to solve the coupled equations of the motions. Numerical simulations show that the interlayer vdW interactions play a significant role in the natural frequencies and the stability of TWCNTs. The critical flow velocities—associated with divergence, restabilization and flutter—are determined. The effects of different inner radius and the value of mode N used in Galerkin discretization on the dynamical behaviors of the fluid-conveyed TWCNTs are also examined in detail. Results reveal that the internal moving fluid plays an important role in the instability of TWCNTs.

The effect of van der Waals interaction modeling on the vibration characteristics of multiwalled carbon nanotubes

An elastic multiple shell model is used for the vibration analysis of multiwalled carbon nanotubes (MWCNTs). The van der Waals (vdW) interaction between any two layers of the MWCNT is modeled as the radius-dependent function. Based on the simplified Donnell shell equations, explicit formulas are obtained for the radial-dominated natural frequencies and mode shapes of double- and triple-walled carbon nanotubes. The natural frequencies are calculated for MWCNT with various radii and number of tubes. The numerical results show that the effect of vdW interaction on the torsionally and longitudinally dominated natural frequencies is very small and can be neglected, and the vdW interaction has only a small influence on the lowest radial-dominated natural frequency, but plays a significant role in the higher radial-dominated natural frequencies for various combinations of m (number of longitudinal) and n (number of circumferential) waves in the mode even for the MWCNTs of small innermost radius. Especially, due to the effect of vdW interaction, there exists a change over in the order of the modes, from radially dominated mode to longitudinally dominated mode, or from longitudinally dominated mode to torsionally dominated mode even when the innermost radius of the MWCNT is very small, indicating that the interlayer vdW interaction plays a significant role in the vibration of MWCNTs with small radius. The effect of the mode order on the natural frequencies of MWCNT is also examined in detail.

Free vibration of multiwall carbon nanotubes

A multiple-elastic shell model is applied to systematically study free vibration of multiwall carbon nanotubes (MWNTs). Using Flugge [Stresses in Shells (Springer, Berlin, 1960)] equations of elastic shells, vibrational frequencies and associated modes are calculated for MWNTs of innermost radii 5 and 0.65 nm, respectively. The emphasis is placed on the effect of interlayer van der Waals (vdW) interaction on free vibration of MWNTs. Our results show that the interlayer vdW interaction has a crucial effect on radial (R) modes of large-radius MWNTs (e.g., of the innermost radius 5 nm), but is less pronounced for R modes of small-radius MWNTs (e.g., of the innermost radius 0.65 nm), and usually negligible for torsional (T) and longitudinal (L) modes of MWNTs. This is attributed to the fact that the interlayer vdW interaction, characterized by a radius-independent vdW interaction coefficient, depends on radial deflections only, and is dominant only for large-radius MWNTs of lower radial rigidity but less pronounced for small-radius MWNTs of much higher radial rigidity. As a result, the R modes of large-radius MWNTs are typically collective motions of almost all nested tubes, and the R modes of small-radius MWNTs, as well as the T and L modes of MWNTs, are basically vibrations of individual tubes. In particular, an approximate single-shell model is suggested to replace the multiple-shell model in calculating the lowest frequency of R mode of thin MWNTs (defined by the innermost radius-to-thickness ratio not less than 4) with relative errors less than 10%. In addition, the simplified Flugge single equation is adopted to substitute the exact Flugge equations in determining the R-mode frequencies of MWNTs with relative errors less than 10%.

Pressure effect on radial breathing modes of multiwall carbon nanotubes

This paper studies the pressure effect on radial breathing modes (RBMs) of multiwall carbon nanotubes (MWNTs). The analysis is based on a multiple-elastic shell model which assumes that each of the concentric tubes of a MWNT is an individual elastic shell and coupled with adjacent tubes through van der Waals interaction. The pressure effect on RBMs of MWNTs is mainly attributed to the pressure-induced reduction of interlayer spacing and the increase of the interlayer vdW interaction coefficient defined by the second derivative of the energy-interlayer spacing relation of MWNTs. In the absence of external pressure, the RBM frequencies and vibration modes predicted by the present shell model are found to agree very well with the available experimental and molecular-dynamics simulation results. In the presence of an external pressure, our results show that high external pressure considerably raises the vdW interaction coefficients especially between the outermost few layers of MWNTs. As a result, some of the RBM frequencies of MWNTs increase significantly with increasing external pressure. The most significant pressure effect occurs for the highest-frequency mode of large-diameter MWNTs (with the innermost diameter greater than 2nm) or an intermediate-frequency mode of small-diameter MWNTs (with the innermost diameter less than 2nm), and is always associated with those RBMs in which adjacent outermost layers vibrate in opposite directions with significant change in interlayer spacing.

Hard numbers on soft matter

Graphitic systems are ideal examples of the soft-matter challenge for quantum mechanics that must account for both strong local atom bonds and weak nonlocal van der Waals interactions between atoms separated by empty space. Here a new density functional (DF), which encompasses nonlocal correlations among the electrons, is applied successfully to obtain structure, bonding, and compressibility, documenting the decisive role of the interlayer vdW interactions. The understanding emerging from this new extended-DF formulation has bearing on broad classes of problems, including surfaces, in physics, chemistry, biology, medicine, and technology, where we can now provide an efficient and accurate DF-theory account.