In this paper, using molecular dynamics simulations we report spontaneous curling behaviors of freestanding Janus monolayer S-Mo-Se (MoSeS) structures. Density functional theory calculations are performed to obtain the phonon dispersion and phonon spectra of the Janus monolayer MoSeS for analyzing its structural stability. The results show that the Janus monolayer MoSeS is structurally stable. Due to the lattice mismatch between MoS and MoSe domains, the Janus monolayer MoSeS at the freestanding state always spontaneously rolls up in a constant temperature and pressure system. The direction of curling is preferred along the armchair orientation. Specifically, as for the Janus monolayer MoSeS whose size is larger than ∼30 nm, it can spontaneously roll up into a nanotube structure. The underlying physical mechanisms of these phenomena are well uncovered by using classical Timoshenko plate theory and the minimum energy principle.

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Freestanding indentation is a widely used method to characterise the elastic properties of two-dimensional (2D) materials. However, many controversies and confusion remain in this field due to the lack of appropriate theoretical models in describing the indentation responses of 2D materials. Taking the multilayer gallium telluride (GaTe) as an example, in this paper we conduct a series of experiments and simulations to achieve a comprehensive understanding of its freestanding indentation behaviours. Specifically, the freestanding indentation experiments show that the elastic properties of the present multilayer GaTe with a relatively large thickness can only be extracted from the bending stage in the indentation process rather than the stretching stage widely utilised in the previous studies on thin 2D materials, since the stretching stage of thick 2D materials is inevitably accompanied with severe plastic deformations. In combination with existing continuum mechanical models and finite element simulations, an extremely small Young’s modulus of multilayer GaTe is obtained from the nanoindentation experiments, which is two orders of magnitude smaller than the value obtained from first principles calculations. Our molecular dynamics (MD) simulations reveal that this small Young’s modulus can be attributed to the significant elastic softening in the multilayer GaTe with increasing thickness and decreasing length. It is further revealed in MD simulations that this size-induced elastic softening originates from the synergistic effects of interlayer compression and interlayer shearing in the multilayer GaTe, both of which, however, are ignored in the existing indentation models. To consider these effects of interlayer interactions in the theoretical modelling of the freestanding indentation of multilayer GaTe, we propose here novel multiple-beam and multiple-plate models, which are found to agree well with MD results without any additional parameters fitting and thus can be treated as more precise theoretical models in characterising the freestanding indentation behaviours of 2D materials.

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By using molecular dynamics (MD) simulations, we find in this work that due to the piezoelectric characteristic of boron nitride (BN) nanosheets their resonance frequencies can be efficiently tuned by applying an external electric field. This finding suggests that BN nanosheet can be treated as a good building block for designing novel piezoelectrically tunable two-dimensional nanoresonators. As BN nanosheets possess an inversely stacked structure, the applied electric field has different effects on the resonance frequency of BN nanosheets with odd and even layers. The influence of piezoelectric effect on the vibration behaviours observed in MD simulations is found to significantly deviate from the prediction of the conventional Euler-Bernoulli beam model (EBM), since the EBM cannot account for the weak van der Waals interaction between neighbouring layers in BN nanosheets. To take into account the interlayer interaction in the mathematical modelling of the piezoelectric effect on the vibration of BN nanosheets, we propose here a novel multiple beam model (MBM), which can account for both interlayer stretching and shearing deformations. The MBM result is found to be in a good agreement with the MD result without any additional parameters fitting, which indicates that the present MBM can be treated as a more precise theoretical model in the future study of the vibration properties of BN nanosheets.

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