Multi-walled MoS2 nanotubes. First principles and molecular mechanics computer simulation
Introduction
In recent years, MoS2 nanotubes (NT) have gained a lot of scientific interest due to their outstanding properties and great potential for significant influence in various technological areas [1]: optical resonators and nanophotonic devices [2], field-effect transistors [3,4], photocatalytic activity [5], gas storage [6], lubricants [[7], [8], [9]].
The MoS2 nanotubes were discovered by the Tenne group as a result of the vapor-gas-solid (VGS) reaction [10]. Since this pioneering work a number of synthesis strategies were developed to fabricate MoS2 nanotubes [5,[11], [12], [13], [14]]. In the recent study [15] the mechanism of VGS reaction was investigated in details and the synthesis strategy improved. As a result of the parameters controlled growth of MoS2 NT, Chithaiah et al. [15] produced nanotubes with a length of tens μm and diameter varying in the intervals 10–20, 20–50 and 40–100 nm. Wang et al. [14] report that their synthesis process allows one to construct MoS2 uniform hollow nanotubes. A typical multi-walled nanotube (MWNT) consists of 5–8 MoS2 single wall nanotubes (SWNTs) with the nanotube's inner diameter of 30 nm and outer one of 50 nm. A two-step process, used by Deepak et al. [16], starts from MoO3 nanobelts synthesis. Subsequently sulfidization of these nanobelts allows authors to produce MoS2 multi-walled nanotubes with 12 concentric walls and zigzag chirality. The diameters of MoS2 nanotubes, obtained using a chemical transport reaction, vary from 10 nm up to micrometers [17]. Scanning electron micrographs reveal a MWNT of diameter 52 ± 0.2 nm which includes 25–26 single wall tubes and has been classified as a chiral NT. At last, multi-walled MoS2 nanotubes consisting of tens of SWNTs were grown to study their optical properties [2]. The MWNT, synthesized and studied in this research, has the outer diameter close to 2 μm and consists of 45 SWNTs.
As far as we know the first attempt of MoS2 multi-walled nanotubes molecular dynamics (MD) study has been undertaken using the Lennard-Jones interaction potential [18]. Somewhat earlier, Bucholz and Sinnot [19] used molecular dynamics and a reactive empirical bond-order (REBO) force field [20] to simulate mechanical behavior of MoS2 single wall and double-walled nanotubes (DWNTs). Also, some special case of toroid MoS2 MWNTs was considered by Wu et al. [21], using the same force field. Taking into account the previous results, we believe that systematic modelling of the MoS2 MWNTs would be useful to understand the structural properties and the stability of these objects.
In our previous paper [22] we proposed a many-body force-field for the description of the interatomic interactions in various systems based on MoS2. This SWIGFD force field comprised the following potentials: Stillinger-Weber, Inverse Gaussian, Grimme, Fermi-Dirac. It was applied to investigate the thermodynamic properties of SWNTs using molecular mechanics in the temperature interval l0 K < T < 700 K. Further study of SWNTs' behavior at different temperatures was performed by the molecular dynamics method applying SWIGFD force field. However, these calculations revealed that the simulation of the thermal atomic movement of the SWNTs leads to a collapse of the object at rather low temperature ≈150 K.
In the present paper a revised force field, providing adequate thermal atomic movement along the molecular dynamics trajectories, is reported. As it is shown below, the SWMB-C force field model includes Stillinger-Weber three-body potential, Morse and Buckingham pair potentials and Coulomb interaction. That is why the abbreviation SWMB-C for the references to the revised force field model is adopted.
To check the applicability of the new version of the force field, we perform the Young's modulus calculations in the frame of quasi harmonic (QH) approximation. The results, obtained within SWIGFD and SWMB-C force fields were compared in these calculations.
Then, a number of single-, double- and triple-walled nanotubes (TWNTs) were simulated by DFT method and by molecular mechanics technique applying SWMB-C force field. The satisfactory agreement between the results of the two different methods validates the revised SWMB-C force field.
At last, for the first time multi-walled MoS2 zigzag (zz) as well as armchair (ac) nanotubes from double-walled up to 12-walled ones were modelled applying the SWMB-C force field. The energetic and structural properties of these MWNTs are discussed.
Section snippets
Computational details
Our quantum mechanical (QM) calculations have been performed within the periodic DFT using the hybrid exchange-correlation functional HSE06 [23]. Basis set of localized atomic orbitals, implemented in CRYSTAL17 computer code [24], has been used to expand the crystalline orbitals. To describe the interaction between the core and valence electrons of Mo and S atoms the effective core pseudopotentials CRENBL [25] have been used. The 4s- 4p-, and 4d-subvalence shells of Mo atom were explicitly
Quantum mechanical calculations of single wall, double- and triple-walled NTs
In the present study the DFT simulations on single-, double- and triple-walled MoS2 nanotubes have been performed. The nanotubes with armchair and zigzag chirality have been considered in our quantum mechanical study. It was simulated 13 armchair and 18 zigzag SWNTs, 13 ac and 15 zz DWNTs, 5 ac and 5 zz TWNTs. In Table 2, Table 3, Table 4 we demonstrate the most important results of the DFT simulations and the whole set of data is collected in Tables S3 and S4.
The aim of our quantum mechanical
Conclusions
The hybrid DFT calculations and molecular mechanics simulations with the SWMB-C force field have been employed to investigate armchair and zigzag MoS2 MWNTs. The SWMB-C force field has a moderate ability to reproduce phonon frequencies of MoS2 polytypes and monolayer, but it well reproduces the structure and various energetic characteristic of MoS2 polytypes, monolayer and single wall nanotubes.
The first principles calculations were used to simulate thin double- and triple-walled NTs with outer
CRediT authorship contribution statement
Andrei V. Bandura: Conceptualization, Methodology, Software, Writing - review & editing. Sergey I. Lukyanov: Data curation, Writing - review & editing, Visualization, Investigation. Dmitrii D. Kuruch: Visualization, Investigation. Robert A. Evarestov: Writing - review & editing, Supervision, Project administration.
Declaration of competing interest
There are no conflicts to declare.
Acknowledgments
The reported study was funded by Russian Foundation for Basic Research, project number 20-03-00271-a. The authors also acknowledge the assistance of the University Computer Center of Saint-Petersburg State University in the accomplishment of high performance computations.
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