Molecular Dynamic (MD) simulation was employed to take the molecular fingerprint of mechanical properties of Beryllium-Oxide nanotubes (BeONTs). In this regard, the effect of the radius, the number of walls (single-, double- and triple-walled), and interlayer distance, as well as temperature on the Young’s modulus, failure stress and failure strain are visualized and discussed. It was unveiled that larger single-walled BeONTs have lower Young’s modulus in zigzag and armchair direction, and the highest Young’s modulus were obtained for the (8,0) zigzag and (4,4) armchair SWBeONTs as of 645.71GPa and 624.81GPa, respectively. Unlike Young’s modulus, however, the failure properties of the armchair structures were higher than those of zigzag ones. Furthermore, similar to SWBEONTs, an increase in the interlayer distance of double-walled BeONTs (DWBeONTs) led to a slight reduction in Young’s modulus value, while no meaningful trend was found among failure behavior. For double-walled BeONTs (TWBeONTs), the elastic modulus was obviously higher in both armchair and zigzag directions compared to DWBeONTs.
Research Article
Mechanical Properties of Multi-walled Beryllium-Oxide Nanotubes: A molecular Dynamics Simulation Study
https://doi.org/10.21203/rs.3.rs-1406814/v1
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Molecular dynamics
Beryllium-Oxide nanotube
Young’s modulus
multi-walled nanotube
Non-carbon nanotubes, also called inorganic nanotubes, are a class of nanomaterials that have recently been widely considered by the researchers, similar to carbon nanotubes, due to their outstanding mechanical, optical, thermal, and electronic properties. These nanostructures mainly include metal-oxide nanotubes such as Zinc-Oxide (ZnO), Beryllium-Oxide (BeO), and Titanium-Oxide (TiO2), nitride-based nanotubes such as Boron-nitride (BN), Aluminum-nitride (AlN), Gallium-nitride (GaN), and also nanotubes composed of the elements of group VI periodic table such as silicon-carbide (SiC) and silicon-germanium (SiGe), widely considered in both theoretical and experimental research studies [1–7]. However, since the experimental approaches usually compel a high amount of expenditure on the research projects, theoretical studies have become more popular over the past few decades.
Ab-initio based density functional theory (DFT) and molecular dynamic (MD) simulation are the most used theoretical techniques in investigating the properties of nanotube structures and the results of these methods have been reported to be close to those of experimental data [8, 9]. In this regard, Jun-Hua et al. investigated the mechanical properties of AlN nanotubes with both zigzag and armchair chirality’s using DFT and found that an increase in the diameter of both types of AlNNTs resulted in higher Young’s modulus as well as band gap energy [10]. Cong et al. studied the mechanical properties of different Boron-nitride/Aluminum nanocomposite by the employment of MD simulations. They reported that higher Young’s modulus, yield strain, and yield stress were obtained in nanotubes with higher diameters [11]. Liu et.al combined MD and DFT to probe the properties of single-walled SiGeNTs with zigzag and armchair chirality and reported that nanotubes with larger dimensions were more stable structures than those with smaller dimensions[12]. In a DFT study, ZnO nanotube was compared with the ZnO sheet with their adsorption properties by Mashahdzadeh and coworkers. They found that ZnO showed better adsorption capacity in nanotube form compared to sheet form [13].
Beryllium oxide (BeO) is a semiconducting oxide which its graphene form was firstly introduced by Contineza in the 1990s [14]. This nanostructure exhibits considerable properties such as high electrical resistivity, outstanding thermal conductivity, acceptable energy storage capability, and good hardness so that it has recently become a subject of many research studies [15–18]. Sorokin et al. made a comparison between the properties of BeO nanotubes and BeO graphene-like structures trough a DFT research work. They found higher stability of these structures compared to single BeO molecules [19]. In another DFT-based study, Fathalian et al. considered the H2 adsorption properties of zigzag BeONTs and showed these nanotubes would be suitable candidates for this purpose [20]. In addition to single nanotubes, the properties of some other nanostructures developed from these nanotubes including multi-walled, functionalized, doped and defective structures have also been attractive for researchers. Anota et al. employed the DFT method to find out the effect of functionalization on the electronic behavior of BeONTs which were functionalized by the hydroxyl (-OH) group and found that the semiconducting properties of nanotubes remained almost unchanged after functionalization [21].
Fereidoon et.al considered Young’s modulus of zigzag and armchair one, two and three wall Boron-Nitride nanotubes (BNNTs) versus the number of walls using molecular dynamic (MD) simulations and found higher moduli versus adding more walls to the nanotube [22]. In a defect investigation work, Andressa et al. used the DFT technique for considering the effect of vacancy defects on the electronic levels of Boron-nitride nanotubes and showed that vacancies could improve the electronic levels of this nanotube and make it an appropriate choice for adsorbing H2 molecules [23]. MD was employed in another study by Yang et al. to consider the fracture mechanism of single-walled CNT under vacancy and Stone-Wales defects. Their results demonstrated that Stone-Wales defects showed lower stress concentration compared to vacancy defects [24].
In a previous work, we studied mechanical properties of multi-walled beryllium oxide (BeO) nanotubes and nanopeapods using DFT computations [18]. However, DFT outcomes are just mathematical outcomes based on modulus performed at absolute temperature. To capture other mechanical properties as a function of time as well as to pattern fracture behavior in a scale which is close to the real case in a computationally cost effective manner, one needs to use MD simulation [25, 26]. Moreover, mechanical properties of nanotubes are severely depended on their length, which can be imaged in MD computational analysis [27]. Herein we used MD simulation to study the effect of diameter, temperature and the number of walls and on mechanical behavior of multi-walled BeO nanotubes in armchair and zigzag chirality. The Young’s modulus, failure stress, and failure strain of one-, two- and three-walled BeO nanotubes were modeled and discussed at constant and variable temperature.
Molecular dynamic (MD) technique which is based on Newton’s second law using classical mechanics [28], was applied in this article to consider the mechanical properties of the armchair and zigzag one, two, and three wall BeONTs. Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) was employed to model the under evaluation nanostructures as well as considering the Long-range Coulomb atomic interactions. MD is able to provide scalable codes so, it makes LAMMPS act on parallel platforms efficiently [29]. Visual Molecular Dynamics (VMD) indicator was selected to analyze the results obtained from simulation due to being an appropriate tool for supporting various formats and outputs particularly those obtained from LAMMPS. Selecting a suitable potential function is a critical factor for simulating through MD because this function directly affects the precision of the results. In this work, classical multi-body Tersoff potential was used to define the interactions among the elements of the simulated systems [30]. Since the interactions defined by Tersoff are based on the bond orders so, this potential function is suitable for determining different bond states of atoms using the same parameters [30]. Furthermore, periodic boundary conditions which should be applied along the axial direction by the employment of isothermal-isobaric ensemble (NPT). The temperature varied between 300°K and 1000°K for all single-walled structures and was set to 300°K for multi-walled and defective ones. Besides, the pressure was set to 1bar and we also applied Non-equilibrium simulation mode to allow the ends of the BeONTs to move along the loading direction at a predefined at a consistent strain rate. In some of the previous studies, the most acceptable results were achieved when the time step was between 0.5–0.8 fs and in other studies this variable was adjusted between 0.1 and 1 fs for uniaxial tensile tests [28, 31]. To perform tensile tests by MD simulations, strain should be applied to the nanotubes at a constant rate and, as far as we know, the failure of the under loading structure is related to the strain rate so, lower strain rates provide the system enough time to be relaxed [32]. Since the strain rates in the range of 0.0005 Ps− 1 and 0.01 Ps− 1 have extensively been employed in MD research studies [22, 27], we selected strain rate and time step equal to 0.01 Ps− 1 and 1fs respectively. To consider the mechanical behavior, different single-walled, multi-walled, and defective BeONTs were put under uniaxial tensile loading to obtain stress-strain evaluation plots and the stress-strain relation was used to calculate the failure stress, failure strain and Young's modulus of all simulated BeO nanotubes.
a. Geometrical design
To investigate the mechanical behavior of one, two and three wall BeONTs all zigzag and armchair samples were designed under the MD framework. Figure 1 presents a schematic of the simulated nanotubes studied in the current article and Table 1 includes all of the structures that were simulated along with their number of atoms. The average Be-O bond length was obtained equal to 1.57Å and 1.58Å for the zigzag and armchair structures respectively which are in good accordance with the results of the earlier studies [33–36].
|
Chirality |
Number of Atoms |
|---|---|
|
(4,4) SWBeONT |
352 |
|
(6,6) SWBeONT |
528 |
|
(8,8) SWBeONT |
704 |
|
(10,10) SWBeONT |
880 |
|
(12,12) SWBeONT |
1056 |
|
(8,0) SWBeONT |
384 |
|
(10,0) SWBeONT |
480 |
|
(12,0) SWBeONT |
576 |
|
(14,0) SWBeONT |
672 |
|
(16,0) SWBeONT |
768 |
|
(18,0) SWBeONT |
864 |
|
(20,0) SWBeONT |
960 |
|
(4,4)@(8,8) DWBeONTs |
1056 |
|
(4,4)@(9,9) DWBeONTs |
1144 |
|
(4,4)@(10,10) DWBeONTs |
1232 |
|
(8,0)@(14,0) DWBeONTs |
1056 |
|
(8,0)@(15,0) DWBeONTs |
1104 |
|
(8,0)@(16,0) DWBeONTs |
1152 |
|
(8,0)@(18,0) DWBeONTs |
1248 |
|
(4,4)@(8,8)@(12,12) TWBeONT |
2112 |
|
(8,0)@(14,0)@(20,0) TWBeONT |
2016 |
|
Chirality |
(4,4) |
(6,6) |
(8,8) |
(10,10) |
(12,12) |
|---|---|---|---|---|---|
|
Young’s Modulus |
624.81 |
619.21 |
613.48 |
605.09 |
583.09 |
|
Failure Stress |
101.62 |
101.37 |
102.42 |
100.86 |
102.40 |
|
Failure Strain |
0.247 |
0.250 |
0.252 |
0.255 |
0.256 |
|
Chirality |
(8,0) |
(10,0) |
(12,0) |
(14,0) |
(16,0) |
(18,0) |
(20,0) |
|---|---|---|---|---|---|---|---|
|
Young’s Modulus |
645.71 |
631.92 |
621.02 |
617.13 |
605.82 |
591.83 |
587.86 |
|
Failure Stress |
83.60 |
82.55 |
82.58 |
82.25 |
82.13 |
81.55 |
83.12 |
|
Failure Strain |
0.192 |
0.189 |
0.186 |
0.186 |
0.185 |
0.182 |
0.182 |
|
Chirality |
Mechanical Properties |
Temperature (°K) |
|||||||
|
300 |
400 |
500 |
600 |
700 |
800 |
900 |
1000 |
||
|
(18,0) |
Young’s Modulus (GPa) |
591.83 |
586.90 |
579.02 |
563.03 |
554.23 |
546.27 |
526.30 |
507.89 |
|
Failure Stress (GPa) |
79.55 |
77.08 |
74.03 |
70.77 |
68.60 |
65.82 |
64.44 |
56.73 |
|
|
Failure Strain |
0.182 |
0.172 |
0.162 |
0.154 |
0.152 |
0.146 |
0.141 |
0.117 |
|
|
(10,10) |
Young’s Modulus (GPa) |
605.09 |
590.25 |
585.73 |
579.00 |
573.39 |
544.89 |
536.66 |
528.64 |
|
Failure Stress (GPa) |
99.86 |
95.51 |
92.85 |
90.74 |
83.70 |
78.97 |
68.85 |
66.67 |
|
|
Failure Strain |
0.255 |
0.229 |
0.220 |
0.214 |
0.189 |
0.180 |
0.153 |
0.149 |
|
b. Mechanical properties of single-walled BeONTs
Concerning the mechanical properties of single-walled BeO nanotubes, seven zigzag nanotube including structures (8,0), (10,0), (12,0), (14,0), (16,0), (18,0), and (20,0) and five armchair structures including (4,4), (6,6), (8,8), (10,10), and (12,12) were simulated using MD. To calculate Young’s modulus, we put all samples under uniaxial tensile loading and stress-strain curves were plotted accordingly. A schematic of a double-walled nanotube under tensile loading is presented in Fig. 2, and Fig. 3a shows the a stress-strain curve which is plotted for zigzag structure (8,0). As seen, the stress-strain relation is not linear so, to calculate young’s modulus, we fitted a second-order polynomial to the linear part of the stress-strain plot regarding Fig. 3b. The elastic modulus was calculated through the following equation:
1.1. Mechanical properties of double-walled BeONTs
At this stage we modeled four zigzag double-walled structures including (8,0)@(14,0), (8,0)@(15,0,), (8,0)@(16,0), and (8,0)@(17,0) and three armchair structures including (4,4)@(8,8), (4,4)@(9,9), and (4,4)@(10,10) as shown in Fig. 7. Interlayer distance has undoubtedly increased with an increase in the based nanotubes’ radius. As well as the previous section, all double-walled structures were put under uniaxial tensile loading and the obtained results are illustrated in Fig. 8, Table 5 and Table 6. Regarding Fig. 8, we can see that armchair and zigzag structures revealed contradictory behavior via interlayer distance. Similar to single-walled structures Young’s modulus of zigzag DWBeONTs generally reduced (except one point) via an increase in the interlayer distance while this property rose constantly via the increase in interlayer distance of the armchair structures. The highest calculated values of Young’s modulus belonged to (8,0)@(15,0,) zigzag and (4,4)@(10,10) armchair DWBeONTs with the magnitudes of 659.75GPa and 640.67GPa respectively. In an MD theoretical approach Fereidoon et l. found a reduction in Young’s modulus of both armchair and zigzag DWBNNTs via interlayer distance rising [15]. Furthermore, the failure properties of the zigzag double-walled structures did not show a significant trend as well as single-walled ones while the failure stress and failure strain of the armchair DWBeONTs increased slightly similar to what we had already observed for Young’s modulus of this chirality. Besides, a snapshot of the failure process of zigzag (8,0)@(14,0) structure is presented in Fig. 9. This figure demonstrates that the failure of the double-walled structure which started from the inner layer occurred at the same length increment compared to single-walled one (19% against 19%) and the inner layer failed sooner than the outer one.
|
Chirality |
(8,0)@(14,0) |
(8,0)@(15,0) |
(8,0)@(16,0) |
(8,0)@(18,0) |
|---|---|---|---|---|
|
Young’s Modulus (GPa) |
649.69 |
659.75 |
643.97 |
629.19 |
|
Failure Stress (GPa) |
83.36 |
83.96 |
83.74 |
85.31 |
|
Failure Strain |
0.191 |
0.188 |
0.189 |
0.194 |
|
Chirality |
(4,4)@(8,8) |
(4,4)@(9,9) |
(4,4)@(10,10) |
|---|---|---|---|
|
Young’s Modulus (GPa) |
636.12 |
638.67 |
640.67 |
|
Failure Stress (GPa) |
101.59 |
102.98 |
103.46 |
|
Failure Strain |
0.250 |
0.250 |
0.251 |
1.2. Mechanical properties of triple-walled BeONTs
To study more about the effect of adding walls on the properties of nanotubes, a triple-walled (8,0)@(14,0)@(20,0) zigzag BeONT and a triple-walled (4,4)@(8,8)@(12,12) armchair BeONT were simulated using MD as seen in Fig. 10. By putting both samples under uniaxial tensile loading we obtained the values of Young’s modulus equal to 668.04GPa and 647.57GPa for zigzag and armchair TWBeONTs respectively shown in Table 7. These results are in agreement with those of single-walled and double-walled results which had demonstrated higher modulus for the zigzag BeONTs compared to armchair ones. Similarly, failure properties of the armchair TWBeONTs were higher than those of zigzag ones similar to what we had already found in SWBeONTs (see Fig. 4). The variation of Young’s modulus with adding walls is displayed in Fig. 11. This figure confirms that with raising the number of walls from one to two and then three Young’s modulus of both chirality’s increased slightly so adding walls could result in nanotubes with better mechanical properties.
|
Chirality |
(8,0)@(14,0)@(20,0) |
(4,4)@(8,8)@(12,12) |
|---|---|---|
|
Young’s Modulus (GPa) |
668.04 |
647.57 |
|
Failure Stress (GPa) |
96.26 |
102.41 |
|
Failure Strain |
0.22 |
0.24 |
In this article, we considered the mechanical properties of single, double and triple-walled Beryllium-oxide nanotubes (BeONTs) using molecular dynamic (MD) simulation. After putting all simulated zigzag and armchair samples under uniaxial tensile loading we found that Young’s modulus of single-walled BeONTs decreased via increase in radius as well as temperature so that the highest obtained values of this property occurred in the zigzag structure (8,0) and armchair structure (4,4) with the magnitudes of 645.71GPa and 624.81GPa respectively and Young’s modulus of the zigzag SWBeONTS were higher than those of armchair ones. In terms of failure properties, an increase in the diameter made no meaningful trend on the failure stress and failure strain of the SWBeONTs while temperature growing dwindled these properties for bot chirality’s slightly. Unlike Young’s modulus, failure properties of the armchair structure were better than those of zigzag structures. Furthermore, concerning the modulus of DWBeONTs, an interlayer distance increment resulted in Young’s modulus reduction as same as SWBeONTs. Moreover, adding another wall to double-walled BeONTs improved young’s modulus of both chirality’s so that, the modulus of the triple-walled structures (8,0)@(14,0)@(20,0) and (4,4)@(8,8)@(12,12) with the corresponding magnitudes of 668.04GPa and 647.57GPa were higher than those of DWBeONTs (8,0)@(14,0) and (4,4)@(8,8) with the values of 649.69GPA and 636.12GPa as well as SWBeONTs (8,0) and (4,4) with the magnitudes of 645.71GPa and 624.81GPa respectively.
Funding: No funding was received.
Conflicts of interest/Competing interests: The authors declare no competing interests.
Availability of data and material: Available by the corresponding author per request through the email ([email protected])
Code availability: Available by the corresponding author per request through the email ([email protected])
Authors' contributions: Navid Shahab analyzed the data, discussed the results, and designed the figures and tables. Yasser Rostamiyan analyzed and rechecked the results for correctness and wrote the original draft of the article. Amin Hamed Mashhadzadeh designed the case study, wrote the LAMMPS code of the present article, and carried out the computational measurements. All authors have read and agreed to the published version of the manuscript.
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