Molecular Dynamics Simulations of Effects of Geometric Parameters and Temperature on Mechanical Properties of Single-Walled Carbon Nanotubes

Abstract

Carbon nanotubes (CNTs) are considered an advanced form of carbon. They have superior characteristics in terms of mechanical and thermal properties compared to other available fibers and can be used in various applications, such as supercapacitors, sensors, and artificial muscles. The properties of single-walled carbon nanotubes (SWNTs) are significantly affected by geometric parameters such as chirality and aspect ratio, and testing conditions such as temperature and strain rate. In this study, the effects of geometric parameters and temperature on the mechanical properties of SWNTs were studied by molecular dynamics (MD) simulations using the Large-scaled Atomic/Molecular Massively Parallel Simulator (LAMMPS). Based on the second-generation reactive empirical bond order (REBO) potential, SWNTs of different diameters were tested in tension and compression under different strain rates and temperatures to understand their effects on the mechanical behavior of SWNTs. It was observed that the Young’s modulus and the tensile strength decreases with increasing SWNT tube diameter. As the chiral angle increases, the tensile strength increases, while the Young’s modulus decreases. The simulations were repeated at different temperatures of 300 K, 900 K, 1500 K, 2100 K and different strain rates of 1 × 10⁻³/ps, 0.75 × 10⁻³/ps, 0.5 × 10⁻³/ps, and 0.25 × 10⁻³/ps to investigate the effects of temperature and strain rate, respectively. The results show that the ultimate tensile strength of SWNTs increases with increasing strain rate. It is also seen that when SWNTs were stretched at higher temperatures, they failed at lower stresses and strains. The compressive behavior results indicate that SWNTs tend to buckle under lower stresses and strains than those under tensile stress. The simulation results were validated by and consistent with previous studies. The presented approach can be applied to investigate the properties of other advanced materials.

1. Introduction

Since the discovery of carbon nanotubes (CNTs) in 1991 [1], their excellent physical and mechanical properties have attracted efforts from researchers to realize CNT-based nanodevices. As the dimensions of electronic devices shrink to the nanometer scale, heat generation becomes an important issue because of the need to dissipate large amounts of thermal energy within tiny volumes. In fact, recent studies have shown increasing interest in the thermal conductivity of CNTs, which is hypothesized to be very high along the cylindrical axis [2,3,4,5]. Furthermore, due to their excessive mechanical properties, CNTs are often used to enhance the mechanical properties of nanocomposites without significantly increasing their weight [6,7]. Understanding the mechanical properties of single-walled carbon nanotubes (SWNTs) is crucial because they have a wide range of potential applications in a variety of advanced fields. For instance, in the development of supercapacitors, the high tensile strength and flexibility of SWNTs can improve energy storage capability and durability [8]. In the field of sensors, the unique mechanical and electrical properties of SWNTs can enable highly sensitive and responsive detection systems [9]. In addition, SWNTs are being explored for the manufacture of artificial muscles, whose strength and ability to contract and expand mimics the behavior of natural muscles, opening the possibility of more advanced and efficient robotics and biomedical devices [10]. CNTs can be categorized into three main types based on their number of layers: single-walled CNTs (SWNTs), double-walled CNTs (DWNTs), and multi-walled CNTs (MWNTs) [11,12,13].

Studies of CNTs have shown that they have different elastic and strength properties. The discrepancy in mechanical properties of CNTs observed in these studies may be attributed to different factors, including the chirality and aspect ratio of the CNTs tested, production and preparation methods that lead to structural defects in the CNTs, ambient temperature, and the type of loading [14,15].

The performance of CNT-modified composites is affected by numerous factors, some of them acting at the nanoscale, making it difficult to fully characterize the materials with traditional experimental techniques and continuum modeling methods. Traditional trial-and-error experimental approaches are not only expensive and time-consuming, but also impractical in some cases [16]. Therefore, effective design strategies are crucial to facilitate the development of novel composites with properties tailored for specific applications. Molecular dynamics (MD) or first principles simulations become a powerful tool for studying material properties at the nanoscale. MD is an atomistic-scale simulation method that uses inter-atomic potentials to explain the interactions among atoms. In classical MD, electronic effects are averaged, and the simulation focuses on computing the time evolution of atomic positions and velocities based on Newton’s equations of motion. This approach provides valuable insights into the dynamic behavior of materials, especially at the atomic level.

Interatomic potentials, also known as force fields, are derived from first principles or from experimental data to elucidate the interactions between atoms. The reliability of these potentials is critical as it significantly affects the accuracy of MD simulations and their ability to effectively bridge mesoscale methods [17,18,19,20].

Among the prominent interatomic potentials, the Lennard-Jones potential is the most prominent. It has long been used to describe gas atoms, simple metals, and highly ionic systems. At the same time, many-body potentials (including additional terms dealing with many-body interactions) have been introduced and applied to a variety of materials such as semiconductors and polymers [21,22,23]. Together, these potentials increase the robustness and versatility of MD simulations in a variety of materials and systems. A review of studies on the mechanical properties of CNTs shows inconsistencies caused by the different numerical techniques employed and the characteristics, physics, and principles of input parameters and interatomic potentials. For instance, for SWNTs with an aspect ratio of 3, Zhang et al. [24] and Wang et al. [25] reported a critical buckling strain of 7.5%, using the second-generation reactive empirical bond order (REBO) [26] and LJ potentials, respectively, which is larger than the values 6.3% and 5.7% obtained using COMPASS [27] and AIREBO [28] potentials, respectively. It is worth noting that REBO potential is a type of empirical potential used in MD simulations to model the interactions between atoms in a reactive manner. Unlike traditional force fields, REBO potentials explicitly account for the breaking and forming of bonds during chemical reactions. The REBO potentials were developed to address the limitations of traditional force fields, particularly in scenarios involving bond dissociation and formation, which are crucial for simulating chemical reactions. It introduces a bond-order term that represents the strength of the bond between two atoms, allowing a more realistic description of the bond-breaking and bond-formation processes. These potentials have been applied to simulate a variety of materials, including organic molecules, polymers, and nanomaterials, providing valuable insights into reactive behavior at the atomic and molecular levels. Because tensile tests involve stretching the materials, resulting in bond elongation and potential bond rupture, the REBO potentials provide a realistic representation of these processes, making them ideal for studying the mechanical response of materials under tension [29,30].

Extensive studies have been conducted to explore the correlation between the mechanical properties of CNTs and various influential factors, including the length, temperature, and diameter of CNTs, to determine the optimal conditions for industrial applications. Dereli et al. [31] used MD simulations to study the effect of temperature on the tensile properties of SWNTs. Their observations indicated that as the temperature increases from 300 K to 900 K, the Young’s modulus and tensile strength decrease. Goel et al. [32] investigated the effect of temperature on armchair and zigzag nanotubes with identical diameters and lengths. They found that the armchair tube exhibited the maximum failure strain and tensile strength and these values decreased with increasing temperature. Mousavi et al. [33] studied the effect of temperature on the mechanical properties of carbon-basalt fibers/epoxy hybrid composites and reported that when the temperature increased to 130 °C, the flexural strength and modulus of the samples decreased. Giannopoulos et al. [34] explored the mechanical properties of CNTs using spring elements. Using the atomistic microstructure of CNTs, they found that the armchair nanotubes have a slightly higher Young’s modulus than that of the zigzag nanotubes. Najmi et al. [35] studied the effect of CNTs on the compressive and flexural strengths of epoxy honeycomb sandwich panels. The results showed that the compressive strength of honeycomb panels is directly related to the increase in the percentage of CNTs.

With the increasing number of advanced applications of CNTs in various manifestations, understanding their properties, such as mechanical properties, is of vital importance. To model the mechanical properties of CNTs, the adaptive intermolecular reactive empirical bond order (AIREBO) potential for hydrocarbons has been widely used. This potential was introduced in 1990 and can be represented as a sum of pairwise interactions, including covalent bonding REBO interactions, van der Waals interactions described by using the Lennard-Jones potential, and torsion interactions. In 2002, the so-called second-generation REBO potential was proposed by Brenner et al. [26]. The second-generation REBO potential allows for covalent bond breaking and forming, as well as the associated changes in atomic hybridization within the classical potential, thus producing a powerful method for modeling complex chemistry in large many-atom systems. Compared to the earlier version of AIREBO potential, this revised potential contains improved analytic functions and an expanded database. These allow for a better description of the bond energies, lengths, and force constants for hydrocarbon molecular, as well as the elastic properties, interstitial defect energies, and surface energies for diamond.

There is very limited research on evaluating the dependence of chirality, length, diameter, temperature, and strain rate on the mechanical properties of SWNTs. Therefore, this study will investigate the effects of geometric parameters and temperature on the mechanical properties of SWNTs. The mechanical properties were studied using the second-generation REBO potential along with tensile and compressive tests. The second-generation REBO potential can accurately model the bonding interactions between carbon atoms, which is critical for capturing the mechanical properties of carbon-based materials such as SWNTs. It balances computational efficiency and accuracy by considering the bond order, which changes dynamically based on the local atomic environment. This allows the REBO potential to effectively simulate the breaking and forming of covalent bonds under various mechanical loads, capturing the anisotropic nature of carbon–carbon interactions [36]. The simulations results were compared with the experimental and computer modeling results from the literature for validation.

2. Molecular Dynamics Simulation Methodology

All the presented simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open-source MD simulation package. Details of the simulations are described in the following sections.

Simulation Details

Flexible boundary conditions were applied along three dimensions to simulate the finite size of the SWNTs. The REBO potential and the corresponding parameters were used to define the interactions between carbon atoms in the SWNTs [26]. A time step of 0.002 fs (10⁻¹⁵ s) was used for the simulations (determined after a simulation convergence study on the time step). The lower end of the CNT models remained fixed and the other end was laterally fixed (clamped–clamped boundary condition) while being displaced (stretching upward or pushing downward depending on the types of loading: tension or compression loading) with a strain rate of 0.001 ps⁻¹ (as shown in Figure 1). Numerical experiments were carried out at four temperatures: 300, 900, 1500, and 2100 K. For each temperature, the simulation was run for 20 ps (for a total of 120,000 time steps), using a constant number of atoms, volume, and temperature (NVT) ensemble to relax any energetic configurations at the prescribed temperature.

The strain (ε) is determined as the ratio of the change in length of the simulation box in the CNT tube axial z-direction ($∆L_z$) to its initial length (L₀), calculated by the following expression [37]:

$${\epsilon }_z={\displaystyle \frac{∆L_z}{L_0}}$$

(1)

The stress in the Z-direction (the CNT axial direction, in this work) can be calculated using the force component p_z, divided by the area the force component is acting on. The force components p_x, p_y, and p_z are calculated based on the forces exerted by particles on each other within the system. Specifically, p_z represents the cumulative force acting in the Z-direction on a plane perpendicular to the Z-direction. In other words, the total force exerted by the system per unit area in the Z-direction is calculated as follows [37]:

$${\sigma }_z={\displaystyle \frac{P_z}{A_z}}$$

(2)

where A_z is the equivalent cross-sectional area of a SWNT. There are two methods to calculate A_z. One method considers the nanotube as a solid cylinder with a radius of r. A_z can be calculated as follows:

$$A_z=\pi r^2$$

(3)

Secondly, a SWNT can be considered as a tube with a diameter of d and a thickness of t, and its cross-sectional area A_z can be calculated as follows:

$$A_z=\pi dt$$

(4)

Since this study is part of the study on CNT-reinforced composite materials, and considering that SWNTs are the reinforcement to be incorporated into the polymer matrix and will be treated as solid cylinders, in this work, the cross-sectional area A_z of a SWNT was therefore calculated using Equation (3).

3. Results and Discussion

3.1. Tensile Behavior

Figure 2 shows the tensile behavior and failure modes of selected SWNTs with a diameter of approximately 0.75 nm and a length of 5 nm. Figure 2A is the SWNT configuration before displacement, B is the SWNT when necking occurs, and C is shows the SWNT after failure.

Figure 3 shows the tensile stress–strain behavior and failure modes of selected SWNTs with (10,0) chirality (zigzag SWNTs), a diameter of approximately 0.75 nm, strain rate of 0.001/ps, and nanotube length of 5 nm at different temperatures (300, 900, 1500, and 2100 K). The results indicate that all simulated CNTs exhibit nonlinear elastic behavior. It can also be seen from the failure modes that cooler SWNTs have higher slopes, and failure occurs at higher stresses and strains. In other words, the SWNTs stretched at higher temperatures fail at lower stresses and strains. This observation can be explained by the mobility of atoms, which means that at higher temperatures, thermal energy increases the mobility of atoms or molecules within the material. This increased mobility makes it easier for dislocations to move through the crystal lattice, leading to plastic deformation at lower applied stresses.

3.1.1. Diameter and Temperature Dependence of Mechanical Behavior

Figure 4 and Figure 5 show the effect of diameter on the tensile strength of armchair and zigzag SWNTs, respectively. The results show that larger-diameter SWNTs have lower tensile strength and fail at lower strains. In other words, as the diameter increases, the tensile strength decreases, and the SWNTs exhibit higher tensile strength at lower temperatures. The main reason is that when the diameter increases, the cross-sectional area (A) increases, so the strength decreases according to Equation (2), and as the temperature increases, the bondings between the carbon atoms within the SWNTs become weaker, so the tensile strength decreases and the SWNTs become weaker. On the other hand, the SWNTs exhibit higher tensile strength at lower temperatures. As shown in

Table 1. Power-law regression results for tensile strength at different temperatures based on data from Figure 4.

Temperature	Regression Formula of Tensile Strength (TPa)	R2
T = 300 K	$S=0.0927d^{-0.647}$	0.94
T = 900 K	$S=0.07422d^{-0.558}$	0.94
T = 1500 K	$S=0.05779d^{-0.552}$	0.94
T = 2100 K	$S=0.04367d^{-0.686}$	0.96

and

Table 2. Power-law regression results for tensile strength at different temperatures based on data from Figure 5.

Temperature	Regression Formula of Tensile Strength (TPa)	R2
T = 300 K	$S=0.0796d^{-0.618}$	0.95
T = 900 K	$S=0.06876d^{-0.516}$	0.87
T = 1500 K	$S=0.05151d^{-0.432}$	0.75
T = 2100 K	$S=0.03720d^{-0.611}$	0.93

, a power-like trend is observed for SWNTs of both chiralities (i.e., armchair and zigzag SWNTs) where the coefficient of determination R² > 0.94.

S = A D^B      (TPa)

(5)

The results show that for armchair SWNTs at T = 300 K, A = 0.927 and B = −0.647, and for zigzag SWNTs at T = 300 K, A = 0.796 and B = −0.618, and for other temperatures, the quantities of A and B are listed in Table 1 and Table 2. When comparing the two figures (Figure 4 and Figure 5), it is observed that the armchair SWNTs exhibit higher tensile strength than that of the zigzag SWNTs.

Figure 6 and Figure 7 show the effect of diameter on the Young’s moduli of the armchair and zigzag SWNTs, respectively. The results show that the Young’s modulus decreases with increasing diameter, and the SWNTs exhibit higher Young’s modulus at lower temperatures. As shown in

Table 3. Power-law regression results for Young’s modulus at different temperatures based on data from Figure 6.

Temperature	Regression Formula of Yong’s Modulus (TPa)	R2
T = 300 K	$Y=1.0662d^{-0.081}$	0.96
T = 900 K	$Y=$ $1.045d^{-0.069}$	0.99
T = 1500 K	$Y=$ $1.0295d^{-0.066}$	0.96
T = 2100 K	$Y=$ $1.0163d^{-0.061}$	0.99

and

Table 4. Power-law regression results for Young’s modulus at different temperatures based on data from Figure 4.

Temperature	Regression Formula of Yong’s Modulus (TPa)	R2
T = 300 K	$Y=1.0792d^{-0.089}$	0.98
T = 900 K	$Y=1.0582d^{-0.064}$	0.93
T = 1500 K	$Y=1.0424d^{-0.06}$	0.97
T = 2100 K	$Y=$ $1.0424d^{-0.073}$	0.98

, a power-like trend is observed for both chirality SWNTs (i.e., armchair and zigzag SWNTs) where the coefficient of determination R² > 0.93.

Y = A D^B      (TPa)

(6)

The results show that for the armchair SWNTs at T = 300 K, A = 1.0662 and B = −0.081, and for the zigzag SWNTs at T = 300 K, A = 1.0792 and B = −0.089, and for other temperatures, the quantities of A and B are listed in Table 3 and Table 4.

When comparing the two figures (Figure 5 and Figure 6), it is observed that the zigzag SWNTs exhibit a higher Young’s modulus than that of the armchair SWNTs.

3.1.2. Chiral Angle and Temperature Dependence of Mechanical Behavior

Figure 7 and Figure 8 show the effects of chirality and temperature on the tensile strength and Young’s modulus of SWNTs, respectively. The results show that the tensile strength and Young’s modulus increase steadily as the chiral angle increases from 0 to 30°. It can also be seen that the SWNTs stretched at higher temperatures fail at lower stresses, while SWNTs at lower temperatures exhibit a higher tensile strength and Young’s modulus. This observation is consistent with the findings of Xiao and Hou [38], who used molecular mechanics to study the mechanical properties of CNTs and concluded that the Young’s modulus of the CNTs depends on their chirality. As shown in

Table 5. Exponential law regression results for tensile strength at different temperatures based on data from Figure 8.

Temperature	Regression Formula of Tensile Strength (TPa)	R2
T = 300 K	$S=0.08642e^{0.0116\theta }$	0.91
T = 900 K	$S=0.07134e^{0.0084\theta }$	0.93
T = 1500 K	$S=0.04882e^{0.0115\theta }$	0.95
T = 2100 K	$S=0.03791e^{0.0129\theta }$	0.84

and Table 6, an exponential trend is observed for the tensile strength and Young’s modulus, where the coefficient of determination R² > 0.84 and R² > 0.98 for the tensile strength and Young’s modulus, respectively.

S = A e^Bθ      (TPa)

(7)

The findings indicate that at a temperature of 300 K, the regression constants for the tensile strength of single-walled carbon nanotubes (SWNTs) with a tube length of 5 nm and diameter of 0.75 nm are A = 0.8642 and B = 0.0116, the regression constants for the Young’s modulus are A = 1.104 and B = −0.0009, and for other temperatures, the quantities of A and B are listed in Table 5 and Table 6.

Table 6. Exponential law regression results for Young’s modulus at different temperatures based on data from Figure 9.

Temperature	Regression Formula of Young’s Modulus (TPa)	R2
T = 300 K	$Y=1.104e^{-0.0009\theta }$	0.94
T = 900 K	$Y=1.0838e^{-0.0050\theta }$	0.96
T = 1500 K	$Y=1.0838e^{-0.0004\theta }$	0.96
T = 2100 K	$Y=1.0424e^{-0.0002\theta }$	0.97

Table 6. Exponential law regression results for Young’s modulus at different temperatures based on data from Figure 9.

Temperature	Regression Formula of Young’s Modulus (TPa)	R2
T = 300 K	$Y=1.104e^{-0.0009\theta }$	0.94
T = 900 K	$Y=1.0838e^{-0.0050\theta }$	0.96
T = 1500 K	$Y=1.0838e^{-0.0004\theta }$	0.96
T = 2100 K	$Y=1.0424e^{-0.0002\theta }$	0.97

The observed trends that the Young’s modulus and tensile strength of SWNTs decrease with increasing tube diameter, while the tensile strength increases and the Young’s modulus decreases with increasing chiral angle, have significant implications for the design and selection of SWNTs for various applications. For structural reinforcement in the aerospace and automotive industries, SWNTs with smaller diameters and higher chiral angles are preferable due to their higher strength. Conversely, for applications requiring higher elasticity, such as flexible electronics and artificial muscles, SWNTs with larger diameters and smaller chiral angles are preferred due to their greater flexibility. Furthermore, in energy storage devices such as supercapacitors, selecting SWNTs with the optimal diameters and chiral angles can improve durability and efficiency, balancing tensile strength and Young’s modulus. These findings can help in materials optimization and predictive modeling, guiding the synthesis and fabrication of SWNTs with desired properties, thereby improving the performance and reliability of advanced technologies [39,40,41].

3.1.3. Strain Rate and Temperature Dependence of Mechanical Behavior

As shown in Figure 10, the tensile strength of the zigzag SWNTs with the chirality of (10,0) strongly depends on the strain rate and temperature. The tensile strength shows an increasing trend with increasing strain rates, while the SWNTs at lower temperatures exhibit significantly higher tensile strength at similar strain rates. As shown in

Table 7. Exponential law regression results for tensile strength at different temperatures based on data from Figure 10.

Temperature	Regression Formula of Tensile Strength (TPa)	R2
T = 300 K	$S=0.04399e^{753.13\epsilon }$	0.99
T = 900 K	$S=0.04399e^{753.13\epsilon }$	0.97
T = 1500 K	$S=0.03088e^{500.4\epsilon }$	0.98
T = 2100 K	$S=0.02465e^{535.9\epsilon }$	0.94

, an exponential trend is observed for the tensile strength changing with the strain rate where the coefficient of determination R² > 0.94.

$$S=A{e}^{B\epsilon }\left(\mathrm{TPa}\right)$$

(8)

The results show that at a temperature of 300 K, the regression constants for the tensile strength of the zigzag SWNTs with a tube length of 5 nm and a diameter of 0.75 nm are A = 0.4399 and B = 753.13, and for other temperatures, the quantities of A and B are listed in Table 7.

At higher strain rates, the tensile strength of SWNTs increases because the carbon atoms within the nanotube do not have enough time to relax before tension is applied. This lack of relaxation can lead to computational instabilities, causing the nanotube to fail near the location of tension. Essentially, at high strain rates, the structure of nanotube is unable to cope effectively with rapid deformation, resulting in increased tensile strength because the nanotube cannot withstand significant plastic deformation before failure. Additionally, at lower temperatures, reduced thermal vibrations may help strengthen interatomic bonding, thereby improving the mechanical properties [42,43].

3.2. Compressive Behavior

Figure 11 shows the buckling behavior of zigzag SWNTs (10,0) with a diameter of approximately 0.75 nm and a length of 5 nm. Figure 11A is the initial configuration of the SWNT before displacement, and B and C are post-buckling configurations.

Figure 12 shows the compressive stress–strain behavior and failure modes of the zigzag SWNTs with (10,0) chirality, a diameter of approximately 0.75 nm, strain rate of 0.001/ps, and a nanotube length of 5 nm at different temperature (300, 900, 1500, and 2100 K). The compressive stress–strain behavior is similar to the tensile stress–strain behavior. All simulated SWNTs exhibit nonlinear elastic behavior, with cooler SWNTs having higher slopes and failing at higher stresses and strains. In other words, the SWNTs compressed at higher temperatures fail at lower stresses and strains. But the compressive behavior results indicate that the SWNTs tend to buckle under lower stresses and strains compared to the tensile tests.

Table 8. Comparison of tensile and compressive behavior of zigzag SWNTs with a nanotube length of 5 nm and a diameter of 0.75 nm at different temperatures.

Type of Mechanical Test	T = 300 K	T = 900 K	T = 1500 K	T = 2100 K
Tensile Strength (MPa)	91,950	73,130	50,218	41,125
Initial Buckling Stress (MPa)	75,935	58,557	34,023	26,810
Ultimate Tensile Strain	1.26 × 10−1	1.11 × 10−1	9.22 × 10−2	8.40 × 10−2
Initial Buckling Strain	6.96 × 10−2	5.76 × 10−2	4.20 × 10−2	4.08 × 10−2

compares the stress and strain of zigzag (10,0) SWNTs under tensile and compression tests at different temperatures. It can be seen that at the same temperature, the tensile strength of 91,950 MPa is higher than the initial buckling stress of 75,935 MPa. In addition, at the same temperature, the ultimate tensile strain is 12.6%, which is higher than the initial buckling strain of 6.96%.

The buckling behavior of CNTs under compression affects a variety of practical applications in the fields of nano- and micro-electromechanical systems (NEMS/MEMS), composite materials, energy storage devices, biomedical implants, and structural reinforcement. Similar to their tensile strength behavior, which has applications in a variety of practical scenarios, studying buckling behavior is crucial. In NEMS and MEMS, understanding and controlling CNT buckling is crucial for designing reliable actuators and sensors. In composites, CNTs provide stiffness and strength enhancement, while buckling affects overall mechanical properties in aerospace and automotive applications. Energy storage devices benefit from the stable CNT structures under compression, thereby improving the efficiency of supercapacitors and batteries. Biomedical implants utilize the strength and biocompatibility of CNTs and require controlled buckling for safe applications. In civil engineering, CNTs reinforce structures, where buckling management ensures the durability of the structure under compressive loads. These examples illustrate how CNT buckling behavior can be managed to optimize performance and reliability in a variety of technical and industrial applications [39,44].

The results obtained in this study were compared with previous research findings. As shown in

Table 9. Comparison of mechanical properties from experiments and computations [43,46,47,48,49,50,51,52,53,54].

Tensile Strength (TPa) Zigzag-Armchair at T = 300	Adil et al.	Kok et al.	Li et al.	This Study
	0.116–0.135	0.121–0.14	0.106–0.114	0.129–0.14
Young’s Modulus (TPa) Zigzag-Armchair at T = 300	Avila et al.	Xiao et al.	Zhong et al.	This Study
	0.978–1.057	1.017–1.13	0.989–1.058	1.13–1.15
Ultimate Tensile Strain at T = 300	Yakobson et al.	Wernik et al.	Shokrieh et al.	This Study
	0.118	0.132	0.112	0.126

, the tensile strength values of zigzag and armchair SWNTs at T = 300 K in this study are 0.129 TPa and 0.14 TPa, respectively. It turns out that these findings are consistent with those reported by Adil et al. [45], Kok et al. [43], and Li et al. [46], who reported the tensile strength values for zigzag and armchair SWNTs at T = 300 K as 0.116–0.135 TPa, 0.121–0.14 TPa, and 0.1–0.12 TPa, respectively. The Young’s modulus values for zigzag and armchair SWNTs at T = 300 K in this study are 0.75 TPa and 0.83 TPa, respectively. The results show that these findings consistent with those reported by Avila et al. [47], Xiao et al. [48], and Hu et al. [49], who reported the Young’s modulus values for zigzag and armchair SWNTs at T = 300 K are 0.978–1.057 TPa, 1.017–1.13 TPa, and 0.989–1.058 TPa, respectively. The ultimate tensile strains from this study were also compared with previous study findings. In this study, the ultimate strain obtained at T = 300 K is 0.126, while Yakobson et al. [50], Werink et al. [51], and Shokrieh et al. [52] reported ultimate tensile strain values are 0.118, 0.132, and 0.112, respectively. The computed failure stress of 0.153 TPa and the resulting plastic deformation shape were consistent with the range of experimentally estimated values for nanotubes [53]. Yazdani et al. [54] reported that the onset of buckling was proportional to the slenderness of the tubes, with shorter tubes buckling at relatively larger strains. In addition, during compression testing, the elastic modulus at a given temperature was not found to be considerably affected by the slenderness ratio or chirality.

The results of this study, obtained via appropriate methods, provide valuable insights into the potential engineering of composite materials with precisely tailored mechanical properties. Understanding how CNTs behave under different loading conditions, such as their enhanced tensile strength and controlled buckling under compression, provides a foundation for designing advanced composites. By strategically incorporating CNTs into polymer or metal matrices, engineers can exploit these unique properties to improve stiffness, strength, and resilience. For instance, integrating CNTs into aerospace applications could produce lighter yet stronger materials capable of withstanding high mechanical stresses. Similarly, in biomedical engineering, composites can be engineered to mimic the mechanical properties of natural tissues, thereby improving the compatibility and durability of implantable devices. Moreover, these insights make it possible to develop composites tailored to specific industrial needs, from automotive components to renewable energy systems, thereby advancing the frontiers of material science and engineering.

4. Conclusions and Future Work

In the present work, an MD computational approach was designed to explore the effects of factors such as chirality, diameter, temperature, and strain rate on the mechanical behavior of SWNTs in tension and compression. The results from extensive numerical experiments show that all SWNTs exhibit nonlinear elastic behavior under tensile and compressive loading, and the SWNTs stretched at higher temperatures fail at lower stresses and strains.

The results also show that as the chiral angle increases from 0 to 30°, the tensile strength increases, and the Young’s modulus decreases. Furthermore, it was observed that larger diameter SWNTs exhibit lower tensile strength and a decrease in their Young’s modulus.

It was observed that the tensile strength of SWNTs strongly depends on the strain rate, and the tensile strength shows an increasing trend with increasing strain rate. Notably, SWNTs exhibit higher mechanical properties at lower temperatures compared to those at higher temperatures.

The compressive behavior of SWNTs shows similar trends to their tensile behavior, with the difference that SWNTs tend to buckle at lower stresses and strains under compression compared to tensile stress.

This study can provide valuable insights into the development of new composite materials, which is of great significance to contemporary mechanical sciences, particularly in the fields of structural mechanics and advanced manufacturing technology.

This work focused on pristine CNTs. However, in practical applications, various defects often occur in CNTs. One of the future research topics can be to study the effects of various defects on the mechanical properties of CNTs.