Compressive Behavior of Carbon Nanotube Reinforced Polypropylene Composites Under High Strain Rate: Insights From Molecular Dynamics

Since the discovery of carbon nanotubes (CNTs), these have received a lot of attention because of their unusual mechanical electrical properties. Strain rate is one of the key factors that play a vital role in enhancing the mechanical properties of nanocomposites. In this study, (4, 4) armchair single-walled carbon nanotube (SWCNT) was employed with the polymer matrix as polypropylene (PP). The inuence of compressive strain rate on SWCNT/PP nanocomposites was evaluated using MD simulations, and mechanical properties have been predicted. Stone-Wales (SW) and vacancy defects, were integrated on the SWCNT. The maximum Young’s modulus (E) of 81.501 GPa was found for the pristine SWCNT/PP composite for a strain rate of 10 10 s -1 . The least value of E was 45.073GPa for 6% SW defective/PP composite for a strain rate of 10 8 s -1 . While the 6% vacancy defective CNT/PP composite showed the lowest value of E as 39.57GPa for strain rate 10 8 s -1 . It was found that the mechanical properties of SWCNT/PP nanocomposites decrease with the increase in percent defect. It was also seen that the mechanical properties were enhanced with the increment in the applied strain rate. The results obtained from this study could be useful for the researchers designing PP-based materials for compression loading to be used for biomedical applications. transistor (FET) materials, nanoscale wire materials, electron emission sources, chemical sensors, optical communication switches, high strength composites, and thermal devices. CNTs acquire high tensile modulus and strength. Strong composites can be designed and fabricated by using the CNTs as reinforcing ller and thus can be used to develop and produce strong composites. The mechanical strength of the composites can decrease due to defective CNTs. Some of the defects are Stone-Wales (SW) and vacancy defects. The outcome of the mechanical properties is important to analyze when any of the parameters are mean to vary. On varying the input values of parameters, the mechanical properties of SWCNT-PP nanocomposites can be affected considerably. This study will be focused on analyzing this impact. Many researchers have been interested in the inuence of strain rates on the mechanical behavior of several nanocomposites in recent years. It was found that strain rate has enhanced the mechanical properties. Thus strain rate is one of the key factors that play a vital role to enhance the mechanical property of nanocomposites. In past studies, the


Introduction
Carbon nanotubes commonly known as CNT, have outstanding properties and an extensive collection of applications. That is why these have gathered considerable attention recently. Researchers across the world have worked tirelessly over the last decade to produce CNT ber, which has emerged as a distinct novel part of the carbon ber family unit. The study of CNT both experimentally and theoretically has increased extensively because of its exceptional mixture of electrical, mechanical, thermal, chemical properties [1]. Synergistic improvement in composite characteristics at small volume fractions is due to the inclusion of CNT in polymer matrices. Many studies and researches have been done regarding the mechanical properties of the interface between CNT and matrix. Because of the outstanding properties of CNTs, these are planned to be used as eld-effect transistor (FET) materials, nanoscale wire materials, electron emission sources, chemical sensors, optical communication switches, high strength composites, and thermal devices. CNTs acquire high tensile modulus and strength. Strong composites can be designed and fabricated by using the CNTs as reinforcing ller and thus can be used to develop and produce strong composites. The mechanical strength of the composites can decrease due to defective CNTs. Some of the defects are Stone-Wales (SW) and vacancy defects. The outcome of the mechanical properties is important to analyze when any of the parameters are mean to vary. On varying the input values of parameters, the mechanical properties of SWCNT-PP nanocomposites can be affected considerably. This study will be focused on analyzing this impact. Many researchers have been interested in the in uence of strain rates on the mechanical behavior of several nanocomposites in recent years. It was found that strain rate has enhanced the mechanical properties. Thus strain rate is one of the key factors that play a vital role to enhance the mechanical property of nanocomposites. In past studies, the SWCNT/PP nanocomposites have not been investigated by varying the strain rate. In this study, the in uence of compressive strain rate on SWCNT/PP nanocomposites has been examined.
Parvaneh and Shariati [2] examined the in uence of SW defects and vacancy defects on Young's modulus of SWCNT. A structural mechanics model was constructed to investigate Young's modulus. The tension test was reported as the best method for measuring Young's modulus of CNT. It was concluded that when CNTs are su ciently large, imperfections have a negligible effect. Jacob et al. [3] reviewed the impact of strain rate on the mechanical properties. It was observed that many researchers have looked into the effect of variable loading rate on the tensile, compressive, shear, and exural properties of berreinforced nanocomposites, with a range of con icting explanations and conclusions. Saxena and Lal [4] investigated the effects on the mechanical properties of SWCNT produced by SW defects and vacancy defects. The vacancy and SW defects ranged from 1 to 4 and their relative positions and orientations were varied. The investigation reported that vacancy defects have reduced the tensile strength and strain more than the SW defects. Yang et al. [5] studied the effect of SW defect on the characteristics of SWCNT/PP composites using the molecular dynamics (MD) simulation technique. A (15,0) zigzag CNT with several defects i.e. 0, 5, 10, 15 were studied. The strain rate was put as 0.0001/ps. The outer strain was ampli ed up to 2% in all defects cases. It was seen that Young's modulus of SWCNTs decreased when the number of SW defects rises. As the number of SW defects increases, the interfacial bonding becomes stronger, improving the transverse Young's modulus and two shear moduli. Sharma et al. [6] investigated the consequence of SW and vacancy defects on Young's modulus of CNTs and their nanocomposites. The impact of varying the diameter of faulty SWCNTs on their Young's modulus was also investigated using MD modeling. The study showed that as the diameter and the number of defects in armchair SWCNT were increased, the elastic moduli were gradually degraded. The moduli of SWCNTs having SW defects declined at a faster rate than the moduli of CNTs with vacancy defects as the number of defects was increased. It was deduced that the presence of SW or vacancy defects in an SWCNT system degrades the mechanical characteristics of the structure. It was also found that in contrast to SWCNTs with SW defects, the percentage rise in different moduli with increasing volume fraction (V f ) was larger for SWCNTs having vacancy aws. Li et al. [7] examined the results of temperature, strain rate, and molecule length on the deformation of graphene/polyethylene composites. It was seen that the host molecules migrated more easily at higher temperatures to suit the strain during deformation. It was observed that the nanocomposite model's atoms were more stress-free to meet the strain when the strain rate was lower. Zhang et al. [8] investigated the impact of strain rate and temperature on the interfacial property of glass ber reinforced PP nanocomposites by MD simulation. Since at higher strain rates atoms do not have enough time, interfacial strength was improved as the strain rate was increased. It was found that with the increase of strain rate the yield stress and elastic modulus were increased. The study suggested that the atoms were less stress-free at greater strain rates, requiring more fracture energies for the ultimate fracture, resulting in higher interfacial strength at the glass ber-PP interface. Khan et al. [9] used functionalized MWCNTs and hydroxyapatite nano-rods reinforced with PP for bio-medical applications.
Schossig et al. [10] observed the consequence of strain rate on mechanical properties of reinforced polyole ns. High-speed tensile tests were performed on glass-ber reinforced thermoplastic materials. PP and polybutene-1 having the weight percentage (%wt) 0, 20, 30, and 40 of glass ber were used. The results of the tests revealed that the glass ber reinforced polypropylene (GFRPP) and polybutene-1 (PB-1) exhibit a positive strain rate dependent relative nature as well. In contrast to low strain rates, high strain rates resulted in a stronger increase in tensile strength. It was reported that PP materials have superior strength levels than PB-1 materials. Fitoussi et al. [11] examined the in uence of the strain rate on the mechanical properties of a discontinuous glass ber reinforced ethylene-propylene copolymer matrix nanocomposite. A 50 percent increase in Young's modulus with the increase in strain rate was observed. A substantial rise in the damaging stress and strain thresholds was observed.
Notta-Cuvier et al. [12] studied the in uence of strain rate and heterogeneous ber orientation on the mechanical behavior of short-glass ber reinforced PP. The composite's tensile macroscopic behavior was investigated in a quasi-static and dynamic range from 1 mm/min to 1 m/s at various angles of loading concerning the injection ow direction and variable displacement rates. It was observed that tensile strength and stiffness increased with the increment in strain rate. Cui et al. [13] studied the impact of strain rates on mechanical characteristics and failure behavior of long glass ber reinforced (LGFR) thermoplastic composites. At high strain rates, the increase in ultimate strength and breakage strain of LGFR-PPs was due to improvements in interfacial bonding characteristics and energy amalgamation capacity. Kim et al. [14] investigated the strain rate-dependent mechanical behavior of glass ber reinforced polypropylene nanocomposites. Zhang et al. [15] investigated the impact of strain rate and temperature on the interfacial property of glass ber reinforced PP nanocomposites by MD simulation. It was reported that the interfacial strength of the glass ber-PP interface reduced when PP molecules shifted more easily to adjust tensile strain.
From the literature, it could be seen that inadequate work has been done to analyze the effect of compressive strain rate on mechanical properties of SWCNT reinforced PP nanocomposites. MD simulation can provide useful atomistic insights into the compressive behavior of SWCNT/PP composites. The effect of SW and vacancy defective CNTs on the mechanical properties of PP composites have also been predicted using MD simulation. The results obtained from this study could be useful for the researchers designing PP based materials for compression loading to be used for biomedical applications.

Methodology
The following steps explain the procedure used in this work to model and simulate the CNT-PP composites. All the simulations were performed using Biovia Materials Studio 2017. By using the "Build nanostructure" module a (4,4) armchair SWCNT was constructed. Simulations were performed on pristine as well as defective SWCNTs. SW and vacancy defects were integrated into the SWCNTs as shown in Fig. 1 and Fig. 2, respectively. 2%, 4%, and 6% defects were formed for both types of defects. A PP chain was created by using the "Build Polymer" module as shown in Fig. 3. The PP chain was cleaned to optimize the bond angles of the chain. A cell was built using the "Build Crystal" option. An isosurface was formed around the SWCNT as shown in Fig. 4. The "Amorphous" module was used to pack the PP chain inside the cell. 18 units of PP were loaded randomly around the SWCNT as shown in Fig. 5. The targeted density was kept at 0.80 g/cm 3 . For this process COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) force eld was selected.
After packing, the geometry optimization was performed. This phase is very important since con gurations are in a greater level of energy at the start and it must be reduced. There are several methods available for geometry optimization. In this study, the "smart" algorithm was used as an optimization technique. 'Smart' algorithm uses other optimization techniques such as conjugate gradient, steepest descent, and Newton-Raphson technique. After the geometry optimization, the energy of the structure gets minimized. It is called a converged structure. Now once the energy is minimized, dynamics run can be performed on the structure. In the dynamics run, simulation is performed on the atoms in a structure that move under the impact of calculated forces regulated by an 'ensemble' mathematical device. The canonical ensemble with a constant number of atoms, volume, and temperature (NVT) and isothermal-isobaric ensemble (NPT) were used in this investigation. Nose-Hoover's extended Hamilton method was used to perform NVT with a time step of 1 fs for 50 ps. The details of the NVT ensemble simulation have been given in Table 1. NPT ensemble was employed for anisotropic management of the pressure tensor that promotes pro cient convergence and command of the unit cell dimension and density. In this process, Nose-Hoover's barostat was used for NPT at 200K and 1 atm for 500ps. Nose-Hoover's barostat was used because it controls the pressure of the unit cell using the NPT ensemble. The detail of the NPT ensemble simulation has been given in Table 2.  After the completion of the dynamics run, a strain rate was applied to the system to study its effect on the mechanical behavior of SWCNT/PP nanocomposites. The stress-strain relationship was obtained by varying the strain rate. Once the strain rate simulation was completed, mechanical properties were predicted from the stress-strain curves. The parameters of strain rate have been mentioned in Table 3.

Stress-strain behavior for 4% SW defect
The stress-strain curve of (4,4) 4% SW defective SWCNT/PP nanocomposites has been depicted in

Stress-strain behavior for 6% SW defect
In Fig. 9, the stress-strain curve of (4,4) 6% SW defective SWCNT/PP nanocomposites for various strain rates has been plotted. The linear variation for the strain rate of 10 8 s − 1 , 10 9 s − 1 , and 10 10 s − 1 was indicated up to the stress of 0.901457 GPa, 0.943118GPa, and 1.328926 GPa respectively. These stresses were found at a strain of 0.02. The stress for a strain rate of 10 9 s − 1 had a 4.6% difference with respect to the strain rate of 10 8 s − 1 . While for strain rate of 10 10 s − 1 the value of the stress varied with 47.4% with respect to strain rate 10 8 s − 1 . Yielding was observed at strain 0.02. Following the yielding, the curve began to rise once more. At 0.068 strain, the ultimate stress was achieved for strain rates 10 8 s − 1 and 10 9 s − 1 . While for strain rate 10 10 s − 1 , ultimate stress was found at 0.078.

Variation of Young's modulus for various strain rates with SW defects
The variation of Young's modulus for (4,4) SW defective SWCNT/PP nanocomposites with a variety of strain rates has been shown in Fig. 10. It could be observed that with the varying strain rate Young's modulus also gets affected as shown in Table 4. As the strain rate increases, Young's modulus of the SWCNT-PP nanocomposites also improved. In this investigation, it was also found that with the increment of the percent SW defects, Young's modulus decreases continuously. This decrement occurred due to the conversion of the C-C polygon chain. In SW defective CNTs, 4 hexagonal C-C chains were converted into two pentagons and two heptagon C-C chains. The maximum Young's modulus was found for the strain rate of 10 10 s − 1 .

Yield strength for various strain rates with SW defects
The yield strength for different strain rates of (4,4) SW defective SWCNT/PP nanocomposites has been plotted in Fig. 11. Table 5 shows the comparison of yield strength with strain rate. It was observed that with the increase in strain rate, the yield strength of the SWCNT/PP nanocomposites enhanced. It was also seen throughout this study that when the percent SW defects increase, yield strength falls. In the SW defect, the C-C polygon chain was converted, which resulted in this decrease. While the formation of the SW defect in SWCNT, four hexagons C-C chains transformed into the two pentagons and two heptagon C-C chains. In the plot, it could be seen that the strain rate of 10 10 s -1 had the maximum yield strength.

Compressive strength for various strain rates with SW defects
The variation of the compressive strength has been shown in Fig. 12 for (4,4) SW defective SWCNT/PP nanocomposites with a variety of strain rates. In this study, it was noted that compressive strength was also impacted by different strain rates. The compressive strength of the SWCNT-PP nanocomposites was enhanced as on increasing the strain rate. The comparison of compressive strength with strain rate has been listed in Table 6. It was found that the value of compressive strength decreases continuously with the increase in the percent SW defects. The conversion of the C-C polygon chain caused this decrease. Due to the SW defects in SWCNT, four hexagon C-C chains were transformed into two pentagons and two heptagon C-C chains. It was observed that the maximum compressive strength was achieved for the strain rate of 10 10 s − 1 . The stress-strain curve for various strain rates of (4,4) 2% vacancy defective SWCNT/PP nanocomposites has been shown in Fig. 13. For the strain rate of 10 8 s − 1 , stress was 1.357994 GPa at a strain of 0.022.
The curve began to rise once more following the yielding. For the strain rate of 10 8 s − 1 , the ultimate stress was achieved at 0.052 strain. It was noted that for the strain rate of 10 9 s − 1 , the yielding occurred at strain 0.22 with the stress of 1.421964GPa. While the value of stress for a strain rate of 10 10 s − 1 was 1.648634GPa at strain 0.022 where the yielding took place. The percentage difference in stress for a strain rate of 10 9 s − 1 and 10 10 s − 1 was 4.71% and 21.4% respectively. It was seen that the ultimate stress was obtained at a strain of 0.056 and 0.078 for strain rates 10 9 s − 1 , and 10 10 s − 1 respectively.

Stress-strain curve for 4% vacancy defects
The stress-strain curve of (4,4) 4% vacancy defective SWCNT/PP nanocomposites has been depicted in The variation of the stress for a strain rate of 10 9 s − 1 was 2.27% for the strain rate of 10 8 s − 1 . At 0.058 strain, the maximum stress was achieved. The linear uctuation for a strain rate of 10 10 s − 1 was noted in the stress-strain curve up to the stress of 1.102689 GPa. Following the yielding at strain 0.02, the curve began to rise once more. It was found that stress varied by 12.89% for strain rate 10 10 s − 1 for a strain rate of 10 8 s − 1 .

Stress-strain curve for 6% vacancy defects
In Fig. 15, the stress-strain curve of (4,4) 6% vacancy defective SWCNT/PP nanocomposites for various strain rates has been plotted. The linear variation for the strain rate of 10 8 s − 1 , 10 9 s − 1 , and 10 10 s − 1 was indicated up to the stress of 0.791399 GPa, 0.831399GPa, and 0.984967GPa respectively. These stresses were found at a strain of 0.02. The stress for a strain rate of 10 9 s − 1 had a 5.05% difference for a strain rate of 10 8 s − 1 . While for strain rate of 10 10 s − 1 the value of stress varied by 24.45% for a strain rate of 10 8 s − 1 . Yielding was observed at strain 0.02. After the yielding, the curve started to increase again. At 0.076 strain, the ultimate stress was achieved for strain rates of 10 8 s − 1 . For a strain rate of 10 9 s − 1 ultimate stress was achieved at strain 0.078. While for strain rate of 10 10 s − 1 , ultimate stress was found at 0.088. After the ultimate stress, the curve again started declining on applying further stress. On further compression after the ultimate stress, the curve started to decrease.

Young's modulus for various strain rates with vacancy defects
The variation of Young's modulus for a (4,4) vacancy defective SWCNT/PP nanocomposites with a variety of strain rates has been shown in Fig. 16. It could be seen that as the strain rate varies, Young's modulus also gets affected as shown in Table 7. As the strain rate increases, Young's modulus of the SWCNT-PP nanocomposites was also enhanced. In this investigation, it was also found that with the increment of the percent vacancy defects, Young's modulus decreases continuously. This decrement occurred due to the reduction in the carbon atom of SWCNT. The maximum Young's modulus was found for a strain rate of 10 10 s − 1 .

Yield strength for various strain rates with vacancy defects
The yield strength for (4,4) vacancy defective SWCNT/PP nanocomposites with different strain rates has been plotted in Fig. 17. It could be seen that the yield strength varied on changing the strain rate. Table 8 shows the comparison of yield strength with strain rate. It was observed that with the increase in strain rate, the yield strength of the SWCNT/PP nanocomposites enhanced. It was also seen all over this study that when the percent vacancy defects increase, the value of yield strength falls. The carbon atom of SWCNT was reduced, which resulted in this decrease. During the formation of vacancy defect, the carbon atom gets deleted from SWCNT. The strain rate of 10 10 s − 1 showed maximum yield strength. The variation of the compressive strength has been shown in Fig. 18 for (4,4) vacancy defective SWCNT/PP nanocomposites with a variety of strain rates. Compressive strength was also impacted by different strain rates. The comparison of compressive strength with various strain rates has been listed in Table 9. The compressive strength of the SWCNT-PP nanocomposites was enhanced with an increase in the strain rate. It was found that the value of compressive strength decreases continuously with the increase in the percent vacancy defects. This reduction occurred because the carbon atom of SWCNT was decreased. The carbon atom in SWCNT is removed during the development of a vacancy defect.
With a strain rate of 10 10 s − 1 , the maximum compressive strength was recorded.

Comparative study
The results of this study have been compared with a previous study by Huang and Rodrigue [1] where the effect of strain rate on pristine SWCNT/PP nanocomposites has been studied. In [1], the opted strain rates were 0.05, 0.5, and 5 min − 1 . The compressive stress values have been compared in Table 10. It could be observed that due to the very high strain rate the difference in the values of compressive stress was also high. From this comparison, it could be inferred that the value of stress gets enhanced with a higher order of strain rate.

Conclusions
SWCNTs have improved the properties of polymers and nanocomposites materials. Nanocomposite made of SWCNTs can offer a novel material that is highly robust and incredibly light in weight. It is very Figure 1 Stone-Wales defect formation.

Figure 5
Polypropylene packed in the cell with SWCNT having 2008 atoms.