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Improved mechanical and tribological properties of polytetrafluoroethylene reinforced by carbon nanotubes: A molecular dynamics study
Computational Materials Science 168 (2019) 131–136
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Improved mechanical and tribological properties of polytetrafluoroethylene reinforced by carbon nanotubes: A molecular dynamics study Jingfu Songa, Hao Leib, Gai Zhaob,c,
T
⁎
a
College of Material and Science Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China c State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Science, Lanzhou 730000, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Polymer Friction and wear Molecular dynamics simulation
Mechanical and tribological properties of polytetrafluoroethylene (PTFE) reinforced with carbon nanotubes (CNTs) are studied by a molecular dynamics (MD) simulation to explore inherent interactions and wear mechanisms of polymer nanocomposites from an atomic scale. The friction models of polymer sliding against metal are developed to examine the friction coefficient and wear rate. The mechanical properties of pure PTFE are also analyzed to explain the inherent mechanisms of friction reduction and wear resistance improvement. The MD simulated results show that the Young’s modulus and shear stress of PTFE increase by 136.58% and 236.3% after carbon nanotubes reinforcement, respectively. The average friction coefficient of PTFE in the steady stage sliding against Cu layer under normal conditions decreases from 0.169 to 0.127 after CNTs reinforcement. The interaction potential energy between CNT and PTFE was calculated to interpret the improvement effect of CNT. The inherent mechanisms of the enhanced mechanical and tribological properties of PTFE are emphatically discussed and interpreted from an atomic view by analyzing the variations of the radius distribution function, relative concentrations and temperature in the thickness direction.
1. Introduction Polymer and polymer composites were widely applied in our daily life and industrial productions due to their excellent mechanical, thermal, electrical and chemical properties. In order to broaden their applications, more efforts had been dedicated to improve their mechanical and tribological properties of polymer in the past decades, especially for structural or frictional materials. For instance, ultrasonic motors (USM) driven by frictional force between its stator and rotor had been applied in the lunar detector with light weight, high precision, non-magnetic and power-off self-locking, which required polymer based materials with high strength, stable friction coefficient and superlow wear rate sliding against copper. The PTFE and PI based polymer composites had been successfully prepared and applied in the USM for different requirements [1–5]. The wear mechanisms were discovered by observing the worn surface evolution. Usually, the adhesive wear, fatigue wear or abrasive wear dominated the wear process under high frequency vibration. Sometimes, multiple effects simultaneously existed on the tribo-interface of the USM under harsh conditions. Actually, the inherent mechanisms between polymer composites and metals were quite complicated. It was rather necessary to reveal the fundamental
⁎
reasons of wear of polymer nanocomposites from an atomic level. With a rapid development of polymer nano-composites, nanomodification had become one of the most promising technology and effective methods to improve the mechanical and tribological properties of polymer. The carbon nanotubes, as an ideal one-dimensional fiber, can greatly increase the mechanical properties of the polymer owing to their excellent mechanical, thermal and high surface area. A number of works have been conducted to study the enhancements of the mechanical and tribological properties of CNT/polymer composites. Chen et al. [6] studied the tribological behavior of PTFE composites filled with CNT and found that 20 vol% CNT/PTFE exhibited the lowest wear rate due to excellent strength of CNT. The similar results were also obtained by Xue’s research that CNT as a reinforcing agent can contribute to restrain the adhesion and scuffing of the PI matrix, thus decrease the friction coefficient and wear volume loss [7]. Besides, Zhu et al. [8] used carbon nanofibers to improve the elongation-to-break, tensile strength, bending strength and impact strength of PI. The tribological properties were also improved due to their better interfacial interaction between the carbon nanofibers and the matrix. Peng [9,10] studied the effect of active CNTs on the tribological behavior of PI nanocomposites and found incorporation of MWCNTs-COOH greatly
Corresponding author. E-mail address: [email protected] (G. Zhao).
https://doi.org/10.1016/j.commatsci.2019.05.058 Received 21 March 2019; Received in revised form 29 April 2019; Accepted 29 May 2019 Available online 10 June 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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J. Song, et al.
Fig. 1. Molecules models of the: (a) (5, 5) CNTs, (b) pure PTFE, (c) CNTs/PTFE composite.
reinforced PTFE nanocomposite were also compared under the same conditions. The emphasis was exploring atomic interactions between CNT and PTFE or copper. In addition, the variations of the radius distribution function, relative concentrations and temperature in the thickness direction between carbon nanotubes and PTFE were systematically monitored and discussed during the process of wear. It aimed to provide the inherent mechanisms of the improved mechanical and tribological properties of PTFE nanocomposite from an atomic view, and provide a theoretical method for designing high performance PTFE nanocomposites as a frictional material of USM.
enhanced thermal stability, mechanical properties and wear resistance under sea water because of strong interfacial adhesion between PI matrix and MWCNTs-COOH. Although a large number of experimental results indicated the outstanding reinforcement effect of the CNTs on the mechanical and tribological properties of the polymer, a very clear inherent mechanism about interaction between carbon atomic and polymer molecules are still not recognized, especially during the process of wear. The main reason can be ascribed to the small length and time scales, which limited researchers to explore the original mechanisms from an atomic level. Recently, MD simulations have been established as a high effective method to compute the properties of materials from an atomic level and provide microcosmic information and details of molecules interactions in addition to massive experimental and theoretical studies. In the past decades, many of researchers used MD simulations to study the mechanical properties of polymer nano-composites. Q.L. Xiong and S.A. Meguid et al. [11–13] investigated the interfacial mechanical characteristics of CNT reinforced epoxy composites and found that the interfacial interactions between CNT and epoxy depended on the length and diameter of CNT. Besides, such simulated results were reliable for predicting the interfacial mechanical properties of CNT-polymer nanocomposites. Chen and Hu [14] also studied the effect of diameter of CNT on the interfacial adhesion of graphene/epoxy nanocomposite. The MD simulation results indicated that larger CNT radius gave a larger contact area with graphene, leading to a stronger interfacial adhesion with polymer matrix. Frankland et al. [15] compared the effects of both long and continuous, short and discontinuous of singlewalled CNT on enhancing stress-strain behaviors of polymer matrix. The results indicated that long and continuous SWCNT can enhance the stress-strain behavior of the polymer obviously. Arash and Wang [16] investigated the tensile strength of CNT/PMMA composite by a MD study and found that the simulated results were identified with the prediction of the three-phase micro-mechanical continuum model. Jiang et al. [17] conducted the effect of volume fraction of the multiwalled CNTs on the elastic properties of polyimide composites. They found that the elastic modulus and tensile stresses increased with an increasing number of MWCNTs. However, the majority of such MD simulations focused on the calculation of mechanical enhancement of polymer by incorporation of CNTs. Only Li et al. [18–22] investigated the mechanical and tribological properties of NBR (Nitrile-Butadiene Rubber)/carbon nanotube composites by MD simulations. It was indicated that both friction coefficient and wear rate can be variously decreased by incorporation of CNTs as reinforcement of NBR. However, there are still very few studies on exploring the wear mechanisms of high performance polymer sliding against metal using MD simulations. There are no findings about mechanical and tribological investigation of PTFE by MD simulations to the authors’ knowledge. Hence, in this study, the PTFE with excellent behavior of self-lubrication was adopted as polymer matrix based on the actual application background of USM. Then, the mechanical and tribological properties of pure PTFE were investigated by MD simulations. In order to study the improved effect of CNT, the tribological properties of the CNT
2. Materials and methods In this work, molecules models of the pure PTFE and CNTs/PTFE composite were built using Materials Studio software (6.0), respectively. The Condensed-Phase Optimized Potentials for Atomistic Simulation Studies (COMPASS) force field was used [23]. The COMPASS force field, the first ab initio force-field, was commonly used to provide the atomic interactions. This force field had been proven to be applicable in describing the mechanical properties of CNTs/polymer [24]. Then, the Ewald method and the atom-based method were employed for analyzing the Coulomb interactions and the van der Waals (VDW) interactions between CNT and polymer, respectively. Fig. 1a showed the molecules model of the (5, 5) CNTs with length of 19.695 Å. In the modeling of pure PTFE as shown in Fig. 1b, 10 chains containing 50 repeat units of C2F4 were packed in the cell with Monte Carlo style with a predefined density of 2.1 g/cm3. For the model of the CNTs/ PTFE composite as shown in Fig. 1c, period boundary condition cells with the size of 3.0 × 3.0 × 3.0 nm3 with the CNTs in the middle and an empty cell was built with 6.625 vol% addition of CNTs. Hydrogen atoms were added to the edges of the CNTs to saturate the dangling bonds. The Amorphous Cell Packing task was used in the packing process. A geometry optimization using smart method with an energy convergence criterion of 10-5 kcal/mol and force convergence criteria of 10-4 kcal/mol/Å was used to get a global minimum energy configuration. To further equilibrate the model, a 5-cycle anneal process was followed under constant temperature and constant volume (NVT ensemble) from 300 K to 500 K. In the anneal process, the construct was further relaxed and obtained a stable state with a local energy minimum. The cell was followed by a 2 ns process with isothermalisobaric under the constant pressure and temperature (NPT ensemble) at a room temperature of 298 K and atmospheric pressure of 101 kPa with 1 ps timestep. During the simulation, Nose thermostat and Berendsen barostat algorithm are applied in the temperature and pressure control. Ewald summation method was applied to calculated the electrostatic interactions with an accuracy of 10-3 kcal/mol. Then, the mechanical properties can be directly obtained using a constant strain method after structure optimization to explain the improved mechanisms of tribology of the CNTs/PTFE composite. Importantly, for predicting the tribological properties of the pure PTFE and CNTs/PTFE composite, two three-layer models were constructed as shown in Fig. 2. The crystal of Cu atoms was selected as a 132
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Fig. 2. Configurations of the molecules models: (a) Pure PTFE, (b) CNTs/PTFE composite sliding against Cu layer. Cu atoms and CNTs are shown by the orange and red color, respectively.
method which was reliable for describing the polymer composites in many publications [22,25]. As described in Section 2, the mechanical properties of PTFE composite can be calculated by uniaxial tension processes in X direction. The stain-stress curves of the two materials were obtained and plotted in Fig. 3. It can be clearly seen from Fig. 3 that the stress of the pure PTFE and CNTs/PTFE composite in X direction firstly exhibited a linearly increase from 0 GPa to 0.08 and 0.16 GPa with an increase of the strain from 0 to 0.05. The slope of the fitting lines of the stress–strain curves was used to calculate the Young’s modulus. The detailed mechanical values were listed in Table 1. It was easily found that the Young’s modulus of PTFE increased from 2.05 GPa to 4.85 GPa after CNTs reinforcement. The function of CNTs as the reinforcements on the mechanical properties of polymer had been verified by an experimental work [26]. The shear modulus of both materials were also obtained. The shear stress of PTFE almost increased by 236.5% by incorporation of CNTs. The reasons for this increment can be ascribed to the strong non-bonding interactions between CNTs and PTFE molecules [11–13,21,27]. It was reported by previous
substrate and top layer according to the actual application of USM. The middle part of both tribo-layer was designed using pure PTFE matrix and CNTs/PTFE composite with the dimension of 3.0 × 3.0 × 3.0 nm3. The dimensions of top layer and substrate are 3.0 × 3.0 × 1.2 nm3. Firstly, a geometry optimization using configuration gradient method with energy convergence tolerance of 2 × 10−5 kcal/mol and a force convergence of 0.001 kcal/mol/Å was used to find the minimum global energy configuration for tribo-layer model. Then, a 5-cycle annealing process under NVT ensemble from 300 K to 500 K for 200 ps was performed to relax the structure in a wider temperature range to obtain an energy minimum of resultant trajectories. Further, the normal loading was applied to the top layer by moving it with a speed of 0.1 Å/ps for 600 ps under the loading of 101 kPa to complete the friction process. The temperature and time step for this wear process were set to be 298 K and 1 fs, respectively. The trajectory of atoms and forces generated in the sliding direction were recorded for calculating the friction coefficient and wear rate. The friction coefficient was calculated using the equation u = f / F (where u is defined as friction coefficient, f and F are the friction force which was automatically recorded during the wear process and normal load, respectively). The average friction coefficient in the stable stage was used to compare the friction reduction of PTFE reinforced by CNTs. The molecules which adhered onto the surface of copper and moved out from the polymer matrix were defined as the worn molecules. The wear rate can be calculated by the ratio of worn off molecules to the total molecules of the polymer matrix. In addition, the radius distribution function (RDF) spectra between Cu atoms and C atoms of the polymer matrix was calculated to explain the reasons about friction reduction. Further, the relative concentration and temperature variations in the thickness direction were investigated for better understanding the mechanisms of improved tribological properties.
0.18 0.16 0.14 Stress (GPa)
0.12 0.10 0.08 0.06 0.04
PTFE CNTs/PTFE
0.02
3. Results and discussion
0.00 0.00
3.1. Mechanical properties In this study, the mechanical properties of pure PTFE and CNTs/ PTFE composite were calculated using constant strain minimization
0.02
0.04 0.06 Strain
0.08
0.10
Fig. 3. The stress-strain curves of the PTFE and CNTs/PTFE composite. 133
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Table 1 Some parameters of PTFE and CNTs/PTFE composite. Proportion of fillers (Vol%)
Density (g/ cm3)
Young modulus (GPa)
Shear stress (GPa)
PTFE CNTs/PTFE
– 6.625
1.9 1.92
2.05 4.85
0.4782 1.6091
Interfacial potential energy (kcal/mol)
Samples
160 140 120 100 80 Fig. 5. Variations of friction coefficient of the PTFE and CNTs/PTFE composite with time.
60 40
both polymer composites with time. It can be easily observed that pure PTFE had a higher friction coefficient than CNTs/PTFE composite. Usually, the average friction coefficient in the stable stage was used to represent the tribological properties of the materials. In this study, the average friction coefficient of both polymer composites in the stable stage after 300 ps was calculated and compared. It was noted that the average friction coefficient of PTFE reduced from 0.169 to 0.127 by introduction of CNTs, decreased by 24.85%. The root reason still can be ascribed to the reinforcement effect of CNTs. Besides, the friction coefficient of pure PTFE at the running-in stage was rather unstable due to strong atomic interactions between Cu atoms and C atoms of pure PTFE. After CNTs reinforcements, more polymer molecules were adsorbed around the surface of CNTs under the effect of VDW forces [18]. So, the atomic interactions between Cu atoms and C atoms of CNTs/ PTFE become weak, which contributed to the stable friction process of CNTs/PTFE composite. To compare the atomic interactions between polymer and counterpart, the RDF values between Cu atoms and C atoms of polymer were extracted during the wear process. Fig. 6 showed the RDF values between Cu atoms and C atoms of polymer composite. It can be found from Fig. 6 that RDF value started to increase with some fluctuations when the contact distance in the z direction was over 2 Å. It indicated that more PTFE molecules acted with Cu atoms under the certain load during the process of wear because of VDW forces and other interactions. However, the average RDF
20 0
20
40
60 80 100 Simulation time (ps)
120
140
Fig. 4. Variations of interaction potential energy between CNTs and PTFE with simulation time.
publications [13,21] that an interfacial interaction space can be formed between CNTs and polymer matrix due to the VDW forces. Hence, the interaction potential energy between CNTs and PTFE matrix during the simulation processes was calculated by Eq. (1) and shown in Fig. 4 to reveal the improved mechanisms.
Einter = Etotal − EPTFE − ECNTs
(1)
Radius Distribution Function
where Etotal is the energy of the CNTs/PTFE nanocomposite, EPTFE is the energy of the PTFE, ECNTs is the energy of the CNTs. Fig. 4 showed the interaction potential energies between CNTs and PTFE matrix at different MD simulation times. It indicated that the interaction potential energy of the CNTs/PTFE cell in the initial (0 ps) and final (60 ps) state was 26.2 kcal/mol and 150.3 kcal/mol, respectively, increased by more than 5 times. This increase of interaction potential energy resulted in an adsorption effect between CNTs and PTFE matrix, suggesting that more PTFE chains were adsorbed around the surface of CNTs due to strong interactions. This strong adsorption interaction contributed to the improved mechanical properties of PTFE. Besides, it was also noted from Fig. 3 that the stress of both polymer composites at some points went down and then went back with an increase of strain. For example, the stress of pure PTFE decreased from 0.088 GPa to 0.064 GPa (27.3% decrease) at the strain of 0.75, while the stress of CNTs/PTFE varied from 0.15 to 0.137 GPa (8.67% decrease). The possible reason can be ascribed to the fracture of partial polymer molecules. Then, the stress fluctuated with a small growth when the strain continuously increased from 0.05 to 0.10. In a word, an improvement of mechanical properties can be found by incorporation of CNTs into PTFE matrix. 3.2. Tribological properties
0.8 0.6 0.4 0.2 0.0
To investigate the effect of CNTs on the tribological properties of the pure PTFE and CNTs/PTFE composite, two friction models of polymer sliding against Cu layer were built for simulating the actual working condition of USM in which polymer nanocomposites were sliding against Cu layer. Fig. 5 showed the variations of friction coefficient of
PTFE CNT/PTFE
1.0
0
5 10 Distance r (Angstrom)
15
Fig. 6. RDF values of the Cu atoms and C atoms of the PTFE and CNTs/PTFE composite during the process of wear. 134
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Fig. 8. Concentration profiles of the PTFE and CNTs/PTFE composite in the thickness direction.
composite. Only deformation can be found from Fig. 7b, 7d and 7f for the CNTs/PTFE composite under the shear stress, which further indicated the reinforcement effect of CNTs on the wear of PTFE. To further reveal the wear mechanisms of both polymer composites, the concentration profiles in the thickness (z direction) of the polymer matrix were calculated and presented in Fig. 8. It can be seen from the curves of relative concentration that pure PTFE had a higher atomic concentration than CNTs/PTFE composite, especially around the contact areas (position 12 Å and 42 Å in the thickness direction) between Cu atomic layer and the polymer composite. The peak concentration of pure PTFE on the top contact area in the 12 Å, as a friction interface, had a 11% difference larger than those of the CNTs/PTFE composite. On the bottom contact area, there still had a 14% concentration difference due to a strong atomic interaction between Cu atoms and PTFE molecules. However, the CNTs/PTFE composite had a maximum concentration difference (27.3%) in the middle part of the whole matrix (about the position of CNTs in the PTFE composite) than those of the pure PTFE. Therefore, it can be recognized that more atoms of pure PTFE tended to move to the friction areas and subject to the shear loading, while more PTFE molecules of the CNTs/PTFE composite were absorbed onto the surface of CNTs. This was a dominated reason why CNTs/PTFE composite showed the improved tribological properties. In addition, the temperature profiles of both polymer composites in the same direction were calculated and shown in Fig. 9. It can be found from the temperature profile of pure PTFE that a much higher temperature of 332.7 K was observed around the top contact areas (around 12 Å in the z direction). The temperature of CNTs/PTFE composite decreased by 11.9% after reinforced with CNTs. According to the above concentration profiles in the same thickness distance, it indicated that more polymer atoms around the friction interface between top Cu layer and polymer molecules contributed to the more energy dissipations. Based on an energy dissipation theory in atomic-scale friction proposed by Yuanzhong Hu [28], frictional work was eventually converted into heat, suggesting that friction was in fact a process of energy transformation. Only small part of the energy can be stored by the material themselves, which lead to a temperature rise for the whole system. Differently, the CNTs/PTFE composite produced little temperature rise than pure PTFE due to weak interactions with Cu atoms and low friction coefficient.
Fig. 7. The snapshots of friction process of the pure PTFE (a) (c) (e) and CNTs/ PTFE composite (b) (d) (f) sliding against Cu layer at 150 ps, 300 ps, 600 ps, respectively.
value of PTFE decreased after filling CNTs. Therefore, it can be concluded that the fewer molecules in the CNTs/PTFE composite moved towards the Cu atoms during the sliding process. Because more PTFE molecules were absorbed by CNTs due to the electrostatic and VDW interactions in the molecules system, which had also been indicated by other results [16]. Correspondingly, the fewer PTFE molecules were worn out from polymer matrix after CNTs reinforcement. In order to better understand the wear mechanisms of both PTFE composite, the snapshots in the different stage during the friction process was shown in Fig. 7. It can be easily recognized that pure PTFE molecules with weak mechanical properties suffered from large deformation (Fig. 7a), fracture (Fig. 7c) and breakage under the shear stress, and finally worn out from the PTFE matrix as shown in Fig. 7e, which can be recognized as the worn molecules. Under the same condition, the wear rate of pure PTFE with Cu reached up to 64.65%, while no worn molecules were observed from the final state of the CNTs/PI
4. Conclusion In this research, MD simulations are developed to investigate the mechanical and tribological properties of pure PTFE and CNTs/PTFE 135
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Fig. 9. Temperature profiles of the PTFE and CNTs/PTFE composite in the thickness direction.
nanocomposites to reveal the inherent mechanisms of polymer composite with metal and improved wear mechanisms from an atomic level. By incorporation of CNTs, the Young’s modulus and shear stress of PTFE increased by 136.58% and 236.3%, respectively. The average friction coefficient also decreased by 24.85% after CNTs reinforcement. Importantly, the wear resistance of PTFE was greatly improved by incorporation of CNTs. Meanwhile, the RDF values, relative concentration profiles, temperature profiles during the friction process all proved these enhanced effect of CNTs on the tribological properties of the PTFE. This MD simulation study provided an effective method to design high performance polymer nanocomposites in the application of USM. Acknowledgements This work is supported by Fundamental Research Funds for the Central Universities (NS2018010), the Major State Basic Research Development Program of China (973 Program, Grant No. 2015CB057501), and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. References [1] G. Zhao, Q. Ding, Q. Wang, Comparative study on the tribological properties of the polyimide composites reinforced with different fibers, Polym. Compos. 37 (2016) 2541–2548. [2] Q. Ding, Y. Zhang, G. Zhao, F. Wang, Properties of POB reinforced PTFE-based friction material for ultrasonic motors, J. Polym. Eng. 37 (2017) 681–687. [3] G. Zhao, C. Wu, L. Zhang, J. Song, Q. Ding, Friction and wear behavior of PI and PTFE composites for ultrasonic motors, Polym. Adv. Technol. 29 (2018) 1487–1496. [4] F. Song, Z. Yang, G. Zhao, Q. Wang, X. Zhang, T. Wang, Tribological performance of filled PTFE-based friction material for ultrasonic motor under different temperature
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Improved mechanical and tribological properties of polytetrafluoroethylene reinforced by carbon nanotubes: A molecular dynamics study Jingfu Songa, Hao Leib, Gai Zhaob,c,
T
⁎
a
College of Material and Science Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China c State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Science, Lanzhou 730000, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Polymer Friction and wear Molecular dynamics simulation
Mechanical and tribological properties of polytetrafluoroethylene (PTFE) reinforced with carbon nanotubes (CNTs) are studied by a molecular dynamics (MD) simulation to explore inherent interactions and wear mechanisms of polymer nanocomposites from an atomic scale. The friction models of polymer sliding against metal are developed to examine the friction coefficient and wear rate. The mechanical properties of pure PTFE are also analyzed to explain the inherent mechanisms of friction reduction and wear resistance improvement. The MD simulated results show that the Young’s modulus and shear stress of PTFE increase by 136.58% and 236.3% after carbon nanotubes reinforcement, respectively. The average friction coefficient of PTFE in the steady stage sliding against Cu layer under normal conditions decreases from 0.169 to 0.127 after CNTs reinforcement. The interaction potential energy between CNT and PTFE was calculated to interpret the improvement effect of CNT. The inherent mechanisms of the enhanced mechanical and tribological properties of PTFE are emphatically discussed and interpreted from an atomic view by analyzing the variations of the radius distribution function, relative concentrations and temperature in the thickness direction.
1. Introduction Polymer and polymer composites were widely applied in our daily life and industrial productions due to their excellent mechanical, thermal, electrical and chemical properties. In order to broaden their applications, more efforts had been dedicated to improve their mechanical and tribological properties of polymer in the past decades, especially for structural or frictional materials. For instance, ultrasonic motors (USM) driven by frictional force between its stator and rotor had been applied in the lunar detector with light weight, high precision, non-magnetic and power-off self-locking, which required polymer based materials with high strength, stable friction coefficient and superlow wear rate sliding against copper. The PTFE and PI based polymer composites had been successfully prepared and applied in the USM for different requirements [1–5]. The wear mechanisms were discovered by observing the worn surface evolution. Usually, the adhesive wear, fatigue wear or abrasive wear dominated the wear process under high frequency vibration. Sometimes, multiple effects simultaneously existed on the tribo-interface of the USM under harsh conditions. Actually, the inherent mechanisms between polymer composites and metals were quite complicated. It was rather necessary to reveal the fundamental
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reasons of wear of polymer nanocomposites from an atomic level. With a rapid development of polymer nano-composites, nanomodification had become one of the most promising technology and effective methods to improve the mechanical and tribological properties of polymer. The carbon nanotubes, as an ideal one-dimensional fiber, can greatly increase the mechanical properties of the polymer owing to their excellent mechanical, thermal and high surface area. A number of works have been conducted to study the enhancements of the mechanical and tribological properties of CNT/polymer composites. Chen et al. [6] studied the tribological behavior of PTFE composites filled with CNT and found that 20 vol% CNT/PTFE exhibited the lowest wear rate due to excellent strength of CNT. The similar results were also obtained by Xue’s research that CNT as a reinforcing agent can contribute to restrain the adhesion and scuffing of the PI matrix, thus decrease the friction coefficient and wear volume loss [7]. Besides, Zhu et al. [8] used carbon nanofibers to improve the elongation-to-break, tensile strength, bending strength and impact strength of PI. The tribological properties were also improved due to their better interfacial interaction between the carbon nanofibers and the matrix. Peng [9,10] studied the effect of active CNTs on the tribological behavior of PI nanocomposites and found incorporation of MWCNTs-COOH greatly
Corresponding author. E-mail address: [email protected] (G. Zhao).
https://doi.org/10.1016/j.commatsci.2019.05.058 Received 21 March 2019; Received in revised form 29 April 2019; Accepted 29 May 2019 Available online 10 June 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Molecules models of the: (a) (5, 5) CNTs, (b) pure PTFE, (c) CNTs/PTFE composite.
reinforced PTFE nanocomposite were also compared under the same conditions. The emphasis was exploring atomic interactions between CNT and PTFE or copper. In addition, the variations of the radius distribution function, relative concentrations and temperature in the thickness direction between carbon nanotubes and PTFE were systematically monitored and discussed during the process of wear. It aimed to provide the inherent mechanisms of the improved mechanical and tribological properties of PTFE nanocomposite from an atomic view, and provide a theoretical method for designing high performance PTFE nanocomposites as a frictional material of USM.
enhanced thermal stability, mechanical properties and wear resistance under sea water because of strong interfacial adhesion between PI matrix and MWCNTs-COOH. Although a large number of experimental results indicated the outstanding reinforcement effect of the CNTs on the mechanical and tribological properties of the polymer, a very clear inherent mechanism about interaction between carbon atomic and polymer molecules are still not recognized, especially during the process of wear. The main reason can be ascribed to the small length and time scales, which limited researchers to explore the original mechanisms from an atomic level. Recently, MD simulations have been established as a high effective method to compute the properties of materials from an atomic level and provide microcosmic information and details of molecules interactions in addition to massive experimental and theoretical studies. In the past decades, many of researchers used MD simulations to study the mechanical properties of polymer nano-composites. Q.L. Xiong and S.A. Meguid et al. [11–13] investigated the interfacial mechanical characteristics of CNT reinforced epoxy composites and found that the interfacial interactions between CNT and epoxy depended on the length and diameter of CNT. Besides, such simulated results were reliable for predicting the interfacial mechanical properties of CNT-polymer nanocomposites. Chen and Hu [14] also studied the effect of diameter of CNT on the interfacial adhesion of graphene/epoxy nanocomposite. The MD simulation results indicated that larger CNT radius gave a larger contact area with graphene, leading to a stronger interfacial adhesion with polymer matrix. Frankland et al. [15] compared the effects of both long and continuous, short and discontinuous of singlewalled CNT on enhancing stress-strain behaviors of polymer matrix. The results indicated that long and continuous SWCNT can enhance the stress-strain behavior of the polymer obviously. Arash and Wang [16] investigated the tensile strength of CNT/PMMA composite by a MD study and found that the simulated results were identified with the prediction of the three-phase micro-mechanical continuum model. Jiang et al. [17] conducted the effect of volume fraction of the multiwalled CNTs on the elastic properties of polyimide composites. They found that the elastic modulus and tensile stresses increased with an increasing number of MWCNTs. However, the majority of such MD simulations focused on the calculation of mechanical enhancement of polymer by incorporation of CNTs. Only Li et al. [18–22] investigated the mechanical and tribological properties of NBR (Nitrile-Butadiene Rubber)/carbon nanotube composites by MD simulations. It was indicated that both friction coefficient and wear rate can be variously decreased by incorporation of CNTs as reinforcement of NBR. However, there are still very few studies on exploring the wear mechanisms of high performance polymer sliding against metal using MD simulations. There are no findings about mechanical and tribological investigation of PTFE by MD simulations to the authors’ knowledge. Hence, in this study, the PTFE with excellent behavior of self-lubrication was adopted as polymer matrix based on the actual application background of USM. Then, the mechanical and tribological properties of pure PTFE were investigated by MD simulations. In order to study the improved effect of CNT, the tribological properties of the CNT
2. Materials and methods In this work, molecules models of the pure PTFE and CNTs/PTFE composite were built using Materials Studio software (6.0), respectively. The Condensed-Phase Optimized Potentials for Atomistic Simulation Studies (COMPASS) force field was used [23]. The COMPASS force field, the first ab initio force-field, was commonly used to provide the atomic interactions. This force field had been proven to be applicable in describing the mechanical properties of CNTs/polymer [24]. Then, the Ewald method and the atom-based method were employed for analyzing the Coulomb interactions and the van der Waals (VDW) interactions between CNT and polymer, respectively. Fig. 1a showed the molecules model of the (5, 5) CNTs with length of 19.695 Å. In the modeling of pure PTFE as shown in Fig. 1b, 10 chains containing 50 repeat units of C2F4 were packed in the cell with Monte Carlo style with a predefined density of 2.1 g/cm3. For the model of the CNTs/ PTFE composite as shown in Fig. 1c, period boundary condition cells with the size of 3.0 × 3.0 × 3.0 nm3 with the CNTs in the middle and an empty cell was built with 6.625 vol% addition of CNTs. Hydrogen atoms were added to the edges of the CNTs to saturate the dangling bonds. The Amorphous Cell Packing task was used in the packing process. A geometry optimization using smart method with an energy convergence criterion of 10-5 kcal/mol and force convergence criteria of 10-4 kcal/mol/Å was used to get a global minimum energy configuration. To further equilibrate the model, a 5-cycle anneal process was followed under constant temperature and constant volume (NVT ensemble) from 300 K to 500 K. In the anneal process, the construct was further relaxed and obtained a stable state with a local energy minimum. The cell was followed by a 2 ns process with isothermalisobaric under the constant pressure and temperature (NPT ensemble) at a room temperature of 298 K and atmospheric pressure of 101 kPa with 1 ps timestep. During the simulation, Nose thermostat and Berendsen barostat algorithm are applied in the temperature and pressure control. Ewald summation method was applied to calculated the electrostatic interactions with an accuracy of 10-3 kcal/mol. Then, the mechanical properties can be directly obtained using a constant strain method after structure optimization to explain the improved mechanisms of tribology of the CNTs/PTFE composite. Importantly, for predicting the tribological properties of the pure PTFE and CNTs/PTFE composite, two three-layer models were constructed as shown in Fig. 2. The crystal of Cu atoms was selected as a 132
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Fig. 2. Configurations of the molecules models: (a) Pure PTFE, (b) CNTs/PTFE composite sliding against Cu layer. Cu atoms and CNTs are shown by the orange and red color, respectively.
method which was reliable for describing the polymer composites in many publications [22,25]. As described in Section 2, the mechanical properties of PTFE composite can be calculated by uniaxial tension processes in X direction. The stain-stress curves of the two materials were obtained and plotted in Fig. 3. It can be clearly seen from Fig. 3 that the stress of the pure PTFE and CNTs/PTFE composite in X direction firstly exhibited a linearly increase from 0 GPa to 0.08 and 0.16 GPa with an increase of the strain from 0 to 0.05. The slope of the fitting lines of the stress–strain curves was used to calculate the Young’s modulus. The detailed mechanical values were listed in Table 1. It was easily found that the Young’s modulus of PTFE increased from 2.05 GPa to 4.85 GPa after CNTs reinforcement. The function of CNTs as the reinforcements on the mechanical properties of polymer had been verified by an experimental work [26]. The shear modulus of both materials were also obtained. The shear stress of PTFE almost increased by 236.5% by incorporation of CNTs. The reasons for this increment can be ascribed to the strong non-bonding interactions between CNTs and PTFE molecules [11–13,21,27]. It was reported by previous
substrate and top layer according to the actual application of USM. The middle part of both tribo-layer was designed using pure PTFE matrix and CNTs/PTFE composite with the dimension of 3.0 × 3.0 × 3.0 nm3. The dimensions of top layer and substrate are 3.0 × 3.0 × 1.2 nm3. Firstly, a geometry optimization using configuration gradient method with energy convergence tolerance of 2 × 10−5 kcal/mol and a force convergence of 0.001 kcal/mol/Å was used to find the minimum global energy configuration for tribo-layer model. Then, a 5-cycle annealing process under NVT ensemble from 300 K to 500 K for 200 ps was performed to relax the structure in a wider temperature range to obtain an energy minimum of resultant trajectories. Further, the normal loading was applied to the top layer by moving it with a speed of 0.1 Å/ps for 600 ps under the loading of 101 kPa to complete the friction process. The temperature and time step for this wear process were set to be 298 K and 1 fs, respectively. The trajectory of atoms and forces generated in the sliding direction were recorded for calculating the friction coefficient and wear rate. The friction coefficient was calculated using the equation u = f / F (where u is defined as friction coefficient, f and F are the friction force which was automatically recorded during the wear process and normal load, respectively). The average friction coefficient in the stable stage was used to compare the friction reduction of PTFE reinforced by CNTs. The molecules which adhered onto the surface of copper and moved out from the polymer matrix were defined as the worn molecules. The wear rate can be calculated by the ratio of worn off molecules to the total molecules of the polymer matrix. In addition, the radius distribution function (RDF) spectra between Cu atoms and C atoms of the polymer matrix was calculated to explain the reasons about friction reduction. Further, the relative concentration and temperature variations in the thickness direction were investigated for better understanding the mechanisms of improved tribological properties.
0.18 0.16 0.14 Stress (GPa)
0.12 0.10 0.08 0.06 0.04
PTFE CNTs/PTFE
0.02
3. Results and discussion
0.00 0.00
3.1. Mechanical properties In this study, the mechanical properties of pure PTFE and CNTs/ PTFE composite were calculated using constant strain minimization
0.02
0.04 0.06 Strain
0.08
0.10
Fig. 3. The stress-strain curves of the PTFE and CNTs/PTFE composite. 133
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Table 1 Some parameters of PTFE and CNTs/PTFE composite. Proportion of fillers (Vol%)
Density (g/ cm3)
Young modulus (GPa)
Shear stress (GPa)
PTFE CNTs/PTFE
– 6.625
1.9 1.92
2.05 4.85
0.4782 1.6091
Interfacial potential energy (kcal/mol)
Samples
160 140 120 100 80 Fig. 5. Variations of friction coefficient of the PTFE and CNTs/PTFE composite with time.
60 40
both polymer composites with time. It can be easily observed that pure PTFE had a higher friction coefficient than CNTs/PTFE composite. Usually, the average friction coefficient in the stable stage was used to represent the tribological properties of the materials. In this study, the average friction coefficient of both polymer composites in the stable stage after 300 ps was calculated and compared. It was noted that the average friction coefficient of PTFE reduced from 0.169 to 0.127 by introduction of CNTs, decreased by 24.85%. The root reason still can be ascribed to the reinforcement effect of CNTs. Besides, the friction coefficient of pure PTFE at the running-in stage was rather unstable due to strong atomic interactions between Cu atoms and C atoms of pure PTFE. After CNTs reinforcements, more polymer molecules were adsorbed around the surface of CNTs under the effect of VDW forces [18]. So, the atomic interactions between Cu atoms and C atoms of CNTs/ PTFE become weak, which contributed to the stable friction process of CNTs/PTFE composite. To compare the atomic interactions between polymer and counterpart, the RDF values between Cu atoms and C atoms of polymer were extracted during the wear process. Fig. 6 showed the RDF values between Cu atoms and C atoms of polymer composite. It can be found from Fig. 6 that RDF value started to increase with some fluctuations when the contact distance in the z direction was over 2 Å. It indicated that more PTFE molecules acted with Cu atoms under the certain load during the process of wear because of VDW forces and other interactions. However, the average RDF
20 0
20
40
60 80 100 Simulation time (ps)
120
140
Fig. 4. Variations of interaction potential energy between CNTs and PTFE with simulation time.
publications [13,21] that an interfacial interaction space can be formed between CNTs and polymer matrix due to the VDW forces. Hence, the interaction potential energy between CNTs and PTFE matrix during the simulation processes was calculated by Eq. (1) and shown in Fig. 4 to reveal the improved mechanisms.
Einter = Etotal − EPTFE − ECNTs
(1)
Radius Distribution Function
where Etotal is the energy of the CNTs/PTFE nanocomposite, EPTFE is the energy of the PTFE, ECNTs is the energy of the CNTs. Fig. 4 showed the interaction potential energies between CNTs and PTFE matrix at different MD simulation times. It indicated that the interaction potential energy of the CNTs/PTFE cell in the initial (0 ps) and final (60 ps) state was 26.2 kcal/mol and 150.3 kcal/mol, respectively, increased by more than 5 times. This increase of interaction potential energy resulted in an adsorption effect between CNTs and PTFE matrix, suggesting that more PTFE chains were adsorbed around the surface of CNTs due to strong interactions. This strong adsorption interaction contributed to the improved mechanical properties of PTFE. Besides, it was also noted from Fig. 3 that the stress of both polymer composites at some points went down and then went back with an increase of strain. For example, the stress of pure PTFE decreased from 0.088 GPa to 0.064 GPa (27.3% decrease) at the strain of 0.75, while the stress of CNTs/PTFE varied from 0.15 to 0.137 GPa (8.67% decrease). The possible reason can be ascribed to the fracture of partial polymer molecules. Then, the stress fluctuated with a small growth when the strain continuously increased from 0.05 to 0.10. In a word, an improvement of mechanical properties can be found by incorporation of CNTs into PTFE matrix. 3.2. Tribological properties
0.8 0.6 0.4 0.2 0.0
To investigate the effect of CNTs on the tribological properties of the pure PTFE and CNTs/PTFE composite, two friction models of polymer sliding against Cu layer were built for simulating the actual working condition of USM in which polymer nanocomposites were sliding against Cu layer. Fig. 5 showed the variations of friction coefficient of
PTFE CNT/PTFE
1.0
0
5 10 Distance r (Angstrom)
15
Fig. 6. RDF values of the Cu atoms and C atoms of the PTFE and CNTs/PTFE composite during the process of wear. 134
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Fig. 8. Concentration profiles of the PTFE and CNTs/PTFE composite in the thickness direction.
composite. Only deformation can be found from Fig. 7b, 7d and 7f for the CNTs/PTFE composite under the shear stress, which further indicated the reinforcement effect of CNTs on the wear of PTFE. To further reveal the wear mechanisms of both polymer composites, the concentration profiles in the thickness (z direction) of the polymer matrix were calculated and presented in Fig. 8. It can be seen from the curves of relative concentration that pure PTFE had a higher atomic concentration than CNTs/PTFE composite, especially around the contact areas (position 12 Å and 42 Å in the thickness direction) between Cu atomic layer and the polymer composite. The peak concentration of pure PTFE on the top contact area in the 12 Å, as a friction interface, had a 11% difference larger than those of the CNTs/PTFE composite. On the bottom contact area, there still had a 14% concentration difference due to a strong atomic interaction between Cu atoms and PTFE molecules. However, the CNTs/PTFE composite had a maximum concentration difference (27.3%) in the middle part of the whole matrix (about the position of CNTs in the PTFE composite) than those of the pure PTFE. Therefore, it can be recognized that more atoms of pure PTFE tended to move to the friction areas and subject to the shear loading, while more PTFE molecules of the CNTs/PTFE composite were absorbed onto the surface of CNTs. This was a dominated reason why CNTs/PTFE composite showed the improved tribological properties. In addition, the temperature profiles of both polymer composites in the same direction were calculated and shown in Fig. 9. It can be found from the temperature profile of pure PTFE that a much higher temperature of 332.7 K was observed around the top contact areas (around 12 Å in the z direction). The temperature of CNTs/PTFE composite decreased by 11.9% after reinforced with CNTs. According to the above concentration profiles in the same thickness distance, it indicated that more polymer atoms around the friction interface between top Cu layer and polymer molecules contributed to the more energy dissipations. Based on an energy dissipation theory in atomic-scale friction proposed by Yuanzhong Hu [28], frictional work was eventually converted into heat, suggesting that friction was in fact a process of energy transformation. Only small part of the energy can be stored by the material themselves, which lead to a temperature rise for the whole system. Differently, the CNTs/PTFE composite produced little temperature rise than pure PTFE due to weak interactions with Cu atoms and low friction coefficient.
Fig. 7. The snapshots of friction process of the pure PTFE (a) (c) (e) and CNTs/ PTFE composite (b) (d) (f) sliding against Cu layer at 150 ps, 300 ps, 600 ps, respectively.
value of PTFE decreased after filling CNTs. Therefore, it can be concluded that the fewer molecules in the CNTs/PTFE composite moved towards the Cu atoms during the sliding process. Because more PTFE molecules were absorbed by CNTs due to the electrostatic and VDW interactions in the molecules system, which had also been indicated by other results [16]. Correspondingly, the fewer PTFE molecules were worn out from polymer matrix after CNTs reinforcement. In order to better understand the wear mechanisms of both PTFE composite, the snapshots in the different stage during the friction process was shown in Fig. 7. It can be easily recognized that pure PTFE molecules with weak mechanical properties suffered from large deformation (Fig. 7a), fracture (Fig. 7c) and breakage under the shear stress, and finally worn out from the PTFE matrix as shown in Fig. 7e, which can be recognized as the worn molecules. Under the same condition, the wear rate of pure PTFE with Cu reached up to 64.65%, while no worn molecules were observed from the final state of the CNTs/PI
4. Conclusion In this research, MD simulations are developed to investigate the mechanical and tribological properties of pure PTFE and CNTs/PTFE 135
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Fig. 9. Temperature profiles of the PTFE and CNTs/PTFE composite in the thickness direction.
nanocomposites to reveal the inherent mechanisms of polymer composite with metal and improved wear mechanisms from an atomic level. By incorporation of CNTs, the Young’s modulus and shear stress of PTFE increased by 136.58% and 236.3%, respectively. The average friction coefficient also decreased by 24.85% after CNTs reinforcement. Importantly, the wear resistance of PTFE was greatly improved by incorporation of CNTs. Meanwhile, the RDF values, relative concentration profiles, temperature profiles during the friction process all proved these enhanced effect of CNTs on the tribological properties of the PTFE. This MD simulation study provided an effective method to design high performance polymer nanocomposites in the application of USM. Acknowledgements This work is supported by Fundamental Research Funds for the Central Universities (NS2018010), the Major State Basic Research Development Program of China (973 Program, Grant No. 2015CB057501), and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. References [1] G. Zhao, Q. Ding, Q. Wang, Comparative study on the tribological properties of the polyimide composites reinforced with different fibers, Polym. Compos. 37 (2016) 2541–2548. [2] Q. Ding, Y. Zhang, G. Zhao, F. Wang, Properties of POB reinforced PTFE-based friction material for ultrasonic motors, J. Polym. Eng. 37 (2017) 681–687. [3] G. Zhao, C. Wu, L. Zhang, J. Song, Q. Ding, Friction and wear behavior of PI and PTFE composites for ultrasonic motors, Polym. Adv. Technol. 29 (2018) 1487–1496. [4] F. Song, Z. Yang, G. Zhao, Q. Wang, X. Zhang, T. Wang, Tribological performance of filled PTFE-based friction material for ultrasonic motor under different temperature
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