Structure, Plastic Deformation of Polyethylene: A Molecular Dynamics Method

This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Polyethylene C2H4 (PE) by the Molecular Dynamics (MD) method with Dreading pair interaction, cyclic boundary conditions and plastic deformation of Polyethylene (PE) be done by stretching method according to the z-axis. The results of structure, plastic deformation of PE are analyzed through size (l), the total energy of the system (Etot), shape and associated energy (Ebond), angular binding energy (Eangle), energy Edihedral, interactive energy Vander Walls (Enon-bonding). When increasing N, t leads to the number of structural units of Face-Centred Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) increasing, but Amorphous (Amor) decreases while the angle between the atoms is a constant corresponding to 109.5 ̊. Besides, the length of the link (r) increases from r = 1.529 Å to r = 1.558 Å while the plastic deformation energy of PE gets an enormous change and the bonding angle at 109.27 ̊. The length of the link r = 1.529 Å and the size (l) of the PE material increase from l = 3.73 nm to l = 6.63 nm while the total energy of system (Etotal) decreases from Etotal = −1586 eV to Etotal = −7891 eV with the transition temperature is T = 103 K. Increasing the number of atoms leads to increasing the length of the link. The total energy Etotal of the system decreases, but the number of structural units in FCC, HCP, BCC and Amor increase, which leads to the length of the link increases, the Etotal decreases, and there is a change in the plastic deformation characteristics of PE. In contrast, increasing T leads to the plastic deformation increases, and PE moves from the amorphous state to the liquid state. The obtained results are very significant for future experimental research. How to cite this paper: Trong, D.N., Quoc, T.T., Minh, H.D.T., Chinh, C.N. and Quoc, V.D. (2020) Structure, Plastic Deformation of Polyethylene: A Molecular Dynamics Method. Advances in Materials Physics and Chemistry, 10, 125-150. https://doi.org/10.4236/ampc.2020.106010 Received: April 19, 2020 Accepted: June 27, 2020 Published: June 30, 2020 Copyright © 2020 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access


Introduction
Polyethylene C 2 H 4 (PE) is a flexible plastic existing in an amorphous state and widely used in consumer products. In particular, PE plays an important role in material science, which is considered as a bright candidate for new industrial materials. When PE is combined with wood, it creates an environmentally Wood Plastic Composite material (WPC) [1] [2] such as reducing energy consumption in production, lightweight, and sound insulation [3] [4] [5]; reducing pollution and greenhouse effect; enhancing biodegradability [6] [7] [8]. Also, WPC is widely used in industries such as automotive, construction, et al. [6] [9]. The flexible plastic resins are made of Polyethylene (PE) [8], Polypropylen [10], Polyvinyl Clorua (PVC) [11] and polystyrene (PS) [12]. The Wood components include wood pulp, cotton, wheat straw, bagasse, and rice husk [13] [14] [15] [16] [17]. PE plastic is used in practice including both High-Density Polyethylene (HDPE) and low-density WPC [18]. PE, as a binder and wood pulp as an additive; HDPE includes material hydrophilic wood pulp and PE hydrophobic wood pulp [19] [20]. Therefore, PE is considered as an important additive component in industrial applications. PE is divided into many types, mainly based on density, monomer, flexibility [21], and copolymer [22] [23] [24]. In particular, with Low-Density Polyethylene (LDPE) which is the most commonly used and commercially produced at high pressure (P), P = 2400 Bar, temperature (T) from T = 363 K to T = 383 K [25].
To study this material, it is good to use the experimental, theoretical, and simulation methods. As for the experimental method, using pressing methods and multi-layer extrusion method with low cost has high durability, ductility [26] and increasing stress [27] [28] as Jatin et al. [29], Kurz et al. [30], Pouriayevali et al. [31] for that plastic deformation of PE is an isotropic function with pressure putting on (the deformation (ε) in the experiment which is always less than ε < 0.12); Epee et al. [32] suggested that the deformation of the polymer with ε < 800 s −1 ; Argon et al. [33] suggested that plastic deformation is due to the twisted bonding pairs along the polymer chain; Roberson suggested that the shear stress is caused by changing angles and movements of molecules [2]; Eyring et al. [1] suggested that the plastic deformation is caused by the shear stress, structural changing, and binding energy [34]- [40]. With the simulation method, Deng et al. [41] suggested that plastic deformation is caused by the local structure. Besides, Maeda, Takeuchi [42], Srolovitz et al. [43] successfully used the molecular statistical method (MS) to study the deformation of three-dimensional metal glasses; Theodorou and Suter [44] [45] successfully simulated the material in the D. N. Trong et al. glass polymer material and studied the deformation. After that, MS. Mott et al. [46], Hutnick et al. [47] [49] successfully investigated the effect of temperature on the bond in glass polyethylene and mechanics of materials. It is said that increasing the plastic deformation and the length of the initial link is necessary. Although there have been many studies on the plastic deformation of PE in the static state or the dynamic state [48] [50]- [57] such as Baltsas et al. [58], Haefele et al. [59], using simulation method with Low-Density Polyethylene (LDPE) at high pressure; Asteasuain et al. [60] use Graphical Optimization Tool (gOPT) of general PROcess Modelling System (gPROMS) simulator program to optimize LDPE; Bezzo et al. [61] successfully used Fluent, gPROMS for liquids by calculating molecular dynamics. Recently, Clarke [48] has successfully performed uniaxial deformation of amorphous Polymers with different deformation levels at low temperatures, which is obtained in qualitative form. Capaldi et al. [42] suggested that the compressive deformation of Polymer is the same as the change of angle, the angle shift along the chain; Li et al. [62] [71] as the liquefaction process which is just below the room temperature T = 300 K, limited by the movement of atoms at transition layer between the crystal area and the amorphous region. This shift occurs very weakly in HDPE with temperature from T = 123 K to T = 173 K and it is linked with the movement of CH 2 groups attached to C 2 H 4 [72], the change in the molecular shape of the polymer depends on the relationship between temperature and pressure [73]; the phase transition depends on the heating rate, the total energy of the system during the deformation process [74]. The results show that the glass transition temperature (T g ) depends on the movement of atoms with valuable in approx from T g = 133 K to T m = 408 K [75], and this is performed on experimental measurements [76].
Besides, many authors have successfully studied the plastic deformation of PE by the z-axis stretching method. The results show the influence of the chain length, the number of chains, the strain rate, and the temperature. This depends D. N. Trong et al.
on the stress-strain [77] [78] [79] [80] which is ended at the source of plastic deformation. Polyethylene is a problem that has not been explained in detail [81]. To solve the problem, we focus on studying the effect of atomic number, temperature, annealing time on the structure, and the plastic deformation of PE.

Method of Calculation
Initially, randomly sow atomic number (N), N = 2000 atoms, 4000 atoms, 6000 atoms, 8000 atoms, 10 With: E bond is the bond energy, E angle is the bond angle energy, the E dihedral is dihedral energy, E non-bonding is van der Waals energy in the Lennard-Jones interaction, E tot is the total energy of the system, K b = 350 kcal/mol, K θ = 60 kcal/mol•rad 2 is the stiffness coefficient, the bond angle coefficient, r 0 = 1.53 Å is the bond length, θ 0 = 1.911 rad (109.5˚) is the link angle, C 0 = 1.736, C 1 = −4.490, C 2 = 0.776, C 3 = 6.99 (kcal/mol) are the coefficients, σ = 4.01 Å is the energy at 0 eV, ε = 0.112 kcal/mol is the dielectric constant, r c = 10Å is the radius interrupt.
After obtaining, all PE samples for running 10 6 steps molecular dynamics (MD) simulation recovery statistics at temperature (T), T = 500 K; 10 6 steps NPT (atomic number, pressure, and constant temperature) MD simulation at T = 500 K. After obtaining PE samples at T = 500 K, the samples were lowered from T = 500 K to T = 100 K. Particularly with N = 10000 atoms at T = 500 K, the temperature is lowered to T = 120 K, 100 K, 80

The Phase Transition of Polyethylene
The result of the phase transition Polyethylene C 2 H 4 (PE) is shown in Figure   1.
The  (Figure 1(a)). Similarly, with the process of running 10 6 steps NPT (with atoms number, pressures, and temperatures is constant) leads to P changes on the range from P = −558 Bar to P = 706 Bar, with PE 10,000 atoms the P has the smallest change (Figure 1(b)). The process of temperature reduction from T = 500 K to T = 100 K shows that the P of PE 10,000 atoms has not changed significantly (Figure 1(c)). The energy values of PE at T = 100 K has value corresponding change. The total energy pair (E pair ) decreases from E pair = −3014 eV to E pair = −15,161 eV (Figure 1(d)), the total electron bond energy (E bond ) increases from E bond = 199 eV to E bond = 994 eV (Figure 1(e)), the total angle bond energy (E angle ) increases from E angle = 223eV to E angle = 1158 eV ( Figure 1(f)), the total dihedral energy (E dihed ) increases from E dihed = 719 eV to E dihed = 3544 eV (Figure 1(g)) and E tot decreases from E tot = −1873 eV to E tot = −9465 eV (Figure 1(h)). Basing on the given result, after 10 6 steps moving of recovering statistics, then PE reached equilibrium; 10 6 steps moving NPT at temperature (T), T = 500 K lead to PE existed in a liquid state. When the temperature decreases from T = 500 K to T = 100 K leading to PE changes from the liquid state to a new crystalline state, running stably 10 6 steps NPT at T = 100 K obtained PE in the new crystalline state corresponds to the shape of PE ( Figure   1(i)). As a result, when increasing atoms number (N) leads to the size (l) increases, but E tot decreases.

Plastic Deformation Process of Polyethylene
The results of the plastic deformation process of Polyethylene (PE) at temperature (T), T = 100 K are shown in Figure 2, Table 1.
The obtained result shows that after the process of the temperature reduction from T = 500 K down to T = 100 K with 10 6 step MD simulation, the       Table 2). When increasing N from N = 2000 atoms to N = 4000 atoms, 6000 atoms, 8000 atoms and 10,000 atoms leads to the total energy pair (E pair ) decreases from E pair = −2756 eV to E pair = −13,866 eV ( Figure 4(b)), energy bond (E bond ) increases from E bond = 163 eV to E bond = 812 eV (Figure 4(c)), angular bond energy E angle increases from E angle = 256 eV to E angle = 1264 eV (Figure 4(d)), the energy dihedral increases from E dihed = 751 eV to E dihed = 3899 eV (Figure 4(e)), and E total decreases from E total = −1586 eV to E total = −7891 eV (Figure 4(f)), free volume change the number of atoms ( Figure   4(g)), the plastic deformation process of PE (Figure 4(h)), the PE shape ( Figure   4(i)) after deformation at T = 100 K, and the number of structural units of FCC     Figure 4. The plastic deformation process as the energy E (a), the total energy pair E pair (b), the total electron bond energy E bond (c), the total energy angle E angle (d), the total dihedral energy E dihed (e), the total energy E tot (f), free volume change the number of atoms (g), stress (h), the PE shape (i) after deformation at T = 100 K with atomic number and different moving the number of steps.   [77], the size of the PE material increase from l = 3.73 nm to l = 6.63 nm, the total energy E total decreases from E total = −1586 eV to E total = −7891 eV. This means that when increasing the number the atoms leads to increase the link length, E total decreases and changes the plastic deformation characteristics of PE.

The Effect of Annealing Time
Similarly, the effect of annealing time of PE material with N = 10,000 atoms at T = 100 K, the results are shown in Figures 5-7.
The results show that with t = 50 ps, the shape (Figure 6

Influence of Temperature
The result of the effect of T on the plastic deformation of PE 10,000 atoms, is shown in Figure 8, Figure 9.
The result shows that at the temperature (T), T = 40 K in which the number of structural units 47 FCC, 307 HCP, 18 BCC (Figure 9(a)) corresponding to the plastic deformation characteristics of PE (Figure 8). When increasing the temperature from T = 40 K to T = 60 K, 80 (Figures 9(b)-(e)), the shape and plastic deformation characteristics of PE (Figures 8(a)-(f)). In addition, the E tot increases ( Figure 5(e)), which shows that when increasing temperature leads to the plastic deformation increases, and the structure is unchangeable. The obtained result shows that when increasing N leads to l increasing, E tot decreases, and the number of structural units increases. When increasing the time of elongation and temperature, l increases, E tot increases, and the number of structural units of the system decrease. This result is the basis for future empirical research.

Conclusion
After studying the effect of the atomic number (N), temperature (T), and an-  (e) (f) Figure 8. The plastic deformation process of PE 10,000 atoms with the total energy pair E pair (a), the total electron bond energy E bond (b), the total energy angle E angle (c), the total dihedral energy E dihed (d), the total energy E tot (e), the free volume change the number of atoms (f) at the temperature T = 100 K with different temperatures. Advances in Materials Physics and Chemistry