Tribological study of amorphous polyethylene under different rough surfaces of chromium based on molecular dynamics simulation

Abstract

Due to its excellent friction and wear properties, polyethylene is often used in bearings, seals and driveline systems together with metal-coated components. Therefore, how to study the contact friction behavior and wear mechanisms of polyethylene molecular chains with metal surfaces on a microscopic scale is a current scientific problem to be solved. In this study, molecular dynamics simulations were used to investigate the changes in contact interface morphology, plastic deformation, friction temperature, and friction properties of amorphous polyethylene and chromium under different conditions. The results show that during the friction process, the movement of amorphous polyethylene chains is mainly affected by the roughness peaks on the surface of the chromium plate and the inter-chain entanglements, forming a “migration-detachment-migration” process, which leads to the generation of a plastic flow layer. The height of the roughness peak on the contact surface is critical for the regulation of frictional properties. At a normal load of 1 GPa, the number of contact atoms on the surface increased by 20% as the height of the rough peak increased to 6 Å compared to a smooth surface. During friction, the plastic flow layer thickness increased from 10 Å to 16 Å as the normal load increased from 1 GPa to 5 GPa, which is about 60% increase in the plastic flow layer thickness. And as the sliding velocity increases to 3 Å/ps, the thickness of the plastic flow layer increases by 70%, which in turn leads to higher atomic mobility and atomic wear. In addition, the modulation of chain entanglement by normal load and sliding velocity is revealed by analyzing the distribution of C-C-C bond angles, with normal load being more sensitive to the angular change of amorphous polyethylene chains. As the normal load increases, some of the C-C-C bond angles begin to shift from 110° to 115°, which in turn increases atomic wear. This study has certain theoretical guiding significance for studying the tribological behavior of amorphous polyethylene and metal.

Introduction

Polyethylene (PE) as a macromolecular polymer^1,2 is widely used in many fields such as packaging, electronics, medical, automotive, and textile. Due to its high wear resistance, good self-lubricating ability, low coefficient of friction and other properties^3,4,5, it is often used as sealing rings, hydraulic bearings, stern tubes and other parts with metal parts as a friction vice^2,6,7, which can reduce the wear and tear of the material and improve the use of performance. At present, some scholars have optimized the performance of polyethylene by modifying the material^8,9 to adjust its crosslinking³ and microstructure¹⁰. However, contact friction is unavoidable when metal parts are used in conjunction with polyethylene, leading to wear and tear of the polyethylene, which in turn reduces its mechanical properties. Therefore, understanding the friction behavior of polyethylene is important to optimize the performance of the material in use.

With the development of computer simulation technology, molecular dynamics (MD) simulation has become an important analytical tool for studying the friction behavior of polymer materials at the nanoscale^11,12. In the actual polyethylene friction experiment, due to the influence of environmental factors (such as humidity, temperature, etc.), it is difficult to accurately control the microscopic factors. MD simulation can reveal the interaction in the friction process at the atomic scale. The friction process simulation is not affected by environmental factors, and can more accurately analyze the friction characteristics, especially the friction characteristics at the micro scale. Compared with macroscopic experiments, molecular dynamics simulations allow in-depth analysis of friction behavior without relying on complex experimental equipment, especially at the microscopic scale to explore friction properties, friction forces and wear mechanisms at the nanoscale. Simulating the structural changes of materials on an atomic scale and revealing the microscopic mechanisms in the friction process by calculating the interatomic interactions and motion trajectories can lead to a deeper understanding of the motions, interactions, and deformation behaviors of polyethylene molecular chains under different conditions and how these behaviors affect the macroscopic friction properties. Through MD simulation, researchers can explore the friction behavior under different conditions in advance, so as to optimize the experimental design and reduce the experimental cost and time. In practice, friction between polyethylene and metal parts can cause invisible damage within the material, such as plastic material flow and energy loss, which in turn leads to a reduction in the life of the material. MD simulation can help researchers understand the microscopic mechanism of these friction problems from the atomic scale and adjust the working parameters to improve the performance of materials. Through the combination of molecular dynamics and experiments^13,14, the researchers revealed the friction characteristics and wear mechanism of polymer materials, confirmed the feasibility of MD simulation, provided strong support for understanding the tribological properties of polymer materials, and provided a theoretical basis for optimizing the application of related materials.

In recent years, the study of friction behavior of polymers is still a hot issue in the field of tribology^15,16,17. Some researchers have conducted in-depth studies on the friction characteristics, micro-morphology, and wear mechanism of polymers under different conditions through molecular dynamics, and explored the changes in the mechanical properties of the polymer materials as well as the micro-damage mechanism during the friction process^18,19,20. Currently, in response to these issues, some scholars have conducted relevant research on polyethylene. Among them, Cheng et al.²¹ used MD simulations to discuss the diffusion behavior of squalene into polyethylene and its effect on the plastic deformation of polyethylene. The results suggest that squalene enters (UHMWPE) by molecular diffusion, reduces polyethylene interchain interactions, promotes its plastic deformation, and leads to structural loosening, thus accelerating the wear process. In addition, changes in the contact interface affect the contact area, pressure distribution, contact point shape, and surface properties, etc., which in turn have an important effect on friction force, wear, etc. Therefore, there are studies²² on the effects of static friction and dynamic friction of high-density polyethylene (HDPE) through physical experiments, and the measurement of roughness, debris formation and mechanical properties. It is found that static friction and dynamic friction are affected by surface roughness, and roughness can change the surface contact area and interaction mode. However, the influence of roughness on the frictional heat effect and microscopic wear mechanism of polyethylene on the nanoscale needs to be explored in depth. Polyethylene as a thermoplastic material, polyethylene has a certain molecular chain mobility during friction, this mobility can be micro-deformation at the friction interface, thus changing the friction force and wear mechanism. During friction, migration, rearrangement, and local plastic deformation of the polyethylene chains occur, which together determine the tribological properties. In particular, the flow of molecular chains within the polyethylene during the friction process and the microscopic contact state have a certain influence on its friction performance and wear mechanism. Qiang et al.¹² performed joint atom MD simulations to reveal the interfacial frictional warming mechanism of amorphous polyethylene (PE) in single sliding friction (SSF) and reciprocating sliding friction (RSF) modes. Hosoya et al.²³ analyzed the nanomechanical properties of high-density polyethylene (HDPE) by MD simulation to investigate the relationship between the surface structure, contact state and mechanical properties of polyethylene. By corroborating with atomic force microscopy (AFM) results, it was found that differences in molecular behavior at the contact location significantly affect the mechanical characteristics of HDPE. Linking the macroscopic to the microscopic provides insights into the frictional properties of materials at the nanoscale. Therefore, the tribological properties of polyethylene are influenced by a combination of factors, including contact friction surface roughness, molecular diffusion, contact state, and the intrinsic structure of the material, all of which have a significant effect on the friction, and wear mechanism. Based on the above studies, the present study employed molecular dynamics simulations to investigate the sliding friction behavior of polyethylene under different normal loads, sliding velocities, and contact surface morphologies. The friction force, temperature change, wear mechanism and the angular distribution of amorphous polyethylene chains under different conditions were analyzed to investigate the friction characteristics of amorphous polyethylene in depth and to provide certain theoretical support for improving the material properties, reducing wear and increasing reliability.

The friction behavior of amorphous polyethylene under different loading parameters and different environments has been investigated by many scholars, while the microscopic study for the contact friction between amorphous polyethylene and metal with different rough peak surfaces is still unclear. However, the roughness of the contact surface is also the cause of wear, because when metal and polymer materials produce friction, the mechanical interlock between the roughness peak of the metal surface and the polymer will lead to the transfer of the polymer material²⁴, and then produce wear behavior. Therefore, the material deformation and wear mechanisms of polyethylene under friction with different rough peak surfaces need to be investigated in depth. Based on the method of molecular dynamics, the friction process between amorphous polyethylene and chromium on different rough surfaces was simulated in this study. Under different normal loads and sliding speeds, the changes in microstructure and friction and wear properties of amorphous polyethylene were analyzed. The motion of amorphous polyethylene chains, interatomic interactions, migration of atoms, and wear mechanisms during friction under different conditions were investigated. In this study, the friction mechanical properties of amorphous polyethylene under different loading parameters were investigated, and the microscopic deformation mechanism of amorphous polyethylene during friction between smooth and rough surfaces was revealed, aiming to optimize the friction properties of metal and polyethylene and provide effective insights for reducing the wear of polyethylene materials.

Materials and methods

In this study, the all-atom model is chosen for MD simulations. The all-atom model can accurately describe the behavior of each atom and the interactions between atoms, including the changes of molecular chains and interatomic interactions. The model includes amorphous polyethylene (PE) and chromium plate. The lattice constant of chromium is 2.88. To better adapt to the changes of atomic structure during the construction process and movement process of the model and avoid the unsaturated phenomenon of atoms in the chromium plate during the simulation process. Therefore, when constructing the chromium plate model, the lattice constant of chromium is kept in an integer multiple relationship, and the size of the top chromium plate is set to 46.16 Å × 46.16 Å × 28.84 Å. The lower layers of the three types of chromium plates are smooth and conical rough surfaces, and the heights of the rough surfaces are 4 Å and 6 Å, respectively, which ensures the consistency of the number of rough peaks and avoids the influence of the number of rough peaks on the friction process. Polyethylene (PE) is a thermoplastic polymer with repeating units (-CH₂-CH₂-) prepared by polymerization of ethylene (CH₂=CH₂) monomer. High density polyethylene is widely used because of its high strength and good wear resistance. The density of high-density polyethylene is about 0.94 ~ 0.97 g/cm³. Tervoort, T.A.e t al.²⁵ found that the wear of various polyethylene increased with the decrease of crystallinity, which indicated that the study of wear in the amorphous region of polyethylene materials was very important. In this study, the friction behavior of amorphous polyethylene was discussed. The bottom was composed of 20 amorphous PE chains, forming an amorphous PE block with a size of 46.16 Å×46.16 Å×46.16 Å and a density of 0.95 g/cm³. The single PE chain contains 100 monomers, consisting of 98 methylene (-CH₂-) and 2 methyl (-CH₃). The molecular chain structure is consistent with the simulation of Ting Zheng et al.². This is also to match the size of the two materials in the contact area, and the density is consistent with the density of the polyethylene material in the experiment, which ensures the rationality of the model and avoids the interference of periodic boundary conditions on the results. And this is consistent with the number of polyethylene molecular chains selected by Alejandro A. Pacheco et al.²⁶. The disordered amorphous polyethylene block was constructed by using the AC module in MS software. The chrome plate is placed 5 Å away from the top layer of the amorphous PE block. A 3 Å vacuum layer is inserted at the top layer to separate the two materials to avoid structural chaos caused by periodic boundary conditions, and then the model is geometrically optimized.

All simulations are performed in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) in three phases. The first stage is the equilibrium stage, where the whole system is first grouped into five layers from bottom to top, as shown in Fig. 1. The upper and lower boundary layers are rigid moving and rigid fixed layers, respectively, which are set as rigid bodies due to the possible deformation of the atoms in the moving and fixed layers during the simulation. To avoid the movement of the whole amorphous polyethylene block at the bottom along with the chromium plate, the atoms in the bottom boundary layer will be fixed and their spatial positions will be constrained. A Nosé-Hoover thermostat was used to set the thermostatic layer at 6 Å from the boundary layer to maintain the equilibrium of the whole system and to ensure the stability of the simulation process. The remaining layers are Newtonian layers, and the Newtonian layer atoms can move freely during the simulation, i.e., the atoms in this layer are not constrained. Throughout the simulation, periodic boundary conditions are set along the X and Y directions, and non-periodic boundary conditions are set along the Z direction. Before relaxation is performed at the equilibrium stage, the model needs to be energy minimized using the conjugate gradient method to minimize the model and make the structure more rational. Subsequently, the model was relaxed under the NVT system, and the model temperature was controlled to a target temperature of 300 K using a Nosé-Hoover thermostat and held for 100 ps to bring the model to thermal equilibrium.

Fig. 1

Friction modeling of amorphous polyethylene with chromium plates of different roughness peak heights. (a) Height of 0 Å (smooth surface), (b) Height of 4 Å, (c) Height of 6 Å.

The second stage is the downward pressure stage. The normal load (P) is applied to the rigid moving layer along the Z direction. The process is carried out under the NVE ensemble with an initial temperature of 300 K and a holding time of 150 ps, so that the chromium plate reaches the predetermined normal load. The third stage is the sliding friction stage, in which a normal load along the Z-direction and a constant velocity (V) along the X-direction are applied to the rigid moving layer atoms, causing the top chromium plate to move linearly along the X-positive direction, at a temperature of 300 K, and a sliding friction time (t) of 150 ps. In this study, the effects of different normal loads and different velocities on the friction process are analyzed by applying the same velocity and different normal loads (V = 1 Å/ps, P = 1, 2, 3, 4, and 5 GPa), and the same normal loads and different velocities (V = 1, 1.5, 2, 2.5, and 3 Å/ps, and P = 1 GPa) to the top atoms of the three models. The influencing factors in the simulation process are shown in Table 1.

Table 1 Parameter changes under the action of different factors during friction.

The selected potential function is the reaction force field (Reaxff) developed by Shin et al.²⁷ and Adri C. T. van Duin et al.²⁸. The reaction force field consists of two parts: intraatomic interaction and interatomic interaction, that is, the potential energy of the force field includes bonding and non-bonding interactions. Among them, van der Waals interaction and electrostatic interaction energy belong to non-bonding interaction potential energy. This treatment of non-bonding interactions enables ReaxFF to describe covalent materials, ionic materials, and materials in between, thereby significantly improving its applicability. The Reaxff force field has been applied to the molecular dynamics simulation of the friction between Cr metal and polymer^29,30,31,32. It can accurately describe the fracture and formation of bonds, and can also consider the interaction of non-bonds. The energy expressions and parameters are listed in detail in the study of Adri C. T. van Duin et al. The energy of the Reaxff force field³² is given by:

$${E_{system}}={E_{bond}}+{E_{over}}+{E_{under}}+{E_{val}}+{E_{pen}}+{E_{tors}}+{E_{conj}}+{E_{vdWaals}}+{E_{Coulomb}}$$

(1)

Where ${E_{system}}$ is the total energy of the system, ${E_{bond}}$ is the bond energy between atoms; ${E_{over}}$ and ${E_{under}}$ refer to the energy correction for over-coordination of atoms in the system and the energy compensation for under-coordinated atoms, ${E_{val}}$ is valence angle energy, ${E_{pen}}$ is double-bond valence angle penalty, ${E_{tors}}$ is torsion energy, ${E_{conj}}$ is conjugation energy, ${E_{vdWaals}}$ is van der Waals energy, and ${E_{Coulomb}}$ is coulomb energy.

Results and discussion

Friction behavior

Changes in contact surface morphology

To analyze the change of contact surface morphology with different roughness peak heights, the contact surface morphology of three models with a normal load of 1 GPa and no friction was extracted, and the number of atoms on the contact surface with different roughness peak heights was calculated. Since the friction between the chromium plate and the amorphous polyethylene is “hard on soft”, the smooth contact surface can be seen to be flatter by looking at Fig. 2a. As the height of the roughness peak increases, the depression of the surface becomes more pronounced, increasing the number of atoms in contact between the chromium plate and the amorphous polyethylene (e.g., Fig. 2b), which can lead to changes in friction properties. Because the amorphous polyethylene chain itself has a cross-linked, irregular structure, in the sliding friction process, amorphous polyethylene will inevitably produce entanglement. During friction, when the surface roughness peaks are large, the polyethylene molecular chains will be stretched and deformed due to the tiny surface bumps, and these deformations may lead to intertwining of the molecular chains in the localized areas, producing tangles. This entanglement leads to increased interaction between molecular chains, which increases frictional resistance and increases wear. Entanglement increases the internal friction of the molecular chain, making it more difficult to slip between chain segments. This phenomenon leads to an increase in friction, which is due to the generation of interaction forces between more atoms. Entanglement increases the binding forces between molecular chains, making it necessary to overcome greater resistance to slip during friction. This entanglement effect is especially pronounced on rough surfaces, as rough summits exacerbate molecular chain interactions, leading to greater friction and wear. However, as the height of the roughness peaks increases, so that the number of contacting atoms increases, this may lead to an enhanced entanglement effect on the chromium plate and an increase in frictional resistance.

Fig. 2

Contact of amorphous polyethylene with chromium plates of different roughness peak heights at a load of 1 GPa. (a) Contact surface morphology, (b) Number of contacting atoms.

Friction morphology change

In the study of the sliding friction process between the chromium plate and the amorphous polyethylene, since the amorphous polyethylene chain is connected through carbon-carbon bonding, an amorphous polyethylene fragment with 12 carbon atoms connected is selected as the research object, and the movement behavior of the amorphous polyethylene chain is quantitatively analyzed by calculating its displacement along the X-direction ($\Delta$X), as shown in Fig. 3. Notably, the amorphous polyethylene chain slips along the direction of movement of the chrome plate. Observation of Fig. 3b reveals that the sliding distance of the amorphous polyethylene chains increases as the friction time increases. The displacement of the amorphous polyethylene chains did not undergo a large change when the amorphous polyethylene chains were subjected to contact friction action with the smooth chromium surface. This is because the amorphous polyethylene did not produce stable covalent bonds with the chromium plate and did not produce a large mechanical occlusion, so the polyethylene chains moved a smaller distance. When it has friction effect with rough surface, the moving distance of amorphous polyethylene chain increases with the increase of friction time and increases with the increase of the height of rough peak, which indicates that the atom movement of amorphous polyethylene is more intense when it is in contact and friction with the rough surface, so that the atoms inside the amorphous polyethylene collide, which will lead to the friction temperature increase.

Fig. 3

Movements of amorphous polyethylene chain fragments during friction of amorphous polyethylene with different coarse peaked high chromium plates (P = 1 GPa, V = 1 Å/ps). (a) Friction process, (b) Displacement change.

Fig. 4

Strain cloud of amorphous polyethylene during friction with chromium plates of different roughness peak heights (Amorphous polyethylene) (P = 1 GPa, V = 1 Å/ps, t = 150 ps).  (a) 0 Å, (b) 4 Å, (c) 6 Å.

To observe the sliding friction effect of different roughness peaks on amorphous polyethylene more intuitively, the shear strains of three different models were analyzed, as shown in Fig. 4. It was found that the deformation region of amorphous polyethylene does not continue to increase with friction time, but rather a shear-slip interface is formed in the top layer, and the amorphous polyethylene with a smooth surface has the smallest thickness of the shear-slip layer, and therefore the amorphous polyethylene is subjected to less wear. During the friction of amorphous polyethylene against a rough surface, the formation of a shear slip layer is due to the slip behavior of the molecular chains under shear force. The shear slip layer appears near the friction interface and manifests itself as a slip of molecular chains in a localized region, resulting in a continuous slip interface. The thickness and stability of the shear slip layer are influenced by the surface roughness and loading parameters. Convex summits on rough surfaces increase the localized pressure at the friction interface, leading to more significant formation of shear slip layers. The formation of a slip layer helps to reduce friction force as it reduces direct contact and entanglement between molecular chains. During friction, molecular chain interactions within the slip layer lead to a localized increase in friction temperature, which in turn accelerates plastic deformation damage to the material. The thickness of the shear slip layer increases as the height of the roughness peak increases, which corresponds to the distance traveled by the amorphous polyethylene chains in Fig. 3. This shows that with the increase of the roughness peak height of chromium plate, more amorphous polyethylene chains move, and then the wear of amorphous polyethylene is intensified.

Friction wear properties

Friction force

To analyze the effect of different loads on the friction force, the friction force (F_f) was calculated for different loads. F_f is quantitatively analyzed by calculating the sum of the forces along the x-direction for all the atoms in the rigid layer on the top of the chromium plate^20,33. It was found that the friction force is divided into two phases, phase I is the violent oscillation phase and phase II is the stabilization phase. The friction force curve oscillates violently at the initial stage and then fluctuates steadily and takes on a jagged shape. In the early stage of friction, when the amorphous polyethylene chain is in contact with the surface of the chromium plate, due to the disordered arrangement of the molecular chain and the mechanical interlocking effect of the rough peaks, violent entanglement and collision between the molecular chains occurs. This interaction causes the friction force to oscillate violently. When the amorphous polyethylene chain contacts with the rough peak of the chromium plate, the molecular chain needs to overcome the large van der Waals force and entanglement force to slip, which leads to a large peak of the friction force in the initial stage, so that the friction force fluctuates violently in a short time. With the friction, the system formed a dynamic equilibrium state, that is, the molecular chain in the rough peaks between the continuous occurrence of “migration-detachment-migration” cyclic process, the movement of molecular chain becomes more organized. The fluctuation range of friction force decreases and enters the stable friction stage. At this time, the movement of amorphous polyethylene chain is mainly manifested as localized slip along the sliding direction, and the entanglement between molecular chains is weakened, but there still exists a certain interaction, resulting in friction fluctuation within a small range, and this cyclic action leads to an irregular jagged change in the overall friction force.

Fig. 5

(a–c) Friction force variations for three models of 0 Å, 4 Å and 6 Å under different normal loads, (d) Average friction force variations under different normal loads. (e–g) Friction force variation of three models of 0 Å, 4 Å and 6 Å under different sliding velocities, (h) Average friction force variation at different sliding velocities.

Through Fig. 5a–d, it is found that the friction force increases gradually with the increase of load, and the effect of load on the friction force is larger, which is consistent with the classical tribological theory. The increase in normal load means that the contact pressure is also increasing, the contact between the bottom amorphous polyethylene and the chromium plate is closer, the number of contact atoms on the friction surface increases, the interaction force between the two increases, and the frictional resistance increases, leading to an increase in friction force as well. The variation of friction at different speeds was then analyzed, as shown in Fig. 5e–h. The results show that similar to the variation of friction with time for different loads, the friction increases with increasing speed, but the variation is small. This is due to the fact that under the same load, the amorphous polyethylene chain, at the initial stage, moves violently as the sliding speed increases, and the amorphous polyethylene chain does not have enough time to adjust, thus interacting with the chromium plate, hence the friction force is elevated. However, the friction force increases slightly with sliding speed because the amorphous polyethylene produces frequent renewal of the surface layer at high speeds, which causes the frictional resistance to reach the stabilization stage quickly.

Fig. 6

Sliding friction process of amorphous polyethylene with chromium plates of different roughness peak heights (P = 1 GPa, V = 1 Å/ps).

To analyze the effect of contact surfaces with different roughness peak heights on friction force, the friction force calculations were carried out for three kinds of chromium plates with roughness peak heights at the same speed with different loads, and at the same load with different speeds. Combined with Fig. 5, comparing the friction force curves of the three models under different conditions, it is found that all three show a tendency to oscillate violently in the initial stage and then tend to stabilize. The higher the height of the roughness peak, the higher the average friction force, and the friction force increases gradually with the increase of load and speed, which indicates that the frictional resistance is also elevated, which will lead to the increase of the wear of the bottom amorphous polyethylene.

By analyzing the three-dimensional morphology of the model with different rough peak heights during the friction process, the reasons for the difference in friction force can be more clearly understood. When the contact friction between the amorphous polyethylene chain and the chrome plate occurs, the initial phase of the friction starts to produce a violent interaction, which leads to a large peak in the friction force in the initial phase. As the friction time increases, the atoms in the top layer of amorphous polyethylene move with the chromium plate. However, due to the entanglement of the amorphous polyethylene chains, the amorphous polyethylene chains did not completely follow the continuous movement of the chromium plate, and only the amorphous polyethylene atoms in the top layer moved more vigorously. By observing Fig. 6, it can be found that amorphous polyethylene does not form a stable transfer film on the surface of the chromium plate, but forms a “migration-detachment-migration” process. The molecular chains are subjected to shear forces at the friction interface and begin to slip locally along the friction direction, resulting in migration. Then, as the polyethylene does not produce a more stable chemical bond with the surface of the chromium plate, the interaction force between the two is weak, and the molecular chain gradually breaks away from the contact with the chromium plate, thus producing detachment. The detached molecular chains will come back into contact with the rough peaks on the surface of the chrome plate as well as other areas during friction and migrate again. The whole process is repeated in the friction process, forming a cycle of “migration-detachment-migration”, resulting in plastic flow, which is consistent with the experimental results of K.G. Plumlee et al.³⁴. This migration process leads to the formation of a shear-slip interface in the top layer of amorphous polyethylene, which in turn creates a plastic flow layer at the friction contact interface, generating a plastic flow that leads to a self-lubricating effect on the amorphous polyethylene, helping to reduce the frictional resistance between the amorphous polyethylene and the metal surface, and the friction force begins to fluctuate stably.

The amorphous polyethylene did not move significantly when contact friction was generated between the amorphous polyethylene and the smooth surface. However, when the amorphous polyethylene is in contact with a rough surface, the atoms in the amorphous polyethylene follow the chromium plate in a violent motion, producing significant plastic flow. This is due to the fact that when the amorphous polyethylene is in contact with the rough peaks of friction, the entanglement of the amorphous polyethylene chains creates a resistance to the chromium plate, and thus this results in the friction on the rough surface being much greater than on the smooth surface. As the height of the roughness peak increases, the thicker the amorphous polyethylene plastic flow layer is (e.g., Fig. 6), indicating that the amorphous polyethylene is better embedded in the surface of the chromium plate, which generates more entanglements and collisions with the chromium plate, which in turn leads to higher friction force. In the application of hydraulic bearings and sealing rings, amorphous polyethylene is often in contact with the metal surface. If the metal surface is too rough, it will lead to a significant increase in friction, thereby increasing the start-up and operation resistance of the equipment. This phenomenon is particularly obvious under high load conditions. For example, in heavy-duty hydraulic equipment, rough surfaces may lead to increased energy consumption of the equipment, and even cause local overheating and material failure. By optimizing the surface roughness of the metal, the friction force can be significantly reduced, thereby improving the operating efficiency and reliability of the equipment. The results show that the friction of smooth surface is less than that of rough surface, so the metal matching surface should be selected reasonably in the design. In addition, by adjusting the normal load (e.g., by optimizing the structural design of the equipment), the friction force can be further reduced and the service life of the equipment can be prolonged.

Friction temperature

The average temperature of the amorphous polyethylene in the stable friction phase was calculated since the variation of the temperature during friction between the chromium plate and the amorphous polyethylene can significantly affect the friction properties. According to the energy dissipation theory of atomic-scale friction proposed by Hu³⁵, most of the friction work is converted into heat, which indicates that the change of temperature during friction is actually a form of energy conversion^36,37. In this section, the friction temperature of the Newtonian layer of amorphous polyethylene is analyzed for the stable friction phase, and the average friction temperature of the Newtonian layer of amorphous polyethylene is calculated by the relationship between the average temperature of the atoms and the average kinetic energy^11,36,38,39. Where T is the average temperature, E_k is the kinetic energy of each atom, and k_B is the Boltzmann constant. E_k is obtained from the mass and velocity of the atoms, m is the mass of each atom, v_i and v are the velocity of the ith atom and the velocity of the center of mass, respectively, and N is the total number of atoms. The formula is given below:

$$E_{k} = \frac{1}{{2N}}\sum\limits_{{i = 1}}^{N} {m\left( {v_{i} - v} \right)} ^{2}$$

(2)

$$T=\frac{{2{E_k}}}{{3{k_B}}}$$

(3)

Fig. 7

Variation of average friction temperature and average kinetic energy for different normal loads (P = 1, 2, 3, 4, 5 GPa, V = 1 Å/ps) and different sliding velocities (V = 1, 1.5, 2, 2.5, 3 Å/ps, P = 1 GPa). (a) Different normal loads, (b) Different sliding velocities.

Fig. 8

Variation of RDF values of amorphous polyethylene C-C bonds when different normal loads are applied to chromium plates with different rough peak heights (P = 1, 2, 3, 4, 5 GPa, V = 1 Å/ps). (a) Unapplied load, (b) 0 Å, (c) 4 Å, (d) 6 Å.

It is shown that the friction temperature of amorphous polyethylene increases with increasing normal load and velocity as shown in Fig. 7. The radial distribution function (RDF) is a key parameter for analyzing the spatial distribution of particles and is a direct method for studying interatomic interactions⁴⁰. As shown in Fig. 8, the peak RDF of the carbon-carbon bond (C-C) is 1.54 Å. This value is consistent with the C-C bond length of amorphous polyethylene. Further analysis reveals that the peak RDF of the C-C bond gradually decreases with increasing normal load, leading to the weakening of the intermolecular force of the C-C bond, which reduces the stability of the amorphous polyethylene chain. In the process of friction, this change causes the movement of atoms in the amorphous polyethylene chain to become more intense, and the extrusion collision between atoms occurs, which leads to the rise of the friction temperature. By observing the average temperature change and average kinetic energy change for different load and velocity conditions in Fig. 7, it can be found that the change in velocity has a more significant effect on the temperature. This is due to the fact that the change in sliding velocity significantly affects the average kinetic energy, which gradually increases as the sliding velocity increases. According to the atomic-scale energy dissipation theory, most of the kinetic energy is converted in the form of heat and the friction temperature increases. Therefore, adjusting the sliding speed can effectively control the temperature during the friction process.

By observing Fig. 7, it can be seen that the average friction temperature of the amorphous polyethylene increases as the height of the roughness peak of the chromium plate increases. When friction is performed on a smooth surface, the range of temperature changes is small. This is because the temperature change originates mainly from the movement of atoms within the amorphous polyethylene, and the more violent the movement of the atoms, the higher the temperature. The top atoms of the amorphous polyethylene have not formed stable covalent bonds with the chromium atoms, so the movement of the atoms of the amorphous polyethylene is through the action of the rough peaks at the bottom of the chromium plate, which causes the displacement of the cross-linked amorphous polyethylene. Therefore, the movement of atoms on a smooth surface is smaller, resulting in a smaller range of temperature changes. The average friction temperature increases gradually with increasing load and velocity when the roughness peak heights of the chromium plates are 4 Å and 6 Å. The average friction temperature of the chromium plates increases gradually with increasing load and velocity. This is due to the increased frictional resistance on the surface of the rough chromium plate, which is able to drive more amorphous polyethylene chains to move. The results show that the friction temperature of rough surfaces is generally higher than that of smooth surfaces, and the increase in the height of the roughness peaks of the chromium plate contributes to a more plastic flow of the amorphous polyethylene, which in turn exacerbates the wear of the amorphous polyethylene.

Fig. 9

Variation of plastic flow layer thickness for different normal loads (P = 1, 2, 3, 4, 5 GPa, V = 1 Å/ps) and different sliding velocities (V = 1, 1.5, 2, 2.5, 3 Å/ps, P = 1 GPa). (a) Different normal loads (b) Different sliding velocities.

During the friction process between amorphous polyethylene and chromium plate, the plastic flow between molecular chains is the key factor affecting the friction performance. It is found that with the increase of normal load, the contact between the amorphous polyethylene chain and the surface of the chromium plate is closer, which makes it subject to greater shear action. However, due to the increase in load, the polyethylene molecular chain is subjected to greater extrusion deformation and entanglement, and the entanglement of atoms will cause the strength of more molecular chains to decrease, which in turn leads to a rise in the strength of the coupling between molecular chains and a decrease in the stability of the C-C bond, which will lead to the intensification of the wear of the atoms as shown in Fig. 8. According to the simulation results, when the roughness is low, the migration behavior of the polyethylene chain is relatively stable, the friction contact is relatively simple, and the fluctuation of the friction resistance is small, so the thickness of the plastic flow layer changes more smoothly. With the increase of the height of the rough peak, the non-uniformity of the friction contact is enhanced, and the chromium plate and more polyethylene molecular chains migrate and separate on the interface. As the height of the rough peak increases to 6 Å, the thickness of the plastic flow layer increases significantly, which indicates that more atoms participate in the cycle of “migration-detachment-migration”, resulting in a positive correlation between the fluctuation of the friction force and the change of the height of the rough peak.

When the height of the rough peak is 6 Å and the sliding speed is 1 Å / ps, the normal load increases from 1 GPa to 5 GPa, the thickness of the plastic flow layer increases from 10 Å to 16 Å, and the thickness of the plastic flow layer increases by about 60%, which leads to the aggravation of atomic wear, as shown in Fig. 9. At the same time, the sliding speed also has a certain effect on the strength of the chain segments, with the increase of the sliding speed, the kinetic energy of the atoms is enhanced, which indicates that a large number of atomic entanglements occur between the molecular chains, and the strength of the coupling interaction between the molecular chains is increased, which leads to the aggravation of atomic wear. According to the simulation results, the amorphous polyethylene chains have enough time to regulate and rearrange when the sliding speed is low, the atomic migration frequency is small, and the self-lubrication effect is better. When the height of the roughness peak is 6 Å and the normal load is 1 GPa, the thickness of the plastic flow layer increases by about 70% with the increase of the sliding velocity to 3 Å/ps, and the frequency of “migration-detachment-migration” of atoms as well as the thickness of the plastic flow layer increase significantly. The thermal effect under high-speed sliding may lead to large plastic deformation in some areas of the polyethylene chain, thereby enhancing the plastic flow during the migration process and reducing the friction resistance, which is also one of the reasons for the small friction fluctuation, as shown in Fig. 5 (e-g). In sealing systems, friction between the metal and the sealing liner generates a lot of heat. If the mating surfaces are too rough, the friction temperature rises significantly, leading to severe localized softening or plastic deformation of the sealing liner material surface, which reduces the sealing performance, especially in the case of frequent friction at high speeds under heavy loads. According to the atomic-scale energy dissipation theory, most of the kinetic energy is converted in the form of heat. The MD simulation results show that under the condition of high speed and heavy load, a large amount of kinetic energy will be generated inside the amorphous polyethylene, resulting in a large amount of heat, and the friction temperature will increase, which will accelerate the wear of the polyethylene material and even lead to the failure of the sealing system. By optimizing the surface roughness of the metal mating surface (e.g. through precision machining or coating technology), the generation of heat can be effectively reduced, thereby improving the stability and safety of the sealing system.

Atomic wear

In the friction process between chromium plates and amorphous polyethylene, the wear occurs mainly on the amorphous polyethylene substrate, and to measure the degree of atomic wear during the friction process, the number of atoms worn (Q) of the amorphous polyethylene for the three models at different loads and different velocities has been calculated. Since material wear can be defined as plastic damage⁴¹, it includes not only material removal but also plastic flow. Especially at the nanoscale, atomic wear is not entirely accurate when it is defined only as the removal of material. Recently, some authors^31,42,43,44 have measured atomic wear by calculating the change in displacement of the worn atoms, an approach that avoids the above effects to some extent. In this study, the wear of amorphous polyethylene atoms was evaluated based on the atomic displacement method, and since the polyethylene backbone is connected by C-C bonds, the wear atoms were calculated using carbon atoms as an example. When the carbon atom is worn, the carbon atom will escape from its neighboring carbon atom or the C-C bond, and the escape of the atom requires a shift of at least two C-C bond lengths. Therefore, to calculate the wear atoms in the stable friction state, the carbon atom of amorphous polyethylene is set to change its atomic displacement by more than 2 times the C-C bond length (1.54 Å) compared with a certain friction time t (t > 25 ps), which is considered as a wear atom.

Fig. 10

(a) Variation of wear volume under different normal loads, (b) Variation of wear volume under different sliding velocities.

It can be observed from Fig. 10 that the overall atomic wear tends to increase with the increase of load and velocity, indicating that load and velocity have some influence on atomic wear. By observing the atomic wear of amorphous polyethylene under different roughness peak heights, it is found that the atomic wear during friction on different rough surfaces varies greatly, and the higher the roughness peak height of the chromium plate, the more serious the atomic wear. Therefore, the roughness peak height of the chromium plate surface has the most significant effect on the atomic wear. On smooth surfaces, amorphous polyethylene shows less wear, and atomic wear from friction of amorphous polyethylene on rough surfaces is much greater than on smooth surfaces. In addition, the wear of the amorphous polyethylene increased as the height of the roughness peak increased, suggesting that the rough friction surface caused greater migration of the amorphous polyethylene. To analyze the atomic migration of amorphous polyethylene during friction with chromium plates with different roughness peak heights, the mean square displacements (MSD) of amorphous polyethylene are calculated in this section under different normal loads and sliding velocities.

Fig. 11

(a) Variation of mean square displacement (MSD) under different normal loads, (b) Variation of mean square displacement (MSD) under different sliding velocities.

To better observe the effect of normal load (P) and sliding velocity (V) on the atomic wear, therefore, only the mean square displacements of P = 1, 3, 5 GPa, V = 1 Å/ps and V = 1, 2, 3 Å/ps, P = 1 GPa were calculated with time as shown in Fig. 11. The MSD was calculated using the following formulae^18,20,45:

$$MSD\left( t \right)=\frac{1}{N}\left( {\sum\limits_{{i=1}}^{N} {{{\left| {{r_i}\left( t \right) - {r_i}\left( {{t_0}} \right)} \right|}^2}} } \right)$$

(4)

Where N is the total number of particles in the amorphous polyethylene, $\:{r}_{i}\left({t}_{0}\right)$ is the original displacement of particle i, and $\:{r}_{i}\left(t\right)$ is the moving position of particle i. The migration of the atoms was analyzed by the change of MSD values⁴⁶. During the initial phase of friction, some of the atoms of the polyethylene molecular chain will start to move in the direction of the molecular chain as a result of friction, with the atoms occurring mainly in the friction contact region. As the friction process progresses, the atoms of the polyethylene chain migrate along the direction of the chain, and more chain segments will participate in the migration, resulting in an increase in the mobility of the polyethylene material. Due to the local stretching and plastic deformation of the migrated molecular chains, more atoms are worn out. And the migrated atoms will convert some of the mechanical energy into heat energy, resulting in an increase in the temperature of the friction interface. With the increase of load and sliding speed, the friction temperature increases, and the plastic deformation and fluidity of polyethylene increase, which makes the material more prone to wear.

The larger the MSD value is, the greater the mobility of amorphous polyethylene and the farther the atoms move, thus aggravating the atomic wear of amorphous polyethylene²⁰. As can be seen in Fig. 11, the atomic mobility of the amorphous polyethylene changes less when rubbing on the smooth chromium plate surface, which corresponds to the smaller atomic wear in Fig. 10. The bumps on the rough surface cause tensile deformation of the polyethylene chain at the point of contact, and the atoms within the chain begin to move in the sliding direction, as shown in Fig. 3. Due to the entanglement of the molecular chain, the repeated contact between the rough peak and the amorphous polyethylene will cause the atoms in the contact area to be continuously subjected to the shear force, and the amorphous polyethylene will be detached. This “migration-detachment-migration” phenomenon becomes more pronounced as the height of the roughness peak increases. During friction, rough surfaces cause more atoms to be involved in friction by increasing the number of surface contact points, which is increased by the localized bumps (rough peaks) on rough surfaces compared to smooth surfaces. As the number of contacting atoms increases, more atoms in the polyethylene chain are exposed to the friction interface, and when the surface roughness peaks are in contact with the polyethylene surface, the interaction between the surface atoms and the polyethylene chain drives the slip of atoms within the chain, thus exacerbating the phenomenon of “migration-detachment-migration” of atoms. The results show that the higher the roughness peak height of the chromium plate, the higher the MSD value of the amorphous polyethylene, and the larger slip of the molecular chain, as shown in Fig. 4. At this time, a large kinetic energy is generated inside the polyethylene material, which is then dissipated in the form of heat, and the friction temperature gradually increases, resulting in polyethylene being more prone to wear, as shown in Fig. 7. This implies that the mobility of amorphous polyethylene increases with the height of the roughness peak on the contact surface, while intensifying the wear of polyethylene atoms. The results show that the wear of amorphous polyethylene can be effectively reduced by adjusting the height of the roughness peak on the surface of the chromium plate. Therefore, the wear performance of amorphous polyethylene can be effectively modulated by adjusting the height of the roughness peak on the surface of the chromium plate. When designing bearings or seals of polyethylene materials, if the surface roughness of the mating surface is too high, the cyclic action of the rough peak of the mating surface and polyethylene will cause more polyethylene molecular chains to be sheared, which promotes the slip in the polyethylene chain and produces fatigue wear, thus affecting the service life of the material. In the design of bearings and seals, excessive atomic migration will accelerate the heat generation and plastic deformation of materials during the friction process, and reduce the performance of components. Therefore, selecting the appropriate surface roughness height can not only reduce the friction temperature, but also effectively slow down the wear of polyethylene materials.

Angular distribution

During the friction between the chromium plate and the amorphous polyethylene, an increase in the angle of the amorphous polyethylene chains may be induced, which can lead to the untangling of the amorphous polyethylene chains⁴. One of the reasons for the higher abrasion resistance of polyethylene is due to its high degree of chain entanglement⁴⁷. Therefore, the angular variation of amorphous polyethylene chains has an important effect on its atomic wear. As migration of amorphous polyethylene chains occurs more readily when rubbing against a rough chrome plate, more amorphous polyethylene chains are untangled, which weakens the entanglement between the chains, and more atoms migrate, ultimately leading to an increase in the amount of atomic wear. Therefore, in this section, the friction process of amorphous polyethylene with a chromium plate with a rough peak height of 6 Å is analyzed in detail. For this purpose, the friction time (t) of amorphous polyethylene with a chromium plate with a rough peak height of 6 Å was extended to 200 ps, and the angular change of C-C-C bonds in amorphous polyethylene during the sliding friction was analyzed.

Fig. 12

Bond angle distribution of C-C-C under different normal loads and different sliding velocities. (a) and (d) are the bond angle distributions without applied load, (b) and (e) are the bond angle distributions for friction 25 ps, (c) and (f) are the bond angle distributions for friction 175 ps.

By analyzing Fig. 12, it can be found that the C-C-C bond angle has an angular peak of about 110° when the downward pressure and friction loads are not applied. Under the friction of different normal loads, the peak at the angle of 110° starts to decrease at the initial stage (t = 25 ps); by t = 175 ps, the peak at the angle of 110° continues to decrease and appears to be shifted to the right. As the normal load increases, the peak of the C-C-C bond angle shifts to the right more significantly. This suggests that an increase in normal load during friction increases the bending angle of the polyethylene chains, thus weakening the interchain entanglement effect and possibly leading to increased wear. On the other hand, at different sliding friction velocities, the peak at the 110° angle also decreases at the initial stage (t = 25 ps), but the angular peak does not show a significant rightward shift as the friction load increases (t = 175 ps).

In the molecular structure of amorphous polyethylene, the change of C-C-C bond angle reflects the change of molecular chain structure of polyethylene. The increase in normal load leads to a shift to the right of the peak C-C-C bond angle at which the friction process takes place, and the geometry of the chain segments changes. This is because higher normal loads increase the degree of deformation of the molecular chain segments, which affects the overall structure of the molecular chain. When the normal load increases, the deformation of the polyethylene chain segments is enhanced as the friction process proceeds and the chain’s degree of freedom increases, which makes the molecular chain less rigid and enhances the slip. As the bond angle increases, the interactions between the molecular chains are weakened and are able to deform more violently during the friction process, leading to increased friction and localized wear. In addition, changes in the C-C-C bond angles lead to adjustments in the spatial positions of the molecular chains, increasing the slip distances between the molecular chains and making the interaction forces between the molecular chains weaker, which may contribute to the weakening of the entanglement between the chain segments, and consequently increase the surface wear of the material. Relatively speaking, the increase in sliding velocity has less effect on the C-C-C bond angle. However, due to the structural change of the molecular chain, the sliding and contact frequency of the chain segments increases, and the deformation of the chain segments at the friction interface becomes more frequent. The continuous deformation and sliding of the chain segments lead to more violent collisions and extrusion between atoms in the local region, which in turn promotes the wear effect in the friction process. Therefore, the results show that the normal load is more sensitive to the change in the angle of the amorphous polyethylene chains, and the entanglement of the amorphous polyethylene chains in the friction process decreases with the increase of the normal load, which intensifies the wear.

Conclusions

In this paper, a nano-scale friction model with three different roughness peak heights was established by molecular dynamics method. The friction process of different friction models under different normal loads and sliding speeds was simulated. The contact interface morphology, plastic deformation, friction force, temperature and wear mechanism of amorphous polyethylene under different conditions were analyzed. The results show that the mechanical properties (stability, plastic deformation, etc.) and tribological properties (friction force, wear, friction temperature, etc.) of amorphous polyethylene change significantly due to the difference of atomic migration, surface contact state and C-C bond interaction under different roughness peak heights, sliding speeds and normal loads. The results of the study are as follows:

• 1. The height of the roughness peaks on the contact surface significantly affects the frictional performance of amorphous polyethylene. The primary factor influencing the movement of amorphous polyethylene chains is the entanglement between the rough peaks of the chromium substrate and the polyethylene chains. Amorphous polyethylene does not form stable chemical bonds with the chromium substrate. Instead, its surface undergoes a “migration-detachment-migration” process, producing a self-lubricating effect. At a normal load of 1 GPa and a sliding velocity of 1 Å/ps, as the height of the roughness peak increased to 6 Å, the number of atoms at the contact interface increased by 20% compared to the smooth surface, and the plastic flow layer increased from 1 Å to 6 Å, with increased slip and atomic motion of the amorphous polyethylene chains. With the increase of normal load from 1 GPa to 5 GPa, the thickness of the plastic flow layer increased from 10 Å to 16 Å, and the thickness of the plastic flow layer increased by about 60%. And the thickness of the plastic flow layer increased by 70% as the sliding velocity increased to 3 Å/ps. This leads to an enlarged shear deformation region and more severe surface wear.

• 2. Analysis of the friction properties under different operating conditions showed that the friction increased with the increase of roughness peak height, normal load and sliding speed. The friction temperature was positively correlated with the roughness peak height, and the friction interface temperature increased by about 10% as the roughness peak height increased to 6 Å for a normal load of 1 GPa and a sliding speed of 1 Å/ps. The friction temperature increases as the roughness peak height increases. The entanglement between rough chromium surfaces and amorphous polyethylene chains increases surface friction resistance. The smooth surface can limit the excessive slip of the molecular chain, reduce the plastic flow and local deformation of polyethylene, and reduce the wear caused by deformation. At the same time, the smooth surface has less heat accumulation due to the small frictional resistance, which helps to reduce temperature-induced wear. This shows that reducing the height of the surface roughness peak can reduce the friction resistance and reduce the wear. Analysis of friction temperature under steady-state conditions showed that friction temperature increases with higher normal loads and sliding velocities. Since the motion of internal atoms significantly affects friction temperature, sliding velocity has a notable impact on temperature variation, indicating that adjusting sliding velocity can effectively reduce the influence of friction temperature on wear. In addition, as the normal load increases, the RDF peak height of the C-C bond of the carbon-carbon bond decreases, and the stability of the amorphous polyethylene chain decreases, which in turn leads to increased wear of the amorphous polyethylene.

• 3. To analyze the wear mechanisms of amorphous polyethylene, the atomic displacement method was used to quantitatively describe the atomic wear of amorphous polyethylene. The study found that interface morphology plays a significant role in the wear of amorphous polyethylene. Rough surfaces exacerbate atomic wear, as the atomic migration rate (mean squared displacement, MSD) of amorphous polyethylene increases with roughness peak height, leading to more severe wear. Additionally, since wear is more pronounced on rough surfaces, the distribution of C-C-C bond angles during friction with rough surfaces was investigated. It was found that changes in normal load significantly influence the bond angle distribution. As the normal load increases, some of the peak C-C-C bond angles begin to shift from 110° to 115°, the entanglement effect begins to weaken, and wear increases.