A molecular dynamics study on water lubrication of amorphous cotton fiber sliding against chromium

Cellulose is a linear polysaccharide of β-D- pyran glucose-group linked by 1–4-β- glycosidic bonds, and two glucose units forming a celllobiose which is the repeat unit of cellulose. Cellulose includes crystalline region which is arranged in a highly ordered structure and amorphous region which is disordered [8, 27, 50, 51] as shown in figure 1. The properties of crystalline region and amorphous region are very different and need to be studied separately, in this paper, amorphous cellulose is taken as the object. The amorphous cellulose with degrees of polymerization (DP) of 30 were constructed, and packed 3 chains in the cell with a density of 1.5 g cm⁻³ [52] in the simulation model as shown in figure 2.

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The simulation model has two Cr layers with 300 water molecules and the ACF are placed between them as show in figure 2. The two Cr layers have the same size of 34.6 Å × 34.6 Å × 23.1 Å, and each of layer has 2304 Cr atoms. The model includes three layers, and the outermost layers are rigid layers which consists of Rigid Fixed Layer (RFL) in the bottom and Rigid Moving Layer (RML) in the top along the z-direction. The geometry of Cr atoms in the rigid layers keep unchanged during the simulation. In addition, the RFL is fixed and the RML is used to undertake the loading to the simulation model along the z-direction and the sliding velocity along the x-direction. Adjacent to the rigid layers are the thermostatic layers, where the temperature is kept constant at 300 K by rescaling their atom velocity. Except for the rigid layers and the thermostatic layers, the rest of atoms are defined as Newtonian layer consists of Cr atoms, water molecules and the ACF. The atoms in the Newtonian layer can move freely on the basis of Newton's second law of motion. Before the MD simulation starts, five anneal processes were performed under constant temperature and constant volume (NVT ensemble) from 300 K to 500 K with a rate of 4 K ps⁻¹ and decreases to 300 K with a high rate of 80 K ps⁻¹ to further equilibrate the simulation model.

The friction simulation consists of three stages. In the first stage, the relaxation at a constant temperature of 300 K is followed to eliminate the internal stress in the model and promote the movement of water molecules to distribute them randomly. In the second stage, applies the loading (F_n) to the RML along the z-direction by adding a uniform force to the Cr atoms. In the last, a sliding velocity (v_x) along the x-direction is applied to the RML to achieve a relative sliding between Cr layer and ACF. Boundary conditions are all periodic in the x and y-directions to solve the problem of the boundary effect of ACF on the Cr substrate, while aperiodic boundary is taken in the z-direction. The timestep of simulation is 0.25 fs, and the simulation time of three stages are 100 ps, 200 ps and 100 ps to ensure them becoming stable. The two considered factors that v_x is set as 1 Å/ps, 2 Å/ps, 3 Å/ps, 4 Å ps⁻¹ and 5 Å ps⁻¹ when the F_n is 5 GPa and F_n is set as 1 GPa, 3 GPa and 5 GPa when the v_x is 1 Å/ps. Hence, there are 7 simulations were performed in the study.

All the simulations were done by the large-scale atomic/molecular massively parallel simulator (LAMMPS) which is an open-source coding for MD simulation [53]. The interactions among atoms are evaluated by the reactive force field (ReaxFF) developed by Shin et al [54] which is agreement with YanZhe et al [5, 6] investigated the dry friction between Cr and cotton fiber. The ReaxFF allows for bonds to break and form during the simulation and the connectivity is determined by bond orders calculated from interatomic distances. The overall system energy E_system in ReaxFF consists of various partial energy terms as shown in equation (1):

$$\begin{eqnarray}&&{E}_{system}={E}_{bond}+{E}_{under}+{E}_{over}+{E}_{val}+{E}_{pen}+{E}_{tors}+{E}_{conj}+{E}_{vdWaals}+{E}_{Coulomb}\end{eqnarray} \tag{ 1 }$$

where E_bond is the covalent interaction energy, E_under and E_over are atom under/overcoordination, E_val is the bond angle interaction energy, E_pen is the compensation energy, E_tors is the dihedral torsion energy, E_conj is the bond binding energy, and E_vdWaals is the van der Waals action energy, E_Coulomb is electrostatic action energy.

The movement of water molecules between contact interfaces significantly affects the friction behavior of Cr and ACF due to they act as lubricants. The mean-squared displacement (MSD) is a significant parameter to reflect the movement of liquid which was used to study the movement of water molecules during sliding to clarify its influence on the friction mechanisms [48, 49]. The MSD of water molecules in different conditions as shown in figure 3. It is seen from figure 3(a) that the movement of water molecules along the x-direction (the sliding direction) (MSD_x ) changes significant to a high value while almost unchanged in a low value along the y-direction (MSD_y ) and the z-direction (the loading direction) (MSD_z ) during the friction process in the condition of F_n is 5 GPa and v_x is 1 Å/ps. This indicates that the total movement of water molecules (MSD_w ) is dominated by the movement along the sliding direction (MSD_x ) not than the loading direction (MSD_z ) or the other direction (MSD_y ). The MSD_w in other conditions (different F_n and v_x) are not shown because of they have the same result.

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The v_x and F_n can influence the movement of water molecules as shown in figure 3(b) and figure 3(c) which shows that the MSD_w decreases with the increase of v_x and F_n. During the sliding process, the water molecules located between the contact interfaces and distributed uniformly due to the adjust movement such as translate and rotate of them with the sliding of Cr. However, the adjust movement of water molecules is slowly relative to the v_x and fail to adjust sufficiently at a large v_x, then affects the distribution of water molecules on the contact surface. Hence, the large sliding velocity inhibits the movement of water molecules and decreases their lubrication behavior. The viscosity of liquids confined between two objects increases as the pressure increases, so that the viscosity of water molecules located between the contact interfaces increased at a large F_n and affected their movement and distribution. Therefore, a large loading increases the viscosity of water molecules and decreases their lubrication behavior. For these reasons, a large sliding velocity and a large loading affect the activities of water molecules induce to the decrease of MSD_w .

The different v_x and F_n affect the COF of contact interfaces as shown in figures 4 and 5. In all the conditions, the COF and its fluctuation magnitude are quite high at the beginning of sliding (stage I:S_I) due to the fact that the water molecules located between contact interfaces stay static and need some time to flow to act as lubricants. That means the S_I is a non-stable lubricated friction state and the COF is large and changes significantly. The water molecules start to act as lubricants which reduce the friction of contact interfaces since their movement tends to stabilize with the sliding going on, and then enters a stable lubricated friction state (stage II:S_II). The COF changes smoothly and its fluctuation magnitude within a small range during the S_II process and using its average value to compare the effect of water lubrication in the condition.

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In the condition of F_n is 5 GPa, the v_x (1 ∼ 5 Å ps⁻¹) affects the COF as shown in figures 4(a)–(e). The sliding time of S_I increases with v_x since the large v_x inhibits the movement of water molecules and requires more time to complete lubrication. It can be seen from figure 4(f) that the average COF also increase with v_x in the S_II process, it is because that the lubrication of water molecules decreases with v_x resulted from the large v_x inhibits their movement. However, the change in the average COF becomes progressively smaller with the increase of v_x due to the fact that its ability to inhibit the movement of water molecules decreases, which is consistent with the trend of MSD_w shown in figure 3(b). Under given v_x (1 Å ps⁻¹), the different F_n affects the COF shown in figures 5(a)–(c). As shown in figure 3(c), the water molecules are more easy to get the stabilization because of their movement activity decrease at a large F_n which is caused by their viscosity increase, so the sliding time of S_I decreases with F_n. In addition, the lubrication of water molecules decrease affected by their viscosity induce to the increase of average COF while decrease of its fluctuation magnitude as shown in figure 5(d).

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After a period of friction between Cr and ACF, the chemical changes take place at the contact surfaces which is generated by oxygen atoms in the ACF and Cr atoms produce Cr=O bonds to produce Cr₂O₃ and induce to the damage to Cr [5]. The Cr=O bonds are manifestations of damage on the surface of Cr substrates, so the number of Cr=O bonds was calculated to analyze the damage to Cr during friction process. The formation and breaking of Cr=O bonds are evaluated according a cutoff length of 1.96 Å, and the number of Cr=O bonds generated by oxygen atoms in the ACF with Cr atoms in the upper layer is NU and the number generated with lower layer is NL. The NU and NL in the condition of v_x is 1 Å/ps and F_n is 5 GPa are used to compare the damage to Cr by friction with and without water molecules as shown in figure 6. It is noted that NU is much smaller than NL since water molecules act as lubricants protect Cr and decrease its damage. During the friction with lubrication of water molecules, the ACF and Cr are not contact directly because of the lubricants separated them and formed a lubricating film between them. In the situation, the sliding between contact interfaces is mainly depends on the flowing of the lubricants. In the influence of water molecules act as lubricants, both the friction force between Cr and ACF and the damage to Cr are decreased which resulted in the NU is very small relative to NL. And it is contrary to what happens during friction without lubricant. To show the variation of NU and NL clearly, using their average value as shown in figure 6.

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The NU is used to analyze the damage to Cr at different v_x and F_n during water-lubricated friction as shown in figure 7. It is noted that the NU increases with v_x and F_n, and moreover, the effect of v_x is greater than F_n due to the fact that the movement of water molecules located between contact interfaces is more dependent on sliding than loading as shown in figure 3(a). In addition, the COF increased with v_x and F_n since the movement of water molecules is inhibited, and then causing more damage to Cr. But in the case of lubrication, the ACF and Cr are not contact directly with each other under the action of loading, avoiding the serious damage to Cr caused by the large friction force. Hence, the water molecules act as lubricants is an important way to protect Cr.

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