Extra low friction coefficient caused by the formation of a solid-like layer:Anew lubrication mechanism found through molecular simulation of the lubrication of MoS2 nanoslits☆

Jiahui Li,Yudan Zhu ,*,Yumeng Zhang ,Qingwei Gao ,2,Wei Zhu ,Xiaohua Lu ,Yijun Shi

1 College of Chemical Engineering,State Key Laboratory of Materials-oriented Chemical Engineering,Nanjing Tech University,Nanjing 210009,China

2 Energy Engineering,Division of Energy Science,Lule? University of Technology,Lule? 971 87,Sweden

3 Division of Machine Elements,Lule? University of Technology,Lule? 971 87,Sweden

Keywords:Molecular dynamics simulation Microstructure Molybdenum disulfide Residence time distribution

A B S T R A C T Monolayer molybdenum disulfide(MoS2)is a novel two-dimensional material that exhibits potential application in lubrication technology.In this work,molecular dynamics was used to investigate the lubrication behaviour of different polar fluid molecules(i.e.,water,methanol and decane)confined in monolayer MoS2 nanoslits.The pore width effect(i.e.,1.2,1.6 and 2.0 nm)was also evaluated.Results revealed that decane molecules exhibited good lubricating performance compared to the other two kinds of molecules.The friction coefficient followed the order of decane＜methanol＜water,and decreased evidently as the slit width increased,except for decane.Analysis of the spatial distribution and mobility of different confined fluid molecules showed that a solid-like layer was formed near the slit wall.This phenomenon led to the extra low friction coefficient of confined decane molecules.

1.Introduction

MoS2is a widely used lubricating material[1–5].The lubrication at the nanoscale becomes a topic that researchers are focused on at present,because of the urgent requirement of precision machinery and high-tech manufacturing,especially the need from emerging disciplines promoted by nanotechnologies such as nanoelectronics,nanobiology and micromechanics[6–8].As the lubrication film thickness shrinks into the nanoscale,the interactions between the confined lubricant molecules and the solid material wall have a great influence on the lubricating behaviour[9].Therefore,the application of twodimensional(2D)materials in lubrication has received great attention and many materials have been synthesized into 2D form[10–12].

Monolayer MoS2,as a novel 2D material,has great potential in various applications such as nanoelectronics,humidity and gas sensors[13–16].Monolayer MoS2is comparable to or even beyond the performance of graphene in many applications.Water flux of nanoporous monolayer MoS2was found to be 2 orders to 5 orders of magnitude higher than that of other known nanoporous membranes.MoS2pores with only Mo atoms on their edges lead to high fluxes,which are 70%greater than that of graphene nanopores[17].Liu et al.also revealed that MoS2has a better performance than graphene in DNA sequencing[18].Luan and Zhou reported that the friction coefficient of bulk water on the surface of monolayer MoS2is as low as that of graphene[19].Recently,Kwac et al.demonstrated that the flow behaviour of water molecules confined in the MoS2slit is completely different from those in bulk[20].Given that the fluid molecules at the nanoscale can produce many different properties from their bulk counterpart,the fluid behaviour within the MoS2confinement becomes a focused topic in the academe.On the other hand,MoS2is widely used as an additive for different kinds of lubricants which in most cases involved the interface relative movement between MoS2and liquids[1,21–23],which suggests that the type of liquids has a significant influence on the lubricating properties of MoS2.It will be very interesting to study the lubrication mechanism of different liquids on the MoS2surface.To get a deep understanding,investigation at the molecular level is essential.Therefore,it is necessary to understand the confined behaviors of different liquids near the MoS2interface under shear and to investigate the friction reduction mechanism.

Many possible mechanisms for lubrication at the nanoscale are available,as proposed by different researchers.One of the most convincing mechanisms is related to the microstructure variation of confined lubricant molecules,such as ionic hydration[24],hydrogen bonding[25]and unique lamellar structure[26].Klein and Kumacheva demonstrated that the effective viscosity can increase by 7 orders of magnitude when a simple fluid is confined in the gap with several molecular thicknesses[27].In addition,they conjectured that the fluid can undergo a fluid–solid phase change,which affects the friction coefficient[28,29].However,investigating the molecular-level behaviour is extremely difficult.

Currently,molecular simulation is an effective method to study the lubrication under nanoscale.One of the superiorities of molecular simulation is that it can provide microstructure variations of nanoconfined fluids under shear and other extreme conditions[30,31].Christoph et al.found that the shear regimes of 2-methacryloyloxyethyl phosphorylcholine monolayers in water were dominated by ionic hydration through molecular simulation[32].He et al.demonstrated that there was a strong correlation between the number of hydration water molecules and the friction coefficient under molecular simulation under shear[33].The focus of the present work is to establish the relationship between the microstructure variation of fluid molecules under confinement and their lubrication performance.

The aim of this work was to study the lubrication behaviour of different fluid molecules(i.e.,water,methanol,and decane)confined in MoS2nanoslits.We focused on answering these following questions:(i)What is the effect of confined fluid molecule polarity on lubrication?(ii)How does the friction coefficient vary with the increase of the monolayer MoS2gap width?(iii)Will the molecular structure of fluids change under nanoconfinement,and will that change result in any change in lubrication?

2.Simulation Details

A nanoslit was constructed by two monolayers of MoS2.The fluid molecules were confined inside the slit gap,as shown in Fig.1.The upper plate moved along the Y-axis at a constant velocity of 50 m·s-1.The plate size of each MoS2is 4.43 nm×3.11 nm×0.32 nm(X×Y×Z).Three-dimensional periodic boundary condition was adopted in the simulation box.Two vacuum layers of 1 nm were left in the outside regions of the slit to ensure no interaction between the slit wall and its mirror will occur.

Three representative fluid molecules(i.e.,water,methanol and decane)were selected in this work.Polarities of these three fluids were ordered as follows:decane＜methanol＜water.Moreover,considerable studies demonstrated that the fluid molecules often exhibit unique behaviour,compared with their bulk counterpart,when the pore size is below 2 nm[26,34,35].For this reason,the gap width effect was also evaluated in the present study,and three different slit widths below 2 nm(i.e.,1.2,1.6 and 2.0 nm)were chosen.

All molecular dynamic simulations were carried out by using the LAMMPS package[36].SPC/E model was utilized for the water molecules[37].OPLS-AA force field parameters were used to describe methanol and decane molecules[38].For MoS2,the force field developed by Varshney et al.was used[39].This force field reproduces the crystal structure and experimental vibrational spectra of MoS2.Li et al.usedthis force field to study nanoporous MoS2filter for water desalination[40].Detailed force field parameters used in this work are shown in Table 1.

Table 1Force field parameters used in the simulation(1 kcal=4184 J)

Interactions for all molecules have been treated as a combination of Lennard–Jones(L–J)interactions and a Coulomb term for electrostatic interactions,as follows:

εijis the energy interaction parameter,and σijis the size action parameter,followed by the Lorentz–Berthelot mixing rule:

rijis the distance between atoms,and q is the charge.

As shown in Table 2,the number of confined fluid molecules in each case is different.Slits with different gap widths can accommodate different fluid molecules under equilibrium state.Thus,we obtained the number of fluid molecules by using the equilibrium molecular dynamics method.The procedures were as follows:(i)Two MoS2plates with constant slit width were immersed in the centre of a procedure simulation box(11 nm×3.2 nm×3 nm)with a density of the bulk fluid.The slit was placed along the X and Y-axes.(ii)A molecular dynamics simulation was performed in an isobaric–isothermal ensemble.The system was maintained at a constant temperature of 300 K,and the pressure was setat106Pa to avoid the appearance of nanobubbles.After the energy minimization,1 ns molecular dynamics was carried out with an integral step of 1.0 fs to obtain the equilibrium configuration(the number of fluid molecules in the slit is stable).(iii)Afterwards,the fluid molecules outside the slit were deleted,and the ones confined inside the slit were retained.These fluid molecules inside the slit were used as the initial configuration for non-equilibrium molecular dynamics simulations.

Fig.1.Simulation model of water molecules confined in a monolayer MoS2 slit(The yellow and blue atoms represent the sulfur and molybdenum atoms in MoS2 molecules,respectively.The red and white atoms represent the oxygen and hydrogen atoms in water molecules,respectively).The black line represents the periodic simulation box.

Table 2The number of fluid molecules confined in slits with different widths

The details of the non-equilibrium molecular dynamics simulation were as follows.As shown in Fig.1,the size of the simulation box with three-dimensional periodic boundary conditions was 4.45 nm×3.13 nm×2.34 nm(X×Y×Z)(the size of Z-direction was changed with the gap width).The upper plate moved along the Y-direction at a constant velocity of 50 m·s-1.The temperature in the system was controlled by a Nosé–Hoover thermostat[41],and the simulated temperature was maintained at 300 K.The particle–particle particle–mesh method[42]was used to calculate the long-range electrostatic interaction,with a cut-off for a real space of 1.0 nm.The Ewald method was used for full electrostatic interactions and a cut-off distance of 1.0 nm was used to calculate the short-range van der Waals interactions.The force field parameters of the system were the same as Table 1.To investigate the influence of fluid polarity on the fluid molecule behaviour under shear,each case was performed for 13 ns in the canonical(NVT)ensemble with 1.0 fs time step.The data was saved to ensure the friction coefficient remains constant during the production stage every 1.0 ps.The last 3.0 ns trajectory was used for analysis.

3.Results and Discussions

3.1.Friction coefficient analysis

Friction coefficients of different confined fluid molecules for the slits with different gap widths were calculated to evaluate the polarity effect on the lubrication ability of confined fluid molecules.The friction coefficient was obtained by dividing the frictional force by the normal force.Frictional force is the sum of all forces exerted on the bottom wall in the lateral direction(the Y-direction),whereas the normal force is those in the normal direction(the Z-direction).Similar method was adopted to study nanoscale friction for alkyl monolayers terminated with--CH3and--OH on Si(1 1 1)in the presence of water molecules[43].

As shown in Fig.2,the friction coefficient increases as the polarity of the fluid increases(i.e.,decane＜methanol＜water)for all studied slit widths.Cheng et al.[44]used different polarity solvents(i.e.,hexadecane＜toluene＜chloroform＜dichloromethane)to investigate the lubrication properties on silicon,and their results also indicated that the higher polarity shows a larger friction coefficient.This observation indicated that decane molecules have the best lubrication performance.For water and methanol molecules,the friction coefficient decreases evidently as the slit width increases.In our previous study[45],similar friction reduction with the decrease in slit gap size was also found in the investigation of water molecules confined in the TiO2slits.However,the situation for decane is totally different.The friction coefficient of decane increases with the increase of slit width;however,the amplitude of variation is so small that it can be negligible compared with the two other fluids.The lowest friction coefficient is only 0.0106 for decane molecules.

Fig.2.The friction coefficient of water,methanol and decane molecules confined in the MoS2 slits with different slit widths under shear.The labels of“d12”,“d16”and “d20”indicate that the slit widths are 1.2 nm,1.6 nm and 2.0 nm,respectively.The red,olive and blue represent water,methanol and decane molecules,respectively.

For the same type of fluid molecules,the change of slit width induced a maximum of 7-fold change in the friction coefficient.However,for the same slit width of the different fluid molecules,the change of friction coefficient can reach up to 81-fold.These phenomena suggest that the polarity of lubricant has a dominant role in the confined lubrication.In the following sections,the analysis of the microstructure of different confined fluid molecules was focused to investigate the underlying mechanism of the low friction coefficient of decane at the nanoscale.As lit with a width of1.2 nm was selected for the in-depth investigation because the difference of the friction coefficient among the three fluids in such width is the most evident.

3.2.Spatial distribution of nanoconfined fluid molecules

Different density profiles were adopted to reflect the spatial distribution of different fluid molecules confined in the nanoslit.For water molecules,the density profile of oxygen atom was used for characterization because the oxygen atom is slightly near the water molecular mass centre.For the methanol molecules,the density profile of oxygen atom and carbon atom was adopted to characterize the spatial distribution of their polar and non-polar groups,respectively.For the decane molecules,the density profiles of a methyl group and methylene group were adopted to get a better reflection of the spatial configuration of the chain molecule.The density profiles of three fluid molecules for the slit with 1.2 nm width along the Z-direction under shear are shown in Fig.3.

Fig.3(a)shows that the water molecules in the slit are symmetrically distributing with respect to the central axis and form three peaks.This phenomenon indicates that the adjacent region of the wall could form a water layer,which leads to a weak concentrated distribution of water molecules in the central axis position.One pronounced peak at 0.31 nm that clearly signifies the formation of one layer of water molecules(Fig.3(a)).Molecular simulation of water in graphene slits showed that the maximum peak distance from the surface is 0.325 nm[46].

As shown in Fig.3(b),methanol molecules mainly form two peaks in the slit.The density in the middle position is 1,indicating that the density of methanol molecules in the central region is similar to that of methanol molecules in bulk.The height of the first layer of methanol molecules is higher than that of water molecules,indicating that the methanol molecules are restricted more tightly than water molecules.The peak positions of carbon atom are similar to the positions of oxygen atom near MoS2walls,which are 0.33 nm and 0.32 nm respectively.These results show that most methanol molecules confined in the slit are nearly parallel to the slit wall.

Fig.3.Left:Density profiles of fluid molecules for slits with 1.2 nm width along the Z-direction.ρ0 represents the density of bulk.(a)The oxygen atom density is used as the density distribution of water molecules,(b)methanol and(c)decane.Right:X–Z direction snapshot of(a)water(the red and white atoms represent the oxygen and hydrogen atoms in water molecules,respectively);(b)methanol(the dark blue,olive green and white atoms represent the carbon,oxygen and hydrogen atoms in methanol molecules,respectively);and(c)decane(the light blue and white atoms represent the carbon and hydrogen atoms in decane molecules,respectively)molecules confined in a 1.2 nm MoS2 slit.

In Fig.3(c),two obvious peaks symmetrically distributed in the density profiles are observed.The peak positions of methyl groups are almost the same as the peak position of methylene groups.These observations can reflect the preferential orientations of decane molecules.These observations also indicate that the methyl atom and methylene atom are located parallel to the MoS2wall.The peak distances from the surface are 0.35 nm for methyl and 0.34 nm for methylene.Thus,higher polarity of fluid molecules could result in less pronounced density distribution peaks.The peaks of decane molecules are the most pronounced.Moreover,in the central region of the slit,the values of the density of decane become 0,which is different from the other two types of fluid molecules.This observation suggests the presence of only two layers of decane molecules in the slit.

The snapshot of different molecules confined in 1.2 nm MoS2slits is shown in Fig.3.The sharpness of the density peaks indicates more ordered molecular layer formed near the slit wall.The sharpest peaks represent the most uniform layers in contact with the MoS2surfaces.The sequence of uniform degree is decane＞methanol＞water.Terrones et al.investigated the behaviour of a range of polar and non-polar organic fluids confined in 2D graphene nanochannels.They observed similar results,i.e.,the structural order was gradually decreasing towards the centre of the slit gap[47].

To understand the microstructure variation of confined fluid molecules,the mobility of fluid molecules along X-direction and Y-direction was further analysed.

3.3.The mobility of the confined fluid molecules along the sliding direction of the wall(Y-direction)

Velocity distributions of the three fluid molecules in the 1.2 nm slit are shown in Fig.4.The confined fluid molecules exhibit pronounced velocity distribution along the slit width(Z-direction)because the velocity of upper plate moves along the Y-axis direction.The statistical method of velocity is as follows:the fluid molecules within the slit are divided into 120 layers(0.01 nm)along the Z-direction.A total of 3000 frames in the trajectory were used to analyse all the atomic velocity within the certain layer to obtain the average velocity of the layer.

As shown in Fig.4,a closer distance from the sliding wall leads to the greater velocity of the fluid molecules along the Z-direction.Combining this result to the density profiles of fluid molecules in Fig.3,we found that the first layer of decane molecules near the sliding wall can almost reach the velocity 50 m·s-1,suggesting that the decane molecules in the vicinity of the upper wall can reach the sliding velocity.On the contrary,water and methanol molecules cannot reach the sliding velocity,indicating that there are slippages between the fluid molecules and the sliding wall.These phenomena can be inferred to affinities between MoS2and fluid molecules,i.e.,decane＞methanol＞water.

Fig.4.Velocity distribution of water,methanol and decane molecules for slits with 1.2 nm width.The point represents the average velocity and the line is the fitting velocity.

Combining the peak positions derived from the spatial distribution of nanoconfined fluid molecules(Fig.3),the velocity of most water molecules in the first layer(less than around 0.47 nm away from the upper wall)reaches the sliding velocity.The velocity of decane molecules in the first layer is almost the same.For water and methanol molecules,the distances are farther away from the sliding wall,which could result in the lower velocity.The nearly same velocity of the decane molecules in the first layer indicated that the first layer of decane molecules is more stable compared with the two other kinds of fluid molecules.

Furthermore,Fig.4 also indicates that the velocity distribution fluctuates,which implies that statistical thermal motion is dominant.We tested the velocity of 200 m·s-1and,we found that the higher velocity,could lead to the smaller velocity fluctuations.

3.4.Mobility of the confined fluid molecules along the slit width direction(Z-direction)

To quantify the mobility of the confined fluid(i.e.,water,methanol and decane)molecules along the slit width direction,we calculated the residence autocorrelation function CR(t)within the first layer.Argyris et al.found that the faster the reduction of the autocorrelation function,the shorter the time that the fluid molecules remain in that particular layer[46].According to the results of spatial distribution in Fig.3,the thicknesses of the first layer of water,methanol,and decane are 0.23 nm,0.23 nm and 0.4 nm,respectively.For comparison,the residence autocorrelation function for fluid molecules in bulk was also calculated.The correlation function formula(4)is as follows:

Apparently,the confined fluid molecules in the first layer have much less mobility compared with those in the bulk.The values of residence time for different fluids in 2 ns are listed in Table 3.For water molecules,the residence time in the first layer is approximately 2.17-fold higher than that in the bulk.Mukhopadhyay et al.found that the residence time of confined water in porous alumina is larger than that of the bulk water by neutron-scattering study[48].Although the system is different,these findings can,to some extent,supportour simulation result.For methanol molecules,the residence time in the first layer is about 3.14-fold higher than that in the bulk.The results demonstrate that the mobility of the confined water molecules is greater than that of methanol molecules.Surprisingly,the difference in residence time between the confined decane molecules and their bulk counterpart is dramatic.The calculated residence time of decane molecules in the first layer near the MoS2surfaces is 2.0 ns,which indicates that the values of CR(t)remain unchanged at 1 with time evolution.We also extended the simulation to calculate the residence time and found that the decane molecules in the first layer do not leave the MoS2surface even in 13 ns simulation.Therefore,we believe that the residence time of decane molecules in the first layer near the wall surfaces is more than 13 ns.This phenomenon suggests that the first layer of adsorbed decane molecules prefer to stay near the solid wall and its mobility is lower compared with those of confined methanol and water molecules(Fig.5).

Recently,the molecular friction behaviour of n-dodecane with added stearic acid at an interface was studied using sum frequencygeneration(SFG)spectroscopy and a tribometer.Watanabe et al.observed the n-dodecane on a stearic acid adsorption film is highly aligned.Moreover,from the sliding direction dependence of the SFG measurements,the molecular orientation of n-dodecane was deduced,that was,n-dodecane on stearic acid adsorption films orients parallel to the sliding direction.Thus,they speculated that the adsorbed stearic acid film behaved as a solid-like film and might lead to the friction reduction[49].In this work,we investigated the lubricating properties of nanoconfined fluid molecules in monolayer MoS2by molecular dynamics simulations.Our result demonstrates at the molecular scale the formation of a solid-like layer towards extra low friction coefficient.

Table 3The residence time of fluids molecules within 2 ns

Fig.5.The residence autocorrelation functions of the first layer of confined fluid decane molecules in slits with 1.2 nm width and their bulk counterpart with time evolution:(a)water,(b)methanol and(c)decane.

Fig.6.Top view of X–Y direction.The left is the top view of the bulk fluids,and right is the top view of the firstlayer of confined(a)water,(b)methanol and(c)decane molecules in a 1.2 nm MoS2 slit.

Fig.6 shows the snapshots of the X–Y direction.The confined fluid molecules in the first layer are much more uniform compared with their counterpart in bulk.Decane molecules have the highest stability.On the basis of the results of density profiles and the mobility of X and Y directions,the decane molecules in the first layer would remain for a very long time.This result might result from the fact that decane molecules in the first layers provide a very tight structure,suggesting a transition into a solid-like phase.The change of water molecules and methanol molecules is weaker than that of decane molecules.Therefore,the order of forming solid-like degree is decane＞methanol＞water molecules and the fluid molecules are more likely to form a solid-like structure which would result in a better lubrication effect.

3.5.Effect of hydrogen bond(H-bond)lifetime of water and methanol on friction coefficient

Water molecules in bulk can form a tetrahedral hydrogen-bonded structure.However,the hydrogen-bonded structure of the methanol molecules is different.The behaviour of H-bonds has a strong relationship to the macroscopic properties.In this study,the H-bond lifetime was adopted to evaluate the properties of the H-bond.

A geometric definition was used to determine the formation of H-bonds[50].Three criteria were used to determine whether two water molecules(one acts as a donor,and another acts as an acceptor)form the H-bond or not,as follows:(i)the distance between the oxygen atoms of both molecules is smaller than 0.35 nm;(ii)the distance between the oxygen atom of the acceptor molecule and the hydrogen atom of the donor is smaller than 0.245 nm and(iii)the angle of H--O…O(the first two atoms H--O belong to a donor molecule and the third oxygen atom belongs to an acceptor molecule)should be less than the threshold value of 30°.An H-bond can be formed between the two molecules only if the three criteria are simultaneously met.

On the basis of H-bond lifetime,the survival probability of the H-bond was calculated by tracing the continuity of H-bond as done by Rapaport[51]and Matsumoto and Gubbins[52].The variable ηij(t)=1 agrees when each pair of molecules bonds to form an H-bond at the time t(ns)is zero.The autocorrelation function of ηijis defined by:

Fig.7.Hydrogen bond lifetime of water molecules and methanol molecules confined in the first layer of 1.2 nm slits.

Fig.7 shows the SHB(t)of the first layer of water and methanol molecules;it also presents that the H-bond lifetime of methanol molecules is longer than that of water molecules.This phenomenon can reflect the situation at the molecular level to some extent,where the formed H-bond microstructures of water molecules within the first layer are easier to be broken,whereas those for methanol molecules are more uniform.This observation suggested that the solid-like degree of methanol molecules is greater than that of water molecules.

4.Conclusions

A series of molecular dynamics simulations were conducted to investigate the lubrication behaviour of different polar fluid molecules(i.e.,water,methanol and decane)confined in different monolayer MoS2nanoslits(i.e.,1.2,1.6 and 2.0 nm).The friction coefficients were analysed to characterize the performance of lubrication.To better illustrate the internal relations between the microstructure and friction coefficient of confined fluid molecules,the spatial distribution,mobility and H-bond structure of different confined fluid molecules were analysed in detail.

The friction coefficient results demonstrated that decane molecules exhibited good lubricating performance.For all the studies of slit width,the order of friction coefficient is decane＜methanol＜water.The friction coefficient shows an evident decrease as the slit width increases,except for decane.On the basis of detailed analysis of microstructures of different confined fluid molecules,all the fluid molecules are layered within nanoslits,and the stability of the first layer formed near the slit wall may be responsible for the difference in friction coefficients of different fluid molecules.The tendency of the formation of a solid-like structure in the first layer near the slit wall was decane＞methanol＞water.

This work reveals that the formation of the solid-like layer is beneficial to achieving extra low friction coefficient at the molecular level.Moreover,these findings suggested a novel avenue for preventing oxidation and reducing friction by introducing the decane molecules on the MoS2surface.

Acknowledgements

We are grateful to the High Performance Computing Center of Nanjing Tech University for supporting the computational resources.The State Key Laboratory of Materials-Oriented Chemical Engineering(KL15-03),the Swedish Kempe Scholarship Project(JCK-1507),the Swedish Research Council for Environment,Agricultural Sciences and Spatial Planning(Formas,2016-01098)and the support of MISTRA foundation of Sweden(MI16.23).