Atomic-Scale Superlubricity in Ti2CO2@MoS2 Layered Heterojunctions Interface: A First Principles Calculation Study.

The two dimensional (2D)-layered transition-metal carbides and nitrides (MXene) have been proved to be an excellent solid lubricant owing to their high mechanical strength, low shearing strength, and self-lubricating properties. However, the interfacial friction behavior between Ti n+1C n (n = 1, 2) MXene and its heterogeneous system is not thoroughly exploited yet. Here, four types of van der Waals structures (Ti2CO2@Ti2CO2, Ti3C2O2@Ti3C2O2 MoS2@MoS2, and Ti2CO2@MoS2) have been investigated by density functional theory (DFT) calculations. The results exhibit that Ti2CO2@MoS2 possesses the lowest sliding energy barrier around 0.015 eV/oxygen(O) atom compared with the other three constructed models. Therefore, this work mainly focuses on the inner relation of Ti2CO2@MoS2 interlayer friction behaviors and its attributing factors, including normal force and charge density. The DFT analysis shows that the roughness of the potential energy corrugated plane is positively correlated with normal force and predicted the ultralow friction coefficient (μ) at 0.09 when sliding along the minimum energy potential route. Moreover, friction coefficient fluctuates at the normal force less than 10 nN determined by the combined effect of interfacial charge interlock and redistribution. This work reveals the intrinsic connection between the friction and charge interaction at heterogeneous interfaces.

Introduction

The two dimensional transition-metal carbides families, collectively referred to as MXenes, have garnered increasing attention in energy storage, catalysis, and mechanotribological aspects since its first discovery in 2011.[1−4] TiC (n = 1, 2 or 3), as widely used 2D nanosheet materials, has been investigated experimentally and computationally.[5−7] The majority of studies have shown that the introduced oxygen(O) terminated on the MXene surface during the etching process,[8,9] which weaken interlayer coupling between adjacent layers.[10−12] Recent works on the MXene family have proven it to be a new and promising candidate of the solid sliding friction lubricant in both theoretical calculations and experimental analysis,[10,13] owing to its excellent characteristics. Such as weakly bonded multilayer structure, high mechanical strength, low shearing strength, and self-lubricating capability.[14,15] Recent works on the good lubrication performance of TiC has been reported, such as a Ti3C2(OH)2 nanometer sheet as an additive in base oil for effective improvement of the friction-reducing and antiwear ability.[16]

In past years, studies have observed that heterostructure synthesis and fabrication together obviously provide us with more opportunities to change the interfacial properties and then enable better lubrication performance, such as fluorographene (FG)/molybdenum disulfide (MoS2),[17] graphene/MoS2, and graphene/h-BN heterogeneous interface.[18−20] The observation of the graphene/MoS2 heterostructure reveals that the sliding energy barrier is much smaller than that of the homogeneous bilayer,[21] which is in good agreement with the experimental results.[17] Recent techniques based on atomic force microscopy in the lateral fore mode have been used to experimentally explore the tribological properties between scanning probes and 2D nanosheets.[22,23] However, since the reported frictional measurements were performed on only a homogeneous layer, and significant changes in probe shape or nanosheet surface chemistry cannot be ignored during the experiments. It is still a challenge to accurately simulate 2D materials interfacial friction behavior and investigate friction properties. In order to further explore the 2D TiC-MXene (n = 1,2) interlayer friction mechanism and broaden its tribological applications, quantum mechanics-based first principles methods provide a powerful alternative to explore tribological properties of 2D materials at the atomic scale. Here, MoS2 was selected as the heterogeneous nanosheet mainly based on the following two factors: (1) the superior mechanical properties, including large in-plane Young’s modulus and low bending rigidity;[24−26] (2) good lattice matching with TiC; and (3) low intrinsic friction response.[27]

TiC and MoS2 are easily affected by ambient air and humidity because of oxidation under vacuum conditions.[8,9,28] Therefore, the well-optimized structural models in this paper are decorated with oxygen atoms. This work aims to explore sliding energy barriers between adjacent layers using density functional theory (DFT) methods and predicts the lowest friction coefficient (μ) of the Ti2CO2@MoS2 heterogeneous interface when sliding along the minimum energy potential (MEP) route. The Ti2CO2@MoS2 heterogeneous interfacial friction mechanism and its attributing factors, including normal force and charge density, have been carefully studied as well.

Results and Discussion

In order to exploit the atomic level interfacial friction behavior of 2D-dimensional TiC (n = 1, 2) and its heterostructure, we performed DFT calculation on the Ti2CO2, Ti3C2O2, and MoS2 bilayers, as well as the Ti2CO2@MoS2 heterostructure. The demonstration of interfacial sliding friction simulation is shown in Figure a referring to the reported studies.[25,31,35] Different stacking sequences can be fabricated by moving the relative atoms positions of adjacent layers, respectively. Figure b,c shows top views of sliding routes with different underlying layers. Because Ti2CO2@Ti2CO2, Ti3C2O2@Ti3C2O2, and Ti2CO2@MoS2 models have the same top view of underlying layer, in other words they have the same stacking sequences. Three typical stacking sequences are illustrated in Figure d–f. Additionally, three typical stacking sequences of MoS2@MoS2 are shown in Figure g–i.

Figure 1

(a) Picture represents a schematic diagram of the fabricating interfacial sliding model of Ti2CO2@MoS2, (b) top view of sliding routes when the underlying layer is TiCO2 (n = 1, 2); (c) top view of sliding routes when the underlying layer is MoS2, and (d–f) type T1, type T2 and type T3 stacking sequences, respectively, when underlying layer is TiCO2 (n = 1, 2). (g–i) type M1, type M2, and type M3 stacking sequences, respectively, when the underlying layer is MoS2@MoS2. For clarity, the upper layer oxygen atoms are indicated by the black pentagram and the underlying layer oxygen atoms by the red balls.

In this paper, the sliding energy barrier ΔE is a descriptor that measures sliding difficulty. MoS2@MoS2, Ti2CO2@Ti2CO2, bilayer and Ti2CO2@MoS2 heterogeneous interlayer without considering the normal force have been calculated, as shown in Figure . The detailed results of ΔE are listed in Table .

Figure 2

(a) Energy changes when sliding along the x-axis for Ti2CO2@MoS2, MoS2@MoS2, and Ti2CO2@Ti2CO2; (b) energy changes when sliding along the x-axis and y-axis for the Ti2CO2@MoS2 heterogeneous interlayer. The minimum energy is set to the energy of highly symmetrical oxygen layer stacking models.

Table 1

Maximum Energy Corrugation along the x Direction in Different Heterogeneous Interfaces

bilayer/heterogeneous interface	ΔE (eV/atom)
Ti2CO2@Ti2CO2	0.08
Ti3C2O2@Ti3C2O2	0.13
MoS2@MoS2	0.09
path1-Ti2CO2@MoS2	0.02
path2-Ti2CO2@MoS2	0.015

The calculated results show that the Ti2CO2@MoS2 heterogeneous interface shows the lowest energy barrier compared with MoS2@MoS2, Ti2CO2@Ti2CO2, and Ti3C2O2@Ti3C2O2 when sliding along the x-axis. The maximum energy barriers of MoS2, Ti2CO2, and Ti3C2O2 are 0.09, 0.08, and 0.13 eV/atom, respectively, which is significantly larger than 0.02 eV/atom calculated from Ti2CO2@MoS2. At the same time, as shown in Figure a, a saddle point corresponds to the T3 stacking appears on the curve of Ti2CO2@MoS2 and Ti2CO2@Ti2CO2. The maximum ΔE corresponds to the T2 stacking sequence, which the bottom oxygen atoms of the upper layer and top oxygen atoms of the underlying layer are in a high symmetry. The sliding energy barrier ΔE increases because of the strong Coulomb force between adjacent oxygen atom layers.

Furthermore, the interfacial friction behavior of Ti2CO2@MoS2 when sliding along different directions have been explored, as illustrated in Figure b. The results show that Ti2CO2@MoS2 has the property of energy surface corrugation anisotropy which is obviously dependent on the stacking configurations. The maximum, minimum, and saddle point correspond to different stacking configurations. When sliding along the x-axis, the maximum sliding energy barrier is 0.02 eV/atom and the saddle point corresponds to the T3 stacking configuration. However, when sliding along the y-axis, there is no saddle point and Ti2CO2@MoS2 shows a lower sliding energy barrier (0.015 eV/atom). This phenomenon can be attributed to the broken highly symmetrical interface stacking models when sliding along the y axis, which weakened the interfacial Coulomb force. The results show that lower ΔE was achieved by assembling heterogeneous nanosheets together.

In theoretical explorations, the potential energy configuration has been universally accepted for nanotribology even superlubricity performance. To understand the energy surface corrugation of different stacking sequences, we sampled the potential energy surface (PES) using DFT calculations, by considering all configurations across a 7 × 8 grid above an identical underlying layer, with its interlayer distance fixed under 1 GPa for Ti2CO2@MoS2.

Figure a–c represents three typical stacking sequences. The PES landscape calculated under 1 GPa (Figure d) presents an exceptionally mild corrugation of 0.015 eV/oxygen(O) atom, which is lower than 0.02 eV/O atom along the same path 2 (0.2671 eV), as listed in Table . In other words, a smaller ΔE was achieved when a low normal force applied on Ti2CO2@MoS2. The minimum energy path of Ti2CO2@MoS2 has been determined and indicated by the red arrow in Figure d. When sliding along the minimum energy path, and the lowest energy barrier is 0.1429 eV (0.19 eV/nm2), which is much lower than the reported 0.38 eV/nm2 for Ti3C2O2.[10] Additionally, the friction coefficient along the minimum energy path, as demonstrated in Figure e, is predicted at 0.09 through an instantaneous slope of the spline that fitted to the results of energy versus sliding distance, showing superlubricity of Ti2CO2@MoS2. From the PES landscape, we found an interesting phenomenon that a low normal force prompts easier interlayer sliding, which can be attributed to the surface charge redistribution.

Figure 3

(a–c) Represent three typical stacking sequences in the sliding process and (d) PES generated by shifting MoS2 layers across underlying Ti2CO2 layers with A, B, and C marked as three main stacking structure. D represent maximum energy barrier; (e) friction energy difference when sliding along MEP for Ti2CO2@MoS2.

In this work, Ti2CO2@MoS2 possesses the lowest ΔE around 0.015 eV/O atom compared with the other three constructed models. Therefore, this work mainly focuses on Ti2CO2@MoS2 interlayer friction behaviors. The calculated friction force is obtained through the instantaneous slope of the spline that fitted to the results of energy versus sliding distance. The fitting slope is used to estimate friction coefficient, as shown in Figure .

The data, as shown in Figure a, clearly shows the linear fitting straight-line of friction force versus normal force and provides the average frictional coefficient of Ti2CO2@MoS2 in different sliding paths. The DFT calculations reveal that Ti2CO2@MoS2 exhibits a lower friction coefficient (0.20 along path 1 and 0.22 along path 2) compared with the 0.273 of Ti2CO2@Ti2CO2.[10] Through the upper layer sliding in different directions, the correlation coefficient value of R1 and R2 are almost the same when sliding along different paths, indicating that the friction force positively correlates to the normal force.

Figure 4

(a) Effect of normal force load on Ti2CO2@MoS2, and R1 and R2 represents linear fitting straight-line along path 1 and path 2, respectively, (b) enlargement of linear fitting straight-line in the shaded area, (c) friction coefficient as a function of the normal force when sliding along path 1 (x-axis) and path 2 (y-axis), and (d) potential energy profile of Ti2CO2@MoS2 at different interlayer distances.

The correlation coefficient R12 and R22 decreases when the normal force is less than 5 nN, as shown in Figure b. Despite the small deviation, the wild fluctuation of the friction coefficient cannot be ignored when the normal force is at less than 5 nN. The friction coefficient as a function of normal force is reported in Figure c. The friction coefficient irregularly fluctuates at a low normal force. The calculated friction coefficient is 0.195 along path 1 and 0.265 along path 2 when the normal force is at 0.9 nN.

In order to explain the reasons for irregular fluctuation, the sliding energy barriers under the incremental interlayer distance when sliding along path 2 have been calculated. The higher sliding energy barrier needs to be overcome when the interlayer spacing decreases, as illustrated in Figure d. Moreover, the increment of the sliding barrier increased and then became stable at an atomic scale level friction, the nature of the normal force at the atomic scale is the charge interaction between adjacent layers. The reasons for irregular fluctuation can be attributed to the charge environment.

In order to deeply exploit the relationship between the interface charge distribution and the surface energy corrugation, we calculated the charge difference maps under zero loads of Ti2CO2@Ti2CO2, Ti2CO2@MoS2, and MoS2@MoS2 bilayers, as well as the Ti2CO2@MoS2 heterogeneous interlayer under 20 nN, as shown in Figure .

Figure 5

Charge density difference of (a) Ti2CO2@MoS2 (at balanced interlayer distance), (b) Ti2CO2@MoS2 with 20 nN normal force, (c) Ti2CO2@Ti2CO2 (at balanced interlayer distance), (d) MoS2@MoS2 (at balanced interlayer distance), (e) plane-averaged charge density difference of Ti2CO2@MoS2 under 0 and 20 nN, and (f) enlargement of the interfacial plane-averaged charge density profiles in the shadow area.

We have carefully studied the interface charge density and its distribution under a different normal force. As demonstrated in Figure a, the electrons of the monolayer are accumulated around oxygen atoms, thus causing a rich electron environment. When Ti2CO2@MoS2 is at the balanced interlayer distance (2.7 Å), the weak Coulomb force interaction between adjacent layers flatten potential energy corrugation. Once the normal force increases to 20 nN (shown in Figure b), the interlayer potential energy corrugation becomes rough. Additionally, because of the increasing charge interaction between adjacent oxygen atoms layers, the electrons enriched surrounding the oxygen atomic layers are transferred back to the sulfur atomic layer. The charge depletion causes lower potential corrugation, whereas charge accumulation gives rise to higher potential corrugation, and thus higher friction.[18]

According to the reported studies, the geometric interlock of the bilayer has been used to explain the basic mechanism of the MoS2 fracture.[36] Because of the high symmetry and strong charge interlocking, the interface charge ripple of Ti2CO2@Ti2CO2 (Figure c) shows rough corrugation. Therefore, the reason for lower energy corrugation of Ti2CO2@MoS2 is that the introduction of hetero-interface weakens the charge interlock and changes the charge redistribution. Then, the interface charge become more delocalized, resulting in a much smaller ΔE. The MoS2@MoS2 bilayer (Figure d) shows no obvious anisotropy in friction along different directions. Despite lower potential corrugation, the accumulated charge layer strengthens Coulomb force causing large ΔE.

In order to describe the inner relationship between the interlayer friction and the interfacial electronic properties quantitatively, the plane-averaged charge density difference Δρ in the z axis has been calculated. Figure e shows the plane-averaged charge density difference of Ti2CO2@MoS2 under a different normal force. The results show that the normal force promotes the accumulated interlayer charge of MoS2 nanosheet transfer to the outer layer obviously but has little effect on the Ti2CO2 layer. The enlargement of the interfacial plane-averaged charge density, as shown in Figure f, provides more details for interfacial charge interaction. The charge accumulated in the oxygen atomic layer is transferred to the sulfur atomic layer. Moreover, the shape of the peak near the oxygen layer widens, indicating that interface charge distribution become more delocalized. Therefore, the interlayer charge interlock and the charge redistribution that the two factors affecting potential energy corrugation are competitive and jointly determine the sliding energy barrier, which correspond to the curve of friction coefficient μ versus normal force, as shown in Figure c. In other words, better lubrication would be achieved if the quantity of the electric charge could be bound to the interface and prevented from being transmitted to the subsurface.

Conclusions

In summary, atomic friction behaviors of Ti2CO2 and MoS2 bilayers, as well as the Ti2CO2@MoS2 heterogeneous interlayer have been exploited by using DFT calculations. The PES landscape of Ti2CO2@MoS2 calculated at 1 GPa exhibits superlubricity along the minimum energy path with the friction coefficient at 0.09 and an exceptionally mild corrugation of ∼0.015 eV/O atom, proving the Ti2CO2@MoS2 heterostructure as an excellent solid lubricant. The introduction of the heterogeneous interface breaks the interlayer charge symmetry and promotes the interface charge redistribution, causing mild energy corrugation of Ti2CO2@MoS2. Furthermore, the frictional force is positively correlated with the normal force and increases with the normal force. The charge density difference and plane-averaged charge density difference reveals that the competitive relationship between the interlayer charge interlock and the charge redistribution results in the irregular fluctuation trend of the friction coefficient in the Ti2CO2@MoS2 heterostructure.

Computational Details

The theoretical calculations were performed by using the Vienna Ab initio Simulation Package (VASP 5.3.5) under the framework of the well-defined DFT simulation.[29,30] The projector augmented-wave method and Perdew–Burke–Ernzerhof functionals in the generalized gradient approximation method were used to describe the interaction between the core–valence electrons and electron exchange–correlation interaction, respectively. The cutoff energy was set to be 450 eV. The tolerance of energy precision of 10–5 eV and force convergence of 0.02 eV Å–1 were employed in the structure geometric optimization. Monkhorst–Pack k-points meshes of 7 × 7 × 1 was used for all the structure geometric optimization and DFT-D3 method for correcting dispersion in the system.[31] The supercells of 3 × 3 × 1 have been fabricated for theoretical calculations at the atomic scale. In addition,15 Å vacuum in the z-axis direction was employed to the upper layer to prevent interaction with the periodic layer. Because an induced lattice mismatch of 3.2% is within a reasonable range when the heterogeneous interlayer is fabricated, the construction of the heterogeneous interlayer model is reliable.

The adhesion energy Eads is used to describe the bonding strength between adjacent layers without considering the normal force, which can be acquired by subtracting the corresponding two monolayer energies from the bilayers calculated and defined aswhere Etotal is the total energy of the heterogeneous or homogeneous models. Eu and Et represent the total geometry optimized energy of the underlying layer and top layer, respectively.

Single-point self-consistent field calculations were employed to calculate sliding energy barriers under different normal forces when sliding along the x-axis (path 1) and y-axis (path 2). We scanned single-point energy with the interlayer distance ranging from 1.9 to 2.7 Å in steps of 0.1 Å. The calculated normal force is obtained through the instantaneous slope of the spline that fitted to the curves of energy versus interlayer distance. The average normal force can be expressed as

Lateral force (FL) can be calculated by the same method, and more details refer to previous literature studies.[32] The static friction coefficient is obtained according to the standard definition.

To quantify interfacial friction of adjacent layers, the PES of the Ti3C2O2@MoS2 heterogeneous interlayer is mapped by calculating adhesion energy on a 7 × 8 grid. At each configuration of the grid, the upper layer was allowed to move along the plane of the underlying layer (the xy-plane) with a fixed interlayer distance in the direction of the z axis. Then, the PES landscape under 1 GPa can be obtained by adjusting the interlayer distance. The maximum energy corrugation is defined aswhere Emax and Emin represent the maximum and minimum energy of the PES when sliding along different directions.

The reported studies reveal that various functional groups, such as −O, −OH, and −F groups are easily terminated on the surface of MXenes.[33] However, the oxygen-decorated MXene model is universally accepted in theoretical calculations based on the following considerations:[34] (1) in most cases, oxygen functional groups dominate during the etching process; (2) the high-temperature post-treatment or lithiation reactions will induce the conversion of −OH groups to −O groups; and (3) O-decorated MXenes show stability in thermodynamics and kinetics. Therefore, all structures in this work are fully covered oxygen. Additionally, the Ti2C monolayer was obtained from the experimental synthesis by exfoliating the aluminum atomic layer. Then, the results of complete adsorption site tests show that the −O termination is more favorable absorbed at the carbon (C) site at the surface of TiC (n = 1, 2) and sulfur (S) site at the surface of MoS2, respectively.