Electro-lubrication in Janus transition metal dichalcogenide bilayers

Lubrication induced by a vertical electric field or bias voltage is typically not applicable to two-dimensional (2D) van der Waals (vdW) crystals. By performing extensive first-principles calculations, we reveal that the interlayer friction and shear resistance of Janus transition metal dichalcogenide (TMD) MoXY (X/Y = S, Se, or Te, and X ≠ Y) bilayers under a constant normal force mode can be reduced by applying vertical electric fields. The maximum interlayer sliding energy barriers between AA and AB stacking of bilayers MoSTe, MoSeTe, and MoSSe decrease as the positive electric field increases because of the more significant counteracting effect from the electric field energy and the more significant enhancement in interlayer charge transfer in AA stacking. Meanwhile, the presence of negative electric fields decreases the interlayer friction of bilayer MoSTe, because the electronegativity difference between Te and S atoms reduces the interfacial atom charge differences between AA and AB stacking. These results reveal an electro-lubrication mechanism for the heterogeneous interfaces of 2D Janus TMDs.


Introduction
To increase the capability and service life of engineering equipments, lubrication for reducing friction and energy dissipation in mechanical devices and components is crucial. Many effective methods, such as designing interfacial or contacting structures, decreasing surface roughness and mechanical loading, and adding solid or liquid lubricant additives, have been developed to control and reduce friction and wear. Previous studies have shown that applying external electric fields can modify the molecular structure and charge transfer at solid-solid interfaces, thereby decreasing the interfacial friction and resistance [1,2]. Moreover, the distribution or orientation of ions at solid-liquid interfaces can be controlled and changed via electric fields to achieve the desired lubricating effect [3][4][5][6][7]. Electric-field-mediated lubrication is an attractive and promising route for improving tribological performance.
Two-dimensional (2D) van der Waals (vdW) crystals, including graphene, hexagonal boron nitride (h-BN), and transition metal dichalcogenides (TMDs), exhibit ultra-low friction and superlubricity behaviors, depending on the stacking commensurability [8][9][10][11][12][13], interface interaction and structure [14][15][16][17][18], mechanical stiffness [18][19][20][21], substrate effect, and adhesion [22,23]. Nevertheless, the friction of 2D vdW crystals in the presence of bias voltages or vertical electric fields is enhanced, and ultra-low friction states cannot be maintained as electric fields result in surface state changes and interlayer charge exchange [24][25][26][27][28]. Lubrication induced by the bias voltage is not typically applicable to 2D vdW crystals. Recently, Janus TMD monolayers were successfully synthesized via chemical vapor deposition and thermal selenization methods [29,30]. The Janus configuration of TMD MXY (M = Mo or W, X/Y = S, Se, or Te, and X ≠ Y) monolayers breaks the out-of-plane structural symmetry, and results in a vertical dipole moment. Theoretical studies [31][32][33][34] further reveal that in addition to their excellent in-plane piezoelectricity, Janus MXY monolayers and multilayers exhibit significant out-of-plane piezoelectric polarization. In multilayer Janus TMDs, their interfacial atoms indicate different electronegativities; hence, the response of their interlayer interactions to the electric field will differ from that of multilayer graphene, h-BN, and TMDs. However, the effect of the vertical electric field on the interlayer friction properties of Janus TMDs has rarely been considered and remains elusive.
In this study, the interlayer friction behaviors of Janus TMD MoXY (X/Y = S, Se, or Te, and X ≠ Y) bilayers under vertical electric fields and a constant normal force mode were extensively investigated using first-principles calculations. For bilayer MoSTe, the maximum interlayer sliding energy barrier between AA and AB stacking decreases as the positive or negative electric field increases, indicating a reduction in the interlayer friction. The maximum interlayer sliding energy barriers of bilayers MoSeTe and MoSSe decrease under a positive electric field but increase under a negative electric field. The fewer charge changes between AA and AB stacking under positive electric fields and the different electronegativities of interfacial atoms result in a more significant counteracting effect from the electric field energy to the maximum interlayer sliding energy barrier, thereby reducing the interlayer friction of Janus TMD bilayers. These results can provide insights into the lubricating mechanism and performance of Janus TMD bilayers in the presence of vertical electric fields. Figure 1 shows the models of 2H MoSTe, MoSeTe, and MoSSe bilayers with initial AB stacking in rhombus unit cells, where each MoSTe, MoSeTe, and MoSSe monolayers contain one Mo and two different chalcogen atoms. A vacuum region exceeding 25 Å perpendicular to the plane was applied. For comparison, a 2H MoS 2 bilayer with an initial AB stacking was considered in our study. All computations were performed within the framework of density functional theory (DFT), as implemented in the Fritz Haber Institute ab initio material simulations (FHIaims) code with "tight" computational settings [35], in which the Perdew-Burke-Ernzerhof (PBE) [36] exchange-correlation functional was employed. The effect of vdW interactions was considered using a many-body dispersion (MBD) vdW model [37,38]. A k-point grid measuring 15 × 15 × 1 was used throughout the study. First, the entire system was relaxed using the PBE + MBD method until the force on each atom was less than 0.01 eV/Å. The optimized lattice constants of MoSTe, MoSeTe, MoSSe, and MoS 2 unit cells were 3.329, 3.398, 3.215, and 3.147 Å, respectively. To simulate interlayer sliding, the entire a 1 -a 2 planes of the unit cells were equally partitioned into 81 positions (Fig. S1 in the Electronic Supplementary Material (ESM)), where the nearest positions were separated by 0.37, 0.378, 0.357, and 0.35 Å for MoSTe, MoSeTe, MoSSe, and MoS 2 , respectively. The top monolayer was shifted both transversely with respect to the bottom monolayer and relative to the positions partitioned; subsequently, the chalcogen atoms at the top and bottom surfaces were fixed. Next, an electric field [35] was applied in the direction perpendicular to the a 1 -a 2 plane. The interlayer distances d of the TMD bilayers were modified by changing the z-direction coordinates of the atoms in the top layers. Next, those systems were relaxed again using the PBE + MBD method, and the normal forces at different d and shifted positions were calculated by summing the z-direction forces of all atoms in one monolayer. By adjusting the d between the two monolayers, the normal forces at the 81 shifted positions were maintained at approximately the same value. Hence, an interlayer sliding simulation under a constant normal force mode was realized for the considered TMD bilayers. For the case of a zero normal force, the total z-direction forces of all atoms in one monolayer at different shifted positions were less than 0.01 eV/Å (Fig. S2 in the ESM). In other cases, the deviations between the desired and calculated normal forces at different shifted positions were less than 1% (Fig. S3 in the ESM). Based on the maximum and minimum normal forces in the errors, the corresponding deviations in the energies and d were obtained and regarded as errors in the energies and d, respectively.

Model and methods
www.Springer.com/journal/40544 | Friction After relaxation, the total energies of the bilayers at different shifted positions were calculated using the PBE + MBD method, and the corresponding potential energy surface (PES) for interlayer sliding under a normal pressure P n (P n = n / F A , where n F is the normal force and A is the area of the unit cell) was constructed based on the differences in energy , where E is the total energy of the system and min E is the lowest total energy (Figs. S4 and S5 in the ESM).  in the Janus TMD bilayers with heterogeneous interfaces indicates that the vertical electric field can reduce the interlayer friction, and serves as electrolubrication in the Janus TMD bilayers. Meanwhile, the interlayer friction of the Janus TMD bilayers is associated closely with interlayer adhesion or binding interactions. We calculated the interlayer binding energy difference b E  between AA and AB stacking.

Results and discussion
As shown in Fig. S7(a) [41]. To understand the effect of the electric field on the interlayer interactions of Janus TMD bilayers, the electric field energy EF E of the systems at different shifted positions were calculated. Here, the system energy excluding the electric field energy is defined by S In contrast to the Janus TMD bilayers, the EF E  of bilayer MoS 2 increased, whereas its S E  decreased under both positive and negative electric fields, as shown in Fig. S8 in the ESM. The effect of positive electric fields on the interlayer friction of the Janus TMD bilayers differed completely from that of bilayer MoS 2 .
To better elucidate the roles of electron kinetic energy, exchange-correlation, vdW, and electrostatic interactions in the interlayer friction, we separately calculated the energy differences in exchangecorrelation energy Owing to the heterogeneous interfaces of Janus TMD bilayers and the different electronegativities of interfacial atoms, charge changes in interfacial atoms under electric fields must be analyzed to understand the electro-lubrication of Janus TMD bilayers.   of the interfacial atoms of the Janus TMD bilayers between AA and AB stacking were consistent with the interlayer sliding energy barriers max E  shown in Fig. 1. Furthermore, the charge density differences   in the presence and absence of electric fields for AB and AA stacking were calculated as follows: is the charge density of the bilayer under an electric field and noelec bilayer  is the charge density without an electric field. Among the S, Se, and Te atoms, the electronegativity of the S atom was the highest, whereas that of the Te atom was the weakest. At the interface of the bilayer MoSTe, charge transfer from Te to S atoms occured for both AA and AB stacking. The applied positive electric field facilitated and enhanced the charge transfer from Te to S atoms, as shown in Fig. 5(a). Under positive electric fields, enhancement in charge transfer from Te to Se atoms and Se to S atoms was indicated in bilayers MoSeTe and MoSSe, as shown in Figs. 5(b) and 5(c). This facilitating effect of charge transfer induced by positive electric fields was more significant for AA stacking, which resulted in a relative decrease in the total energy of AA stacking with respect to that of AB stacking. The more prominent charge transfer of AA stacking was consistent with the decrease in the absolute value of of the interfacial atoms, as shown in Fig. 3. However, the negative electric fields induced charge transfer from Se to Te atoms and S to Se atoms, which was opposite to the charge transfer caused by the electronegativity of the interfacial atoms. The interlayer charge transfer and exchange of bilayers MoSeTe and MoSSe under negative electric fields were more prominent for AA stacking; this resulted in a relative increase in the total energy of AA stacking with respect to that of AB stacking. For bilayer MoSTe, no interlayer charge transfer and exchange occured under a negative electric field because of the significant electronegativity difference between Te and S atoms, as shown in Fig. 5(a), which reduced the interlayer resistance when the bilayer slid from AB to AA stacking. Under a normal pressure of 2 GPa, similar charge density differences in the presence and absence of electric fields at AB and AA stacking were observed, as shown in Fig. S13 in the ESM. Moreover, we investigated the interlayer friction of Janus TMD WXY (X/Y = S, Se, or Te, and X ≠ Y) bilayers under vertical electric fields using the same method.
| https://mc03.manuscriptcentral.com/friction Similar to Janus TMD MoXY bilayers, the maximum sliding energy barriers of the WXY bilayers decreased as the positive electric field increased, as shown in Fig. S14 in the ESM, and the negative electric field reduced the interlayer friction of the WSTe bilayer.

Conclusions
In summary, by performing comprehensive DFT calculations, we demonstrate that the interlayer friction and shear resistance in Janus TMD bilayers under a constant normal force mode can be reduced by applying vertical electric fields. Under positive electric fields, bilayers MoSTe, MoSeTe, and MoSSe exhibited interlayer friction reduction because of the more prominent counteracting effect from the electric field energy and the more significant enhancement in interlayer charge transfer for AA stacking induced by electric fields. The interlayer friction of bilayer MoSTe was reduced by negative electric fields because the significant electronegativity difference between Te and S atoms decreased the charge differences in the interfacial atoms between AA and AB stacking. These results revealed an electro-lubrication mechanism for the heterogeneous interfaces of 2D Janus TMDs and can provide insights into the friction behaviors of 2D Janus TMDs under external electric fields.

Electronic Supplementary Material
Supplementary material is available in the online version of this article at https://doi.org/10.1007/s40544-021-0562-9.
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