Sliding Properties of MoS2 Layers: Load and Interlayer Orientation

Subscriber access provided by UNIV NEW ORLEANS

Article

Sliding Properties of MoS2 Layers: Load and Interlayer Orientation Effects Giacomo Levita, Albano Cavaleiro, Elisa Molinari, Maria Clelia Righi, and Tomaš Polcar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4098099 • Publication Date (Web): 30 May 2014 Downloaded from http://pubs.acs.org on June 2, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Sliding Properties of MoS2 Layers: Load and Interlayer Orientation Effects G. Levita,1,2 A. Cavaleiro,2 E. Molinari,1,3 T. Polcar,4,5 and M.C. Righi1

1

CNR Institute of Nanoscience, S3 Center, Via Campi 213/A, I-41125 Modena, Italy

2

SEG-CEMUC, Mechanical Engineering Department, University of Coimbra, 3030-788, Coimbra,

Portugal 3

Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, I-

41125 Modena, Italy 4

Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in

Prague, Technická 2, Prague 6, Czech Republic 5

nCATS, Faculty of Engineering and Environment, University of Southampton, Highfield Campus,

Southampton SO17 1BJ, UK

Amongst the members of the transition metal dichalcogenides (TMD) family, molybdenum disulfide has the most consolidated application outcomes in tribological fields. However, despite the growing usage as nanostructured solid lubricant due to its lamellar structure, little is known about the atomistic interactions taking place at the interface between two MoS2 sliding layers, especially at high loads. By means of ab initio modeling of the static potential energy surface and charge distribution analysis we demonstrate how electrostatic interactions, negligible in comparison with van der Waals and Pauli contributions at zero load, progressively affect the sliding motion at increasing loads. As such, they discriminate the relative stability and the frictional behaviour of bilayers where the two monolayers defining the interface have a different relative orientation. In particular for antiparallel sliding layers we observed a load-induced increase of both the depth of the minima and the height of the energy barriers compared to parallel ones, which may have important consequences for the fabrication of more efficient ultralow friction devices at the nanoscale.

KEYWORDS: Friction; TMD; Potential Energy Surface; Solid Lubricant; DFT

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 35

1 – INTRODUCTION Transition metal dichalcogenides (TMDs) have been the subject of increasing attention in very recent years. Numerous experimental and theoretical papers have started investigating their outstanding optical, electronic, catalytic and tribological properties1,2. Such widespread interest is closely entwined to that developed – only few years earlier – towards graphene. TMDs are in fact lamellar compounds whose layers, characterised by strong chemical bonds, are held together by weak van der Waals interactions. As such, it is relatively easy to peel off few or even one S-Mo-S layer from a well ordered TMD crystal3. Each layer consists of an atomic plane of molybdenum sandwiched between two atomic planes of sulfur in a trigonal prismatic arrangement. As in graphene, confinement effects enhance the electronic or optical properties and open the way for a wide array of technological applications; moreover, TMDs are naturally abundant and a careful choice of the specific metal/chalcogenide composition (and their possible functionalisation) determines a versatility unattainable for graphene. Therefore it does not come as a surprise the number of recent investigations about the fundamental characteristics of molybdenum disulfide4-10, which can be regarded as the forefather of the whole TMD family. Strangely, compared to the numerous studies aimed at determining catalytic, vibrational or electronic properties, a relatively lower number of theoretical papers11-15 has dealt with the MoS2 feature which first gave rise to technological applications, that is its tribological behaviour. Molybdenum disulfide has in fact been largely used as an additive in lubricant oils – or even as a solid lubricant – well before the recent advances in nanostructure fabrication16. Its low friction coefficient, especially in vacuum or controlled atmosphere, renders it one of the most promising candidate materials when ultra-low friction is required in automotive or aerospace industrial applications. The possibility of alloying it into much harder matrices such as amorphous carbon greatly stimulates the production of efficient self lubricating coatings17, therefore avoiding the negative outcomes of using fluids which can interfere with the mechanical process or simply deteriorate. This implies an ever deeper need of a clear understanding of its tribological properties, especially regarding its behaviour under pressure: for example, while ballon-flat experiments revealed a decrease of friction coefficient with the applied load, 18 the AmontonsCoulomb law was observed on the nanoscale 19. Moreover, Lee et al.20 report that samples made up by few MoS2 layers perform tribologically better than monolayer structures. All these evidences are still to be fully rationalised at the atomistic level; particular attention must also be paid to unraveling the nature of the interlayer forces, as an interplay of electrostatic interactions, van der Waals forces and ACS Paragon Plus Environment

Page 3 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Pauli repulsion has been shown to affect its properties13,20-22. Relevant frictional properties of layered materials can be extracted from a first-principles modeling of the potential energy surface (PES) associated with the interlayer sliding. In particular, to understand the microscopic origin of frictional forces is important to identify which interactions determine the PES corrugation and control its behavior as a function of load. We have shown, for example, that the PES corrugation for graphene on graphene is determined by Pauli repulsion and increases upon bilayer compression with the same z dependence. The microscopic origin of such behavior is a pressureinduced charge transfer from the interlayer region towards the carbon planes 23.Here we find that the non-planar structure and chemical nature of the S-Mo-S layers determine a more complex situation. For some layer orientations we identify, in fact, a pressure-induced charge-transfer towards the interlayer region driven by the tendency to form chemical S-S bonds across the interface. Moreover, while accurate studies on the individual monolayer structures of TMDs have been carried out by Ciraci and coworkers24, their reported lateral energy profile for a MoS 2 bilayer sliding under an applied pressure of 15 GPa11 seems not to agree with the one previously calculated at 0.5 GPa by Liang et al.14, namely in the energy ratio of the two minima of the profile. Hod and coworkers15 interpreted such discrepancy as the mere effect of the applied pressure, but the possibility that the two profiles actually refer to different bilayer orientations can not be ruled out. To our knowledge, no study has so far dealt with the effect of the relative orientation of commensurate layers on the sliding mechanism: Liu et al.9 have in fact analysed the effect of the stacking only on the electronic structure, while Onodera and coworkers have mostly focused 12,13 on the role of incommensurability and rotational disorder. Here we consider interlayer sliding in the 3R and 2H polytypes of MoS2. The 2H is the hexagonal form ordinary found in nature and the 3R is the rombohedral form which has been observed in synthetic materials as well as in nature25. Both polytypes are composed by the same type of S-Mo-S layer, with trigonal-prismatic coordination of the metal. However, the orientation of neighbouring layers is parallel in 3R and antiparallel in 2H. The interplay between Pauli repulsion and short range electrostatic attraction gives rise to a change in the PES shape with the load that is not observed in graphene. Furthermore, it splits the degeneracy between the 2H and 3R polytypes. Our aim is to provide a first-principles analysis of the commensurate interfaces between two MoS 2 monolayers with different orientations, and to relate the static potential energy surfaces associated with their motion to the interlayer forces. Commensurate layers give rise to the most stable stacking sequences, and therefore represent the configurations with highest statistical weight. Incommensurate structures obtained by small in-plane rotation of the layers will play a significant role mostly in dynamical studies, and as such will not be discussed here. This static approach will help providing a ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 35

rationale of the microscopic processes which could lead to further insights into the tunability of the macroscopic frictional properties of TMDs and allow screening the wide array of the specific chalcogenide/metal pair. Our first-principles determination of the Potential Energy Surface of undefected MoS 2 layers sliding on top of each other is carried out by considering the effect of i) their relative orientation and ii) the load applied perpendicularly to the surface of the layers. We will describe the behaviour without any external pressure on the layers (Section 3.1) before moving to discuss the effect of increasing applied loads (Section 3.2). The two sections will consider the role played by the two possible mutual orientations of the bilayer: these can be simply labeled as “2L-R0” and “2L-R180” and will be described in detail in Section 3.

2 – COMPUTATIONAL DETAILS For an accurate description of the geometrical and electronic structure of molybdenum disulfide we carried out DFT calculations including van der Waals dispersion forces. The ionic species were described by ultrasoft pseudopotentials and the electronic wavefunctions expanded in terms of plane waves using the Quantum-ESPRESSO package26; the cut-off on the kinetic energy was set as 40 Ry and the convergence threshold on energy and residual forces fixed respectively at 10 -4 Ry and 10-3 Ry/bohr. Considering the honeycomb geometry of the MoS 2 layer, a hexagonal unit cell was employed containing two layers, each made up by one MoS2 unit. A Methfessel-Paxton smearing27 of 0.01 Ry was used to help the integration in the first Brillouin zone. We first calculated the bulk properties and compared the results from local density approximation (LDA) with those from the PBE+D scheme proposed by Grimme 28, where an empirical term describing the van der Waals interactions is added to the DFT total energy calculated within the Perdew-BurkeErnzerhof29 (PBE) approximation. The comparison with other theoretical and experimental data is reported in Table S1 included in the Supplemental information. We chose the PBE+D scheme to carry out the overall analysis, due to the good agreement between the resulting geometrical parameters and the experimental and high-accuracy theoretical data30. The bulk lattice parameters a and c were calculated respectively as 3.198 and 12.454 Å: both values lie within a 1.5% margin from the experimental data (3.15 and 12.30 Å) and are consistent with previous computational results at a similar level of theory4,5,7,9,10. The monolayer and the bilayer were modeled by means of supercells with 15 Å of vacuum along the z direction so to avoid interactions between ACS Paragon Plus Environment

Page 5 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


replicas. In this case the k-point sampling was carried out using a 12x12x1 Monkhorst-Pack grid. The geometry of an optimised MoS 2 monolayer is reported in Figure 1: it is characterised by three honeycomb planes, the two outmost consisting of S atoms and the inner of Mo atoms. The sulfur planes overlap, while the metal centre lies in one of the hollow positions defined by the S honeycomb. The potential energy surface (PES) experienced by the upper monolayer upon translation above the lower one is constructed by calculating the interlayer interaction energy for different relative lateral positions of the two layers31; in particular we considered 12 symmetry locations (the six indicated in Fig. 1 plus the intermediate ones) which can be obtained by shifting the upper layer by steps of 0.46 Å along the [1100] direction corresponding to the long diagonal of the unit cell and that we label for simplicity as the y direction. Due to the hexagonal system symmetry, this sampling is equivalent to the sampling of the edges of the lattice irreducible zone. At each location the x-y coordinates of the Mo atoms of both stacked layers were kept fixed while all the others were left free to evolve during the optimisation. With this approach the relative layer displacement is simulated in the most realistic way because both the interlayer distance (defined as the resulting Mo-Mo vertical distance) and the intralayer structure are optimized at each lateral position: the layer relaxations are therefore fully taken into account.

FIG. 1. Top and side view of a MoS2 monolayer. The unit cell edges and the origin (labeled as O) are indicated. To construct the PES for the sliding motion of two commensurate MoS 2 monolayers the origin of a second layer (not shown) is placed on the six points indicated by black squares plus their intermediate points; the energy for all of these systems are calculated after relaxation ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 35

In order to investigate the effect of increasing loads we considered compressed bilayer configurations where the interlayer distance was fixed at different values. We evaluated the load necessary to maintain the layers at each considered distance z0 as the ratio L = Fz/A between the z component of the residual force on each Mo atom and the cell area. After relaxation, in fact, all forces become negligible except those corresponding to the fixed degrees of freedom. We verified that the process of structural optimization under the effects of constant vertical forces of magnitude L applied with opposite signs to the facing Mo atoms converges when the interlayer separation reaches the z0 value. The kinetic contribution to the total energy has been evaluated by computing the integral of the product of the charge density and the external ionic potential, as generated by post-processing 26. The kinetic energy term was obtained by subtracting this integral from the one-electron term generated by the code.

3 – RESULTS AND DISCUSSION 3.1 – Bilayer sliding at zero load A top-view representation of the two considered commensurate MoS 2 bilayer orientations is reported in Figure 2. The top layer (brighter atoms) is placed with its Mo atoms slightly shifted along the y direction with respect to the bottom layer (darker atoms). The latter is common between the two cases. The difference lies in the fact that the top layer in the structure on the left is rotated by 180° around the z axis with respect to the lower one, while the top layer of the structure on the right is not rotated. The first double layer will consequently be named as “2L-R180” (Fig. 2a) henceforth, in conformity to the 2H-MoS2 nomenclature used for the associated bulk structure, while the second one (Fig. 2b) will be defined as “2L-R0”.


Page 7 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


FIG. 2. Top view of two MoS 2 layers superimposed either in the R180 (a) or in the R0 (b) configuration. Light (dark) colors are used for the upper (lower) S-Mo-S layer

We calculated the interlayer binding energy by subtracting twice the total energy of an isolated monolayer from the total energy of the optimised bilayer: we obtained 150.4 meV per cell in both the R180 and R0 bilayers. Such value is in good agreement with the values of 140-160 meV reported in previous theoretical papers32,33 for the R180 case. In addition to isolated bilayers, we also considered bulk structures characterised by R0 and R180 layer orientations and again we found no difference in energy. Finally, we modeled the 3R polytype, made up of unrotated layers just like R0 and reported as occuring in natural MoS2 samples along the more common 2H polytype25: again its bulk structure is degenerate with those from 2H-R0 and 2H-R180. On the grounds of these degeneracies we decided to carry out our investigation on both R0 and R180 bilayers, as they are likely to be equally found at the tribological interface even if their sliding properties may be different. The PES profiles along the y direction obtained for the R180 and R0 bilayers are represented in Fig. 3 with dashed and continuum lines, respectively.

FIG. 3. Left: Potential Energy profile for the linear translation of a MoS 2 layer above a fixed one in both the R180 (dashed line, empty circles) and the R0 configuration (solid line, filled circles). Right insets: geometric arrangement for the most relevant positions (minima, maximum and saddle) along the R180 (top) and R0 (bottom) profiles The profiles are characterized by two different minima (labelled as Min1 and Min2 henceforth)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 35

connected by a relative maximum (corresponding to a saddle point in the 2D PES), along with a much higher maximum (labelled as Max). While the heights of the maxima are almost identical in the R180 and R0 structures, the relative depth of minima is different: in R180 Min2 is higher in energy with respect to Min1, while in R0 they are degenerate (this is obvious by inspecting the R0 structures in the lower insets of Fig. 3, where Min1 and Min2 are actually the same structure observed from two different sides). The energies relative to Min1 and the interlayer distances consequent to relaxation for these structures are reported in Table 1. The type and spatial separation of “on-top couples” present in each structure, namely the atoms belonging to the two stacked layers that fall one on-top the other, are also reported. Favoured geometries are characterised by lower interlayer distances; the spatial corrugation on the z axis therefore follows the energetic corrugation. A closer look at the most significant structures (Figure 3, right) reveals that the largest contribution to the energetic order arises from the relative positioning of the sulfur atoms at the interface: minima are characterised by S atoms in hollow with respect to each other, saddles by bridge positions and maxima by S atoms facing each other in an on-top position which maximizes Pauli repulsion between their lone pairs (which extend perpendicularly from the layer). TAB. 1. Summary of some geometrical and energetical parameters for the most relevant structures along the sliding path of R180 and R0 MoS2 bilayers, both at 0 and 10 GPa applied loads

MoS2 is a covalent compound, with partial charges evaluated in +0.4 e - and -0.2 e- on the Mo and S centres respectively34: attractive/repulsive interactions between on-top atoms of different/equal charge may influence the energetics of the system. However the fact that R180-Min1 (with two on-top Mo-S pairs) is isoenergetic with the R0 minima (just one on-top Mo-S pair each) indicates that at these ACS Paragon Plus Environment

Page 9 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


interlayer distances such interlayer monopole-monopole interaction is relatively weak. This is consistent with the analysis performed by Hod on boron nitride 35, where electrostatic interactions between partially charged atomic centers have a minor contribution to the interlayer binding. To further explain the role of the electronic structure in the energetics of the sliding layers, we investigated the charge transfer ∆ρ induced on the single MoS2 layer as consequence of the bilayer formation in the Min and Max geometries, calculated as the difference between the total charge of the bilayer and the sum of the individual monolayers kept in the same positions. For the R0 configuration, Figure 4(a,b) reports the z dependence of the charge transfer averaged on the xy plane (a, b) and Fig. 4(c,d) the spatial distribution of such transfer; the same analysis performed on the R180 case yields similar results and is reported in the Supplementary Material. The main feature is the formation of an extended charge accumulation area at the centre of the interface for the minimum energy structure (Fig. 4 a,c). This does not arise in the case of the maximum (Fig. 4 b,d) where on-top arrangement between S atoms occurs: here the interface region is depleted and accumulation occurs only on the S atoms. Pauli repulsion can be minimised when transferring electrons to a favourable region in the interface: this stabilizes the minimum structure over the maximum one. Furthermore, a difference can be observed between the sulfur atoms at the interface of the minimum structure (Fig.4a): the lower one, facing a hollow position, displays a larger electronic rearrangement than the upper one above a Mo atom. Our interpretation is that at these equilibrium distances the charge is transferred mainly to reduce Pauli repulsion between the S 3pz orbitals and not as consequence of major electrostatic attractions between Mo and S atoms on adjacent layers. This is consistent with previous findings regarding the short-range nature of the electrostatic contribution between layered materials35,36 and points at the fact that with no external applied load the sliding properties of layered materials are mostly affected by the modulation of the Pauli contribution along the sliding path.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 35

FIG. 4. Plane-averaged profiles of the z distribution of the charge transfers associated with the formation of a R0 MoS2 bilayer in the Min (a) and Max (b) configurations. The position of the S (Mo) planes along the z direction is indicated by orange (black) lines. (c) and (d) panels: spatial distribution of the charge transfer (red areas: accumulation; blue areas: depletion). Isosurface set at 1.5·10-4 el/(a.u.)3

3.2 – Bilayer sliding at increasing load The effect of the load on the relative stability of the different orientations is evidenced by Figure 5, where the energies of the most significant structures are plotted as function of the external load. For R180, Max and Min1 show the slowest increase upon compression (dashed blue and green lines), while Min2 (dashed red line) is highly destabilized, at the point that it becomes the energetically highest structure already at about 8 GPa. By applying increasing loads a dramatic change in the PES shape is therefore expected from the R180 bilayer. In the R0 configuration a more regular behaviour is displayed by the different structures. The minima (dark green line) are degenerate even at high loads – an expected behaviour considering their geometric equivalence – while the maximum (solid blue line) displays an even lower increase. On the other hand, a comparison between the minima in R180 and R0 reveals that the R0 ones display an intermediate increase between those of R180-Min1 and R180-Min2. This implies that the energy of the R0 minima increasingly grows over the R180-Min1, contrary to what happened at zero load where they shared the same zero point.

FIG. 5. Energy behaviour under load for selected lateral configurations for a MoS 2 bilayer in the most relevant R180 and R0 arrangements


Page 11 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A rationale for these results requires to compare the spatial and energetic corrugation of the different structures along the sliding paths. Both types of corrugation undergo limited modifications for the R0 structures (Table 1) while the R180 ones are deeply affected by the load: Min2 is the most easily compressed structure despite its large energy increase. Min1 and Max show much more limited changes, in both energy and spatial corrugation. We can relate this evidence to the number of on-top configurations involving interfacial S atoms (Table 1): the Max has the two sulfur facing each other, and both S atoms of Min1 sit on top of Mo atoms of the opposite layer; on the other hand Min2 places both S atoms in a hollow site. The load dependence of the interlayer distance is therefore explained on the grounds that the 3p orbitals of the interfacial on-top S atoms act as Pauli-driven rigid springs keeping the two MoS2 layers closer to their zero-load distances, while the lack of any on-top S allows the load to easily compress the R180-Min2 bilayer. A larger compression corresponds then to a higher energy increase. The R0 minima, which place one S atom on-top of a Mo centre and the other in hollow, represent an intermediate case between the two-on-top structures (the maxima and R180-Min1) and the zero-on-top one (R180-Min2). The fact that the R0 Max is characterised by on-top S-S couples is mirrored by its lower energy increase with respect to the minima.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 35

FIG. 6. Load-induced changes of the profiles of the z distribution for the charge transfers associated with the formation of a R180 bilayer in the Min1 (a), Min2 (b) and Max (c) configurations (left panels). In each, darker colours are associated with higher applied loads, whose specific values are reported in the insets. The overall effect of the load is to enhance both accumulation and depletion areas, with the exception of the accumulation at the centre of the interface for Min1. In the right panels are reported planar sections of the charge transfer at 10 GPa for the centre of the interface (red areas: accumulation; blue areas: depletion) highlighting the accumulation between interfacial S atoms in the Min2 structure. The relative position of interfacial S and S' atoms is indicated by the yellow spots Electrostatic effects begin playing a role in the energy modulation of the sliding path at increasing loads, especially for R180-Min2 for which a 10 GPa load brings the on-top metal centers just 5.42 Å away. The charge transfer plots reported in Figure 6 highlight that – contrary to Min1 and Max for which the centre of the interface is progressively depleted by the load – for Min2 charge is increasingly located between its interfacial S atoms (darker curves correspond to higher loads). This is related to the initial stages of a covalent S-S bonding between the layers already reported by Guo et al.21 for Min1 but much more consistent in the case of Min2 where all the S atoms are free of any on-top hindrance. The overall consequence is that unlike any other structure the R180-Min2 bilayer markedly confines the interfacial electrons along such S-S axis thus leading to an increase of the Pauli repulsion. As was done by Hod35 in the case of boron nitride, in the Supplementary Material we compare the kinetic and electrostatic contributions to the total energy of the system to tackle the issue of the interplay between Pauli and Coulombic interactions. The outcome shows at that short interlayer distances the increase of kinetic energy of Min2 over Min1 cancels out the electrostatic gain due to the initial formation of the SS interfacial bond and is responsible for the overall instability of the Min2 structure. Min1 and Max are less destabilized by the load due to the Mo-S and S-S on-top pairs preventing a large compression of the bilayer. It is worth noting that when the interfacial sulfur atoms are located on-top no sign of S-S bond formation is evidenced by the charge transfer plots, pointing at the fact that disulfide bonding only occurs for the dihedral angles characterizing Min2 but not the Max. In the minimum of the R0 configuration only one of the two S atoms has no on-top hindrance, again as an intermediate between R180 Min1 and Min2: this explains why at 10 GPa R0 and R180 bilayers have a different interlayer separation and a 21 meV difference between their absolute minima. For a more thoroughful evaluation, we reconstructed the PES at 10 GPa: while not having significance per se, this load allows to observe deep changes in the PES, considering the crossings evidenced in Figure 5. Moreover, despite being well beyond the average loads applied in tribology experiments, we deem this value as frequently attainable in micro-asperities. ACS Paragon Plus Environment

Page 13 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The 2D Potential Energy Surfaces for the sliding motion are obtained by mapping the one-dimensional profiles onto two dimensions, exploiting the six-fold symmetry of the single MoS 2 layer (the onedimensional profile along y is presented in the Supplementary Material). The outcomes are reported in Figure 7 where the upper panel refers to the R0 configuration at 0 and 10 GPa load and the lower panel to the R180 configuration at the same loads. The colour scale has been set in all images to fit the energy range for the most corrugated case, i.e. the R180 structure at 10 GPa. Minimum Energy Paths (MEP) connecting the wells and passing through the saddle points are also reported as red/yellow lines.

FIGURE 7. Potential energy surfaces for the sliding motion of MoS 2 bilayers in the R0 (upper row) and R180 (lower row) configurations at zero load (left column) and at 10 GPa load (right column). Unit cells (black lines) and Minimum Energy Paths (red/yellow lines) are reported for completeness. The colour scale refers to the energy range of the surface in meV and is reported on the right. As expected, very little difference is observed between the R0 and R180 PESs at zero load (left column), namely the fact that the former displays a six-fold arrangement of the wells while the latter is ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 35

characterised by a three-fold disposition, due to the inequivalency of the two kinds of minima (see Fig. 3). On the contrary, the picture clearly underlines the load-induced modification of the PES shape in the R180 case which evolves from the pattern of maxima surrounded by different wells and low saddle points to that of a high plateau with isolated, deep wells. For the R0 configuration the changes with respect to the zero load profile are much less pronounced: the saddle connecting the minima shows a limited increase relative to the minima (+15 to +20 meV), while the most evident modification – apart from the 21 meV upwards shift which renders the R0 wells at 10 GPa of a fainter blue than those of R180 at the same load – appears in the maximum region which now assumes a volcano-like shape: this is due to the much lower energy increase of the Max structure with respect to its shoulders and leads to an overall decrease of the energy modulation along y. Finally, we note that while our energy surface for the R0 configuration closely resembles the one obtained at 15 GPa load by Cahangirov et al.11, the paper by Liang et al.14 reports a 0.5 GPa profile in agreement with the R180 configuration. Our high-load results do not support the suggestion that the difference is due to the external pressure15: we deem that the two investigations have actually modeled different layer orientations. The ambiguity in the choice between the two configurations may have arisen precisely from the degeneracy of their minima at zero load. The paths with highest statistical weight for the interlayer sliding are the MEPs represented in Fig. 8. Upon compression, the R0 MEP does not change significantly apart from the limited raise of the saddle point; on the contrary, connecting the wells in the R180 case is much more energetically demanding. Given the degeneracy at zero load, multilayer coatings are likely to initially display both orientations: however, at higher loads the sliding properties would be affected solely by the R0 interfaces whose MEPs are flatter and therefore with lower expected friction coefficient. The increased instability of its minima compared to R180-Min1 seems also to imply that at high loads the R0 interface may undergo a favourable in-plane rotation of one of the layers: this in turn could produce an incommensurate stacking which can lay the grounds for ultralow friction.


Page 15 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


FIGURE 8. Comparison of the Minimum Energy Paths for the sliding motion of MoS2 R0 (solid lines) and R180 (dashed lines) bilayers at zero load (black lines) and at 10 GPa (red lines). The profiles refer to the paths shown in Figure 7 The very limited change of the MEP for the R0 orientation is remarkable especially when considering the behaviour of graphene for which higher increases of the sliding barriers were calculated 23. On the contrary, the load has a huge impact on the shape of the R180, again differing from graphene where the PES retained its shape despite the associated energy barrier increase. This is related to the insurgency of S-S covalent bondings at 10 GPa whereas the scenario at zero load was affected by the weaker Pauli repulsions: the same does not apply in graphene where no polarity is present on the sliding layers and therefore no electrostatic forces arise. Load-induced changes of the PES as the one observed here are able to produce anomalous frictional behaviour: for example, the friction of rare-gas monolayers adsorbed on metal surfaces37,38 decreases with pressure because of the anticorrugated to corrugated modification of the PES. Of course a detailed tribological study would have to take into account numerous variables such as the temperature, the sliding velocity or the magnitude of the lateral forces. A comprehensive study of the dynamical properties of the MoS2 sliding is beyond the scope of this article. Here we simply aim at pointing at different possible consequences of the modifications of the reported Potential Energy Surfaces, some of which could effectively rationalise the experimental evidences and help to establish the most suited conditions to achieve ultralow friction according to the different working environments.

4 – CONCLUSIONS By means of first-principles calculations we have reconstructed the Potential Energy Surfaces for the ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 35

sliding motion of commensurate MoS2 layers in order to determine their frictional properties according to different parameters such as the applied load or the lateral orientation. We could establish that: i) the two possible 2L-R0/ 2L-R180 layer orientations are isoenergetic both in the bulk and as an isolated bilayer; ii) the Minimum Energy Path at zero load is characterised by energy barriers not exceeding 18 meV per MoS2 unit; the maximum PES corrugation is roughly 55 meV; iii) at zero load no major differences arise between the R0 and R180, differentiating their PESs configurations. Upon increasing loads the relative strengths of the electrostatic and Pauli interactions increase differently in R0 and R180: the R180 minimum becomes the single most favoured structure, but the sliding path of the R0 is the least corrugated both spatially and energetically, suggesting its better lubricant properties. The delicate interplay between electrostatic, van der Waals and Pauli contributions to the MoS 2 sliding interface has been described, showing that interlayer covalent S-S bonds start forming at high loads for some lateral arrangements; the behaviour of the different bilayer configurations under load is rationalised in view of the number of on-top pairs between interfacial atoms, and compared to the analogous behaviour of other relevant tribological layered systems such as graphene. A complete determination of the frictional properties requires further dynamical analysis which would integrate the static picture presented here. We believe that this combined study on MoS 2 can rationalize the mechanisms behind the tribologic properties of Transition Metal Dichalcogenides; moreover, it provides indications for further investigations focusing on the most suited conditions for experimental applications – for example regarding the influence of a substrate altering the partial charges within the monolayer.

ACKNOWLEDGMENTS: This work was supported by the Czech Science Foundation through the project 108/10/0218 and project PTDC/CTM-MET/120550/2010 funded by FCT.

SUPPORTING INFORMATION AVAILABLE: Geometrical and energetical bulk parameters with different exchange-correlation functionals; comparison of the charge-transfer plots upon formation of bilayers with different orientations; oneACS Paragon Plus Environment

Page 17 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


dimensional profile of the sliding energy of the bilayer at 10 GPa load; energy contributions of 2LR180 as a function of the external load. This information is available free of charge via the Internet at http://pubs.acs.org.

REFERENCES: (1) Chhowalla, M., Shin, H.S., Eda, G., Li, L.-J., Loh, K.P., Zhang, H., The Chemistry of TwoDimensional Layered Transition Metal Dichalcogenide Nanosheets, Nature Chem., 2013, 5, 263-275 (2) Ramasubramaniam, A., Naveh, D., Towe, E., Tunable Band Gaps in Bilayer Transition-Metal Dichalcogenides, Phys. Rev. B., 2011, 84, 205325-205335 (3) Topsakal, M., Ciraci, S., Effects of Static Charging and Exfoliation of Layered Crystals, Phys. Rev. B., 2012, 85, 045121-045127 (4) Molina-Sanchez, A., Wirtz, L., Phonons in Single-Layer and Few-Layer MoS 2 and WS2, Phys. Rev. B., 2011, 84, 155413-155421 (5) Ataca, C., Ciraci, S., Functionalization of Single-Layer MoS 2 Honeycomb Structures, J. Phys. Chem. C, 2011, 115, 13303-13311 (6)

Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V., Kis, A., Single-Layer MoS 2

Transistors, Nature Nanotech., 2011, 6, 147-150 (7) Ataca, C., Sahin, H., Akturk, E., Ciraci, S., Mechanical and Electronic Properties of MoS 2 Nanoribbons and Their Defects, J. Phys. Chem. C, 2011, 115, 3934-3941 (8) Lee, C., Yan, H., Brus, L.E., Heinz, T.F., Hone, J., Ryu, S., Anomalous Lattice Vibrations of Singleand Few-Layer MoS2, ACSNano, 2010, 4, 2695-2700 (9) Liu, Q., Li, L., Li, Y., Gao, Z., Chen, Z., Lu, J., Tuning Electronic Structure of Bilayer MoS 2 by Vertical Electric Field: A First-Principles Investigation, J. Phys. Chem. C, 2012, 116, 21556-21562 (10) Kumar, A., Ahluwalia, P.K., A First Principle Comparative Study of Electronic and Optical Properties of 1H-MoS2 and 2H-MoS2, Mat. Chem. Phys., 2012, 135, 755-761 (11) Cahangirov, S., Ataca, C., Topsakal, M., Sahin, H., Ciraci, S., Frictional Figures of Merit for Single Layered Nanostructures, Phys, Rev. Lett., 2012, 108, 126103-126107 (12) Onodera, T., Morita, Y., Nagumo, R., Miura, R., Suzuki, A., Tsuboi, H., Hatakeyama, N., Endou, A., Takaba, H., Dassenoy, F., Minfray, C., Joly-Pottuz, L., Kubo, M., Martin, J.-M., Miyamoto, A., A Computational Chemistry Study on Friction of h-MoS2. Part II. Friction Anisotropy, J. Phys. Chem. B, 2010, 114, 15832-15838 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 35

(13) Onodera, T., Morita, Y., Suzuki, A., Koyama, M., Tsuboi, H., Hatakeyama, N., Endou, A., Takaba, H., Kubo, M., Dassenoy, F., Minfray, C., Joly-Pottuz, L., Martin, J.-M., Miyamoto, A., A Computational Chemistry Study on Friction of h-MoS2. Part I. Mechanism of Single Sheet Lubrication, J. Phys. Chem. B, 2009, 113, 16526-16536 (14) Liang, T., Sawyer, W.G., Perry, S.S., Sinnott, S.B., Phillpot, S.R., First-Principles Determination of Static Potential Energy Surfaces for Atomic Friction in MoS 2 and MoO3, Phys. Rev. B, 2008, 77, 104105-104110 (15) Blumberg, A., Keshet, U., Zaltsman, I., Hod, O., Interlayer Registry to Determine the Sliding Potential of Layered Metal Dichalcogenides: The Case of 2H-MoS2, J. Phys. Chem. Lett., 2012, 3, 1936-1940 (16)

Martin, J.-M., Donnet, C., Le Mogne, Th., Epicier, Th., Superlubricity of Molybdenum

Disulphide, Phys. Rev. B, 1993, 48, 10583-10586 (17)

Polcar, T., Cavaleiro, A., Review on Self-Lubricant Transition Metal Dichalcogenide

Nanocomposite Coatings Alloyed with Carbon, Surf. Coat. Technol., 2011, 206, 686-695 (18) Singer, I.L., Bolster, R.N., Wegand, J., Fayeulle, S., Stupp, B.C., Hertzian Stress Contribution to Low Friction Behavior of Thin MoS2 Coatings, Appl. Phys. Lett., 1990, 57, 995-997 (19) Miura, K., Kamiya, S., Observation of the Amontons-Coulomb Law on the Nanoscale: Frictional Forces between MoS2 Flakes and MoS2 Surfaces, Europhys. Lett., 2002, 58, 610-615 (20)

Lee, C., Li, Q., Kalb, W., Liu, X.-Z., Berger, H., Carpick, R.W., Hone, J., Frictional

Characteristics of Atomically Thin Sheets, Science, 2010, 328, 76-80 (21) Guo, H., Yang, T., Tao, P., Wang, Y., Zhang, Z., High Pressure Effect on Structure, Electronic Structure, and Thermoelectric Properties of MoS2, J. Appl. Phys., 2013, 113, 013709-013715 (22) Cheng, Y., Zhu, Z., Schwingenschlogl, U., Role of Interlayer Coupling in Ultra Thin MoS 2, RSC Adv., 2012, 2, 7798-7802 (23) Reguzzoni, M., Fasolino, A., Molinari, E., Righi, M.C., Potential Energy Surface for Graphene on Graphene: Ab Initio Derivation, Analytical Description, and Microscopic Interpretation” Phys. Rev. B, 2012, 86, 245434-245440 (24)

Ataca, C., Sahin, H., Ciraci, S., Stable, Single-Layer MX 2 Transition-Metal Oxides and

Dichalcogenides in a Honeycomb-Like Structure, J. Phys. Chem. C, 2012, 116, 8983-8999 (25) Winer, W.O., Molybdenum Disulfide as a Lubricant: A Review of the Fundamental Knowledge, Wear, 1967, 10, 422-452 (26) Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo I., et al., Quantum ESPRESSO: a Modular and Open-Source Software ACS Paragon Plus Environment

Page 19 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Project for Quantum Simulations of Materials, J. Phys. Condens. Matter, 2009, 21, 395502-39520 (27) Methfessel, M., Paxton, A., High-Precision Sampling for Brillouin-Zone Integration in Metals, Phys. Rev. B, 1989, 40, 3616-3621 (28) a) Grimme, S., Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction, J. Comput. Chem., 2006, 27, 1787-1799. b) Bucko, T., Hafner, J., Lebegue, S., Angyan, J.G., Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections, J. Phys. Chem. A, 2010, 114, 11814-11824 (29) a) Perdew, J.P., Burke, M., Ernzerhof, K., Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77, 3865-3868. b) Vanderbilt, D., Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism, Phys. Rev. B, 1990, 41, 7892-7895(R) (30) Bjorkman, T., Gulans, A., Krasheninnikov, A.V., Nieminen, R.M., van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations, Phys. Rev. Lett., 2012, 108, 235502-235506 (31) Zilibotti, G., Righi, M.C., Ab Initio Calculation of the Adhesion and Ideal Shear Strength of Planar Diamond Interfaces with Different Atomic Structure and Hydrogen Coverage, Langmuir, 2011, 27, 6862-6867 (32) Weiss, K., Phillips, J.M., Calculated Specific Surface Energy of Molybdenite (MoS 2), Phys. Rev. B, 1976, 14, 5392-5395 (33) Ataca, C., Topsakal, M., Akturk, E., Ciraci, S., A Comparative Study of Lattice Dynamics of Three- and Two-Dimensional MoS2, J. Phys. Chem. C, 2011, 115, 16354-16361 (34) Todorova, T., Alexiev, V., Prins, R., Weber, T., Ab initio Study of 2H-MoS2 using Hay and Wadt Effective Core Pseudo-Potentials for Modelling the (1010) Surface Structure, Phys. Chem. Chem. Phys., 2004, 6, 3023-3030 (35) Hod, O., Graphite and Hexagonal Boron-Nitride have the Same Interlayer Distance. Why”, J. Chem. Theory Comput., 2012, 8, 1360-1369 (36) Israelachvili, J.N., Intermolecular and Surface Forces, Boston Academic Press (1992) (37) Righi, M.C., Ferrario, M., Pressure Induced Friction Collapse of Rare Gas Boundary Layers Sliding over Metal Surfaces, Phys. Rev. Lett., 2007, 99, 176101-176104 (38) Reguzzoni, M., Ferrario, M., Zapperi, S., Righi, M.C., Onset of Frictional Slip by Domain Nucleation in Adsorbed Monolayers, PNAS, 2010, 107, 1311-1316



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TABLE OF CONTENTS:


Page 20 of 35

Page 21 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a) b)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2L-R180

a)

2L-R0

b)


Page 22 of 35

Page 23 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2L-R180

Min1

Saddle

Min2

2L-R0


Max


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)


Page 24 of 35

Page 25 of 35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


Page 26 of 35

2L-R0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0 GPa 10 GPa

70 60 50

a)

40 30 20 10

0 GPa

70

10 GPa

FIG. 4

60 50 40 30 20 10

2L-R180 2L-R180

a)

2L-R0

FIG. 7

b)

FIG. 2

FIG. 8 ACS Paragon Plus Environment

Page 27 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Min1

a) S

S'

10 GPa Min2

b)

S S'

10 GPa

c)

Max S S'

10 GPa

FIG. 6 a) R180-Min1

S1 + Mo2

b) R180-Min2

c) R0-Min

Mo1 + S2

SM ACS2 Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Min1

Min2

Page 28 of 35

Max

SM 4

SM 1 a)

b)

a)

c)

b)


c)

SM 3

Page 29 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Min1

a) S

S'

10 GPa Min2

b)

S S'

10 GPa

c)

Max S S'

10 GPa



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 35

2L-R0 0 GPa 10 GPa

70 60 50 40 30 20 10

0 GPa

70

10 GPa

60 50 40 30 20 10

2L-R180


Page 31 of 35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)

b)


Page 32 of 35

c)

Page 33 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a) R180-Min1

S1 + Mo2

b) R180-Min2

Mo1 + S2


c) R0-Min


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)

b)


Page 34 of 35

c)

Page 35 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Min1

Min2

Max


Sliding Properties of MoS2 Layers: Load and Interlayer Orientation

Recommend Documents