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Computational Study of Low Interlayer Friction in Ti C (n=1, 2 and 3) MXene Difan Zhang, Michael Ashton, Alireza Ostadhossein, Adri C.T. van Duin, Richard G Hennig, and Susan B. Sinnott ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09895 • Publication Date (Web): 08 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017

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ACS Applied Materials & Interfaces

Computational Study of Low Interlayer Friction in Tin+1Cn (n=1, 2 and 3) MXene Difan Zhang1,2, Michael Ashton1, Alireza Ostadhossein3, Adri C.T. van Duin3,4, Richard G. Hennig1 and Susan B. Sinnott2,* 1

Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32601

2

Department of Materials Science and Engineering, The Pennsylvania State University,

University Park, PA 16802 3

Department of Engineering Science and Mechanics, The Pennsylvania State University,

University Park, PA 16801 4

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University,

University Park, PA 16801 *

Corresponding Author: [email protected]

Keywords: MXene, Friction coefficient, Density functional theory, ReaxFF, Defect, Functional group

ACS Paragon Plus Environment

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Abstract

The friction of adjacent Tin+1Cn (n=1, 2 and 3) MXene layers is investigated using density functional theory (DFT) calculations and classical molecular dynamics (MD) simulations with ReaxFF potentials. The calculations reveal the sliding pathways in all three MXene systems with low energy barriers. The friction coefficients for interlayer sliding are evaluated using static calculations. Both DFT and ReaxFF methods predict friction coefficients between 0.24 and 0.27 for normal loads less than 1.2 GPa. The effect of titanium (Ti) vacancies in sublayers and terminal oxygen (O) vacancies at surfaces on the interlayer friction is further investigated using the ReaxFF potential. These defects are found to increase the friction coefficients by increasing surface roughness and creating additional attractive forces between adjacent layers. However, these defective MXenes still maintain friction coefficients below 0.31. We also consider functionalized Ti3C2 MXene terminated with -OH and -OCH3 and find that compared to the -O terminated surface, both groups further reduce the interlayer friction coefficient to 0.10 - 0.14.

1. Introduction The past decade has witnessed a rapid increase in research on two-dimensional (2D) materials, inspired by the discovery of the attractive properties of freestanding single-layer graphene.1,2,3 In recent years, tremendous attention has been paid to a new class of 2D layered transition metal carbides and nitrides known as MXenes.4,5,6 MXenes are synthesized by chemically etching bulk ceramics known as MAX phases, which have the general formula Mn+1AXn, where M is an early transition metal, A is a group IIIA or IVA element, X is either C or N, and n = 1, 2 or 3.6 During


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etching, the A element is removed from the MAX phase, leaving MX (MXene) layers bound by dispersion forces. The composition of a MXene system is based on the MAX phase from which it is etched. As an important member of the MXene family, the structures and properties of Tin+1Cn (n=1, 2 or 3) MXenes have been investigated both computationally and experimentally.6,7,8,9,10 It is predicted that the majority of their surface area is terminated with oxygen (O) that is introduced from solution during the etching process9,10,11, which gives each Tin+1Cn MXene a final composition of Tin+1CnO2, and is responsible for the relatively weak dispersion bonds between neighboring MXene layers.12,13,14 These dispersion bonds can be overcome mechanically to isolate single-layer MXenes, or left intact to preserve a multilayer structure similar to graphite. MXenes possess properties that make them candidates for several applications15,16, such as nanoelectronic devices17,18, sensors19 and catalysts20,21,22. The Ti3C2 MXenes have also been explored as additives for tribological applications, but the friction behavior between Tin+1Cn MXene layers is not well established.23,24,25 Because of the low friction coefficients between layers in similar dispersion-bound systems like graphite and MoS2, it is expected that these MXenes will also have relatively low friction coefficients. In this work, we have carried out first principles density functional theory (DFT) calculations in conjunction with classical molecular dynamics (MD) simulations using the ReaxFF reactive force field26 to investigate the friction of adjacent layers in Ti2CO2, Ti3C2O2, and Ti4C3O2 MXenes. In particular, we have determined the minimum energy sliding pathways of adjacent layers as predicted by DFT and ReaxFF methods, and predicted the friction coefficients of these three MXene systems. We further investigated the influence of structural defects, including Ti vacancies at sublayers and terminal O vacancies at surfaces, on interlayer sliding and their friction coefficients. Lastly, we considered functionalized Ti3C2


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MXenes and compared the friction coefficients of Ti3C2 MXenes terminated by -O, -OH and OCH3, respectively.

2. Computational Methods First-principles calculations were performed using DFT as it is implemented in the Vienna Ab initio Simulation Package (VASP), using the projector augmented wave (PAW) method and the generalized gradient approximation (GGA) for exchange and correlation.27,28,29,30,31 The reciprocal space integration was performed with the Monkhorst-Pack scheme using a k-mesh density of 1000 points per atom for each MXene structure. The plane-wave cutoff energy was set to 520 eV for all calculations, a value for which all systems’ energies are converged to less than 1meV/atom. Spin polarization has been included in all calculations; Ti atoms are initialized with a large magnetic moment of 6 ߤ஻ , and all other elements are initialized with a small magnetic moment of 0.5 ߤ஻ . The unit cells of all three Tin+1Cn (n=1, 2 or 3) MXenes were built as described in previous work4,32. Each was initialized as a multilayer structure of two formula units per layer with 2.5 Å between layers, and re-optimized to estimate its equilibrium interlayer spacing. For bilayer structures, a 10 Å vacuum was added above the upper layer to prevent its interaction with the periodic image of the lower layer and isolate a single interlayer interaction. To preserve this vacuum spacing, the c components of cell vectors are not optimized, but atomic positions are optimized in all directions. The PBE functional and the conjugate-gradient algorithm are used to obtain accurate relaxed structures during structure optimization for each MXene. Geometric optimizations are stopped after Hellman−Feynman forces on all atoms are less than 1 meV/Å and the stresses on the unit cell are below 0.1 GPa within each layer. The


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dispersion interactions were also included using the vdw-DF2 method of Langreth and Ludqvist.33 The classical MD simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source MD code made available by Sandia National Laboratory.34 A new reactive force field developed for Tin+1CnTx MXenes (T = O, F and OH) was used in all the MD simulations. This ReaxFF potential has been shown to successfully describe water dynamics on the internal surfaces of Tin+1CnTx MXenes.35 The geometric optimization of Tin+1CnO2 (n=1, 2 or 3) structures in the MD simulations was again achieved using the conjugate gradient algorithm when the x and y directions of simulation cell vectors were relaxed. The temperature of MD systems was fixed at 10 K and 298 K using the Langevin thermostat, and the time step was 0.1 fs.

3. Results and Discussion 3.1 Minimum Energy Pathways The multilayer nature of the Tin+1CnO2 structures was captured through periodic boundary conditions as described above, and an example of the unit cell is illustrated in figure 1(a). An example of two-layer systems of Tin+1CnO2 MXenes built based on the relaxed unit cell from DFT calculations is illustrated in figure 1(b). Different stacking sequences can be achieved in these two-layer systems by shifting the relative locations of two layers in their a and b directions. Three high-symmetry stacking sequences exist for all three Tin+1CnO2 MXenes: one in which the bottom oxygen atoms of the upper layer were located at the face centered cubic (FCC) positions


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relative to the atoms in the underlying layer, one in which bottom oxygen atoms of the upper layer were located at the hexagonal close packed (HCP) positions relative to the atoms in the underlying layer, and one in which the bottom oxygen atoms of the upper layer were immediately above the top oxygen atoms in the underlying layer. We referred to these stacking sequences as Type S1, Type S2, and Type S3, respectively, as illustrated in figure 1(c)-(e). Only Ti2CO2 is illustrated in figure 1 as an example of the models used for all three Tin+1CnO2 MXenes considered here.

Figure 1. (Color online) Visual aids for Ti2CO2 structures: (a) View along the a-axis of the small (two formula units) model and (b) view along the a-axis of the two-layer (four formula units) cell used for subsequent calculations. Also provided are views along the c-axis of the (c) Type S1 stacking sequence, (d) Type S2 stacking sequence, and (e) Type S3 stacking sequence. Carbon atoms are represented as brown circles and Ti atoms are represented as cyan circles. For clarity, only the atomic layers in the boxed region in (b) are shown in (c)-(e), with the upper


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oxygen atoms represented as black circles and the lower oxygen atoms represented as white circles.

To understand the energetics of these stacking sequences, we sampled the potential energy landscape using DFT calculations as the upper layer was shifted across a 10×10 grid of evenly spaced locations above an identical underlying layer, with its vertical location fixed at the equilibrium interlayer spacing for each MXene. The potential energy surfaces of three Tin+1CnO2 MXenes are illustrated in figure 2. It was found that Type S1 sequences (blue valleys in figure 2) in all three Tin+1CnO2 MXene structures showed the lowest stacking energy. Type S2 sequences represented local minima in the potential energy surface, but were slightly higher in energy than Type S1 sequences. The S3 sequences (red peaks in figure 3) resulted in local maxima in the potential energy surfaces because of the unfavorable repulsive force between eclipsing oxygen atoms of adjacent layers. The different scales in the potential energy surfaces of three MXene structures should be noted. Besides, our goal here is to reveal the surface pattern of three MXenes and find their corresponding sliding pathways. Employing additional grid points to plot potential energy surface will provide more detail of these surfaces and make the surface image smoother but it also results in more unnecessary calculations. Therefore, although the image of potential energy surface is not refined in detail, a 10×10 grid here is accurate enough in this work as long as the sliding pathways can be identified.


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Figure 2. (Color online) Potential energy surfaces generated by shifting (a) Ti2CO2, (b) Ti3C2O2 and (c) Ti4C3O2 MXene layers across underlying identical layers. White circles represent Type S1 sequences (energy minima), large black circles represent Type S2 sequences, and red peaks represent Type S3 sequences (energy maxima). Black lines indicate the minimum energy


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pathways (MEPs) for interlayer sliding. The small black circles indicate energy saddle points in sliding pathways.

Based on the potential energy surfaces, the minimum energy pathway (MEP) in each structure was also predicted and shown in figure 2. We predicted that interlayer sliding took place along the [100] and [520] directions with relatively low energy barriers for Tin+1CnO2 (n=1, 2 and 3) MXenes. This zigzag sliding path was consistent with the predicted interlayer sliding paths of other similar surfaces with hexagonal crystal structures36. Although the values we calculated did not include any consideration of applied external pressure, the exceptionally low barrier for interlayer sliding in the Ti3C2O2 MXene (~0.02 eV/O atom) suggested that this material be considered for use as a solid lubricant and other applications where interlayer sliding was likely to be of importance. For comparison, calculations of the static potential energy surface of MoS2, a popular solid lubricant, predicted a sliding barrier of 0.34 eV/nm2 (0.03 eV/ S atom)36, while the barrier we predicted for Ti3C2O2 was around 0.24 eV/nm2 (0.02 eV/ O atom). Note that the atom in the unit “eV/atom” here indicates terminal atoms on the surface of each structure. The area in the unit “eV/nm2” here is defined as the cross-sectional area of unit cell in a and b directions in figure 1. The energies along the MEP for sliding in Ti2CO2, Ti3C2O2, and Ti4C3O2 are illustrated in figure 3 (a). The existence of saddle points along the MEP in all three TiMXenes was also predicted.


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Figure 3. (Color online) Energy changes associated with sliding along the MEP between Type S1 and S2 sequences for Ti2CO2, Ti3C2O2, and Ti4C3O2, calculated using (a) DFT and (b) the ReaxFF potential. The zero-energy for each path is set to the energy of the MXene with Type S1 stacking sequence.

Classical MD simulations with ReaxFF potentials were carried out to investigate larger Tin+1CnO2 (n=1, 2 and 3) MXene bilayer systems. These MD simulations were capable of modeling structures at nanometer scale and studying defects in such large structures. DFT results above were used as a benchmark for justification of ReaxFF results. These larger MXene systems contained 40000-70000 atoms with simulation cells of around 19×18×3 (nm). At least 10 Å vacuum was added above the upper layer in the c-axis direction, as defined in figure 1, to isolate a single interlayer interaction. The larger Ti3C2O2 structure used in the ReaxFF calculations is shown in figure 4 as an example. The energies of the typical stacking sequences of the larger MXene structures as calculated by ReaxFF are provided in table 1 and are compared to the corresponding DFT results. The ReaxFF calculations produced the same trends as the DFT calculations for the S1, S2 and S3 stacking sequences. They further predicted the same MEP for the sliding of adjacent layers, although ReaxFF did not resolve the saddle point between the S1 and S2 sequences. The energy changes along the sliding direction calculated by ReaxFF method is illustrated in figure 3 (b). Similar to DFT calculation results, the ReaxFF calculation results predicted that Ti3C2O2 had the lowest energy barrier in the MEP among the three Tin+1CnO2 (n=1, 2 and 3) MXenes considered, with a barrier of around 0.38 eV/nm2 (0.032 eV/ O atom). Note that ReaxFF and DFT did not produce exact the same values. In general, the ReaxFF calculations produced higher energy barriers than the DFT results in all three MXenes because


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this ReaxFF potential overestimated the stacking energies of the S2 sequences as indicated in figure 3. This ReaxFF potential was developed for the study of water interacting with these MXenes, not for the interlayer friction in MXenes. The energetic detail such as saddle points was not trained by first principle calculations during the development of this potential, thus it may not be able to capture all properties during interlayer sliding, and additional fitting has to be carried out to satisfy all these energy details. Nonetheless, the ReaxFF potential results still provided fundamental guidelines on the way in which interlayer friction behaves at the atomic scale and reproduced the preferred pathway for interlayer sliding. The overestimation of stacking energies primarily affects the calculation of friction and normal forces. Based on the approach we apply to evaluate normal and friction forces, the detail of which is demonstrated in next section, the exaggerated energetic differences between S3 and S1 sequences result in an overestimation of both the friction and normal forces by the ReaxFF potential. A comparison of friction coefficients, which is the friction force divided by normal force, calculated by DFT and ReaxFF will be discussed in the next section.


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Figure 4. (Color online) Snapshots of Ti3C2O2 MXene systems considered in the ReaxFF calculations: (a) close view along c-axis and (b) view along a-axis. The C, Ti and O atoms are represented by brown, blue and red circles, respectively. This structure contains 60480 atoms which is 18.4 and 19.3 nm long in a and b directions, respectively.

Table 1. Relative stacking energy per unit cell predicted by ReaxFF and DFT Structure

ReaxFF results (eV) S1

S2

S3

Saddle

Ti2CO2

0

0.061

0.247

0.063

Ti3C2O2

0

0.038

0.147

0.043

Ti4C3O2

0

0.074

0.341

0.085

DFT results (eV)


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Ti2CO2

0

0.094

0.381

0.089

Ti3C2O2

0

0.064

0.214

0.060

Ti4C3O2

0

0.125

0.701

0.121

3.2 Friction Coefficients The interlayer friction predicted for the three Tin+1CnO2 (n=1, 2 and 3) MXenes was determined using both DFT and ReaxFF static calculations. The small unit cell structures shown in figure 1 were used in the DFT calculations and the larger structures shown in figure 4 were used in the ReaxFF calculations. For each MXene bilayer system, its structure of Type S1 stacking was relaxed and the energy of system was calculated, then the upper layer was shifted to the Type S3 stacking sequence, and the energy of system was also calculated. By varying the spacing between layers, the normal force between adjacent layers was controlled. After the energy of S3 stacking at each spacing was calculated, a three-order B-spline representation was fitted to the results of energy vs. spacing. The instantaneous slope of the spline gave the normal force at each spacing. For the evaluation of friction force, a sine wave was plotted at each spacing, whose maximum and minimum were the maximum and minimum energy site (i.e. S3 and S1 sequences). The slope at the ascending inflection point was used as an estimation of friction force.37. The result of Ti3C2O2 MXene is illustrated in figure 5 as an example. Since the trends of friction force vs. normal force for three Tin+1CnO2 (n=1, 2 and 3) MXenes were similar, results for the other two MXenes are shown in the supporting materials. The variation of friction force along the sliding pathway for Ti3C2O2 MXene is illustrated in the supporting materials.


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The data in figure 5 clearly showed that the friction coefficient, or friction force divided by normal force, varied for different normal forces. A linear fit of each plot provided the average friction coefficient across this range, which is reported in table 2. The ReaxFF results were in general agreement with the DFT results when the normal force was less than 1.2 GPa. At normal forces above 1.2 GPa, the ReaxFF prediction deviated from the DFT results. Both methods predicted low friction coefficients (0.24~0.27) in these MXene systems despite of small discrepancies. A similar ReaxFF calculation was also performed at 298 K for MXene structures, and the friction and normal loadings for Ti3C2O2 was illustrated in the supporting materials. Compared to the results at 10 K, the friction coefficients of these MXene systems decreased by 0.03-0.04 at 298 K. Such effect of temperature due to the aid of thermal motion was observed in earlier work.38 Similar to previous studies39,40, the type of friction considered here was atomicscale friction and our calculated friction coefficients could vary from experimental conditions where external factors such as water, atmospheric factors, or thermal vibrations would be present. These complicate factors have various effects on different systems. For instance, the friction of graphite in vacuum is reduced by exposure to O2 or H2O, while for diamond-like carbon, exposure to dry and humid air increases friction, and even chemical bonding formation is observed.41,42,43 Water absorbed on the surface of MoS2 is suggested to double its friction coefficient compared to dry conditions.44 Also, our calculations in this work focused on static friction that neglects kinetic factors, such as sliding speed41.


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Figure 5. (Color online) The comparison of DFT and ReaxFF results for interlayer friction in Ti3C2O2.

Table 2. Comparison of friction coefficients predicted by DFT and ReaxFF Structure

Friction coefficient DFT

ReaxFF

Ti2CO2

0.273

0.246

Ti3C2O2

0.243

0.251

Ti4C3O2

0.240

0.249


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3.3 Influence of Point Defects Similar to other 2D materials, intrinsic defects in Tin+1Cn (n=1, 2 and 3) MXenes and their influence on electronic and surface properties have been studied.45,46,47 For instance, Ti vacancies in sublayers of Ti3C2 MXenes have been observed and found to influence the surface morphology but not strongly influence metallic conductivity.48 Here, we investigate the effects of Ti vacancies in sublayers and terminal O vacancies on the friction of Tin+1Cn MXenes. Several percentages of Ti and O vacancies were considered in the large MXene bilayer systems, and the as-built structures were investigated with the ReaxFF calculations. Ti3C2O2 is illustrated in figure 6 as an example. For O vacancies in MXene surface, we removed different O atoms from the “O2” surface as shown in figure 6. For Ti vacancies in the MXene sublayers, three Ti sublayers (Ti1, Ti-2, Ti-3) were identified in each Ti3C2O2 MXene layer and we removed different Ti atoms in the “Ti-3” sublayer.


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Figure 6. (Color online) Two O surfaces (O-1, O-2) and three Ti sublayers (Ti-1, Ti-2, Ti-3) identified in each Ti3C2O2 MXene layer of a bilayer structure.

For terminal oxygen vacancies, 10%, 20% and 30% of terminal O atoms in “O-2” layer were removed from the surface, and the structures were relaxed using ReaxFF potential. The same procedure described above was then used to determine the friction and normal forces, and the calculated friction forces and friction coefficients are illustrated in figure 7 (a) and (b). Again, since the three Tin+1CnO2 (n=1, 2 and 3) MXenes show similar trends, we show Ti3C2O2 as an example here and the other two MXenes are shown in the supporting materials. The friction coefficients slightly increased by less than 0.03 as the percentage of O vacancies increased in all three Tin+1CnO2 (n=1, 2 and 3) MXenes when the normal force was under 1.2 GPa. The average rate of friction coefficient change is 2.0×10-5 per O vacancy. Such an increase in interlayer friction was likely the result of both increased surface roughness and an additional Columbic attraction between adjacent layers. Similar study on the roughness and Columbic interaction has been explored in MoS2 systems in earlier work.49 Here, the root mean squared roughness (Rq) was employed to characterize the surface roughness of these MXene structures. As shown in figure 7 (c), the O vacancies on the surface resulted in the increase of surface roughness compared to pristine surface. At least in the vacancy range of this study, increasing the amounts of O vacancies up to 30% lead to the increase of Rq. The roughness increased rapidly as O vacancies appeared. After the vacancy amount reached around 10%, the change of Rq became slower. On the other hand, the change of Columbic interaction energy was used to characterize the Columbic attraction between layers in figure 7 (c). We used


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the pristine system as a reference and evaluated how much the Columbic interaction changes due to the presence of O vacancies. It was suggested that increasing the amount of O vacancies resulted in higher Columbic interactions, which indicated a greater attraction between two layers. In these MXene systems, the Columbic repulsion was mostly contributed by the terminal O-O interaction between layers. Therefore, O vacancies on the surface of one layer reduced these repulsion interactions. Further, when Ti atoms in the sub-surface were exposed due to O vacancies, these positively charged atoms could also provide additional attractive forces to the negatively charged oxygen in adjacent layers that were shielded by their neighbor oxygen in the pristine system. To help illustrate the additional attraction between Ti and O atoms, the charge differences of Ti and O atoms in the defective and pristine surfaces of Ti3C2O2 are shown in figure 8 as an example. In the surface with O vacancies, the oxygen atoms maintained charges similar to those in the pristine surface if there was no O vacancy next to them. Otherwise, the charges of the O atoms became slightly (additional 0.02e to 0.08e) more negative. As expected, larger changes were observed for O atoms with higher numbers of vacant neighboring sites. Similarly, the Ti atoms in the sublayer maintained their charges if there was no oxygen vacancy in a nearest neighbor position. Because of the O vacancies, the Ti atoms in the sublayer were exposed to vacuum with dangling bonds and they held different positive charges depending on their environments. In particular, the fewer bound oxygen atoms they had, the smaller their positive charges were. The completely exposed Ti would retain charges around 0.7e.


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Figure 7. (Color online) (a) The effect of surface terminal O vacancies on interlayer friction for Ti3C2O2 MXene. (b) The changes of friction coefficient as a function of O vacancy coverage in three MXenes at 1 GPa. (c) The changes of surface roughness and Columbic interaction energy as a function of the amount of O vacancy in Ti3C2O2 MXene.


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Figure 8. (Color online) The charges of terminal oxygen and their neighboring Ti atoms in the surface of Ti3C2O2 MXene (a) without O vacancy and (b) with O vacancy. Small circles indicate oxygen in the surface and large circles indicate Ti in the sublayer. Color-bars indicate the


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charges (e) of atoms in the figures. Numbers in bracket give the exact charges (e) of Ti (blue bracket) and oxygen (green bracket) atoms as examples.

To examine the effect of Ti vacancies in Ti3C2O2 MXene, 5%, 10%, 15%, 20% and 25% of Ti atoms in the “Ti-3” sublayer were removed. Due to the existing bonds between terminal O and Ti, if all three neighboring Ti atoms of an O atom were removed, this O atom would be nonbonded and was thus also removed from the system. In this way, high percentages of Ti vacancies also resulted in a small portion of terminal O vacancies. However, the amount of O vacancies created in this way was less than 3%, which was much smaller than the designed oxygen vacancy structures and thus would have limited effect. These modified structures were relaxed using ReaxFF potential, and the friction force and normal force were evaluated. The calculated forces and corresponding friction coefficients of these defective Ti3C2O2 MXenes are illustrated in figure 9 (a) and (b). For normal forces under 1.2 GPa, the friction coefficients increased as the number of Ti vacancies increased in Ti3C2O2. The average rate of friction coefficient change is 4.8×10-5 per Ti vacancy, which is more than 2 times larger than O vacancy. Again, this was suggested to be the result of the increased roughness of surface and the additional attractive forces between adjacent layers. The changes of roughness Rq and Columbic interaction energy as a function of the amounts of Ti vacancies are illustrated in figure 9 (c). As the amount of Ti vacancies increased, Rq increased rapidly when Ti vacancies were less than 10%, and it remained around 0.011 nm until 20% Ti vacancies. The surface roughness slightly dropped when Ti vacancies reached 25%, possibly because of the formation of large area of vacancies by gathering multiple single Ti


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vacancies as observed in experiments48. Similar to O vacancies, the Columbic energy was also increased by the presence of Ti vacancies. In general, Ti vacancies increased both surface roughness and Columbic interaction greater than O vacancies did. The configurations and charges of these Ti and O atoms were analyzed and shown in figure 10. The charges of Ti and O atoms were similar to their charges in the pristine system if there was no Ti vacancy next to them. When there was any Ti vacancy in their closest neighbors, Ti atoms would display more positive charges up to 1.7e and oxygen atoms would display less negative charges up to -0.4e. As the number of neighboring Ti vacancies increased, the magnitude of these changes were magnified. Furthermore, compared to the pristine surface shown in figure 8(a), the geometry of terminal O was rearranged due to the Ti vacancies as illustrated in figure 10(c), which was not obvious in structures with only terminal O vacancies in figure 8(b). Such rearrangement was also observed in experiments48. Compared to the friction coefficients in figure 7(b), the Ti vacancies increased friction coefficients up by 0.06, whose effect was more significant than the O vacancies. Although both point defects increased the friction coefficient of MXene structures, these defective MXenes still maintained friction coefficients below 0.31, which is comparable to results of previous work50,51.


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Figure 9. (Color online) The effect of Ti vacancy on interlayer friction in Ti3C2O2. (a) The friction forces vs. normal forces, (b) Friction coefficients for different amounts of Ti vacancies at 1 GPa. (c) The changes of surface roughness and Columbic interaction energy as a function of the amount of Ti vacancy in Ti3C2O2 MXene.


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Figure 10. (Color online) Visual aid for the charges of terminal oxygen atoms and their neighboring Ti atoms in the surface of Ti3C2O2 MXene along (a) a-axis and (b) c-axis. Color-bar indicates the charges (e) of atoms in the figure. Numbers in bracket give the exact charges (e) of


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Ti (blue bracket) and oxygen (green bracket) atoms as examples. Also shown in (c) is the rearrangement of terminal oxygen atoms. For clarity, only the Ti and oxygen atoms of the atomic layers in the boxed region in (a) are shown in (b) and (c), with the Ti atoms represented as large circles and the oxygen atoms represented as small circles.

3.4 Influence of Surface Species Two-dimensional hybrid materials have drawn much attention in recent years due to their robust properties52,53,54. Among these materials, Ti3C2 MXene functionalized by different organic groups has been investigated for electronic applications.55,56,57 Besides, the surfaces of Tin+1Cn (n=1, 2 or 3) MXenes may also be terminated with -OH groups as considered in earlier experiments and simulations.9,10,11 Therefore, we further considered Ti3C2 MXene functionalized with -OH and -OCH3 groups, similar to those considered by earlier work.48,57 In particular, we replaced the O atom on one surface of Ti3C2O2 by OH or OCH3, respectively. Their structures were then optimized using first principle calculations as illustrated in figure 11 (a-c). The calculations revealed that the H atom in -OH groups stayed on top of O atom, and the structures retained the same symmetry as the original O-terminated Ti3C2. The -OCH3 groups rotated 30° along their C-O bonds compared to initial configuration in Reference 57, which minimized the repulsion of H atoms in the same surfaces in favor of the energy of system. Based on these relaxed structures, the double-layered MXene systems were built, and their relaxed structures by first principle calculations are illustrated in figure 11 (d) and (e). The -OH groups had a slight tilt due to the interaction of H between layers but generally remained the same geometry compared to the surface of single layers (figure 11 (a)). Unlike the -OH groups, the -OCH3 groups


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exhibited a large change of the orientation of C-O bonds compared to the surface of single layers as indicated in figure 11 (b). Such rearrangement of surface -OCH3 groups minimized the repulsion of H atoms from two layers as well as within the same layer.

Figure 11. (Color online) Visual aids for Ti3C2 structures with different surface groups: (a) view along the a-axis of Ti3C2 with -OH groups; view along the (b) a-axis and (c) c-axis of Ti3C2 with -OCH3 groups. Also provided are views along the a-axis of Ti3C2 double-layered structures with (d) -OH groups and (e) -OCH3 groups. Ti, C, O, H atoms are represented as cyan, brown, red, and white circles, respectively. For clarity, few bonds are presented to illustrate the group orientation of -OCH3 in (b), (c) and (e).


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We evaluated the potential energy surface of Ti3C2 MXene terminated with -OCH3 groups, and results are illustrated in figure 12. The sliding pathway was changed due to the presence of surface methyl groups and the energy barrier along the sliding pathway was increased to around 0.93 eV/nm2 (0.10 eV/ CH3 group). Furthermore, when two adjacent Ti3C2 layers were both terminated with O atoms, their stacking of energy maximum and minimum could only be reached by the movement of the whole top layer. However, when they were both terminated with -OCH3, the dangling -CH3 had more freedom to move that could accelerate the transition between stacking of energy maximum and minimum. Therefore, in the potential energy surface of such double-layered systems, the energy maximum (red peak in figure 12) and minimum (blue valley in figure 12) were closer to one another compared to the same system without surface functional groups. The friction coefficients of Ti3C2 MXenes terminated with O, OH and OCH3 are illustrated in figure 13. At normal loadings less than 2.5 GPa, the three structures showed similar responses to the applied loading. However, as the applied normal force increased, the Ti3C2 MXene with -OH group exhibited the lowest friction coefficients of around 0.10, and the friction coefficient of Ti3C2 functionalized with -OCH3 group is around 0.14. Both of these values are substantially lower than the friction coefficient of Ti3C2 terminated with O atoms, possibly because of the strong van der Waals repulsion of hydrogen atoms between layers. Similar reductions of friction coefficients by surface groups were observed in earlier computational and experimental studies58,59,60.


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Figure 12. (Color online) Potential energy surface of Ti3C2 with -OCH3 groups using a 2×2×1 supercell. Black solid lines indicate sliding pathway. The snapshots show the structural geometry corresponding to the map. Ti, C, O, H atoms are represented as cyan, brown, red, and white circles, respectively. For clarity, few bonds are presented to illustrate the group orientation of OCH3.


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Figure 13. (Color online) The effect of surface groups on interlayer friction for Ti3C2.

4. Conclusions This work considered the results of first principles DFT calculations and classical MD simulations with ReaxFF potentials to investigate the interlayer friction in Tin+1CnO2 (n = 1, 2 and 3) MXene structures. We explored the stacking sequence and sliding pathways between adjacent MXene layers. Both DFT and ReaxFF calculations predict the minimum energy pathway for interlayer sliding with low energy barriers along the [100] and [520] directions. The interlayer friction coefficient of these MXene structures was evaluated using static calculations, and both DFT and ReaxFF calculations revealed average friction coefficients between 0.24 and 0.26 for normal forces below 1.2 GPa. The influence of Ti vacancies in the sublayer and terminal O vacancies in the surface on the interlayer friction were also investigated using ReaxFF


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calculations. These point defects increase the roughness of surfaces and lead to changes in the charges of terminal O and sublayer Ti atoms, resulting in additional attractive forces between adjacent layers, thus increasing the friction coefficients between sliding layers. However, such defective MXene structures still possess friction coefficients below 0.31 when normal loadings are less than 1.2 GPa. We further considered Ti3C2 MXenes with surfaces functionalized with OH and -OCH3 groups, or hybrid 2D materials. These groups were predicted to reduce the friction coefficient to 0.10-0.14. This work thus suggests that MXenes are good candidates for use as solid lubricants.

Supporting Information (1) The comparison of DFT and ReaxFF results for interlayer friction in Ti2CO2 and Ti4C3O2, (2) Friction forces along the sliding pathway in Ti3C2O2, (3) the friction vs. normal loadings in Ti3C2O2 at 298K calculated by ReaxFF method, and (4) the effect of O vacancies on friction forces in Ti2CO2 and Ti4C3O2 are provided in the supporting material.

Acknowledgements D.Z. is supported by UNCAGE-ME, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC0012577. D.Z. and S.B.S acknowledge Scienomics MAPS platform61 for building structures and performing DFT calculations. M.A. and S.B.S. acknowledge the support of the National Science Foundation (DMR-1307840). A.O. and A.C.T.vD. acknowledge funding by the Fluid Interface


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Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences for validating the MXene/Oxygen defect ReaxFF description. R.G.H. gratefully acknowledges the support of the National Science Foundation (DMR-1056587 and ACI1440547). The calculations were performed using the resources of the University of Florida's High Performance Computing clusters.

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Computational Study of Low Interlayer Friction in ... - ACS Publications

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