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Graphene-Titanium Interfaces from Molecular Dynamics Simulation Alexandre F. Fonseca, Tao Liang, Difan Zhang, Kamal Choudhary, Simon R. Phillpot, and Susan B Sinnott ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09469 • Publication Date (Web): 04 Sep 2017 Downloaded from http://pubs.acs.org on September 5, 2017

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ACS Applied Materials & Interfaces

Graphene-Titanium Interfaces from Molecular Dynamics Simulation Alexandre F. Fonsecaa*, Tao Liangb, Difan Zhangb,c, Kamal Choudharyc, Simon R. Phillpotc and Susan B. Sinnottb* a

b

Applied Physics Department, State University of Campinas, Campinas, SP, 13083-970, Brazil. Department of Materials Science and Engineering, The Pennsylvania State University,

University Park, PA 16801, United States. c

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

32611-6400, United States. Corresponding Authors * Email: Alexandre F. Fonseca – [email protected], Susan B. Sinnott – [email protected] ABSTRACT: Unraveling the physical and chemical properties of graphene-metal contacts is a key step towards the development of graphitic electronic nanodevices. While many studies have revealed the way that various metals interact with graphene, few have described the structure and behavior of large pieces of graphene-metal nanostructures under different conditions. Here, we present the first classical molecular dynamics study of graphene-titanium (G-Ti) structures, with and without substrates. Physical and chemical properties of equilibrium structures of G-Ti

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interfaces with different amounts of titanium coverage are investigated. Adhesion of Ti films on graphene is shown to be enhanced by vacancies in graphene or electrostatic influence of substrates. The dynamics of pristine G-Ti structures at different temperatures on planar and nonplanar substrates are investigated and results show that G-Ti interfaces are thermally stable, i. e., not prone to any reaction towards the formation of titanium carbide. Keywords: graphene-titanium; COMB3; molecular dynamics; interface; work of adhesion.


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I. Introduction In the last decade, the existence and stability of isolated single layers of graphite, or graphene, have been demonstrated.1,2 Interest in graphene has grown exponentially and has led to the experimental determination of its interesting physical and chemical properties.3 Curiously, the formation of graphene on metal surfaces had been known for decades before the production of free standing graphene.4,5 At that time, the production of graphene was motivated by the need to determine the influence of carbon on catalytic and thermionic activities of the metal surfaces.3,6 The excellent mobility of charge carriers in graphene,7 regardless of its zero band-gap limitations8 has revived interest in investigating the structure and properties of graphene-metal interfaces, as they are key to the development of nanoelectronic devices.9-11 The advancement of chemical vapor deposition (CVD) methods to grow a single layer or a few layers of graphene on metal substrates4 has also motivated the increased number of studies of graphene-metal interfaces. Graphene sheets have been grown on copper by CVD on the centimeter scale,12 which opens up the possibility of large scale and low cost production of devices containing single layer graphene-metal interfaces. Graphene-metal interfaces are critical for applications in catalysis,5,1315

sensors,16,17 nanoelectronics,9-11 hydrogen storage,18-25 and others.3 Unexpected properties of

graphene-metal interfaces have also been reported, including especially high electric resistance of some metal-graphene contacts11 and the formation of wrinkles in graphene due to significant differences in the thermal expansion coefficients of graphene and metals.26-28 The reader is referred to Ref. 3 for a good review on graphene properties and mechanisms associated with its growth on metal substrates. Metals can be either weakly physisorbed or strongly chemisorbed onto graphene depending on the type of metals and the configuration of interfaces.5,29-31 Ag, Al, Cu, Cd, Ir and


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Au tend to form physisorbed interfaces with graphene, while Co, Ru, Pd, and Ti tend to form chemisorbed ones. Interestingly, some metals engage in both physisorbed and chemisorbed bonding configurations to graphene, as recently demonstrated for the graphene-Ni (111)32 and graphene-Pt (111) 33 interfaces. In the case of graphene-titanium (G-Ti) structures, previous work indicated that Ti chemisorbs to graphene,29,34 adsorbs water when bonded to graphene,35 has great potential for water dissociation36 and hydrogen storage,20,23,24 can n or p-dope graphene,37,38 presents asymmetries in the electron-hole conductance,39 and manifests high electric contact resistance11 at the graphene-metal interface. Hence, theoretical descriptions of G-Ti structures at the atomic level are of fundamental importance because they provide knowledge of G-Ti structure-property relationships necessary for prediction and development of applications. Density functional theory (DFT) calculations with van der Waals (vdW) corrections examined the physical properties of single Ti atoms on graphene40 and the effect of Ti - Ti interactions on the bonding of small Ti clusters onto graphene.41 In addition, experiments on Ti nanoparticles and thin films on large graphene samples with42 and without24,34,38 defects reveal that the relation between atomic-level structure and properties of G-Ti is worth investigating at the level of classical MD simulations. There is a controversy regarding the stability of graphene structures after being wetted by Ti thin films. Some experiments34,38 showed that the wetting of Ti on graphene is reversible, i.e., the graphene hexagonal structure is preserved even when Ti thin films are removed from the graphene. This indicates that the interface between graphene and Ti thin films is stable. Another recent experiment indirectly supports this assertion: according to Matruglio et al.,43 a 15 nmthick layer of Ti film was deposited on a graphene sample grown on cooper substrate in order to move graphene from the substrate to a silicon device. They showed that this method can


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efficiently replace the commonly used poly(methyl methacrylate) (PMMA) in removal and transfer of as-synthesized graphene without damaging graphene.43 On the other hand, Gong et al.44 reported an experiment showing that wetting Ti on graphene led to titanium-carbide formation, thus forming end-contact type of contact between graphene and Ti film. Yang et al.45 synthesized Ti-graphene composites using microwave sintering methods and observed also the formation of titanium-carbide. These are controversial results regarding the stability of G-Ti interfaces that deserve more detailed studies. Computational methods could be, then, valuable tools to unravel the reasons behind these experimental results. Numerous13,18,19,20-23,29,32-37,46 DFT studies have been carried out of graphene-metal interfaces, including calculations that make use of vdW corrections.40,41,47 However, only a few classical molecular dynamics (MD) studies of graphene-metal systems27,48-50 exist and, to our knowledge, no previous MD studies of graphene-titanium structures have been carried out using classical reactive or nonreactive force-fields. We are aware of only one MD study of fullerenes decorated with small titanium clusters that used a classical Lennard-Jones potential,51 and one recent study of Ti clusters on carbide-derived carbon.52 This used the third generation of the Charge Optimized Many Body (COMB3) potential,53 recently parameterized to simulate Ti-C-OH multicomponent systems.54 Here, we report the first classical MD study of G-Ti interfaces, using the COMB3 potential.53 The structure and adhesion energies of Ti thin films on graphene are calculated and the results are compared with those from both experiments and first principles calculations. The effects of graphene defects and carbon, metal and metal-oxide substrates on the structure and energy of G-Ti interfaces are also investigated. As an application of the COMB3 potential, MD simulations of G-Ti structures at elevated temperatures, laid on different types and shapes of substrates are carried out to address the above question about the stability of G-Ti


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interfaces for non-defective graphene. The results show that the interfaces of Ti films bonded to pristine graphene remain stable at high temperature and deformed substrates. This work is organized as follows. In Section II, we describe the computational methods employed here. In Section III, we employ the COMB3 potential to study the effects of some graphene defects and different substrates on the structure and adhesion energies of titanium film on graphene. Section IV presents the results for the thermal stability tests of G-Ti interfaces on different substrates at different temperatures. In Section V, we summarize the results and present the conclusions. II. Computational Methods The empirical potential considered in this work is the COMB3 potential,53 and the parameters for multicomponent Ti-C-O-H systems is used,54-56 with additional parameterization for interactions between Ti atoms and graphene as explained in Supporting Information. This additional parameterization has no effect on the original Ti-C previous data.54 COMB3 allows for the dynamical breaking and formation of chemical bonds through the calculation of their corresponding bond order. It adopts a self-consistent charge equilibration approach to dynamically determine the atomic charge of each atom during an MD simulation.57,58 The COMB3 potential is given by the following main equation: COMB3 = , + , + + , (1)

where {r} and {q} represent the set of system atom positions and charges, respectively, and VES, VSHORT, VvdW and VCORR are the electrostatic, short-range, vdW and correction energy terms.


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COMB3 adopts as VSHORT the same functional used by the well-known reactive empirical bond order (REBO) potential, developed by Brenner et al.59 The electrostatic term, VES, includes the energy of formation of the charge on each atom, charge-charge and charge-nucleus interactions, and atomic polarizability. In addition, the van der Walls energy term, VvdW, is given by the classical Lennard-Jones expression60; the correction term, VCORR, consists of a set of functions added to prevent the reactive force-field from predicting non-physical or non-chemical processes/species. COMB3 parameters are determined from a training set obtained from ab initio calculations and experimental data. The details regarding the parameterization of graphenetitanium interactions are presented in Supporting Information and in Ref. 54. The only previous graphene-metal study performed with COMB3 was a recent work describing wrinkle formation in graphene-copper interfaces.27 All the terms given in Eq. (1) depend on parameters that are defined for all elements and pair of different elements that interact, as described in detail in Ref. 53. The MD software LAMMPS61 is used in the simulations. COMB3 with updated Ti-C-OH parameters54-56 is available within this package. COMB3 has also been parameterized to simulate copper and copper-oxide structures.56 We will take advantage of this versatility to study the effects of Cu and Cu2O substrates on the adhesion energy of titanium on graphene. MD simulations and energy minimizations were performed as follows. The Langevin thermostat62 with a damping factors of 100 fs was used in the simulations. Timesteps from 0.1 to 0.25 fs were considered according to the temperature chosen for the simulations: the larger the temperature, the smaller the timestep. The energy minimizations by conjugate gradient methods were performed for both structure and box sizes with force and relative energy tolerances of 10-12 eV/Å and 10-14, respectively. Sets of energy minimizations are performed until the total energy


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of the structure fully converges, i.e., no change is observed after at least three sequences of different energy minimizations. This is done as suggested in the LAMMPS manual63 to ensure that both the structure and box sizes are fully relaxed. In all MD and energy minimization calculations, periodic boundary conditions were considered in the plane of the G-Ti interface. Other details about the MD simulations performed in this work are described along with the presentation of results. III. Graphene on Ti and Ti-Graphene-on Various Substrates: Static Equilibrium Calculations In this section, two different influences on the structure and adhesion of Ti layers on graphene are addressed. The first is the effect of number of Ti layers in G-Ti structures and the effect of existence of defects (vacancies and interstitial) in graphene on the structure and adhesion of Ti layer to graphene. The other is that of placing Ti-G structure on top of different types of substrates. The motivations for these are recent experimental results reporting different coverage behavior of Ti atoms and nanoparticles on graphene with and without vacancies42 and the fact that the DFT estimates for the adsorption energy or work of adhesion of a Ti thin film on graphene are not available when the graphene is supported. DFT methods cannot be used for large systems when lattice parameters of substrates are incommensurable to graphene, requiring large surfaces to minimize any strains when matching graphene and substrate surfaces (see, for example, Ref. 64). The fact that COMB3 has been parameterized for copper,56 copper oxide56,65 and organic-copper systems66 permits us to investigate not only metallic and inert substrates composed of these materials in a seamless manner, but also the interaction of graphene on those substrates.


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III.1 Graphene on Ti We first analyze the dependence of the energies of G-Ti structures on the number of commensurate Ti layers on a graphene surface, from 1 to 35. The graphene structure that is used to generate Ti-G interfaces has the √3 × √3 R30˚ reconstruction with respected to the graphene conventional unit cell. This is the same G-Ti interface considered in Ref. 34. The lattice parameter of the reconstructed graphene cell is 4.26 Å. Considering the lattice parameter of hcp Ti is 2.92 Å, the final Ti-G interfaces used in this study are constructed by stacking 3×3 (8.76×8.76 Å) Ti slab on the 2×2 (8.52×8.52 Å) reconstructed graphene, as shown in Figure 1. Due to the lattice mismatch, about 3% tensile strain is applied to graphene to build the coherent interfaces between graphene and Ti slabs.

Figure 1: The coherent interface between Ti (pink balls) and graphene (cyan sticks). Blue and red diamonds are the unit cells for graphene and Ti. The purple diamond is the superlattice of the Ti-graphene interface, which is the 3×3 Ti on the top of the 2×2 reconstructed graphene lattice with √3 × √3 R30˚ reconstruction.


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Each of Ti-G interfaces with different numbers of Ti layers is then subject to energy minimization to calculate the work of adhesion (WA): A = + !"#$ % & /( ,

(2)

where EG-Ti is the total energy of the relaxed G-Ti interface and A is the area of the interface. EG and ETi_SLAB in Eq. (2) are the total energies of the isolated graphene and Ti metal slab with the same X and Y dimensions with the relaxed G-Ti interface. In order to make comparisons to the results present in literature, the work of adhesion is also computed in energy per carbon atom of graphene by proper change of units from J/m2 to eV/C.

Figure 2: Work of adhesion of Ti layers on graphene as a function of number of Ti layers. Dashed line shows the value to which the work of adhesion converges (~ 2.12 J/m2).


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Figure 2 shows that the WA slightly increases as the number of layers increases, and the value ultimately converges to about 2.12 J/m2 or 0.365 eV/C where eV/C means eV per carbon atom of graphene. This small increase makes senses since it has been recently shown that the maximization of Ti-Ti bonds in Ti clusters bonded to graphene is energetically more favorable than the formation of additional Ti-C bonds.41 The G-Ti interface distance, d, is about 2.37 Å for 6 Ti layers from COMB3 calculation. These interlayer separation and the work of adhesion (2.12 J/m2 or 0.365 eV/C) agree with those from DFT calculations in literature: 0.327 eV/C and d = 2.1 Å for G-Ti - 6 layers;29 0.417 eV/C and d = 2.13 Å for G-Ti - 12 layers;31 and 0.258 eV/C and d = 2.08 Å for G-Ti - 6 layers.34 Recently, Mashoff et al.42 showed that when sputtering Ti atoms on graphene, many small Ti nanoparticles formed when the graphene contained numerous, small vacancies. By contrast, just a few large Ti nanoparticles form on pristine graphene. They also observed that, in the first case, nanoparticles preferentially covered these vacancies. This is not surprising since the binding energy of Ti atom on a vacancy site is large, as shown in Table S1. Here, we examine the formation of thin films of Ti on graphene with vacancies and diinterstitial carbon atoms. Four G-Ti interfaces with these types of defects were studied. For the single vacancy (SV), we considered two cases: one where Ti atoms of the G-Ti interface form bonds to carbon dangling bonds of vacancy (Fig. 3a); and the other where no Ti atom form such a bond (Fig. 3b). Also, for comparison, we tested the adhesion of Ti layers on other two graphene samples with one divacancy (DV) structure called “555-777” and with one diinterstitial (DI) defect, which are considered being very close to or having the smallest formation energies.67,68 The 555-777 DV structure is built according to Ref. 67 (Fig. 3c). According to Ref.


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68, the carbon atoms form 575757 member rings around a 6-member ring near DI region in Graphene (Fig. 3d). We have, thus, considered eight different G-Ti structures formed by 1 and 6 layers of Ti on four defective graphene samples: two samples with one SV, one with Ti atoms bonded to dangling bonds of vacancy sites on graphene, and the other with Ti atoms not-bonded to them; one sample of graphene sample with one “555-777” DV; and one graphene sample with one DI. These eight G-Ti structures with graphene defects are then subjected to relaxation and calculate WA using Eq. (2).

Figure 3:

Top-down views of graphene-defect-centered magnifications of G-Ti structures

formed by 1 Ti layer on defective graphene samples: a) and b) graphene with one single vacancy (SV) with Ti atoms on graphene vacancy sites not-bonded (a) and bonded (b) to the dangling carbon atoms; c) Graphene with “555-777” di-vacancy (DV) and d) di-vacancy (DI). The ring number is shown inside the defects in c) and d). Carbon (titanium) atoms are shown in cyan (pink) color.


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Figure 3 illustrates top-down views of defect-centered magnifications of the relaxed G-Ti structures of 1 Ti layer on graphene with the above defects. Table I shows the differences in the work of adhesion for all eight cases of defective G-Ti above described. Amongst all cases, the GTi structures with Ti atoms bonded to the dangling carbon atoms has the strongest adhesion. This indicates that having the Ti bonding to the carbon dangling bonds is more energetically favored than forming more or stronger Ti - Ti bonds. This behavior might be explained by the large binding energy of Ti on graphene vacancy site46 and because Ti layers already have many Ti - Ti bonds.41 The differences in adhesion energy of the Ti layers on pristine graphene are quite independent of the number of Ti layers. Results presented in Table I show that thin films of titanium more strongly adhere to graphene with vacancies than to pristine graphene. TABLE I. Work of adhesion, in J/m2, of eight G-Ti structures formed by 1 and 6 Ti layers on four defective graphene samples: two samples with SV, with Ti atoms on graphene vacancy sites bonded, or not, to the dangling carbon atoms (“Ti - SV bonded” or “Ti - SV non-bonded” columns in the table, respectively), one graphene sample with one “555-777” DV, and one graphene sample with one DI. In parenthesis, the difference (in J/m2) to the adhesion energies of the same G-Ti structures on pristine graphene: WA = 2.162 (2.043) J/m2 for G-Ti with 1 Ti layer (6 Ti layers).

# of Ti layers

Graphene defect type: Ti - SV bonded

Ti - SV non-bonded

DV

DI

1

2.227 (+0.065)

2.140 (-0.022)

2.164 (+0.002)

2.134 (-0.028)

6

2.108 (+0.065)

2.014 (-0.029)

2.030 (-0.013)

2.014 (-0.029)

III.2 G-Ti Structures on Various Substrates


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The effects on the work of adhesion of placing the G-Ti structures on a substrate are investigated here. The following substrates are considered: i) several additional layers of graphene; ii) Cu (111) and Cu (100); and iii) Cu2O (110) that is either oxygen-terminated or both copper- and oxygen-terminated, from now on called “Cu2O:Cu” and “Cu2O:CuO”, respectively. The structure details as equilibrium sizes and lattice mismatches between G-Ti and substrate are shown in Table II. Figure 4 shows the structures and Tables III and IV present the results for the work of adhesion of G-Ti structures with 1 Ti layer, as calculated using Eq. (2), where the constituent slabs are 1 Ti layer and G-substrate interface. The work of adhesion computed this way represents the energy of attaching one Ti layer to the graphene free side of a G-substrate system. TABLE II. Equilibrium sizes, lattice mismatch and graphene-substrate orientation of each G-Ti – substrate structure studied here. Lattice mismatches are calculated as follows: (16aGRA – 9dCu111) for G-Ti-Cu (111); (16aGRA – 11aCu) for G-Ti-Cu (100); and (16aGRA – 9aCu2O) for G-TiCu2O:Cu (110) and G-Ti-Cu2O:CuO (110), where dCu111 = )3/2 aCu, aGRA = √3 dCC, dCC = 1.42 Å, aCu = 3.62 Å65 and aCu2O = 4.27 Å.65 The orientation between graphene and substrate is given for substrates where the lattice is parallel to the G-Ti plane. Substrate

8 layers of graphene

Cu (111)

Cu (100)

Cu2O:Cu (110)

Cu2O:CuO (110)

Equilibrium sizes (X × Y) [Å]

39.4 × 42.6

39.5 × 43.0

39.4 × 43.0

39.7 × 42.6

39.7 × 42.7

Lattice mismatch [Å]

0

-0.54 Å

-0.46 Å

-0.93 Å

-0.93 Å

Graphene – substrate orientation [rads]

0

-

0

0

0

In Table III, we present the work of adhesion of 1 Ti layer on graphene in terms of the number of additional graphene layers. It clearly shows that there is a small increase in the work


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of adhesion energy by the addition of one graphene layer behind the G-Ti interface, and that this gain decreases and converges to a specific value as the number of layers increases.

Figure 4: Pieces of the G-Ti structures on the different substrates considered in this study. The planar sizes of the simulated structures are given in Table II. From a) to e): Cu (111), Cu (100), graphene layers, Cu2O:Cu (110), and Cu2O:CuO (110), respectively. Cu2O:Cu (Cu2O:CuO) means Cu2O surfaces with Cu (Cu and O) terminated atoms. G-Ti (substrate) structures are shown in ball and stick (van der Waals) models. Cyan, pink, brown and red represent carbon, titanium, copper and oxygen atoms, respectively.


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TABLE III. Work of adhesion, WA in J/m2 of the G-Ti interface, and variation of the work of adhesion with respect to that of free standing G-Ti structure, of 1 Ti layer on graphene in terms of the number of additional graphene layers. “# layers” is the number of additional layers of graphene. “0 layers” means the free standing G-Ti structure. # layers

0

1

2

3

4

5

6

7

8

WA [J/m2]

2.162

2.218

2.212

2.213

2.214

2.214

2.214

2.214

2.215

∆WA [J/m2]

0

+0.056

+0.050

+0.051

+0.052

+0.052

+0.052

+0.052

+0.053

TABLE IV. Work of adhesion, WA in J/m2 of the G-Ti interface, and variation of the work of adhesion with respect to that of free standing G-Ti structure, of 1 Ti layer on graphene on different substrates. Substrate

Free standing G-Ti

1 layer of graphene

Cu (111)

Cu (100)

Cu2O:Cu (110)

Cu2O:CuO (110)

WA [J/m2]

2.162

2.218

2.508

2.501

2.704

2.462

∆WA [J/m2]

0

+0.056

+0.346

+0.339

+0.542

+0.300

Table IV shows the work of adhesion of 1 Ti layer on graphene for the substrates rendered in Figure 4. The work of adhesion of a Ti layer on graphene increases as a result of the presence of all of the substrates considered. This interesting result might be qualitatively explained in terms of the role played by the induced charges on the interactions between substrate and G-Ti structure. Table V shows the signs of the electrostatic charges of the


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uppermost atoms of the substrate in comparison to the sign of the charges of the carbon atoms of G-Ti structure. In the equilibration charge calculations of COMB3, the charge of all atoms is allowed to change in order to reach the thermodynamic equilibrium of the electronegativity. In free standing G-Ti structures, carbon atoms acquire net negative charge and titanium atoms on the top sites acquire positive charge. When a substrate is included in the system, the sign of the induced charges on the top layer of atoms of the substrate is positive. The sign of the charges of the carbon and titanium atoms in the G-Ti interface remains the same. However, the absolute values of the induced charges on the carbon atoms not bonded to titanium atoms can increase, in average, up to 4 times that of free standing G-Ti structures (Table V). Then, the attractive force between Ti layer and graphene increases, thus increasing the work of adhesion. The approximate average values of the induced charges on the carbon atoms not bonded to titanium atoms for each substrate considered is shown in the third row of Table V. We can see that these values correlate to the amount of variation of the work of adhesion with respect to that of free standing G-Ti structure, of 1 Ti layer on graphene on different substrates, shown in third row of Table IV. TABLE V. Signs of the electric charges acquired by the uppermost atoms of the substrate, as the result of the charge equilibration calculations of COMB3. The type of the uppermost atoms on the substrate is shown in parentheses. Third row shows the approximated average amount of times the sign of the charges of the carbon atoms not bonded to titanium atoms in G-Ti interface increases due to the substrate. 1 layer of graphene + (C) 1.5

Cu (111) + (Cu) 3.8

Cu (100) + (Cu) 3.7

Cu2O:Cu (110) Cu2O:CuO (110) + (Cu) + (Cu) 4.4 3.8


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In the case of Cu2O:CuO (110) structure, we would expect to observe a repulsive behavior between G-Ti and substrate because of the presence of oxygen atoms on the uppermost surface of the substrate. Oxygen atoms possess large electronegativity and would lead to an electrostatic repulsion between them and the carbon atoms of G-Ti interface. However, the relaxed structure shows that the oxygen atoms at the uppermost layer of the Cu2O:CuO (110) substrate move away from the G-Ti surface. This might be an effect of the electrostatic repulsion by the carbon atoms of graphene. Figure S1 of Supporting Information presents the lateral views of initial and relaxed structures of G-Ti on Cu2O:CuO (110) and G-Ti on Cu2O:Cu (110). In the Cu2O:Cu case, the copper atoms are already on the uppermost surface, and as the first row of oxygen atoms are relatively far away from the graphene, the electrostatic attraction is the largest among the substrates studied, which is reflected in the largest increase of the work of adhesion of Ti layer on graphene. The slight deformation on the Cu uppermost atoms on Cu2O:Cu substrate is a consequence of attractive forces between them and the carbon atoms of graphene. IV. Thermal Stability of Pristine Graphene-Ti Interfaces Here, we will take advantage of the parameterization of graphene - titanium interactions, as described above, to test the thermal stability of the structure of G-Ti interfaces in different situations, including laying the G-Ti structure on a substrate and studying finite G-Ti layers on substrates of different shapes. We want to verify if substrate properties can lead to any possible reaction between carbon atoms of graphene and titanium atoms of the first Ti layers, under large thermal fluctuations. Although we performed the tests running the simulations at several values of temperature, between 300 K and 1000 K, the results for only two values of temperature will be shown here: 600 K and 1000 K. The results are presented and discussed below.


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IV.1 G-Ti Structures on Various Substrates Thermal tests of integrity of G-Ti structures with 6 Ti layers on several substrates were performed by MD simulations at different temperatures. The Langevin thermostat was used in these simulations with different values of damping factor as described above. Two sets of structures were considered. One set consists of G-Ti structures completely covering the substrate, and with sizes about 116 × 129 Å, thus much larger than those shown in Figure 4. In this case, periodic boundary conditions along planar directions were applied to all structure. For these structures, timesteps of 0.25 fs (0.1 fs) were used for the simulations at temperature of 600 K (1000 K), with a thermostat damping factor of 100 fs chosen in order to quickly obtain energy convergence. The other set of structures consists of simulating finite G-Ti samples on substrates of different shapes. In these cases, a timestep of 0.2 fs was used, periodic boundary conditions along planar directions were applied only to the substrate and we used a thermostat damping factor of 100 fs. Figures 5 and 6 present snapshots of some structures of the first and second sets of structures (completely and not completely covering the substrate), respectively. The reason for the consideration of the second set of structures is to investigate the possible effect of the finite size of the G-Ti structure and substrate planarity effects on the integrity of the G-Ti interfaces. In all cases, the bottom two layers of atoms of the substrate were kept fixed in order to simulate the structural order of a thick substrate. Figure 5 shows the snapshots of relevant examples of G-Ti completely covering the substrates. We can see that the G-Ti interfaces remained stable even after several picoseconds of MD simulations at 600 K and/or 1000 K. Lateral views of these structures show that for 1000 K (central and right panels of Figure 5), the surface of graphite and pure cooper substrates, as well as the G-Ti interface, deform significantly in a way that would help promote chemical reactions.


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However, even for these cases, no chemical reaction happened between carbon and titanium atoms towards the formation of titanium-carbide. At least, it was not observed within the total time of simulations that went from a minimum of 150 ps to a maximum of 500 ps.

Figure 5: Inclined and lateral views of snapshots of G-Ti structures of sizes about 116 × 129 Å on three substrates: Cu2O:Cu (110) at T = 600 K, after 150 ps (left); graphite at T = 1000 K, after 300 ps (center); and Cu (100) at T = 1000 K, after 260 ps (right). Upper structures are shown in van der Waals models, and lower structures are shown in ball and stick (G-Ti) and van der Waals (substrate) models. Cyan, pink, brown and red represent carbon, titanium, copper and oxygen atoms, respectively. Before concluding the study of thermal fluctuations of G-Ti interfaces, we performed additional tests on finite G-Ti samples laid on substrates with different shapes. The idea is to investigate if edges or substrate shape could induce any new chemical reaction between carbon and titanium atoms. Graphene structures, in these cases, are passivated by hydrogen atoms to avoid spurious deformations of the edges. G-Ti finite structures with sizes about 180 × 90 Å and 6 Ti layers on Cu (111) substrates of different shapes: regular, curved, kinked and suspended,


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were prepared and simulated. The orientations of graphene, titanium and cooper substrate along x and y directions in these structures are the same as shown in Figures 1 and 4a. Figure 6 shows snapshots of three relevant finite G-Ti structures on Cu (111) after, at least, 100 ps of MD simulation at 600 K of temperature.

Figure 6: G-Ti structures on the Cu (111) substrates of different shapes after, at least, 100 ps of MD simulation at 600 K. Left: upper view of the initial structure, where the Ti thin film has 6 layers and dimensions of 180 x 90 Å. Right: snapshots of G-Ti structures on (from top down) regular, curved, kinked and suspended substrates. All structures are shown in van der Waals models. Cyan, white, pink, brown and red represent carbon, hydrogen, titanium, copper and oxygen atoms, respectively. Close inspection of the G-Ti interfaces of the samples displayed in Figure 6 shows that there is no carbon-titanium reaction towards the formation of titanium-carbide. It is a remarkable result because COMB3 is parameterized for the description and formation of titanium-carbide. It predicts a negative heat of formation of titanium-carbide from graphite and bulk Ti of about 1.64 eV/TiC.54 However, as the ratio of Ti to C atoms at the G-Ti interface is about 3 Ti atoms to 8 C atoms, and the titanium-carbide has a rock salt structure with 1:1 stoichiometry, the formation of the titanium-carbide structure at the interface would require a significant amount of


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carbon diffusion towards the Ti thin film. Carbon-carbon sp2 bonds are too much strong to be easily broken by thermal fluctuations, even at large temperatures (graphene is predicted to melt at temperatures larger than 4500 K69), so it is reasonable that G-Ti interfaces remain stable. Therefore, as far as COMB3 is accurate, this implies that pristine graphene can be considered resilient to the formation of titanium carbide in G-Ti interfaces. These tests were also made at 900 K (data not shown) and showed no formation of titanium carbide species. Above 900 K, the titanium nanostructure was observed to form irregular upper surface of the Ti thin film of the structures shown in central and right panels of Figure 5. The above results are consonant with a theoretical study of the destruction of graphene by metal adatoms by Boukhvalov and Katsnelson.70 They showed that carbide local structures can be easily formed when small clusters of metal atoms bind to a divacancy in graphene. So, the growth of Ti film on defective graphene might explain the experimental controversy mentioned in the Introduction. Thermal fluctuations of G-Ti interfaces formed by defective graphene should also be examined; as this is beyond the scope of the present work, further simulations on defective graphene-titanium interfaces will be subject of a future publication. V. Conclusions We have performed the first comprehensive study of the adhesion and structural properties of G-Ti structures using the COMB3 force field. We have verified the ability of the recently developed set of COMB3 parameters to simulate Ti-C-O-H multicomponent systems5456

to describe the structure of Ti thin film on graphene. We obtained good agreement with the

literature results on both experiments (the ones that reported the stability of G-Ti interfaces) and DFT calculations on G-Ti structures. One advantage of using COMB3 in this study is the fact


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that there is no need to combine different force fields to simulate different subsystems and no need to make use of simple functionals, with adjustment of parameters, for the interaction between them. Also, COMB3 is a reactive potential that can capture the bond breaking and formation during a dynamical simulation. In summary, our results show that COMB3 reproduces the chemisorption of Ti thin film on graphene and that the work of adhesion of Ti layers on a graphene structure changes only slightly with the number of Ti layers, converging to a value of ~ 2.12 J/m2. The hexagonal structure of graphene remains with few distortions independent of the number of Ti layers, i. e., the perfect graphene structure is completely recovered after removing the Ti thin film (data not shown) as observed experimentally. Adhesion energies of Ti layers to graphene were shown to increase when vacancies are present. The results regarding the effects of substrates on the work of adhesion of Ti on graphene show that, due to electrostatic effects, the choice of substrate can increase or decrease the adsorption of Ti thin film on graphene depending on the surface termination of the substrate. Although first principles calculations for the equilibrium charges of the atoms of these structures can be expected to have higher materials fidelity, the trends observed here for the induced charges in both substrates and G-Ti structures suggest that the electronic properties of G-Ti might be influenced by the substrate. Disregarding the limitations of small system sizes when using DFT, the above results could be, at least qualitatively, confirmed by ab initio calculations. We believe these results will motivate new experimental and theoretical studies on the G-Ti structures with and without substrates.


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One important experimental issue was partially addressed here through MD simulations of G-Ti structures on different substrates. The thermal stability of G-Ti interfaces at planar and non-planar substrates were verified indicating that pristine graphene is resilient to reactions towards the formation of titanium-carbide, as observed in some experimental reports.34,38,43 Although the heat of formation of titanium-carbide is negative,54 the inertness of G-Ti interfaces predicted here can be understood to be the consequence of kinetic effects since the stoichiometry of the G-Ti interface is different from what is required to form titanium-carbide. Additionally, there is a substantial energy cost to break carbon-carbon bonds in graphene and for the carbon atoms to diffuse within the Ti film. This issue will be further investigated in future by simulating defective graphene-titanium interfaces at different temperatures and on different substrates. Other issues arising from the results include how other types of defects in graphene and grain boundaries affect the work of adhesion of Ti on graphene, as well as the interactions between graphene oxide and titanium atoms. Now that a reliable force field for classical MD simulations of Ti-C-H-O systems does exist, these and other issues related to mechanical and thermal properties of G-Ti structures can be addressed using the same force field. These will also be subject of future investigations. Acknowledgments The authors acknowledge helpful discussions with Dr. Stephen McDonnell. A.F.F. is a fellow of the Brazilian Agency CNPq (#302750/2015-0) and acknowledges grant #2016/00023-9 from São Paulo Research Foundation (FAPESP). This research also used the computing resources and assistance of the John David Rogers Computing Center (CCJDR) in the Institute of Physics “Gleb Wataghin”, University of Campinas. T.L., D.Z., K.C. and S.B.S. were supported


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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. Supporting Information: It contains the details regarding the parameterization of graphenetitanium interactions and one figure showing the lateral views of initial and relaxed structures of G-Ti on Cu2O:CuO (110) and G-Ti on Cu2O:Cu (110).

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