van der Waals-Corrected Ab Initio Study of Water Ice–Graphite

Article pubs.acs.org/JPCC

van der Waals-Corrected Ab Initio Study of Water Ice−Graphite Interaction Alberto Ambrosetti* Fritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

Francesco Ancilotto and Pier Luigi Silvestrelli Dipartimento di Fisica e Astronomia, University of Padova, via Marzolo 8, I−35131, Padova, Italy CNR-IOM-Democritos, Trieste, Italy ABSTRACT: The interaction between a water−ice bilayer and graphite is investigated by means of standard and van der Waals-corrected density functional theory. The long-range van der Waals attraction proves to be dominant in this context due to the absence of strong chemical bonding between the ice bilayer and graphite. Our calculations suggest that both adsorption of the ice bilayer on graphite and its intercalation between graphene layers are energetically favorable. This second configuration, however, is expected not to be easily realizable due to the elevated energy barrier with respect to the intercalation of a single water molecule. The energy barriers relative to the sliding of the ice bilayer on graphite are also computed. Interestingly, these appear to be two orders of magnitude lower than those relative to graphene−graphene sliding in graphite. This result suggests that the sliding of water on the graphite surface might play a relevant role in determining the well-known lubricating properties of graphite in the presence of humidity.

I. INTRODUCTION The interaction between water and graphite represents a topic of particular interest. Graphite can be considered as a valuable model for investigating adsorption mechanisms on carbonaceous systems. Among these, it is certainly worth mentioning carbon nanotubes due to their scientific and technological interest and to the peculiar conformations they induce in confined water clusters.1 The study of the water−graphite interaction is related to the understanding of the structure and reactivity of ice films and of the behavior of water clusters on the nanoscale. As a consequence, during the last years, several theoretical investigations were carried out on the topic, making use of diverse many-body approaches.1−4,7 Despite the intense theoretical and experimental work on graphite, some fundamental issues relative to the water− graphite interaction remain still open. One of the most intriguing is certainly the understanding of the role of water in the lubricating properties of graphite. Graphite has long been known for its slipperiness and still represents one of the predominant materials used in solid lubrication. Although the low friction was initially considered to be an intrinsic property of graphite, in the late 1930s, it became clear how its lubricating properties were strictly connected to the presence of humidity in the environment. In fact, under dry conditions, graphite cannot be considered as a good lubricant any longer, as it undergoes a substantial increase in friction and wear rate.8 In the last decades, several interpretations were given to the graphite lubrication properties.9−12 These typically involved the © 2012 American Chemical Society

shearing of basal planes, induced by either the intercalation of water between the topmost layers or a chemisorption of water molecules on the surface, resulting in a weakened interplanar interaction. Experimentally,13,14 no change of interplanar spacing was found from X-ray diffraction upon exposure to water vapor, in contrast with the hypothesis of water intercalation or basal plane chemisorption. A lattice shear model thus seems to be excluded. As an alternative, Deacon and Goodman13,15 suggested that the dangling bonds of the outmost planes might be saturated by vapor molecules, resulting in a reduced adhesion force at the surface. This hypothesis, in particular, could not be ruled out from the experimental point of view. A further mechanism, involving a sliding of water on the graphite surface, seems so far to have been overlooked. Such a mechanism would clearly require low-energy barriers upon lateral displacement of water molecules. Interestingly, previous theoretical investigations found no significant preference for the adsorption site2 and predicted ultrafast diffusion of water on graphene at low temperatures.4 These results support the hypothesis of a relatively flat potential energy surface, corresponding to weak lateral energy barriers. Moreover, in the last years, atomic-scale friction measurements suggested the Received: September 27, 2012 Revised: December 7, 2012 Published: December 11, 2012 321

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presence of condensed water films having crystalline structure, between tungsten tip and graphite surface.5,6 In the present article we address by means of a theoretical ab initio approach some of the open questions regarding the water−graphite interaction. In particular, we outline how the sliding of a water ice bilayer on graphite is strongly favored with respect to the shear of graphene layers. This suggests that water might give a lubricating effect when in contact with graphite and graphene surfaces.

The binding energy, defined as E bind = −Etot + (Egraphite + E BL)

(1)

where Etot is the energy of the complex and Egraphite and EBL are those of isolated graphite and water BL, respectively, was computed using different functionals. Two basic configurations were investigated: ice BL adsorption on graphite and ice BL intercalation in graphite. We consider first adsorption of ice BL on graphite. Two different views of the equilibrium structure are shown in Figures 1 and 2. All calculations for this configuration were

II. METHOD We have performed a series of density functional theory (DFT) calculations, making use of plane-wave basis sets and pseudopotentials, as implemented in the Car−Parrinello molecular dynamics (CPMD)16 and quantum espresso17 codes. Different exchange−correlation (xc) functionals were employed, such as LDA and PBE.18 To achieve an accurate description of dispersion (which is known to play a key role in physisorption processes), van der Waals (vdW) corrections were also introduced. This was accomplished through the vdWDF,19,20 vdW-DF2,21 and the DFT/vdW-WF22 methods. The first two schemes introduce a nonlocal term in the xc functional. The third is a post-processing highly efficient approach, in which the vdW energy contribution is computed as a pairwise summation of Cij6/R6ij terms damped at short distance. The pairwise C6 coefficients are obtained from the DFT ab initio electronic structure by means of a charge partitioning based on the maximally localized Wannier functions.23 Graphite was modeled with two graphene layers with A−B stacking. The periodic cell contained 144 C atoms, and an empty region of 16 Å width was left among the graphite replicas, in the direction orthogonal to the graphene planes. The interatomic C−C distance was fixed to the experimental value24 of 1.421 Å, and the graphene interlayer spacing was set to 3.34 Å.

Figure 1. Water ice BL adsorbed on graphite.

Figure 2. Water ice BL adsorbed on graphite, side view.

carried out by keeping the graphene interlayer distance fixed at the experimental value. From Table 1, we observe how the

III. RESULTS To assess the possibility of water intercalation in graphite, we preliminarily computed the energy of a water molecule located between the two graphene layers using the LDA approximation. Although LDA lacks a correct accounting of dispersion and of water−water hydrogen bonding, it is also known to provide a reasonable description of the interlayer spacing in graphite at a rather low computational cost.7,25−28 A geometry optimization was thus performed keeping the lower graphene layer frozen to mimic intercalation at the basal planes. The relaxation resulted in a strong deformation of the upper graphene layer due to the water−graphene short-range repulsion. Moreover, the relaxed configuration appeared to be unfavored with respect to separated water and graphite by ∼3 eV. This large energy difference suggests that the onset of water intercalation will be strongly hindered by the adhesion of graphene planes. The present result agrees with the experimental evidence, showing the absence of interlayer expansion. As a next step, toward a more realistic description of the interaction of graphite with water films, we considered a periodically repeated water ice bilayer (BL) consisting of 24 molecules per cell. The crystalline structure of BL was taken from the cubic ice structure and relaxed over the graphite surface using the PBE functional29,30 due to its good description of water−water interactions.

Table 1. Binding Energies Per Water Molecule and Equilibrium Distances (the Average Distance between the Upper Graphite and the Lowest Ice O Atoms) for Water Ice BL and ML (only vdW-DF) Adsorbed on the Graphite Surface xc functional

distance (Å)

Ebind (meV)

LDA (BL) PBE (BL) vdW-DF (BL) vdW-DF2 (BL) DFT/vdW-WF (BL) vdW-DF (ML)

3.06 3.70 3.33 3.22 3.09 3.38

56.3 9.6 99.6 88.1 121.6 138.2

adsorption of ice BL on graphite appears to be energetically favored with all considered DFT approaches. Clearly, the largest part of the BL−surface attraction will be provided by the long-range dispersion interactions. The PBE xc functional, due to the lack of a correct description of long-range correlation, misses a substantial contribution to the overall binding, thus leading to severely underestimated BL−graphite attraction. Interestingly, the vdW-DF/vdW-DF2 and DFT/vdW-WF methods, including vdW energy corrections, appear to be in 322

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relatively good agreement. This certainly supports the validity of both vdW correction approaches. The LDA functional, although predicting weaker binding with respect to both vdWDF and DFT/vdW-WF, provides a larger attraction than PBE. To investigate the nature of the binding, we computed the electron density difference between interacting and isolated fragments (ice BL and graphite) using vdw-DF. (See Figure 3.)

Figure 4. Water ice BL intercalated in graphite, side view.

Table 2. Binding Energies Per Water Molecule and Equilibrium Distances (between the Upper and the Lower Graphite Plane) for Water Ice BL and ML (only vdW-DF) Intercalated in Graphitea

Figure 3. Electronic density difference between interacting and isolated fragments computed with vdW-DF. Blue and orange areas correspond to isosurfaces of −0.006 and +0.006 e Å−3, respectively.

The charge rearrangement appears to be relatively small and localized around the water H atoms pointing toward the surface. For comparison, the density difference in a hydrogenbonded water dimer with respect to the isolated molecules was about seven times larger. This suggests that there is a weak tendency to form a hydrogen-like bonding between water and surface, which, however, does not lead to large charge rearrangements and leaves a dominant role to the long-range vdW attraction. Concerning the equilibrium geometries, DFT/vdW-WF gives a BL−graphite distance in agreement with LDA and somewhat smaller than vdW-DF/vdW-DF2. All of these, however, indicate a preference for closer distances with respect to PBE, due to the inclusion of vdW attraction. Although our initial results suggest that the presence of a single water molecule between two graphene layers will be strongly unfavored (at least in absence of defects), a different picture might come out by considering the intercalation of a full water layer (see Figure 4). In fact, from Table 2, one observes how all DFT approaches predict ice BL intercalation to be energetically favored. This is due to the absence of the large deformations of the graphene layers that occur when a single molecule is inserted and to the contemporary presence of a BL−graphene attraction, compensating for the graphene− graphene increased separation. The binding energies were computed using two different reference configurations for isolated graphite. In the first, the graphene interlayer distance was set to the experimental value, whereas in the second it was fixed to the equilibrium value in the presence of the intercalated BL. Especially in view of the tiny binding energies, we warn that the present approach does not account for possible finite temperature effects, which might actually lead to a somewhat different picture in experimental realizations. The fourth column of Table 2 shows once more the agreement between vdW-DF and DFT/vdW-WF. The PBE functional predicts substantially lower binding, whereas LDA gives an intermediate behavior between PBE and vdW-corrected DFT. Moreover, all methods except PBE yield larger binding energy when

xc functional

distance (Å)

Ebind1 (meV)

Ebind2 (meV)

LDA (BL) PBE (BL) vdW-DF (BL) vdW-DF2 (BL) DFT/vdW-WF (BL) vdW-DF (ML)

7.09 8.20 7.67 7.46 7.19 6.84

37.4 63.4 60.2 48.9 144.6 54.8

115.1 21.7 183.4 161.7 164.7 260.7

a

In Ebind1, the reference Egraphite is computed at graphene interlayer experimental distance. For Ebind2, the graphene−graphene spacing was set to the distance of equilibrium in the presence of ice bilayer intercalation.

experimental graphene interlayer spacing is considered (see column 3). This is due to the energy cost related to the separation of the graphene sheets. Interestingly, the PBE functional predicts a relatively strong graphene−graphene repulsion (∼1.38 eV per cell at experimental spacing), thus favoring large interlayer distances. This also explains the large difference existing between vdW-DF/vdW-DF2 and DFT/ vdW-WF in the third column. As implemented in QE, the vdW-DF method relies on a revPBE short-range xc functional, and this yields a presumably better estimate of the graphene interlayer binding. The deviation between the two vdW methods should thus be attributed to the short-range behavior of the underlying xc functionals and not to an incorrect estimate of the long-range vdW effects. The qualitative agreement between the LDA binding energies with vdW−corrected estimates does not seem surprising because LDA is known to often provide an improved description of the adsorption energy with respect to PBE. This result, however, should not be overemphasized, the larger LDA attraction being due to an overestimate of long-range part of the exchange contribution. More importantly, LDA could not reproduce the long-range behavior of dispersion interactions; hence, it will suffer further accuracy loss at larger distances. Concerning equilibrium distances, the picture is similar to that found for the adsorbed ice BL: DFT/vdW-WF is in 323

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substantial agreement with LDA, whereas vdW-DF/vdW-DF2 shows a somehow intermediate behavior with respect to PBE. The water ice BL is commonly rewarded as the thinnest stable crystalline water film.31−33 In fact, the relaxation of an isolated ordered structure of water molecules having all oxygen atoms placed on a single plane eventually leads to a BL-type structure to optimize the geometry of the hydrogen bonds structure. However, in the presence of adsorption, the interaction between the surface and the water molecules might lead to slightly different geometries. In fact, the relaxation of a water monolayer (ML) having 12 water molecules per cell adsorbed on graphite simply leads to a rearrangement of the hydrogen atoms. (See Figure 5.) The water−graphite attraction

Figure 6. Dotted line indicates the sliding direction.

Table 3. Sliding Barriers (per cell) for Ice BL and ML with Respect to Graphite in Both Adsorbed and Intercalated Configurationsa BL adsorbed BL intercalated ML adsorbed ML intercalated graphene graphene−BL adsorbed

ΔE (meV)

0.62 0.62 0.62 0.62 1.23 1.23

5 47 8 42 410 382

a Energy barriers for graphene−graphene shear are given both for pure graphene and in case of adsorbed BL.

Figure 5. Water ice ML adsorbed on graphite.

is sufficient to compete with the optimization of the H-bonding geometry due to the low density of water molecules. From Tables 1 and 2, one sees how the graphite substrate provides a similar attraction for BL and ML. One should, however, keep in mind that the formation of a BL starting from single water molecules is clearly favored with respect to the ML due to the stronger H-bonding structure. By defining the binding energy with respect to isolated graphite and isolated water molecules as E bind,H2O = ( −Etot + Egraphite + NH2OE H2O)/NH2O

distance (Å)

relaxation of the ice BL, whereas graphite was kept frozen at experimental graphene spacing. In the absence of geometry relaxation of water, the results are not substantially changed (4.7 meV), confirming the existence of a highly flat energy surface upon lateral displacement. One can notice how the isolated ice BL structure has a different number of H atoms pointing upward (8) and downward (4). Whereas adsorbing the BL upside-down does not change the adsorption energy substantially (3.3 meV per water molecule, corresponding to 3% of the whole binding energy), slightly lower energy barriers (3.6 meV in absence of BL relaxation) are found for the case in which 8 H atoms (instead of 4) are pointing toward the graphite surface. Interestingly, the energy barrier relative to graphene− graphene shear (410 meV) appears to be about two orders of magnitude larger. This value is only slightly reduced when an adsorbed water BL (382 meV) is considered in the calculation. For completeness, we also investigate the friction properties of intercalated ice BL. By displacing the BL within the graphene sheets while leaving C atoms frozen, an energy barrier of 45 meV was found. Similar results were obtained (47 meV) by sliding the BL with respect to the lower graphene and contemporarily displacing the upper graphene sheet in the same direction. Moreover, displacing only the upper graphene and subsequently relaxing the water BL again resulted in a similar estimate (46 meV). Although one order of magnitude larger than the barrier for adsorbed water BL, these are still 1 order of magnitude smaller than those relative to graphite− graphite shear. Considering the sliding of both the adsorbed and intercalated water ML (see Table 3), the picture is analogous: the sliding barriers (8 and 42 meV for adsorbed and intercalated film, respectively) are almost equivalent to those of the BL. We thus expect the water−graphite friction not to be highly sensitive on the thickness of the adsorbed ice slab. The above results suggest that water molecules mainly interact with graphite through vdW forces, without the formation of strong chemical bondings. The rather homoge-

(2)

where EH2O is the energy of the single water molecule and NH2O is the number of water molecules in the system, we found using vdW-DF a value of 138 meV for adsorbed ML and 478 meV for adsorbed BL (206 and 439 meV for intercalated ML and BL, respectively). As a consequence, although the present calculations indicate the water ML structure as a stable configuration, this will be probably hard to realize in practice due to the competition with the energetically more favorable BL. Because of the particular interest in the lubricating properties of graphite, we also performed a study of the energy barriers associated with the sliding of adsorbed ice BL with respect to the underlying graphite substrate. The calculations were performed with the vdW-DF method, which, as evident from Table 2, appears to be free from graphene−graphene fictitious repulsion. Given the relatively isotropic structure of graphene sheets, we restricted our study to the sliding along the direction shown in Figure 6. The energy of the system was computed for several values of the lateral displacement. The barriers were then estimated as the difference between the highest energy and that of the initial configuration (the lowest energy). Also, in this case, we stress that the present estimates for the energy barriers do not account for possible entropic effects. A more accurate evaluation of the energy barriers at finite temperature could be achieved through the use of free-energy sampling techniques. Table 3 shows a very low-energy barrier for ice BL sliding on the graphite surface. The result of 5 meV was obtained after 324

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(12) Teo, K. M.; Lafdi, K. Tribol. Trans. 2001, 44, 664−670. (13) Deacon, R. F.; Goodman, J. F. Proc. R. Soc. London, Ser. A 1958, 243, 464−482. (14) Yen, B. K.; Schwickert, B.; Toney, M. F. Appl. Phys. Lett. 2004, 84, 4702−4704. (15) Skinner, J.; Gane, N.; Tabor, D. Nat. Phys. Sci. 1971, 232, 195− 196. (16) Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471−2474. We have used the code CPMD developed by Hutter, H.; et al. (1990− 2006): http://www.cpmd.org/ (accessed Aug 15, 2012). (17) Giannozzi, P.; et al. J. Phys.: Condens. Matter 2009, 21, 395502− 395520. (18) Perdew, J. P.; Burke, K.; Ernzerhof, M.i Phys. Rev. Lett. 1996, 77, 3865−3868. (19) Andersson, Y.; Langreth, D. C.; Lundqvist, B. I. Phys. Rev. Lett. 1995, 76, 102−105. (20) Roman-Perez, G.; Soler, J. M. Phys. Rev. Lett. 2009, 103, 096102−096105. (21) Lee, K.; Murray, E. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Phys. Rev. B 2010, 82, 081101−081104(R). (22) Silvestrelli, P. L. Phys. Rev. Lett. 2008, 100, 053002−053005. (23) Marzari, N.; Vanderbilt, D. Phys. Rev. B 1997, 56, 12847−12865. (24) Baskin, Y.; Meyer, L. Phys. Rev. 1955, 100, 544−544. (25) Sheng, L.; Ono, Y.; Taketsugu, T. J. Phys. Chem. C 2010, 114, 3544−3548. (26) Graziano, G.; Klimes, J.; Fernandez-Aloso, F.; Michaelides, A. J. Phys.: Condensed Matter 2012, 24, 424216. (27) Chen, X. R.; Oshiyama, A.; Okada, S. Chem. Phys. Lett. 2003, 371, 528−534. (28) Ooi, N.; Rairkar, A.; Adams, J. B. Carbon 2006, 44, 231−242. (29) Ambrosetti, A.; Costanzo, F.; Silvestrelli, P. L. J. Phys. Chem. C 2011, 115, 12121−12127. (30) Ruan, C. Y.; Lobastov, V. A.; Vigliotti, F.; Chen, S.; Zewail, A. H. Science 2004, 304, 80−84. (31) Bergeld, J.; Gleeson, M.; Kasemo, B.; Chakarov, D. J. Geophys. Res. 2004, 109, E07S11. (32) Silvestrelli, P. L.; Toigo, F.; Ancilotto, F. J. Phys. Chem. C 2009, 113, 17124−17131. (33) Hodgson, A.; Haq, S. Surf. Sci. Rep. 2009, 64, 381−452.

neous charge distribution on the graphite surface will also contribute in providing the observed flat energy surface. Because of the low water−graphite energy barriers, water might actually play a lubricating role in this context. Although X-ray diffraction experiments suggest the absence of a macroscopic chemisorbed layer,14 it is likely that even an incomplete water microscopic film adsorbed on the graphite surface will strongly reduce the overall friction and wear rate. Regarding the intercalated ice BL, we expect this configuration not to be frequently observable due to the high-energy barrier that a single water molecule would encounter in entering between two graphene sheets. Moreover, this configuration seems to be intrinsically unfavored with respect to adsorbed BL.

IV. CONCLUSIONS We performed a study for the adsorption and intercalation of water ice BL. The dispersion-corrected DFT methods considered here gave comparable results in the absence of large repulsive contributions of the underlying xc functional. This certainly supports the validity of the present results and corroborates the reliability of the methods. Both adsorbed and intercalated ice BL turn out to be stable configurations, although adsorption is energetically favored and its onset does not imply high-energy barriers. The ice−graphene sliding in both configuration is characterized by substantially lower energy barriers than graphene−graphene shear. In particular, for the adsorbed BL configuration, we found energy barriers about 2 orders of magnitude lower than for graphene− graphene. We thus believe that the major role played by water in graphite lubrication is related to the low water−graphite friction.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Flavio Toigo, Francesca Costanzo, and Alexandre Tkatchenko for useful discussion and fruitful suggestions. REFERENCES

(1) Hernandez-Rojas, J.; Calvo, F.; Breton, J.; Gomez Llorente, J. M. J. Phys. Chem. C 2012, 116, 17019−17028. (2) Cabrera-Sanfelix, P.; Darling, G. R. J. Phys. Chem. C 2007, 111, 18258−18263. (3) Gordillo, M. C.; Marti’, J. Phys. Rev. B 2008, 78, 075432−075436. (4) Ma, J.; Michaelides, A.; Alfe’, D.; Schimka, L.; Kresse, G.; Wang, E. Phys. Rev. B 2011, 84, 033402−033405. (5) Jinesh, K. B.; Frenken, J. W. M. Phys. Rev. Lett. 2006, 96, 166103−166106. (6) Jinesh, K. B.; Frenken, J. W. M. Phys. Rev. Lett. 2008, 101, 036101−036104. (7) Ambrosetti, A.; Silvestrelli, P. L. J. Phys. Chem. C 2011, 115, 3695−3702. (8) Savage, R. H.; Schaeffer, D. L. J. Appl. Phys. 1956, 27, 136−137. (9) Bragg, W. H. An Introduction to Crystal Analysis; Bell: London, 1928. (10) Arnell, R. D.; Teer, D. G. Nature (London, U. K.) 1968, 218, 1155−1156. (11) Bryant, P. J.; Gutshall, P. L.; Taylor, L. H. Wear 1964, 7, 118− 126. 325

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