Graphene: An impermeable or selectively permeable membrane for atomic species?

CARBON

6 7 ( 2 0 1 4 ) 5 8 –6 3

Available at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/carbon

Graphene: An impermeable or selectively permeable membrane for atomic species? L. Tsetseris

a,b,*

, S.T. Pantelides

b,c,d

a

Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA c Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235, USA d Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA b

A R T I C L E I N F O

A B S T R A C T

Article history:

Graphene is generally thought to be a perfect membrane that can block completely the

Received 24 July 2013

penetration of impurities and molecules. Here we use density-functional theory calcula-

Accepted 21 September 2013

tions to examine this property with respect to prototype atomic species. We find that

Available online 1 October 2013

hydrogen and oxygen atoms have, indeed, prohibitively large barriers (4.2 eV and 5.5 eV) for permeation through a defect-free graphene layer. We also find, however, that boron permeation occurs by an intricate bond switching synergistic process with an activation energy of only 1.3 eV, indicating easy B penetration upon moderate annealing. Nitrogen permeation has an intermediate activation energy of 3.2 eV. The results show that by controlling annealing conditions, pristine graphene could allow the selective passage of atoms.  2013 Elsevier Ltd. All rights reserved.

1.

Introduction

In addition to several other exceptional properties [1–3], graphene is known to be built by nature’s strongest r chemical bonds. Because the re-arrangement of these bonds carry high energy costs, graphene has been explored as an ideal membrane that blocks the motion of species from one side to the other [4]. Indeed, experiments have provided evidence that graphene mono-layers, despite being only one-atom thick, can effectively suppress the permeation of noble gases [5], encase bacteria [6], and inhibit corrosion when used as protective coating on metals [7]. Alternately, the opening of small holes on graphene can be used to enable the site- and species-selective permeation of small molecules, leading to interesting applications on gas separation and filtering [8–10]. Theoretical studies have provided evidence for the impermeability of defect-free graphene with respect to helium [11], oxygen [12], and hydrogen atoms [13–16]. The calculated barriers for He and O penetration are so high (11 eV [11] and

5.6 eV [12]) that these processes cannot be thermally activated even at extremely high temperatures. For the case of hydrogen, reported results are rather ambiguous as the corresponding activation energies range from [13] 15 eV all the way [14,15] down to 2.4 eV [16]. This perplexing variation of results relates to differences in the methods employed to simulate the actual process of H permeation through the center of a graphene hexagonal ring. In this research paper, we use the state of the art nudged elastic band method [17] (NEB) within density-functional theory (DFT) to calculate the barriers for a number of technologically important atomic species to pass through a graphene sheet. We thus clarify the issue of H permeation activation energies and confirm the impermeability of graphene towards O atoms. Moreover, we find that nitrogen and boron, the most typical graphene dopants, have lower penetration barriers. Boron, in particular, has a surprisingly small permeation barrier of only 1.3 eV, suggesting rapid passage through graphene even at moderate temperatures.

* Corresponding author. E-mail address: [email protected] (L. Tsetseris). 0008-6223/$ - see front matter  2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.09.055

CARBON

2.

6 7 (2 0 14 ) 5 8–63

Methodology

The results were obtained with the plane wave-based DFT code VASP [18]. We used a generalized gradient approximation (GGA) functional [19] for exchange–correlation (xc) and projector-augmented waves (PAW) [20] in the description of interactions between valence electrons and ionic cores. We have also carried out a full set of calculations using a local density approximation (LDA) xc-functional [21] and ultra-soft pseudopotentials (US). [22] Unless stated otherwise, the results we report below are based on the PAW–GGA investigations. All calculations were performed on a large graphene supercell with 160 C atoms, were spin-unrestricted, and used the C point for k-point sampling. We obtained also energies of the most relevant stable configurations and associated transitions states using a 3 · 3 · 1 k-grid (the z-axis was selected perpendicular to the graphene layer) and confirmed that activation energies are converged within about 0.1 eV with respect to the size of the reciprocal space mesh. The energy cutoff for the plane wave basis was set at 400 eV (300 eV) for the PAW–GGA (US–LDA) studies. The NEB calculations of the minimum energy pathways (MEP) for atom penetration employed at least 16 images as intermediate configurations between proximal local energy-minimum structures. Similar methodology has provided activation energies in satisfactory agreement with experiment in previous studies [23–25].

3.

Results and discussion

Hydrogen is a common impurity in electronic devices [25,26] and is expected to play an important role in graphene-based systems as well. The lowest-energy configuration for a hydrogen atom on graphene is the top position [27,28], wherein the adsorbate is located directly above a C site. The configuration is depicted in the (a) and (c) insets of Fig. 1. We have investigated two main paths for the penetration of the adsorbate through the graphene sheet. The second path resembles partly the one described below for oxygen, but leads to an

59

activation energy that is larger than 10.0 eV. In the first path, the H atom moves on the other side of the layer through positions within one of its nearest hexagonal carbon ring. In fact, the first path has two variants with almost equal barriers and transitions states that are very close to each other with respect to atom coordinates. Fig. 1 shows the energy variation along the minimum energy pathway (MEP) for H permeation through graphene. Despite being the smallest atom, an H adsorbate has to overcome a substantial barrier of 4.2 eV. The corresponding value from US-LDA calculations is 3.7 eV. In the transition state (TS) shown in Fig. 1, the H ˚ atom is located within the graphene plane and 1.28 A ˚ (1.47 A) away from a pair of first (second) nearest C neighbors. It should be noted that this TS is very close structurally and in terms of energy to the configuration with the H atom at the center of a hexagonal carbon ring. Fig. 2 shows the details of the lowest-barrier MEP for oxygen penetration. The oxygen adatom maintains a bridge position between two neighboring carbon atoms of graphene throughout the penetration process. The path is the same as the one described in a previous DFT study [12]. There is a small difference between the two studies with respect to the value of the permeation barrier. We obtained an activation energy of 5.5 eV, compared to the 5.6–5.8 eV value reported before [12]. The small discrepancy could be related to specific differences in methodology between the two studies, namely the use by us of a larger supercell and of the NEB method. We should note that, as in the case of hydrogen, the LDA calculation for the MEP of Fig. 2 gives a significantly lower barrier of 4.6 eV. The selection of GGA over LDA is particularly important when the configurations involved lead to significant distortion of the delocalized electron cloud around an aromatic carbon ring. As in previous DFT studies [29–31], we found that the most stable configuration for a nitrogen adatom on graphene is the bridge geometry depicted in structure (a) of Fig. 3. The penetration MEP shown in Fig. 3 starts with a nitrogen-bridge structure and goes through a sequence of configurations with a nitrogen substitutional atom and a proximal carbon adatom

Fig. 1 – Energy variation during penetration of a hydrogen atom through a graphene layer. Insets depict the (a) initial, (b) transition state, and (c) final configuration. (Carbon: gray, Hydrogen: white spheres).

60

CARBON

6 7 ( 2 0 1 4 ) 5 8 –6 3

Fig. 2 – Energy variation during penetration of an oxygen atom through a graphene layer. Insets depict the (a) initial, (b) transition state, and (c) final configuration. (Carbon: gray, Oxygen: dark gray (red) spheres). (A colour version of this figure can be viewed online.)

Fig. 3 – Energy variation during penetration of a nitrogen atom through a graphene layer. Insets depict the (a) initial, (b) transition state, and (c, d) intermediate configuration. The reverse steps starting from the C-symmetric configuration (d) towards (a) can bring the N atom to the other side of the graphene layer. (Carbon: gray, Nitrogen: light gray (cyan) spheres). (A colour version of this figure can be viewed online.)

configuration. When the carbon adatom assumes a symmetric dumbbell position, then the process can be reverted to lead back to an N-bridge geometry, but with the nitrogen adatom on the opposite side of graphene compared to the structure (a) of Fig. 3. The overall activation energy in this MEP is 4.1 eV. An alternative MEP for N penetration is depicted in Fig. 4. In this case, a lower activation energy (Ea) of 3.2 eV is obtained when the C-dumbbell is formed in a second nearest position with respect to the N substitutional. The rate-limiting step in this second MEP is the migration of the carbon bridge adatom one step away from the nitrogen site. It should be noted that this migration step was found to have a larger Ea value of about 3.8 eV in earlier studies [30], perhaps due to the use of a smaller supercell. We should also note that, unlike the earlier description [30] of parts of the minimum energy pathways of Figs. 3 and 4, here we include all necessary transformation

steps to complete the nitrogen penetration process. Let us also note that the processes described in this work have some resemblance to the mechanisms of escape of a nitrogen atom [32] from endohedral fullerenes. The lowest-energy configurations for a boron adatom on graphene are the top (over a carbon atom), hollow (over a hexagon center) and the dumbbell structures. The top and dumbbell geometries are depicted in insets (a) and (b) of Fig. 5. Within LDA, these configurations are degenerate with respect to energy. GGA calculations find the top position slightly lower in energy (by 0.2 eV) than the other two. These results are in agreement with those reported in previous DFT studies [31]. Starting from the top geometry, there is a small barrier for transformation to the dumbbell arrangement. Subsequently, the boron atom can push its nearest carbon atom out to a bridge position, as shown in inset (c) of Fig. 5.

CARBON

6 7 (2 0 14 ) 5 8–63

61

Fig. 4 – Energy variation during penetration of a nitrogen atom through a graphene layer. This figure describes a path that is alternative to the one of Fig. 3. Label (a) refers to inset (a) of Fig. 3. The reverse steps starting from the C-symmetric configuration (d) towards (a) can bring the N atom to the other side of the graphene layer. (Carbon: gray, Nitrogen: light gray (cyan) spheres). (A colour version of this figure can be viewed online.)

Fig. 5 – Energy variation during penetration of a boron atom through a graphene layer. Insets depict the (a) initial, and (b–d) intermediate configurations. The reverse steps starting from the C-symmetric configuration (d) towards (a) can bring the B atom to the other side of the graphene layer. (Carbon: gray, Boron: light gray (pink) spheres). (A colour version of this figure can be viewed online.)

The transition state of this transformation step is very close to the metastable configuration (c). By switching to the symmetric carbon dumbbell geometry of inset (d), the transformation is half-way through the completion of a boron penetration step. Clearly, moving back from geometry (d) to structure (a) of Fig. 5, the boron atom may be forced to the other side of graphene with respect to its initial position. The data of Fig. 5 suggest an overall barrier of only 1.3 eV. Using a simple Arrhenius expression we can estimate that this process is activated within seconds to minutes for temperatures in excess of 150–200 C. As shown in the figures and discussed in the above, the penetration mechanisms for the atomic impurities are distinct. In fact, in each particular case we investigated the

feasibility of penetration with minimum energy pathways that resemble those of the other atoms. These investigations led invariably to paths with extremely high energy states and for this reason they are not discussed here. On the other hand, the set of permeation mechanisms presented in this work offer useful guidelines to investigate the penetration of other impurities (as individual species, or in small groups of atoms) through graphene. Three main pathways emerge as atomic-scale mechanisms: permeation through the center of a hexagon without breakup of C–C bonds, penetration with the breakup and reformation of one C–C bond, and more complex processes involving an intermediate configuration with a substitutional impurity and a neighboring carbon dumb-bell structure. These pathways may be tested either for individual

62

CARBON

6 7 ( 2 0 1 4 ) 5 8 –6 3

atoms, or for small atom complexes and molecules. Such future studies will likely address whether boron is unique in terms of high permeability through graphene, or whether other atoms and atom complexes exhibit similar behavior. Let us finally note that in certain experiments other processes may be operative. For example, if impurities are introduced from molecular precursors, then a comprehensive study of permeation would entail large scale simulations including all relevant steps, namely molecular dissociation on graphene, diffusion, atomic-scale penetration mechanisms, recombination, and desorption. Likewise, in the case of high impurity concentrations, adatom clustering and its effect on permeation barriers should be considered. Nevertheless, the detailed description of the penetration of individual atoms is a key first step in a comprehensive study of permeation. First, the case of low concentration of atomic impurities is relevant to several setups and processes of technological importance. Examples are the bombardment of graphene with beams of energetic ions [13,14,29–31] to achieve doping or examine radiation hardness, and the diffusion of isolated impurities from neighboring (e.g. B-rich or Nrich) materials in nano-electronic devices. Moreover, even when additional reactions and transformations are active in a particular permeation experiment, the results presented in the above could be useful in deciding about the so-called rate-limiting step of the overall process.

4.

Summary

We have obtained with first-principles DFT calculations the activation energies for penetration of H, O, N, and B atoms through a defect-free graphene sheet. While the calculated barriers confirm in the first three cases the widely perceived impermeability of graphene, we find that boron can easily pass through the honeycomb carbon layer upon moderate annealing.

Acknowledgements The work was supported by the McMinn Endowment at Vanderbilt University and by Grant No HDTRA 1-10-10016. The calculations used resources of the EGEE and HellasGrid infrastructures.

R E F E R E N C E S

[1] Geim AK. Graphene: status and prospects. Science 2009;324(5934):1530–4. [2] Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK. The electronic properties of graphene. Rev Mod Phys 2009;81(1):109–62. [3] Pantelides ST, Puzyrev Y, Tsetseris L, Wang B. Defects and doping and their role in functionalizing graphene. MRS Bull 2012;37(12):1187–94. [4] Berry V. Impermeability of graphene and its applications. Carbon 2013;62:1–10. [5] Bunch JS, Verbridge SS, Alden JS, van der Zande AM, Parpia JM, Craighead HG, et al. Impermeable atomic membranes from graphene sheets. Nano Lett 2008;8(8):2458–62.

[6] Mohanty N, Fahrenholtz M, Nagaraja A, Boyle D, Berry V. Impermeable graphenic encasement of bacteria. Nano Lett 2010;11(3):1270–5. [7] Prasai D, Tuberquia JC, Harl RR, Jennings GK, Bolotin KI. Graphene: corrosion-inhibiting coating. ACS Nano 2012;6(2):1102–8. [8] Jiang DE, Cooper VR, Dai S. Porous graphene as the ultimate membrane for gas separation. Nano Lett 2009; 9(12):4019–24. [9] Schrier J. Helium separation using porous graphene membranes. J Phys Chem Lett 2010;1(15):2284–7. [10] Qin X, Meng Q, Feng Y, Gao Y. Graphene with line defect as a membrane for gas separation: design via a first-principles modeling. Surf Sci 2013;607:153–8. [11] Leenaerts O, Partoens B, Peeters FM. Graphene: a perfect nanoballoon. Appl Phys Lett 2008;93(19):193107. [12] Topsakal M, Sahin H, Ciraci S. Graphene coatings: an efficient protection from oxidation. Phys Rev B 2012;85(15):155445. [13] Ito A, Nakamura H, Takayama A. Molecular dynamics simulation of the chemical interaction between hydrogen atom and graphene. J Phys Soc Jpn 2008;77(11):114602. [14] Sun J, Li S, Stirner T, Chen J, Wang D. Molecular dynamics simulation of energy exchanges during hydrogen collision with graphite sheets. J Appl Phys 2010;107(11):113533. [15] Despiau-Pujo E, Davydova A, Cunge G, Delfour L, Magaud L, Graves DB. Elementary processes of H2 plasma-graphene interaction: a combined molecular dynamics and density functional theory study. J Appl Phys 2013;113(11):114302. [16] Ehemann R, Krstic PS, Dadras J, Kent PRC, Jakowski J. Detection of hydrogen using graphene. Nanoscale Res Lett 2012;7:198. [17] Mills G, Jo´nsson H, Schenter GK. Reversible work transition theory – application to dissociative adsorption of hydrogen. Surf Sci 1995;324(2–3):305–37. [18] Kresse G, Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 1996;54(16):11169–86. [19] Perdew JP, Wang Y. Accurate and simple analytic representation of the electron gas correlation energy. Phys Rev B 1992;45(23):13244–9. [20] Blo¨chl PE. Projector augmented-wave method. Phys Rev B 1994;50(24):17953–79. [21] Perdew JP, Zunger A. Self-interaction correction to densityfunctional approximations for many-electron systems. Phys Rev B 1981;23(10):5048–79. [22] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 1990;41(11):7892–5. [23] Tsetseris L, Pantelides ST. Adatom complexes and selfhealing mechanisms on graphene and single-wall carbon nanotubes. Carbon 2009;47(3):901–8. [24] Tsetseris L, Pantelides ST. Adsorbate-induced defect formation and annihilation on graphene and single-wall carbon nanotubes. J Phys Chem B 2009;113(4):941–4. [25] Tsetseris L, Zhou XJ, Fleetwood DM, Schrimpf RD, Pantelides ST. Hydrogen-related instabilities in MOS devices under biastemperature stress. IEEE Trans Device Mater Reliab 2007;7(4):502–8. [26] Tsetseris L, Fleetwood DM, Schrimpf RD, Zhou XJ, Batyrev IG, Pantelides ST. Hydrogen effects in MOS devices. Microelectron Eng 2007;84(9–10):2344–9. [27] Boukhvalov DW, Katsnelson MI, Lichtenstein AI. Hydrogen on graphene: electronic structure, total energy, structural distortions and magnetism from first-principles calculations. Phys Rev B 2008;77(3):035427. [28] Ferro Y, Teillet-Billy D, Rougeau N, Sidis V, Morisset S, Allouche A. Stability and magnetism of hydrogen dimers on graphene. Phys Rev B 2008;78(8):085417.

CARBON

6 7 (2 0 14 ) 5 8–63

[29] Kotakoski J, Krasheninnikov AV, Ma Y, Foster AS, Nordlund K, Nieminen RM. B and N ion implantation into carbon nanotubes: insights from atomistic calculations. Phys Rev B 2005;71(20):205408. [30] Ma Y, Foster AS, Krasheninnikov AV, Nieminen RM. Nitrogen in graphite and carbon nanotubes: magnetism and mobility. Phys Rev B 2005;75(20):205416.

63

[31] Pontes RB, Fazzio A, Dalpian GM. Barrier-free substitutional doping of graphene sheets with boron atoms: Ab initio calculations. Phys Rev B 2009;79(3):033412. [32] Tsetseris L. Stability of group-V endohedral fullerenes. J Phys Chem C 2011;115(9):3528–33.