Enhanced Gas Adsorption on Graphitic Substrates ... - ACS Publications

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Enhanced Gas Adsorption on Graphitic Substrates via Defects and Local Curvature: A Density Functional Theory Study Debosruti Dutta,*,†,∥,⊥ Brandon C. Wood,*,‡,§,⊥ Shreyas Y. Bhide,† K. Ganapathy Ayappa,† and Shobhana Narasimhan‡,# †

Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India § Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States # Sheikh Saqr Laboratory of the International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India ‡

ABSTRACT: Using van-der-Waals-corrected density functional theory calculations, we explore the possibility of engineering the local structure and morphology of highsurface-area graphene-derived materials to improve the uptake of methane and carbon dioxide for gas storage and sensing. We test the sensitivity of the gas adsorption energy to the introduction of native point defects, curvature, and the application of strain. The binding energy at topological point defect sites is inversely correlated with the number of missing carbon atoms, causing Stone−Wales defects to show the largest enhancement with respect to pristine graphene (∼20%). Improvements of similar magnitude are observed at concavely curved surfaces in buckled graphene sheets under compressive strain, whereas tensile strain tends to weaken gas binding. Trends for CO2 and CH4 are similar, although CO2 binding is generally stronger by ∼4 to 5 kJ mol−1. However, the differential between the adsorption of CO2 and CH4 is much higher on folded graphene sheets and at concave curvatures; this could possibly be leveraged for CH4/CO2 flow separation and gasselective sensors.

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INTRODUCTION Because of the anticipated shortage of petroleum as well as the adverse environmental impact of conventional gasoline vehicles, alternative transportation systems based on natural gas or hydrogen are being actively researched. Because cryogenic storage is expensive and compressed gas storage is energyintensive with associated safety factors, the search is on for suitable materials that can store natural gas adsorptively.1,2 Similarly, the pressing need to reduce atmospheric greenhouse gases has motivated the investigation of new absorptive materials to capture carbon dioxide.3,4 Selective carbon dioxide capture also has direct relevance for next-generation transportation systems because it can be used to enrich the relative methane content in CH4/CO2 gas mixtures for enhanced oil recovery, biogas production, and natural gas purification technology.5 The methane-rich gas stream can subsequently be used in an on-board transportation system. Porous and disordered carbon-based materials are excellent adsorbents for gas storage and separation. They have been widely used due to their high specific surface area, low cost, minimal environmental impact, and good mechanical and chemical stability.1,2,6−8 Theoretical assessment of materials adsorption capacity for gas storage involves computational analysis on several length scales. For instance, binding energies of the gas molecule with the adsorbent can be determined using © 2014 American Chemical Society

suitable ab initio methods, then classical grand canonical ensemble simulations with appropriate interaction potentials can be used to obtain the adsorption isotherms. Adsorption simulations have been carried out using simple slit graphitic pore geometries9 as well as with more realistic representations of disordered porous carbons.10 The gas adsorption isotherms have been used in continuum transport models for packed carbon beds or reservoirs to assess heat effects associated with nonisothermal adsorption11,12 and desorption conditions.13 Nevertheless, although classical simulations have been widely used to assess the storage capacity of carbon-based materials and make comparisons with experiments, they are limited in their flexibility to accurately describe molecular-scale interactions. Ab initio methods such as those based on density functional theory (DFT) are useful in this regard, allowing one to assess the impact of chemical and structural modifications on the gas binding energies and overall adsorption characteristics. Such calculations, which form the focus of this work, can also be used to explore the possibility of tailoring materials on the molecular scale to enhance gas uptake.14−17 Received: November 18, 2013 Revised: March 19, 2014 Published: March 24, 2014 7741

dx.doi.org/10.1021/jp411338a | J. Phys. Chem. C 2014, 118, 7741−7750

The Journal of Physical Chemistry C

Article

pristine graphene. We point out that similar modifications have been shown to significantly affect the electronic properties of graphene-based devices30−32 and have demonstrated potential usefulness for hydrogen storage33 and gas sensing.34,35 We further emphasize that with increased interest in graphenebased devices, these same topological heterogeneities have been experimentally observed or realized in graphene-based nanostructures.30,36 For instance, in addition to forming naturally, a variety of point defects can be induced during processing with Ar bombardment.35 Buckles and folded graphene structures (“grafolds”) can be synthesized by highpower sonication in solution37 or by high-temperature (2000 °C) heat treatment of graphite.38 Multiply folded grafolds have also been synthesized using a chemical vapor deposition process,39 and edge-closed flattened nanotubes have been grown using an etching process.40

Carbon-based adsorbents do not yet meet capacity targets for on-board vehicular storage of natural gas. Similarly, their CO2 storage capacity limits their usefulness in carbon capture technologies.3 Efforts to further improve gas uptake in high surface-area porous carbon substrates have followed several directions. One of these is chemical modification by additives and surface functionalization to enhance the per-site binding energy, which has been the subject of several recent investigations.15−22 Using van-der-Waals-corrected DFT, we recently explored the effects of edges and chemical functional groups on gas adsorption on graphene and found that functional groups containing the polar OH moiety increase binding with respect to unfunctionalized edges.15 Similarly, classical grand canonical ensemble Monte Carlo (GCMC) simulations with edge-functionalized graphene nanoribbons revealed enhanced methane binding with COOH functional groups with increasing pressure.16 Specific functionalization to enhance local binding has also been used as a strategy for improving methane uptake in metal organic frameworks (MOFs).18 Using DFT and GCMC simulations, surface functionalization of graphite with OH groups has been suggested to enhance CO2 adsorption and significantly improve selectivity in CO2/CH4 and CO2/N2 mixtures relative to bare graphite.17,19,23 The influence of edge-containing functional groups in disordered porous carbons on CO2 uptake and separations has been further illustrated in recent GCMC simulations.20,21 Graphene nanoplatelets22 edge-functionalized with COOH and SO3H were formed during ball milling of graphite in the presence of suitable gases, indicating the potential for large scale production of selectively edgefunctionalized carbons with enhanced uptake. Beyond chemical modification, recent progress in the chemical and thermal processing of activated carbons, carbon aerogels, and other porous and disordered carbon-based substrates5,24−28 has permitted unprecedented tunability of morphological features on the micro, meso, and macro scales. To properly leverage these advances as part of a broader design roadmap, it is highly desirable to understand which local modifications might lead to measurable improvements in binding energetics and gas uptake. Although the precise microstructure of most porous carbons is difficult to characterize, the products tend to be largely graphitic, with significant local deviations from the ideal planar, six-membered ring structure.29 Given this uncertainty in defining the topological and chemical heterogeneity of natural porous carbons, graphene-based models that have simpler and well-defined defect motifs can be used to systematically investigate the influence of specific local modifications on the adsorption of gases. Investigating binding energies on these graphene-based systems also assists in choosing or developing a suitable classical force field for carrying out Monte Carlo simulations for adsorption isotherms.16,17 Following this strategy, we explore a viable approach for enhanced gas uptake that has received comparatively little attention, namely, altering the local (as opposed to macroscale) morphology and structure of the carbon framework. We use graphene models to introduce native point defects, such as vacancy complexes and bond rotations, as well as local strainrelated effects, including tension, surface buckling, and folds. Using van-der-Waals-corrected DFT calculations of CO2 and CH4 binding on the defective graphene-derived surface models, we next assess which of these local topological modifications provide the greatest adsorptive enhancement with respect to

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COMPUTATIONAL DETAILS We have used DFT calculations to determine the fully relaxed geometries and energetics of CH4 and CO2 molecules adsorbed on graphene sheets with point defects, local strain, or morphological defects. All DFT calculations were performed using the plane-wave Quantum-ESPRESSO code.41 Normconserving pseudopotentials with a plane-wave cutoff of 80 Ry were used. To minimize spurious interactions between graphene sheets across periodic supercell images, a vacuum spacing of 20 Å was introduced along nonrepeating directions. Brillouin zone sampling was performed using a k-point density based on a 24 × 24 × 1 Monkhorst-Pack mesh in the graphene primitive cell, scaled appropriate to the supercell size. Marzari− Vanderbilt cold smearing42 with a smearing width of 0.007 Ry was introduced for improved convergence and for savings in kpoint density. Because physisorption dominates the interactions between the adsorbate and substrate, it is important to select a method of treating van der Waals dispersion forces adequately within a DFT framework. We have chosen to use the nonlocal van der Waals density functional (vdW-DF).43,44 Spin-unpolarized DFT was used, as the formulation of the nonlocal correlation in vdW-DF is formally defined only for this case.44 The revised Perdew−Burke−Ernzerhof (revPBE) functional has been used to compute the reference exchange term.45 The defect formation energy Ef was calculated using the formula ⎛ n Ef = −⎜E(defect) − E(graphene) − ⎝ N

{ 12 E(H )}⎞⎟⎠ 2

(1)

where n and N are the number of carbon atoms in the defective supercell and the corresponding pristine graphene supercell, respectively. The last term applies only for the hydrogenterminated monovacancy, for which the gas reference energy is also subtracted. For each adsorbate−substrate pair, the adsorption energy was calculated as Eads = −(Eg + s − Eg − Es)

(2)

where Eg+s is the total energy of the adsorbed system, Eg is the total energy of the isolated gas molecule (CH4 or CO2), and Es is the total energy of the bare substrate. For each adsorption energy calculation, both ring-center and atom-center initial adsorption geometries were tested, and all atoms were allowed to relax until residual forces were 3 kJ mol−1. For the unterminated monovacancy defect, the CH4 molecule sits on top of the unsaturated carbon atom in the nine-member ring such that one of its C−H bonds is oriented toward the defect site. For the H-terminated monovacancy defect, the CH4 sits on top of the carbon atom in the pentagon that is farthest away from the defect site, with a geometry and orientation similar to the unterminated monovacancy. The CH4 molecule sits with its H-tripod down for both the 5−8−5 and 555−777 divacancy defects; however, the CH4 molecule sits on top of the carbon atom adjoining the pentagon and octagon for the 5−8−5 defect, whereas for the 555−777 defect, CH4 sits above a heptagon center. In the case of the SW defect, the CH4 molecule sits on a bridge between a C−C bond that is farther away from the defect site, in one of the pentagons formed in the SW defect. For all of these configurations, the CH4 molecule sits with its tripod facing toward the substrate, at a distance of ∼3.6 Å from the carbon atom of the methane to the graphene plane. The adsorption sites for the CO2 molecule on the various tested defects in the graphene sheet after geometry optimization are similar to those for CH4 adsorption. However,

Figure 1. Final adsorption geometries of methane adsorbed on the tested point defects: (a) Stone−Wales (55−77), (b) divacancy (5−8− 5), (c) divacancy (555−777), (d) monovacancy (5−9), and (e) monovacancy (5−9) with hydrogen termination. Atomic color code: graphene C, yellow; methane C, gray; H, light blue. The red lines show the defect geometry.

three carbon atoms with unsaturated dangling bonds. This causes considerable restructuring and bond formation between two of the carbon atoms due to a Jahn−Teller distortion, resulting in five- and nine-member rings (denoted 5−9 in the text).48,63 Because the monovacancy may be further stabilized upon binding of a hydrogen atom on the remaining unsaturated carbon,64 we have also studied this configuration. The presence of divacancies (two adjacent missing carbon atoms) results in reorientation of the honeycomb lattice to form nonhexagonal rings. Here we consider two common divacancy reconstruc7743



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Table 1. CH4/CO2 Adsorption Energies (Eads) and Formation Energies (Ef) for Graphene Sheets with Various Point Defects systema graphene monovacancy divacancy Stone−Wales a

defect type

Ef (kJ mol−1)

Eads (CH4) (kJ mol−1)

Eads (CO2) (kJ mol−1)

Eads (CO2) − Eads (CH4) (kJ mol−1)

unterminated H-terminated 5−8−5 555−777 55−77

731.6 544.9 755.5 676.3 495.3

16.9 18.8 18.2 15.9 16.3 20.8

21.4 21.9 23.1 21.1 20.2 25.1

4.5 3.1 4.9 5.2 3.9 4.3

Calculations were done in a (3√3 × 3√3) graphene supercell.

Table 2. CH4/CO2 Adsorption Energies (Eads) and Formation Energies (Ef) for Strained Graphene Sheets systema unstrained linear strain (uniaxial)b

areal strain (biaxial)b

a

tensile straina

Ef (kJ mol−1 atom−1)




+2.5% +5% +7.5% +10% +2.5% +5% +7.5% +10%

1.7 6.3 13.4 22.8 3.8 14.2 29.8 49.6

16.9 16.7 16.5 16.3 16.2 16.6 16.1 15.8 15.5

21.4 21.3 21.1 21.0 20.8 21.2 20.7 20.4 20.1

4.5 4.6 4.6 4.7 4.6 4.6 4.6 4.6 4.6

Calculations were done in a (4 × 4) graphene supercell. bStrains represent percent increases in the linear lattice parameter.

due to the presence of a quadrupole moment. The binding energy difference between CO2 and CH4 is a useful indicator of the efficiency of the medium for gas separation; this value is largest for the 5−8−5 divacancy but is not significantly enhanced with respect to the graphene baseline. The enhanced binding energy for CO2 over CH4 is consistent with trends observed in finite-temperature Monte Carlo simulations in carbon nanotubes65 and porous carbons.66 The calculated formation energies of the point defects in Table 1 compare well with previously reported values in the literature30 and give an idea of the relative native prevalence of these defects and the ease with which they can be introduced externally. The SW defect has the lowest formation energy among the tested point defects67,68 and hence is likely to exist in relative abundance. Because it also demonstrates by far the largest adsorption strength enhancements, we conclude that a low-energy substrate treatment that causes bond reorientation without ejecting carbon atoms from the lattice would be a good potential improvement strategy. In contrast, higher energy treatments that introduce vacancies are unlikely to lead to appreciable gas storage enhancement. Local Strain and Morphology. Local lattice strain is inherent in amorphous systems such as nanoporous carbon due to intrinsic stresses that arise in the planar graphene sheet from the presence of defects and altered microstructure.36 In addition, atomic resolution imaging of graphene directly shows the presence of both small and large undulations and folds in the graphene sheet.38,69,70 These local strain and morphological transformations may be exploited to increase adsorption. A similar effect has been observed in the context of strain-enhanced binding of metal atoms71 and hydrogen72 to graphene surfaces, for example. We point out that there exists a connection between the local morphological features discussed here and mesostructural properties such as pore geometry. In addition, with proper levels of control during materials processing, local morphological features may be tuned independently.

for the monovacancy, they differ somewhat from other DFT studies,59,60 which tend to show the CO2 molecule sitting closer to the vacancy center. The differences may arise from the use of van der Waals corrections, which were not included in the previous studies. In most cases, we find that the linear CO2 molecule sits at a distance of ∼3.5 Å, oriented parallel to the basal plane. In the case of the strongest-binding SW defect, the distance reduces to 3.35 Å, indicative of the stronger binding in this configuration. Our results for the adsorption energies for CH4 and CO2 gas molecules on the monovacancy, divacancy, and SW defects as well as the corresponding formation energies of the defect complexes are summarized in Table 1. For comparison, we also present the results for adsorption on a pristine graphene sheet. From the adsorption energies, one can conclude that, in general, the greater the number of atoms that are removed from the graphene sheet to create the defect, the less favorable binding becomes for both CH4 and CO2. This suggests that the symmetry breaking and rehybridization induced by the defects are competing with the possible loss of van der Waals dispersion interactions due to missing carbon atoms. We see the largest enhancement with respect to pristine graphene for the SW defect, where no carbon atoms are removed from the lattice. In this case, the presence of the nonhexagonal rings enhances binding by 23% for CH4 and 17% for CO2, making it by far the best candidate among those tested, for enhanced uptake of both gases. For monovacancies, the loss of a single carbon atom translates to a more modest enhancement, whereas for the divacancies, the absence of two atoms entirely offsets any gain that might otherwise be observed. The stronger binding to the monovacancy with respect to the divacancy complexes qualitatively agrees with previous reports on CO2, as does the similarity between the binding energies of the divacancy complexes and pristine graphene.59 Interestingly, the hydrogen passivation of a monovacancy defect slightly increases CO2 adsorption while decreasing CH4 adsorption. CO2 demonstrates consistently higher binding strength with respect to CH4 by 4 to 5 kJ mol−1, presumably 7744



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To examine the effects of lattice strain and morphology on the gas adsorption energy, we have introduced two additional sets of models. First, both linear and areal in-plane tensile strain were assessed, that is, axial strain applied along one or both of the hexagonal primitive lattice vectors. Next, we tested the effect of out-of-plane variations in the graphene morphology by introducing ripples and folds into the sheet and fixing the inplane boundary conditions. (We did not separately consider inplane compressive strain because we found that graphene is more likely to undergo a low-energy, out-of-plane corrugation transformation upon compression.) Results for the CH4 and CO2 adsorption calculations on strained and rippled/folded graphene are discussed in the following two sections. In-Plane Tensile Strain. Our results for the adsorption energies for CH4 and CO2 on the systems with tensile strain are listed in Table 2. We observe that the formation energies of the areal strain on graphene are roughly double those of the linear strain. We also see that the presence of in-plane linear and areal tensile strains on the graphene sheet tends to slightly decrease the binding strengths of CH4 and CO2. The dependence on strain is approximately linear, as shown in Figure 3. However, Figure 4. Final adsorption geometries of methane (a,c,e) and carbon dioxide (b,d,f) for the rippled (a−d) and folded (e−f) graphene surfaces. For the rippled sheet, results for the tested valley (concave; a−b) and peak (convex; c−d) adsorption sites are shown. Atomic color code: graphene C, yellow; carbon dioxide/methane C, gray; O, red; H, light blue.

experimentally.38,39,69,73,74 We refer to this as “folded” graphene (Figure 4e−f; sometimes referred to in the literature as “grafolds”). In our model, the interlayer spacing at the fold center is matched to that of bulk graphite, meaning it should bear some properties of both single-layer rippled and bulk graphitic materials. Because the adsorption of a gas molecule in the valley site of a fold is limited by pore diffusion, we have only studied the gas adsorption at the peak (convex) site. The final geometries for CH4 and CO2 adsorption on the rippled and folded graphene models at each tested adsorption site are illustrated in Figure 4. The corresponding adsorption energies are listed in Table 3 and shown graphically in Figure 5. We see that in the case of rippled graphene, gas adsorption is significantly enhanced at a valley site but reduced at a peak site. The adsorption strength initially increases with curvature but saturates at a compressive strain of ∼10%. At 10% rippling strain, CH4 and CO2 adsorption at the valley site increases by 26 and 31%, respectively, over the baseline adsorption on graphene. There are two likely reasons for the enhanced adsorption at valley sites. First, there should be a larger van der Waals interaction with the adsorbate molecule due to the increase in close-proximity carbon atoms present in the ripple sidewalls. Second, the rippling induces partial sp 2-to-sp3 carbon rehybridization at the point of highest curvature, which changes the local electron density in the π manifold that is available for binding. From these observations, it can be concluded that the binding strength of the gas molecule is strongly dependent on the adsorption site. In addition, the curvature of the ripple matters, although only up to a certain limit (∼10% compressive strain). Adsorbates will therefore tend to preferentially aggregate at concave perturbations in the graphene surface. Such perturbations might also be expected at pore walls in

Figure 3. Adsorption energy of CH4 (top) and CO2 (bottom) under tensile strain. Percent areal strain is calculated according to 100 × (A − A0)/A0, where A0 and A are the initial and final supercell areas.

the magnitude of decrease is quite small (within the range of room-temperature thermal fluctuations). We draw two conclusions from our tensile strain results: first, introducing tensile strain on the graphene sheet is not a viable engineering strategy for enhancing gas uptake; and second, the magnitude of decrease is small enough that the unintentional introduction of local tensile strain due to defect- or morphology-induced stresses will not detract appreciably from the measured absorptive capacity. The latter point is especially important when considering the deliberate introduction of point defects, which may induce residual lattice strain. Ripples and Folds. We modeled surface sheets of graphene, rippled under compressive strain via a sinusoidal variation along the zigzag direction. The undulation leads to two likely adsorption sites, which we term the peak (convex) and valley (concave) sites of a “ripple” (Figure 4a−d). Both of these were tested independently. We also tested the limiting case when the amplitude of the undulations is sufficiently large, and the curvature sufficiently strong, that a fragment of the graphene sheet folds on itself. A similar transformation has been observed 7745



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Table 3. CH4/CO2 Adsorption Energies (Eads) and Formation Energies (Ef) for Various Undulations of Graphene Sheets system graphene rippleda

fold

cell size

compressive strainb

Ef (kJ mol−1 atom−1)




× × × × × × ×

−5% −7% −10% −15% −20%

6.8 11.6 18.4 29.5 40.5 11.6

16.9 19.4/14.6 20.6/13.1 21.3/12.1 21.2/11.1 20.8/10.9 12.7

21.4 24.6/17.9 26.7/16.0 28.0/14.8 28.0/14.0 27.6/13.6 20.5

4.5 5.2/3.3 6.1/2.9 6.7/2.7 6.8/2.9 6.7/2.7 7.8

(4 (4 (4 (4 (4 (4 (4

4) 8) 8) 8) 8) 8) 13)

a

For the rippled graphene, adsorption energies for both the valley (first) and peak (second) sites are provided (see Figure 4). bStrains represent percent decreases in the linear lattice parameter.

maintains a fixed geometry in which the molecule is aligned perpendicular to the fold direction, regardless of the adsorption site. Structurally, the fold represents a combination of graphite and a tightly curved ripple.38,39 At a folded edge, one might therefore assume that the binding energy would be similar to the peak site of the rippled sheets. This is the case for CH4, where Eads = 12.7 kJ mol−1 is near the mean value for rippled graphene. However, the binding of CO2 (Eads = 20.5 kJ mol−1) is stronger than expected, much closer to the value for pure graphene. As a result, the difference in binding strengths between CO2 and CH4 is larger (8 kJ mol−1) than for any other tested system. The reason for this discrepancy is not immediately clear, although it is quite possibly related to the unique electronic structure of folded graphene, where hybridization of π states between fold layers is observed.32,39,78 We suggest that the fold in the graphene sheet represents a distinct species that merits further study, with potential use in the adsorptive flow separation of CH4 from CO2. Electronic Structure and Origin of Binding. As previously noted, CO2 binding is consistently stronger than CH4 binding, with especially large differences observed for the rippled and strained samples (Table 3). We suggested that this difference is primarily due to the presence of a quadrupole moment in CO2, which induces more significant charge rearrangement within the π manifold of the graphene substrate. To better quantify this rearrangement, we performed a Löwdin partial-charge occupation analysis of the carbon atoms within the graphene sheets, comparing the occupations before and after gas binding. This approach has an advantage over the more commonly used charge density difference analysis in that it is more robust with respect to subtle changes in the substrate geometry upon adsorption. For pristine graphene in the 54atom unit cell, the absolute charge on each carbon atom (ΔqC) changed by an average of 2.9 × 10−4e and 1.0 × 10−3e for CH4 and CO2 binding, respectively. No appreciable change was observed in the sum-total charge on the graphene sheet upon binding of either gas, indicating no significant charge transfer between the adsorbate and the substrate. Accordingly, the calculations support the notion that both gases induce internal charge rearrangement within the graphene substrate but that the magnitude of this rearrangement is larger in the presence of the stronger-binding CO2 than the weaker-binding CH4. The connection between physisorption strength and the facility and magnitude of internal charge rearrangement in graphitic systems due to static and induced multipoles is explored in greater depth in an upcoming paper on H2 binding from our group.79 We point out that although charge transfer between the adsorbate and the substrate is not observed, the ease of internal charge rearrangement is nevertheless related to local

Figure 5. Top: Adsorption energies of CH4 and CO2 upon surface rippling under compressive strain. Bottom: Comparison of adsorption energies between gases and differences between peak (convex) and valley (concave) sites. Percent compressive strain is calculated according to 100 × (L0 − L)/L0, where L0 and L are the initial and final supercell lengths along the rippling direction.

nanoporous or disordered carbon. The final loading of the gas molecules at valley sites of corrugated graphene ripples will be determined by the competition between the inferior accessibility of valley/pore interiors and their superior thermodynamics. In other words, both kinetic and thermodynamic considerations should be taken into account when devising an effective design strategy. We point out that the curvature-induced binding enhancement is of interest not only for curved elemental carbon structures75 but also because the adsorption of various other atoms on a graphene sheet (such as metal adatoms,76 or as happens in the formation of graphene oxide77) can lead to significant buckling of the graphene sheet. This can lead to increases in local curvature, thus providing concave sites that could become favored sites for gas binding. According to Table 3 and Figure 5, the enhancements at the valley site are larger for CO2 than for CH4, which leads to a difference of nearly 7 kJ mol−1 between CO2 and CH4 binding at higher curvatures. This difference could potentially be leveraged for CH4 flow purification. In contrast, the two gases show very similar binding for the peak site. For adsorption at the valley site on the more weakly rippled surfaces, the CH4 molecule orients with its hydrogen tripod toward the valley. At 15−20% compressive strain, this orientation makes a transition to one in which only two hydrogen atoms point directly toward the valley. At the peak site, the tripod always orients toward the surface. CO2 7746



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measures of surface acidity/basicity, which describe the energetic penalties associated with filling states in one region while simultaneously depleting them at another.80 Nevertheless, although internal charge rearrangement can account for the relative differences between CH4 and CO2 binding on a given substrate, it cannot account fully for the strength of binding to one substrate over another. For example, the values of ΔqC for graphene with a SW defect (3.6 × 10−4e and 1.2 × 10−3e for CH4 and CO2, respectively) are comparable to the corresponding values for pristine graphene. This is true despite the fact that SW defects bind more stongly than pristine graphene by ∼4 kJ mol−1 (Table 1). In addition, we find that ΔqC increases to 5.3 × 10−4e for CH4 binding on the rippled surface, yet the binding energy is identical to the SW case. One might instead suspect that the binding is related to the spatial extent or geometric distribution of the charge density rearrangement; however, the maximum and variance of the per-atom occupation are nearly identical for the pristine, SWcontaining, and rippled graphene sheets despite the significantly higher binding associated with the latter pair. Our observed trends are also unsupported by rationalizations based on London dispersion effects alone because these would suggest no apparent difference between structurally similar SW and pristine graphene sheets. Instead, we can gain some insight into the reasons for enhanced binding by examining the electronic density of states (DOS) upon adsorption. We do this for two of the most promising cases, namely, the valley site of rippled graphene and the SW defect, and compare the results to binding on pristine graphene in Figure 6. The adsorption-induced changes in the DOS are plotted on top of the background p states of the nearest carbon atom, which provide a reference for how the electronic structure of the substrate is perturbed by the adsorbate. First, we point out that slight changes to the electronic structure are visible even for the pristine graphene

case (Figure 6a and d), especially for CO2 where some hybridization with the carbon p states is evident (e.g., at −6.5 and −2.3 eV with respect to the Fermi level, EF). More significantly, both of the stronger-binding substrates (Figure 6b−c,e−f) demonstrate additional hybridization of the gasmolecule levels with the p orbitals of nearby carbon atoms. In the energy range of −2 to −8 eV with respect to EF, overlap with the molecular states tends to correlate with a partial mixing of pz states with the px and py states, which is not observed in pristine graphene. The rehybridization is particularly apparent in rippled graphene, where it can be interpreted as a curvature-induced loss of sp2 character in favor of more sp3-like binding. Note also that in each instance, a greater degree of hybridization is evident for CO2 adsorption than CH4 adsorption, consistent with the stronger binding of the former. We suggest that this subtle mixing between molecular and the carbon p states plays a significant role in enhancing binding.

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CONCLUSIONS We have used van-der-Waals-corrected DFT to investigate the possibility of engineering the local morphology of sp2 carbon substrates for improved gas uptake and separation, with particular emphasis on CO2 and CH4 binding. Binding energies have been calculated on a wide variety of experimentally realizable topological defects on graphene, including native point defects (monovacancies, divacancies, and SW defects), compressive and tensile-strained graphene, and graphene folds (grafolds). Each of these heterogeneities may be experimentally introduced into graphene-based structures by proper choice of processing conditions; accordingly, the models can be expected to provide a reasonable assessment of their effects on the uptake of CO2 and CH4. On the basis of zero-temperature binding energetics, we find that the best structural candidates for improvement are the concave sites in rippled graphene geometries and SW defect sites. Among the point defects, the SW and monovacancy sites were found to enhance binding for both CH4 and CO2 when compared with bare graphene, with the largest binding enhancements of about 20−25% observed with the SW defects. Similar degrees of enhancement were achieved for the rippled samples that form under compressive strain. By contrast, application of tensile strain did not significantly affect the binding energies. For the strongest-binding substrates, electronic structure analysis reveals that additional enhancements in the binding energies of both gases can be traced to partial mixing of the p orbitals with proximal carbon atoms. We find a universal preference for binding CO2 over CH4, which is attributable to greater induced internal charge rearrangement in the substrate in the case of CO2, likely due to its quadrupole moment. However, the results demonstrate variability in the relative binding energies of CO2 and CH4 on a given substrate, which has implications for the species selectivity of the binding site when exposed to a mixture of CO2 and CH4. These differences range from 3.1 to 5.2 kJ mol−1 for the point defects and from 5.2 to 7.8 kJ mol−1 for the ripples and folds. (By comparison, this difference is 4.5 kJ mol−1 for bare graphene.) Accordingly, local curvature is expected to be more effective for CH4/CO2 gas separation than point defects. Interestingly, the greatest difference was observed for folded graphene (grafold) due to a greater binding energy decrease with respect to pristine graphene for CH4 compared with CO2.

Figure 6. Change in the total density of states (ΔDOS) upon CH4 (a−c) and CO2 (d−f) adsorption (black solid curve) on (a,d) pristine graphene, (b,e) rippled graphene under 20% compressive strain (valley site), and (c,f) graphene with a Stone−Wales defect. The pz (blue dashed) and px + py (red dotted-dashed) contributions to the background (i.e., prior to adsorption) projected density of states from the carbon atom nearest to the adsorption site are shown for reference. Large peaks in ΔDOS that extend beyond the axis limits correspond to CH4/CO2 molecular states. 7747



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Because our calculations focus on models derived from experimentally observed topological defects, they have direct implications for providing molecular strategies to enhance binding energies in carbon-based adsorbents. By deliberately introducing such features in porous carbons, enhancements of 20−30% in binding strength can be expected, translating to commensurately higher storage capacity and better selectivity toward CO2 in a CO2/CH4 mixture. The results are also useful in guiding the design of graphene-derived gas sensors, for which gas-selective binding strength is an important consideration. We point out that these suggestions are derived from dilute adsorption calculations at zero temperature and should therefore be considered primarily as an initial approximation to the low-coverage low-temperature heats of adsorption. However, the DFT binding energies may be used to parametrize classical force fields, which would allow the examination of uptake and separations at higher pressures and temperatures. Finally, we point out that fully incorporating the specific binding energies in naturally disordered porous carbons would require a more detailed characterization of the atomic arrangement at the defect site than the simple models we consider here; for instance, expected binding energies could be modified by the presence of multilayered carbon fragments.

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AUTHOR INFORMATION

Corresponding Authors

*D.D.: E-mail: [email protected]. *B.C.W.: E-mail: [email protected]. Present Address ∥

D.D.: Department of Chemical & Biomedical Engineering, University of South Florida, Tampa, Florida 33620, United States. Author Contributions ⊥

D.D. and B.C.W are joint first authors.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge funding from Bharat Petroleum Corporation Limited (BPCL), India. Helpful conversations with G. Vasudev, N. V. Choudary and B. Newalkar of BPCL, India are gratefully acknowledged. B.C.W. was funded by U.S. National Science Foundation Grant 701180. Computations were performed using the facilities of the Centre for Computational Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, India. A portion of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DEAC52-07NA27344.

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NOTE ADDED AFTER ASAP PUBLICATION A second affiliation for Shobhana Narasimhan was missing in the version published in April 7, 2014. This was added in the version published on April 9, 2014.

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