A comparative study of mechanisms of the adsorption of CO₂ confined within graphene–MoS₂ nanosheets: a DFT trend study

Abstract

The space within the interlayer of 2-dimensional (2D) nanosheets provides new and intriguing confined environments for molecular interactions. However, atomic level understanding of the adsorption mechanism of CO₂ confined within the interlayer of 2D nanosheets is still limited. Herein, we present a comparative study of the adsorption mechanisms of CO₂ confined within graphene–molybdenum disulfide (MoS₂) nanosheets using density functional theory (DFT). A comprehensive analysis of CO₂ adsorption energies (E_AE) at various interlayer spacings of different multilayer structures comprising graphene/graphene (GrapheneB) and MoS₂/MoS₂ (MoS₂B) bilayers as well as graphene/MoS₂ (GMoS₂) and MoS₂/graphene (MoS₂G) hybrids is performed to obtain the most stable adsorption configurations. It was found that 7.5 Å and 8.5 Å interlayer spacings are the most stable conformations for CO₂ adsorption on the bilayer and hybrid structures, respectively. Adsorption energies of the multilayer structures decreased in the following trend: MoS₂B > GrapheneB > MoS₂G > GMoS₂. By incorporating van der Waals (vdW) interactions between the CO₂ molecule and the surfaces, we find that CO₂ binds more strongly on these multilayer structures. Furthermore, there is a slight discrepancy in the binding energies of CO₂ adsorption on the heterostructures (GMoS₂, MoS₂G) due to the modality of the atom arrangement (C–Mo–S–O and Mo–S–O–C) in both structures, indicating that conformational anisotropy determines to a certain degree its CO₂ adsorption energy. Meanwhile, Bader charge analysis shows that the interaction between CO₂ and these surfaces causes charge transfer and redistributions. By contrast, the density of states (DOS) plots show that CO₂ physisorption does not have a substantial effect on the electronic properties of graphene and MoS₂. In summary, the results obtained in this study could serve as useful guidance in the preparation of graphene–MoS₂ nanosheets for the improved adsorption efficiency of CO₂.

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1 Introduction

Identifying stable systems with improved CO₂ capture has become an essential goal for carbon capture and storage technologies.^1,2 In recent years, gas-adsorbent materials (GAMs) have received significant attention from many researchers across the globe due to the increased rate of effluent gases (for example, CO_x, NO_x, SO_x, Hg⁰, etc.) from industries.³ Among all these, carbon dioxide (CO₂) concentration in the atmosphere has been found to be increasing rapidly (313 ppm, 1960 to 407 ppm, 2017),⁴ and this has been linked to the increased reliance on fossil fuels within the past century. Accordingly, reduction and capture of green-house gases have been among the most challenging issues in environmental protection.⁵ In the past decades, the use of capturing and separation techniques like absorption, adsorption, use of membranes and the ilk was widespread, however, the efficiencies of these processes seem to pose a serious challenge.⁶ In the bid to tackle the issue of global warming, energy-efficient capture of CO₂ and other green-house gases through industrially proven and simple processes like adsorption is of critical importance. Although a large number of gas-adsorbent materials have been computationally and experimentally developed in the past, nanostructured GAMs are at the cutting-edge of potentially revolutionary advancements in fast growing technological fields such as molecular sensing, energy storage and harvesting, environmental and sustainability engineering, etc.^1–3,7,8 This has led to the rapid increase in the development of novel nanostructured GAMs. Their properties, which include high surface to volume ratio, regular atomic composition, tunable reactivity, effective transport properties and assembling affinity to form supramolecular systems, have warranted their applications in CO₂ capture technologies.³

Among these nanostructured materials, two-dimensional (2D) nanomaterials like graphene and hexagonal-BN (hBN) sheets have attracted greater interest because of their extraordinary properties attributed to their ultrathin thickness, which is related to quantum effects.^9–11 These 2D nanomaterials vary in terms of their electronic properties and functionality. For instance, graphene is a low-work function metallic electrode, hBN is an insulator, and MoS₂ is generally an n-type semiconductor (very active potential site for CO₂ capture). However, their synergetic function is more attractive for technological application. Recently, several new classes of 2D nanostructures like transition metal dichalcogenides (TMDs) have been studied with more emphasis on molybdenum disulfide (MoS₂), which exhibits a number of interesting properties such as high catalytic activity,¹² bandgap variation with number of layers,^13,14 high carrier mobility^15,16 and gas sensing capability that have made it widely used in the adsorption of gas molecules especially toxic gases.^17–19 In parallel with the efforts on graphene-like materials, recent studies have focused on the advantage of merging individual properties of different 2D materials. To this end, multilayer heterostructure materials are produced by stacking 2D-crystals of each nanomaterial,²⁰ bonded by relatively weak van der Waals (vdW)-like forces. For example, the possibility of making a graphene/MoS₂ bilayer heterostructure has been demonstrated experimentally. Experimental findings show that synthesized materials are more thermally stable with high adsorption capacity.⁸ Moreover, the space within the interlayer separation of these 2D nanosheets has often provided new and intriguing confined environments for molecular interactions due to the nanoconfinement effect.^21–24 The confined space between layers of these nanosheets has provided lower loss and stronger localization of active sites. In addition, the tunability of this spacing can enhance the physico-chemical properties of these nanostructures. Examples of these properties include surface area, penetration depth, adsorption capacity and catalytic activity. Therefore, understanding the underlying principles of CO₂ adsorption mechanisms within this nanoconfinement will provide in-depth knowledge into the materials science involving stacking routes of 2D nanomaterials.

The motivation to carry out this present study stems from the impact of interlayer orientation on the electronic properties and binding energy of substrate-grown monolayers^25,26 and multi-layered structures of the same material.²⁷ Also, experiments have shown that combining MoS₂ and graphene provides tremendous active sites for molecular adsorption that could responsibly remove smoke particles, CO and other toxic volatiles.⁸ Therefore, it is possible to attune the structural parameters of these sites to facilitate CO₂ adsorption. Moreover, experimental and theoretical studies have shown that this nano-space presents new and extraordinary behaviours for molecular intercalations²¹ and catalytic activities.^22–24 In this work, the effect of interlayer distance between 2D materials, graphene/graphene (GrapheneB) and MoS₂/MoS₂ (MoS₂B) bilayers as well as graphene/MoS₂ (GMoS₂) and MoS₂/graphene (MoS₂G) hybrids, on CO₂ adsorption mechanisms from first principles was investigated, with the aim of finding the most stable conformation for CO₂ adsorptions. The orientations and binding energies of CO₂ molecule on these surfaces are determined as well.

2 Computational methods and models

All calculations are carried out using DFT²⁸ in conjunction with the projector-augmented wave (PAW)^29,30 method, as implemented in Vienna ab initio simulation package (VASP).^31,32 The exchange and correlation potentials are treated with the generalized gradient approximation (GGA) functional of Perdew, Burke and Ernzerhof (PBE).³³ Valence electrons for Mo and S are generated in 4p⁶5s¹4d⁵ and 3s²3p⁴ respectively, while the valence electron for C is generated in 2s²2p². Different dispersion schemes are employed to understand the effects of vdW forces on the adsorption of CO₂. Firstly, we include Grimme's³⁴ DFT-D2 method, which adds a semiempirical pairwise force field to conventional DFT calculations. Then, we employ the vdW-DF functional of Langreth and Lundqvist et al., which adds a non-local correlation functional that approximately accounts for dispersion interaction.^35–37 The vdW-DFT methods with exchange-correlation energy given by revPBE,³⁵ the opt functionals (optPBE and optB88)³⁸ for accurate exchange functionals for vdW correlation, and vdW-DF2 of Langreth and Lundqvist groups^39,40 are considered.

Calculations are performed with a 4 × 4 × 1 supercell of monolayer MoS₂ (1H-MoS₂) containing 16 Mo atoms and 32 S atoms, and a 5 × 5 × 1 supercell of monolayer graphene containing 50 C atoms for the monolayers. The MoS₂ bilayer contains two 4 × 4 × 1 supercells of monolayer MoS₂ (32 Mo atoms and 64 S atoms) while the graphene bilayer contains two 5 × 5 × 1 supercell monolayers of graphene (100 C atoms). For the hybrid structure, a supercell containing 5 × 5 × 1 lateral periodicity of graphene and 4 × 4 × 1 lateral periodicity of MoS₂ monolayer (16 Mo atoms, 32 S atoms and 50 C atoms) were employed which includes 1.9% lattice mismatch⁴¹ in order to impose a commensurability condition between the graphene and MoS₂ monolayer. To illustrate the fundamental properties of the graphene–MoS₂ hybrid, we chose a lateral lattice parameter for the triangular lattice a = 12.34 Å that was optimized for isolated graphene, which is in agreement with graphene-based hybrid systems investigated previously⁴¹ to ensure a smaller lattice mismatch. A large vacuum layer of 15 Å is used in the direction to the interface as an isolated slab boundary condition to avoid interlayer interactions. The test for cutoff energy and k-point grid is required for convergence and the result is summarized in the ESI.† The Gaussian smearing width was set to 0.2 eV. The total energy was converged to <10 meV for a plane-wave cutoff of 500 eV and 5 × 5 × 1 Monkhorst–Pack (MP)⁴²k-point sampling for the Brillouin zone. Because of the large quasiparticle dynamics of graphene, the Brillouin zone sampling of electronic states was performed using a finer MP mesh with size 40 × 40 × 1 per unit cell.⁴³ The tetrahedron method with Blöchl corrections for a pure graphene monolayer and bilayer DOS was also adopted. Finer MP mesh and Fermi smearing width of 0 eV was used to ensure accurate prediction of the DOS of semiconductors like graphene. For geometry relaxation, we used the method of conjugate gradient energy minimization. The convergence criterion for energy is chosen to be 10⁻⁴ eVbetween two consecutive steps, and the maximum Hellmann–Feynman force exerting on each atom is less than 0.03 eV Å⁻¹ upon ionic relaxation. Using Bader charge analysis, charge transfer between the substrate and the adsorbate is obtained.⁴⁴

The adsorption energy of a CO₂ molecule on multilayer and monolayer structures is investigated. Adsorption energy is calculated as:

E_AE = E_surf+CO2 − (E_surf + E_CO2) (1)

where E_surf+CO2 is the total energy of the optimized structure with an adsorbed CO₂ molecule and E_surf and E_CO2 are the total energies of the pristine structure and isolated CO₂ molecule respectively. A negative value of E_AE indicates that the adsorption is exothermic which means that the adsorption of CO₂ molecules on the surface of the structures is favoured energetically.

3 Results and discussion

3.1 Bulk structure parameters

Graphene and MoS₂ have hexagonal structures consisting of C–C and S–Mo–S layers respectively. Bulk graphene has two layers and each layer known as a unit cell consists of a central carbon atom connected to three carbon atoms with an adjacent carbon atom on both sides of the layers. Bulk MoS₂ also has two such layers, with molybdenum (Mo) atoms of one layer directly above the sulphur (S) atoms of the other layer and vice versa. The lattice constant of pristine graphene and MoS₂ sheets using a unit cell were calculated and compared with the literature in order to validate this method and its pseudopotentials. Calculated values are 2.468 Å and 3.186 Å for graphene and MoS₂ respectively, which are in excellent agreement with previous theoretical results of 2.463 Å and 3.20 Å.⁴⁵ Based on this agreement, all other calculations were carried out, which are discussed in the subsequent sections.

3.2 Effects of interlayer distance on CO₂ adsorption

To obtain a clear understanding of the effect of the multilayer structures on CO₂ adsorption, the adsorption energies of CO₂ (E_AE) at various interlayer distances of multilayer structures comprising graphene/graphene bilayer (GrapheneB), MoS₂/MoS₂ bilayer (MoS₂B), graphene/MoS₂ hybrid (GMoS₂) and MoS₂/graphene (MoS₂G) hybrid were computed and the results are reported in Table 1. At the start of each geometry optimisation procedure, CO₂ molecule is placed horizontally along the z-axis, at the middle distance between the two surface layers. This is assumed in order to avoid the repulsive effect between the electrons of the surface atoms and the lower oxygen atom of the CO₂ molecule. Such a repulsive effect was commonly encountered in a configuration where the CO₂ molecule is perpendicularly oriented to the surface. This was one of the initial configurations proposed for CO₂ physisorption on pristine graphene⁴⁶ and graphene sheets with (0001) defects.⁴⁷

Table 1 Adsorption energies of CO₂ per carbon atom on different structures determined from different interlayer distances using the PBE of GGA^a33

Interlayer distance (Å)	Adsorption energies EAE (meV)
	GMoS2	MoS2G	MoS2B	GrapheneB
a NA: not adsorbed.
3.5	237.20	27.98	(NA)	179.98
6.0	61.10	44.87	(NA)	67.54
7.0	−17.10	−9.01	−36.00	−10.50
7.5	−23.55	−24.00	−38.00	−32.00
8.5	−24.11	−25.09	−28.25	−17.15
9.5	−15.76	−15.45	−16.90	−12.99
10.5	−8.90	−9.00	−8.13	−4.57
11.5	−9.76	−6.28	−4.76	−1.03
12.5	−2.54	−1.84	−2.30	0.68
13.5	−0.49	−0.55	−1.36	1.17

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As shown in Table 1, a more negative value means stronger CO₂ adsorption. The positive values at separations below 6.0 Å indicate that the spacing between layers is so small that overlapping with CO₂ occurred. Hence, energy is required to promote CO₂ adsorption. According to Ataca et al.,⁴⁵ an interlayer spacing of 6.145 Å was estimated via DFT to be the suitable spacing for molecular interaction in the MoS₂ interlayer. Below this, no adsorption (NA) will be observed, which corresponds to the results for MoS₂B in Table 1. Similarly, the most-suitable interlayer distance that permits molecular adsorption in GrapheneB has been determined to be between 7 Å and 10 Å.⁴⁸ However, unlike MoS₂B, energy is required to facilitate adsorption below this interlayer distance. This is attributed to the structural flexibility of graphene, in contrast to MoS₂. Furthermore, it can be stipulated that the required interlayer distance for CO₂ adsorption in the GMoS₂ hybrid should be the sum of the equilibrium distance between the GMoS₂ substrate and the kinetic diameter of CO₂ (3.30 Å⁴⁹). The equilibrium distance between the GMoS₂ substrate in different arrangements was measured to be around 3.32 Å.^41,50 Hence, energy is demanded for CO₂ adsorption at interlayer distances less than 6.62 Å for the GMoS₂ hybrid. Considering that CO₂ molecule has a kinetic diameter of 3.30 Å,⁴⁹ it is expected that CO₂ intercalation should enlarge the distance between graphene sheets and MoS₂ surface and that of the bilayer surfaces. By expanding the vdW gap between the two sheets, a charge transfer between the guest and the host surface is expected to occur with a very large repulsive energy.⁵¹

Fig. 1 demonstrates the variation of interlayer spacing with CO₂ adsorption energies. This figure shows that 7.5 Å and 8.5 Å interlayer spacings are the most stable conformations for CO₂ adsorption on the bilayer and hybrid structures respectively. Also, as the interlayer distance increases, the CO₂ binding energy increases as well, but comes to a local minimum at 7.5 Å and 8.5 Å for the bilayer and hybrid structures respectively. It is estimated that GrapheneB has the least total adsorption capacity given the considered range of interlayer distance. It can be assumed that the presence of MoS₂ in the hybrid buttressed CO₂ adsorption beyond interlayer spacing greater than 8.0 Å. The plot for the GMoS₂ hybrid structure is in good agreement with the work of Ma et al.,⁴¹ although only graphene adhesion on MoS₂ was considered. The peak binding energies per C atom for GMoS₂, MoS₂G, MoS₂B and GrapheneB are −24.11 meV, −25.09 meV, −38.00 meV and −32.00 meV, respectively. Moreover, the adsorption energies of these multilayer structures seem to be a simple sum of the contributions from the constituents with decreasing binding energies in the order: MoS₂B > GrapheneB > MoS₂G > GMoS_2. These values are low which correspond to weak interactions between the layers and CO₂ molecule. This is due to the inability of conventional DFT approaches to describe dispersion force in adsorption systems. These values were improved when factors like CO₂ orientation and addition of vdW interactions between the CO₂ molecule and the surfaces were considered. Furthermore, two different configurations of the bilayer heterostructure were considered. This is to explain the effect of structural anisotropy on the adsorption energies of heterostructures. In the first structure graphene is the substrate (GMoS₂) while in the second case MoS₂ is the substrate (MoS₂G). Optimization results depict that there is discrepancy in the binding energies of CO₂ adsorption on these hybrid structures (GMoS₂ and MoS₂G). This can be ascribed to the modality of the atom arrangement (C–Mo–S–O and Mo–S–O–C) just like in the case of zigzag and armchair arrangements of bilayer graphene²⁷ and the interlayer orientation effect on bilayer heterostructures. This indicates that the conformational anisotropy of this structure determines to a certain degree its CO₂ adsorption energy. The most appropriate orientation of this hybrid for optimal adsorption performance is subject to further investigation.

Fig. 1 CO₂ adsorption energy as a function of interlayer distance. Adsorption energy as a function of interlayer distance between the two monolayers for all the studied multilayer structures. Separate plots of each case are included in the ESI.

3.3 Effects of CO₂ orientation and position

To further understand the interaction of CO₂ within these multilayer structures, we calculated CO₂ adsorption energy at different CO₂ orientations and positions using the same optimum interlayer distance presented earlier. Table 2 summarizes the calculated adsorption energies per carbon atom for the most stable adsorption configuration of the multilayer structures in comparison with the most stable monolayers. In all calculations, CO₂ was placed at the mid-point of the interlayer distance for the multilayer structure and the same value was chosen for the monolayers for proper comparison. Also, since the test for cutoff energy and k-point grid is required for convergence, we calculated total energies using different cutoffs and k-points and the results are summarized in the ESI.† The total energy was converged to <10 meV for a plane wave cutoff of 500 eV and 5 × 5 × 1 Monkhorst–Pack⁴²k-point sampling for the Brillouin zone. The adsorption energies of the multilayer structures also seem to be a simple sum of the contributions from the constituents. The structures displayed low energies, which explains the difficulty of conventional DFT approaches to accurately reflect the vdW force in adsorption systems. Our goal here is to gain insight into the surface most active site, which is the CO₂ adsorption energies with respect to its positions and orientation on the surface. From the obtained results, it is evident that CO₂ molecule prefers to interact with a parallel or inclined orientation with the adsorbent surface than the perpendicular orientation. For instance, considering the edge position of GrapheneB bilayer, the adsorption energy for parallel and 30° parallel-rotation are −27.05 and −23.62 meV respectively, but the value is −5.65 meV for perpendicular attack of CO₂ at the same position. This is due to the repulsive effect between the electrons in C-atoms (graphene) and the lower O-atom (CO₂ molecule). Consequently, the molecule stays less bounded to the surface compared to the optimum adsorption site. The same effect was addressed by Cabrera-Sanfelix, when CO₂ was placed initially perpendicular on graphene sheets with defects.⁴⁷ Parallel attack of CO₂ at the edge position is observed to be the most favourite adsorption site for GMoS₂, MoS₂B and MoS₂G composites with stable adsorption energies of −27.16, −40.37 and −27.07 meV respectively, while the centre position was the most favourable adsorption site for GrapheneB (−32.37 meV). GMoS₂ and MoS₂G retained this position as their active site for CO₂ inclined (30° and 45° respectively) attack on the surface, in contrast to GrapheneB, which favoured the centre position as the favourite adsorption site. These differences can be attributed to changes of the electronic environment causing charge redistribution culminating to variation in adsorption capabilities. In addition, the adsorption capacity derived from the edge site of MoS₂ (ref. 52 and 53) can contribute to these changes. For instance, MoS₂ monolayer (M4 × 4) favoured the edge position as the favourite adsorption site while graphene monolayer (G5 × 5) favoured the centre position as the favourite adsorption site. Therefore, it is expected that the edge position will be the most favourite adsorption site for the GMoS₂ and MoS₂G due to the inclusion of the MoS₂ layer, whose catalytic activity occurs at the edge sites. Also, since M4 × 4 has higher adsorption energy (−20.33 meV) than G5 × 5 (−16.38 meV), it is expected that M4 × 4 will determine to a certain extent the adsorption properties of the hybrid structures (GMoS₂ and MoS₂G).

Table 2 Adsorption energies of possible initial configurations of CO₂ adsorption on perfect multilayer and monolayer structures using PBE^a.³³

Position/orientation to the surface	Adsorption energies EAE (meV)
	GMoS2	MoS2G	MoS2B	GrapheneB	G5 × 5	M4 × 4
a G5 × 5 and M4 × 4 are 5 × 5 and 4 × 4 supercells of graphene and MoS2 monolayers respectively.
Centre/parallel	−25.49	−26.98	−27.99	−26.47	−15.15	−17.13
Edge/parallel	−26.48	−26.54	−40.37	−27.05	−13.21	−20.33
Centre/perpendicular	11.27	11.77	100.02	−25.64	−3.10	−9.92
Edge/perpendicular	38.00	47.97	−27.31	−5.65	−3.90	−4.23
Centre/parallel (rotated 30°)	−23.27	−26.73	−37.44	−26.04	−16.38	−16.60
Edge/parallel (rotated 30°)	−27.16	−26.60	−35.98	−23.62	−13.94	−19.37
Centre/parallel (rotated 45°)	−24.03	−25.05	−37.75	−32.37	−14.07	−17.47
Edge/parallel (rotated 45°)	−26.16	−27.07	−35.98	−28.23	−14.41	−19.23

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Improved adsorption energies were obtained when the dispersion correction to DFT is considered. To take dispersion force into account, we carried out a spin-polarized calculation using different dispersion force methods and compared the results with conventional DFT approaches. The adsorption energies significantly improved by incorporating vdW interactions between the CO₂ molecule and the surfaces as shown in Table 3. However, there are no detailed experimental or computational data for CO₂ adsorption on hybrid and bilayer structures so far. Based on previous calculations of CO₂ adsorption on pristine monolayer graphene^46,54 and MoS₂,⁵⁵ the results obtained using optPBE functional for the monolayers should be reliable. Also, we find that CO₂ binds strongly on these multilayer structures. In fact, graphene bilayer gives the highest CO₂ adsorption energy among the multilayer structures when vdW-DF2 interactions are included, in contrast to conventional PBE results. This is in contrast to the previous suggestion from conventional PBE results that the adsorption energy of the bilayers is approximately a simple sum of the contributions from the constituents. In addition, it is expected that adsorption energy of CO₂ on perfect graphene and MoS₂ sheets should be lower because of lack of dispersive interactions in DFT. Due to the addition of vdW interactions, there is a tendency for overestimation of molecular adsorption.^56,57 For instance, vdW-DF2 correlation overestimates the adsorption energy of graphene bilayer, while revPBE and optPBE correlations overestimate the adsorption energy of MoS₂ bilayer. Furthermore, it is observed that CO₂ adsorption energies obtained when revPBE and optPBE correlations are included are similar. Likewise, there are similarities in the adsorption energies calculated using DFT-D2 and vdW-DF2 correlations except for the adsorption energy of bilayer graphene which is overestimated by vdW-DF2 correlation. Also, the results of these correlations for the MoS₂ monolayer are in good agreement with the previous calculation.⁵⁵ On the other hand, the stronger binding between CO₂ and graphene monolayer when using DFT-D2 correlation is in agreement with reported values given for CO₂ adsorption on perfect monolayer graphene, ∼147–151meV.^56,57 Generally, the increase in CO₂ adsorption energy with the introduction of vdW interactions indicates that vdW interaction dominates during the adsorption process. This is comparable with previous theoretical results that incorporated vdW interaction.^1,55

Table 3 Comparison of the adsorption energies (E_AE, meV) of CO₂ on bilayer, hybrid and monolayer structures determined from different methods

Structures	This work						Reference^a
	PBE	DFT-D2	revPBE	optPBE	optB88	vdW-DF2	PBE	DFT-D2
a The corresponding values of previous calculations for monolayer graphene and MoS2 are given for the sake of comparison. The PBE adsorption energy of ref. 55 for MoS2 monolayer appears to be too small, this is because ref. 55 did not consider CO2 orientation, a similar value was obtained when we considered CO2 orientation (Table 2). Similarly, the DFT-D2 adsorption energy of ref. 1 for graphene monolayer is too small due to the same reason. But the revPBE and optPBE adsorption energies of MoS2 monolayer are in good agreement with the adsorption energy of ref. 55.
GMoS2	−27.16	−145.17	−321.73	−333.01	−242.13	−161.31	—	—
MoS2G	−27.07	−169.14	−300.47	−313.54	−254.74	−186.46	—	—
MoS2B	−40.37	−195.33	−1157.28	−1069.94	−829.09	−232.65	—	—
GrapheneB	−32.37	−241.34	−405.23	−450.26	−368.47	−1694.0	—	—
G5 × 5	−16.38	−153.30	−209.58	−249.98	−224.41	−160.21	−17.10(ref. 46)	−60(ref. 1)
M4 × 4	−20.33	−126.30	−201.25 (−210 (ref. 55))	−232.40 (−253 (ref. 55))	−204.50	−152.38	−4.00 (ref. 55)	−139.0 (ref. 55)

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3.4 Structural parameters

The optimized adsorption configuration of CO₂ on most stable multi-layered structures determined by PBE calculations and the stacking type of the structures are shown in Fig. 2. The bond length (C=O), angle of CO₂ molecule, interlayer distances, C=C, Mo=S bond lengths and the molecular distance are presented in this figure. To further understand the interaction between CO₂ and the surface, several structural parameters are calculated and compared with previous studies. The calculated bond length and angle for free CO₂ molecule are 1.177 Å and 179.87° respectively, which is in line with 1.16 Å and 180° from experiments,⁵⁸ and 1.175 Å and 178° from previous theoretical calculation.⁴⁶ Based on experimental values, bond angles of adsorbed CO₂ decreased by about 0.05–0.13°, depending on the structures of the nanocomposite (Table 4). There is no chemical bonding observed, and interactions are dominated by weak vdW forces. In other words, the entire adsorption is purely physisorption due to the small adsorption energy and large separation height (molecular distance). Moreover, only the stable configurations obtained from PBE calculations are presented. This is because the inclusion of vdW interactions slightly changes the stable configurations.

Fig. 2 The most stable configuration of the multilayered structures with adsorbed CO₂. (a–d) are the top views of GMoS₂, MoS₂G, MoS₂B and GrapheneB and (e and f) are side views of the same structures respectively. Color code: Mo, blue, S, yellow, C, grey, and O, red. The lines define the interlayer distances, bond lengths, and molecular distance while the curved lines define the bond angle. AA stacking type is chosen for both MoS₂B and GrapheneB. This is because AA stacking of graphene has been shown to be more preferable for intercalation of molecules according to ref. 59 and ref. 60. Although the binding energy of AB stacking of graphene bilayer is lower than that of AA stacking, which makes AB stacking more stable than AA stacking, AA stacking intercalation structures are more favorable than AB stacking ones, ref. 60. For the hybrid structures, the stacking type is chosen according to ref. 50, where one C atom in the unit cell of graphene sits exactly below a Mo atom. It is reported in ref. 41 that another configuration called TS, where the stacking is such that C atom sits below an S atom, is equivalent in both the binding and electronic properties.

Table 4 Amount of charge transferred to CO₂ molecule (single atom and CO₂ molecule), amount of charge transferred from adjacent Mo, S and C atoms on the surface nearer to the adsorbed CO₂ molecule, and the change in bond length and bond angle after CO₂ adsorption (length and angle, with angle change in parentheses)^a

Structures	Amount of charge transferred (e)							Bond length (Å) angle (deg)
	O1	C	O2	CO2	Mo	S	Cg	C=O	O=C=O
a Bader charge analysis is used for the charge transfer calculations. Cg is the adjacent carbon atom of graphene surface that is nearer to the adsorbed CO2 molecule, while Mo and S are adjacent molybdenum and sulphur atoms of the MoS2 surface that are nearer to the adsorbed CO2 molecule. The adjacent atoms were chosen arbitrarily based on their proximity to the adsorbed CO2 molecule. Negative charge denotes electron gain.
GMoS2	−0.001	−0.018	−0.009	−0.028	0.001	−0.002	−0.001	1.18	179.95 (0.05)
MoS2G	0.804	0.036	−0.030	0.810	0.000	0.000	−0.003	1.18	179.93 (0.07)
MoS2B	0.035	−0.033	0.015	0.017	0.000	0.000	N/A	1.18	179.92 (0.08)
GrapheneB	0.021	−0.012	−0.016	−0.007	N/A	N/A	−0.004	1.18	179.92 (0.08)
G5 × 5	0.001	0.020	−0.015	0.006	N/A	N/A	−0.004	1.18	179.89 (0.11)
M4 × 4	0.035	−0.047	0.002	−0.010	0.000	0.084	N/A	1.18	179.87 (0.13)

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Bader charge analysis shows that the interaction between CO₂ and these surfaces causes charge transfer and redistributions (Fig. 3). The amount of charge transferred from Bader charge analysis is summarized in Table 4. It can be seen that while 0.028e of charge is transferred to CO₂ on the GMoS₂ surface where graphene is the bottommost layer, 0.810e of charge is transferred from CO₂ to MoS₂ where MoS₂ is the topmost layer. This could indicate that the modality of the atom arrangement (C–Mo–S–O and Mo–S–O–C) in both structures affects the charge transfer between the molecule and surface atoms. In order words, the conformational anisotropy of this structure determines to a certain point the charge transfer and redistribution just like in its CO₂ adsorption energy. Meanwhile, in some cases, the adjacent S atom of MoS₂ and C atom of graphene nearer to the adsorbed CO₂ gain electrons, while Mo atom loses an electron in all cases. This is because of the higher electronegativity of S and C atoms compared to the Mo atom. Fig. 3 presents the charge density difference plots for CO₂ molecule-surfaces obtained using the formula:

Δρ = ρ_mole+surf − (ρ_mole + ρ_surf) (2)

where ρ_mole+surf, ρ_mole and ρ_surf are the charge densities of non-interacting components (CO₂ and surfaces), isolated CO₂ molecule and pure surface of the structures, respectively.

Fig. 3 Top and side views of charge density difference plots for (a) graphene/MoS₂ hybrid, (b) MoS₂/graphene hybrid, (c) MoS₂ bilayer, (d) graphene bilayer, (e) 4 × 4 supercell MoS₂ monolayer, and (f) 5 × 5 supercell graphene monolayer. The pink and green distributions correspond to charge accumulation (electron excess) and depletion (electron loss) respectively. Isosurfaces: ±5 × 10⁻⁵e⁻¹ ų.

The pink region shows the charge accumulation (electron excess) while the green region indicates the charge depletion (electron loss). In all the structures, it can be shown that there is a noticeable polarization of the surfaces upon CO₂ adsorption, and electrostatic interaction plays a role in the attractive interaction. Moreover, there is charge accumulation on GMoS₂, MoS₂G, MoS₂B, GrapheneB, G5 × 5 and M4 × 4 upon CO₂ adsorption, which suggests that CO₂ also has a charge-donor characteristic. In addition, polarization in GrapheneB and MoS₂B structures showed to be stronger than in MoS₂G, G5 × 5, GMoS₂ and MoS₂ structures, which gives rise to larger adsorption energies. This explains why GrapheneB and MoS₂B displayed larger adsorption energies (−241 and −195 meV, respectively) than MoS₂G, G5 × 5, GMoS₂ and MoS₂ (−169, −153, −145, and −126 meV, respectively) after spin-polarized DFT-D2 calculations mentioned earlier.

3.5 Density of states (DOS) plots

To analyse the electronic properties of the adsorbed CO₂ interaction on the multilayer structures, the total electronic density of states (DOS) was studied for graphene and MoS₂ monolayer and bilayer surfaces before and after CO₂ adsorption. Fig. 4 shows that the DOS spectra for either the valence or conduction band of the monolayer and bilayer surfaces do not show significant changes before and after adsorption. This indicates that the CO₂ interaction with these surfaces is purely physisorption, involving weak interaction forces such as vdW and Lewis acid–base interaction. Subsequently, this will not affect the electronic structure of surface atoms significantly. Although it is observed that the adsorption of CO₂ introduces several distinct states at the lower-lying valence bands within the energy level of −22 eV to −25 eV, and offsets some peaks at the conduction bands within energy levels 2.5–5.0 eV, there is no noticeable modification of the DOS near the Fermi level, which also concludes that CO₂ physisorption does not have a substantial effect on the electronic properties of graphene and MoS₂. DOS spectra of graphene (G5 × 5) and MoS₂ (M4 × 4) monolayer, bilayers (GrapheneB and MoS₂B) and hybrid (GMoS₂ and MoS₂G) structures were compared. It is observed that the DOS spectra of the monolayer and bilayer structures are nearly the same. MoS₂ (monolayer and bilayer) displayed a spectrum of an intrinsic semiconductor with direct bandgap of 1.66 eV before and after CO₂ adsorption, which fairly correspond to both previous experimental (1.80 eV) and computational (1.58 eV) results obtained for pure MoS₂ monolayer, whereas graphene (monolayer and bilayer) exhibited a semi-metal spectrum with a small overlap between the valence and conduction band (zero bandgap material).^61,62 However, it is noted here that 5 × 5 × 1 k-point mesh produced an un-converged sampling of Brillouin zone for pure graphene, and introduced small peaks around the Fermi level. This is attributed to the large quasiparticle dynamics of graphene,⁴³ particularly at fewer k-point meshes like 5 × 5 × 1. To correct this anomaly, a very fine k-point mesh without increasing the computational cost was proposed. Accordingly, a finer MP mesh of size 40 × 40 × 1 in the unit cell and the tetrahedron method with Blöchl corrections was used to reproduce the Brillouin zone sampling of electronic states. The 40 × 40 × 1 k-point mesh centered at Г gave a faster convergence and accurately predicted the DOS of pure graphene. It also eliminated the small peaks around the Fermi level. As shown in Fig. 4, the Dirac cone was obtained in pure graphene monolayer and bilayer, which is unaffected after CO₂ adsorption. The plots are in good agreement with the work of ref. 63, which tested different k-point meshes to generate the DOS of graphene monolayer and bilayer structures. However, the DOS spectra of the bilayer heterostructure seem to be a simple sum of those of each constituent with a shift of the valence and conduction bands. The conduction band shifted closer to the Fermi level, a characteristic of an n-type semiconductor. There is a noticeable modification of DOS spectra near the Fermi level, as the conduction band shifted closer to the Fermi level. This indicates a small band gap opening due to the variation of on-site energy induced by MoS₂ that is found in graphene/MoS₂ bilayer heterostructures.⁴¹ As shown in Fig. 4 (1 and 2), the calculated bandgap is 0.04 eV irrespective of the modality of the atom arrangement in both structures. This specifies that the graphene monolayer in the heterostructure loses its metallic nature, and massless electron characteristics and becomes more semiconducting with a direct narrow bandgap, while significantly increasing the conductivity of the MoS₂ monolayer. This is comparable with other hybrid structures.⁴¹ It is also observed that the DOS spectra of the hybrid structures are the same, which indicates that the conformational anisotropy does not have any effect on the DOS spectra bilayer heterostructures unlike in its CO₂ adsorption energy.

Fig. 4 Total DOS spectra before (1) and after (2) CO₂ adsorption. (a) 5 × 5 supercell graphene monolayer, (b) 4 × 4 supercell MoS₂ monolayer, (c) graphene bilayer, (d) MoS₂ bilayer, (e) graphene/MoS₂ hybrid, and (f) MoS₂/graphene hybrid. The dashed line represents the Fermi level.

4 Conclusion

In this work, a comprehensive first-principles study of the CO₂ adsorption mechanism on graphene/graphene, MoS₂/MoS₂ bilayers and graphene/MoS₂, MoS₂/graphene hybrids using GGA-PBE is presented. CO₂ adsorption energies, indicative of adsorption capacity, were calculated at various interlayer spacings. 7.5 Å and 8.5 Å interlayer spacings are the most stable conformations for CO₂ adsorption on the bilayer and hybrid structures respectively, with the bilayers displaying higher adsorption capacities. Beyond an interlayer spacing of 8.0 Å, CO₂ adsorption was promoted by the presence of MoS₂ in the hybrid. However, this varied with the configuration of the bilayer structure. Moreover, the most active adsorption site was determined by varying CO₂ molecule orientation. A parallel CO₂ attack at the edge position of the surface exhibited the highest adsorption energies. Parallely inclined orientations also showed promising adsorption potential, however this varied in attack positions for each nanocomposite. The total electronic density of states analysis reveals that CO₂ interaction with these surfaces is purely physisorption, which mainly involves weak interaction forces. The Bader charge analysis indicates that there is charge transfer and redistribution between the substrate and the adsorbate. In addition, it was demonstrated that conformational anisotropy could affect CO₂ adsorption and other properties due to the modality of the atom arrangement (C–Mo–S–O and Mo–S–O–C) in both heterostructures. In general, the modification of interlayer spacing and structural configuration during the synthesis route is the key to enhancing the adsorption performance of these nanocomposites. This is attainable given the improving successes in atomic level studies and combination of the design of experiments like nanoparticle tracking analysis. Finally, the incorporation of vdW interactions boosted the adsorption energies, thus portraying the importance of doping and functionalization in improving the adsorption performance of these composites.

Conflicts of interest

There is no conflicts to declare.

Acknowledgements

Following funding bodies are acknowledged for partially sponsoring this research: National Key Research and Development Projects (2017YFC0210400 and 2017YFB0603202), National Natural Science Foundation of China (51706114). Special thanks to the Advanced Energy and Environmental Materials Technology (AEEMT) research group at the University of Nottingham Ningbo China. The computational resources are fully provided by the High-Performance Computer (HPC) System of UNNC. The author (Francis Enujekwu) thanks Bamidele Akinwolemiwa for his helpful discussions.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8na00314a

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