Research Article | Open Access

# CO_{2} and SO_{2} Pressure-Driven Adsorption by 3D Graphene Nanoslits: A Molecular Dynamics Study

**Academic Editor:**Renyun Zhang

#### Abstract

Nonequilibrium molecular dynamics simulations are employed to study the adsorption and blockage properties of a 3D graphene membrane. Specifically, we are interested in the mixtures of carbon dioxide (CO_{2}) and sulfur dioxide (SO_{2}), two of the most relevant pollutant gases for the anthropogenic effect in global warming. We simulate cases with distinct proportion of gases in the mixture. Our results indicate that the 3D graphene slit is able to absorb 90% or more of the gas molecules. We show that this property came from the fact that both CO_{2} and SO_{2} molecules are attracted by the graphene pore, which compensates for the entropic barrier that exists when leaving the bulk state to the confined state. Also, the simulation results show that changing the interlayer separation between the graphene sheets is possible in order to change the membrane properties, from absorbent to blockage. These results help to understand the properties of 3D graphene nanoslits and their application as highly selective filters.

#### 1. Introduction

The demand for clean energy and global warming stand among the major challenges of our time and require extensive investigation towards technological advances. However, while renewable energy often demands massive investments, coal is the least expensive and widespread fossil fuel across the globe, specially in developing countries [1]. On the other hand, burning coal in electric power plants is a major source of carbon dioxide (CO_{2}) emissions [2]. Even after the combustion gases have passed through macroscopically refined membranes before exiting the smokestack, they contain oxides of nitrogen and sulfur dioxide that lead to smog and acid rain [3]. Reducing the coal-derived emissions, such as CO2 and SO_{2}, is, therefore, timely and environmentally imperative.

Nanotechnology represents a huge step in this direction, providing the possibility of high gas selectivity and storage. The capture of gases such as CO_{2} and SO_{2} is critical for the control and reduction of emissions of pollutant gases. Graphene and graphene-based materials have attracted great attention in the last decades due to their potential applications in molecular sieves, gas sensing, and energy storage. The large specific surface area (~ m^{2}/g^{4}) and versatile modification make them excellent adsorbents. A three-dimensional porous graphene can exhibit even higher specific surface area. Ganesan and Shaijumon [4], for instance, synthesized nanoporous graphene with a specific surface area of and total pore volume of . A similar specific surface area has been obtained for 3D graphene samples [5].

Experiments have indicated rather low hydrocarbon uptake by 2D graphene [6]. 3D graphene created through activation processes can enhance its adsorption properties. For instance, an activated graphene-derived carbon exhibited an adsorption of 11.3 mmol/g of CH_{4} at room temperature and 35 bar [4]. The introduction of suitable micro- and nanopores can also be important for the adsorption of CO_{2} and methane. Chandra et al. have found an impressive adsorption of 4.3 mmol/g of CO_{2} in highly microporous activated graphene [7]. In fact, the combination of multilayered 3D graphene membranes with nanopores has been used in desalination [8] and molecular separation [9] and in biomolecular and gas sensors [10, 11].

Recent computational studies have contributed to shed some light on the adsorption properties of mixtures of pollutant gases in carbon-based membranes, as disordered carbon [12] and porous aromatic frameworks [13]. Carbon nanotubes were proposed as filters for mixtures of CO_{2} and SO_{2} [14], showing good adsorption rates [15–17]. In these cases, the main part of the adsorption occurs in the outside of the nanotubes—the optimal pore size for capture is small [18]—and controlling the nanotube radius is an experimental challenge that has not been achieved yet.

Since the adsorption of CO_{2} and SO_{2} occurs on the surface of the carbon materials, an alternative is the use of graphene, the carbon-based material with the highest available surface area that shows good adsorption properties [19–22]. Among the graphene-based structures, 3D membranes made of stacked porous membrane have been proposed for several applications, which includes water desalination [23–25], water-ethanol separation [26], chemical protection [27], and gas separation [28].

In the specific case of CO_{2}, experimental studies have shown that these molecules are adsorbed in the graphene sheet [29–31]. However, as far as we know, there are no experimental studies on the adsorption of a mixture of CO_{2} and SO_{2} in graphene. In order to better understand this subject, in this paper, we study the adsorbing properties of a 3D porous graphene membrane when a CO_{2} and SO_{2} mixture is pushed through the membrane by an external pressure-driven force. Our goal is to obtain information on how 3D graphene structures can be employed as selective and, principally, effective filters for CO_{2} and SO_{2} gases. Our results indicate a high adsorption, with the membrane acting as a sponge that absorbs 90% or more of the gas molecules. Also, by changing the interlayer distance between the graphene sheets, we can change the membrane from an adsorbent to a blocker, with no gas passing through it. This change in the distance can be experimentally done varying the type and amount of reducer used in the graphene chemical production [32, 33]. This feature makes it more experimentally attainable than controlling the radius of produced nanotubes.

Our paper is organized as follows. In Section 2, we present the computational details of our simulations. The results and discussions are shown in Section 3, while the conclusions are done in Section 4.

#### 2. Computational Details

Our gaseous system consists in 1000 CO_{2} and SO_{2} molecules initially placed at the left of the simulation box, as shown in Figure 1. A pressure gradient forces the solution against the nanoporous membrane located at the center of the box with dimensions nm in the , , and directions. The membrane consists of three graphene sheets, each one with randomly distributed nanogaps. The interlayer separation () was set to 1 nm and the nanogap size range from 0.5 to 2 nm. Due to the simulation time scale (10 ns), we used 100 MPa as the standard ∆P, higher than the osmotic pressure used in the experiments (0.1 to 30 MPa [34]), because low pressures yield low gas fluxes that would not go above the statistical error.

To study the influence of distinct gas mixtures, we employed simulations with distinct gas fractions , where and stand for the number of CO_{2} and SO_{2} molecules, respectively.

The SHAKE algorithm [35] was employed to maintain the rigidity of CO_{2} and SO_{2} molecules. Nonbonded interactions are described by the Lennard-Jones (LJ) potential with a cut-off distance of 1 nm, and the parameters are tabulated in Table 1. The Lorentz-Berthelot mixing rule [36] was used to obtain the LJ parameters for different atomic species. The long-range electrostatic interactions were calculated by the *Particle*-*Particle Particle*-*Mesh* method [37], and periodic boundary conditions were applied in all directions.

For each nonequilibrium simulation with nanopores, the system was first equilibrated in the NVT ensemble for 1 ns at . During equilibration, the graphene atoms were held fixed in space and a repulsive plug prevented the gas molecules from entering the nanoslit. After equilibration, the plug is removed and the pressure gradient is applied to characterize the gas flux through the nanopores. We carried out five independent simulations for each system collecting the trajectories of atoms every picosecond for 10 ns. All molecular dynamics simulations were implemented within the Extensible Software Package for Research on Soft Matter (ESPResSO) [39, 40].

#### 3. Results and Discussion

##### 3.1. Gas Adsorption: The Influence of Molar Fraction

Environmentally friendly companies aim to reduce their CO_{2} emissions through dedicated membranes that selectively filter the impurities from the air. In the coal-based industry, it is particularly complicated to separate the carbon from the sulfur dioxide coming from the burning fossil fuel. Therefore, the membrane’s ability of effectively recovering the mixture of CO_{2} and SO_{2} is crucial. It is usually associated with the percentage of gas molecules adsorbed by the membrane.

In Figure 2, we show the percentage of molecules trapped inside the graphene nanoslits or adsorbed at the graphene walls as a function of the CO_{2} and SO_{2} fraction. When , there are only CO_{2} molecules in the system, while for , only SO_{2} are present. By varying this fraction, we notice a blockage higher than 88% for all the samples. Markedly, for (50% of each species), we observed higher SO_{2} blockage compared with the CO_{2}, which highlights the sulfur dioxide selectivity of the membrane. This is an important result as SO_{2} is the main ingredient of acid rain. Also, both gases have high adsorption, which is a direct result of the graphene’s high available surface area. It prevents one of the main problems in current filters, where SO_{2} is blocked and the CO_{2} escapes to the atmosphere [12].

In order to analyze the adsorption dynamics, we plot in Figure 3 the percentage of adsorbed molecules as a function of time. Figure 3(a) shows the situation in which we have only CO_{2} or SO_{2}, while Figure 3(b) refers to the 50% mixture. Both situations show similar adsorption dynamics, with sulfur dioxide being fully adsorbed for longer times: it reaches a plateau of ~90% in adsorption after 2 ns, while CO_{2} takes only 1 ns. Sulfur atoms are larger and their electronegativity makes SO_{2} much more polar than CO_{2}, which is a determinant for the entropic barrier at the nanopore entrance as it goes from the bulk to the nanoconfined state. This entropic penalty occurs since the entropy is higher in the bulk state, while inside the Nanoslit, there is a decrease in the entropy due to the geometric constriction [41]. It would explain the slightly larger adsorption rate of SO_{2} in Figure 3(a). Markedly, both carbon and sulfur dioxides are highly adsorbed by the graphene nanoslits and remain inside the slits, even under a large pressure gradient . The oscillations observed after 2 ns originated from the method used to calculate the number of adsorbed molecules. If the central atom of one molecule outside the nanopore—C for CO_{2} or S for SO_{2}—was closer than the interatomic separation, given by the *σ* in Table 1, it was considered as adsorbed. Due to the thermal fluctuations, the absorbed atom position can fluctuate beyond the *cut-off* employed in our methodology, leading to fluctuations around the mean value of the percentage of absorbed molecules. Increasing the *cut-off* could lead to less fluctuations but also to spurious results, since it could account for atoms that are not absorbed in the external surface of the graphene nanopore.

**(a)**

**(b)**

The conjunction of forces acting on the nanoscale leads to most varied behaviors in fluid dynamics. The entropic contribution to the water molecules leaving the bulk reservoir and entering the nanopore is also relevant [42]. In order to understand how these phenomena are affecting our system, we plot in Figure 4 the potential of mean force (PMF) of a single molecule as a function of the distance between the molecule and the nanoporous graphene. The changes in the PMF as a function of the intermolecular distances provide qualitative insights on the attractive/repulsive nature of the interaction. For this evaluation, we consider only one graphene sheet placed at the center of the simulation box. The molecule is pulled through the center of the slit, and the force is evaluated at each 0.1 nm and then integrated to obtain the PMF. The results show that regardless of the molecular orientation (if parallel or orthogonal to the graphene surface), both molecules (CO_{2} and SO_{2}) are attracted to the nanopore. Interestingly, the carbon dioxide presents half of the attraction (~0.8) suffered by the sulfur compound (~1.5) in the vicinity of the graphene nanopore. In other words, the dense packing at the graphene interface observed in Figure 5(b) and the high adsorption rate of SO_{2} in Figure 3 can be explained in terms of the attraction between the SO_{2} molecules and the graphene nanopore. The combination of these factors with the pressure gradient applied to the solution makes the graphene nanoslits very promising for the adsorption of CO_{2} and SO_{2}.

**(a)**

**(b)**

In the nanoscaled flow, the molecular structure is often a determinant for the fluid dynamics: as the molecules get together to form highly packed structures (e.g., at graphene interfaces [43], in nanotubes [44], and in zeolites [45]), the molecular structure slows down the flux. In order to investigate the impact of the molecular structure in the adsorption of CO_{2} and SO_{2}, we plot in Figure 5 the density profile of both species along the simulation box ( direction). Once the densities are different, we plot the normalized density

From Figure 5(a), we can observe sharp, dense peaks between the graphene nanoslits, indicating a high adsorption rate of CO_{2}. As we increase the fraction of SO_{2} in the solution, we observe an increase in the number of CO_{2} molecules rejected by the graphene nanopore, as can be seen by the increase in the first peak (left) and the density deflation at the right of the graphene layers.

In Figure 5(b), we found the SO_{2} molecules arranged in a very densely packed structure close to the third graphene sheet (in the opposite direction of the applied pressure) for small fractions of SO_{2}. Conversely, as we increase , the sulfur dioxide molecules become more homogeneously distributed at the graphene interfaces. This aggregation at the graphene surface is important either for the separation of CO_{2} and SO_{2} or for the storage of these substances.

##### 3.2. Gas Adsorption: The Influence of Interlayer Separation

The geometry of the nanopore is determinant for the structural and dynamical properties of the confined fluid. In nanotubes, for instance, a change in the diameter can produce phase transitions at ambient pressure and temperature [46, 47]. The same is valid for 2D confinement of fluids. A small variation in the interlayer distance of graphene can promote dynamical anomalies in the fluid viscosity [48] and diffusion [49] and even in their phase diagram [50]. Additionally, the interlayer separation () yields important consequences on the graphene membrane’s adsorption capacity [51, 52].

In Figure 6, we show the adsorption as a function of the interlayer separation for a system with fraction . If the interlayer separation is smaller than 1.0 nm, such as 0.5 nm, the particles are not absorbed by the nanoslit but blocked by it, as we can see in Figures 7(a) and 7(b). The inner space is so small that the molecules get blocked between the second and third graphene layers. Interestingly, if only one graphene sheet is used (a 2D membrane), the gas would pass, once it crosses through the first graphene layer in our system. Nevertheless, this result indicates that a 3D graphene membrane can block the passage of gases. On the other hand, for interlayer separations between 1.0 nm and 2.0 nm, the adsorption and the structure are not affected by , as we can see in the results shown in Figures 6 and 7. Therefore, we can easily change the properties of the 3D graphene filter just by varying : if nm, it works as a sponge that absorbs both CO_{2} and SO_{2}, while if nm, it blocks the gas passage. This blockage happens due to geometric effects—the interlayer distance 0.5 nm is comparable to the excluded volume of the molecules.

**(a)**

**(b)**

#### 4. Summary and Conclusions

In this work, we investigated the CO_{2} and SO_{2} absorption properties of graphene nanoslits using molecular simulations. Our results indicate that 3D graphene membranes are a promising material for selective filters, absorbing both gases with more than 90% efficiency. Also, it is more selective for sulfur dioxide, as we show by the PMF calculations. Also, we show that by controlling the interlayer separations, the 3D membrane can be used either as an absorbing filter or as a blocking filter, where no gas can pass through the membrane. The 3D characteristic of the graphene nanoslits is essential to ensure the blockage, as our analysis has shown. These results indicate that 3D graphene structures are promising filters for pollutant gases, with high selectivity and efficiency.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflict of interest.

#### Acknowledgments

The authors acknowledge the Brazilian agencies CAPES, CNPq, and FAPERGS for the financial support.

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#### Copyright

Copyright © 2019 Amanda Caroline Borges et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.