Molecular Simulation Study of the Adsorption and Diffusion of a

Article pubs.acs.org/jced

Molecular Simulation Study of the Adsorption and Diffusion of a Mixture of CO2/CH4 in Activated Carbon: Effect of Textural Properties and Surface Chemistry Shanshan Wang, Linghong Lu,* Di Wu, Xiaohua Lu, Wei Cao, Tingting Yang, and Yudan Zhu College of Chemical Engineering, State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech University, 5 Xinmofan Road, Nanjing, 210009, P.R. China S Supporting Information *

ABSTRACT: In this study, the effect of pore textural property and surface functionalization in activated carbon (AC) on the competitive adsorption and diffusion of a binary mixture of CO2/CH4 was examined by grand canonical Monte Carlo simulations and equilibrium molecular dynamics. The simulation results indicated that AC with a high surface area exhibited a low CO2/CH4 selectivity, while a high CO2 adsorption capacity was observed. To obtain high CO2 adsorption capacity and high CO2/CH4 selectivity at the same time, surface chemistry (adsorbent−adsorbate interaction) and pore textural property (pore size) were investigated. On this basis, two types of AC were prepared: (I) with different pore sizes, attributed to building ordered pores and (II) with different surface chemistry properties, attributed to modification with different functional groups. The results showed that the effects of surface chemistry properties are factors more important for improving the CO2/CH4 capacity and selectivity.

1. INTRODUCTION Biogas produced from biomass is one of the most cost-effective, facile methods for alternative fuel generation.1 Biogas is composed of 50−70% CH4 and 30−40% CO2, with marginal H2, N2, H2O, and trace H2S. Biomethane, formed after the removal of CO2 from biogas, contains ≥97% CH4 and can be applied as natural-gas vehicle fuel.2 Several technologies exist for CO2 upgrading: cryogenic distillation, chemical absorption, and physical adsorption; physical adsorption using microporous materials (zeolites, carbon nanotubes, nanoporous carbons, and covalent organic frameworks, etc.)3 ismore cost-effective and efficient than the other technologies. Considering near-future applications, activated carbon (AC) is undoubtedly the most attractive adsorbent, because of its low price, well-developed activation processes, high pore volumes and surface areas, high stability, and low chemical reactivity.4,5 In the process of physical adsorption, the desorption of the strongly adsorbed component occurs so that the adsorbent can be reused.6 At a molecular level, the diffusion of gas molecules in the adsorbent can reflect the adsorption or desorption rate. However, regular AC exhibits low CO2/CH4 selectivities, limiting its applications for biogas upgrading.7 Essentially speaking, selective adsorption occurs when different substances on the surface of an adsorbent exhibit different affinities under given conditions. For the adsorbent, as the textural properties and surface chemical properties affect its interaction with the gas adsorbate,8−18 it is imperative to understand how the factors affect the gas adsorption and diffusion behavior for the purpose of designing optimal AC materials exhibiting high adsorption capacity and high selectivity. © XXXX American Chemical Society

Textural properties (such as pore size, pore structure, surface area, and pore volume) are important factors that affect the adsorption and diffusion of CO2/CH4.8 Typically, adsorbents with large open volumes and large surface areas exhibit high CO2 capacity, for example, carbon foam structures with large open volumes exhibit high CO2 capacity,9 and the increase of the interlayer spacing in carbon nanoscrolls results in the significant improvement of CO2/CH4 adsorption capacities.10 However, high selectivity is mandatory for gas separation, and the open nature of the structure exerts a detrimental effect on selectivity and adsorbents, where the most controlled confinement (small size) exhibits high selectivity.11Furthermore, in pressure swing adsorption (PSA), two adsorption regimes are observed:12,13 at low pressure, adsorption is closely related to surface chemistry but not to porosity, while at high pressure, CO2 adsorption capacity is dominated by surface area and pore volume. Adsorption of CO2 in a series of renewable nitrogencontaining granular porous carbons revealed in pressure higher than 5.0 bar, CO2 adsorption capacity is dominated by its surface area and pore volume, while in pressure decreased to 0.1 bar, CO2 capture ability is closely correlated to its nitrogen content but not to its porosity.13 The adsorption performance of CO2 can also be related to surface interactions, in addition to textural properties, such as Special Issue: Proceedings of PPEPPD 2016 Received: June 30, 2016 Accepted: October 26, 2016

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DOI: 10.1021/acs.jced.6b00554 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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acid−base interaction, polar interaction, and hydrogen bonding between CO2 molecules and functional groups.14,15 As CO2 is a polar molecule, as compared to CH4, it is significantly more affected by electrostatic force. However, the treatment of AC by activation processes changes not only surface chemistry (introduce some functional groups) but also textural properties (increase of specific surface area, pore volume, and pore size).16 Notably, not all of the activation processes can increase the specific surface area, and the pore size values need to be in a certain range to afford high adsorption CO2 capacity and selectivity.17 At this time, two opposing and competitive effects of induced surface areas and induced gas−adsorbent interaction exist. Plaza has previously reported that, despite the reduction of porous volume and acidic surface, as compared to the starting carbon, oxidized samples exhibit a higher CO2 adsorption capacity, attributed to Lewis acid−base interactions with the CO2 molecule.18 Determining how the effects of textural properties and surface functionalization compete with each other is crucial for designing an efficient nonporous adsorbent. Hence, in this study, the effects of textural properties and surface chemistry on the competitive adsorption and diffusion of the CO2/CH4 mixture are examined. In this study, grand canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) methods were employed for studying the adsorption and diffusion of equimolar binary mixtures of CO2/CH4 in AC. The effects of textural properties and surface chemistry were investigated by preparing different AC structures (details explained below). The key factors affecting adsorption and diffusion were observed by calculating the interaction energy between adsorbent and adsorbate and between adsorbate and adsorbate. By employing this theoretical approach, the intrinsic mechanism was elucidated, and the potential use of AC for the competitive adsorption, capture, and separation of a binary mixture of CO2/CH4 was highlighted; thus, this method offers an effective, superior alternative approach for the design and screening of adsorbent materials for the purification of biogas.

Figure 1. Initial configurations for the adsorption and diffusion of CH4 and CO2. The graphitic basis structural units (a) are randomly assembled for generating the activated carbon model (b).

frameworks. The textural properties of AC were characterized by various computational methods. In this study, the surface area was geometrically determined, corresponding to the area of the surface created by a probe corresponding to a spherical molecule with a diameter of 3.62 Å, rolled along the atoms of AC.22 The pore size distribution was calculated using the method proposed by Gelb and Gubbins,23 which defines the pore size at a given point in the simulation cell based on the diameter of the largest sphere that can encompass the point without overlapping with the AC models.11 In this study, for an AC framework, atomic force LennardJones (L-J) parameters are taken from the UFF (UFF force field is successfully employed for metal complexes and organic molecules);24 this model has been successfully employed by numerous authors in previous simulations using similar systems.21 Functional groups, such as −COOH, −OH, and −CO (details described below), were described as united atom 4-center, 2-center, and 2-center models, respectively, and the C atoms of AC connected with groups were assigned as partial charges. All of the models were considered to be rigid; hence, the contribution from intramolecular effects is not considered, which is a common practice in molecular fluid simulations.25−27 The CH4 model is a rigid regular tetrahedron with five charged L-J interaction sites, and the L-J potential parameters are taken from the TraPPE model (TraPPE force field developed by Potoff, Siepmann28 and Sun29). For CO2 molecules, to consider the quadrupole effect and linear geometry, the EPM2 model30 is employed. Molecular interactions assumed the L-J form, mainly including L-J 12−6 potential energy and Coulomb potential, as shown in eq 1:

2. SIMULATION MODEL AND METHODOLOGY 2.1. Simulation Models. For predicting the adsorption and diffusion of CO2/CH4 by molecular simulations, the internal structure of a specific AC should be modeled. The slit pore model, which is too oversimplified, is the most commonly employed model for describing AC in the past decades.19 Thus, different elements of heterogeneity are added to the slit pore model for offsetting its simplicity, such as structural defects, active sites, functional groups, as well as pore connectivity effects. However, the slit pore model still fails to adequately describe the complex nature of actual carbon materials. Experimental data indicated that AC exhibits a very complex internal structure, in which the structural elements are not arranged along a common vertical axis, but in chaotic layers, and the structure is composed of a so-called basic structural unit (BSU);20 the BSU consists of a few roughly aligned small polyaromatic molecules. Using the BSU structure of coronene, Di Biase et al. have reported a three-dimensional disordered porous model by random packing, which can realistically simulate the internal structure of AC; this model has also been employed to explain the adsorption of CO2/CH4 and CO2/ N2,21 which further demonstrates the accuracy of this structure. Hence, in this study, an AC model consisting of a coroneneshaped graphitic BSU is described, as shown in Figure 1; the graphitic basis units are randomly assembled for generating AC

⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij U (rij) = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + 2 r rij ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

(1)

Here, rij denotes the distance between atoms i and j, and qi denotes the quantity of electric charges of atom i. εij and σij denote energy and size parameters, respectively. All of the interaction parameters conformed to the Lorentz−Berthelot mixing rules. All the L-J parameters and atomic partial charges used in this work are tabulated in the Supporting Information (Table S1). 2.2. Methods. Music 4.0 code31 was employed for performing GCMC simulations using an equimolar mixture of CO2/CH4 in ACs, where temperature, chemical potential, and pore volume are specified in advance and are maintained constant throughout the simulation. In the simulation, the structure of functionalized ACs was assumed to be rigid, where MC moves were randomly attempted with 50% probability for B



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Figure 2. Pore size distribution of three AC samples with different surface areas.

where μ means the average values of xi and N equals three as each simulation was carried out three times.” 3.1. Effect of Specific Surface Area. Specific surface area is one of the key factors affecting the adsorption and diffusion performance of materials. Generally, adsorbents with large open volumes and large surface areas exhibit high gas capacity;34 nevertheless, the pore size distribution of the adsorbents is also a factor that needs to be addressed. Previously,35 the narrow pore size distribution of adsorbents has been reported to be conducive to the improvement of adsorption capacity. However, a certain pore size range is required. In this section, six structures with increasing surface area were considered, and each of these structures was obtained by the increase of the size of the simulation box from the initial denser structure. The sizes of the simulation boxes used here are tabulated in the Supporting Information (Table S2). Notably, surface areas greater than 6000 m2/g were not examined, which has recently been reported to be the theoretical limit for the surface area of carbon materials.36Accordingly, high surface areas naturally result in structures with a broad and high pore size distribution, as shown in Figure 2 (The detailed data are tabulated in the Supporting Information (Table S3)). Hence, competition exists between high surface area and broad, high pore size distribution for attaining high CO2/CH4 adsorption capacity and high CO2/CH4 adsorption selectivity. Hence, it is imperative to examine the adsorption and diffusion performance of these structures in conjunction with their surface areas and pore size distribution. Table 1 shows the adsorption capacities and selectivities of CH4 and CO2 in an equimolar mixture at pressures of 0.1 and 3.0 MPa as a function of the AC surface area (Figure 1S shows the adsorption capacities for CH4 and CO2 in their equimolar mixture at pressures from 0.05 to 10.0 MPa as a function of surface area). The results confirmed our analysis that with increasing specific surface area, the adsorption capacities for CO2 and CH4 increase, but selectivities of CO2/CH4 decrease. The results can be concluded as follows: Generally, at low pressure (0.1 MPa), the increase of surface area marginally affects capacity and selectivity; on the other hand, at higher pressure (3.0 MPa), the increase of surface area is always accompanied by the increase in the amount of fluid that can be adsorbed, albeit with decreased CO2/CH4 selectivity. CO2/CH4 capacity as well as CO2/CH4 selectivity versus specific surface area exhibits different trends, which is similar to those observed for CNTs and slit pores.34,37 In CNTs and slit pores, the monolayer adsorption of CO2/CH4 is observed at low pressure, which is mainly attributed to the interaction between the fluid and pore walls. Moreover, with increasing pressure, adsorption performance is significantly dominated by surface area and pore size distribution. Because interaction

translation or rotation and 50% probability for creation or deletion for CO2 and CH4, respectively. Periodic boundary conditions were imposed in all directions. For every state, 2 × 107 configurations were generated. The former 107 configurations were discarded for guaranteeing equilibration, whereas the latter 107 configurations were employed for averaging the desired ensemble properties. All of the MD simulations were calculated by LAMMPS32 software. The initial configurations of the molecular dynamics simulations are the final equilibrium configurations of the grand canonical Monte Carlo simulations, and the numbers of CO2/ CH4 molecules in the system depend on the adsorption capacity of CO2/CH4. The numbers of CO2/CH4 molecules are listed in Table S2, Table S4, Table S5 and Table S8. The simulation was divided into two steps: (1) 1.0 ns time was utilized to attain system balance at the NVT ensemble. Then, (2) 100 ps time was utilized for data collection, involving the collection of coordinate data for each molecule every 1.0 ps at the NVE ensemble. The ACs were maintained constant with no initial velocity. The radius of van der Waals interaction was 1.0 nm. Atomic displacement was calculated by the classical Newton’s equations of motion, with a time step of 1.0 fs. The Ewald summation was employed for the evaluation of long-range force,33 and the Nose−Hoover hot bath regulation method was employed for controlling the system at 300 K (constant time of 0.1 ps).

3. RESULT AND DISCUSSION Adsorption capacity and selectivity are two important indicators used for evaluating the performance of an adsorbent. CO2/CH4 selectivity can be defined by eq 2: SCo2 /CH4 =

(xCO2 /xCH4)pore (xCO2 /xCH4)bulk

(2)

Here, xi denotes the molar fraction of component i, and (···)pore (···)bulk denote the pore and bulk properties, respectively. For a system composed of an equimolar gas mixture, a selectivity of Si/j > 1 indicates that the fluid component i is preferentially adsorbed over the other component j in the binary mixture. In this work, each simulation was carried out three times to reduce the inaccuracy. The uncertainty of xi (including CO2/CH4 adsorption capacities, CO2/CH4selectivities and CO2/CH4 diffusion coefficients) was estimated by the standard deviation which was calculated using the equation: σ=

1 N

N

∑ (x i − μ)2 i=1

(3) C



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Table 1. Adsorption Capacities and Adsorption Selectivities of CO2/CH4 in AC with Different Surface Areas at 298 K and 0.1 and 3.0 MPa adsorption capacity, mol/kg surface area, m2/g 166.99 601.12 1427.14 2209.36 3320.04 4367.67 5058.38 166.99 601.12 1427.14 2209.36 3320.04 4367.67 5058.38

CO2

CH4

p = 0.1 MPa 0.465 ± 0.0112 0.0640 ± 0.00501 0.497 ± 0.00972 0.0857 ± 0.00501 0.323 ± 0.00912 0.0883 ± 0.00521 0.308 ± 0.00892 0.0992 ± 0.00621 0.325 ± 0.00822 0.116 ± 0.00721 0.285 ± 0.00812 0.122 ± 0.00821 0.243 ± 0.00762 0.113 ± 0.00681 p = 3 MPa 2.30 ± 0.0538 0.253 ± 0.0186 3.66 ± 0.0558 0.504 ± 0.0196 4.99 ± 0.0658 0.943 ± 0.0200 6.26 ± 0.0698 1.32 ± 0.0206 7.58 ± 0.0758 1.84 ± 0.0216 8.35 ± 0.0788 2.48 ± 0.0226 8.74 ± 0.0858 2.85 ± 0.0236

selectivity 7.28 5.80 3.66 3.10 2.80 2.34 2.14

± ± ± ± ± ± ±

0.155 0.145 0.139 0.125 0.105 0.0950 0.0850

8.76 7.56 5.33 4.62 4.06 3.45 2.97

± ± ± ± ± ± ±

0.109 0.0887 0.0787 0.0687 0.0587 0.0487 0.0427

Figure 3. Probability distribution of CO2/CH4 with the basic structural unit (BSU) in three AC samples at different surface areas and pressures of 0.1 and 3.0 MPa.

increasing specific surface area, the distribution of CO2 and CH4 is more disordered, predominantly filling in the micropores. Table 2 lists the self-diffusion coefficients of CO2 and CH4 in AC samples having different surface areas. At a surface area of

between adsorbents and CO2 is greater than that between adsorbents and CH4, CO2 is preferentially adsorbed. With increasing pressure, the CO2 adsorption sites extend from the pore walls to the center of the tubes or slit pores; hence, the CO2 adsorption capacity increases with the size of the CNTs or the width of the slit pores. However, with increasing pressure, CH4 can be further compressed into the pores, following the pore-filling mechanism, resulting in the reduction of CO2/CH4 selectivity. Although the models of AC used herein were disordered, still small slit-like pores existed between the unit structures. At low pressure, CH4 and CO2 are thought to be preferentially adsorbed in the vicinity of the BSU; hence, a relatively small amount of CO2/CH4 is adsorbed at this time with the change of surface area. At high pressure, the adsorption capacity of CH4 increases after the preferential adsorption of CO2;38 therefore, decreased CO2/CH4 selectivity is observed. This phenomenon is more obvious in the case of AC with high surface area. With increasing surface area, the pore size distributions are more extensive, and the gas molecules tend to be adsorbed in the middle regions of the BSUs. Figure 3 clearly shows the adsorption density distribution of CO2 and CH4 on AC with different specific surface areas at different pressures. The values on the horizontal coordinate “distance” denote the nearest distance of carbon atoms of CO2 and carbon atoms of CH4 to the carbon atoms of AC. At low pressure, the distributions of CO2 and CH4 are relatively concentrated, and the distance between the gas molecules and the BSU is approximately 0.38 to 0.42 nm; considering that the dynamic diameter values of CO2 and CH4 are 0.33 and 0.38 nm, respectively, we can conclude that CO2 and CH4 is close to the BSU at low pressure. The distance between the C atom of CO2 and the AC wall is closer than that of CH4 and the AC wall, and the difference is approximately 0.05 nm; in other words, this observation implies that the interaction between CO2 and the AC wall is stronger than that of CH4 and the AC wall. However, with increasing pressure, in the AC with a low specific surface area (1427.14 m2/g), attributed to the relatively narrow pore size distribution, CH4 and CO2 still tend to exhibit a single layer distribution, but with

Table 2. Self-diffusion Coefficients (Dself) of CO2/CH4 in AC with Different Surface Area specific surface area, m2/g 166.99 601.12 1427.14 2209.36 3320.04 4367.67 5058.38

Dself of CH4,10−8 m2/s 0.0215 0.0273 0.0308 0.0384 0.0612 1.02 1.40

± ± ± ± ± ± ±

3.11 3.85 3.68 2.45 4.08 8.47 8.04

× × × × × × ×

−3

10 10−3 10−3 10−3 10−3 10−3 10−3

Dself of CO2,10−8 m2/s 0.0344 0.0412 0.0464 0.0497 0.0643 1.256 1.65

± ± ± ± ± ± ±

2.50 3.49 9.68 5.55 4.89 3.73 5.64

× × × × × × ×

10−3 10−3 10−4 10−3 10−3 10−3 10−3

less than 3320.04 m2/g, the self-diffusion of CO2 and CH4 is almost not affected by surface area. However, with increasing surface area, the self-diffusion coefficient of CO2 and CH4 exhibits an increasing trend, mainly attributed to the fact that for AC with a high surface area, pore size distribution is wide, and the degree of gas confinement is less; hence, the frequency of collisions with AC is less, which in turn results in a high diffusion coefficient. Typically, the adsorption and diffusion performance of CO2/ CH4 in AC is related to adsorbent−adsorbate and adsorbate− adsorbate interactions. Figure 4 plots the ensemble average adsorbent−adsorbate and adsorbate−adsorbate interaction energy as a function of pressure in AC having different surface areas using eq 1. For both CH4 and CO2, from Figure 4, with increasing surface areas, interaction energy clearly decreases. Moreover, at low pressures, this property is dominated by the adsorbate molecules located either in close vicinity to or at the surface of the platelets. Moreover, at high pressures and with AC with broad pore sizes, with increased loading, a high proportion of molecules occupies regions of porous space D



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Figure 4. Average adsorbate−adsorbent interaction energy and adsorbate−adsorbate interaction energy expressed in kJ/mol of adsorbate as a function of surface area (a, b) and as a function of pressure (c, d).

further away from the platelets; as a result, the average solid− fluid interaction energy decreases with pressure. Overall, from this section, although AC with high specific surface areas exhibits a low CO2/CH4 adsorption selectivity, AC samples can be concluded to exhibit high CO2/CH4 adsorption capacity and high CO2/CH4 diffusion rate, attributed to the wide pore size distribution and low interaction between adsorbent and adsorbate. Hence, high CO2 capacity and CO2/CH4 selectivity can be simultaneously obtained by two approaches: (I) As a large pore size (approximately 1.0 nm) is beneficial to adsorption capacity and diffusion coefficient, while micropores with pore sizes less than 0.7 nm are conducive for the improvement of CO2/CH4 selectivity, we constructed ordered pores with a pore diameter of greater than 1 nm based on AC to investigate the contribution of mocirpores on the CO2/CH4 adsorption and diffusion; (II) As CO2 is a polar molecule and more sensitive to surface chemistry, AC was modified with different functional groups to investigate the contribution of surface chemistry on the CO2/ CH4 adsorption and diffusion as the surface chemistry enhance the adsorbate−adsorbent interaction to a great extent. 3.2. Effect of Ordered Large Pores. The pores in AC used herein are disordered, and the network structure of this type of carbon consists of disordered carbon atoms. Ordered mesoporous carbon (OMC)39 exhibits a uniform pore size distribution, and its pores are ordered, but the carbon atoms arranged on the pore walls of the structure do not exhibit a long-range order. A certain similarity existed between AC and OMC, in which both of the cell walls consisted of amorphous carbon, albeit with different pore structures. To investigate whether ordered pores facilitate adsorption and diffusion, ordered cylindrical pores were constructed in the center of AC, as shown in Figure 5. Two AC samples with different surface areas were chosen to construct ordered mesopores: one is AC with a surface area of 122.08 m2/g, the wall of which is very dense and did not allow for the adsorption of either CH4 or CO2, while the other is AC with a surface area of 3320.04 m2/g, which is rich in micropores (pore size distribution < 1 nm). We investigated the effect of cylindrical pore diameters in AC with a surface area of 122.08 m2/g. Table 3 and Table 4 show the adsorption capacity, adsorption selectivity, and self-diffusion coefficient for five ordered pore structures with different cylindrical pore diameters (1.0, 1.6, 2.0, 2.6, and 3.0 nm). The adsorption capacities for CO2 and CH4 increase with increasing cylindrical pore diameter, similar to the adsorption behavior in CNTs with different diameters.40 With respect to the diffusion performance of CO2/CH4, with increasing pore size, the self-

Figure 5. Two AC samples with different surface areas with ordered cylindrical pores. (a) AC with a surface area of 122.08 m2/g. (b) AC with surface area of 122.08 m2/g and ordered cylindrical pores with diameter of 2.0 nm. (c) AC with surface area of 3320.04 m2/g. (d) AC with surface area of 3320.04 m2/g and ordered cylindrical pores with diameter of 2.0 nm.

diffusion coefficients of CO2 and CH4 also increase. A small pore size affords a small space and results in the increased crowding degree of gas molecules, which is not conducive to adsorption capacity. On the other hand, in the ordered cylindrical pores, CH4 and CO2 molecules tend to exist in a cylindrical configuration for monolayer adsorption at low pressure; however, with increasing pressure, gradually, CH4 and CO2 molecules exhibit multilayer adsorption; this observation is clearly observed from the density profiles of CO2 and CH4 (Figure 6), showing the probability distribution of molecules to the AC wall. With increasing diameter of constructed pores and increasing pressure, the gas molecules not only appear near the wall of the ordered pores but also distribute in the middle of the pores. Hence, ordered cylindrical pores with a large diameter, providing more adsorption space, afford high adsorption capacity. From the above results, the large ordered pore is not conducive to the separation of CO2/CH4, and we proposed that the optimal CO2/CH4 separation selectivity is obtained in AC with sufficient disordered micropores with a pore size between 0.5 and 0.8 nm. To investigate the contribution of E



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Table 3. Adsorption Capacities and Adsorption Selectivities of CO2/CH4 in AC with Different-Sized Ordered Pores with a Surface Area of 122.08 m2/g at 298 K and 0.1 and 3.0 MPa adsorption capacity, mol/kg ordered pore size, nm

CO2

CH4

CO2/CH4 selectivity

p = 0.1 MPa 1.0 1.6 2.0 2.6 3.0

0.0114 0.0521 0.0632 0.0849 0.0925

± ± ± ± ±

3.56 5.44 4.75 8.23 8.49

× × × × ×

10−3 10−3 10−3 10−3 10−3

1.0 1.6 2.0 2.6 3.0

0.331 0.707 0.970 1.561 1.930

± ± ± ± ±

3.68 4.34 8.76 1.98 2.21

× × × × ×

10−3 10−3 10−3 10−2 10−2

0.0134 0.0134 0.0170 0.0256 0.0325

± ± ± ± ±

2.56 1.91 3.20 4.29 3.65

× × × × ×

10−3 10−3 10−3 10−3 10−3

8.486 3.875 3.717 3.315 2.844

± ± ± ± ±

8.65 6.90 7.85 6.36 5.95

× × × × ×

10−2 10−2 10−2 10−2 10−2

0.0138 0.0790 0.154 0.316 0.529

± ± ± ± ±

4.69 5.72 4.21 5.23 1.06

× × × × ×

10−3 10−3 10−3 10−3 10−2

24.0 8.95 6.30 4.94 3.65

± ± ± ± ±

2.02 1.47 5.42 8.23 5.63

× × × × ×

10−2 10−2 10−3 10−3 10−3

p = 3.0 MPa

calculated (Figure 7). The contribution of the disordered micropores (Cmicropores) can be evaluated by applying eq 4:

Table 4. Self-Diffusion Coefficients (Dself) of CO2/CH4 in AC with Different-Sized Ordered Pores with a Surface Area of 122.08 m2/g ordered pore size, nm 1.0 1.6 2.0 2.6 3.0

Dself of CH4,10−8 m2/s 0.0045 0.0683 0.2200 0.5322 1.4823

± ± ± ± ±

3.20 9.52 5.24 4.89 4.09

× × × × ×

−5

10 10−4 10−3 10−3 10−3

Dself of CO2,10−8 m2/s 0.0793 0.2708 0.2526 0.2722 0.5723

± ± ± ± ±

9.09 5.28 9.87 6.23 5.74

× × × × ×

10−4 10−3 10−3 10−3 10−3

Figure 7. Disordered-pore contribution of AC with a surface area of 3320.04 m2/g and with different pore sizes of ordered pores on the selectivity of CO2 over CH4.

Cmicropores% =

Sdisordered − Sordered × 100 Sdisordered

(4)

Here, Cmicropores denotes the contribution of the disordered micropores on CO2/CH4 adsorption selectivity, Sdisordered/ Sordered denotes adsorption selectivity in the part of disordered pores and in the part of ordered pores in the AC with a surface area of 3320.04 m2/g, whose model is shown in Figure 5. The results show that the existence of large ordered pores is not favorable for the separation of CO2/CH4. 3.3. Effect of Surface Chemistry. AC is treated by activation processes for increasing the specific surface area; this procedure will result in the formation of some functional groups, especially by chemical activation. The modification of groups is also a significant factor for gas adsorption. Previously, AC has been modified using some groups (−OH groups) after activation.16,41 Lu et al.21 have investigated the effect of different functionalized edges of NPC on the adsorption of CH4. The introduction of functional groups can enhance the adsorption capacity for CH4 in the whole pressure range in the following sequence: OH−NPC > H−NPC > NH2−NPC > COOH−NPC/NPC. In this study, to investigate whether

Figure 6. Probability distribution of CO2 and CH4 in AC constructed with different sizes of ordered pores. The values on the horizontal coordinate “distance” denote the distance between the C atom of CO2 and the pore wall as well as that between the C atom of CH4 and the pore wall.

micropores on CO2/CH4 selectivity, we investigated the effect of cylindrical pore diameters in AC with a surface area of 3320.04 m2/g. The sizes of the simulation boxes used here are tabulated in the Supporting Information (Table S5). For further observation, the CO2/CH4 adsorption capacity and selectivity in ACs with the surface area of 3320.04 m2/g with different sizes of ordered pores are shown in the Supporting Information (Table S6 and Table S7), and the contribution of the micropores on CO2/CH4 selectivity in those structures are F



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surface chemistry facilitates the adsorption and diffusion, ACs functionalized with different functional groups were constructed, as shown in Figure 8. The BSUs with 24 carbon

Table 5. Adsorption Selectivities of CO2/CH4 in AC with Different Functional Groups at 298 K with and without the Electrostatic Interaction between the Adsorbents and the Adsorbates CO2/CH4 selectivity pressure, MPa

Figure 8. (a) Initial configurations of CO2/CH4 adsorption on the functionalized basic structural unit. (b) Visualization of unit cell of ACs functionalized with −OH groups.

atoms were modified with 12 functional groups, −OH groups, −CO groups, and −COOH groups, respectively. The same numbers of modified BSUs were chosen into the simulation box with the same sizes. The sizes of the simulation boxes used here are tabulated in the Supporting Information (Table S8). At this time, adsorption and diffusion behavior resulting from a double effect of textural properties and adsorbent−adsorbate interaction must be focused on particularly the effect of electrostatic potential. For further understanding the effect of electrostatic interactions, we performed one more simulation, in which the electrostatic interaction between the gas molecules and AC atoms was switched off42 by setting the charges of modified AC to zero. The CO2/CH4 adsorption selectivities in ACs with different functional groups with or without the adsorbent− adsorbate electrostatic interaction are shown in Table 5. We found a very interesting phenomenon that CO 2 /CH 4 adsorption selectivities in the three modified ACs are almost the same without the adsorbent−adsorbate electrostatic interaction, and the selectivities in modified ACs without the adsorbent−adsorbate electrostatic interaction are less than the ones with electrostatic interaction. This further proves that the presence of electrostatic interaction enhances the CO2/CH4 adsorption selectivity. To further grasp the effect of electrostatic interaction on the adsorption selectivity of CO2 over CH4, the electrostatic contribution (Celectrostatic) on CO2/CH4 selectivity was evaluated by applying eq 5: Celectrostatic% =

Swith − Swithout × 100 Swith

with electrostatic interaction

0.25 0.50 0.75 1.0 2.0 3.0 5.0 7.0

41 35 27 22 14 12 11 10

± ± ± ± ± ± ± ±

8.1 5.6 3.9 3.5 5.2 4.9 7.1 8.5

0.25 0.50 0.75 1.0 2.0 3.0 5.0 7.0

32 31 24 21 17 15 12 11

± ± ± ± ± ± ± ±

8.4 6.2 7.4 4.4 6.3 5.9 7.8 5.2

0.25 0.50 0.75 1.0 2.0 3.0 5.0 7.0

55 50 46 40 39 33 28 22

± ± ± ± ± ± ± ±

5.4 2.9 5.1 8.5 5.2 9.4 7.1 6.2

without electrostatic interaction

OH−AC 10−2 10−2 10−2 10−2 10-2 10−3 10−3 10−3 CO−AC × 10−3 × 10−3 × 10−2 × 10−2 × 10−2 × 10−2 × 10−3 × 10−3 COOH−AC × 10−2 × 10−1 × 10−1 × 10−2 × 10−2 × 10−2 × 10−2 × 10−2

× × × × × × × ×

4.5 4.7 5.0 5.3 6.7 8.2 9.0 9.0

± ± ± ± ± ± ± ±

6.5 6.1 3.2 2.6 4.4 2.4 9.2 6.3

× × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

4.7 5.4 5.9 6.2 7.7 8.3 9.5 9.1

± ± ± ± ± ± ± ±

8.8 4.9 7.5 7.8 6.4 6.5 3.9 7.6

× × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2

4.3 4.6 4.9 5.0 6.3 7.6 8.7 9.3

± ± ± ± ± ± ± ±

3.7 9.1 6.4 3.8 4.2 1.9 2.5 2.9

× × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−2 10−2

(5)

Here, Celectrostatic denotes the contribution of the electrostatic interaction on CO2/CH4 adsorption selectivity, Swith/Swithout denotes selectivity with or without the adsorbent−adsorbate electrostatic interaction. Figure 9 shows the electrostatic contribution of the AC samples to the CO2/CH4 adsorption selectivity. ACs modified with functional groups clearly exhibit an extraordinarily large electrostatic contribution at low pressure, reaching even up to 95% at an ultralow pressure level in COOH−ACs, indicating that electrostatic interaction plays a more significant role in the selectivity at low pressure than at high pressure. Subsequently, electrostatic contribution

Figure 9. Electrostatic contribution of the funcitional groups of the AC on the selectivity of CO2 over CH4.

decreases with increasing pressure, until it reaches a constant value after ∼3 MPa. The results can be easily understood by analyzing the filling process. First, the gas molecules occupy the region near the pore surface, attributed to the strong electrostatic interaction at low pressure. In this process, the functional groups exhibit strong electrostatic interactions, attributed to their high electron-accepting or -donating densities; therefore, the total CO2 uptake is enhanced. With G



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increasing pressure, the gas molecules are gradually filled in the whole pore space, and the gas−gas interaction becomes stronger, thereby increasing the effect from PSD at high pressure. In general, larger pore spaces with a high atomic partial charge exhibit high total gas uptake.21

Science Foundation of China (Grant Nos. 21176113, 91334202, and 21490584), and the Qing Lan Project. Notes

The authors declare no competing financial interest.

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4. CONCLUSION The adsorption and diffusion of CO2/CH4 on activated carbon with different surface structures and different surface chemistry properties were investigated. The following conclusions were made: (1) The specific surface area exhibits opposite effects on adsorption capacity and selectivity. The analysis of adsorbent−adsorbate interaction and pore size distribution reveals that the interaction between adsorbent and adsorbate exerts more effect on adsorption and diffusion performance at low pressure, while the pore size distribution exerts a predominant effect at high pressure. 2) On the basis of the effect of adsorbent−adsorbate interaction and pore size distribution analysed above, ACs with ordered large pores (with pore diameter from 1.0 to 3.0 nm) and ACs with different surface chemistry (modified with the functional groups of −COOH, −CO, −OH) were constructed to investigate the contribution to the CO2/CH4 selectivity. The results indicate that large pore size (larger than 1.0 nm) is not conducive to the increase of CO2/CH4 selectivity, while micropores with pore sizes less than 0.7 nm are conducive for the improvement of CO2/CH4 selectivity. However, it should be noted that ACs modified with functional groups, especially the −COOH groups, clearly exhibit an extraordinary increase on CO2/CH4 selectivity, and a large electrostatic contribution at low pressure, reaching even up to 95% at an ultralow pressure, indicates that electrostatic interaction plays a more significant role in the selectivity. This study not only highlights the potential of surfacefunctionalized AC as excellent candidates for the competitive adsorption, capture, and separation of a binary mixture of CO2/ CH4 but also provides an effective, superior alternative strategy for the design and screening of adsorbent materials for applications of carbon capture and storage (CCS).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00554. Tables: size of the simulation box and number of atoms in the simulation box; Lennard-Jones parameters for the adsorbents and the adsorbates; Adsorption capacities and adsorption selectivity of CO2/CH4. Figures: adsorption capacities, adsorption selectivity of CO2/CH4 (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

* E-mail: [email protected]. Funding

This work was supported by the National Basic Research Program of China (Grant No. 2015CB655301), Jiangsu Natural Science Foundation (BK20130062), National Natural H



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Molecular Simulation Study of the Adsorption and Diffusion of a

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