Energy Procedia 64 ( 2015 ) 150 – 159

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1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the Scientific Committee of TGTC-3doi: 10.1016/j.egypro.2015.01.018

3rd Trondheim Gas Technology Conference, TGTC-3

Simulation of pore width and pore charge effects on selectivities of CO2 vs. H2 from a syngas-like mixture in carbon mesopores

Thuat T. Trinha, Thijs J.H. Vlugtb, May-Britt Häggc, Dick Bedeauxa Signe Kjelstrup a,b,* a Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway

bDepartment of Process and Energy, Delft University of Technology, Delft, The Netherlands c Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway

Abstract

Classical molecular dynamics simulations were performed to study the effect of pore width and surface charge in carbon mesoporous materials on adsorption and diffusion selectivities of CO2/H2 in a syngas-like mixture (mole fraction of CO2 = 0.30). The pore width of the graphite slit varied from 2.5 to 5.0 nm, while the temperature varied from 300K to 400 K. Both selectivities were relatively insensitive to the pore width. Metal contamination, mimicked with localized charges within an electroneutral pore surface, was found to increase the adsorption selectivity ratio for CO2 vs H2 and decrease the diffusion selectivity for CO2 vs H2. Such surface charges interact with CO2 molecules only and can enhance the separation of H2 from the syngas mixture, retaining CO2. Rising temperature will enhance diffusion selectivity, however reduce the adsorption selectivity of CO2. The results imply that surface charges can be used to favor the enrichment process of CO2. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of TGTC-3.

Keywords: Adsorption; CO2,/H2 selectivity; pore width; surface charge; carbon membrane

1. Introduction

The production of cheap membranes for CO2 gas separation purposes is of primary importance for the realization of carbon capture and sequestration technologies [1-4]. Nano-porous, fibrous, carbonaceous materials are promising candidates to separate CO2 from a gas mixture of CO2 and H2 [5]. Knowledge of the molecular behavior, in particular of selectivities and transport properties, is required to design energy efficient separation processes. To

* Corresponding author. Tel.: +47-735 94179; fax: +47-735 50877.

E-mail address: signe.kjelstrup@ntnu.no

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the Scientific Committee of TGTC-3

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make further progress and produce molecular sieve membranes for adsorption and separation of CO2/H2 gas mixtures, we need to better understand several issues such as the effect of pore size, contamination effects, effects of carbon structure and composition. The purpose of the membrane is to retain CO2, while facilitating H2 movement through the membrane.

Several experimental and simulation studies have been devoted to the understanding of adsorption of single component CO2 or H2 on carbon based material such as activated carbon and graphite [6-13]. Adsorption and diffusion of single component H2 on graphite have also been measured experimentally [10, 14]. Fewer computational results are reported on the selective adsorption of a mixture of CO2 and H2 on a graphite surface. Cao et al. described the graphite surface selectivity of mixtures with bulk compositions 50:50 and 20:80, with slit pore sizes(or widths) up to 3.0 nm, and pressures up to 100 atm, using Monte Carlo simulations [15]. The adsorption selectivity of CO2 over H2 decreased as the temperature increased. There was an optimum pore width in the micro pore range (< 20 Å) for the adsorption selectivity which depended on the mixture composition. Other CO2 / H2 mixture ratios (10:90 and 20:80) were studied by Kumar et al. [16]. These authors reported that the carbon nanotube was better than the slit pore to separate CO2 from mixtures at room temperature. In our previous work, adsorption and diffusion of CO2 and H2 (ratio 30:70 as in syngas) was studied as a temperature function on a graphite surface [17]. The suggestion was to enrich CO2 from the syngas mixture by a multistep process, which allows hydrogen to go preferentially through the membrane, controlling the temperature in each step.

There is limited information on adsorption and diffusion of CO2 and H2 in mesopores. The effect of surface heterogeneity of microporous carbon on the adsorption separation of CO2 in a mixture of CO2/CH4 and CO2/N2 was studied by Liu et al. [18]. These authors showed that different functional groups on surface greatly increase the adsorption of CO2 through altered electrostatic interaction and van der Waals forces. Surface charges are likely to be present from the production process of the membrane, as it is difficult to avoid metal impurities. Work reported by Lie et al. [19] also documented the positive effect on carbon membrane separation properties by adding selected metal ions (salts) to the precursor of the membrane. They furthermore studied the effect of using low voltage current to regenerate carbon membranes in which CO2 or other components had been too strongly adsorbed [20]. To the best of our knowledge, effects of electrostatic interaction due to defects have not been addressed by others in literature.

Our aim is now to study the effect of pore width and surface charges on the adsorption, diffusion and separation of the same CO2 and H2 gas mixture. These studies will provide basic knowledge for design of carbonaceous membranes for syngas separation. Molecular dynamics (MD) simulations are well suited to determine such properties, as pore widths and surface charges can be varied in a controlled way. In the next section, we will introduce briefly method and models used in MD simulations. We will show that the mesopores size has no effect on the diffusion selectivity of CO2 vs H2 while the surface charge plays an important role, but only for CO2 adsorption and diffusion.

Figure 1. (Left) Typical snapshot of a gas mixture of CO2 and H2 in a slit of width W=50 Å, in equilibrium with the graphite. A relatively dense gas mixture is shown, with (5000 molecules with mole fraction CO2 =0.3). The green, red and white represent carbon, oxygen and hydrogen atom, respectively. (Right) An example of a random distribution of surface charges (see text for further explanations).

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2. Model and Method

2.1. Simulation details

We have earlier observed that the thickness of the adsorbed layers on graphite can extend up to 10 Å away from the graphite layer. This means the width of the pore slit must be larger than 20 Å, in order to contain bulk gas as well as adsorbed layer. Hence we considered carbon mesopores in range 25 Å to 50 Å. We performed classical molecular dynamics (MD) simulations using the LAMMPS package[21]. The system consisted of a graphite crystal and a mixture of CO2 and H2 molecules. The mixture had always a mole fraction of carbon monoxide equal to 0.3. This is considered as representative for the synthesis gas from steam reforming or water gas shift process[22].

The graphite had a hexagonal structure without any defects. It contained 32000 carbon atoms and was constructed from 10 sheets of graphene. The graphene sheets in the simulation box were oriented such that the surfaces of the sheets were perpendicular to the z direction. The surface of graphite was 98x85 Å2. In the z direction, the system consisted of two graphite layers, and the distance between the graphite layers is the pore width. We used W=25 Å, 30 Å, 40 Å, 50 Å (Figure 1). We used periodic boundary conditions in all directions. At each pore width, W, at least ten systems with different total number N of molecules (250 < N < 5000) were simulated. The simulation was performed at temperature 300 K and 400 K. A snapshot of the gas mixture in equilibrium with the graphite is shown in Figure 1.

Local charges were added to the graphite layer in the following manner. The total surface was always kept electroneutral. One carbon atom in the graphite layer was positively charged; and this atom was surrounded by 3 negatively charged atoms. The distribution of charges around the positive atom was thus [C3 + - 3C -], as pictured in Figure 1. 30% of the total atoms in the surface layer were charged positively or negatively in this manner. These atoms were chosen randomly. The value of the charge - was either -0.10(e) or -0.50(e).

In total, 240 simulations were performed to study the effect of pore sizes and charge effects on the selectivity of CO2 vs H2 in a syngas-like mixture. The MD simulation had time steps of 1fs. The initial configuration was constructed by randomly distributing the CO2 and H2 mixture over the graphite surface. The system was stabilized during 2 ns by NVT runs with the Nosé-Hoover thermostat.[23] When the system was in thermal equilibrium, we performed another 2 ns run with microcanonical ensemble conditions (NVE) to study adsorption and transport properties. The average values of temperature and pressure in NVE simulation were within 1% of expected values. In total 4x106 MD steps was performed and this is sufficiently long to obtain good statistics and consistent trajectories.

2.2. Potential energies of the all atom model

The all atoms model was used in our simulation. We employed the rigid body model of Transferable Potentials for Phase Equilibria (TraPPE) for the CO2 molecule. This potential can describe well the vapor-liquid and the liquid-solid equilibria of CO2 [24]. The Morse potential was used for H2 bond stretching:

2

0(r ) D 1 exp ( )M ij e ijV a r r (1)

where De , 0r and a are the parameters of the potential and ijr is the distance between atom i and j. A flexible graphite model was used. The carbon-carbon bond stretching in graphite was calculated with the harmonic potential

20

1( ) ( )2S ij S ijV r k r r (2)

where Sk is the force constant. The graphite bending was calculated with the harmonic potential

20

1( ) ( )2B ijk B ijkV k (3)

where ijk is the angle between atoms i,j,k. Bk is the force constant. The torsion energy in graphite was calculated as

21( ) 1 cos(2 )2T TV k (4)

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where is the torsion angle, and Tk is the force constant. The intermolecular potential contained long-range Coulombic interactions, and a shifted and truncated 12-6 Lennard-Jones (LJ) potential. See ref [25] for more details. The parameters, taken from the DREIDING [26], TraPPE [24] force fields and the Delft Molecular Mechanics force field [27] are listed in Table 1. These parameters yielded good results for simulations of H2 and CO2 on graphite surfaces [14, 17].

Table 1. Force field parameters used in simulation

Lennard-Jones

Atom (Å) /kB (K) charge (e) C (in CO2) [24] 2.80 27 0.7 O (in CO2) [24] 3.05 79 -0.35

C (graphite) [14, 26] 3.34 26 0 H (in H2 ) [27] 2.64 28 0 Hydrogen [27]

Bond stretching (Morse) De = 458.0 kJ/mol a =1.946 Å-1 0r 0.74 Å

Graphite[14, 26]

Bond stretching (harmonic) Sk 4393.9 kJ/mol 0r 1.42 Å

Angle bending Bk 418.2 kJ/mol/rad2 0 120 (degrees)

Torsion Tk 26.15 kJ/mol

3. Results and discussions.

3.1. Adsorption of mixtures

Figure 2. The adsorption of CO2 and H2 as a function of partial pressure of CO2 (left) and H2 (right) at different pore widths, of 25 Å, 30 Å, 40 Å and 50 Å at T=300 K and T=400 K. No atom in the graphite surface has a charge.

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We use the surface excess concentration (adsorption) (molecules /nm2) , as defined originally by Gibbs, see Kjelstrup and Bedeaux [28] for a detailed description. For the CO2 / H2 mixture, we repeated the essential method as described in our previous work [17]. See ref [17] for more details.

Figure 2 shows the partial adsorption of CO2 an H2 at 300 K and 400 K in different pore sizes. At 300 K, the adsorption of CO2 increases slightly with pore size, from W=25 Å to 50 Å. Adsorption of H2 does not depend much on the pore size. At 400 K, the adsorption of both CO2 and H2 no longer depends on pore size. This behavior was also observed with the CO2 /H2 mixture at high temperature, 505K, and by Cao et al. [15].

Figure 3. The adsorption of CO2 and H2 from the gas mixture, as a function of partial pressure of CO2 (left) and H2 (right) at W=25 Å,

T=300 K with different local surface charge. Adsorption of CO2 increases at high density of local charges, while adsorption of H2 is insensitive to charging the surface. Figure 3 shows the isotherm adsorption of CO2 and H2 with differently charged surfaces at W=25 Å. Similar trends were observed for other pore sizes (W=30 Å, 40 Å and 50 Å). Adsorption of CO2 is strongly enhanced with charging of the surface. The effect of the charge distribution can be explained by the large quadruple moment of CO2 molecule (-14.27x10-40 C m2 )[29]. This moment favor interaction between the molecule and charged carbon atoms on surface.[18] The H2 molecule has no dipole or quadruple moment, so charging of the surface has no effect on its adsorption.

3.2. Adsorption Selectivity

The adsorption selectivity is defined by the separation ratio of CO2 versus H2 in the mixture: CO (adsorbed) H (gas)2 2

CO (gas) H (adsorbed)2 2

2/ 2 n nn n

CO HAdsS (5)

We see that the parameter is only meaningful if the pore is so large that it allows bulk gas. This condition is met here by taking the pore width larger than 20 Å. This parameter gives the most common way to characterize the separation properties of a membrane for components in a gas mixture. In molecular simulations it is often used with grand-canonical Monte Carlo based studies [15, 18, 30, 31].

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Figure 4. Adsorption selectivity of CO2 relative to H2 vs the total pressure of the system with various pore widths at T=300 K and 400 K

Figure 4 shows the pore width effect on the adsorption selectivity of CO2 over H2. At 300 K there are small selectivity changes with pore size. At 400 K, all pore widths show the same selectivity. The adsorption selectivity decreases with increasing total pressure. This observation is similar to that found earlier with a graphite surface [17]. The selectivity at 400 K is half of that at 300 K. The value of the selectivity compare well with the results of Cao et al. [15]. The finding that the selectivity of CO2/ H2 does not depend on pore widths which are larger than two times the thickness of the adsorbed layer, is consistent with our previous prediction of typical surface thicknesses in this system [17].

Figure 5. Adsorption selectivity of CO2 vs H2 vs the total pressure at differently charged surfaces, for all with pore widths, T=300 K and 400 K.

Figure 5 shows the selectivity of CO2 for all pore widths (all pore widths have the same symbol) with differently charged surfaces at 300 K and 400 K. The selectivity of CO2 increases when the charge strength increases. A higher local surface charge leads to preferred adsorption of CO2 to the surface. This surface charge effect is similar to the effect of hetero functional group-formations on graphite as reported previously [18-20, 30]. These authors observed that formation of organic groups on surfaces of micropores (e.g hydroxyl, carbonyl, epoxyl groups), increased the adsorption selectivity of CO2 in mixtures of CO2/CH4 or CO2/N2. It is not surprising that the selectivity deceases with increased temperature and total pressure. The electrostatic effect is less important at low temperature for the CO2 adsorption selectivity. By increasing the temperature from 300 K to 400 K, the adsorption selectivity of CO2 over H2 reduces to half the value, with or without surface charge. This means that conditions are favorable for hydrogen escape or carbon dioxide retainment.

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3.3. Self-diffusion and diffusion selectivity

The self-diffusion of CO2 and H2 along the surface of the pore inside the surface layer was computed. The self-diffusion coefficient of molecule was obtained from: [32]

2

1

1lim ( ) (0)2

Nsi i it i

D tdNt

r r (6)

where d is the dimensionality (for surface d = 2), N is the total molecules, ( )i tr and (0)ir are the projections of the position of molecules on the surface at time t and time 0. All molecules were included in the mean-squared displacement calculations as described in previous studies [10]. At any temperature, H2 moves faster than CO2, since H2 is much lighter than CO2. When the graphite pore is charged, CO2 self-diffuse slightly slower than along the non-charged pore. A pore charge distribution has no effect on H2 diffusion. The self-diffusion coefficients of CO2 and H2 are shown in Figure 6. The pore width had no effect on these coefficients. These self-diffusion coefficients of CO2 are in the range 10-7 m2/s, similar to those along a graphite surface [17], and much faster than in micro pores ( <10 Å) where values have been reported in the range 10-

9 m2/s [11]. The self-diffusion coefficient of H2 is also comparable to that along a graphite surface [17].

Figure 6. Self-diffusion coefficients of CO2 (left) and H2 (right) as function of total pressure at T=300 K (top) and at different surface charge densities (bottom). The self-diffusion of CO2 and H2 is relatively insensitive to changes in mesopore size. Only CO2 diffuses slower when the surface charge density increases.

The effect of the surface charge distribution on the self-diffusion coefficients at 300 K is also shown in Figure 6. A similar trend was observed for 400 K (not shown). The larger the pore charge, the slower the movement of CO2. The charging of a pore has no effect on H2 transport. The diffusion selectivity of a binary mixture [33] of CO2 and H2 is estimated from:

2/ 22 2/CO H S S

Diff CO HS D D (7)

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Figure 7. Diffusion selectivity of CO2 relative to H2 vs the total pressure at different charged surface with all pore width at T=300 K and 400 K.

Figure 7 shows the effect of a charge distribution on the surface on the diffusion selectivity at 300 K and 400 K. The value of 2/ 2CO H

DiffS decreases as the local charge density increases. CO2 diffuses always slower than H2 at ambient

temperature. It is interesting to see that 2/ 2CO HDiffS increases as with the total pressure. At very high pressures, the

diffusion rate of both CO2 and H2 decrease (Figure 7), more for CO2 than for H2. At 300 K, the electrostatic effects are more important than at 400 K.

3.4. 3.5 Permeation selectivity:

The permeation selectivity of between CO2 and H2 is defined as: [33] 2/ 2 2/ 2 2/ 2CO H CO H CO H

Per Ads DiffS S S (8)

Figure 8. Permeation selectivity of CO2 relative to H2 vs the total pressure at different charged surface with all pore width at T=300 K and 400 K.

Figure 8 shows the permeation selectivity of CO2 / H2 mixture in various mesopores at 300K and 400K. At 300K, CO2 is favored for adsorption provided that the mesopores are charged. The gas has also a retarded diffusion. At 400K, the diffusion selectivity of CO2 vs H2 is enhanced, but the adsorption selectivity is low, however. Hence, at both temperatures, the system has low total permeation selectivity for CO2 vs H2. However, the permeation selectivity of CO2 vs H2 is higher at 300 K than at 400K. In a membrane separation process, where pore sizes > 2nm, this favored mechanism is called surface selective flow. The adsorption of CO2 on the pore surface will cause

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constrictions of the pore diameter, favoring the passage of the small H2 molecules, retaining the larger CO2 molecules. For process conditions below the critical values for CO2 and for the mentioned pore size, the pore may be almost blocked by condensation and the smallest molecule may also be retained – CO2 can then be favored by the solution diffusion selectivity. The addition of surface charges increases the adsorption selectivity significantly, and can therefore play an important role for the process. The situation where high adsorption is accompanied by low diffusion, is commonly observed in separation of binary mixture in porous material [34].

The results are consistent with earlier findings, that adsorption and diffusion of CO2 and H2 in pores are not significantly affected by mesopore widths. This is reasonable because such pore widths are larger than two times the surface thickness [17]. Therefore they allow bulk gas in the pore. Introduction of a surface charge distribution increases the adsorption of one of the gases strongly. It increases CO2 adsorption and decreases CO2 diffusion. Both changes will help retain carbon dioxide, and enhance hydrogen transport through the pore giving favorable conditions for enrichment of CO2 in the syngas mixture. The effect will be enhanced by lowering the pore width below 20 Å. This observation is supported by the experimental work of Lie and Hägg [19, 20]. They reported that including metal and metal oxide into the carbon membrane will increase adsorption of CO2 but decrease CO2 transport.

4. Conclusions

We have used equilibrium molecular dynamics to study the effect of pore width and surface charge on the adsorption and diffusion selectivity of CO2 vs. H2 in a carbon slit model membrane. The use of pore widths < 2nm (micropore), close to two times of the thickness of adsorbed layer [17], and introduction of metal impurities in the carbonaceous material will enhance an enrichment of CO2 gas from a CO2/H2 syngas mixture, and could be exploited in practice. Increasing the temperature will increase the diffusion and diffusion selectivity, however reduce the adsorption selectivity. A strategy to facilitate hydrogen transport through the membrane is to lower the permeation selectivity of CO2. This can be accomplished by either decreasing the diffusion selectivity of CO2 (using low temperatures) or increase the adsorption selectivity (using high temperatures, adding surface charges). This knowledge is useful for process enrichment studies of CO2.

Acknowledgements

The authors acknowledge The Research Council of Norway NFR project no 209337 and The Faculty of Natural Science and Technology, Norwegian University of Science and Technology (NTNU) for financial support. The calculation power was granted by The Norwegian Metacenter for Computational Science (NOTUR).

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