Molecular Simulation of Capture of Sulfur-Containing Gases by

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Molecular Simulation of Capture of SulfurContaining Gases by Porous Aromatic Frameworks Difan Zhang, Xiaofei Jing, David S. Sholl, and Susan B. Sinnott J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03767 • Publication Date (Web): 27 Jul 2018 Downloaded from http://pubs.acs.org on July 28, 2018

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The Journal of Physical Chemistry

Molecular Simulation of Capture of Sulfur-Containing Gases by Porous Aromatic Frameworks Difan Zhang1,2, Xiaofei Jing3,4, David S. Sholl3, Susan B. Sinnott2,* 1

Department of Materials Science and Engineering, University of Florida, Gainesville, FL, 32611, USA

2

Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16801, USA 3

School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

4

Key Laboratory of Polyoxometalate Science of Ministry of Education, Department of Chemistry, Northeast Normal University, Changchun, 130024, China

*Author to whom correspondence should be addressed. Email is [email protected]

1 ACS Paragon Plus Environment

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Abstract The adsorption of pure SO2 and H2S and their selective adsorption from various gas mixtures by porous aromatic frameworks (PAFs) are investigated using grand canonical Monte Carlo (GCMC) simulations and first-principles density functional theory calculations. The influence of functional groups including -CH3, -CN, -COOH, -COOCH3, -OH, -OCH3, -NH2 and -NO2 on the adsorption of pure SO2 and H2S as well as selective capture of SO2 and H2S from SO2-N2, SO2-CO2, H2S-CO2 and H2S-CH4 mixtures, are explored. Our calculations indicate that PAFs exhibit high loadings for pure SO2 and H2S gas adsorption at 298 K up to 40 bar compare to other gases such as CH4 and CO2. Additional functional groups enhance gas uptake at low pressures due to stronger interaction with the gas molecules while reducing gas uptake at high pressures because of a decrease in pore volume. The contributions of electrostatic interactions to gas adsorption loadings are analyzed in GCMC simulations. Ideal adsorbed solution theory (IAST) calculations generally overestimate SO2 and H2S adsorption selectivity in gas mixtures but qualitatively predict the trends seen in GCMC simulations for these systems. The GCMC simulations further show that the inclusion of any of the functional groups we considered increases the selectivity of SO2/N2, SO2/CO2, H2S/CO2 and H2S/CH4 relative to unfunctionalized materials. Electron withdrawing groups such as -CN, -COOH, -COOCH3 and -NO2 are more effective at enhancing adsorption selectivity in this work. The highest selectivity in the PAFs functionalized by these groups is predicted at the lowest temperature we considered (273 K) while it occurs at 298 K for PAFs with other functional groups.


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1.


Introduction Gases that contain sulfur are some of the most harmful that are emitted through the combustion of

sulfur-containing fuels such as coal and heavy fuel oils, natural gas processing, and from natural sources1,2. Sulfur dioxide (SO2) and hydrogen sulfide (H2S) are the two most studied sulfur gases in chemistry and biology. SO2 is a major atmospheric pollutant that contributes to acid rain and has substantial impacts on human health, terrestrial and aquatic ecosystems and industrial gas post-processing3,4,5. H2S is a compound that is poisonous to living organisms, is a precursor for acid rain, and causes corrosion in power plants6,7. Reducing emissions of these gases is important to reduce the environmental impact of industrial gases and to improve atmospheric conditions worldwide. Many experimental and computational efforts have been made to explore the effective removal of SO2 and H2S from gaseous emissions and mixtures. In additional to the surfaces of transition metal oxides8,9, adsorption within porous materials has been shown to be one effective approach for capturing acid gases. Specific materials that have been considered include metal organic framework materials10, zeolites11, activated carbons12,13,14, and carbon nanotubes15. A developing class of materials that may also be useful in this context are porous aromatic frameworks (PAFs)16,17. These materials have structures with high internal surface area that are inspired by the stable structure of diamond, in which carbon atoms are tetrahedrally connected by covalent bonds, and that involve replacing C-C covalent bonds with rigid phenyl rings. Guided by this concept, the first PAF structure (PAF-1) was synthesized using tetrakis(4-bromo-phenyl)methane as the tetrahedral building units, and coupling phenyl rings through the nickel(0)-catalyzed Yamamoto-type Ullmann cross-coupling reaction17. PAF-1 has long-range disorder with locally crystalline structures17. Following the synthesis of PAF-1, many other PAFs with porous structures containing heterogeneous species such as O, N, Si, Ge have also been synthesized. In general, these PAF materials possess good thermal and chemical stability, high surface areas and narrow pore size distributions16,17. They are therefore being considered for adsorption of gases such as H2, CH4 and CO218. As might be expected for high surface area porous materials, PAFs exhibit high CO2 uptake and good selectivity of CO2 from gas mixtures such as CO2/H2, CO2/N2 and CO2/CH4 under ambient conditions18,19. PAFs have also been



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functionalized with metal and organic groups, and these functionalized PAFs exhibit enhanced CO2 gas uptake relative to the unfunctionalized materials20,21,22,23. The robustness and relative ease of functionalization of PAFs may make them useful materials in applications involving the capture of other acid gases. To the best of our knowledge, the adsorption and selectivity of SO2 and H2S in PAFs relative to other gases has yet to be investigated. Computational studies using Grand Canonical Monte Carlo (GCMC) and density functional theory (DFT) calculations have been applied to gases such as H2 and CO2 in different PAFs, and these methods are well positioned to provide insights into gas-adsorbent interactions that can guide experimental work24,25,26. Here we perform GCMC simulations to investigate the adsorption of pure SO2 and H2S and their selective uptake in SO2-N2, SO2-CO2, H2S-CO2, H2S-CH4 binary mixtures by both pristine and functionalized PAFs. The specific gas mixtures were chosen based on prototypical examples of post-combustion gas, flue gas, and biogas

27,28

. We investigate the influence of several functional groups, including -CH3, -CN, -COOH,

-COOCH3, -OH, -OCH3, -NH2 and -NO2, on gas adsorption and separation. Similar studies on the effect of functional groups have been carried out in other porous structures

26,29,30,31,32,33

. DFT calculations are

used to evaluate the binding of sulfur gases on various sites within the functionalized and pristine PAFs, and to assess the viability of the force fields used in our GCMC calculations. The contributions of electrostatic interactions to the gas adsorption loadings are also analyzed in GCMC simulations. Overall, this work provides fundamental insights into the adsorption of sulfur gases within PAF materials, and reveals the influences of functional groups and temperatures on both gas adsorption and selectivity that will assist the development of more effective adsorbent materials for acid gases.

2. Computational Details 2.1 Grand Canonical Monte Carlo Simulations GCMC simulations were used to evaluate the adsorption isotherms of single component gases and gas mixtures. A periodic PAF-1 unit cell was built by replacing each C-C bond in a diamond lattice with a biphenyl group and rescaling the size of unit cell, as was done in earlier work17. This model was used as the pristine, unfunctionalized PAF structure, and has been shown previously to capture the locally


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crystalline bonding and to exhibit CO2 adsorption in agreement with experimental results.17,26 Next, -CH3, -CN, -COOH, -COOCH3, -OH, -OCH3, -NH2 and -NO2 functional groups were added to the PAF-1 framework. In these functionalized PAF models, a functional group replaced one aromatic H atom on each aromatic ring. These structures were relaxed using the COMPASS force field34 and atomic partial charges in the frameworks were assigned using an atoms-in-molecules method35. Details of these models are provided in Figure S1 and Appendix S1 of the supplementary materials. A 1×1×1 unit cell of each framework was considered in the GCMC simulation volume, giving a simulation volume ranging from 12.8 to 13.1 nm3, and periodic boundary conditions were used in all three dimensions. The cutoff used in the simulations was 11.7 Å to ensure that it was less than half the size of the simulation boxes. Using larger cutoff values, such as 12.8 Å, required 2×2×2 unit cells and higher computational costs with no major change in results, as illustrated in Figure S2. At least 10 million Monte Carlo events were used in the GCMC simulation of each state point. Among these trials, the first half were used for system equilibration and the second half were used to determine average properties. Six types of moves with equal probability were included: insertion, deletion, translation and rotation of gas molecules, swap with reservoir and exchange of molecular identity. The isosteric heats of adsorption ( ), defined as the difference in the partial molar enthalpy of the adsorption between the gas phase and the adsorbed phase, were calculated in GCMC simulations using a standard fluctuation formula36. All GCMC simulations were carried out using the RASPA software37. N2, CO2, SO2 and H2S were modeled as three-site rigid molecules with charges on each site, while a united-atom model was used for CH4. The PAF structures were kept rigid during the GCMC simulations. The gas-adsorbent and gas-gas interactions were evaluated using a combination of pairwise site-site Lennard-Jones (LJ) dispersion and repulsion terms and Coulombic potentials. The LJ potential parameters of the framework atoms were adopted from the DREIDING force field38 and the parameters for the gas molecules were taken from earlier work26,27,39. These parameters have been used in previous simulations of PAF materials and produced results in agreement with experiments.24,26 The parameters used to model SO2 and H2S are able to reproduce the bulk phase properties of these species;40,41 they have been widely used to investigate adsorption in porous carbons, zeolites and MOFs.42,43 The void



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fraction of each PAF structure was determined in the GCMC simulations using spherical probes that were representative of He atoms. Details of the force field parameters for the gases and PAF adsorbents are provided in Table S1 of the supplementary materials. Lorentz-Berthelot mixing rules were employed to calculate cross-LJ interactions. For binary gas mixtures, the adsorption selectivity of component 1 over component 2 is defined as Eq. (1) where ( ) and ( ) indicate the mole fraction of component 1 (2) in the absorbed and bulk phases, respectively.

/ =

(1)

2.2 First-Principles Calculations First-principles calculations were performed using DFT as implemented in the Vienna Ab initio Simulation Package (VASP), using the projector augmented wave (PAW) method and the PBE generalized gradient approximation (GGA) exchange-correlation functional44,45,46,47. Dispersion interactions were included using the vdw-D2 method of Grimme48 and reciprocal space was sampled with a 3×3×3 Monkhorst-Pack grid. The plane-wave cutoff energy was set to 520 eV for all calculations. Geometry optimizations were carried out using a conjugate gradient algorithm using convergence criteria of 10−4 eV and 10−3 eV·Å−1 for energies and forces, respectively. Due to the substantial number of atoms in each unit cell of PAF adsorbent, the DFT calculations were performed on a cluster model cleaved from the unit cell. To maintain the original hybridization, the cleaved bonds of the cluster were terminated by methyl groups. A vacuum spacing of approximately 10 Å was added in each direction to minimize interaction with periodic images. Illustrations of these cluster models are provided in Figure S1. The binding energies of gas molecules on the frameworks were calculated by Eq. (2), where

+ is the total energy of gas and adsorbent when the gas molecule is not adsorbed on adsorbent, and / is the energy of gas and adsorbent after the gas molecule is adsorbed on adsorbent.

= + − / 6 ACS Paragon Plus Environment

(2)

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3. Results 3.1 Binding Energy Calculations First principles DFT calculations were used to evaluate the energetics associated with the binding of SO2 and H2S molecules with unfunctionalized and functionalized frameworks. Similar to an earlier DFT investigation on the binding of CO2 molecules with functionalized benzenes49, we primarily considered two binding sites for a gas molecule in each PAF structure: one on the top of the aromatic ring (top site), the other one on the side of the aromatic ring or with functional groups (side site). To allow comparison with results from our force field-based calculations, the heats of adsorption of SO2 and H2S in each PAF structure were evaluated using GCMC simulations at 0.1 bar. The heat of adsorption is not precisely the same as the molecular binding energy in the most strongly binding site50, but these two quantities are useful for qualitatively comparing our DFT and force field calculations. The results of DFT and GCMC calculations are provided in Figure S3 in detail. In the unfunctionalized PAF structure, the SO2 and H2S molecules are both mainly adsorbed at the top site via the interaction between positively charged S in SO2 and H in H2S with the delocalized electrons of aromatic rings, respectively. The H atoms on the side of the aromatic rings barely interact with the SO2 and H2S molecules. The additional groups in functionalized PAFs provide new sites that have stronger interactions with SO2 and H2S gas molecules. Furthermore, electron donating groups such as -CH3, -OH, -OCH3 and -NH2 increase the binding energies at the top site of aromatic rings, while electron withdrawing groups such as -CN, -COOH, -COOCH3 and -NO2 reduce the binding energies at the top site. A comparison between the heat of adsorption at low loadings from GCMC and the binding energy of the most stable site observed with DFT in each material is illustrated in Figure 1(a). In general, the GCMC results underpredict the binding energies from the DFT results. Part of this underprediction arises because the two quantities are not identical. In one example that carefully studied this issue, Fang et al. showed that the heat of adsorption of CO2 in zeolites was 0.07 eV smaller than the binding energy of most favorable site50. It is likely, however, that this difference does not account for all of the



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difference between GCMC and DFT seen in Figure 1, indicating that the force field underlying our GCMC calculations is not in quantitative agreement with DFT. Methods exist to develop force fields for adsorption that are consistent with DFT51, but it would be time consuming to do this for the full range of functional groups we have considered. Similar results can be seen in Figure 1(b) when we further compare these values to the binding energies calculated by classical methods at 10 K and 298 K using the same parameters we used in the GCMC simulations. The calculated results by DFT and GCMC at 298 K are in good qualitative agreements with classical methods at 10 K and 298 K, respectively. A key observation from Figure 1 is that the general trends across the set of PAFs we considered are captured in a reasonable way by our GCMC calculations. On this basis, we focus in the rest of this paper on results from force field-based calculations.

Figure 1. Comparison of (a) the most favorable binding energy from DFT and the low loading heat of adsorption from GCMC in the same PAFs and (b) the binding energy calculated by DFT, GCMC and classical methods at 10 K and 298 K, respectively.

3.2 Adsorption of Single-component Gases The simulated adsorption isotherms for pure SO2 and H2S gases in different PAFs at 298 K are shown in Figure 2. The adsorption isotherms of both gases exhibit a type-IV adsorption isotherm52, 8 ACS Paragon Plus Environment

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where the S-shape is due to attractive adsorbate-adsorbate forces. Similar adsorption results were observed in previous studies of SO2 adsorption in amorphous porous carbons and H2S adsorption in multilayer graphene39,53. In the isotherms in Figure 2, SO2 and H2S adsorption reaches saturation at pressures above 5 bar and 20 bar, respectively. The pristine PAF-1 structure exhibits a saturation loading of ~50 mmol/g for SO2 and ~53 mmol/g for H2S, which is larger than for the functionalized PAFs structures. At low pressures, however, the functionalized PAFs have higher gas uptake than the unfunctionalized PAF-1. Similar trends were observed in earlier work of CO2 gas adsorption in PAFs26, and also in simulations of a variety of small molecules in functionalized UiO-6633. The Henry coefficients of SO2 and H2S in these PAF adsorbents calculated by Widom insertion and GCMC simulation are also in quantitative agreement, as indicated in Figure S4. The variations in adsorption uptake among the various PAFs we considered can be understood in terms of adsorption affinity and available pore volume of each structure. The loading-dependent isosteric heats of adsorption for single component SO2 and H2S in each structure are provided in Figure 3. In each PAF, the heat of adsorption increases with gas loading. Similar behavior is seen in the adsorption of polar species in large pore materials54. Uptake of SO2 and H2S at low pressures is higher in materials with large heats of adsorption. In particular, the PAF structures with -COOCH3, -COOH, -NO2 and -CN functional groups exhibit the strongest interactions with these gas molecules. At larger gas loadings (i.e. higher gas pressures), uptake of SO2 or H2S is controlled by the availability of pore volume. Large functional groups, in general, reduce pore volume and therefore reduce the saturation loadings of adsorbates that can be achieved. This observation is illustrated in Figure 4, which shows that uptake of SO2 as a function of pore volume at a relatively low pressure (0.4 bar) and a relatively high pressure (10 bar). Here, the pore volumes for empty PAF structures were evaluated based on their helium void fractions calculated by RASPA simulations; the resulting pore volumes and pore fractions are listed in Table S2. At low gas pressures (low gas loading), there is little correlation between pore volume and uptake, while a strong correlation exists between these two quantities at higher pressures.



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Figure 2. Adsorption isotherms at 298K from GCMC simulations at high and low pressures of (a) pure SO2 and (b) pure H2S. The unfunctionalized PAF-1 is shown in blue, while functionalized materials are shown as indicated in the legends.


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Figure 3. The isosteric heat of adsorption as a function of loading of pure (a) SO2 and (b) H2S in different PAF structures.

Figure 4. The effect of pore volume on SO2 gas adsorption at two different gas pressures in (a) gravimetric units and (b) volumetric units.



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Figure 5. The normalized molecular distribution of SO2 in unfunctionalized PAF at (a) 0.1 kPa, (b) 0.2 bar, (c) 0.7 bar, and (d) 1 bar


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Figure 6. The normalized molecular distribution of SO2 in unfunctionalized PAF (left) and -CN functionalized PAF (right) at (a) 0.2 bar and (b) 5 bar

To better illustrate the gas adsorption in these PAF materials, we further analyzed the molecular distribution of SO2 and H2S gas in PAFs. For example, Figure 5 illustrates the normalized molecular distribution of SO2 in the unfunctionalized PAF adsorbent at various gas pressures, where the framework atoms are not shown for clarity. At low pressures (e.g. 0.1 kPa), denser regions of gas molecules are observed above the aromatic rings of PAF due to their stronger interactions with gas molecules. As pressure increases, more gas molecules accumulate above the aromatic rings and the dense regions grow. This suggests that the existing gas molecules that have been adsorbed aid the adsorption of additional 13 ACS Paragon Plus Environment


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molecules by gas-gas interactions. This could be the reason for the rapid increase of gas loadings in adsorption isotherms. In Figure 6, we compared the molecular distribution of SO2 in the unfunctionalized and -CN functionalized PAF adsorbent at the same pressures. At 0.2 bar, additional dense regions are observed close to the functional groups in the functionalized PAFs, suggesting that these groups offer more preferred sites for gas molecule interaction. As the pressure increases, the dense regions in functionalized PAFs grow starting at both the aromatic rings and functional groups. This might be the cause of the rise of gas loadings in functionalized PAFs at smaller pressures compared to the unfunctionalized PAF in Figure 2. In general, there are two types of electrostatic interactions considered in our GCMC simulations: gas-framework and the gas-gas electrostatic interactions. We further investigated the influences of these electrostatic interactions on SO2 and H2S gas adsorption loadings by switching them off in some selected GCMC simulations. As an example, Figure 7 provides the SO2 adsorption loadings in -COOH functionalized PAF when both electrostatic interactions are on, gas-framework electrostatic interactions are off, and no electrostatic interaction is used, respectively. As expected, switching off electrostatic interactions decreases the gas adsorption loadings in PAFs. At low pressures (e.g. < 0.7 bar), the gas loadings are reduced by up to 80% without gas-framework electrostatic interactions. However, at higher pressures (e.g. > 1 bar), the differences are only within 10%. This suggests that gas-framework electrostatic interactions dominate at lower pressures, and they are important to the rapid rise of gas loadings at these pressures. Furthermore, when pressures are below 0.5 bar, the adsorption loadings with no electrostatic interaction are similar to those loadings without only gas-framework electrostatic interactions. This indicates that gas-gas interactions are weak under these pressures. At pressures from 0.5 bar to 2 bar, the changes of gas loadings range from 80% to 20% due to the absence of gas-gas electrostatic interactions, indicating the significant contribution of gas-gas electrostatic interactions to the overall behavior of the absorbent. For pressures larger than 2 bar, the gas-gas electrostatic interactions still play non-negligible roles, resulting in changes within 20%. We also simulated the adsorption isotherms of single component N2, O2, CH4 and CO2 in these PAF adsorbents at 298 K. As an example, adsorption loadings and heats of adsorption of all gases at a low


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gas pressure (0.4 bar) and a high gas pressure (30 bar) are illustrated in Figure 8. Full details of single component adsorption of N2, O2, CH4 and CO2 are provided in Figure S5. At low pressures, the higher of SO2 suggests a stronger binding between SO2 and PAF adsorbents compared to other gases, and this results in higher SO2 adsorption loadings. The additions of functional groups increase gas loadings as a result of their higher . At high pressures, is governed more by adsorbate-adsorbate interactions. The SO2 adsorption loadings are slightly lower than H2S loadings despite the higher of SO2 because of the inhibition of larger volumes of SO2 gas molecules.

Figure 7. (a) The adsorption isotherms of SO2 in PAF-COOH with different types of electrostatic interactions. (b) The relative changes of adsorption loadings by switching off electrostatic interactions. The inset plot in each figure address the data at low pressures.



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Figure 8. The adsorption loadings and heats of adsorption for single component gases at (a) a low pressure (0.4 bar) and (b) a high pressure (30 bar) in a variety of functionalized PAFs at 298K.

3.2 Selective Capture of Gas Mixtures Ideal adsorbed solution theory (IAST) calculations were carried out to evaluate the multicomponent isotherms of gas mixtures based on their pure-component adsorption loadings. IAST is a widely used 16 ACS Paragon Plus Environment

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method for predicting mixture adsorption equilibria from single component data55. All IAST calculations were performed using the pyIAST software package56. Each simulated pure-component adsorption data was fitted to an analytical model using a least-squares loss function56. Langmuir models were applied to N2 and CH4 gas loadings, and quadratic models were applied to CO2 and H2S adsorption loadings using Eqs. (3) and (4), respectively. These models show good fitting of the results from GCMC adsorption loadings in the PAF adsorbents considered in this work. Single component SO2 adsorption was modeled using linear interpolation due to unsatisfactory fitting results with typical analytical models. The fitted parameters and adsorption isotherms of the PAF adsorbent functionalized by -COOH groups are provided in Figure S6 and Table S3, and similar results were obtained in other PAF structures in this work.

= =

1 +

+ 2! " 1 + + !

(3) (4)

The selectivity of adsorption in SO2-N2, SO2-CO2, H2S-CH4 and H2S-CO2 binary mixtures by various PAFs at 298 K were determined by both IAST and with GCMC simulations. The molar compositions of the gas mixtures considered were 0.002:0.998 (H2S-CH4), 0.02:0.98 (H2S-CO2), 0.006:0.994 (SO2-N2) and 0.05:0.95 (SO2-CO2), based on prototypical examples of post-combustion gas, flue gas, and biogas27,28. Figure 9 illustrates the selectivity of gas mixtures in PAF-COOH predicted by IAST and GCMC. In the limit of dilute loading IAST is exact and the selectivity for a binary mixture is the ratio of the single component Henry’s constants55. The deviations that exist between the IAST and GCMC results in Figure 9 at low total pressures are therefore associated with imprecision in the Henry’s constants of the fitted single component isotherms, not an inaccuracy of IAST. In general, IAST overpredicts the adsorption of the species with the higher heat of adsorption in each example provided in Figure 9 (e.g. SO2 in the N2/SO2 mixture). This means that IAST overpredicts the adsorption selectivity, particularly at higher total pressures. Despite this quantitative discrepancy between IAST and our GCMC data, IAST performs adequately in capturing the qualitative trends in selectivity as a function of pressure for each mixture.




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Figure 9. Adsorption loadings and selectivity of gas mixtures in PAF-COOH at 298K predicted with IAST (lines) and simulated with binary GCMC (symbols) for (a) SO2/N2 (0.006:0.994), (b) SO2/CO2 (0.05:0.95), (c) H2S/CH4 (0.002:0.998) and (d) H2S/CO2 (0.02:0.98).



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Figure 10. Selectivity of SO2 and H2S in gas mixtures determined from binary GCMC simulations at 298K: (a) SO2/N2 (0.006:0.994), (b) SO2/CO2 (0.05:0.95), (c) H2S/CH4 (0.002:0.998) and (d) H2S/CO2 (0.02:0.98). Here, pressure indicates the total pressure of gas mixtures.

Figure 10 illustrates the results of selectivity calculated by GCMC simulations in each PAF adsorbent. Further details of adsorption loadings are provided in Figure S7. All inclusion of functional groups on the porous frameworks increases the selectivity of SO2/N2, SO2/CO2, H2S/CO2 and H2S/CH4 relative to unfunctionalized PAF-1. The -COOCH3 group leads to the highest SO2/N2 selectivity, followed by the -CN, -COOH and -NO2 groups, as a result of their stronger interaction with SO2 due to its dipole moment and polarizability. In the case of SO2-CO2 gas mixtures, the -CN and -NO2 groups 20 ACS Paragon Plus Environment

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exhibit the highest SO2/CO2 selectivity, followed by the -COOH and -COOCH3 groups. The SO2/CO2 selectivity is generally lower than the SO2/N2 selectivity in these adsorbents, and the SO2/CO2 selectivity peak in each PAF suggests competitive adsorption of two gases in these adsorbents. Similar results are observed in H2S/CH4 and H2S/CO2 adsorption selectivity but the selectivity is much lower due to closer gas-adsorbent affinity in these gas mixtures. The increase of selectivity with increasing pressures was also observed in previous work on acid gas uptake in carbon nanotubes27,57. Although the concentrations of SO2 and H2S in gas mixtures are small, these gas molecules are preferably adsorbed due to stronger interactions with framework atoms, and fill the interacting space first when the pressures of gas mixtures increase until they saturate those sites in PAFs. This results in the increase of their selectivity with increasing gas mixture pressures.

3.4 The Effect of Temperature on Selectivity We explored the effect of temperature on adsorption selectivity using GCMC simulations of gas mixtures at 273, 298, 323 and 348K. The results for SO2-N2 and SO2-CO2 mixtures in PAF-NH2 and PAF-COOH are provided in Figure 11 as an example. Similar results are observed in H2S/CH4 and H2S/CO2 gas mixtures. For SO2-N2 gas mixture, their adsorption selectivity across different gas pressures reduces as temperature is increased. In PAF structures functionalized by -CN, -COOH, -COOCH3 and -NO2 groups, a sharper increase of selectivity at the lowest temperature we simulated (273K) is observed when the pressures of gas mixture are high (e.g. > 20 bar), which is not found in other PAFs considered in this work. A possible reason is that lower temperatures provide less kinetic energy for gas molecules, and this makes the potential energy associated with gas-framework interactions dominant. Therefore, at 273 K, the frameworks that have stronger interactions with SO2 molecules exhibit higher selectivity as gas pressures increase. At higher temperatures, the effects of gas-framework interactions are relatively weaker, and thus the SO2/N2 selectivity is reduced. A previous study in carbon nanotubes observed similar results27. The behavior of SO2/CO2 mixtures under the conditions we examined is more complex. At 273 K, the SO2/CO2 selectivity reaches a maximum at a total pressure around 2 bar then decreases strongly at



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higher total pressures. At approximately this pressure, the pore volume is saturated with adsorbed molecules, so adsorption at higher pressures is driven by entropic effects rather than the enthalpic effects that dominate at lower loadings58. This effect can be understood by analysis of simple models of adsorption involving Langmuir isotherms59. A similar trend is seen at higher temperatures, but the maximum in the selectivity is shifted to higher total pressures because the total pressure needed to achieve near-saturation of the pores increases with temperature. As a result, the highest selectivity at a given total pressure under the conditions we examined is not necessarily at the lowest temperature. In fact, the PAFs functionalized by -CN, -COOH, -COOCH3 and -NO2 groups show the highest selectivity at 273 K while the other PAFs have the highest selectivity at 298 K in this work.


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Figure 11. The GCMC simulated adsorption selectivity of (a) SO2/N2 (0.006:0.994) and (b) SO2/CO2 (0.05:0.95) gas mixtures in PAF-NH2 and PAF-COOH at different temperatures

4. Summary In this work, first principles density functional theory calculations and grand canonical Monte Carlo simulations were employed to explore the adsorption of pure SO2 and H2S gas and their selective adsorption from gas mixtures in different porous aromatic frameworks. The influences of additional functional groups to PAF-1 such as -CH3, -CN, -COOH, -COOCH3, -OH, -OCH3, -NH2 and -NO2 groups, and temperatures between 273K and 348K on gas adsorption loadings are investigated. DFT calculations show that SO2 and H2S are mainly adsorbed at the top site of aromatic rings in unfunctionalized PAF-1 adsorbent. Additional interacting sites with gas molecules at the side of aromatic rings are provided by all functional groups. The binding energies at the top site are increased by electron donating groups such as -CH3, -OH, -OCH3, -NH2 or decreased by electron withdrawing groups such as -CN, -COOH, -COOCH3 and -NO2. The binding energies calculated from GCMC single-component simulations are lower than DFT results, but the general trends of all PAFs qualitatively agree with DFT data. GCMC simulations reveal that single-component SO2 and H2S gas loadings exhibit type-IV, S-shape adsorption isotherms due to the adsorbate-adsorbate interactions in PAFs. The unfunctionalized PAF-1 23 ACS Paragon Plus Environment


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show pure-gas loadings of up to 50 mmol/g for SO2 and 53 mmol/g for H2S. These gas loadings are higher than other gases such as CH4 and CO2 that have been explored in PAFs in previous work. The addition of functional groups enhances SO2 and H2S gas take at low pressures due to their stronger interaction with gas molecules, but reduce adsorption loadings at higher pressures because of their lower available free pore volumes. The electrostatic interactions between gas-framework and gas-gas are two important reasons for the rapid increase of SO2 and H2S gas loadings at lower pressures in functionalized PAF adsorbents. The adsorption selectivity of SO2 and H2S in SO2-N2, SO2-CO2, H2S-CO2 and H2S-CH4 binary gas mixtures suggests quantitative discrepancy between IAST predictions and GCMC multi-component simulations, but IAST performs adequately in capturing the qualitative trends in selectivity as a function of pressure for each gas mixture compared to GCMC results. The GCMC simulations indicate that the inclusion of functional groups increases the adsorption selectivity relative to unfunctionalized PAF material, and electron withdrawing groups such as -CN, -COOH, -COOCH3 and -NO2 groups are more effective at enhancing the adsorption selectivity of sulfur-containing gas mixtures in PAF adsorbents. Note that most actual PAF materials have degrees of long-range disorder17,19,23,25, while the models we have used are for entirely crystalline materials. Although atomistic methods can be applied to partially ordered or amorphous materials, or even more complicated heterogeneous disordered systems when appropriate structural models are available26,60,61,62, generation of accurate models of this kind is challenging and is beyond the scope of this work. It seems unlikely that the overall trends identified in our calculations with crystalline models would change substantially if a thorough assessment of disorder effects in PAFs was made. All of our calculations have assumed that adsorption of sulfur-containing gases in PAFs occurs by physisorption and that no degradation of the adsorbents is induced by these species. Studies of acid gas adsorption in metal-organic framework materials have shown that synergistic interactions between adsorbed water and acid gases can initiate defect formation and degrade these materials even when the materials are stable under dry acid gases at high pressure63,64,65. The fully covalent nature of the bonding in PAFs is likely to mean that PAFs are more resistant to this kind of degradation than MOFs, where


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weaker bonds can be attacked by acid species. It would be interesting to test our suggestions via experiments, and we hope that the predictions regarding adsorption in PAFs described in this paper provide a useful way to select materials for future work of this kind.

Supporting information Table-S1: Force field parameters used in GCMC simulations; Table S2: Pore volumes of different PAF structures; Table S3: Parameters for IAST analytical models in PAF-COOH at 298 K; Figure S1: Structures of PAFs and their corresponding cleaved models; Figure S2: H2S gas adsorption isotherms in PAF using two cutoff values; Figure S3: The binding energies of SO2 and H2S calculated by DFT and GCMC in different PAFs; Figure S4: The Henry coefficient of SO2 and H2S in different PAFs calculated by GCMC simulation and Widom insertion; Figure S5: GCMC adsorption isotherms and heats of adsorption for pure N2, O2, CH4, and CO2 gas at 298 K; Figure S6: Single-component adsorption loadings in PAF-COOH at 298K from GCMC and IAST; Figure S7: Adsorption loadings at 298 K of each component in binary gas mixtures of SO2-N2, SO2-CO2, H2S-CH4 and H2S-CO2; Appendix 1: Structural information of different PAFs

Acknowledgements This work is supported by UNCAGE-ME, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC0012577. D.Z. and S.B.S acknowledge Scienomics MAPS platform for building structures and performing calculations. X.J. acknowledges National Nature Science Foundation of China (NSFC No. 21503038) and China Scholarship Council (CSC).

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Molecular Simulation of Capture of Sulfur-Containing Gases by

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