SO2 gas mixture in a Cu-BTC metal organic framework

Journal of Molecular Graphics and Modelling 96 (2020) 107533

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Experimental and numerical study of SO2 removal from a CO2/SO2 gas mixture in a Cu-BTC metal organic framework H. Wang a, J.Q. Bai a, *, Y. Yin b, S.F. Wang c a

School of Aeronautics, Northwestern Polytechnical University, Xi’ an, Shaanxi, 710072, China MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi’ an Jiaotong University, Xi’ an, Shaanxi, 710049, China c School of Engineering, Newcastle University, Newcastle, NE1 7RU, UK b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 October 2019 Received in revised form 31 December 2019 Accepted 6 January 2020 Available online 9 January 2020

The mechanism of SO2 removal from a CO2/SO2 gas mixture in a copper benzene-1, 3, 5-tricarboxylate (Cu-BTC) material is investigated at the molecular level by the grand canonical Monte Carlo method. The effects of seven kinds of force-field relationships among CO2, SO2 and Cu-BTC on the selectivity for a SO2/CO2 gas mixture at different temperatures are studied in detail. The accuracy of the simulation model is validated by the experimental data. The results show that more SO2 molecules are adsorbed than CO2, and the electrostatic interactions involving SO2 are more sensitive to temperature than CO2 is. The multilayer desorption for SO2 and CO2 occurs in large-square channels. The effect of the electrostatic interactions involving SO2 is stronger than the interactions of CO2. The forms of CO2 and SO2 adsorption in Cu-BTC with electrostatic interactions are Cu2þ∙∙∙O]C]O and Cu2þ∙∙∙O]S]O, respectively. © 2020 Elsevier Inc. All rights reserved.

Keywords: Cu-BTC Adsorption GCMC Electrostatic interactions Gas separation

1. Introduction The flue gas which is emitted from coal-fired power plants includes carbon dioxide (CO2) and sulfur dioxide (SO2). SO2 owning high corrosivity can cause adverse effects to environment and human health. Thus, SO2 should be removed away from the flue gas before CO2 is captured and gathered [1,2]. Recently, solid adsorbents are becoming popular for the removal of SO2 because of their simplicity of operation and the availability of a wide range of adsorbents. Metal organic frameworks (MOFs), as a promising adsorbent, have a high surface area, large pore volume, and adjustable chemical functionality, which has caused them to draw much attention in gas adsorption [3,4] and separation [5]. As a typical MOF, copper benzene-1,3,5-tricarboxylate (Cu-BTC) has a building unit composed of four benzenetricarboxylate (BTC) groups coodinated to two Cu(II) ions [6], which is a promising material for removing SO2 gas from a CO2/SO2 gas mixture during postcombustion in a fossil power plant, due to highly selectivity for SO2 over CO2 in CO2/SO2 gas mixtures [7]. This is because of its unique structure, which has three domain types: tetrahedron side pockets, large square-shaped channels and cuboctahedral cages as

* Corresponding author. E-mail address: [email protected] (J.Q. Bai). https://doi.org/10.1016/j.jmgm.2020.107533 1093-3263/© 2020 Elsevier Inc. All rights reserved.

described by Assche et al. [8]. Many studies have reported different kinds of gas adsorption and storage in Cu-BTC [9e11]. In addition, the selectivity properties for Cu-BTC have also been considered. Cao et al. [12] synthesized a Cu-BTC material and showed that it exhibits higher ideal selectivity for CO2/He compared with other MOFs. Hamon et al. [13] adopted a grand canonical Monte Carlo (GCMC) method and determined that 30%e50% of the CO2/CH4 selectivity occurred in the side pockets of Cu-BTC. Yang et al. [14] used GCMC to indicate that the geometry and pore size are the main factors affecting the separation efficiency when studying the selective behavior in Cu-BTC at different
rez et al. [15] simulated the pressures (0 kPae5.0  103 kPa). Pe adsorption of several quadrupolar and nonpolar gases in Cu-BTC to verify their strong selectivity because of open metal sites and the pore size relative to the adsorbate size. Wang et al. [16] also showed that adsorbates with higher affinity with Cu-BTC have a higher adsorption heat at low pressures compared with CO and C2H4 adsorption in Cu-BTC. Yu et al. [17] adopted the molecular modeling method to estimate the influence of SO2 in flue gas mixtures present in postcombustion CO2 capture in Cu-BTC. They found the CO2/ N2 selectivity in a CO2/N2/H2O/SO2 mixture gas is lower compared that in a CO2/N2/H2O mixture because of the strong SO2 physicalbinding with Cu-BTC. Ding et al. [18] found the SO2 and CO2 adsorption in Cu-BTC is physical adsorption by adopting Density functional theory (DFT) to predict binding energies at different

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Nomenclature a Coefficient b Coefficient ECR The contribution rates Eb Binding energy (kJ$mol1) ECuBTCCO2=SO2 Total energy of adsorbed Cu-BTC(kJ$mol1) ECuBTC Total energy of Cu-BTC(kJ$mol1) ECO2=SO2 Total energy of adsorbate (kJ$mol1) f The fugacity (kPa) k The Boltzmann constant (1.38  1023 J$K1) m The mass (kg) Ma The relative molecular mass of the adsorbent (44 for CO2 and 64 for SO2) Ms The substance amount of a single crystal (9696) N The excess adsorption amount (mol$kg1) Na The number of the structure cell (8) NA Avogadro’s constant (6.022  1023) Nam The final number of adsorbates p The pressure (kPa) pm/n The accepted probabilities q The partial charges (e) Q The isosteric heat of adsorption (kJ$mol1) r The distance (nm) R The constant S The selectivity T Temperature ( C) V Simulation box volume (m3) (1.25  1026 m3 for Vfree )

pressures. As mentioned above, most researches focus on SO2 affecting the CO2 adsorption in Cu-BTC at different pressures. However, the selectivity properties of SO2/CO2 mixture gas in CuBTC at different temperatures are not reported. Electrostatic interactions (EI) have an obvious influence on the gas separation in the gas mixture because of the different polarities of the gas components. Karra et al. [19] found that the EI between the framework atoms and gas molecules clearly dominates the adsorption mechanism by turning on/off the EI. Then, Yang et al. [20] studied the effect of EI on CO2 selectivity for a CH4/CO2 gas mixture at different pressures (0 kPae2.0  103 kPa). Their results show that EI for separation becomes strong with increased pressure. Yang et al. [21] further studied the CO2/N2/O2 separation with and without EI at different pressures (0 kPae5.0  103 kPa) and found that both gas composition and EI are important for the gas selectivity; they found that the EI play a dominant role in the gas selectivity process. Wang et al. [22] found that the percent of the EI contribution to the selectivity of CO2/CH4 mixture gas in Ni/DOBDC can reach up to 62.0%e68.3% with pressure ranging from 0 to 100 kPa at 298 K. However, the influence of EI on the competitive relationship in the mixture gas separation, which considers both adsorbates to be charged in the MOFs, remains unclear, especially for two kinds of the polar adsorbates existing in MOFs. Most studies focus only on gas selectivity in Cu-BTC at different pressures. The effect of temperature on gas adsorption and separation in Cu-BTC is not involved. Besides, the effects of EI on mixture gas selectivity in Cu-BTC at different temperatures have not been considered quantitatively and not been expressed clearly at all, especially for two kinds of the polar adsorbates. The characterization of as-synthesized Cu-BTC is carried out first in the present study. The effects of pressure on the CO2 adsorption

U x y Z

Potential energy (kJ) The mole fractions in the adsorbed phase The mole fractions in the bulk phase The compressibility coefficient

Greek symbols ε The L-J depth (K) ε0 The dielectric constant (8.85  1012 F$m1) s The L-J diameter (nm) m Chemical potential x The rand number (0e1) L The de Broglie thermal wavelength r The density (kg$m3) Subscript * þ

The accepted probabilities Insert or delete atom

Superscript m The initial configuration n The final configuration i The interaction atom i j The interaction atom j Lennard-Jones LJ The electrostatic potential Eq Adsorbate-adsorbate ff Adsorbate-adsorbent fs CðiÞ Case i

amount and heat are investigated by experiments. The GCMC method is adopted to study the mechanism for the induced charge and the effect of temperature on the SO2/CO2 gas mixture selectivity. 2. Experimental study 2.1. Material preparation and characterization The Cu-BTC is synthesized as follows [23]: a certain amount of copper(II) nitrate trihydrate (Cu (NO3)2∙3H2O) is dissolved into deionized water, and benzene-1, 3, 5-tricarboxylic acid (H3BTC) is dissolved into ethanol (EtOH) separately. Then, these two solutions of deionized water and ethanol are stirred together for 30 min. The mixed solution is transferred into a 100 mL autoclave and further capped and heated at 85  C for 24 h to yield blue crystals. After vacuum filtration and rinsing twice with dimethyl formamide, the product is thoroughly washed with deionized water. Finally, the sample is dried in an oven (100  C) to remove residual solvent under vacuum to obtain the final sample. Fig. 1 displays the SEM (scanning electron microscopy) for the synthesized Cu-BTC crystals and the structure of the sample morphology. Cu-BTC has three types of microstructures: large square-shaped channels, tetrahedron side pockets and cuboctahedral cages as described by Assche et al. [8] and Agrawal et al. [24]. To validate the reliability of our synthesis, the synthetic Cu-BTC is characterized. Powder X-ray diffraction (XRD) analysis is applied to show the structure of the sample. A Cu target X-ray tube is set to 40 kV and 30.0 mA. The scanning angle ranges from 3 to 50 . Fig. 2 shows the XRD pattern of the synthesized Cu-BTC. Its pattern also matches well with the aforementioned literature [25]; this result

H. Wang et al. / Journal of Molecular Graphics and Modelling 96 (2020) 107533

means that the synthesized material has a good crystallinity, as shown in Fig. 1. Thermal gravimetric analysis (TG) are performed to investigate the structural stability. A powder sample is heated and weighed from 50 to 600  C at a rate of 10  C/min under a high purity N2 atmosphere. Fig. 3 shows the weight loss and heat changes. Approximately 16.87% of the weight is lost from the starting temperature to 140  C due to the removal of the water and adsorbed molecules. In this stage, an exothermic process occurs, and the stability analysis of Cu-BTC shows that the regeneration temperature of Cu-BTC is nearly 140  C. A plateau is observed from 140 to 300  C, which indicates that a stable structure can be maintained under this temperature range. With an increase in temperature, a sharp weight loss is observed, which shows that structure collapse occurrences are endothermic. The results from analysis of the structural stability show that Cu-BTC has good thermostability. The Brunauer Emmett Teller (BET) surface area of Cu-BTC is tested using an automatic gas sorption analyzer (Quantachrome Autosorb IQ, USA) via N2 adsorption and desorption experiments at a temperature of 196  C. The samples are pretreated at 120  C under vacuum for 20 h before the experiment; then, N2 as adsorbate is used to test the amount adsorption in Cu-BTC at different relative pressures. Fig. 4 shows the N2 adsorption/desorption isotherms measured for as-synthesized Cu-BTC. The curve is fitted for a type-I isotherm. The Brunauer Emmett Teller (BET) surface area of Cu-BTC is calculated to be 1332 m2/g (0:005  p=p0  0:05). The BET surface is comparable to those reported by Liang et al. [25] (about 1570 m2 g1), Aprea et al. [26] (1400 m2 g1) and Wang et al.

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Fig. 2. Powder XRD pattern of synthesized Cu-BTC.

[27] (964.5 m2 g1 - 1333 m2 g1). 2.2. Experimental apparatus and procedure Fig. 5 displays the schematic of four parts of the test apparatus: gas supply system, adsorption system, data acquisition system, and calorimetric system. The adsorption and calorimetric system used is a PCTProE&E and Calvet Calorimeter (PCT and C80, French). The

Fig. 1. The structure and SEM for the synthesized Cu-BTC crystals (a) Cu-BTC structure. Cu atoms (orange sphere); C atoms (gray sphere); O atoms (red sphere); and H atoms: white atoms (b) The SEM for the synthesized Cu-BTC crystals.

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H. Wang et al. / Journal of Molecular Graphics and Modelling 96 (2020) 107533

Fig. 3. Thermogravimetric (TG) analysis.

Cu-BTC powder is placed in a C80 cell maintained at 150  C by heating the C80 under vacuum for 20 h to remove the water and gas absorbed by Cu-BTC powder in the air as a pretreatment. The gas supply system is connected to the adsorption system, which has three gas supply lines: nitrogen (N2), carbon dioxide (CO2), and helium (He). Nitrogen is adopted to push the pneumatic valves in the PCT. The sample cell in C80 is passed through by helium for volume calibration. The CO2 treated as the adsorbate gas is fed to the sample cell to meet the setting pressure. The temperature is controlled by the C80. During the adsorption process, the CO2 adsorption amount and heat are tested synchronously using the PCT and C80. The testing signals are then recorded by the data acquisition system. The CO2 is introduced into the system using a step-by-step method, and each dose is allowed to stabilize in a reference volume before being brought into contact with the CuBTC adsorbent, located in the C80. The introduction of the CO2 to the Cu-BTC adsorbent is accompanied by an exothermic thermal signal, measured by the thermopiles of the C80. The peak in the calorimetric signal is integrated over time to give the total energy released during that adsorption step. At the same time, the adsorption amount of CO2 in Cu-BTC can be tested by the PCT. Thus, the isosteric heat of adsorption can be obtained as described by Grajciar et al. [28]. The uncertainties in the amount of adsorption and isosteric heat of adsorption are just 1.5% and 1.6% as described in Ref. [22], respectively.

Fig. 5. The systems used for measurement of CO2 adsorption.

3. Simulation model and method 3.1. Simulation model Separation characteristics are simulated by adopting the GCMC model with a constant simulation box volume (V), chemical potential (m), and temperature (T). The input parameters only contain the pressure and temperature. The GCMC calculation are performed in the Sorption module of Material Studios [28]. Fig. 6 displays the simulation box with eight unit cells used in present work. The developed and optimized Cu-BTC adsorbent is regarded as a rigid structure with a periodic boundary condition [29]. The CO2 gas is regarded as a rigid linear triatomic molecule, and the CeO bond length is 0.116 nm. The total potential energy (Uij ) depends on the interactions between the Cu-BTC framework and CO2 molecule or between two CO2 molecules. i and j are the interacting CO2 molecules or atoms in Cu-BTC. The values of the Lennard-Jones (L-J) potential parameters and the atomic partial charges of Cu-BTC are shown in Fig. 7 and Table 1. These values have been widely used and validated in the literatures [16,30]. Force fields play an important role in molecular simulations. We have used CO2 model from the TraPPE force field for simulations [31], because such potential model has been successfully used to simulate the impact of H2O, O2, and SO2 on postcombustion CO2 capture [17]. The values of the Lennard-Jones (L-J) parameters and partial charges for CO2 are shown in Table 2. Uij contributes the L-J potential (ULJ ) as well as an electrostatic potential (UEq ), which is the coulomb potential. The total potential energy Uij is obtained as follows:

Uij ¼ ULJ þ UEq

(1)

ULJ and UEq are defined in Eqs. (2) and (3), respectively. UEq can be artificially turned off during the simulation process to study the effects of EI on the adsorption and selectivity.

" ULJ ¼ 4εij

UEq ¼ Fig. 4. Nitrogen adsorption isotherm.

sij rij

qi qj 4pε0 rij

!12 

sij rij

!6 # (2)

(3)

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Table 1 Partial atomic charges and L-J parameters for the Cu-BTC adsorbent. 

atoms

qðeÞ

sðА Þ

ε=kB ðKÞ

O C1 C2 C3 H Cu

0.665a 0.778a 0.092a 0.014a 0.109a 1.098a

2.96b 3.75b 3.55b 3.55b 2.42b 3.11c

73.98a 44.91a 35.23b 35.23b 15.10b 2.52c

a

fFrom Yang and Zhong et al. [14]. From the OPPLS-AA force field described by Jorgen et al. [32]. c From the all-atom UFF force field [33] (which are excluded in the OPPLS-AA force field). b

Fig. 6. Computational physical model for SO2 and CO2 adsorption in Cu-BTC.

The Ewald summation technique is used in electrostatic interaction [34]. The cutoff radius for the L-J interactions is set to be 1.3 nm. LorentzeBerthelot mixing rules are used during the simulation process for all L-J cross-interaction parameters [35]. In addition to the CO2 molecule described above, SO2 is also chosen as an adsorbate in the selective process. The process of SO2 adsorption in Cu-BTC is physical adsorption as indicated in Ref. [18]. The SO2 model includes a harmonic OeSeO, whose angle is 119.3 with a SeO bond length of l ¼ 0.1432 nm [36]. This is because such potential model has been successfully used to simulate the effect of SO2 on CO2 capture in MOF materials [37]. Seven types of combinations of L-J and electrostatic interactions are used. The five electrostatic interactions occur between the SO2 and Cu-BTC, CuBTC and CO2, SO2 and SO2, CO2 and SO2, and CO2 and CO2. The L-J forces are defined as all the interactions between the adsorbent and adsorbate, and vice versa. The calculated potential energy of the atoms between the adsorbent and adsorbate, and vice versa, is similar to that of the CO2 adsorption process. The L-J parameter values and partial atomic charges for the SO2 atoms are also shown in Table 2. 3.2. Simulated method The GCMC method begins with the initial configuration. The adsorbate number and total potential energy of SO2/CO2 in Cu-BTC during the initial configuration (m) is assumed to be Nm and Um , respectively. The initial configuration should be updated with the

Table 2 The partial atomic charges and L-J parameters for CO2 and SO2 atoms. 

Species

Atom

sðА Þ

ε=kB ðKÞ

qðeÞ

CO2

O C S O

3.05 2.80 3.39 3.05

79.0 27.0 73.8 79.0

0.35 0.70 0.59 0.295

SO2



lðА Þ 1.16 1.432

procedures of insertion, deletion, and random movement for the SO2 and CO2 molecules under the same probability. The detailed solution process is given in Ref. [35]. The accepted probabilities for the occurrence of insertion, random movement, and deletion are shown in Eqs. (4)e(6):

   fV 1 ðUn  Um  mÞ > x p*þ exp  m/n ¼ min 1; kTNn kT

(4)

   1 ðUn  Um Þ > z p*m/n ¼ min 1; exp  kT

(5)

   kTNm 1 ðUn  Um þ mÞ > x exp  p* m/n ¼ min 1; kT fV

(6)

The pressure ðpÞ can be obtained from the fugacity (f ) by adopting the PengeRobinson equation [38], as shown in Eq. (7), and m is the chemical potential as defined below in Eq. (8):

    bp a  pffiffiffi f ¼ p exp Z  1  ln Z  ln RT 2 2bRT  pffiffiffi bp  pffiffiffi bp    Zþ 1 2  Z þ 1þ 2 RT RT

m ¼  kT ln



V ðNm þ 1ÞL3

(7)

  kT lnCexp½  ðUn  Um Þ=ðkTÞDNm (8)

The detailed values above are shown in Table S1 in supporting information. CD is the ensemble average, which is only an operator [35]. For the insertion and deletion steps, the total number of adsorbate molecules in the simulated box is either incremented or decremented by one unit, respectively. The adsorbate number for the modified configuration (n) is also shown in Eqs. (9) and (10) as follows:

Fig. 7. Cluster atoms in Cu-BTC for partial charges.

Nn ¼ Nm þ 1

(9)

Nn ¼ Nm  1

(10)

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The above steps of insertion, movement, and deletion should be repeated for 1  107 steps to make sure that the chemical potential in the bulk and adsorbed phases is identical. This condition means that the number of desorption and adsorption molecules are the same, as shown in Eq. (11).

Nn , p*m/n ¼ Nm ,p*n/m

(11)

7

Another 1  10 steps (described as above) are also adopted to calculate the average converged number of adsorbates and total potential energy. Therefore, the final adsorbate molecule number (Nam ), adsorbateeadsorbent potential energy (Ufs ), and adsorbateeadsorbate potential energy (Uff ) can be obtained. The final adsorbate molecule is converted to the excess adsorption amount (N), which can then be compared with the experimental data, as described in Ref. [39].

 N ¼ 1000

Nam Ma  rVfree NA Na

 ðMs Ma Þ

(12)

The free volume of the adsorbent cell is estimated by using the “Atoms Volume & Surfaces” calculation within the Materials Studio package [28]. r is the bulk density given by the following equation:

r¼

pMa ZRT

(13)

The isosteric adsorption heat Q can be obtained by using Eq. (14) [40] as follows:

Q ¼ RT 

CUff Nam D  CUff DCNam D CN2 D  CNam DCNam D



CUfs Nam D  CUfs DCNam D CN 2am D  CNam DCNam D

(14)

The calculation processes for the isosteric heat and adsorption amount in the separation processes are the same as those mentioned in Eqs. (12) and (14). The initial concentration ratio of SO2/CO2 is controlled by the pressure, with this ratio set to be the same in this study. The selectivity of the SO2 component relative to the CO2 component is described as follows:



S ¼ xSO2 =xCO2  yCO2 =ySO2

(15)

where xSO2 and xCO2 are the mole fractions of the SO2 and CO2 components in the absorbed phase, ySO2 and yCO2 are the mole fractions of the SO2 and CO2 components in the gas phase, whose values are set to be equal as 0.5. The binding energies of CO2 and SO2 adsorption in Cu-BTC are calculated by DFT calculations with DMol3 [41], which employs the generalized gradient approximation correlation functional of Perdew-Burke-Ernzerhof parametrization with the double numerical plus polarization basis set. The detail can be found in Ref. [42], which can be expressed as follows:

Eb ¼  ECuBTCCO2=SO2  ECuBTC  ECO2=SO2

(16)

4. Results and discussion 4.1. Validation of the force-field parameters Fig. 8(a) and (b) show the simulation results for the adsorption amount and heat compared to the experimental data at 0e250 kPa and 35  C and at 0e120 kPa and 25  C, respectively. The relative deviations of the adsorption amount and heat range from 1.09% to 14.82% and 5.96%e15.68%, respectively when

compared with experimental data. The simulated data at 25  C also matches well with the experimental data of adsorption amount [27] and simulated data of adsorption heat [43], respectively. This means that the simulated CO2 adsorption amount and heat matches well with the experimental data. What’s more, the value of the low-loading experimental adsorption heat of CO2 that we obtain for Cu-BTC is about 22 kJ mol1, which is lower than those reported by Wang et al. [43] and Arstad et al. [44]. The possible reasons are that, firstly, the methods to obtain the adsorption heat of CO2 in Cu-BTC are difference: the adsorption heat of CO2 in Cu-BTC is obtained directly while the experimental adsorption heat values in literatures are usually determined through the Clausius-Clapeyron equation. Secondly, the adsorption properties of the synthesized samples are a little different in each paper as described by Wu et al. [45]. In general, the value of the low-loading experimental adsorption heat of CO2 that we obtain for Cu-BTC is reasonable (22 kJ mol1-35 kJ mol1) as described by Feldmann et al. [46]. Fig. 8(c) shows the simulated adsorption amount compared with the simulated data obtained by Song et al. [47] at different pressures and a temperature of 25  C. The relative deviation for the SO2 adsorption amount is 0%e1.0%. Fig. 8(d) displays the simulation adsorption heat compared to the simulation data obtained by Supronowicz et al. [7] at a temperature of 25  C. The results obtained from the two models are very similar. As the experimental data of SO2 adsorption in Cu-BTC is difficult to be obtained from this experimental apparatus and literatures, we validate the force field of SO2 to compare with simulated results from the literatures. Once we have a chance in the future, we can compare the simulation data with experimental data at different pressures and calculate the selectivity of SO2/CO2 at different pressures by using ideal adsorption solution theory. The L-J and Coulomb force parameters in this study are sufficiently precise to investigate the adsorption selectivity behavior of the Cu-BTC adsorbent.

4.2. Effects of electrostatic interactions on selectivity at varied temperature The method of turning the EI on and off to investigate the effect of EI on adsorption and separation has been widely reported in literatures [20,21,48]. Thus, in this work, the same method are used to study effect of EI on selectivity properties of the SO2/CO2 gas mixtures. The selectivity properties of the SO2/CO2 equimolar binary mixtures for different temperatures at 102 kPa are used to investigate CO2 separation from streams that contain SO2 during postcombustion in a fossil power plant. Seven typical cases: Case 1 (C1), Case 2 (C2), Case 3 (C3), Case 4 (C4), Case 5 (C5), Case 6 (C6), and Case 7 (C7) are studied to investigate the effect of EI on the selectivity of a SO2/CO2 gas mixture. The status of the electrostatic and L-J interactions for each case is displayed in Table 3. The total isosteric heat of adsorption for each case in Table 3 is expressed as follows:

Q CðiÞ ¼

NSO2 ðiÞ NCO2 ðiÞ Q þ Q NSO2 ðiÞ þ NCO2 ðiÞ CðiÞSO2 NSO2 ðiÞ þ NCO2 ðiÞ CðiÞCO2 (17)

where Q CðiÞ , QCðiÞSO2 , and QCðiÞCO2 represent the isosteric heat for the total, SO2, and CO2 adsorption, respectively, of the ith case (ranging from 1 to 7) in Table 3. The contributions of all EI on the adsorption heat are described in Eq. (18):

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Fig. 8. Comparison of the CO2 and SO2 adsorption amount and heat with experimental data and simulated data in literatures (a) Simulated CO2 adsorption amount compared with experimental data at 35  C in the present work and 25  C in the literature [27], respectively (b) Simulated CO2 adsorption heat compared with the experimental data at 35  C and simulated data in Ref. [43] at 25  C (c) SO2 adsorption isotherm simulation compared to the simulated data calculated by Song et al. [47] (d) Predicted adsorption heat compared to the simulated data calculated by Supronowicz et al. [7].

Q Cð17Þ ¼ Q Cð1Þ  Q Cð7Þ

(18)

Thus, the ECR for the L-J and electrostatic potential for the adsorption heat are defined in Eq. (19) as follows:

ECRQ ð7Þ ¼

QCð7Þ QCð17Þ  100% ECRQ ð17Þ ¼  100% QCð1Þ QCð1Þ

(19)

ECRQ ð7Þ and ECRQ ð17Þ represent the adsorption heat contribution rates for the L-J and EI, respectively, in Eq. (19). Fig. 9(a) displays the selectivity for the SO2/CO2 equimolar binary mixtures at different temperatures ranging from 25  C to 105  C in the seven cases. The SO2/CO2 selectivity clearly decreases in C1, C3, C4, and C5, but remains almost unchanged in C2, C6, and C7 with increasing temperature. In fact, the amounts of CO2 and SO2

adsorption decrease with an increase in temperature in all cases because the force fields between the CO2 or SO2 molecule and CuBTC molecule are physical bond with weak dispersion interactions [18]. The CO2 and SO2 molecules will be difficult to be remained in the cavity of Cu-BTC when the temperature increases. Besides, the SO2 electrostatic interactions are considered in C1, C3, C4, and C5. The electrostatic interactions involving SO2 are sensitive to temperature. Thus, the decrease in SO2 adsorption is faster than that for CO2 adsorption with all interactions. While only the L-J force for SO2 is considered in C2, C6, and C7. The decreasing rate of SO2 adsorption will decrease due to the L-J force and is almost equal to that of CO2 adsorption considering all interactions, which results in an insensitive variation in selectivity for SO2/CO2 with temperature in C2, C6, and C7. Fig. 9(b) displays the contribution of EI and the L-J potential to

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Fig. 8. (continued).

the adsorption heat for the adsorption selectivity of the SO2/CO2 mixture. Considering all interactions, the isosteric adsorption heat (Q Cð1Þ ), which is the sum of Q Cð17Þ and Q Cð7Þ , is provided for reference. The isosteric adsorption heat for electrostatic forces Q Cð17Þ decreases with increasing temperature increase in Fig. 9(b) because of multilayer desorption of CO2 and SO2 in large-square channels. The occupying probability of CO2 and SO2 molecules on the strong adsorption site becomes weak at higher temperature.

Table 3 Status of the electrostatic interactions for the seven cases.

Case Case Case Case Case Case Case

1 2 3 4 5 6 7

L-J

SO2eSO2

CO2eSO2

CO2eCO2

SO2eCu-BTC

CO2eCu-BTC

on on on on on on on

on off on on on off off

on off off on off off off

on on off on off on off

on off on off off off off

on on off off off off off

Note: “On” indicates that the interactions are considered, whereas “off” indicates that the interactions are not considered.

The isosteric adsorption heat from the L-J force (Q Cð7Þ ) remains constant with an increase in temperature, as described in Fig. 9(b). This variation trend is different from the CO2 adsorption heat [49] because of the competitive adsorption of SO2 and CO2 in the selectivity adsorption. Fig. 9 (c) shows the contribution rates for EI (Q Cð17Þ ) and the L-J force (Q Cð7Þ ). The contribution rate for the L-J force (Q Cð7Þ ) ranges from 59.33% to 92.51%, and the contribution rate for EI ranges from 7.49% to 40.67% in the studied temperature range. For instance, the contribution rates for Q Cð7Þ and Q Cð17Þ are 65.36% and 34.64%, respectively, at 45  C. This trend shows that the L-J potential accounts for a majority of the isosteric heat in the selection process. The snapshots of the adsorption structures have been widely used to study the adsorption properties in MOFs [50e52]. Thus, the competitive adsorption of SO2 and CO2 in selectivity adsorption is further understood from snapshots of the adsorption structures at a molecular level. Fig. 10(a), (b), 10(c) and 10(d) display single cell snapshots for adsorbed SO2 and CO2 for C1, C2, C3, and C7 in Table 3, respectively. The temperature is selected to be 25  C, 65  C, and 105  C for each case, and the pressure is fixed at 102 kPa. The number of adsorbed CO2 and SO2 molecules decreases with

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Fig. 9. Selectivity and isosteric heat for SO2/CO2 equimolar binary mixtures for different temperatures at 100 kPa (a) Selectivity for SO2/CO2 equimolar binary mixtures (b) Isosteric adsorption heat for SO2/CO2 equimolar binary mixtures (c) Contributions for isosteric adsorption heat for SO2/CO2 equimolar binary mixtures.

increasing temperature in all four cases. The multilayer desorption of CO2 and SO2 occurs in the large-square channels, followed by the tetrahedron side pockets (Fig. 1(a)). The adsorbed SO2 molecule number is more than the number of adsorbed CO2 molecules, as indicated in Fig. 10(a). This condition is determined by the

competitive adsorption between CO2 and SO2 molecules, which is controlled by the L-J potential and electrostatic interactions. Besides, the dispersive interactions in the smaller tetrahedron-shaped side pockets are much stronger than those in larger square-shaped channels (Fig. 1(a)). Comparing C3 (Fig. 10 c) and C2 (Fig. 10 b)

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Fig. 10. Snapshots of the effect of EI on SO2/CO2 adsorption selectivity on Cu-BTC. C atoms (gray sphere); O atoms (red sphere); and S atoms (yellow sphere). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

reveals that the effect of the SO2 electrostatic interactions is stronger than the effect of the CO2 electrostatic interactions. Fig. 10(d) shows that the number of absorbed SO2 molecules is even higher than the number of absorbed CO2 molecules but only under the L-J potential. This scenario implies that the SO2 has a higher L-J potential than CO2. Furthermore, the oxygen atom in the SO2 or CO2 molecule is very close to the copper ion in the Cu-BTC crystal, as

shown in Fig. 10(a), (b), and 10(c). This scenario indicates that the form of CO2 and SO2 adsorption in Cu-BTC is Cu2þ∙∙∙O]C]O and Cu2þ∙∙∙O]S]O, respectively, because the Cu2þ in the structure can accept electrons provided by the oxygen atom in the CO2 or SO2. The binding energies for Cu2þ∙∙∙O]C]O and Cu2þ∙∙∙O]S]O are 21.3 kJ mol1 and 32.7 kJ mol1 calculated by DFT method, and calculated results are in accord with Ref. [18]. The according

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calculated Cu2þ$$$O distances for CO2 and SO2 in Cu-BTC as obtained through both GCMC and DFT calculations are shown in Table S2 in supporting information. Both GCMC and DFT that the Cu2þ$$$O distance is shorter for SO2 compared to CO2, and the binding energies for Cu2þ∙∙∙O]S]O is higher compared to that for Cu2þ∙∙∙O]C]O. These phenomena mean that the adsorption of SO2 is much more favorable than that of CO2 due to the strong electrostatic interactions [18]. The CO2 and SO2 adsorption in CuBTC in C7 is random, as shown in Fig. 10(d), when the L-J potential is considered. To further validate above phenomena, the radial distribution function (RDF) of oxygen atoms of the CO2 and SO2 molecules, respectively, about the Cu2þ ions in Cu-BTC in C1 (25  C) is shown in Fig. 11 and Fig. S1 in supporting information. The RDF describes the loading probability of a certain particle as a function of distance from a reference particle, which can reflect the affinity between the two particles. As shown in Fig. 11, the distance between oxygen atoms of the SO2 and Cu atom in the first peak is shorter than the values of CO2, which indicates that SO2 is more preferentially adsorbed on the sites of Cu atom of Cu-BTC compared with that for CO2 in C1. Once the electrostatic interactions between adsorbate (CO2 or SO2) and Cu-BTC are ignored, the Cu2þ∙∙∙O distances in C2, C3 and C7 as shown in Fig. S1 become longer compared with those in C1.

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SO2 molecules is greater than the number of adsorbed CO2 molecules because the electrostatic interactions and L-J potential for SO2 are both stronger than CO2. For the electrostatic interactions, the CO2 and SO2 adsorption forms in Cu-BTC are Cu2þ∙∙∙O]C]O and Cu2þ∙∙∙O]S]O, respectively. Declaration of competing interest To the best of our knowledge and belief, neither I nor any authors have any possible conflicts of interest. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 51806178), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2019JQ-622) and the Fundamental Research Funds for the Central Universities (No. G2018KY0303). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jmgm.2020.107533. References

5. Conclusions The simulated adsorption amount and heat calculated using the GCMC model matches well with the experimental data. More SO2 is adsorbed compared to CO2. The EI involving SO2 are more sensitive to varying temperature compared to CO2. When the temperature increases, CO2 and SO2 molecule desorption begins with multilayer adsorption in the larger square-shaped channel, followed by the smaller tetrahedron-shaped side pockets. The effect of the EI involving SO2 on the selectivity for a SO2/CO2 gas mixture is stronger than the effect of the EI involving CO2. The adsorption contributions from EI and the L-J force both decrease with increasing temperature. The selectivity decreases remarkably with temperature for the CO2/SO2 selectivity process, which can be primarily attributed to the EI between SO2 and Cu-BTC being sensitive to temperature. The contribution of the L-J potential towards the isosteric adsorption heat remains almost unchanged because of the existing competitive adsorption process between SO2 and CO2. In an equimolar SO2/CO2 binary mixture, the number of adsorbed

Fig. 11. Radial distribution function (g(r)) between O_CO2, O_SO2 and Cu in Cu-BTC.

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