CO in graphite nanofiber and C60 intercalated graphite

Journal Pre-proofs Ideal Adsorbed Solution Theory, Two-Dimensional Equation of State, and Molecular Simulation for Separation of H2/N2/O2/CH4/CO in Graphite Nanofiber and C60 Intercalated Graphite Xuan Peng, Qibing Jin PII: DOI: Reference:

S1383-5866(19)31455-8 https://doi.org/10.1016/j.seppur.2019.116369 SEPPUR 116369

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Separation and Purification Technology

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10 April 2019 25 November 2019 30 November 2019

Please cite this article as: X. Peng, Q. Jin, Ideal Adsorbed Solution Theory, Two-Dimensional Equation of State, and Molecular Simulation for Separation of H2/N2/O2/CH4/CO in Graphite Nanofiber and C60 Intercalated Graphite, Separation and Purification Technology (2019), doi: https://doi.org/10.1016/j.seppur.2019.116369

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Ideal Adsorbed Solution Theory, Two-Dimensional Equation of State, and Molecular Simulation for Separation of H2/N2/O2/CH4/CO in Graphite Nanofiber and C60 Intercalated Graphite Xuan Peng*,† and Qibing Jin †

College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, P R China

ABSTRACT We performed grand canonical Monte Carlo (GCMC) simulations to investigate the adsorption separation of H2, N2, O2, CO and CH4 gas mixtures in graphite nanofibers (described by slit pore model), and C60 intercalated graphite (CIG). The presence of C60 molecules between the layers resulted in less than half of the adsorption of O2 and CH4 in CIG, compared to the slit pore. However, the adsorption selectivity of O2/N2, CH4/N2, CH4/H2, and CO/H2 systems in CIG is much higher than that of slit pores. These observations indicate that the slit pore and CIG are suitable for gas storage and gas separation, respectively. We used the two-dimensional Zhou-Gasem-Robinson (2D ZGR) EOS and the dual-site Langmuir-Freundlich (DSLF) to correlate the pure component adsorption isotherms simulated by GCMC method, and further predicted the adsorption of the binary gas mixtures by the ZGR model and ideal adsorbed solution theory (IAST), respectively. We found that neither adsorption model can accurately predict the adsorption properties of the four gas mixtures in the two materials simulated by GCMC method. IAST has a satisfactory predictive effect on the adsorption of N2-O2, N2-CH4 and H2-CO gas mixtures in CIG, while ZGR can accurately predict the gas adsorption of N2-O2, H2-CH4 and H2-CO in CIG. However, both models perform poorly in predicting gas adsorption in the slit pore. Consequently, experimental study or molecular simulation should be carried out for the validation of the results, when using the adsorption theory such as IAST and 2D EOS to predict the adsorption of a gas mixture.

* Corresponding author. E-mail address: [email protected] (X. Peng). 1

1.

Introduction Developing reliable models to predict the adsorption behavior of supercritical gases on

porous materials is becoming more important, especially in the gas separation industry. Many theoretical models have been developed for the description of adsorption data for pure components and mixtures, such as the Langmuir model[1], vacancy solution theory (VST) [2–4], ideal adsorbed solution theory (IAST) [5–8], and two-dimensional equations of state (2D EOS)[9–14]. IAST and VST models are based on analogies drawn from solution thermodynamics, whereas Langmuir model is not thermodynamically rigorous. However, Langmuir model is explicit with respect to the adsorption amount and therefore is superior to the thermodynamic models for the modeling of adsorption behavior.[15] Freundlich[16] developed a model to describe adsorption properties of heterogeneous systems and Langmuir[17] proposed to describe monolayer adsorption on homogeneous surfaces. Although considerable information is available on the single-component adsorption, more concerns are paid to the multi-component adsorption processes. A model for multicomponent adsorption was first developed by Markham[1], based on the same assumptions as the Langmuir theory for pure gases. The ideal adsorbed solution theory (IAST)[5] proposed by Myers and Prausnitz, assumes the adsorbate mixture behaves like an ideal solution, and is not appropriate to predict non-ideal adsorption behavior at high concentrations of adsorbed species. Nevertheless, IAST only requires single-component equilibrium data to predict the mixture adsorption and is therefore one of the most widely studied theories. If an adsorbed fluid is visualized as a two-dimensional nonideal compressed gas, it is appealing to use a two-dimensional analog of such as van der Waals (VDW)[10,18], virial[11] and Eyring[14,19] EOSs to describe pure adsorption isotherms. In 2-D EOS model, adsorbed molecules are free to move over the two-dimensional adsorbent surface, which is analogous to the movement of molecules in three-dimensional space. This analogy also extends to the representation of thermodynamic quantities via equations of state. Thus, the EOS representation of adsorption arises naturally from thermodynamic considerations.[19] Zhou et al. presented a generalized form of 2-D EOS, where the corresponding fugacity equations are derived in order to establish rigorous equilibrium relations between an adsorbed phase and a gas phase. By setting m=1 and U=W=0, an analogue of the VDW EOS is obtained, and similarly, for the Soave-RedlichKwong, m=U=1 and W=0, Peng-Robinson (m=1, U=2, and W=-1), and Eyring (m=1/2 and U=W=0) EOS.[12,13] Actually, the pure-gas isotherms vary considerably in shape and Zhou et al. determined that an equation with m=1/3 and U=W=0 (Zhou-Gasem-Robinson, 2

ZGR)[9,12,13] fits pure adsorption isotherms more accurately than the Langmuir model. With the mixing rules, the 2D ZGR EOS could be applied to the adsorbed phases containing mixtures. Reliable experimental measurements of the adsorption of fluids on well-characterized solids are essential in order to test the different theories of adsorption. One of the best adsorbents for this purpose is graphite nanofibers (GNFs)[20,21], which provides a molecularly smooth, and energetically homogeneous surface. GNFs consist of parallel graphitic platelets that stacked in layers forming fibers many micrometers in length. Recent studies have showed that the interlayer distance of the GNFs is the key to determine the gas adsorption capacity. At the original interlayer distance of 0.335 nm, the adsorbate-graphene interaction is repulsive and thus no gas molecules can penetrate between the graphite layers. However, if the graphene sheets are intercalated by spacer molecules, the interlayer distance could be increased to meet the requirement of the optimum pore size for maximum adsorption capacity. Using C60 fullerenes as spacer molecules[22,23], Saito et al.[24] designed the structure model of C60 intercalated graphite, while Gupta and co-workers[25] synthesized this material by directly combining two carbon allotropes of C60 and graphite. During the intercalation process, the vdW contact between two adjacent parallel layers is broken and a two-dimensional hexagonal symmetry of C60 fullerenes is formed. The transmission electron microscopy (TEM) image indicates that no covalent bonds exist between fullerenes and between the fullerenes and the layers[25]. As far as we are concerned, very few studies have been reported on comparing the predicted performance of the gas mixture adsorption models of 2D EOS and IAST[18]. In this situation, more systematic evaluations of the prediction capability of the two models are still needed. As we know, the difference between CIG and slit pore is the presence or absence of C60 molecules. In this way, we can ignore other material structural factors and only consider the influence of pore volume on the prediction of the adsorption theoretical model. We choose the separation of four pairs of binary gas mixtures of N2-O2, N2-CH4, H2CH4 and H2-CO as research objects. As we know, N2-O2 separation[26,27] is highly demanded to produce the oxygen-enriched air for various industrial applications such as medical, chemical and enhanced combustion processes. An effective N2-CH4 separation technology[7,8,28] is required to meet the large energy consumption by purifying natural gas and increasing the natural gas energy content. Prior to the process of methane steam reforming, H2-CH4 separation[29,30] is widely used techniques to produce hydrogen, an alternative clean energy to reduce pollutant emissions. Hydrogen gas can also be generated 3

by a steam reforming process of naphtha. Pressure swing adsorption method for H2-CO separation[7,31] is necessary to remove the by-product, carbon dioxide. The difficulty of separating these four gas mixtures is also one reason why we chose them. N2-O2 is the most difficult to separate because of its closest potential and critical parameters[32]. The other three systems consist of very weak adsorbed H2, strong adsorbed CH4, and N2 and CO with intermediate adsorptive capacity. This combination covers all kinds of gases with different adsorption capacity, so it is more able to test the advantages and disadvantages of different adsorption models. In this work, we will use the gas mixture adsorption data calculated by molecular simulation[33] as a benchmark to measure the prediction performance of two adsorption theoretical models. Compared to experimental research, molecular simulation is a very useful tool for understanding interfacial phenomena at a microscopic level. As long as the potential energy model describing the interaction between molecules is sufficiently accurate, molecular modeling techniques can be used to extrapolate and predict the mesoscopic and macroscopic properties of products and materials from the microscopic properties of molecules. The results and conclusions obtained may be helpful for engineering modeling need that bridges the gap between the simple and sophisticated models and has predictive capability. 2. 2.1.

Methodologies Two-dimensional equation of state We use the generalized 2D EOS to fit the pure adsorption isotherms and to predict the

adsorption of gas mixture. The formula is analogous to the popular three-dimensional EOS in vapor-liquid equilibrium calculations[9,12,13]    2 A   (1  (  ) m )  RT  2  1  U  W (  )  

(1)

where A is the surface area per mass of adsorbent,  is the spreading pressure,  is the total amount adsorbed per mass adsorbent,  and  are regressed model constants, R is the gas constant, and T is temperature. The model coefficients U, W, and m must be specified to obtain a specific form of the 2D EOS, and for ZGR EOS[9,12] their values are U=W=0 and m=1/3. The following mixing rules[9,12,13] can be introduced to apply to the multi-component system:

   xi x j  ij i

(2)

j

4

   xi x j  ij

(3)

 ij  (1  C ij )( i   j ) / 2

(4)

 ij   i  j (1  Dij )

(5)

i

j

where xi and x j are the mole fractions of components i and j in the adsorbed phase, respectively, C ij and Dij are the binary interaction parameters. If binary experimental data are available, the interaction parameters can be determined and then used to predict adsorption of multi-component system. In the present work, we have explored only the case of predictive mode where C ij and Dij are both set to be zero. The adsorption equilibrium between the adsorbed and bulk phases will lead to the following equation[9,12,13],

Axi i  k i RTf i

(6)

where f i is the gas fugacity calculated by the Peng-Robinson EOS[34], ki is the model constant, denoting the slope of the pure component isotherm at the origin, and i is the fugacity coefficient in adsorbed phase, given by[9,12,13] ln i 

2  ij  j   j

 

1 m

 







1 2 m ln 1     ln Z a  m RT



ij

j

(7)

j

where Z a is the compressibility factor in the absorbed phase, Z a  A / RT . 2.2.

Ideal adsorption solution theory We use the dual-site Langmuir-Freundlich (DSLF) adsorption model[8,35] to correlate

the pure-component equilibrium data, which is given by

N 1 k1 f n1 N 2 k 2 f n2 N f   1  k1 f n1 1  k 2 f n2 

(8)

where f is the fugacity of bulk gas at equilibrium with adsorbed phase and in the unit of MPa here, Ni, ki and ni are model parameters of maximum adsorption amount at site i (i=1 or 2), the affinity constant, and the deviation from the simple Langmuir equation, respectively. Using these regressed DSLF model parameters, we can predict the multi-component adsorption by the ideal adsorption solution theory (IAST)[5]. Adsorption equilibrium reached between adsorbed and gas phases will meet the following requirement: Py i i  xi f i   

(9)

where f i  is the fugacity of the equilibrium gas phase corresponding to the spreading 5

pressure 

for the adsorption of pure gas i,  i is the gas fugacity coefficient of

component i calculated from Peng-Robinson EOS, and xi and y i are the molar fraction of component i at adsorbed and bulk phases, respectively. For each component, the spreading pressure  is constant, indicated by



f1

0

f 2

N 1  f1 d ln f1   N 2  f 2 d ln f 2 0

(10)

where the single-component adsorption amount and selectivity are determined by numerical integration and root exploration. 2.3.

Material structure and molecular simulation Figure 1 gives the structural models of slit pore and CIG materials. As shown in Figure

1a, three parallel graphite planes with equivalent interlayer spacing of 1.27 nm constitute a structural model of slit pore. For CIG material, the C60 molecules are intercalated between the parallel planes to form a hexagonal structure. The lattice constant and the distance between the centres of C60 on the same horizontal plane and two adjacent planes are observed experimentally to be 1.25 and 1.27 nm, respectively. One C60 molecule and one graphite plane with a chirality of (13,0) and a length of 3.2 nm have been reproduced by 15 and 2 times to create the structure of the CIG. Then, they are moved to the suitable positions and tailored to generate a rectangular simulation box according to the structural schematic proposed by Kuc et al.[36] Therefore, there are 1080 carbon atoms in the unit cell and the cell size is 2.5, 2.165 and 2.54 nm in x, y and z dimensions, respectively. In the simulations, it is assumed that no geometrical variation occurs for the structure of the material. All the fluid molecules are regarded as a single sphere and the classical Lennard-Jones (LJ) potential is used to calculate their interactions.[33] The potential parameters of N2, H2, CH4 and carbon atom on the materials are taken from our previous study[37]. For CO molecule, they are taken from the research of Gu et al.[31] For O2, we used the potential parameters from Bojan et al.[38,39] The size and energy parameters of adsorbates and adsorbent are given in Table 1, and the crossing interaction parameters are calculated by the Lorentz-Berthelot combining rules. We use the standard grand canonical ensemble Monte Carlo (GCMC) algorithm[33] to simulate the adsorption and separation of gases in slit pore and CIG. Periodic boundary conditions are imposed in three directions and the cut-off radius is set to half of the box size for the LJ potentials. A total number of 2×107 configurations are generated, where the first 40% configurations are discarded to guarantee the equilibrium and the others are divided into 20 blocks for ensemble average. 6

The predictions of the adsorption behavior of the gas mixture from the two-dimensional state of equation and the ideal adsorption solution theory both are based on the absolute adsorption isotherm of the pure component. However, in order to compare with the experimental data, it is necessary to convert the absolute adsorption isotherm in the simulation into an excessive adsorption amount. The absolute adsorption amount N ab obtained from GCMC simulations is converted into the excess one N ex that can be measured experimentally

N ex  N ab   bVav

(11)

where  b is the bulk density obtained by Peng-Robinson EOS[34]. and Vav is the available volume to fluid molecules calculated by a Monte Carlo integration with the reentrant surface definition[40]. The isosteric heat qst that reflects the interaction between adsorbent and fluid molecules is approximated by[35]

 U  q st  RT     N  T ,V

(12)

where R and T are the universal gas constant and temperature, and U and N are the total adsorbed energy and number of fluid particles, respectively. The adsorption selectivity in binary mixtures is defined as

 x  y j S i j   i    y i  x j

   

(13)

where the subscripts i and j denote the first and second component, and the x and y denote the molar fractions of species in adsorbed and bulk phases, respectively. 3. 3.1.

Results and discussion Adsorption of pure N2, O2, CH4, H2 and CO Figure 2 shows the excess adsorption isotherms of pure gases in slit pore and CIG at

298 K from GCMC simulations. Because of the synergistic effect of physisorption and gas compression, the adsorption isotherms except for H2 in CIG appear a maximum of uptake. As well known, physisorption dominates over gas compression at low pressures. As a result, the pore density will increase more quickly than bulk density. Oppositely, at high pressures the change of bulk density plays a more important role to affect the excess adsorption. For H2 adsorption in CIG, a similar maximum should appear if the pressure becomes large enough. For both adsorbents, the uptake of H2 is the smallest, the uptake of CO is slightly 7

higher than that of N2, and CH4 or O2 has the greatest uptake. Furthermore, CH4 is more adsorbed than O2 at low pressures but it is inverse at high pressures. For CH4 and O2, whether the weight adsorption amount or the volume adsorption amount, its value in the slit pore is more than double that of CIG, because the adsorption of these two components is mainly affected by the pore volume under high pressure. Because of the existence of C60 in CIG, its pore volume is 0.298 cm3/g, much smaller than 0.872 cm3/g of slit pore, as shown in Table S1 (see supporting information). For CO, N2 and H2, we found that their amounts of adsorption in the two materials are not very different. This is because the adsorption capacity of these gases is relatively weak and does not reach saturated adsorption, in which case both materials still can provide sufficient pore volume and surface area. Table 2 gives the maximum amount of excess adsorption and the corresponding pressure for the two materials. At 5 MPa, the maximum weight adsorption capacity and volume adsorption capacity of CH4 in the slit pore are 12.07 mmol/g and 235.3 v/v, respectively, and the maximum weight adsorption capacity and volume adsorption capacity of O2 in the slit pore at 10 MPa are respectively 10.45 mmol/g and 203.8 v/v. Obviously, the slit pore is better than the CIG for the adsorption storage of CH4 and O2, but for the other three components the slit pore is no more advantageous than the CIG material. It should be noted that the common slit pore model[41] is slightly different from that used in this paper. The former is usually used for modeling fluid adsorption on activated carbon. The same point between the two models is that the individual pore is represented as two parallel graphitic slabs separated by a distance (namely, pore width) between the centers of the surface carbon atoms. The difference lies in that in the former three graphite layers in each slab are separated by a uniform spacing, while in our slit model there is only one graphite layer in each slab. This makes the carbon density of our slit model much smaller than the common model. Moreover, for the former, the solid-fluid interaction potential for adsorbate interacting with a single graphitic slab is described by the Steele 10-4-3 potential[41]. Whereas in our slit model, the solid-fluid potential is calculated by point-topoint interaction between carbon atom in the layer and fluid molecule. In our slit model, the pore width is specified as 1.27 nm, while the actual activated carbon material has a wide pore width distribution (typically 0.7 to 1.5 nm)[42]. Even with different activated carbon materials, the amount of gas adsorbed varies greatly. For example, the excess adsorption amount for CH4 in activated carbon at 318 K and 0.55 MPa measured by Sudibandriyo et al.[12] is 1.87 mmol/g, while that at 313 K and 0.547 MPa in Wu et al.’s work[43] is 2.26 mmol/g. At 0.5 MPa and 298 K, our slit model gives a much higher excess CH4 uptake of 8

6.97 mmol/g. This situation is reasonable, because the difference of carbon density of both models results in a large difference in the amount of adsorption. Anyway, the differences in the slit models will make it difficult to make an appropriate comparison with the experimental data. In addition, we did not find gas adsorption experimental data for CIG material. Since we emphasize more about the ability of two typical thermodynamic adsorption models to predict gas separation on different material structures, no more experimental data have been presented in this paper. Figure 3 shows the isosteric heat of pure gases in slit pores and CIG material at 298 K. It can be seen from the figure that the adsorption heat of CH4 is the highest, with the values of 16-20 kJ/mol and 20-28 kJ/mol in slit pore and CIG, respectively, followed by CO, N2 and O2, and the lowest is H2. Since the C60 molecules existing between the layers increase the interaction energy between the gas molecules and the surface of the adsorbent, the heat of adsorption of each component in the CIG is significantly higher than that of the slit pore. In addition, the heat of adsorption of CO, N2, and O2 almost coincides for both materials due to their similar molecular potential energy parameters (see Table 1). Figure 4 shows the absolute adsorption isotherms from GCMC simulations and the corresponding fitting of the DSLF equation and ZGR EOS to GCMC for the slit pores and CIG. The average relative deviations (ARDs) from GCMC simulations are given in Tables 3 and 4 for slit pores and CIG, respectively. We can see that the fitting of both models is excellent. The ARDs are <1% for all pure gas isotherms, except that of 2.55% for O2 in slit pores by ZGR EOS. Clearly, the obtained DSLF and ZGR EOS parameters are suitable for the adsorption predictions of binary mixtures. 3.2.

Separation of N2-O2, N2-CH4, H2-CH4 and H2-CO binary mixtures Figure 5 shows the comparison of adsorption models with GCMC simulations for the

adsorption separation of N2-O2 at 298 K. From Figure 5a, we see that the GCMC simulated selectivity of O2 over N2 in slit pores increases slightly with the pressure, around the range of 0.85~1.11. Furthermore, their adsorption isotherms by GCMC simulations reveal that N2 is preferentially adsorbed at P<3 MPa, while O2 is preferentially adsorbed at P>3 MPa (see Figure 5b). However, the slit pores with a pore size of 1.27 nm still can’t provide a good separation ability for N2 and O2 mixture. Similar to the slit pore, the GCMC simulated selectivity in the CIG material gradually increases as the pressure (see Figure 5c). The difference is that since the C60 existing between the layers enhances the interaction between the gas molecules and the pore walls, the separation ability of the CIG material is 9

significantly higher than that of the slit pore, which selectivity is as high as 1.5 or more. This can also be verified from the large gap between the two adsorption isotherms of CIG material (see Figure 5d). It is interesting to compare the prediction ability of the two adsorption models with that of GCMC results. For slit pores (see Figure 5a), we can see that the adsorption selectivity calculated by the two adsorption models of IAST and ZGR almost coincide. However, the selectivities of both models are lower than the GCMC results at P<4 MPa and much higher than the GCMC results at P>4 MPa. From Figure 5b, we can see that the adsorption isotherms of N2 for IAST and ZGR models exhibit a maximum at near 4 MPa, and their loadings are much lower that of GCMC simulations. However, for CIG materials, the adsorption selectivity and adsorption isotherms of both models agree well with the GCMC simulations, although the selectivity of ZGR is slightly higher than the IAST results. Figure 6 compares the adsorption separation of N2-CH4 mixtures at 298 K by adsorption models with GCMC simulations. We can see that the GCMC simulated adsorption selectivity on CIG materials reach up 5-8 at the whole pressure range, which is almost double that of slit pores. However, since the presence of C60 reduces the pore volume between the layers, the adsorption amounts of the two components on CIG material are only about one third of the slit pores. For slit pores (see Figure 6a), although the adsorption selectivity predicted by IAST is higher than ZGR, the adsorption selectivity curves predicted by the two models are completely different from the GCMC results. The selectivities calculated by both models increase with increasing pressure, while the GCMC results decrease with increasing pressure. We can see from Figure 6b that the adsorption isotherms of CH4 predicted by the two models are in good agreement with the GCMC results below 4 MPa, and as the pressure continues to increase, the adsorption isotherms of the two models are higher and higher than the GCMC results. The adsorption isotherms of N2 by both models underestimates the GCMC results. Similar to the N2-O2 mixture, the two models have better predictive power in CIG materials than slit pores. From Figure 6c, we see that the both models predict the adsorption selectivity curve as the GCMC with a monotonic decrease in pressure. However, the results of IAST are almost identical to the GCMC simulation, and the adsorption selectivity predicted by ZGR is significantly higher than the IAST and GCMC results. From the adsorption isotherms in Figure 6d, we can also see that the loadings of N2 and CH4 from the ZGR model are slightly lower and slightly higher than the GCMC results, respectively. Figure 7 shows the comparison of adsorption models with GCMC simulations for the 10

adsorption separation of H2-CH4 at 298 K. It is shown that for both slit pores and CIG materials, the GCMC simulated adsorption selectivity decreases with increasing pressure. We see that the effect of pressure on the adsorption separation in CIG is more pronounced. Although the adsorption selectivity in CIG is significantly higher than that of slit pore when the pressure is less than 6 MPa, its selectivity decreases more rapidly with pressure. When the pressure is higher than 6 MPa, the adsorption selectivity in the two materials is about 15-18, which is not much different. However, the amount of methane adsorbed in the slit pores is up to 13 mmol/g, which is about three times that of CIG material. Therefore, the slit pore material under high pressure (>6MPa) is more suitable for the separation of the H2CH4 mixture. In addition, we found that the adsorption selectivity predicted by the two models in CIG is closer to the GCMC results than the adsorption selectivity in slit pores. The difference is that the IAST method in both materials overestimates the adsorption selectivity, while in CIG, the adsorption selectivity predicted by the ZGR model is almost in agreement with the GCMC results. For slit pores, the adsorption selectivity predicted by ZGR is closer to the GCMC results than IAST, but the adsorption isotherms predicted by ZGR are significantly higher than the GCMC results, and the adsorption isotherms predicted by IAST are closer to the GCMC results. For the CIG material, the IAST predicted CH4 adsorption isotherm is slightly closer to the GCMC result than the ZGR, while the IAST and ZGR predicted N2 adsorption isotherms are slightly lower and slightly higher than the GCMC results, respectively. It can be seen that the ZGR method is more suitable for the prediction of N2-CH4 adsorption separation in CIG materials. Figure 8 shows the comparison of adsorption models with GCMC simulations for the adsorption separation of H2-CO mixtures at 298 K. Similar to the N2-CH4 mixture, when the pressure is less than 4 MPa, the adsorption selectivity calculated by GCMC in the CIG material drops rapidly from 40 to about 10, while the adsorption selectivity in the slit pore decreases slowly from 14 to about 9. When the pressure is greater than 4 MPa, the effect of pressure on the adsorption selectivity in the two materials is less pronounced. In addition, for both materials, IAST predicts higher adsorption selectivity than GCMC results, but in CIG, IAST results are closer to the latter. The selectivity predicted by ZGR is higher than the GCMC results at low pressure, and slightly lower than the latter under high pressure. Overall, the adsorption selectivity predicted by ZGR is closer to and comparable to the GCMC results in slit pores and CIG material, respectively. The above situation is different from the viewpoint of the amount of adsorption. For slit pores, the H2 and CO adsorptions predicted by ZGR were higher and lower than the GCMC results, respectively, while the 11

two components predicted by IAST were lower than the GCMC results. However, the prediction by ZGR is closer to GCMC results than IAST. For CIG materials, the IASTpredicted adsorption isotherms agree well with GCMC, while the adsorption isotherms by ZGR predictions are higher than the GCMC results. Furthermore, the overestimate of H2 adsorption amount predicted by ZGR under high pressure is significantly higher than that of CO adsorption, resulting in the adsorption selectivity predicted by ZGR in Figure 8c is lower than that of GCMC results. Recently, based on Configurational-Bias Monte Carlo (CBMC) simulations, Krishna et al. summarized two different scenarios that the IAST estimations could fail[44], (1) molecular clustering caused by strong hydrogen bonding between the adsorbates, such as water/alcohol, alcohol/alcohol, and alcohol/aromatic mixtures, (2) inhomogeneous, distribution of adsorbates within the pore network, caused by preferential siting and locations of guest molecules. For the latter scenario, Krishna et al. particularly investigated the non-idealities in adsorption of CO2-bearing mixtures in cation-exchanged zeolites[45]. They found that in NaX zeolite, the inhomogeneity is a direct consequence of strong binding of CO2 with extra-framework cations, leading congregation effects around cations. In LTA zeolites, CO2 locates preferentially at the window regions, causing an inhomogeneous distribution of adsorbates. However, the gases we examined in this work have neither hydrogen bonds, nor do the carbon material models have complex pore topologies and surface ions like zeolites. Therefore, the failure of IAST prediction in our case is not within the two scenarios proposed by Krishna et al.[44] IAST and 2D-EOS were derived from different thermodynamic forms, and the assumptions of the two models are not the same. IAST assumes that the adsorbate behaves like an ideal solution, while 2D-EOS assumes that the adsorbate behaves like a three-dimensional equation of state. However, both thermodynamic models failed to predict the adsorption separation in the slit pores. A more reasonable theoretical explanation is expected for this anomalous behavior. In order to interpret the adsorption separation, we plot in Figure 9 the GCMC simulated snapshots of gas mixture in slit pore and CIG material at 298 K and 15 MPa. For the N2-O2 and N2-CH4 systems, we can see that the mole fractions of O2 and CH4 in the CIG material are evidently higher than those of the slit pores, indicating that CIG material can better separate these mixtures. In contrast, in the H2-CH4 and H2-CO systems, we did not observe evident enhance of mole fractions of CH4 and CO in CIG material. All of these observations are consistent with the changes in adsorption selectivity and adsorption isotherms in Figures 5-8. 12

In order to answer the question that which adsorption of fluid molecules on C60 spheres or 2D graphite layers plays a leading role in separation, we performed additional GCMC simulations of separation of N2 and CH4 mixture (as an example) in C60 model. As shown before, we remove the C60 molecules in the CIG model to get the slit model. Similarly, remove the 2D graphite layers, and get the C60 model. Thus, the separation capability of C60 spheres on their own is delineated, without consideration of adsorption on the intervening 2D graphite layers. Figure S1 (see Supporting Information) gives the adsorption selectivities of CH4 over N2 in C60, slit and CIG models from GCMC simulations. We can see that the adsorption selectivity of the C60 model is slightly lower than that of the slit model. Table S1 (see Supporting Information) gives the structural properties of the three models. It can be seen from Table S1 that the CIG model has the smallest pore volume, while the C60 model has the largest pore volume. We know that the larger the pore volume, the more unfavorable the separation. Figure S1 also gives the energy difference between CH4 and N2. This energy difference is equal to the sum of the interactions between the CH4 molecules and between the CH4 molecules and the wall minus the sum of the interactions between the N2 molecules and the N2 molecules and the walls. We see that the CIG model has the largest energy difference, followed by the slit model and the lowest C60 model. Clearly, the order of pore volume and energy difference of the three models is consistent with the selectivity. In addition, the adsorption selectivity of the CIG model is much higher than that of the C60 model and the slit model. This shows that the combination of C60 spheres and graphite layers makes the separation ability of CIG material greatly improved. 4.

Conclusions Grand canonical Monte Carlo (GCMC) simulations were carried out to investigate the

adsorption separation of H2, N2, O2, CO and CH4 gases in slit pores and C60 intercalated graphite (CIG). Due to the presence of C60 between the layers, the adsorption amounts of pure O2 and CH4 gases in CIG material are less than half of those in slit pore. Therefore, the slit pore is better than the CIG for the adsorption storage of CH4 and O2. For CO, N2 and H2, the amounts of adsorption in the two materials are not very different. We also found that the heat of adsorption of each component in the CIG is significantly higher than that of the slit pore, since the C60 molecules existing between the layers increase the interaction energy between the gas molecules and the adsorbent. We further performed the GCMC simulations for the equimolar mixtures of N2-O2, N2CH4, H2-CH4 and H2-CO in slit pores and CIG. It is shown that CIG presents better 13

separation ability for all the gas mixtures than slit pores. In addition, in the two materials, the adsorption selectivity of O2/N2 increases slowly with increasing pressure, and the adsorption selectivity of CH4/N2, CH4/H2 and CO/H2 decreases monotonously with increasing pressure. We correlated the pure component adsorption isotherms obtained from GCMC simulations by using the pure component 2D ZGR EOS and the dual-site LangmuirFreundlich (DSLF). The average relative deviations from GCMC simulations are lower than 2.5%, indicating that the obtained adsorption model parameters are suitable for predicting the adsorption of mixtures. We predicted the mixture adsorption by ZGR and IAST, and compared the results with those from GCMC simulations. For N2-O2 and N2-CH4 mixtures, the trend of IASTpredicted adsorption selectivity in the slit pore is completely opposite to the GCMC simulations. In CIG, the adsorption selectivity of the two mixtures predicted by IAST is in excellent agreement with GCMC simulation. In addition, the adsorption selectivity of O2/N2 predicted by ZGR in CIG is consistent with the GCMC results, while the ZGR-predicted adsorption selectivity of CH4/N2 is significantly higher than the GCMC results. For the adsorption of H2-CH4 and H2-CO in two materials, the adsorption selectivity calculated by ZGR is closer to GCMC results than IAST, while IAST significantly overestimates the adsorption selectivity. In addition, in the slit pore, the adsorption isotherms of H2 and CH4 predicted by ZGR are significantly higher than the GCMC results, while the adsorption isotherms of H2 and CO predicted by ZGR and IAST deviate significantly from the GCMC results. Acknowledgement The research work is supported by the National Natural Science Foundation of China (No.21676006) and the “CHEMCLOUDCOMPUTING” project of BUCT. REFERENCES [1] [2] [3] [4] [5]

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Table and Figure Captions Table 1. Critical properties and potential parameters of pure fluids and carbon materials. Table 2. Optimal pressures and maximum excess uptakes for pure gas adsorption in slit pore and CIG at 298 K Table 3. Regressed parameters of DSLF equation for slit pore and CIG, as well as the average relative deviation ARD% from absolute adsorption isotherms by GCMC simulations Table 4. Regressed parameters of ZGR-EOS for slit pore and CIG, as well as the average relative deviation ARD% from absolute adsorption isotherms by GCMC simulations Fig. 1. Structural models of carbon materials: (a) slit pore and (b) CIG. Fig. 2. Excess adsorption isotherms of pure gases at 298 K. (a) slit pore in unit of mmol/g, (b) CIG in unit of mmol/g, (c) slit pore in unit of v/v. (d) CIG in unit of v/v. Fig. 3. Isosteric heat versus absolute adsorption amount of pure gases at 298 K. (a) slit pore, (b) CIG. Fig. 4. Absolute adsorption isotherms of pure gases in CIG at 298 K. The open symbols are GCMC simulation results, and the solid and dashed-dotted lines are fits of the DSLF equation and ZGR EOS to GCMC simulation results, respectively. Fig. 5. Adsorption selectivities and adsorption isotherms of equimolar N2-O2 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively Fig. 6. Adsorption selectivities and adsorption isotherms of equimolar N2-CH4 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively Fig. 7. Adsorption selectivities and adsorption isotherms of equimolar H2-CH4 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively Fig. 8. Adsorption selectivities and adsorption isotherms of equimolar H2-CO mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively Fig. 9. Snapshots of equimolar gas mixture adsorption at T=298 K, P=15 MPa in slit pores and CIG, (a) N2-O2, (b) N2-CH4, (c) H2-CH4, (d) H2-CO. The grey, blue, red, green, white and yellow colours denote C, N2, O2, CH4, H2 and CO, respectively. For slit pores, the two carbon layers in top view are removed for better visualization, while for CIG all the carbon layers are removed

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Table 1. Critical properties and potential parameters of pure fluids and carbon materials fluid Tc (K) Pc (MPa) ω σ (nm) (ε/kb) (K) N2 126.2 3.4 0.038 0.3549 94.95 CH4 190.6 4.599 0.012 0.381 148.2 H2 33.19 1.313 -0.216 0.296 34.2 O2 154.6 5.043 0.022 0.3467 106.7 CO 132.9 3.499 0.048 0.3763 100.2 C 0.34 28.0

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Table 2. Optimal pressures and maximum excess uptakes for pure gas adsorption in slit pore and CIG at 298 K slit pore CIG fluid Nex Nex Nex Nex P(MPa) P(MPa) (mmol/g) (v/v) (mmol/g) (v/v) N2 3.0 4.93 96.2 5.0 3.07 107.6 CH4 5.0 12.07 235.3 3.0 4.03 141.4 H2 8.0 1.51 29.5 15.0 1.73 60.6 O2 10.0 10.45 203.8 6.0 3.88 136.1 CO 3.0 5.12 99.8 5.0 3.15 110.6

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Table 3. Regressed parameters of DSLF equation for slit pore and CIG, as well as the average relative deviation ARD% from absolute adsorption isotherms by GCMC simulations adsorbent fluid N1 k1 n1 N2 k2 n2 ARD % slit N2 7.965 1.298 0.670 2.301 0.031 0.970 0.11 CH4 8.072 0.675 0.675 11.194 1.217 0.725 0.14 H2 12.269 0.057 0.980 0.648 0.371 1.128 0.30 O2 8.367 1.121 1.003 12.534 0.098 1.088 0.11 CO 8.210 1.399 0.654 1.557 0.017 1.305 0.15 CIG N2 3.217 0.585 0.525 2.212 1.517 0.710 0.37 CH4 4.291 4.659 0.647 1.374 0.271 0.819 0.13 H2 6.939 0.067 0.965 0.063 1.249 1.723 0.32 O2 2.247 3.034 0.901 4.955 0.367 0.582 0.12 CO 4.333 1.527 0.666 1.507 0.039 0.905 0.17

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Table 4. Regressed parameters of ZGR-EOS for slit pore and CIG, as well as the average relative deviation ARD% from absolute adsorption isotherms by GCMC simulations adsorbent fluid α β lnk ARD % slit N2 4552.5 0.065 2.826 0.15 CH4 3390.1 0.033 2.938 0.88 H2 -1599.3 7.6×10-7 -2.335 0.70 O2 3309.0 0.029 1.351 2.55 CO 4300.8 0.065 3.091 0.21 CIG N2 5370.9 0.107 2.448 0.81 CH4 58.5 0.097 5.296 0.94 H2 -2937.8 2.0×10-7 -2.940 0.70 O2 5255.7 0.087 2.323 0.69 CO 4515.1 0.106 2.752 0.84

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Fig. 1. Structural models of carbon materials: (a) slit pore and (b) CIG.

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Fig. 2. Excess adsorption isotherms of pure gases at 298 K. (a) slit pore in unit of mmol/g, (b) CIG in unit of mmol/g, (c) slit pore in unit of v/v. (d) CIG in unit of v/v.

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Fig. 3. Isosteric heat versus absolute adsorption amount of pure gases at 298 K. (a) slit pore, (b) CIG.

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Fig. 4. Absolute adsorption isotherms of pure gases in slit pores (left) and CIG (right) at 298 K. The open symbols are GCMC simulation results, and the solid and dashed-dotted lines are fits of the DSLF equation and ZGR EOS to GCMC simulation results, respectively

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Fig. 5. Adsorption selectivities and adsorption isotherms of equimolar N2-O2 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively

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Fig. 6. Adsorption selectivities and adsorption isotherms of equimolar N2-CH4 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively

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Fig. 7. Adsorption selectivities and adsorption isotherms of equimolar H2-CH4 mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively

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Fig. 8. Adsorption selectivities and adsorption isotherms of equimolar H2-CO mixtures in slit pores (top) and CIG (bottom) at 298 K, where the selectivity is defined as the second component over the first one. The closed symbols are GCMC simulations and the solid and dashed-dotted lines are the predictions of IAST and ZGR EOS, respectively

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(a)

(b)

(c)

(d)

Fig. 9. Snapshots of equimolar gas mixture adsorption at T=298 K, P=15 MPa in slit pores and CIG, (a) N2-O2, (b) N2-CH4, (c) H2-CH4, (d) H2-CO. The grey, blue, red, green, white and yellow colours denote C, N2, O2, CH4, H2 and CO, respectively. For slit pores, the two carbon layers in top view are removed for better visualization, while for CIG all the carbon layers are removed.

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Highlights  Prediction performance of two-dimensional equation of state and ideal adsorption solution theory for gas mixture separation was systematically evaluated based on molecular simulation.  The adsorption and separation of N2-O2, N2-CH4, H2-CH4 and H2-CO were systematically studied, which covers various kinds of gases with different adsorption capacity.  The separation performance of two carbon materials (graphite nanofiber and C60 intercalated graphite) with only C60 difference was compared.

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Xuan Peng: Conceptualization, Investigation, Writing Qibing Jin: Resources, Funding acquisition

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