Molecular Simulation Study of the Stepped Behaviors of Gas

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Langmuir 2009, 25, 2302-2308

Molecular Simulation Study of the Stepped Behaviors of Gas Adsorption in Two-Dimensional Covalent Organic Frameworks Qingyuan Yang and Chongli Zhong* Laboratory of Computational Chemistry, Department of Chemical Engineering, Beijing UniVersity of Chemical Technology, Beijing 100029, China ReceiVed October 29, 2008. ReVised Manuscript ReceiVed December 12, 2008 In this work, grand canonical Monte Carlo simulations were performed to investigate the adsorption behaviors of three important gases (CO2, CH4 and H2) in two two-dimensional (2D) covalent organic frameworks (COFs) with different pore sizes. The simulation results show that stepped behavior is common in gas adsorption in 2D COFs, and multilayer formation is likely to be the underlying mechanism. For CO2 adsorption in 2D COFs, stepped phenomena easily occur, and the electrostatic interactions between CO2-CO2 molecules play a dominant role, while, within the temperature range studied, no stepped behaviors were found in isotherms for H2 adsorption in 2D COFs because of the too weak interactions in the systems. In addition, this work demonstrates that the stepped behaviors are highly affected by temperature, pore size, and the interaction strengths between adsorbates as well as those between adsorbates and adsorbents.

1. Introduction Knowledge of the adsorption properties of gases in nanoporous materials is a prerequisite for tailoring the performance of them as adsorbents and catalysts. Thus, the effects of confinement on adsorption and diffusion of gases in activated carbon, carbon nanotubes, zeolites, and metal-organic frameworks (MOFs) have received great attention from both fundamental and practical aspects.1-3 Unusual step occurring in the adsorption isotherms is a striking feature for gas adsorption in nanoporous media. Up to now, different mechanisms resulting in the stepped isotherms have been recognized: capillary condensation,4-6 different adsorption sites,7,8 flexible framework,9-12 multilayer formation,13 and so forth. Recently, a new class of nanoporous materials termed covalent organic frameworks (COFs) has been synthesized and structurally characterized,14-16 which retain the attracting characteristics of MOFs but have even lower crystal density. Over the past decade, although the adsorption behaviors of gases in MOFs have been * Corresponding author. Tel: +86-10-64419862; E-mail: zhongcl@ mail.buct.edu.cn. (1) Sholl, D. S. Acc. Chem. Res. 2006, 39, 403. (2) Beerdsen, E.; Dubbeldam, D.; Smit, B. Phys. ReV. Lett. 2006, 96, 044501. (3) Salles, F.; Ghoufi, A.; Maurin, G.; Bell, R. G.; Mellot-Draznieks, C.; Fe´rey, G. Angew. Chem., Int. Ed. 2008, 47, 8487. (4) Jiang, J. W.; Sandler, S. I.; Smit, B. Nano Lett. 2004, 4, 241. (5) Coasne, B.; Hung, F. R.; Pellenq, R. J. M.; Siperstein, F. R.; Gubbins, K. E. Langmuir 2006, 22, 194. (6) Morishige, K.; Tarui, N. J. Phys. Chem. C 2007, 111, 280. (7) Dubbeldam, D.; Calero, S.; Vlugt, T. J. H.; Krishna, R.; Maesen, T. L. M.; Beerdsen, E.; Smit, B Phys. ReV. Lett. 2004, 93, 088302. (8) van Baten, J. M.; Krishna, R. Microporous Mesoporous Mater. 2005, 84, 179. (9) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742. (10) Dincaˇ, M.; Yu, A. F.; Long, J. R. J. Am. Chem. Soc. 2006, 128, 8904. (11) Ramsahye, N. A.; Maurin, G.; Bourrelly, S.; Llewellyn, P. L.; Loiseau, T.; Serrec, C.; Fe´rey, G. Chem. Commun. 2007, 3261. (12) Bourrelly, S.; Llewellyn, P. L.; Serre, C.; Millange, F.; Loiseau, T.; Fe´rey, G. J. Am. Chem. Soc. 2005, 127, 13519. (13) Walton, K. S.; Snurr, R. Q. J. Am. Chem. Soc. 2007, 129, 8552. (14) Coˆte´, A. P.; Benin, A. I.; Ockwig, N. W.; O’Keeffe, M.; Matzger, A. J.; Yaghi, O. M. Science 2005, 310, 1166. (15) El-Kaderi, H. M.; Hunt, J. R.; Mendoza-Corte´s, J. L.; Coˆte´, A. P.; Taylor, R. E.; O’Keeffe, M.; Yaghi, O. M. Science 2007, 316, 268. (16) Coˆte´, A. P.; El-Kaderi, H. M.; Furukawa, H.; Hunt, J. R.; Yaghi, O. M. J. Am. Chem. Soc. 2007, 129, 12914.

increasingly understood,17-23 the investigations of gas adsorption in COFs are still limited. For example, Garberoglio assessed the adsorption and diffusion of several light gases in COFs using molecular simulations.24,25 On the basis of the first principles calculations, Schmid and Tafipolsky developed a force field to perform the strain energy analysis of COF-102 material.26 Klontzas et al. performed a multiscale theoretical investigation to study the H2 storage in several three-dimensional (3D) COFs.27 However, no studies have been carried out to investigate the stepped behaviors of gas adsorption in COFs. Since unusual behaviors in the isotherms usually occur in confined space with larger pore sizes, in this work, molecular simulations were performed to study the adsorption behaviors of three important gases (CO2, CH4 and H2) in two two-dimensional (2D) COFs (COF-8 with pore diameter of 16.4 Å and COF-10 with pore diameter of 31.7 Å),16 in which particular attention was paid to the stepped behaviors. We select these three gases because CO2 is a greenhouse gas mainly causing the climate change, CH4 is the main component of natural gas, and H2 is a clean energy carrier. On the other hand, the two 2D COFs have different pore sizes, allowing us to examine the effect of pore size on the adsorption behaviors. The results obtained in this work not only can scientifically enrich the knowledge of gas adsorption in COFs, but also may contribute to technologically improve the design efficiency of COFs for practical applications in CO2 capture as well as CH4 and H2 storage. (17) Chen, B.; Zhao, X.; Putkham, A.; Hong, K.; Lobkovsky, E. B.; Hurtado, E. J.; Fletcher, A. J.; Thomas, K. M. J. Am. Chem. Soc. 2008, 130, 6411. (18) Yang, Q.; Zhong, C. J. Phys. Chem. B 2005, 109, 11862. (19) Frost, H.; Du¨ren, T.; Snurr, R. Q. J. Phys. Chem. B 2006, 110, 9565. (20) Liu, J.; Lee, J. Y.; Pan, L.; Obermyer, R. T.; Simizu, S.; Zande, B.; Li, J.; Sankar, S. G.; Johnson, J. K. J. Phys. Chem. C 2008, 112, 2911. (21) Han, S. S.; Deng, W.; Goddard III, W. A. Angew. Chem., Int. Ed. 2007, 46, 6289. (22) Zhao, X. B.; Xiao, B.; Fletcher, A. J.; Thomas, K. M.; Bradshaw, D.; Rosseinsky, M. J. Science 2004, 306, 1012. (23) Walton, K. S.; Millward, A. R.; Dubbeldam, D.; Frost, H.; Low, J. J.; Yaghi, O. M.; Snurr, R. Q. J. Am. Chem. Soc. 2008, 130, 406. (24) Garberoglio, G. Langmuir 2007, 23, 12154. (25) Garberoglio, G.; Vallauri, R. Microporous Mesoporous Mater. 2008, 116, 540. (26) Schmid, R.; Tafipolsky, M. J. Am. Chem. Soc. 2008, 130, 12600. (27) Klontzas, E.; Tylianakis, E.; Froudakis, G. E. J. Phys. Chem. C 2008, 112, 9095.

10.1021/la8035902 CCC: $40.75  2009 American Chemical Society Published on Web 01/20/2009

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Figure 1. Crystal structures of the 2D COFs used in the simulation: (a) COF-8, (b) COF-10. (B, pink; O, red; C, gray, and H, white). Table 1. Structural Properties for the 2D COFs Studied in This Work material

unit cell (Å)

cell angle (degree)

dporea (Å)

Fcrysa (g/cm3)

Vfreeb (cm3/g)

porosityb (%)

COF-8 COF-10

a ) b ) 22.7331, c ) 3.4764 a ) b ) 37.8099, c ) 3.4763

R ) β ) 90, γ ) 120 R ) β ) 90, γ ) 120

16.4 31.7

0.698 0.447

0.93 1.74

64.6 77.7

a

Obtained from the XRD crystal data.16

b

Calculated with the Materials Studio package.28

Table 2. LJ Potential Parameters for CO2, CH4, H2, and the 2D COFs Used in This Work atom/molecule

σ (Å)

ε/kB (K)

CO2_O CO2_C CH4 H2 COF_B COF_C COF_H COF_O

3.05 2.80 3.73 2.958 3.64 3.43 2.57 3.12

79.0 27.0 148.0 36.7 90.58 52.84 22.14 30.19

2. Models and Simulation Method 2.1. COF Structures. In this computational study, the guestfree framework structures of the two selected 2D COFs were constructed from their corresponding experimental single-crystal X-ray diffraction (XRD) data16 using the Materials Studio Visualizer28 (see Figure 1). As shown in Figure 1, for both of the 2D COFs, the trigonal-planar building blocks of 2,3,6,7,10,11hexahydroxytriphenylene (HTTP) are covalently linked by different organic boronic acid linkers, i.e., 1,3,5-benzenetris(4phenylboronic acid) (BTPA) in COF-8, and 4,4-biphenyldiboronic acid (BPDA) in COF-10. Linking the trigonal-planar building blocks in this manner gives planar hexagonal sheets, and these sheets stack in eclipsed structures to form the hexagonally aligned one-dimensional (1D) pore along the z direction. The frameworks of both 2D COFs are periodic in all three dimensions. Details of the structural properties for these two 2D COFs are summarized in Table 1. The total free volume (Vfree) of each 2D COF material was estimated using the “Atoms Volume & Surfaces” calculation within the Materials Studio package,28 where a probe size of 0.0 Å was applied to determine the total free volume not occupied by the framework atoms. It should be noted that this method of calculating free volume, as done by others,19 is based solely on the system geometry. 2.2. Force Fields. In this study, CO2 was modeled as a rigid linear molecule with three charged Lennard-Jones (LJ) sites located on each atom. A combination of the site-site LJ and Coulombic potentials was used to calculate the CO2-CO2 intermolecular interactions. The LJ potential parameters for atoms O and C in CO2 molecule are taken from the TraPPE force field,29 and listed in Table 2. The C-O bond length is 1.16 Å. (28) Accelrys, Inc. Materials Studio, 3.0 V.; Accelrys Inc: San Diego, CA, 2003. (29) Potoff, J. J.; Siepmann, J. I. AIChE J. 2001, 47, 1676.

In this model, partial point charges centered at each LJ site (qO ) -0.35 e and qC ) 0.70 e) approximately represent the firstorder electrostatic and second-order induction interactions. A single LJ interaction site model was used to describe a methane molecule, and the potential parameters were also taken from the TraPPE force field,30 as listed in Table 2. In the case of the H2 molecule, to take into account quantum effects on its adsorption, the fluid-fluid and fluid-solid interaction potentials were described by the quadratic FeynmanHibbs (FH) effective potential,11,20

UFH ) ULJ(r) +

[



2ULJ(r) p2  ULJ (r) + 24µkBT r

]

(1)

where ULJ denotes the classical LJ potential, r is the moleculemolecule distance, p is Planck’s constant divided by 2π, and the prime and double prime denote the first and second derivatives with respect to r, respectively. The second term in eq 1 is the quantum correction, the parameter µ is the reduced mass: µ ) m/2 for H2-H2 interaction, and µ ) m for H2-adsorbent, where m is the mass of the H2 molecule. The LJ parameters for H2 were taken from the work of Darkrim and Levesque,31 which are also listed in Table 2. For the 2D COFs studied here, an atomistic representation was used to model both of them, and the adsorbate-adsorbent interaction is only represented by classical LJ potential with eq 1 used for H2-adsorbent interaction. The potential parameters for the framework atoms in 2D COFs were taken from the universal force field (UFF),32 as listed in Table 2. The above sets of force fields have been widely used to study the adsorption behaviors in MOFs for the gases considered in this work.33-35 In our simulations, all the LJ cross interaction parameters were determined by the Lorentz-Berthelot mixing rules.

2.3. Simulation Details Grand canonical Monte Carlo (GCMC) simulations were employed to study the adsorption of gases in 2D COFs. Details (30) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (31) Darkrim, F.; Levesque, D. J. Phys. Chem. B 2000, 104, 6773. (32) Rappe´, A. K.; Casewit, C. J.; Colwell, W. A.; Goddard, K. S., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024–10035. (33) Keskin, S.; Sholl, D. S. J. Phys. Chem. C 2007, 111, 14055. (34) Du¨ren, T.; Sarkisov, L.; Yaghi, O. M.; Snurr, R. Q. Langmuir 2004, 20, 2683. (35) Garberoglio, G.; Skoulidas, A. I.; Johnson, J. K. J. Phys. Chem. B 2005, 109, 13094.

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Figure 2. Adsorption isotherms of CO2 in the two 2D COFs.

on the method can be found elsewhere.36 The simulation box representing each COF contains 40 (2 × 2 × 10) unit cells. The simulations with larger boxes showed that no finite-size effects existed using the above boxes. Similar to previous works,18-21,24,25 both of the studied 2D COFs were treated as rigid frameworks, with atoms frozen at their crystallographic positions during simulations. A cutoff radius of 17.0 Å was applied to the LJ interactions, and the long-range electrostatic interactions were handled using the Ewald summation technique.36 Periodic boundary conditions were applied in all three dimensions. Gasphase fugacities used to perform GCMC simulations were calculated with the Peng-Robinson equation of state. Note that, in a real adsorption experiment, the adsorbate is introduced progressively to be adsorbed in the previously outgassed porous sample. Thus, an empty box was used as the starting point of the simulation at very low pressure. The pressure of the gas reservoir is then increased by steps to calculate the whole adsorption isotherm. For each step, the initial configuration is the final configuration of the preceding step. To increase the computational efficiency, the potential energies between an adsorbate and the adsorbent were initially tabulated on a series of 3D grid points with grid spacing 0.15 Å. During the simulations, the potential energy at any position in the adsorbent was determined by interpolation.37 For each state point, GCMC simulation consisted of 1.5 × 107 steps to guarantee equilibration followed by 1.5 × 107 steps to sample the desired thermodynamic properties.

3. Results and Discussion 3.1. Adsorption of CO2 in 2D COFs. 3.1.1. Adsorption Isotherms of CO2 in 2D COFs. The simulated isotherms for CO2 adsorption at four temperatures in COF-8 and COF-10 are shown in Figure 2. As can be seen from Figure 2a, the isotherms for CO2 in COF-8 show remarkable steps at T ) 185 and 195 K, and the unusual step is much steeper in the former. As the temperature increases, the step is dramatically reduced. Figure 2b illustrates that, for CO2 adsorption in COF-10, the dependency of stepped behavior on temperature shows a trend similar to that presented in Figure 2a. Because of the larger pore size of COF10 (see Table 1), the pressure at which the step occurs is higher in COF-10 than that in COF-8 for a given temperature. Furthermore, at T ) 205 K, the step in the isotherm of CO2 adsorption in COF-10 is much steeper than that in COF-8, which also results from the larger pore size in the former. In addition, we have also examined the CO2 adsorptions in COF-8 and COF10 at room temperature, and no stepped isotherms are observed (36) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Academic Press: San Diego, 2002. (37) Liu, B.; Yang, Q.; Xue, C.; Zhong, C.; Chen, B.; Smit, B. J. Phys. Chem. C 2008, 112, 9854.

in both materials. Thus, the above observations indicate that both temperature and pore size have significant effect on the stepped behavior in the isotherm of gas adsorption in 2D COFs. Similar observations have also been found for CO2 adsorption in IRMOFs.13 Finally, it should be pointed out that because the pore diameter of COF-10 (31.7 Å) is approximately 2 times of that of COF-8 (16.4 Å), the simulated isotherm for COF-10 at 215 K corresponds to that of COF-8 in a much lower pressure range at the same temperature. Upon further increasing pressure, the shapes of the isotherms in the two materials will be similar at this temperature. 3.1.2. Mechanism for the Stepped BehaViors of CO2 Adsorption in 2D COFs. As mentioned previously, several mechanisms have been identified that result in stepped isotherms. The mechanism of different adsorption sites has been found to result in stepped isotherms for the adsorption of alkanes in silicate, a 3D pore system with straight parallel channels intersected by zigzag channels, which is directly related to the presence of intersections in silicate.7,8 Compared with the structure of silicate, the 2D COFs considered in this work only have aligned 1D pores with large pore sizes, and thus this type of mechanism can be excluded. In addition, since the frameworks of 2D COFs are kept rigid in our simulations, the origin of flexible frameworks for the stepped isotherms also can be eliminated. Thus, it is logical to examine whether capillary condensation occurs that causes the stepped isotherms of CO2 adsorption in the 2D COFs. To illustrate this, desorption isotherms were further simulated for CO2 adsorption in COF-8 and COF-10 at two temperatures, and the results are shown in the Figure 3. Clearly, although the adsorptions of CO2 in both 2D COFs display a type IV isotherm, the simulated adsorption isotherms are not observed to be accompanied with hysteresis. Since capillary condensation is the first-order phase transition, and usually accompanied with hysteresis,38 we can exclude the effect of capillary condensation that causes the stepped isotherms in the temperature range examined in this work. To understand the origin of the stepped phenomenon observed, the snapshots at four state points (A, B, C, D; see Figure 4a) for CO2 molecules adsorbed in COF-8 at T ) 185 K were examined, as shown in Figure 4b. Evidently, at low coverage, molecules are adsorbed near the wall (see state point A in Figure 4b). With the increase of loading, the snapshots show a gradually layering of CO2 molecules near the wall, and at P ) 0.005 MPa (see state point C in Figure 4b), a full monolayer is well defined, and some molecules appears in the place near the first layer. With slightly increasing pressure (see state point D in Figure 4b), the inner space of the pores is filled with CO2 molecules. The snapshots for CO2 molecules adsorbed in COF-10 at T ) 185 K are shown in Figure 5, and a similar sequence for CO2 adsorption was (38) Morishige, K.; Tarui, N. J. Phys. Chem. C 2007, 111, 280.

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Figure 3. Isotherms of CO2 adsorption and desorption in the two 2D COFs.

Figure 4. (a) The examined four state points (A, B, C, D) for CO2 adsorption in COF-8 at T ) 185 K. (b) Snapshots for CO2 molecules adsorbed in COF-8 at the examined four state points.

observed. In addition, it also can be found in Figure 5 that a second layer is formed before the inner space of the pores finally filled with CO2 molecules. Thus, we can conclude that the steps occurring in the isotherms are caused by the mechanism of multilayer formation. A similar conclusion has also been obtained for N2 adsorption in IRMOF-16 at 77 K.13 In order to understand the above stepped isotherms in more detail, the local density profiles for the center of mass (COM) of CO2 molecules adsorbed in COF-8 at T ) 185 K were selected as an example to analyze. The hexagonally 1D pore of COF-8 is roughly divided into 200 concentric cylindrical layers along the radial direction, and the local density in each layer is calculated by F(r) ) 〈dN〉/(2πLr∆r), where r is radial distance from the pore center, 〈dN〉 is the ensemble average of the number of adsorbate molecules in a layer located in r to r + dr, L is the length of the simulation box along the z direction, and the denominator is the volume of this layer. Obviously, the results presented in Figure 6 are in good agreement with the snapshots shown in Figure 4b, which further confirmed that multilayer formation is the mechanism for the stepped isotherms at our examined temperatures. In addition, we have calculated the CO2

densities in the pores of the two COFs at state point D shown in Figures 4a and 5a, and found the densities are 0.91 g/cm3 in COF-8 and 1.11 g/cm3 in COF-10, which are close to the saturated liquid density (1.23 g/cm3).39 3.1.3. Origin of the Forces Inducing the Stepped BehaViors. In our simulation, the intermolecular force between CO2 molecules results from the combination of van der Waals and electrostatic interactions. Thus, the effects of CO2-CO2 electrostatic interactions on the stepped behaviors of CO2 adsorption at T ) 185 and 195 K were further considered. To examine these effects, additional simulations were performed to study the CO2 adsorptions in the two 2D COFs by switching off the CO2-CO2 electrostatic interactions, and the simulated adsorption isotherms are shown in Figure 7. A comparison with the results in Figure 2 clearly indicates that the CO2-CO2 electrostatic interactions have significant effects on CO2 adsorptions, which are essential for the steps occurred in the adsorption isotherms. 3.2. Adsorption of CH4 in 2D COFs. 3.2.1. Adsorption isotherms of CH4 in 2D COFs. Figure 8 shows the simulated (39) Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509.

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Figure 5. (a) The examined four state points (A, B, C, D) for CO2 adsorption in COF-10 at T ) 185 K. (b) Snapshots for CO2 molecules adsorbed in COF-8 at the examined four state points.

Figure 6. The local density profiles for CO2 molecules adsorbed in the pore of COF-8 at T ) 185 K.

adsorption isotherms of CH4 in COF-8 and COF-10 at three temperatures, as a function of pressure. As can be seen from this figure, the effects of temperature on the stepped behavior in the isotherms are similar to those shown in Figure 2. For CH4 adsorption in COF-8, although the simulated temperatures are lower than those considered for CO2 adsorptions in the same

material, the steps that occurred are far less remarkable than those shown in Figure 2, which is caused by the weaker interactions between CH4-CH4 molecules as well as CH4-sorbent. However, for CH4 adsorption in COF-10 with larger pore size, pronounced steps can occur in the adsorption isotherms, as shown in Figure 8b. This observation also indicates that pore size has great effect on the stepped isotherms of CH4 adsorption in 2D COFs. In addition, we have also simulated the desorption isotherms, and no hysteresis was found to accompany with the adsorption isotherm in each 2D COF material at the examined temperatures. 3.2.2. Mechanism for the Stepped BehaViors of CH4 Adsorption in 2D COFs. To analyze the adsorption behavior of CH4 adsorption in COF-8, the local density profiles at five state points in the isotherm given in Figure 9 a were calculated as shown in Figure 9b. It can be found in Figure 9b that, at state point A where the loading is very low, the molecules are only adsorbed near the wall, and a full monolayer near the wall is formed at state point B. As pressure increases, the second layer begins to form (state point C), while at the pressure corresponding to state point D, the local density in the second layer continues to increase,

Figure 7. Isotherms of CO2 adsorption in 2D COFs without considering the electrostatic interactions between CO2 molecules.

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Figure 8. Isotherms of CH4 adsorption in 2D COFs.

Figure 9. (a) The examined five state points for CH4 adsorption in COF-8, and (b) the local density profiles for CH4 molecules adsorbed in the pore of COF-8 at the five state points.

Figure 10. (a) The examined four state points (A, B, C, D) for CH4 adsorption in COF-10 at T ) 100 K. (b) Snapshots for CH4 molecules adsorbed in COF-10 at the examined four state points.

and some molecules also start to adsorb in the pore centers; with further increasing pressure (see state point E), more and more CH4 molecules are filled in the pore center. On the basis of these local density profiles, it can be argued that CH4 molecules are more inclined to gradually fill the pore spaces of COF-8, which results in no remarkable steps occurring in the isotherm of CH4 adsorption in this material.

Because remarkable step occurred in the isotherm of CH4 adsorption in COF-10 at T ) 100 K (see Figure 8b), the adsorption mechanism was analyzed using the snapshots at the four state points shown in Figure 10a.The snapshots given in Figure 10b clearly indicate that the stepped isotherm is also caused by multilayer formation. Similar to the results shown in Figure 5 for CO2 adsorption in COF-10, two layers are also formed before

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Figure 11. Isotherms of H2 adsorption in COF-8 and COF-10.

Figure 12. Influence of quantum effects on H2 adsorption in 2D COFs.

the pores are finally filled with CH4 molecules. In addition, because CH4 is approximately spherical and described by a single LJ site in this work, the more regular packing effect results in more distinct two layers for the adsorbed CH4 molecules than those for the adsorbed CO2 molecules (see Figure 5b). 3.3. Adsorption of H2 in 2D COFs. Figure 11 shows the simulated isotherms of H2 adsorption in the two 2D COFs at T ) 50 and 100 K, as a function of pressure. Clearly, all of the isotherms do not show stepped behaviors. Since quantum effects are considered with FH effective potential to obtain the results shown in Figure 11, additional simulations were further performed without considering quantum corrections in eq 1. The calculated results (denoted by classical) are shown in Figure 12, where the results in Figure 11 (denoted by FH-QM) are also included for comparison. Obviously, no steps occurred regardless of whether the quantum effect is considered. In addition, Figure 12 also shows that the quantum effect on H2 adsorption in 2D COFs is significant at low temperatures, which becomes less evident with increasing temperature. To study the origin of the absence of steps in the isotherms of H2 adsorption in the two COFs, we examined the adsorption snapshots at different loadings; it is found that the microscopic mechanism is dominated by the gradual pore filling instead of multilayer formation, which is similar to that of N2 adsorption in IRMOF-1 at 77 K.13

4. Conclusion The simulation results show that stepped behavior in adsorption isotherms is common in 2D COFs, and multilayer formation is likely to be the underlying mechanism for temperatures higher than that at which capillary condensation occurs. This work shows that stepped behaviors are dramatically reduced with increasing temperature, and, for CO2 adsorption, the electrostatic interactions between CO2-CO2 molecules play a dominant role for the stepped behaviors in isotherms; within the temperature range studied, no stepped behaviors were found in isotherms for H2 adsorptions in 2D COFs because of the too weak interactions between H2 molecules as well as those between H2 and the frameworks of 2D COFs. In addition, the present work demonstrates that the pore size of 2D COFs has important effect on the steps occurring in the adsorption isotherms, and the step behavior becomes steeper with the increase of pore size at a given temperature. The knowledge obtained in this work is helpful for understanding the adsorption behaviors of gases in COFs that provide useful information for guiding the future design of new COFs with improved gas capture and storage capacity. Acknowledgment. The financial support of the NSFC (Nos. 20725622, 20706002, 20876006) is greatly appreciated. LA8035902