Theoretical Prediction of High Pressure Methane Adsorption in Porous

Article pubs.acs.org/Langmuir

Theoretical Prediction of High Pressure Methane Adsorption in Porous Aromatic Frameworks (PAFs) Maurizio Cossi,* Giorgio Gatti, Lorenzo Canti, Lorenzo Tei, Mina Errahali, and Leonardo Marchese Dipartimento di Scienza e Innovazione Tecnologica (DISIT), Centro Interdisciplinare Nano-SiSTeMI, Università del Piemonte Orientale, via T. Michel 11, I-15100, Alessandria, Italy ABSTRACT: The adsorption isotherms of methane in four micro- and mesoporous materials, based on the diamond structure with (poly)phenyl chains inserted in all the C−C bonds, have been simulated with Grand Canonical Monte Carlo technique. The pressure range was extended above 250 bar and the isotherms were computed at 298, 313, and 353 K, to explore the potentiality of these materials for automotive applications, increasing the capacity of high-pressure tanks or storing a comparable amount of gas at much lower pressure. The force field employed in the simulations was optimized to fit the correct behavior of the free gas in all the pressure range and to reproduce the methane−phenyl interactions computed at high quantum mechanical level (post Hartree−Fock). All the examined materials showed a high affinity for methane, ensuring a larger storage of gas than simple compression in all the conditions: two samples exceeded the target proposed by U.S. Department of Energy for methane storage in low-pressure fuel tanks (180 cm3 (STP)/cm3 at 35 bar and room temperature).

1. INTRODUCTION Nanostructured porous materials are raising considerable interest in the field of gas storage and separation, since they promise to substantially increase the capacity of fuel tanks and static storage systems, and to improve the performance of the molecular sieves used in the separation of gas mixtures. One of the approaches proposed to control the greenhouse effect is based on Carbon Capture and Storage, for which the availability of stable adsorbents with high affinity for carbon dioxide and, to a lesser extent, for methane is an essential ingredient. On the other hand, the use of methane as a cleaner fuel (thanks to its carbon to hydrogen ratio lower than in any other fossil fuel) is spreading worldwide, and hydrogen is expected to be a major breakthrough in this field, when the problems related to its large-scale production and distribution will be solved effectively. Presently, methane is used as a fuel in the form of compressed natural gas (CNG), actually a mixture with small amounts of heavier gaseous hydrocarbons: to ensure a convenient range, high-pressure tanks are needed, in which CNG is compressed up to 200−250 bar, with a storage of 9.8− 11.7 mol/L (0.157−0.188 kg/L), respectively. There is a strong need for efficient adsorbents for methane,1−3 able to substantially increase the loading at high pressures, thus improving the capacity of the existing tanks, or to reduce the operating pressure at the same gas loading, in both cases with an important economic impact. For the latter case, the U.S. Department of Energy (DOE) has proposed a methane storage target of 180 cm3 (STP)/cm3, corresponding to 127 mg/cm3, at 35 bar and room temperature.4,5 (Note: The literature is somehow confusing about this target: the value was set in 1997 to 150 cm3 (STP)/cm3,4 and updated to 180 three years later,5 though some authors kept reporting the former value.6−8 Moreover, in some papers, including ref 5, the standard conditions are defined as 1 atm and 298 K, while IUPAC © 2012 American Chemical Society

recommends 1 bar, 273 K. We use the higher value (180 v/v) and the IUPAC STP definition, which lead to the most severe requirement for the storage target, as reported in the text.) In this paper, we explore theoretically the ability of a newly developed class of materials, namely, porous aromatic frameworks (PAFs),9−12 to adsorb gaseous (supercritical) methane at pressures ranging from 1 to ca. 280 bar (i.e., fugacities of 1−200 bar) and temperatures from 298 to 353 K, according to the standard requirements of the automotive industry. PAFs can be modeled starting from the diamond structure, and replacing each C−C covalent bond with one or more phenyl rings. As illustrated in Figure 1, the resulting solids maintain the tridimensional structure of diamond (though lowering the local symmetry to P1 group) with a huge increase of the empty space inside the aromatic backbone, where a network of micro- or mesopores is formed. Despite the novelty of this class of materials, different naming rules have already been proposed for its members, even by the authors who have first described them; in this paper, we adopt the convention proposed in ref 10 to call the materials PAF30n, where n is the number of phenyl rings inserted in the C−C bonds. Monte Carlo simulations with purposely adapted force fields predicted very high microporous surface area for the first elements of the series, PAF-301 and PAF-302: 1880 and 5640 m2/g (BET) or 2350 and 7000 m2/g (Langmuir), respectively.9 These simulations indicated that PAF-302 has one of the highest specific surface areas measured so far for microporous materials; the successive members of the family are expected to have larger and larger surface areas, but due to their wider pores, they fall in the class of mesoporous materials. Received: May 30, 2012 Revised: August 28, 2012 Published: August 30, 2012 14405

dx.doi.org/10.1021/la302195m | Langmuir 2012, 28, 14405−14414

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Figure 1. Top to bottom: aromatic building block, tridimensional structure of the unit cell, and skeletal volume defined as a collection of atomic spheres by the GEPOL procedure for the PAF-30n, n = 1−4. Some structural properties of the PAF-30n models were estimated using the GEPOL procedure,18 implemented in G03 as a part of the Polarizable Continuum Model of solvation.19,20 GEPOL approximates the molecular volume and surface with the envelope of spheres centered on the atoms, and provides a realistic description of the actual molecular shape and size. In the present work, we used atomic radii of 1.7 and 1.2 Å for C and H atoms, respectively; no additional spheres were added, though GEPOL allows this feature to smooth the molecular surface when needed. The methane adsorption isotherms were simulated using the Sorption module included in Materials Studio package,21 in a series of Grand Canonical Monte Carlo (GCMC) simulations.22 Three force fields (FF) provided by Materials Studio were tested, namely, CVFF,23 PCFF,24 and COMPASS:25 finally, the isotherms were computed with a modified version of CVFF, where the Lennard-Jones parameters for nonbonded interactions of H and sp3 and sp2 C atoms were adjusted to fit experimental and ab initio data.

Among the series, only PAF-302 (i.e., the system with biphenyl chains inserted in the diamond structure) has been synthesized and characterized so far. Ben et al. reported the synthesis,9 and found a very good agreement between simulated and experimental properties (porosity, surface area, density) of PAF-302, indicating an almost ideal crystalline reaction product. The same authors measured the adsorption of hydrogen and carbon dioxide in PAF-302,10,11 finding an excess adsorption of 0.075 g/g at 48 bar, 77 K for H2, and 1.3 g/g at 40 bar, 298 K for CO2. These values compare well with the best performing adsorbent materials developed so far and justify the great interest in this class of porous solids; another point of enormous practical interest is the very high thermal and chemical stability exhibited by PAF-302 (and likely shared by other members of the family). Some tests of adsorption were performed also for methane in PAF-302, as well as in strictly related compounds (in which the tetrahedral carbon atoms linking the biphenyl chains were substituted by Si and Ge): though these experiments were limited to low pressures (below 1 bar), they showed a good affinity for methane for these adsorbers, in particular, when the central atom is silicon.11 The chemical structure of these materials, along with their exceptionally high surface area and stability, indicate them as very promising adsorbents for methane even at the high pressures required by the technological applications mentioned above: this prompted us to perform a systematic theoretical study, to simulate the adsorption properties of PAF-30n (n = 1−4) at various temperatures, to devise the most suitable materials and possibly orient the synthesis of methane adsorbents.

3. RESULTS AND DISCUSSION 3.1. Models of PAF-30n. In Figure 1, we show the molecular building blocks, CH3−(Ph)n−CH3 with n = 1−4, used to model the aromatic frameworks. Their structures were optimized at the BLYP, B3LYP, and MP2 levels, with 631G(d,p) basis set, obtaining geometrical parameters very similar with all the methods, except the ring−ring dihedral (twist) angle for n = 2−4. For instance, the dihedral angle in 4,4′-dimethylbiphenyl (PAF-302 in Figure 1) was predicted at 36°, 37°, and 43° by BLYP, B3LYP, and MP2, respectively, while the experimental value is 44.4 ± 1.2° for gas-phase biphenyl.26 The MP2 level confirms the most reliable, and it was chosen for all the successive ab initio calculations, in agreement with previous modeling of polyaromatic frameworks.9,10 To check the stability of results, the MP2 optimization of 4,4′-dimethylbiphenyl was repeated with a larger basis set, namely, 6-311+G(d,p), with negligible variations of the geometrical parameters. The methane molecule was also optimized at the MP2/6-31G(d,p) level.

2. METHODS Ab initio calculations were performed at the DFT level, with BLYP13,14 and B3LYP15 DFT functionals and at the Møller−Plesset second-order perturbation theory (MP2) level, with the 6-31G(d,p) and 6311+G(d,p) basis sets,16 using the Gaussian03 (G03) package.17 14406


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Table 1. Structural and Textural Properties of Crystalline PAF-30n Models

PAF301 PAF302 PAF303 PAF304 a

unit cell length, L (Å)

unit cell formula

unit cell molecular weigth (g mol−1)

density (g cm−3)

specific volume, Vsp (cm3 g−1)

unit cell skeletal volume, Vsk (Å3)

porous volume fractiona

specific porous volume (cm3 g−1)b

specific surface area (m2 g−1)

13.450

C104H64

1312

0.895

1.12

1299

0.47

0.53

5150

23.440

C200H128

2528

0.326

3.07

2483

0.81

2.48

5519

33.379

C296H192

3744

0.167

5.99

3679

0.90

5.39

5626

43.318

C392H256

4960

0.101

9.90

4861

0.94

9.31

5692

f pore = (L3 − Vsk)/L3. bVsp,pore = f pore × Vsp.

calculations were performed at the MP2/6-311+G(d,p) level: the optimized structures are shown in Figure 2, and the computed binding energies are listed in Table 2.

PAF-30n models were built starting from the diamond structure: the standard CIF file was modified by lowering the point symmetry to P1 and increasing the cubic cell edge, so that the neighboring C−C distance matched exactly the distance between the methyl groups in the optimized molecules. Then, the optimized polyphenyl fragments (without the methyl groups) were inserted between each couple of neighboring C−C, and the fragments were rigidly rotated to eliminate all the close contacts between hydrogen atoms. The structural properties of the PAF-30n models are listed in Table 1: the skeletal volume and the effective surface area were estimated by the GEPOL procedure implemented in G03, which is used in another context to define the solute−solvent boundary in polarizable continuum models. Increasing the number of aromatic rings, the PAF density decreases: the values reported in Table 1 are referred to ideal crystalline materials, and can be used as a benchmark to evaluate the degree of crystallization in actual syntheses. The porous fraction grows markedly along the series; however, the pore size also increases, as shown by the largest atom−atom distance inside the pores, passing from 9.9 Å for PAF-301 to 19.6, 27.1, and 34.4 Å for the other members: thus, while PAF301 and PAF-302 can be considered microporous materials, the others are better described as mesoporous. Ben et al. have modeled the first three members of the series and synthesized PAF-302:9 they predicted very similar porous volume fractions (0.41, 0.78, and 0.88 for PAF-301, 302 and 303, respectively) with a different approach, i.e., simulating the adsorption of gaseous H2. They also simulated the adsorption of N2, to estimate the BET surface area of PAF-301 and 302, and found 1880 and 5640 m2/g, respectively. The latter value agrees very well with the GEPOL result reported in Table 1, while for PAF-301, the two approaches provide very different values: this is probably due to the small size of the PAF-301 pores, which does not allow the formation of N2 monolayers. One can observe that GEPOL specific surface areas grow very slowly along the series: in fact, both the unit cell surface area and molecular weight grow almost linearly when a new phenyl ring is added to the aromatic chains, and the two effects balance in the definition of specif ic areas. 3.2. Methane/Aromatic Interactions. Alkanes are known to interact quite favorably with aromatic systems,27 though the nature of this interaction (arising from weak hydrogen bonds or mainly from dispersion forces) is actually debated. To evaluate the energetics of the methane/aromatic bond in the systems under study, we performed some test calculations on small clusters, formed by one CH4 molecule and 1,4-dimethylbenzene (I), 4,4′-dimethylbiphenyl (II), bis-p-tolylmethane (III), and bis-(4′-methylbiphenyl)methane (IV), representing with increasing detail the local environment in PAF lattices. The

Figure 2. Methane/aromatic clusters optimized at MP2/6-311+G(d,p) level. I: CH4/1,4-dimethylbenzene. II: CH4/4,4′-dimethylbiphenyl. III: CH4/bis-ptolylmethane. IV: CH4/bis-(4′-methylbiphenyl)methane.

Table 2. Binding Energies (kJ/mol) Computed for the Clusters Shown in Figure 2a De

I

II

III

IV

8.51

9.68

13.24

15.20

a De defined as the negative of the methane/aromatic interaction energy, without vibrational zero point energy. Counterpoise correction to BSSE included.

In all clusters, the CH4 molecule binds quite strongly to the aromatic rings: in cluster I, with 1,4-dimethylbenzene, one C− H bond points directly toward the ring plane, while in the other structures, one or two aliphatic C−H bonds form angles ranging from 50° to 60° with the rings, pointing approximately toward aromatic carbon atoms. It is well-known that the C−H orientation in methane clusters with benzene and substituted benzenes depends quite critically on the calculation level, and in particular on the size of the basis set.28,29 On the other hand, the potential energy surface is very shallow in these clusters, so that the orientation of the C−H has a very limited effect on the interaction energy. For instance, Morita et al. found that in the CH4/benzene cluster the MP2/6-311++G(d,p) energy changes only by 1.3% when the C−H/ring angle passes from 60° to 0°.29 In the methane/biphenyl cluster, it is noteworthy that, due to the large dihedral angle between the aromatic rings, 14407


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methane cannot bind to both the rings in a bridge conformation, as observed, for instance, in clusters with naphtalene.29 When two ligands are present, as in clusters III and IV which mimic the situation around the sp3 carbon atoms in PAFs, methane binds to both ligands, with slight distorsions from the optimized structures seen above to maximize the total interaction. From Table 2, one can note that biphenyl binds to methane more strongly than dimethylphenyl, even if in both clusters CH4 interacts with one ring. Though aryl and alkyl substituents are expected to have similar inductive effects, in this case the second aromatic ring of biphenyl is more effective than the methyl group: this difference is evident also in clusters III and IV, where methane interacts with two aromatic partners. The binding energies computed at this level are in good agreement with previous theoretical results: for instance, De for methane/ 1,4-dimethylbenzene cluster (8.51 kJ/mol) can be compared to 7.82 kJ/mol, obtained with a larger basis set, close to the coupled cluster (CC) limit.29 The values reported in Table 2 are significantly higher than RT (2.48 and 2.94 kJ/mol at 298 and 353 K, respectively), so that porous frameworks made of these building blocks are expected to adsorb methane efficiently in the desired temperature range. On the other hand, the interaction energies are not so high to prevent the gas desorption from the framework, as discussed below. 3.3. Methane Fugacity Coefficients. GCMC simulations of gas adsorption make use of the chemical potential defined in terms of temperature and fugacity: to relate the theoretical results to actual pressure measures, the fugacity coefficients are needed for all the pressure range of interest. The distinction between fugacities and pressures, sometimes neglected in the literature on simulated adsorptions, is particularly important when high pressures are reached, as in the present case. The molar volumes of gaseous and supercritical methane at 298, 323, and 353 K in the pressure range 0−400 bar were taken from ref 30, and based on the equation of state reported in ref 31. The compression factor Z was computed for all the pressures and temperatures, and the fugacity coefficients ϕ(P, T) were obtained as ϕ(P , T ) =

∫0

P

Z(P ′ , T ) − 1 dP ′ P′

Figure 3. Density (mg/cm3) of gaseous methane computed with different force fields, compared to the EOS. In modified CVFF, the Lennard-Jones parameter for H has been set to 0.048.

densities over the considered pressure range is obtained by putting ε(H) = 0.048 kcal/mol, as shown in Figure 3. To evaluate the interactions between methane and the porous framework atoms, i.e., hydrogen, aromatic sp2 and sp3 carbon atoms, we compared the classical energies provided by the different FF with MP2/6-311+G** results, including the counterpoise correction for the basis set superposition error (BSSE),32 for CH4−benzene and CH4−toluene couples: the energy was scanned with respect to the intermolecular distance, keeping the geometry of the fragments fixed, with three orientations, with the results illustrated in Figure 4. In this case, the standard CVFF provides the best agreement with MP2 results, in particular, when one methane C−H bond is perpendicular to the phenyl plane, but still the classical and ab initio curves are too different. To make CVFF nonbonding terms more attractive, both the Lennard-Jones parameters for sp2 carbon were modified: the best agreement with MP2 was obtained increasing ε(Csp2) from the standard value of 0.148 to 0.448 kcal/mol, and decreasing rm(Csp2) from 4.06 to 3.36 Å. With this choice of parameters, the interactions of methane with saturated C atoms in toluene (Figure 4, c) are also reproduced satisfactorily, so that the standard Lennard-Jones parameters for Csp3 were not changed. The Lennard-Jones parameters used in the following calculations are collected in Table 3: the other FF parameters are the same as in standard CVFF reported in ref 23 and implemented for instance in Materials Studio package.21 Other FF have been proposed recently to model the methane adsorption in porous materials: Wang33 has modified some OPLS34 parameters and used a single-site model for methane, with parameters taken from TraPPE FF,35 to simulate the adsorption in MOFs, obtaining a generally good agreement with experimental data. Mendoza-Cortés et al.36 followed a procedure similar to ours, fitting Lennard-Jones parameters to MP2 calculations to simulate the adsorption isotherms in COFs. 3.5. Simulated Adsorption Isotherms. The density of methane adsorbed in crystalline PAF-30n and in equilibrium with the free gas at various pressures was evaluated with GCMC simulations, exploiting the modified CVFF force field described above, and taking into account the fugacity coefficients obtained from the EOS.

(1)

3.4. Force Field Optimization. To obtain reliable GCMC simulations, the force field is required to accurately reproduce methane−methane and methane−phenyl interactions. To evaluate the former, the density of gaseous methane at 298 K was computed at different pressures (by simulating a formal “adsorption” in an empty box) with different force fields, and compared with the equation of state (EOS).30,31 As shown in Figure 3, the densities computed with all three FF deviate from the EOS at high pressures, though COMPASS performs better than CVFF and PCFF, which are very similar to each other. We decided however to modify CVFF in order to improve the agreement with the EOS, since CVFF exhibits the best performance for methane−phenyl interactions (vide infra), and moreover, it is freely available and can be used with other computational packages. Since standard CVFF densities are underestimated (Figure 3), the nonbonding potential has to be made more attractive. In CVFF, Lennard-Jones 6−12 potentials, VLJ = ε[(rm/r)12 − 2(rm/r)6], are used and the standard values for H atom are ε = 0.038 kcal/mol, rm = 2.75 Å. A satisfactory agreement with EOS 14408


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Table 3. Lennard-Jones Parameters of the Force Field Used in the Monte Carlo Simulations atom type

CVFF name

ε (kcal/mol)

rm (Å)

H Csp2 Csp3

h cp, c′ c

0.048 0.448 0.160

2.75 3.36 3.90

Figure 5. GCMC adsorption isotherms of methane in PAF-30n at 298 K. The density of free gaseous methane (from EOS) is shown for comparison. The black square indicates the storage target proposed by DOE at 35 bar, 298 K.

PAF-303 perform very well also at higher values, up to 280 bar; in general, PAF-302 exhibits the best behavior over the entire considered range of pressures, except in the initial step (P < 10 bar) where it is outperformed by PAF-301. Clearly, the high density of aromatic residues in PAF-301 ensures a very favorable environment for methane molecules, so that the adsorption rises very quickly in this material, but the free volume is too low for the gas to adsorb efficiently when the pressure is increased. On the other hand, the free volume in mesoporous PAF-303 and PAF-304 is too large for all the adsorbed molecules to interact efficiently with the phenyl rings. PAF-302 presents the best combination of large surface area and microporosity, as already found for other gases, and it appears the best choice for large-scale applications. PAF-301, though less useful for automotive and massive storage purposes, could nonetheless be interesting for small size, low-pressure applications possibly in competition with liquefied petroleum gas (LPG). The efficiency of the adsorption in PAF materials can be appreciated by comparison with the liquid methane density at the boiling point (422 mg/cm3 at 112 K and 1.013 bar) or at room temperature and limit pressure (ca. 353 mg/cm3 at 298 K and P > 1000 bar). One can see that at least PAF-302 allows adsorption of methane up to a considerable fraction of the limit value in the pressure range used in automotive applications. As shown in Figure 5, PAF-301 and PAF-302 largely surpass, and PAF-303 almost meets the target fixed by DOE for methane storage at medium pressure (35 bar). Of course, these results are referred to ideal crystalline materials, while PAF materials synthesized and characterized until now are highly disordered: then, lower adsorbed densities have to be expected in actual operative conditions, but these idealized results show the upper limit that can be approached when improving the crystallinity

Figure 4. Interaction energy between methane and benzene and toluene molecules computed at MP2 level and with different FF. Methane C−H orientations: (a) normal to the benzene ring plane; (b) aligned with benzene C−H; directed toward the toluene sp3 carbon.

In Figure 5, the simulated adsorption isotherms at 298 K are reported for PAF-30n, n = 1−4, along with the corresponding density of the free gas. All the considered materials adsorb CH4 very efficiently at low and moderate pressures (below 120 bar), and PAF-302 and 14409


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of the samples. Anyway, PAF-30n are undoubtedly among the most promising materials for methane storage at these pressures. The isotherms in Figure 5 describe the so-called absolute adsorption, i.e., the density of the gas that would be stored in a container filled by the adsorbent. The storage capacity is often discussed, especially in the experimental literature, in terms of other, strictly related quantities: the excess and the effective adsorption. The former is the difference between the absolute adsorption and the amount of gas that would occupy a volume equal to the porous volume of the material at the same pressure and temperature (thus expressing the excess gas that is adsorbed due to the gas/adsorbent interactions); the latter is the difference between the absolute adsorption and the quantity of gas that could be stored in the same container without the adsorbent. Thus, with nads ≡ n(T, P) the density of the gas adsorbed in PAF-30n (curves with symbols in Figure 5), ρfree ≡ ρ(EOS, T, P) the density of the free gas (continuous line in Figure 5), and f pore the material porous fraction (see Table 1), the effective adsorption is neff = nads − ρfree and the excess adsorption is nexc = nads − fpore × ρfree

Simulated excess and effective adsorptions for PAF-30n are reported in Figure 6: note that neff could also be negative, if the use of the adsorbent actually lowered the storage with respect to the compressed free gas, due to the large material skeletal volume. The largest gain with respect to the compressed gas is obtained with PAF-302, whose maximum effective adsorption (neff) falls at 53.8 bar: here, the storage density is increased to 237.5 vs 42.8 mg/cm3 in the free gas, with a gain factor of 5.5. The storage density is also increased by the other materials, though to a lesser extent: neff has a maximum at 21.3 bar for PAF-301 (density gain factor 18.9), and at 86.3 bar for PAF303 (2.6), while it has a large plateau between 100 and 150 bar for PAF-304, with a gain factor of about 1.8. At the largest pressure considered, 280 bar, the methane density in PAF-302 is still 43% higher than the corresponding free gas density (287.5 vs 201.7 mg/cm3). The methane adsorption in PAF-302 has been studied experimentally, at 273 K and for pressures up to 1 atm, in a paper recently published.11 We simulated the adsorption for the same temperature and pressure range, finding that the experimental gas uptake is much smaller than the GCMC simulation: at 1 atm, for instance, the measured uptake is only 12.6 mg/g, compared to the theoretical value of 159.8 mg/g. Such a discrepancy is likely due to poor crystallinity of the sample: in the same experiment reported in ref 11, a similar, strictly related material having the same diamond-like structure as PAF-302 but with the sp3 C atoms substituted by Si (referred to as PAF-3 in ref 11 and as PPN-4 in ref 12), was found to adsorb 46% more methane than the PAF-302 sample. The surface area of PAF-3 sample was measured with BET model to 2900 m2/g, while PAF-302 was not characterized in that work: since the heats of adsorption of methane in the two materials are similar, the surface area for that PAF-302 sample was likely even smaller, well below the expected area for ideal, crystalline PAF-302 (see Table 1). As discussed below, a poor crystallinity has a twofold negative effect in this case: the smaller area reduces the interactions with gaseous methane, and the less

Figure 6. Excess (a) and effective (b) adsorption isotherms of methane in PAF-30n at 298 K.

porous structure increases the material bulk density, making the comparison with theoretical results even less favorable. More results have been presented for methane adsorption in other porous materials, belonging to the class of metal organic frameworks (MOF), which has been studied for a longer time in this kind of applications, and of covalent organic frameworks (COF). A possible complication arises when the experimental gas uptake is reported as gravimetric adsorption (e.g., weight % or milligrams of gas adsorbed per gram of material), without indicating the adsorbent bulk density. In this case, the comparison among different materials can be misleading, since the less dense material (as for instance PAF-304 in our series) could exhibit a very large gravimetric uptake, while the actual adsorption per unit volume is scarce; this problem can be limited by comparing materials with similar porosity. Some older results, referred to microporous carbons and zeolites, are collected in ref 2: in this kind of material, the absolute methane uptake at 298 K and 35.5 bar ranges approximately from 30 to 210 mg/g, corresponding to volumetric uptakes of 20−120 mg/cm3. Not surprisingly, microporous carbons perform worse than PAF-30n, since their specific surface area is usually less than one-half the area expected for crystalline PAFs). The adsorption isotherms of methane in some COFs have been simulated by the same approach used in the present work: 14410


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indicates that the actual sample was of quite good quality, though it could be improved further. 3.6. Temperature Effect and Heats of Adsorption. The effect of the temperature change on CH4 adsorption was evaluated by repeating the simulations at 323 and 353 K: the absolute, excess, and effective adsorption isotherms are shown in Figure 7 for PAF-30n, n = 1−4. The free gas densities, as well as the fugacity coefficients, were recomputed with the EOS at all the temperatures as described above. Temperature has a small effect on the adsorption in PAF301, which saturates at very low pressures: in this material, the adsorption is strongly dominated by the surface interactions. Since the free gas density decreases at higher temperatures, the effective adsorption in PAF-301 is actually increased at 353 K and pressure above 100 bar. On the other hand, PAF-302 and 303 isotherms show the expected reduction of adsorbed gas densities as the temperature rises: the PAF-302 maximum effective adsorption is lowered to 151.2 mg/cm3 at 323 K, 76.9 bar, and to 125.7 mg/cm3 at 353 K, 97.4 bar, while for PAF303, the values are 90.6 at 323 K, 101.8 bar, and 76.3 at 353 K, 126.0 bar. PAF-304 excess and effective adsorptions show a flat plateau in the range 100−180 bar at 323 and 353 K: as pointed out above, the free volume in this system is so high that the adsorbed methane behaves mostly as in the free gas, except for the small fraction of molecules in contact with the material surface. For all the systems, the excess and effective isotherms tend to merge at high pressures for all the temperatures, since the adsorbed densities decrease with the same trend as the free gas density. In other words, at sufficiently high pressure the material surfaces are saturated by the adsorbed gas at all the considered temperatures, and the density variation is due to the “free” gas filling the pores. Adsorption is an exothermic process, as a consequence of the surface/molecule interactions: the excess density in the pores depends on such energy gain, which is effectively measured by the isosteric heat of adsorption, Qst. The enthalpy change associated to the sorption process, ΔH̅ ads, can be calculated through the Clausius−Clapeyron equation at various degrees of surface coverage, so that

three 2D frameworks presented a maximum excess adsorption of 85−113 mg/cm3 at 298 K and pressure around 60 bar;39 four tridimensional COFs were predicted to have excess adsorptions ranging from 70 to 170 mg/cm3 at the same temperature and pressure:40 at least one of these samples exceeded the above-mentioned DOE target. A collection of high-pressure methane adsorption data at 298 K and 30−50 bar is presented in ref 41 for many porous MOFs: the highest adsorption is provided by the material labeled as PCN-14 which largely overpasses the DOE target too. It is useful to analyze these results in more detail, since they are expressed in terms of volumetric uptake and can be directly compared with the simulated performance of PAF-30n. At 35 bar, 290 K the methane adsorption in PCN-14 is 220 (excess) and 230 (absolute) cm3 (STP)/cm3, well above DOE requirements.42 Besides this excellent result, other members of the same class of porous materials perform very well in methane adsorption, as PCN-61 and PCN-66, whose excess uptakes at 35 bar, 298 K are 145 and 110 cm3 (STP)/cm3, respectively.43 In the same conditions, our simulations predict 276 cm3 (STP)/cm3 excess uptake for PAF-302, then markedly above the best-performing material described until now. This result is clearly very appealing, but we emphasize again that the present simulations are referred to an ideal crystalline material. The amount of adsorbed gas is strongly dependent on the microporous volume, or better on the specific surface area, and these parameters in turn depend critically on the adsorbent crystallinity. Then, as pointed out above, actual samples are likely to provide lower uptakes, though PAF-302 is surely of great interest for this kind of application. In Table 4, we compare the gravimetric uptake in other microporous materials with large specific surface areas with the simulated adsorption in microporous PAF-301 and PAF-302. Table 4. Methane Total and Excess Uptake Measured for Different Porous Materials and Simulated for PAF-301 and PAF-302 material

P (bar)

T (K)

total uptake (mg/g)

excess uptake (mg/g)

PPN-4 PCN-68 MOF-210 MOF-5 ZIF-8 3*PAF301

55 100 80 62 62 21.3 17.3 17.3 53.8 57.8 57.8 220.8

295 298 298 270 270 298 323 353 298 323 353 298

389 446 475 280 125 226 215 205 728 655 555 870

269 390 264 230 100 218 209 200 623 554 468 444

4*PAF302

a

ref.

⎛ ∂ ln f ⎞ Q st = −ΔH̅ ads = −R ⎜ ⎟ ⎝ ∂(1/T ) ⎠n

12 12, 43 12, 37 38 38 this worka

exc

(2)

where nexc is the excess adsorbed density, due to the fraction of molecules actually bound to the surface, and f is the fugacity of the free gas in equilibrium with nexc. To apply eq 2, the excess isotherms are measured or simulated at different temperatures, reporting the fugacities corresponding to constant loadings, as illustrated in Figure 8; Qst is properly defined for low surface coverages, in any case before the maximum in the excess isotherms. The isosteric heats of adsorption for PAF-30n are reported in Figure 9. For all the systems, Qst increases with nexc, approaching a maximum toward the maximum excess densities, when the surfaces are saturated by the gas. This is due to the favorable methane−methane interactions in the adsorbed layer, where a sort of condensation occurs. At low adsorbed densities, PAF-304 exhibits the highest Qst, likely due to its larger aromatic character: on the other hand, as pointed out above, PAF-304 and PAF-303 saturates at lower densities. For very low nexc, the heats of adsorption in PAF-302, 303, and 304 are 10.9, 11, and 14.2 kJ/mol, respectively (increasing above 21 kJ/mol for PAF-302 at high surface coverage): these

this worka

GCMC simulation.

These data confirm that PAF-302 is a very promising material for methane storage over a wide range of pressure. Since the simulations provide an upper limit for the expected gas uptake, they can also be used to evaluate the “ideality” of actual samples. For instance, it is instructive to compare the reported CH4 uptake for PPN-4 at 55 bar with the simulation on PAF-302 at 59.4 bar in Table 4, since the two materials have a very similar structure as pointed out above. The PPN-4 absolute adsorption is around 50% of the ideal value, which 14411


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Figure 7. Absolute, excess, and effective adsorptions (mg/cm3) for PAF-30n at 298, 323, and 353 K.

above-mentioned experiments of methane adsorption in PAF302 and similar compounds at low pressure,11 Ben et al. measured an initial heat of adsorption of around 14, 15, and 23 kJ/mol when the sp3 atom in the diamond-like structure is C, Si, and Ge, respectively: the first value is not far from our simulation at low coverage.

values can be compared with the heats measured in microporous carbons and zeolites, ranging from 12.10 to 25.52 kJ/mol,2 or in PCN-14, around 30 kJ/mol.41 Note that, despite the comparable or even higher heat of adsorption, the methane uptake is markedly lower in the latter materials than in the simulated PAFs, likely due to the lower microporous volumes. Considering materials with higher area, the initial Qst is around 12.2 kJ/mol in MOF-5 and 12.0 in ZIF-8 (see Table 4): interestingly, the trend in MOF-5 is similar to that observed in our simulations, with Qst growing up to 19.5 kJ/mol for high uptakes. Note that these values of Qst are very close to the binding energies listed in Table 2, though De has been computed for minimized structures on model systems. In the

4. CONCLUSIONS The adsorption of gaseous methane in a newly developed class of porous materials has been modeled with GCMC simulations, in order to estimate the potential of these materials to enhance the capacity of traditional high-pressure containers, or alternatively to store a comparable amount of gas at much 14412


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298 K and 59.5 bar the methane storage in PAF-302 is 5 times larger than in the compressed gas, and even at 280 bar, the adsorbed gas is 43% more dense than the compressed gas. Both PAF-301 and 302 exceed the limit proposed by DOE for the methane storage at medium pressure (35 bar), specifically thought for automotive applications. The isosteric heat of adsorption, Qst, was also estimated, by simulating the excess adsorption isotherms at different temperatures: PAF-304 has the greatest Qst at low loadings, followed by 303 and 302; increasing the methane loading, Qst grows due to favorable interactions in the adsorbed layer. Eventually, PAF-302 shows the largest heat of adsorption, since it is able to adsorb the greatest amount of methane per unit volume. In conclusion, the present simulations show that some members of the PAF family have an enormous potential as methane adsorbers in a large pressure range. Of course, these results are based on ideally crstalline materials, and lower performances are expected in actual working conditions, but these materials are nonetheless very promising candidates for automotive applications.

Figure 8. Excess adsorbed density of methane in PAF-302 at 298 (circles), 323 (diamonds), and 353 (squares) K. The horizontal lines indicate the fugacities of the free gas in equilibrium with various excess densities at all the temperatures. Inset: the data used to estimate Qst from eq 2 at various methane loadings.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support provided by OMB-Saleri and SOL-Group is gratefully acknowledged. REFERENCES

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Figure 9. Isosteric heat of adsorption for PAF-30n at different methane loadings.

lower pressures. The adsorbers belong to the family of Porous Aromatic Frameworks (PAFs), recently developed and very promising for gas storage due to their high stability, very high specific surface area, and good affinity for a number of light molecules. We have modeled the first four members of the series, with increasingly long aromatic chains connecting sp3 carbons in a diamond-like structure. The Lennard-Jones parameters of CVFF force field were optimized to reproduce the correct equation of state for gaseous methane at 298 K up to 280 bar, and then to provide methane−benzene interaction energies in agreement with highlevel quantum mechanical calculations. These parameters were used to simulate the adsorption isotherms at 298, 323, and 353 K, also estimating the excess and effective adsorptions at all the temperatures. All the PAFs modeled here exhibit a very high affinity for methane, with adsorbed densities always larger than compressed gas density. PAF-302, where the sp3 carbons are connected by biphenyl units, perform better than the other materials in all the conditions, except for pressure lower than 10 bar, where PAF-301 is slightly more efficient: for instance, at 14413


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Theoretical Prediction of High Pressure Methane Adsorption in Porous

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