Low-coverage adsorption properties of the metal–organic framework MIL-47 studied by pulse chromatography and Monte Carlo simulations

Abstract

Low-coverage adsorption properties of the metal–organic framework MIL-47 were determined by a combined experimental and simulation study. Henry constants and low coverage adsorption enthalpies of C5–C8 linear and branched alkanes, cyclohexane and benzene were measured from 120 to 240 °C using pulse gas chromatography. An adapted force field for linear and branched alkanes in MIL-47 was used to compute the adsorption properties of those molecules. A new set of charges was developed for simulations with benzene in MIL-47. The adsorption enthalpy of linear alkanes increases with about 7.6 kJ mol⁻¹ per additional –CH₂– group. Henry adsorption constants of iso-alkanes are slightly lower than those of the linear chains but the MIL-47 framework is not imposing steric constraints on the branched chains. Benzene and cyclohexane are adsorbed less strongly than n-hexane as they have less hydrogen atoms. For the studied non-polar molecules, the adsorption energies are dominated by van der Waals interactions and benzene adsorption is additionally influenced by Coulombic interactions. The simulated tendencies are in good agreement with the experiments.

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Introduction

Since the early work of Barrer in 1956, adsorption of alkanes on zeolites has received a lot of interest.¹ Nowadays, experimental determination of the adsorption of linear and/or branched alkanes is used as one of the many tools to characterize the microporous adsorbent.^2–4 In spite of the simple nature of the alkanes and the absence of specific functional groups, many different adsorption mechanisms have been identified.^2,4–16 For the adsorption of n-alkanes, it was shown that the adsorption enthalpy, reflecting the energetic interaction between the molecule and the zeolite force field, is dominated by the pore shape and diameter rather than by the strength of the electrostatic field in the zeolite, which can be explained by the apolar character of the alkanes. For these molecules, the interaction is mainly governed by the van der Waals (VDW) interactions, which increase with decreasing distance between the interacting atoms or molecules. It was shown that above a critical pore size of 5 Å, the adsorption enthalpy increases with decreasing pore size and that, for pores narrower than 5 Å, the repulsion forces start to dominate leading to lower adsorption enthalpies.^4,7,8 The adsorption enthalpy can be obtained in a direct way from calorimetric measurements, or indirectly via the temperature dependency of the adsorption constants obtained with gravimetric, volumetric or chromatographic adsorption measurements.^{1,4,10–12,14–17} Force fields for the molecular modeling of alkane adsorption in zeolites have been refined during the last decade to such a degree that grand canonical Monte Carlo simulations can now even be used to predict the adsorption behavior of zeolites at high degrees of pore filling.^18–25

Metal–organic frameworks (MOFs) are a relatively new and emerging class of microporous materials, formed by a network of metal ion clusters held together by bridging multidentate organic ligands. Since, in most cases, the metal ions are coordinatively saturated by these ligands, the pore walls are largely organic in composition. In this way their composition differs largely from the inorganic zeolites. Whereas the potential of MOFs as catalysts, molecular sensors, luminescent and magnetic materials and drug delivery materials has already been proven, the most promising applications probably lie in the field of adsorptive storage and separation. Large adsorption capacities of hydrogen, methane, CO₂ and acetylene^26–37 as well as the adsorptive separation of alkane mixtures;³⁸ isobutene/isobutane mixtures;³⁹ C8 alkyl aromatic isomers from binary and quaternary mixtures;^40,41 CO₂/N₂, CO₂/CH_4, CO₂/CO and N₂/CO₂ binary mixtures and CH₄/N₂/CO₂ ternary mixtures;^42–44 selective removal of thiophene from a thiophene/methane mixture⁴⁵ have been reported. Despite the recent interest in adsorption on MOFs little is known about the fundamental adsorption properties of these materials. Up to now, only adsorption enthalpies of linear and branched alkanes, H₂, CO₂, CH₄, benzene, toluene and C8 alkylaromatic compounds have been reported.^41,46–53 Pulse gas chromatographic measurements of linear and branched alkanes have already demonstrated the shape-selective properties of MOFs.^48,54

With respect to molecular simulations of MOFs, force fields have been developed and tested less profoundly as compared to zeolites. First of all, the more complex chemical nature of MOFs and the wide diversity in structure and composition complicates the modelling of the structure, the development of good force fields and increases the computational time. Secondly, few experimental data are available making validation of the simulation methods problematic. Thirdly, several MOF structures exhibit significant framework flexibility, making accurate simulations even more cumbersome.

In this paper, low-coverage adsorption properties of linear and branched alkanes on the MIL-47 MOF were obtained using pulse chromatography. MIL-47 is a porous terephthalate built from infinite chains of V⁴⁺O₆ octahedra, held together by the dicarboxylate groups of the terephthalate linkers.⁵⁵ In this way, a 3-dimensional microporous framework is formed with 1-dimensional diamond shaped channels possessing a free internal diameter of about 0.85 nm (see Fig. 1). Molecular modeling on MIL-47 is very recent and extremely scarce. Adsorption studies focused on carbon dioxide, using both grand canonical Monte Carlo⁵⁶ and density functional theory calculations.⁵⁷ Diffusion has been analyzed only for methane⁵⁸ and for hydrogen using molecular simulations.⁵⁹ Molecular simulations of linear and branched alkanes in this structure have not been reported so far. In the present work, an adapted force field was developed for the simulation of alkane adsorption in this MOF structure. A new set of charges was developed for simulations with benzene in MIL-47. Experimental Henry adsorption constants and adsorption enthalpies are compared to those obtained by simulation.

Fig. 1 Chromatograms of n-hexane (nC6), 2-methylpentane (2Me-C5), cyclohexane (cC6) and benzene on MIL-47 at 180 °C.

Results and discussion

Chromatograms and Henry constants

Fig. 1 shows chromatograms of n-hexane, 2-methylpentane, cyclohexane and benzene obtained after injection of the individual components at 180 °C on a MIL-47 column. Benzene elutes first, followed by cyclohexane, 2-methylpentane and finally n-hexane. As expected, the retention time of linear and branched alkanes increases exponentially with carbon number (not shown). Henry constants of linear and 2-methyl branched alkanes as calculated from the experimental chromatograms are plotted as a function of carbon number in Fig. 2 (at 220 °C) and tabulated in Table 1 (at 240 °C). For each additional –CH₂– group, the experimental Henry constant increases with a factor of about 2.8 for the n-alkanes and a factor of 2.7 for the 2-methyl branched alkanes at 220 °C. Apart from exceptions, Henry constants obtained from the simulations are typically a factor of 2–5 larger compared to the ones obtained experimentally and show a somewhat larger dependency on carbon number. Simulations predict an increase of K′ with carbon number of 3.5 for the n-alkanes and 3.1 for the 2-methyl branched alkanes.

Fig. 2 Henry constants of linear (□,■) and 2-methyl branched alkanes (△,▲) on MIL-47 at 220 °C, calculated from experimental chromatograms (solid symbols) and from GCMC simulations (open symbols) as a function of the total number of carbon atoms.

Table 1 Henry constants and separation factor obtained experimentally and by simulation at 240 °C

	K′/mol kg^−1 Pa^−1		α
	Experiment	Simulation	Experiment	Simulation
n-pentane	2.78 10^−5	1.45 10^−4	—	—
2-methylbutane	2.00 10^−5	6.99 10^−5	1.4	2.1
n-hexane	7.25 10^−5	4.48 10^−4	—	—
2-methylpentane	5.09 10^−5	1.89 10^−4	1.4	2.4
2,2-dimethylbutane	4.43 10^−5	5.80 10^−4	1.6	0.8
2,3-dimethylbutane	5.93 10^−5	1.38 10^−4	1.2	3.2
cyclohexane	4.76 10^−5	—	1.5	—
benzene	4.26 10^−5	9.77 10^−5	1.7	4.6
n-heptane	1.94 10^−4	1.45 10^−3	—	—
2-methylhexane	1.21 10^−4	5.12 10^−4	1.6	2.8
3-methylhexane	1.23 10^−4	7.59 10^−4	1.6	1.9
2,3-dimethylpentane	1.36 10^−4	4.72 10^−4	1.4	3.1
3,3-dimethylpentane	1.32 10^−4	2.41 10^−3	1.5	0.6
n-octane	1.12 10^−3	4.87 10^−3	—	—
2-methylheptane	6.17 10^−4	2.51 10^−3	1.8	1.9
3-methylheptane	5.71 10^−4	3.28 10^−3	2.0	1.5
4-methylheptane	5.06 10^−4	1.38 10^−3	2.2	3.5
2,2-dimethylhexane	4.34 10^−4	1.70 10^−2	2.6	0.3
2,4-dimethylhexane	5.13 10^−4	8.85 10^−4	2.2	5.5
2,5-dimethylhexane	4.89 10^−4	5.23 10^−4	2.3	9.3
2,2,4-trimethylpentane	4.57 10^−4	1.73 10^−3	2.5	2.8

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Adsorption enthalpy

The temperature dependence of the Henry constants follows the van’t Hoff equation (Fig. 3). Zero-coverage adsorption enthalpies obtained from the experiments and simulations are reported in Table 2. Energies, enthalpies, and entropies of adsorption obtained from molecular simulations are tabulated in Table 3. Simulated adsorption enthalpies are very close to the experimental values and systematically 4–5 kJ mol⁻¹ larger. For comparison, adsorption enthalpies on NaY, a faujasite zeolite containing cages with a diameter of 12.3 Å, accessible through windows of 7.3 Å, and mordenite, a zeolite with pores of 5.7 × 7.5 Å, were added. For alkanes trapped inside a micropore, VDW interactions are the main contribution to the adsorptive interaction energy. These VDW interactions are dependent on the nature of the interacting atoms and the distance between them. Typically, smaller pore sizes lead to larger adsorption enthalpies for n-alkanes. In spite of its different chemical nature, the MIL-47 MOF, with its unidimensional pores of 8.5 Å, follows this tendency as its adsorption enthalpies fall in between that of mordenite (5.7 × 7.5 Å) and NaY (12.3 Å). For all microporous materials, the adsorption enthalpy increases linearly with carbon number; every additional –CH₂– group is responsible for additional dispersive interactions. For MIL-47 an increase of 7.6 kJ mol⁻¹ for each additional –CH₂– group was observed experimentally compared to 7.8 kJ mol⁻¹ in the simulations. NaY exhibits an increase of 6.3 kJ mol⁻¹ for every –CH₂– while mordenite shows an increase of 10.7 kJ mol⁻¹. Fig. 4 shows the increase of adsorption enthalpy with carbon number, β, for n-alkanes on MIL-47 and a series of representative zeolites as a function of pore size as determined by pulse chromatography.^6,60 For alkanes, MIL-47 follows the tendency of zeolites.

Fig. 3 van’t Hoff plot of hexane (□,■) and 2-methylpentane (◇,◆), obtained by experiments (solid symbols) and simulation (open symbols).

Fig. 4 Increase of adsorption enthalpy with carbon number for n-alkanes on MIL-47 and a series of representative zeolites as a function of pore size. The solid line is a guide to the eye.

Table 2 Adsorption enthalpy obtained from experiments and simulations on MIL-47. As reference, adsorption enthalpies on mordenite and NaY zeolites are added

	−ΔH0/kJ mol^−1
	MIL-47		Mordenite^a	NaY (Si/Al 2.7)^a
	Experiment	Simulation
a Ref. 68.
n-pentane	43.0	47.2	55.7	39.4
2-methylbutane	42.9	43.5	55.6	39.2
n-hexane	50.6	55.1	67.1	45.5
2-methylpentane	47.7	50.9	65.8	45.3
2.2-dimethylbutane	48.3	53.5	62.9	43.2
2.3-dimethylbutane	48.5	48.6	63.4	44.1
cyclohexane	45.2	—	—	—
benzene	43.4	44.7	—	—
n-heptane	58.1	62.9	77.0	51.9
2-methylhexane	56.2	58.6	75.1	51.6
3-methylhexane	57.3	59.7	75.4	51.4
2.3-dimethylpentane	60.6	56.7	74.7	50.6
3.3-dimethylpentane	58.7	62.0	—	—
n-octane	—	70.7	87.3	57.5
2-methylheptane	—	66.3	85.1	57.2
3-methylheptane	—	67.3	83.1	57.3
4-methylheptane	—	67.2	81.8	57.2
2.2-dimethylhexane	—	68.7	—	—
2.4-dimethylhexane	—	63.6	—	—
2.5-dimethylhexane	—	61.8	—	57.1
2,2,4-trimethylpentane	—	64.9	76.8	56.8

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Table 3 Simulated Gibbs free energy, enthalpy and entropy of adsorption

	−ΔG0/kJ mol^−1	−ΔH0/kJ mol^−1	−ΔS0/J mol^−1 K^−1
n-pentane	23.9	47.2	144.2
2-methylbutane	20.8	43.5	130.5
n-hexane	28.9	55.1	170.2
2-methylpentane	25.2	50.9	154.3
2,2-dimethylbutane	29.9	53.5	168.9
2,3-dimethylbutane	23.8	48. 6	146.7
cyclohexane	34.0	—	196.3
benzene	29.5	44.7	178.7
n-heptane	31.2	62.9	184.4
2-methylhexane	29.1	58. 6	174.1
3-methylhexane	36.0	59.7	198.8
2,3-dimethylpentane	39.2	56.7	222.9
3,3-dimethylpentane	34.7	62.0	204.9
n-octane	35.7	70.7	208.8
2-methylheptane	35.5	66.3	208.1
3-methylheptane	38.5	67.3	217.4
4-methylheptane	32.0	67.2	193.7
2,2-dimethylhexane	29.7	68.7	185.7
2,4-dimethylhexane	34.7	63. 6	202.0
2,5-dimethylhexane	22.2	61.8	135.7
2,2,4-trimethylpentane	23.9	64.9	144.2

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The experimental adsorption enthalpy of benzene is considerably lower than that of n-hexane (43.4 kJ mol⁻¹ compared to 50.6 kJ mol⁻¹). It was suggested in earlier work that the interactions between the alkane hydrogen atoms and the MIL-47 framework play a dominant role in the adsorption mechanism.⁴¹ Interactions between the π-clouds of adsorbed aromatic species and the framework are less important.⁴¹ Therefore, it is not unreasonable to suggest that MIL-47, in contrast to most cation containing zeolites, does not exhibit a significant internal electrical force field. The additional hydrogen atoms of n-hexane compared to benzene lead to stronger interaction and thus longer retention (Fig. 1) or Henry constant (Table 1). For the same reason, cyclohexane is adsorbed more strongly compared to benzene, but retained less compared to n-hexane. Even for benzene, the simulations correspond extremely well to the experimental data (Tables 1 and 2). Also, simulations show a weaker adsorption of benzene compared to n-hexane (44.7 kJ mol⁻¹ compared to 55.1 kJ mol⁻¹) (Tables 1 and 2), even though the united-atom force fields model was used for n-hexane and, thus, the hydrogen atoms were not simulated independently.

Shape selectivity and molecular siting

Preferential adsorption of linear over branched alkanes was observed; all branched alkanes had lower Henry constants compared to their linear isomers (Table 1). This behavior corresponds to what is commonly observed with most zeolites and other amorphous materials.⁶⁰ The separation capacity of a material can be quantified with a separation factor, α, obtained by dividing the Henry constant of the linear alkane by the Henry constant of the branched isomer. Separation factors calculated from the experimental and simulated Henry constants are tabulated in Table 1. Generally, only low separation factors were observed (between 1.2 and 2.5), with small differences between mono- and multibranched alkanes, pointing at the absence of shape selectivity. In some cases, even larger separation factors were found for monobranched alkanes compared to their multibranched isomers. For example, for n-hexane/2,3-dimethylbutane a separation factor of 1.2 is obtained experimentally, compared to 1.4 for n-hexane/2-methylpentane. The same preferential adsorption of linear over branched alkanes was found in the simulations. In general, slightly larger separation factors were found in the simulations than in the experiments. Only in some cases (2,4-dimethylhexane, 2,5-dimethylhexane), simulations give large separation factors. It should be stressed that, considering that the forcefield has not been fitted to reproduce adsorption in MOFs but in zeolites, the observed differences between simulations and experiments are not large.

Experimental and simulated adsorption enthalpies of the branched alkanes are slightly lower than those of the linear chains (apart from the experiments with 2,3-dimethylpentane and 3,3-dimethylpentane). In the experiments, the difference between linear and branched alkanes is lower than 3 kJ mol⁻¹, somewhat larger differences are found in the simulations. As commonly observed, the presence of side methyl groups in the iso-alkanes results in less close contact of all hydrogen atoms with the framework. Altogether, these results show that the pores of MIL-47 are not imposing steric restrictions on the more bulky iso-alkanes. The siting mechanisms of these molecules were further investigated via molecular simulation. Fig. 5 shows the center of mass of the molecules for low coverage conditions, plotted every 10 000 simulation steps. First of all, it can be observed from Fig. 5 that both linear and branched alkanes adsorb in the center of the pores. The molecules are not preferentially adsorbed near the metal centers or the pore walls. The branched alkanes show a tendency to stay close to the center of the pore, as indicated by the condensed cloud of centers of mass for 2-methylpentane, 2,3-dimethylpentane and 2,2-dimethylpentane, whereas the centers of mass for n-hexane are much more distributed. This shows that n-hexane probes a larger area in the cross section of the pore. Also benzene adsorbs in the center of the pore (Fig. 5). At low loading, no preferential orientation of the benzene molecules was detected in the simulations, confirming the specific interaction of this molecule with the framework.

Fig. 5 Adsorption sites of n-hexane (A), 2-methylpentane (B), 2,2-dimethylbutane (C) and benzene (D) inside the pores of MIL-47. Yellow balls indicate the center of mass of a single molecule at a give simulation step. The figure shows the superposition at different simulation steps.

Experimental

Material synthesis and characterization

MIL-47 was synthesized according to the method of Barthelet et al.⁵⁵ After synthesis, the excess terephthalic acid in the pores was removed by high temperature treatment at 300 °C in air. The micropore volume as determined from nitrogen adsorption isotherms at the temperature of liquid nitrogen using the Dubinin–Raduskevitch method was 0.36 ml g⁻¹.

Pulse gas chromatography

Zero-coverage adsorption properties of C5–C8 alkanes, benzene and cyclohexane were determined using the pulse gas chromatographic method. Stainless steel columns of 30 cm with internal diameters of 0.216 cm were packed with binderless pellets of 500 to 630 μm. Prior to the measurements, the MIL-47 material was activated by heating to 300 °C at a heating rate of 1 °C min⁻¹ in helium flow and keeping this final temperature during 10 h. Liquid pulses (0.02 μl) of the investigated components were injected in an inert carrier gas, He, flowing through a chromatographic column filled with MIL-47 pellets. At the column outlet, the response curve was measured with a thermal conductivity detector. Chromatograms were measured from 120 to 240 °C. Absence of diffusion limitations was verified by changing the carrier gas flow rate. Injections of different hydrocarbon volumes demonstrated that the experiments were performed in the linear part (Henry region) of the adsorption isotherm. Henry adsorption constants, K′, were calculated using the methods of moments.⁶¹ The adsorption enthalpy, ΔH₀, was calculated using the van’t Hoff equation.^62,63

Simulations

The Henry coefficients, energies, enthalpies, and entropies of adsorption at zero coverage were computed using MC in the NVT ensemble. We grow test chains during the simulation using the Rosenbluth weight of the adsorbate. Detailed information about this method can be found elsewhere.⁶⁴ The MC moves were performed in cycles and in each cycle one move was chosen at random with a fixed probability of translation, rotation, and regrowth in a random position. We used at least 10⁷ cycles and charge interactions were computed using Ewald sums with a relative precision of 10⁻⁶. The Lennard-Jones potential is cut and shifted with the cutoff distance set to 12 Å. MIL-47 is modeled as a rigid structure with Lennard-Jones parameters taken from the DREIDING forcefield.⁶⁵ except those for vanadium that were taken from the UFF forcefield.⁶⁵ Lorentz–Berthelot mixing rules were used to calculate mixed Lennard-Jones parameters. The crystal structure was taken from ref. 40 (CCDC 632101--632101; these data can be obtained free of charge from the Cambridge Crystallographic Data Centre viawww.ccdc.cam.ac.uk/data_request/cif) and we used 16 (4 × 2 × 2) unit cells of MIL-47 (a = 6.1879 Å, b = 16.1430 Å, and c = 13.9390 Å) in our simulations. The unit cell contains 72 atoms of which 4 are vanadium, 20 oxygen, 16 hydrogen, and 32 carbon. The carbon and oxygen atoms are classified in two and three groups, respectively, depending on the atoms next to them; C_a carbons are bonded to one hydrogen and two carbon atoms, the C_b carbons are bonded to another three carbons, the C_c carbons are bonded to two oxygen atoms, O_a coordinates two vanadium atoms and O_b coordinates one vanadium and one carbon atom.

The interactions between the adsorbed molecules and the MIL-47 host framework are modeled by Lennard-Jones potentials. The alkanes are described with a united atom model, in which CH_x groups are considered as single, chargeless interaction centers with their own effective potentials. The beads in the chain are connected by harmonic bonding potentials U = 0.5k (r−r₀)² with k/k_B = 96 500 K and r₀ = 1.54 Å. The bond bending between three neighboring beads is modeled by a harmonic bending potential U = 0.5k (θ−θ₀)² with k/k_B = 62 500 K and θ₀ = 114°. These models and potentials have been successfully employed to describe the adsorption in zeolites.^20,21 Benzene is described as a rigid molecule, in which C_benz and H_benz are charged.⁶⁶ The framework charges for MIL-47 were obtained applying the CHELPG method on a representative cluster where crystallographic positions were maintained. Calculations were performed with GAUSSIAN03.⁶⁷ The intermolecular parameters used in this work are listed in Table 4.

Table 4 Intermolecular Lennard–Jones parameters and atomic charges used in this work

MIL-47
Atom type	ε/kB/K	σ/Å	q/e^−
V	8.05	3.144	1.68
Oa	48.19	3.03	−0.6
Ob	48.19	3.03	−0.52
Ca	47.86	3.47	−0.15
Cb	47.86	3.47	0
Cc	47.86	3.47	0.56
H	7.65	2.85	0.12

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Adsorbed molecules
Atom type	ε/kB/K	σ/Å	q/e^−
CH4_sp3	158.5	3.72	0
CH3_sp3	108.0	3.76	0
CH2_sp3	56.0	3.96	0
CH_sp3	17.0	4.68	0
C_sp3	0.8	6.38	0
C_benz	30.7	3.6	−0.095
H_benz	25.45	2.36	0.095

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Conclusions

The present study shows that linear and branched alkanes adsorb in an unhindered way in the pores of MIL-47. The combined simulation and experimental study revealed that, despite the significant difference in composition between the metal–organic framework and zeolites, the adsorption potential for alkanes is similar. The carbon number dependency of the low-coverage adsorption properties (Henry constants and adsorption enthalpy) correspond very well between simulations and experiments. Future work will be devoted to the comparison between experimental and simulated isotherms.

Acknowledgements

This work was performed in the frame of the IAP Functional Supramolecular Systems of the Belgian Federal Government. The authors are grateful to the Vrije Universiteit Brussel for financial support in the frame of the concerted research action “Molecular Interactions and Transport Confined Spaces”. The authors thank the Spanish Ministerio de Educación y Ciencia (MEC) (CTQ2007-63229 and CTQ2007-60910) and the Junta de Andalucía (P07-FQM-02595) for financial support. E. García-Pérez wishes to thank the MEC for her predoctoral fellowship.

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