Modeling of Adsorption Thermodynamics of Linear and Branched

Article pubs.acs.org/JPCC

Modeling of Adsorption Thermodynamics of Linear and Branched Alkanes in the Aluminum Fumarate Metal Organic Framework Ege Dundar,† Belgin Bozbiyik,† Stijn Van Der Perre,† Guillaume Maurin,‡ and Joeri F. M. Denayer*,† †

Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium Institut Charles Gerhardt Montpellier, Université de Montpellier, place Eugène Bataillon, 34095 CEDEX 5 Montpellier, France

‡

S Supporting Information *

ABSTRACT: Aluminum fumarate is one of the most stable metal−organic frameworks (MOFs), showing good cycling performance in water adsorption and desorption. Because of its rather small pore size, this MOF shows shape selectivity in the adsorption of linear and branched alkanes. In this work, the interaction of a broad series of alkanes with this MOF was studied through molecular simulations. We expand the transferability of a periodic density functional theory (DFT)-derived force field previously reported by Kulkarni and Sholl to the case of alkane adsorption on this aluminum fumarate MOF. With this force field and using configurational bias Monte Carlo simulations (CBMC), low coverage adsorption enthalpies, adsorption entropies, and Henry’s adsorption constants were calculated. Experimental enthalpies of adsorption (−ΔH0) of C5−C8 n- and iso-alkanes are accurately reproduced by our calculations, e.g., within 5% relative error for n-alkanes. Interestingly, a compensation effect between adsorption enthalpy and adsorption entropy is found in the simulations, with a calculated slope almost identical to the experimental value. This indicates that the force field is very well capable of predicting tendencies with respect to the energetic interactions between the confined molecules and the MOF pore walls. Our calculations also predict separation between linear and branched alkanes with very good accuracy.

1. INTRODUCTION The process of hydrocarbon adsorption in the pores of nanoporous materials is used in a large number of industrial applications like the separation and purification of natural gas,1 the separation of alkanes to increase the octane number of gasoline, catalytic reactions such as the cracking of crude oil fractions,2 or the hydro-isomerization of linear to branched alkanes.3,4 Indeed, a thorough understanding of hydrocarbon adsorption and transport processes in porous materials is essential from a fundamental as well as an applied point of view.4 Microporous materials like zeolites have been used extensively in the petroleum industry to carry out the adsorptive separation or catalytic conversion of hydrocarbon isomers, due to their ability to selectively adsorb guest molecules in their pores.5−7 However, during the last two decades or so, a lot of attention has been paid to metal−organic frameworks (MOFs), a relatively new class of hybrid porous materials that combine inorganic nodes containing metal centers and organic linker moieties (carboxylates, phosphonates, imidazolates, etc.).8,9 The presence of strong coordination bonds between the metal centers and the organic linkers provides a crystallographically well-defined framework architecture sometimes associated with a high specific area.5,11 Furthermore, tailor-made synthesis allows to vary the metal centers and/or organic ligands, which paves the way for a wide © 2017 American Chemical Society

range of morphological and chemical properties like pore size and shape, composition of the framework and presence of functional groups within the pore cavities to be easily varied and fine-tuned.5 One disadvantage of MOFs that was initially evoked concerned their limited thermal and chemical stability; however, among the thousands of synthesized structures, a growing fraction of the solids is stable at relatively elevated temperature or in the presence of humidity.12−14 Aluminum fumarate (Al-fumarate) is one of those MOFs showing good stability in humid conditions, as demonstrated in cyclic water adsorption and desorption experiments.15,16 Moreover, Al-fumarate is one of the rare MOFs to be employed for commercial purposes, where it is used as a sorbent to store and deliver natural gas for automotive applications.16 As a porous metal carboxylate, this material shows many important advantages like low cost, good water stability, an environmentally friendly synthesis route, and largescale production.15 However, despite its promising attributes, Al-fumarate was until recently characterized as having poor crystallinity, which represented a severe obstacle to the resolution of its crystal structure.15 To overcome this hurdle, Alvarez et al. optimized the synthesis procedure of Al-fumarate Received: June 2, 2017 Revised: August 11, 2017 Published: August 21, 2017 20287

DOI: 10.1021/acs.jpcc.7b05414 J. Phys. Chem. C 2017, 121, 20287−20295

Article

The Journal of Physical Chemistry C

Figure 1. View along the 1D lozenge-shaped channels of Al-fumarate. The inset shows the fumaric acid linker connecting the aluminum nodes in the structure.

2. THEORY AND COMPUTATIONAL DETAILS Kulkarni and Sholl have recently proposed a general framework for developing transferable force fields in order to model the adsorption of alkanes in a non-flexible MIL-47(V) MOF by using periodic density functional theory (DFT) calculations.21 By calculating the interaction energies for a large number of energetically favorable adsorbate configurations using DFT, the authors have succeeded in obtaining a force field, VDW-DF2 FF, that is able to accurately predict adsorption isotherms, enthalpies of adsorption, and diffusion properties for a wide range of alkanes and alkenes in MIL-47(V). They have also shown the transferability of this force field to related materials such as MIL-53(Cr) and they have used it to calculate the freeenergy differences for the experimentally observed phases of MIL-53(Fe).21 Herein we extend the transferability of VDWDF2 FF to the Al-fumarate structure and we show that it can be used to correctly predict the energetic interaction properties relative to the adsorption of not only n-alkanes but also monobranched and multibranched alkanes confined in this nanoporous material. 2.1. Atom-Type Additions to VDW-DF2 FF in This Work. In their work, Kulkarni and Sholl calculated interaction energies between each atom type in the MIL-47(V) structure and the CH_sp2, CH2_sp2, CH2_sp3 and CH3_sp3 TraPPE22 adsorbate force field types to fit their Lennard−Jones (LJ) parameters. These atom type interactions were necessary to model the adsorption of linear alkanes and alkenes in the pores of MIL-47(V).21 In this work, since we have attempted to extend the transferability of the VDW-DF2 FF to the adsorption of monobranched and multibranched alkanes in the Al-fumarate structure, some additions to the original force field were required. First, two adsorbate force field types had to be added in order to calculate the interactions of monobranched and multibranched alkanes with the MOF structure, i.e., CH_sp3 and C_sp3. The parameter values for these atom types were taken from the TraPPE force field.23 Second, a force field type for Al, for which the parameters were taken from the Dreiding23 force field, was also added. The impact of this latter addition on the force field balance should not, however, be significant since all adsorbate interactions with the metal node screened by the surrounding oxygen atoms are considered as

A520 and succeeded in obtaining a better crystallized solid, denoted as MIL-53(Al)-FA, which has less defect sites.5,10,16 The structural determination of MIL-53(Al)-FA lead to the same space group as the one obtained for the hydrated form of the MIL-53(Al) MOF, making these two materials isostructural. Both solids are built from linear chains of AlO4(OH)2 octahedra connected by organic linkers, generating 1D diamond-shaped pores, as shown on Figure 1. One of the differences between the two MOFs lies in the linkers between the metal nodes, MIL-53(Al) using a terephtalate linker to connect the AlO4(OH)2 nodes while in the case of Al-fumarate a fumarate linker is employed. Although both have 1D lozengeshaped pores, because of the shorter length of the fumaric acid linker, the size of Al-fumarate’s pores is smaller (5.7 × 6.0 Å2)5,17 than that of MIL-53(Al)’s (8.5 × 8.5 Å2)18 (Figure 1). Finally, while the structure of MIL-53(Al) clearly shows a breathing behavior upon water or CO2 adsorption,18,19 no such structural flexibility has been observed for Al-fumarate.5 Nevertheless, it was revealed that a significant reversible structural contraction of the Al-fumarate occurs under mechanical pressure, translating to a very high mechanical energy storage capacity.17 It is reported that MIL-53(Al) behaves in a non-shape-selective manner5 during adsorption of linear and branched alkanes, where the adsorption properties are dominated by van der Waals interactions while steric effects play no role.20 In contrast, it was demonstrated experimentally in our previous work that Al-fumarate behaves in a more selective way when compared to MIL-53(Al).5 Because of its smaller pore size, steric constraints are imposed by the Al-fumarate framework on the adsorption of branched and cyclic alkanes resulting in a pronounced shape selectivity. As a continuation of this work, here we have investigated these shape-selective properties through configurational bias Monte Carlo (CBMC) simulations. A DFT-derived force field obtained from the work of Kulkarni and Sholl21 was extended to the Al-fumarate structure in order to numerically confirm our experimental results. Enthalpies (−ΔH 0 ) and entropies (−ΔS0 ) of adsorption of C5−C8 n- and iso-alkanes in Al-fumarate were calculated, together with Henry’s constants K′ and separation factors of the n-alkanes versus their isomers. 20288


Article


Table 1. Relative Errors between Simulated Values Predicted with VDW-DF2 FF and Experimental Results for Thermodynamic Adsorption Properties of Alkanes on Al-Fumarate

n-alkanes

monobranched alkanes

multibranched alkanes

alkane, no. of C atoms

Δ(ΔH0) (%)

Δ(ln K′) @453 K (%)

Δ(ln K0′) (%)

Δ(ΔS0) @453 K (%)

n-pentane, 5 n-hexane, 6 n-heptane, 7 n-octane, 8 2-methylbutane, 5 3-methylpentane, 6 3-methylhexane, 7 3-methylheptane, 8 2,3-dimethylbutane, 6 2,3-dimethylpentane, 7 2,5-dimethylhexane, 8 iso-octane, 8

3.51 1.68 3.26 0.348 6.61 3.33 1.77 1.46 3.18 2.89 0.286 19.2

2.09 2.90 2.18 3.59 0.253 0.730 1.72 1.59 0.755 2.55 4.79 6.32

3.01 2.04 3.10 1.09 4.40 2.07 1.80 1.46 2.52 2.49 0.990 11.0

17.4 12.9 14.1 7.93 19.3 12.1 10.2 8.85 1.08 0.435 7.10 22.4

Figure 2. Thermodynamic properties of n- and iso-alkanes on aluminum fumarate at 453 K. The letters a−c refer to n-alkanes, monobranched, and multibranched alkanes, respectively. Black, filled symbols are experimental data obtained by us,5 red, open symbols are our CBMC calculations, and the black, open squares are predictions with the DREIDING force field which have been added for comparison. −ΔS0 and ln K′ values are calculated at 453 K. Numerical values for all data points can be found in Tables S1−S3. For multibranched alkanes, 1 = 2,5-dimethylhexane and 2 = iso-octane. Two numbers mean the points are overlapping each other, e.g., 2,2 represents iso-octane prediction points or experimental data points on top of each other.

negligible in the VDW-DF2 FF.21 It is important to emphasize the fact that the parameter values added in this work are not those for the interactions between atom types but values for the atom types themselves. They are generic TraPPE and Dreiding atom type parameters, and their interactions with other atom types are described with the usual Lorentz−Berthelot mixing rules.22 Thus, as opposed to the interaction parameters in the original VDW-DF2 FF, the parameters added here are not DFT-calculated, and they could be expected to be less accurate. 2.2. Al-Fumarate Structure Used in This Work. The Alfumarate crystallographic information was taken from the work of Yot et al.17 where the model was constructed starting with

the crystal structure of the hydrated form and subsequently optimized through DFT calculations in the absence of the free water molecules (Figure 1). The computational details for the structure solution of the dehydrated form of Al-fumarate used in this work can be found in the ESI of the same paper.17 2.3. Model for the Alkane Molecules. Hydrocarbons were modeled as flexible molecules and use the united atom TraPPE force field.21,22 In this force field, there are no charges associated with the united atoms, the intermolecular interactions being solely characterized by a LJ potential term. To be consistent with the TraPPE force field, the pairwise 20289


Article


and below 7% for monobranched and multibranched alkanes, the only exception being the value for iso-octane (we will address the case of this particular multibranched alkane further in the text). In comparison, the DREIDING force field significantly overpredicts the adsorbate−adsorbent interaction with much higher −ΔH0 and ln K′ values for all alkanes in the study, confirming that the fitting of LJ parameters to the DFTcalculated interaction energies considerably improves the accuracy of the VDW-DF2 FF. However, DREIDING FF’s calculations for the entropy of adsorption are very similar to that obtained with VDW-DF2 FF, the reason being that although the predictions for the variations in internal energy dU and Helmholtz energy dA are different for both force fields, the difference between the two quantities, encountered when calculating the variation of the entropy ΔS0 of adsorption through eq 4 is almost the same. Generally, −ΔH0 increases linearly with carbon number for microporous materials as every additional −CH2− group is responsible for additional dispersive interactions.20,29 In the case of n-pentane to n-octane on Al-fumarate, Table S1 shows an average experimental −ΔH0 increase of 9.3 kJ mol−1 for each additional alkyl group, while the simulations predict an average increase of 9.9 kJ mol−1 for Al-fumarate. Finsy et al. measured an experimental increase of 7.6 kJ mol−1 per alkyl group on MIL-47(V) and also obtained a higher average increase of 7.8 kJ mol−1 in their simulations.5 Bozbiyik et al. reported an average experimental increase of 8.7 kJ mol−1 on MIL-53(Al).5 Since the pore size of Al-fumarate (5.7 × 6.0 Å2)16 is significantly smaller than that of both MIL-47(V) (10.5 × 11.0 Å2)30 and MIL-53(Al) (8.5 × 8.5 Å2),18,31 this larger dependency of adsorption enthalpy on carbon number for Alfumarate is expected.5 Usually, the main difference between linear and branched alkanes is that in porous materials like zeolites and MOFs linear alkanes are able to enter the pore network much more easily and they are very strongly adsorbed while their branched isomers, adopting a more bulky configuration for the same number of carbons, have less enthalpic interactions with the framework.32,33 This is seen in Tables S1−S3 and Figure 2, where for a given number of carbons a decreasing −ΔH0 is observed. Figure 2 shows that the simulated values of Henry’s constant ln K′ also reproduce the experimental data extremely well, with relative errors between experimental and simulated values for all alkanes except iso-octane being under 5% (Table 1). For linear and monobranched alkanes, the predicted values of the adsorption entropy ΔS0 are systematically lower than the experimental values. Nevertheless, the increase with carbon number is similar for experimental and model values. 3.1. Influence of Chain Length on Thermodynamic Property Prediction. From Table 1 and Figure 2, it is noted that (except for iso-octane) the deviation between predicted and experimental values for each property decreases with increasing carbon number. One reason for this could be related to the steric distribution of the alkanes in the pores. When reporting the angles formed between the end-to-end vector of each n-alkane and the z axis on MIL-47(V) (corresponding to the direction along the tunnel), Déroche et al.4 noted a rather broad distribution for the shorter C5 and C6 molecules while the distribution became narrower and centered around increasingly smaller angle values as one moved toward C9. Using molecular simulations, the authors calculated the proportion of chains for each n-alkane that form an angle below 45° with the z axis, with this value being generally used

interactions between the MOF and the adsorbate molecules were modeled using van der Waals terms.21 2.4. Thermodynamic Properties of Adsorption Calculations. The ε and σ parameters from the VDW-DF2 FF were used for the calculations of thermodynamic adsorption properties at zero coverage: enthalpy of adsorption −ΔH0, Henry’s constant K′, and adsorption entropy −ΔS0, where the adsorption of n- and iso-alkanes on Al-fumarate was simulated using CBMC as implemented in the RASPA simulation code.24 The CBMC technique simulates adsorption at affordable computational cost, and because of the biased bead by bead growth process of molecular chains toward energetically favorable configurations, it favors avoiding overlap of the molecules within the structure.24,25 Thus, this technique greatly improves the configurational sampling of molecules and increases the efficiency of chain insertions by many orders of magnitude.24,26,27 During the growth process, since the Rosenbluth weight value Wg is directly related to the excess chemical potential, the free energy, and the Henry’s constant K′,26,27 Wg and the internal energy Ug of the gas are calculated. Then, using the obtained Wg value and the Widom insertion technique, which consists of inserting probe molecules and calculating the system energy at many random positions inside the unit cell,24 the average Widom Rosenbluth weight Whg, the average Henry’s constant K′, and average adsorption energy Ugh − Uh of the system are computed. From these, the internal and Helmholtz energies of the system, dU and dA respectively, can be calculated using eqs 1 and 2, and the enthalpy and entropy of adsorption are obtained using eqs 3 and 4, respectively. Since K′ is calculated directly from the CBMC simulations, the preexponential factor K0′ is obtained from eq 5, the van’t Hoff equation.5,28 dU = (Ugh − Uh) − Ug

(1)

dA = −RT ln(Whg /Wg)

(2)

ΔH0 = dU − RT

(3)

ΔS0 = (dU − dA)/T

(4)

K ′ = K 0′ exp(−ΔH /RT )

(5)

Finally, the calculations considered production runs of 200 000 cycles, a spherical cutoff of 12 Å was used for the pairwise interaction potentials, and the unit cell dimensions were 5 × 2 × 3 to satisfy the requirement of having a minimum length of twice the cutoff size value in every direction.24

3. RESULTS AND DISCUSSION Experimental and CBMC simulation results for zero-coverage adsorption enthalpy −ΔH0, the natural logarithm of Henry’s constant ln K′, pre-exponential factor −ln K0′ and entropy variation −ΔS0 on Al-fumarate are shown in Tables S1−S3 for n-, monobranched, and multibranched alkanes, respectively. Table 1 presents relative errors between experimental and simulated values predicted with the VDW-DF2 FF for each alkane investigated in this work. Figure 2 illustrates the variations of thermodynamic properties as a function of the number of carbons in the molecule, with predictions using the DREIDING force field added for comparison. Surprisingly, without refining any force field parameters, the simulated −ΔH0 values are in good agreement with the experimental results. Relative errors are below 5% for n-alkanes 20290


Article


Figure 3. Center of mass distribution of 1 molecule of (a) n-pentane, (b) n-nonane, and (c) 2,5-dimethylhexane in an Al-fumarate unit cell at the experimental temperature of 453 K over 1 × 106 MC cycles. The upper row is a face view of the 1D channels and the lower row shows a slightly angled representation of the same center of mass positions.

Figure 4. Compensation charts of n- and iso-alkanes adsorbed on Al-fumarate. The letters a−c refer to n-alkanes, monobranched, and multibranched alkanes, respectively. Black, filled lozenges are experimental data obtained by us,5 and red, open symbols are CBMC calculations. The long dashed lines are the slopes of the experimental data (- - -), and the shorter dashed lines are the predicted (·····) slopes.

should be broader than for the n-alkanes because of it. In order to have an idea of the steric distribution of various alkanes in the Al-fumarate pores, MC simulations were performed in the canonical (NVT) ensemble. Figure 3 shows the distribution of center of mass (COM) positions for one molecule of npentane, n-nonane, and 2,5-dimethylhexane in the Al-fumarate porous space at 453 K over 1 × 106 MC cycles. We notice from the larger diameter, i.e., distribution, of its COM positions (Figure 3a top) that the n-pentane molecule tends to reorientate more in the Al-fumarate pore than the n-nonane molecule (Figure 3b top). This is in line with Déroche et al.’s observations that the smaller molecule has more available space to adopt various configurations.4 Figure 3a,b (lower part) shows that the COMs of the n-pentane and n-nonane molecules are distributed homogeneously along the direction of the channel in the center of the pores. This figure shows a line across the porous space, meaning that it is statistically possible for the n-pentane or n-nonane molecule to adsorb at any of these positions. The larger dibranched 2,5-dimethylhexane molecule, while still preferentially located at the center of the pore, shows a non uniform distribution (lower part of Figure 3c, no line across the porous space in this case) adsorbing rather at the pore entrance of the Al-fumarate. Indeed, the methyl groups constituting the lateral branches of

as a threshold to obtain a qualitative trend on the molecular alignment along the pore. They observed that whereas nnonane and n-octane align solely along the direction of the channel the proportion significantly decreases for the shorter nalkanes, reaching only 50% for n-pentane. This trend is mainly governed by the steric constraint involving the difference between the cross section perpendicular to the direction of the MIL-47(V) channel of ∼10.5 Å30 and the increases in chain length for C5 to C9 (from 9.31 to 14.45 Å), resulting in molecules that increasingly adsorb with end-to-end vectors exclusively parallel to the channel.4 It is reasonable to assume that in the case of Al-fumarate the segregation between lower and higher n-alkanes should be greater because of the smaller cross section of the pores. Therefore, since the steric distribution is thought to be narrower for higher alkanes than in the case of MIL-47(V), the chances of sampling the energies in an area of the framework representative of the experimental conditions during the Widom test particle method would be increased. This could contribute to explaining the better prediction of higher n-alkanes’ thermodynamic properties. One can suppose that this principle also applies to the monobranched and branched alkanes, although to a lesser degree, since there will be less alkane-MOF energetic interactions for a given chain length and the steric distribution 20291


Article


although α varies between 4 and 100 for the different n-alkane/ iso-alkane couples. Even though the simulated separation of nalkanes from their branched isomers is not reproduced as accurately, the predictions are still in the correct range. 3.4. Predictions for Iso-Octane. It is noticed from Tables 1, 3, and S3 and Figures 2 and 4 that the only alkane for which the experimental value is not well predicted is iso-octane. It can also be perceived from Tables 2 and 3 that there seems to be a slight decrease in prediction accuracy as the branching level of the alkanes increases. One hypothesis for this is an issue concerning the additional adsorbate force field types mentioned in the Theory and Computational Details section. The LJ parameters for the interactions resulting from the Lorentz− Berthelot mixing rules may prove to be inadequate when paired with the other parameter values from the DFT-derived VDWDF2 FF. Although each branched alkane has a CH_sp3 force field atom type in its structure, its addition does not seem to have harmed the force field interactions in a significant way; the iso-octane molecule is the only alkane in our set to have a C_sp3 force field atom type in addition to a CH_sp3. It is possible that the inclusion of two additional non-DFTcalculated force field atom types in the same molecule may have contributed to a disruption of the force field balance. Additionally, iso-octane with its kinetic diameter of 6.2 Å might be too bulky to efficiently adsorb in the pores of Al-fumarate with a theoretical size of (5.7 × 6.0) Å2).16 The experimental values for adsorption enthalpy and entropy thus would rather reflect adsorption of iso-octane on the surface of the Alfumarate crystals or in the pore mouths. In the simulations, although iso-octane almost never occupies the center of the pore, there remains a probability that it does due to the energetically biased nature of the CBMC simulations. In those moments it is possible that the van der Waals interactions with the MOF structure are higher than in practical conditions. Figure 5 compares the centers of mass for 1 molecule of 2,5dimethlyhexane with those for 1 molecule of iso-octane at 453 K. Although the center of mass positions in the upper row of the figure look similar for both molecules, the light blue dots between the clusters of points in the lower row show that 2,5dimethylhexane can occupy the center of the Al-fumarate pore, whereas this almost never occurs with iso-octane. This can also be seen from the movie frames of Figure 6: Out of the 200 spatial configuration frames that we captured during simulations, the green 2,5-dimethylhexane could be found anywhere in the channel, while the bulkier gray iso-octane rarely moved from the entrance of the structure.

2,5-dimethylhexane contribute to its bulkiness and thus limits the penetration of this molecule in the pore channel This confirms Bozbiyik et al.’s observations about the profound shape selectivity of the Al-fumarate structure.5 3.2. Compensation Chart of n- and Iso-Alkanes on AlFumarate. During the adsorption process, stronger intermolecular interactions or bonding (related to enthalpy) lead to a greater reduction of the configurational freedom and hence to a higher order in the system (related to entropy). This is called the enthalpy−entropy compensation effect, and in adsorption, it often results in a linear relationship between adsorption enthalpy and adsorption entropy. In the case of n- and isoalkanes and taken in conjunction with the linear dependence of the enthalpy of adsorption with carbon number, the compensation effect provides a simple general predictive correlation.34 It is usually best interpreted by plotting the pre-exponential factor −ln K0′ as a function of −ΔH0.5,35 The slope of the compensation chart can be seen as an indication of the available space inside the pores of the material, a smaller pore size leading to more tightly bonded adsorption complexes and as such leading to higher entropy losses.35,36 In the case of n- and monobranched alkanes on Al-fumarate, this tendency is very well characterized by the simulations, with 4.7 and 8.3% relative error between experimental slopes and slopes predicted by the model, as shown in Figure 4 and Table 2. However, the Table 2. Compensation Chart Slopes for n- and Iso-Alkanes Adsorbed on Al-Fumarate at 453 K n-alkanes monobranched multibranched

sim

exp

rel error (%)

0.1115 0.1311 0.0963

0.1065 0.1211 0.1163

4.7 8.3 17.2

predictions are less accurate for the branched alkanes, and the simulated slope indicates a lower entropy loss than that measured experimentally. We hypothesize that the decrease in prediction accuracy with branching level can be at least partially explained by the additional non-DFT-calculated force field types required in the simulation of monobranched and branched alkanes. This issue is addressed in more detail in a further section. 3.3. Separation Factors. The separation capacity of a material can be calculated by defining a separation factor α as the Henry constant of the linear alkane divided by the Henry constant of the branched isomer.37 Separation factors obtained from experimental5 and predicted Henry constants are shown in Table 3. Once again, simulation results involving n-alkane and monobranched alkanes match experimental data very well,

4. CONCLUSION A periodic density functional theory (DFT)-derived force field originally parameterized to n-alkane adsorption on MIL-47(V) and calculated by Kulkarni and Sholl21 is expanded to the adsorption of n- and iso-alkane adsorption on Al-fumarate. With this force field, and using configurational bias Monte Carlo simulations (CBMC), experimental enthalpies of adsorption −ΔH0, Henry’s constants K′, adsorption entropy −ΔS0, and separation factors of C5−C8 n- and iso-alkanes are calculated. The predicted values match the experimental data obtained in our previous work very well. The enthalpies for nalkanes and Henry’s constants fall within 5% relative error of the experimental measurements, and enthalpies for monobranched and branched alkanes falling within 7%. The compensation effect between adsorption enthalpy and adsorption entropy is very well reproduced for n- and

Table 3. Separation Factors α of Alkanes versus Their Isomers on Aluminum Fumarate at 453 K no. of C atoms in the molecule 6

7

8

αSIM

αEXP

n-C6/3-MeC5 5.6 4.4 n-C7/3-MeC6 5.3 5.3 n-C8/3-MeC7 5.2 5.0

αSIM

αEXP

n-C6/2,3-diMeC4 14.0 10.9 n-C7/2,3-diMeC5 25.1 18.6 n-C8/2,5-diMeC6 5.3 6.0

αSIM

αEXP

n-C8/iso-octane 72.4

105.8 20292


Article


Figure 5. Center of mass variations of (a) 1 molecule of 2,5-dimethylhexane and (b) 1 molecule of iso-octane in a 5 × 3 × 3 Al-fumarate cell at the experimental temperature of 453 K over 1 × 106 MC cycles. The upper row is an angled view of the 1D channels, and the lower row shows a representation of the box without the framework atoms to facilitate viewing of the different center of mass positions of the molecules.

Figure 6. Movie frames from a side view of the 1D Al-fumarate channels. These are results of canonical Monte Carlo simulations of 1 molecule of 2,5-dimethylhexane and 1 molecule of iso-octane at 453 K over 1 × 106 MC cycles. The lighter, gray molecule in the second row from the top is isooctane while the green molecule in the second row from the bottom is 2,5-dimethylhexane. Out of 200 frames, the iso-octane molecule could not insert itself into the structure, while its isomer occupies the region from one end of the channel to the other.

monobranched alkanes, but it is not so accurately predicted for branched alkanes. This trend is also seen in the prediction of the separation factors where the accuracy of the simulations decrease with the branching level. One should however bear in mind that calculations involving entropy and separation factors because of the impossibility of direct measurement are hard to

reproduce accurately. The excellent match between our experimental and simulated thermodynamic properties of adsorption foresees the possibility of accurately describing iso-alkane adsorption isotherms on this commercialized Alfumarate material, which could eventually help meet some of the practical needs encountered at an industrial level. 20293


Article


■

Water Adsorption. Microporous Mesoporous Mater. 2009, 120, 325− 330. (14) Yang, Q.; Vaesen, S.; Ragon, F.; Wiersum, A. D.; Wu, D.; Lago, A.; Devic, T.; Martineau, C.; Taulelle, F.; Llewellyn, P. L.; et al. A Water Stable Metal-Organic Framework with Optimal Features for CO2 Capture. Angew. Chem. 2013, 125, 10506−10510. (15) Coelho, J. A.; Ribeiro, A. M.; Ferreira, A. F. P.; Lucena, S. M. P.; Rodrigues, A. E.; Azevedo, D. C. S. de. Stability of an Al-Fumarate MOF and Its Potential for CO2 Capture from Wet Stream. Ind. Eng. Chem. Res. 2016, 55, 2134−2143. (16) Alvarez, E.; Guillou, N.; Martineau, C.; Bueken, B.; Van de Voorde, B.; Le Guillouzer, C.; Fabry, P.; Nouar, F.; Taulelle, F.; de Vos, D.; et al. The Structure of the Aluminum Fumarate MetalOrganic Framework A520. Angew. Chem., Int. Ed. 2015, 54, 3664− 3668. (17) Yot, P. G.; Vanduyfhuys, L.; Alvarez, E.; Rodriguez, J.; Itié, J.-P.; Fabry, P.; Guillou, N.; Devic, T.; Beurroies, I.; Llewellyn, P. L.; et al. Mechanical Energy Storage Performance of an Aluminum Fumarate Metal−organic Framework. Chem. Sci. 2016, 7, 446−450. (18) Loiseau, T.; Serre, C.; Huguenard, C.; Fink, G.; Taulelle, F.; Henry, M.; Bataille, T.; Férey, G. A Rationale for the Large Breathing of the Porous Aluminum Terephthalate (MIL-53) Upon Hydration. Chem. - Eur. J. 2004, 10, 1373−1382. (19) Bourrelly, S.; Llewellyn, P. L.; Serre, C.; Millange, F.; Loiseau, T.; Férey, G. Different Adsorption Behaviors of Methane and Carbon Dioxide in the Isotypic Nanoporous Metal Terephthalates MIL-53 and MIL-47. J. Am. Chem. Soc. 2005, 127, 13519−13521. (20) Finsy, V. Evaluation of the Metal-Organic Frameworks MIL-47, MIL-53 and Cu3(BTC)2 for the Adsorptive Separation of Molecular Mixtures. Ph.D. Dissertation, Vrije Universiteit Brussel (VUB), Brussels, Belgium, 2009. (21) Kulkarni, A. R.; Sholl, D. S. DFT-Derived Force Fields for Modeling Hydrocarbon Adsorption in MIL-47(V). Langmuir 2015, 31, 8453−8468. (22) Martin, M. G.; Siepmann, J. I. Novel Configurational-Bias Monte Carlo Method for Branched Molecules. Transferable Potentials for Phase Equilibria. 2. United-Atom Description of Branched Alkanes. J. Phys. Chem. B 1999, 103, 4508−4517. (23) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. DREIDING: A Generic Force Field for Molecular Simulations. J. Phys. Chem. 1990, 94, 8897−8909. (24) Dubbeldam, D.; Calero, S.; Ellis, D. E.; Snurr, R. Q. RASPA: Molecular Simulation Software for Adsorption and Diffusion in Flexible Nanoporous Materials. Mol. Simul. 2016, 42, 81−101. (25) Smit, B.; Maesen, T. L. M. Towards a Molecular Understanding of Shape Selectivity. Nature 2008, 451, 671−678. (26) Smit, B.; Siepmann, J. I.; et al. Computer Simulations of the Energetics and Siting of N-Alkanes in Zeolites. J. Phys. Chem. 1994, 98, 8442−8452. (27) Frenkel, D.; Smit, B. In Understanding Molecular Simulation, 2nd ed.; Frenkel, D., Smit, B., Eds.; Academic Press: San Diego, CA, 2002; pp 389−408. (28) Denayer, J. F. M.; Ocakoglu, R. A.; Arik, I. C.; Kirschhock, C. E. A.; Martens, J. A.; Baron, G. V. Rotational Entropy Driven Separation of Alkane/Isoalkane Mixtures in Zeolite Cages. Angew. Chem. 2005, 117, 404−407. (29) Jiang, J.; Sandler, S. I.; Schenk, M.; Smit, B. Adsorption and Separation of Linear and Branched Alkanes on Carbon Nanotube Bundles from Configurational-Bias Monte Carlo Simulation. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 045447. (30) Barthelet, K.; Marrot, J.; Riou, D.; Férey, G. A Breathing Hybrid Organic−Inorganic Solid with Very Large Pores and High Magnetic Characteristics. Angew. Chem., Int. Ed. 2002, 41, 281−284. (31) Trung, T. K.; Déroche, I.; Rivera, A.; Yang, Q.; Yot, P.; Ramsahye, N.; Vinot, S. D.; Devic, T.; Horcajada, P.; Serre, C.; et al. Hydrocarbon Adsorption in the Isostructural Metal Organic Frameworks MIL-53(Cr) and MIL-47(V). Microporous Mesoporous Mater. 2011, 140, 114−119.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b05414. Obtained simulation and experimental values and details concerning the force field parameters (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +32 2 629 1798. ORCID

Ege Dundar: 0000-0001-6094-1388 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS J.F.M.D. and E.D. are grateful to FWO Vlaanderen for financial support (G025614N). G.M. thanks Institut Universitaire de France for its support.

■

REFERENCES

(1) Ackley, M. Application of Natural Zeolites in the Purification and Separation of Gases. Microporous Mesoporous Mater. 2003, 61, 25−42. (2) Altwasser, S.; Welker, C.; Traa, Y.; Weitkamp, J. Catalytic Cracking of N-Octane on Small-Pore Zeolites. Microporous Mesoporous Mater. 2005, 83, 345−356. (3) Denayer, J. Influence of the Zeolite Composition on the HydroIsomerisation and Hydrocracking of Alkanes on Pt/USY Zeolites: Modelling of the Reaction Kinetics Using an Adsorption−reaction Approach. Appl. Catal., A 2003, 246, 17−28. (4) Déroche, I.; Rives, S.; Trung, T.; Yang, Q.; Ghoufi, A.; Ramsahye, N. A.; Trens, P.; Fajula, F.; Devic, T.; Serre, C.; et al. Exploration of the Long-Chain N -Alkanes Adsorption and Diffusion in the MOFType MIL-47 (V) Material by Combining Experimental and Molecular Simulation Tools. J. Phys. Chem. C 2011, 115, 13868−13876. (5) Bozbiyik, B.; Lannoeye, J.; De Vos, D. E.; Baron, G. V.; Denayer, J. F. M. Shape Selective Properties of the Al-Fumarate Metal−organic Framework in the Adsorption and Separation of N-Alkanes, IsoAlkanes, Cyclo-Alkanes and Aromatic Hydrocarbons. Phys. Chem. Chem. Phys. 2016, 18, 3294−3301. (6) Ruthven, D. M. M. Principles of Adsorption and Adsorption Processes; Wiley-Interscience: New York, 1984. (7) Couck, S.; Liu, Y.-Y.; Leus, K.; Baron, G. V.; Van der Voort, P.; Denayer, J. F. M. Gas Phase Adsorption of Alkanes, Alkenes and Aromatics on the Sulfone-DUT-5 Metal Organic Framework. Microporous Mesoporous Mater. 2015, 206, 217−225. (8) Zhou, H.-C. Metal−Organic Frameworks (MOFs). Chem. Soc. Rev. 2014, 43 (16), 5415−5418. (9) Maurin, G.; Serre, C.; Cooper, A.; Férey, G. The New Age of MOFs and of Their Porous-Related Solids. Chem. Soc. Rev. 2017, 46 (11), 3104−3107. (10) Yot, P. G.; Boudene, Z.; Macia, J.; Granier, D.; Vanduyfhuys, L.; Verstraelen, T.; Van Speybroeck, V.; Devic, T.; Serre, C.; Férey, G.; et al. Metal−organic Frameworks as Potential Shock Absorbers: The Case of the Highly Flexible MIL-53(Al). Chem. Commun. 2014, 50, 9462−9464. (11) Chae, H. K.; Siberio-Perez, D. Y.; Kim, J.; Go, Y.; Eddaoudi, M.; Matzger, A. J.; O’Keeffe, M.; Yaghi, O. M. A Route to High Surface Area, Porosity and Inclusion of Large Molecules in Crystals. Nature 2004, 427, 523−527. (12) Burtch, N. C.; Jasuja, H.; Walton, K. S. Water Stability and Adsorption in Metal−Organic Frameworks. Chem. Rev. 2014, 114, 10575−10612. (13) Küsgens, P.; Rose, M.; Senkovska, I.; Fröde, H.; Henschel, A.; Siegle, S.; Kaskel, S. Characterization of Metal-Organic Frameworks by 20294


Article

The Journal of Physical Chemistry C (32) Denayer, J. F.; Ocakoglu, R. A.; De Meyer, K.; Baron, G. V. Exploiting Pore or Cavity Size and Shape in Separating Linear and Branched Hydrocarbons by Inverse Selectivity: Enthalpy, Entropy and Packing Effects. Adsorption 2005, 11, 49−53. (33) Jiang, J.; Sandler, S. I. Monte Carlo Simulation for the Adsorption and Separation of Linear and Branched Alkanes in IRMOF-1. Langmuir 2006, 22, 5702−5707. (34) Ruthven, D. M.; Kaul, B. K. Compensation Theory of Adsorption: Correlation and Prediction of Henry Constants for Linear Paraffins on Zeolite Adsorbents. Adsorption 1998, 4, 269−273. (35) De Moor, B. A.; Reyniers, M.-F.; Gobin, O. C.; Lercher, J. A.; Marin, G. B. Adsorption of C2−C8 N -Alkanes in Zeolites †. J. Phys. Chem. C 2011, 115, 1204−1219. (36) Denayer, J. F.; Baron, G. V.; Martens, J. A.; Jacobs, P. A. Chromatographic Study of Adsorption of N-Alkanes on Zeolites at High Temperatures. J. Phys. Chem. B 1998, 102, 3077−3081. (37) Finsy, V.; Calero, S.; García-Pérez, E.; Merkling, P. J.; Vedts, G.; De Vos, D. E.; Baron, G. V.; Denayer, J. F. M. Low-Coverage Adsorption Properties of the Metal−organic Framework MIL-47 Studied by Pulse Chromatography and Monte Carlo Simulations. Phys. Chem. Chem. Phys. 2009, 11, 3515.

20295


Modeling of Adsorption Thermodynamics of Linear and Branched

Recommend Documents