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Structural Transitions in the MIL-53(Al) Metal-Organic Framework Upon Cryogenic Hydrogen Adsorption Jose P.B. Mota, Daniel Martins, Diogo Lopes, Isabel Catarino, and Grégoire Bonfait J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06861 • Publication Date (Web): 12 Oct 2017 Downloaded from http://pubs.acs.org on October 13, 2017

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The Journal of Physical Chemistry

Structural Transitions in the MIL-53(Al) metal-Organic Framework Upon Cryogenic Hydrogen Adsorption José P. B. Mota,∗,† Daniel Martins,‡,¶ Diogo Lopes,‡,§ Isabel Catarino,‡ and Grégoire Bonfait‡ †LAQV-REQUIMTE, Departamento de Química, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal ‡LIBPhys, Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal ¶Current address: Active Space Technologies, 3045-508 Coimbra, Portugal §Current address: Air Liquide Advanced Technology Division (AL/DTA) Sassenage, France E-mail: [email protected] Phone: +351 21 2948300. Fax: +351 21 2948385 Abstract The energetics and phase behavior of the mil-53(Al) metal-organic framework upon low-temperature (15–260 K), sub-atmospheric H2 adsorption are studied experimentally using a volumetric technique and theoretically by grand canonical Monte Carlo simulation. The adsorption equilibrium data are recorded for a fixed amount of H2 in the system at stable increasing temperature steps starting from 15 K while recording the equilibrium pressure attained at each step. The adsorption isotherms are generated by repeating the experiments for different fixed amounts of adsorbate in the system and

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connecting the equilibrium points obtained at the same temperature. The solid–fluid interactions are modeled using the trappe-ua force field and the fluid–fluid interactions using a parametrization consistent with the same force field; quantum effects on H2 adsorption are taken into account via a quartic approximation of the Feynman–Hibbs variational approach. The use of a consistent force field with proven transferability of its parameters provides an accurate description of the experimental adsorption equilibria and isosteric heats of adsorption. Because of the weak solid–fluid interaction, the Henry constant for H2 adsorption in the large-pore (lp) form of mil-53(Al) surpasses that for H2 adsorption in the narrow-pore (np) form at a temperature lower than that at which the dehydrated structure of the material collapses. However, the saturation capacity of the np-form is higher than that of the lp phase. The phase behavior of mil53(Al) upon temperature-induced H2 desorption is interpreted in terms of the osmotic

thermodynamic theory. For the conditions spanned in the experiments mil-53(Al) exhibits at most a single structural transition and its phase behavior depends not only on pressure and temperature but also on the thermal history of the bare material.

Introduction Metal–organic frameworks (mofs) are crystalline materials containing a metal atom or metal cluster bonded to organic linkers, 1–4 and are a subset of the class of materials known as coordination polymers. Because of their very large surface area, gas selectivity, and permanent, open-pore geometry, mofs have emerged as promising materials for gas storage and separation, 5 as well as several other applications. 6 They are highly tunable in both structure and composition, as both metal clusters 7,8 and linkers have the potential to be varied among several possibilities. Of the different types of structural transformation that some mofs undergo in response to external stimuli, the most pronounced one is the so-called “breathing” effect which consists in an abrupt structural change between two stable forms of the same mof upon guest molecule

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adsorption. 9 The most well-known example of this breathing behavior is the mil-53 series of mofs. 10 Interestingly, the large volume change upon breathing can not only be triggered by adsorption stress but also by mechanical pressure, 11,12 temperature, 13 or even electric field. 14 The mil-53 series of porous materials exhibits two stable structures: a large-pore (lp) form with a unit cell volume of ca. 1.03 cm3 /g and an accessible pore volume of 0.56 cm3 /g, and a narrow-pore (np) form with significantly less volume (up to 40% reduction) for the adsorption of guest molecules. Depending upon the temperature and guest molecule, this material can show a single-transition, a double structural transition, or no transition at all. 15–17 Although the breathing effect triggered by adsorption stress in the mil-53 series of mofs has been well documented and explained for various guest molecules, 18–27 far too little attention has been paid to the case of adsorption of a light adsorbate experiencing weak solid–fluid interactions, particularly when the adsorption/desorption process is thermally assisted over a very wide temperature range, which must necessarily span very low temperatures for interesting effects to emerge. The present paper seeks to remedy this problem by investigating the breathing behavior of mil-53(Al)—the aluminum member of the mil-53 series—upon hydrogen adsorption, a gas which is well know to physisorb weakly in most porous materials. More specifically, the energetics and phase behavior of mil-53(Al) upon H2 adsorption have been studied experimentally over an unusually broad temperature range (15–260 K) via volumetric adsorption experiments and theoretically by grand canonical Monte Carlo (gcmc) simulation and classical thermodynamics. We start by describing the volumetric apparatus devised for low-temperature adsorption measurements and the adopted experimental protocol; because of limitations of our capacitor gauges, the maximum recorded pressure cannot exceed a value slightly above one atmosphere. After presenting the force field for modeling the fluid–fluid and solid–fluid interactions and providing some simulation details, it is demonstrated that the use of a consistent force field with proven transferability of its parameters provides an accurate description of the experimental adsorption isotherms and isosteric heats of adsorption.

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It is observed that the plots of the Henry constant versus temperature for H2 adsorption in the lp and np forms of mil-53(Al) cross at a relatively low temperature because of the weak interaction of hydrogen with the mof framework. Before concluding with a brief summary, the phase behavior of mil-53(Al) upon heat-assisted hydrogen desorption is interpreted in terms of the osmotic thermodynamic theory.

Materials and experimental setup The mil-53(Al) crystals were synthesized by basf (Sommerst, NJ) under the trademark Basolite A100 and purchased from Sigma-Aldrich (product no. 688738-10G). The powder sample was degassed and activated at 473 K overnight before characterization. 26 The particle size distribution of the crystals was estimated using the conventional method of Mayer & Stowe 28 applied to low-pressure (0.2–10 MPa) mercury intrusion data measured in an Autopore IV 9500 porosimeter (Micromeritics, Norcross, Georgia). The particle size distribution is well described by a log-normal distribution with mean diameter of 30.0 µm and standard deviation of 1.7 µm, which is in fairly good agreement with the mean value of 32 µm reported by the manufacturer but larger than the 2–3 µm size range reported by other authors 11,17,29 for their in-house synthesized batches. Fig. 1 shows a schematic of our volumetric setup for adsorption measurements in the 15–300 K temperature range. In short, it consists of a measuring cell (Vm = 5 cm3 ) filled with the sample under study and closed leak-tightly using indium O-ring by a lid. This lid includes a stainless steel connection to a thin wall tube connected to a panel of valves at room temperature. The measuring cell is thermally attached to the cold finger of a 10 K Gifford-Mac Mahon type cryocooler and connected to a temperature-controlled calibrated volume (VR ≈ 1000 cm3 , TR = 303 K). The pressure in the whole system is measured at room R type capacitor gauges (13 mbar and 1300 mbar range). temperature using two Baratron

Prior to carrying out a series of measurements, the whole system is firstly evacuated

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Capacitor gauges

SS cappilary tubing VR, TR

Vm, T

Cold finger

Calibrated volume

Thermostated cell

Vaccum pump

Gas reservoir

Cryo-refrigerator

Figure 1: Schematic of the volumetric setup for single-component adsorption equilibrium measurements in the range of temperatures between 10 K and 300 K.

(< 10−1 mbar) and then the calibrated volume pressurized to an initial pressure P0 , the gas mole number being computed using the ideal gas law. Subsequently, the gas in the calibrated volume is expanded to the measuring cell and the cryocooler is turned on to cool the measuring cell down to 15 K, the lowest recorded temperature. The adsorption equilibrium data are recorded automatically at stable increasing temperature steps up to 260 K by means of an accurate temperature controller while recording the equilibrium pressure attained at each step. Pressure gradients due to thermal transpiration were estimated using the empirical equation of Takaishi & Sensui 30 and found to be negligible for the geometry and pressure range used in this study. The dead volumes (valve panel and tubing) have been carefully measured and found to be small compared to the calibrated volume, VR ; in the following, for calculation purposes they are included in the value of VR . Since the initial amount of gas in the reference volume before expansion is known, the amount adsorbed in the cell can be determined from a material balance coupled to the equation of state for the adsorptive gas: 31

ms nex (P, T ) + (Vm − ms vs ) ng (P, T ) = VR [ng (P0 , TR ) − ng (P, TR )].

(1)

Here, Vm and VR are the volumes of the measuring and calibrated cells, respectively, ms and 5



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vs = 1/ρs the mass and specific skeletal volume of the adsorbent (ρs is the skeletal density), nex the excess adsorbed concentration at the equilibrium pressure P and temperature T , ng the gas concentration at (P, T ) conditions, and P0 the initial pressure in the calibrated volume (before expansion) regulated at temperature TR . The total adsorption concentration, na , is related to the measured excess adsorption, nex , by na = nex + vµ ng ,

(2)

where vµ is the specific pore volume of the adsorbent. The apparent specific volume of the solid (skeletal plus pore volume) is vp = vµ + vs = 1/ρp (ρp is the apparent solid density), which for a crystalline porous solid can be determined directly from the crystallographic data obtained by X-ray diffraction analysis. If eq. (2) is inserted into eq. (1), the latter equation can be written in terms of na ; the result is

ms na (P, T ) + (Vm − Vs )ng (P, T ) = VR [ng (P0 , TR ) − ng (P, TR )],

(3)

or in differential form as

ms dna + (Vm − Vs ) dng = −VR dng (P, TR ),

(4)

where Vs = ms vp is the apparent volume (skeletal plus porous) occupied by the adsorbent in the measuring cell. If the experiments are repeated for different fixed amounts of hydrogen in the system, corresponding to different values of P0 , for the same temperature steps, it is then straightforward to generate the isotherms of amount adsorbed versus pressure in the external gas phase by connecting the equilibrium points obtained at the same temperature. Fig. 2a shows the equilibrium measurements of pressure and temperature for hydrogen adsorption in mil-53(Al) using the procedure just described. The data are arranged in

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Figure 2: Experimental equilibrium data for hydrogen adsorption in mil-53(Al). (a) Each set of colored symbols was obtained for a fixed amount of hydrogen in the system, corresponding to a given initial pressure, P0 , in the calibrated volume. The sample is degassed and reactivated and then cooled down to the lowest measured temperature; the gas in the calibrated volume initially at P0 is allowed to expand to the measuring cell. The temperature is then increased in small steps while the system is allowed to equilibrate at each point. (b) The (P, T ) pairs are converted to excess adsorption values via eq. (3). Each adsorption isotherm, of which various examples are shown as solid, piecewise linear curves, is constructed by joining the equilibrium points obtained at the same temperature. 7



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8 sets, each one corresponding to an experiment starting from a different initial pressure P0 , in the range 50–1200 mbar, after which the system is heated from 15 K to 260 K in small temperature steps while allowing the system to equilibrate between temperature changes. Each (P, T ) pair is converted into a corresponding (P, T, na ) trio via eq. (3) and the resulting data are plotted in Fig. 2b as a scatter graph of na against P . The piecewise-linear solid lines in the scatter diagram represent various examples of adsorption isotherms constructed by connecting the equilibrium points measured at the same temperature. The two adsorption isotherms at 15 K and 17.5 K show partial condensation in the measuring cell and will be excluded from further analysis. A glance at the graph in Fig. 2b shows that the points obtained for the same amount of hydrogen in the system, corresponding to a set of symbols with the same color, when plotted as amount adsorbed versus pressure lie very closely about a straight line, as exemplified by the gray dashed line. Moreover, the slope of the straight line is practically the same for all sets of measurements. The reason for this is explained next. First, it must be noted that as the measuring cell is progressively heated, the system pressure increases because more hydrogen is desorbed to the gas phase; inversely, if the measuring cell is progressively cooled, the pressure decreases as more hydrogen adsorbs from the gas phase. Eq. (3) shows that in the limit of vanishing pressure, limP →0 ms nex ≈ VR ng (P0 , TR ); hence, if the straight line in Fig. 2b is extrapolated to P = 0, it crosses the vertical axis at VR ng (P0 , TR )/ms . At the other end of a set of experiments for a fixed amount of hydrogen in the system, say the point measured at T = TR (ambient temperature), the amount of adsorbed hydrogen is negligible compared with the amount of gaseous hydrogen in the system as seen by the points in Fig. 2b clustered around the horizontal axis (na ≈ 0). Under these conditions it is possible to estimate the system pressure, PR , for T = TR . In the experiments reported here PR is very close to P0 because VR ≫ Vm , but it is easy to determine the value of PR for any

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ratio of cell volumes. Resorting again to eq. (3),

0 + (Vm − Vs )ng (PR , TR ) ≈ VR [ng (P0 , TR ) − ng (PR , TR )],

(5)

which, taking into account that hydrogen behaves like an ideal gas at low pressure, becomes

(Vm − Vs + VR )

P0 PR ≈ VR , TR TR

(6)

or solving for PR , PR =

VR P0 . Vm − Vs + VR

(7)

This is the value at which the straight line superimposing onto the set of experiments started from the same initial pressure crosses the horizontal axis. Finally, the slope of the straight line is just the additive inverse of the ratio of these two values: slope = −

V m − m s vp + V R , m s Rg T R

(8)

where Rg is the ideal gas constant. This expression is independent of P0 , which explains why the sets of measurements obtained for different values of P0 fall onto straight lines with the same slope. The gray, dashed line shown in Fig. 2b was plotted using coordinates obtained from eqs. (7) and (8). Eq. (8) shows that enlarging the system volume (Vm + VR ) and/or reducing the temperature of the reference volume, TR , increases the steepness of the straight lines, whereas filling the measuring cell with more adsorbent (i.e., increasing ms ) works the other way round. A shallower slope makes the manometric calculation of na more precise, but also amplifies the uncertainty of the ancillary volumes present in the system with respect to the reference volume. Our choices of Vm = 5 cm3 and VR = 1000 cm3 stem from a compromise between the accuracy of the pressure transducers and the precision with which the various system volumes were measured. 9



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MIL-53(Al)lp

Al

OH

C(3)

O(2)

C(2) C(1) MIL-53(Al)np

Figure 3: Labeling of the pseudo-atoms of mil-53(Al)’s crystallographic framework and crosssectional views of the 1-D lozenge-shaped channels for its narrow-pore (np) and large-pore (lp) forms, where, for clarity, the hydrogen atoms are not shown.

Molecular model and simulation method The mil-53(Al) framework is built up by the interconnection of infinite trans chains of cornersharing (via OH groups) AlO4 (OH)2 octahedra by 1,4-benzenedicarboxylate (DBC) ligands, One notes that this structure contains hydroxyl groups located at the metal–oxygen–metal links. The structural topology of mil-53(Al) consists of a 44 net (Fig. 3) with tilted chains of AlO4 (OH)2 octahedra sharing trans hydroxyl groups; these chains are linked via the carboxylate groups of the 1,4-benzenedicarboxylate ligands, forming a 3D framework. The porous framework of mil-53(Al) is dominated by the organic ligand, and since the polarizability of the aluminum atoms is much lower than those of the oxygen atoms, 22 the dispersive contribution of the inorganic part of mil-53(Al) should be attributed mostly to the oxygens and hydroxyl groups. It is thus likely that a force field whose parametrization is determined from vapor–liquid equilibria, enthalpies of vaporization, and vapor pressures of 10


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organic compounds, namely, alkylbenzenes with ether or hydroxyl functionalities, requires minimum adjustment of its parameters to provide a reasonably accurate quantitative description of the adsorption of small, nonpolar molecules into the porous framework of mil-53(Al). With this in mind, our the parametrization of the solid–fluid dispersion interactions for the system H2 /mil-53(Al) is based on the united-atom (ua) version of the trappe force field 32–34 to take advantage of the transferability of the parameters built into it (see Supporting Information for details). We have already demonstrated that no reparametrization of the dispersive parameters for mil-53(Al) is necessary when the trappe-ua force field is employed for methane, ethane, and ethylene. 26,27 The results presented here show that the same is true for the hydrogen molecule. The good balance between enthalpic and entropic contributions to the free energy in the trappe-ua force field is probably the main reason why it is transferable to different physical conditions, including those where the “pseudo-solvent” is a rigid lattice dominated by an organic ligand in which the metal atoms are shielded from the influence of the adsorbate molecules by organic or inorganic groups (in this case, the oxygens and hydroxyl groups of the inorganic octahedra). In the present work we are mostly interested in studying the first-order phase behavior of mil-53(Al) upon temperature-induced H2 desorption and to further interpret it using classical thermodynamics. That is, we are mostly interested in analyzing the conditions that trigger the occurrence of the abrupt oscillation (or “breathing”) between the two mil-53’s distinct conformations. An analysis of secondary effects of thermal expansion of the lattice around the lp and np forms is outside the scope of the present work. For this reason, in our molecular simulation work the narrow-pore (np) and large-pore (lp) forms of the mil-53(Al) framework were modeled as being rigid with their constituent atoms at the positions reported by crystallography. 13,23 It is known that a flexible lattice can potentially influence diffusion properties because the diffusing adsorbate molecules have to surpass energy barriers posed by the pore channels and its intersections. In a flexible mil53(Al)

framework, lattice fluctuations can affect the size of the pore channels and, thereby,

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the height of these energy barriers. However, our study focuses on the low-energy, solid– fluid equilibrium configurations, so that the fluctuations in the higher-energy configurations in flexible mil-53(Al) models are expected to be negligible. Moreover, the comparison with experiments reported below provides some evidence as to the reasonableness of our assumption. The crystal data for mil-53(Al)lp are as follows: 13 orthorhombic system (Imma), a = 6.638 Å, b = 16.761 Å, c = 12.839 Å and α = β = γ = 90.0◦ , unit cell volume, Vuc = 3

1428.5 Å ; those for mil-53(Al)np are: 23 monoclinic system (C2/c), a = 19.713 Å, b = 8.310 Å, c = 6.806 Å and α = 90.0◦ , β = 105.85◦ , γ = 90.0◦ , unit cell volume, Vuc = 3

1072.5 Å . The top-left pictures Fig. 3 show views of the cross-section of the one-dimensional lozenge-shaped pores of the np and lp forms of mil-53(Al), where, for clarity, the hydrogen atoms are not shown. In our molecular simulations quantum effects on hydrogen adsorption were taken into account via the Feynman–Hibbs (fh) variational approach 35 as it is easily incorporated into our mc simulation code. A quartic approximation 36 was adopted (see Supporting Information for details). The fh approximation works as a correction to the classical interaction potential by including extra terms that depend on the inverse temperature and on the reduced mass of the two interacting molecules. We adopted the lj parameters of H2 –H2 interactions proposed by Kumar et al., 37 which were determined using the same quartic fh approximation for quantum corrections as adopted by us. This set of lj parameters reproduces the bulk physical properties of hydrogen with better accuracy than the often used Buch parameters. 38

Results and discussion Fig. 4 compares hydrogen adsorption isotherms for the lp form of mil-53(Al) in the 30–140 K range simulated with the classical lj intermolecular potential and with quantum corrections incorporated into the classical potential using the fh variational approach. Although quan-

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0.1 80 K 10−2 140 K 10−3 FH

10−4

effective potential

classical LJ potential 10−4

10−3

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0.1

1

Figure 4: Hydrogen adsorption isotherms for the large-pore form of mil-53(Al) in the 30– 140 K range simulated with the classical lj intermolecular potential (symbols) and with quantum corrections incorporated into the classical intermolecular potential using the fh variational approach (lines).

titatively different from those for the lp form, the simulated hydrogen adsorption isotherms for the np form of mil-53(Al) exhibit the same qualitative differences between the classical and quantum fluids; for the sake of brevity they are not reproduced here. Quantum effects, which are clearly visible at temperatures below ca. 80 K, reduce the amount of confined quantum hydrogen compared with that of the classical fluid at the same pressure and temperature, and the deviation from the classical behavior becomes more pronounced at lower temperatures. This difference comes from the quantum reduction in the well depth of the fluid–fluid (ǫff ) and solid–fluid (ǫsf ) interactions, and this decrease is also associated with an increase in the effective size parameter of the fluid–fluid (σff ) and solid–fluid (σsf ) quantum interactions because of the spread in the particle position due to the uncertainty principle. In the fh variational approach this spread is characterized by 13



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a Gaussian with width

p βℏ2 /12µ (see Supporting information), which for the fluid–fluid √ quantum interaction is 2 times that of the solid–fluid quantum interaction because the uncertainty in position of the atoms of the mof framework does not contribute to the solid– fluid interaction for they are assumed to be rigidly linked together. Note also that below ca. 60 K it is clearly visible that the number of quantum hydrogen molecules stored in the mof framework at full occupancy is smaller than that of classical molecules, because of the larger values of σff and σsf for quantum hydrogen compared with those for the classical fluid. This difference is more pronounced in the np form because of its narrower pore structure. We now turn our attention to the analysis of the experimental hydrogen adsorption isotherms for mil-53(Al). The range of temperatures between 40 K and 100 K is analyzed first. Fig. 5 compares the experimental H2 adsorption equilibrium data with the gcmc simulated isotherms for the lp and np forms of mil-53(Al): on the right-hand side there is shown the lines that interpolate the simulated H2 adsorption data for mil-53lp whereas on the right-hand side those that interpolate the gcmc data for mil-53np. When the simulations are matched against the experimental measurements, it is clear that below 70 K and hydrogen pressures up to atmospheric mil-53(Al) is in its np form because the experimental data compare well with the simulations for mil-53np but deviate significantly from those for mil-53lp. The graphical comparison of the results for 80 K and 100 K is less clear because the amounts adsorbed are smaller than those at lower temperatures and a linear ordinate scale masks the differences between the values for the np and lp forms; but a log scale shows that the simulations for the np form match the experiments at 100 K much better than those for the lp form. Anyway, it is not worth wasting too much time discussing these two temperatures at this point, for they and the other higher ones are analyzed in detail below. Overall, we note that the adopted force field gives a reasonable good description of the experimental H2 measurements for the tested thermodynamic conditions. 14


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Figure 5: Hydrogen adsorption isotherms for mil-53(Al) at temperatures between 40 K and 100 K and pressures below 1.2 bar. Colored circles: experimental data; small black circles: gcmc simulation data for (a) the lp form, mil-53(Al)lp, and (b) the np form, mil-53(Al)np; lines: fitting of a Virial-type adsorption isotherm to each set of gcmc isotherm data.

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Since the experimental hydrogen adsorption data were obtained in experiments in which the measuring cell was first cooled to 15 K and then the temperature increased in small steps while the system was allowed to equilibrate at each point, the mil-53(Al) sample was initially in its np form. It is thus apparent that, below ca. 70 K, mil-53(Al) remains in its np form upon H2 adsorption up to the maximum pressure attained experimentally (ca. 1100 mbar). We now move to the range of temperatures between 100 K and 260 K. Fig. 6 compares in a series of log–log graphs the experimental H2 adsorption equilibrium data, represented by the black solid circles, with the gcmc isotherms for the lp and np forms of mil-53(Al): the solid, blue lines interpolate the simulated H2 loadings for mil-53lp, whereas the dashed, red ones interpolate the gcmc data for mil-53np. The vertical logarithmic scale makes it much easier to see details for small values of na , which is not the case in the linear plots of Fig. 5; for example, Fig. 6 shows that the simulated results for mil-53lp match quite well the experimental H2 loadings but not those for mil-53np; this is not clearly ascertained from the inspection of Fig. 5. Before proceeding further with the analysis of the experimental data, the gcmc isotherms for the two structural forms of mil-53(Al) merit a deeper discussion. As the temperature is increased the slight concave curvature of the simulated sub-atmospheric adsorption isotherms disappears and the gcmc adsorption data fall into the linear region of the adsorption isotherm, governed by Henry’s law:

na = KP,

K = K ′ exp(Qst /Rg T ),

(9)

where K is the Henry coefficient and Qst the isosteric heat of adsorption at low coverage. Concomitantly, the simulated H2 isotherm for mil-53lp approaches that for mil-53np. Somewhere between 120 K and 140 K the simulated sub-atmospheric H2 adsorption isotherm for mil-53lp surpasses that for mil-53np. Fig. 7 shows the temperature dependence of the simulated Henry constants, Klp and Knp ,

16


Page 17 of 36

100 K

120 K

140 K

10−3 np 10−4

lp

np lp

lp np

10−5

10−6 160 K

180 K

200 K

10−3

10−4 na (mol/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


lp lp

10−5

lp

np np

np 10-6 220 K

240 K

260 K

10−3

10−4

10−5

lp

lp np

10−6

100

lp np

1,000

np

100

1,000

100

1,000

P (mbar)

Figure 6: Hydrogen adsorption isotherms in mil-53(Al) at temperatures between 100 K and 260 K and pressures below 1.2 bar. Black circles: experimental data; small colored circles: gcmc simulation data for the lp (blue) and np (red) structures; lines: fitting of a Virial-type adsorption isotherm to each set of gcmc isotherm data.

17



4

132 K K (mmol ∙ g−1 ∙ bar−1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 36

1

MIL-53(Al)lp

K = K exp(Qst/RT ) K Qst (mmol ∙ g−1 ∙ bar−1) (kJ/mol)

0.1

LP NP

5.503 × 10−3 1.043 × 10−3

5.06 6.86

MIL-53(Al)np

0.03 3

4

5

6

7 3

8

9

10

11

−1)

10 / T (K

Figure 7: Temperature dependence of the Henry constants, Klp and Knp , for hydrogen adsorption on the two structural forms of mil-53(Al), determined from linear fittings of the low-pressure gcmc simulation data. 130 K is the temperature above which Klp > Knp .

for H2 adsorption in the lp and np forms of mil-53(Al). It is seen that at 130 K the Henry coefficient for mil-53lp surpasses that for mil-53np. Given that (lp) (np) ′ Klp Klp Qst − Qst lim = lim ′ exp T →∞ Knp T →∞ Knp Rg T

!

′ Klp = lim ′ , T →∞ Knp

(10)

it follows that Klp becomes larger than Knp at a sufficiently high temperature because the ′ ′ pre-exponential factors satisfy Klp > Knp , whereas the inverse is true at lower temperatures (np)

because of the relative magnitudes of the isosteric heats, Qst

(np)

> Qst . To the best of our

knowledge, this crossing of the adsorption isotherms in the Henry’s law region for the two forms of mil-53 has never been highlighted or interpreted before. This shift in the Henry constants stems from the weak solid–fluid interaction potential experienced by the confined hydrogen molecules in both structural forms of mil-53(Al), as highlighted by the low isosteric heats of adsorption (5–7 kJ/mol) and the significantly 18


Page 19 of 36

40

K /vp (mmol ∙ cm−3 ∙ bar−1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10 MIL-53(Al)np

1 MIL-53(Al)lp

0.1 0.06 3

4

5

6

7 8 −1 10 / T (kK )

9

10

11

3

Figure 8: Scaled Henry constants, (K/vµ )(lp) and (K/vµ )(np) , for hydrogen adsorption on the two structural forms of mil-53(Al); the scaling consists of dividing Klp and Knp (Fig. 7) by (lp)

the specific accessible pore volume of the corresponding structural form, vµ (np)

and vµ

= 0.166 cm3 /g.

(lp)

different specific pore volumes of the two structures: vµ (np)

vµ

= 0.564 cm3 /g

= 0.564 cm3 /g for the lp form and

= 0.166 cm3 /g for the np form; these values were estimated from gcmc simulations

of methane condensation at its normal boiling point (143 K) inside the two materials. At sufficiently high temperatures the increased interaction potential experienced by the confined hydrogen molecules in mil-53np no longer counterbalances the reduced pore volume of the narrower framework, thereby resulting in a lower loading than in the lp structure. This suggests that if the Henry constant were scaled by the reciprocal of the corresponding specific accessible pore volume, a fairer comparison would be obtained. This is indeed the case as shown in Fig. 8, where the Henry constants scaled by the reciprocals of the corresponding specific accessible pore volumes are plotted as a function of the reciprocal of the temperature. In this graph the temperature range over which the scaled Henry constant for mil-53np is larger than that for mil-53lp is extended well beyond the temperature above 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

which the dehydrated structure of mil-53(Al) collapses (773 K). This scaling brings the ratio of the pre-exponential factors towards 1, since it lowers the ratio from 5.4 to 1.6; the desired value is not attained, however, probably because the extrapolation is based on data obtained at insufficiently high temperatures (100–260 K). The gcmc simulations explain quantitatively well the experimental adsorption data plotted in Fig. 6 by the occurrence of a np-to-lp structural transition at sub-atmospheric pressure. At 100 K and 120 K the simulations for mil-53np are closer to the experimental H2 loadings than those for mil-53lp. At 140 K the amount adsorbed measured at the lowest pressure, ca. 47 mbar, falls on top of the simulated adsorption isotherm for the np form whereas the other values measured at higher pressures are closer to the gcmc isotherm for the lp form. This trend is clearly visible at higher temperatures. Thus, in the range of temperatures between 140 K and 260 K there is clearly a np-to-lp structural transition at sub-atmospheric pressure; at lower temperatures the np-to-lp transition occurs at pressures higher than those measured in the present study. The present results are in agreement with the neutron scattering study of bare mil-53(Al) performed by Liu et al. 13 who observed a reversible np–lp transition accompanied by a large hysteresis in the 125–375 K range: the lp-to-np transition temperature was found to occur around 125 K, while the np-to-lp transition happens gradually between 325 to 375 K. The present results provide another strong evidence that the low-temperature stable form of mil53(Al)

is the np structure in agreement with the conclusions drawn by Boutin et al. 17 from

their work on low-temperature Xeon adsorption in mil-53(Al). Fig. 6 shows that the experimental amounts adsorbed measured by us at ∼200 mbar and temperatures between 200 K and 260 K appear to be outliers, for they are off the trend of the other measurements. We do not have a clear explanation for this. However, these points were all obtained in the same experiment with constant amount of hydrogen in the system; it is thus likely that the initial pressure in the reference cell were poorly measured or its value incorrectly recorded.

20


Page 20 of 36

Page 21 of 36

10

Qst (kJ/mol)

8

6

4

np-form (GCMC) lp-form (GCMC) 2

Isoteric plot of experimental data Henry constants (GCMC)

a 0

0

1

2

3

4

5 6 na (mmol/g)

7

8

103

9

10

na (mg/g) 0.1 0.3 0.7

102 P (mbar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0 2.0 5.0 7.0

10

10.0

1

b 0

5

10

15

20 25 103 / T (kK−1)

30

35

40

Figure 9: (a) Isosteric heat of adsorption, Qst , as a function of hydrogen loading, na , for mil-53(Al). Green circles: Qst values derived from the linear parts of the isosteres shown in the bottom graph, eq. 12; red and blue circles: gcmc simulation values determined from the usual fluctuation formula, eq. 11; red and blue lines: Qst values derived from the temperature dependence of the Henry constants given in Fig. 7. (b) Isosteric plot of the experimental adsorption data (symbols) and fitting of the linear parts (lines) of the isosteres.

21



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Page 22 of 36

The isosteric heat (or differential enthalpy) of adsorption, Qst , is the amount of heat released when an infinitesimal number of molecules is transferred at constant pressure from the bulk gas phase to the adsorbed phase. This quantity can be calculated in a GCMC simulation from statistical mechanical considerations 40 as

Qst = kB T −

ϕ(U, N ) , ϕ(N, N )

(11)

where kB is the Boltzmann constant; ϕ(u, v) = huvi − huihvi is the covariance between two properties u and v; hi denotes the ensemble average; N is the number of adsorbate molecules in the simulation box; and U is the configurational energy of the system. On the other hand, if the temperature dependence of the isosteric heat is assumed to be weak over the temperature range of the adsorption experiments, it is possible to calculate Qst from the adsorption isotherms obtained experimentally using the integrated form of the Clapeyron’s equation: (loge P )na = const − Qst /(Rg T ).

(12)

This expression shows that a plot of ln P versus 1/T should yield a linear isostere of slope Qst /Rg . The top graph in Fig. 9 shows a plot of Qst as a function of the amount adsorbed using the two mentioned approaches. The values of Qst for hydrogen in the np and lp forms of mil-53(Al) calculated from the gcmc simulations using eq. 11 are depicted by the red (np) and blue (lp) symbols. The horizontal straight lines represent the Qst values derived from the temperature dependence of the Henry constants shown in Fig. 7. The green symbols represent the isosteric heats calculated from the experimental adsorption isosteres depicted in the bottom graph. Fig. 9 shows that, as the amount adsorbed is increased, the experimental isosteric heats progressively move from the 6.9 kJ/mol plateau for mil-53np down to the 5.1 kJ/mol plateau for mil-53lp. This is again consistent with a np-to-lp structural transition at sub-atmospheric pressure upon hydrogen adsorption. 22


Page 23 of 36

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Coudert et al. 15,16 have demonstrated that for materials exhibiting clear structural transitions between different metastable framework structures, as is the case of mil-53, the use of an “osmotic sub-ensemble” adequately describes the equilibrium between host structures upon fluid adsorption. A related, but somewhat different, free energy model proposed by Ghysels et al. 41 can also be employed to describe the thermodynamics of the breathing phenomenon in flexible materials. We employ the former approach to help interpreting our data. The osmotic potential 42 of the solid–fluid system for the ith structure of the mil-53 framework, either np or lp, is Ω(i) os (P, T )

=

(i) Fhost (T )

+

P vp(i)

−

Z

P 0

(13)

n(i) a (p, T )vg (p, T ) dp,

or Ω(i) os (P, T )

=

(i) Fhost (T )

+

P vp(i)

Z P − Rg T n(i) a (p, T )Z(p, T ) d ln p,

(14)

0

(i)

(i)

where Fhost (T ) is the free energy of the bare structure at temperature T and vp its apparent specific volume (skeletal, vs , plus porous, vµ ), the latter being formally equivalent to the (i)

specific volume (cm3 /g) of the framework’s unit cell; na (P, T ) is the adsorption isotherm if the framework were rigid and constrained to its ith form, and vg = 1/ng and Z the molar volume and compressibility factor of the pure fluid. The osmotic potential difference between (lp)

(np)

the lp and np structures, ∆Ωos = Ωos − Ωos , is thus given by Z P ∆Ωos (P, T ) = ∆Fhost (T ) + P ∆vp − Rg T ∆na (p, T )Z(p, T ) d ln p,

(15)

0

where ∆φ = φ(lp) − φ(np) is the difference in property φ between the lp and np structures at temperature T . If ∆Ωos > 0, the np structure will be more stable than lp; if ∆Ωos < 0, the (lp)

reverse will be true. 15,16 For mil-53(Al), vp

(np)

= 1.03 cm3 /g and vp

∆vp ≈ 0.26 cm3 /g. 23


= 0.78 cm3 /g, hence


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 36

At the low pressures spanned by our experiments hydrogen obeys closely the ideal gas law (Z ≈ 1), and the previous equation can be further simplified to give Z P ∆Ωos (T, µ) = ∆Fhost (T ) + P ∆vp − Rg T ∆n(i) a (P, T ) d ln p.

(16)

0

Moreover, under low-pressure, linear adsorption conditions, the adsorption isotherm is given by (i) n(i) a (P, T ) = K (T )P,

(17)

where K (i) (T ) is the Henry coefficient at temperature T . Therefore, under these conditions the osmotic potential difference between the lp and np structures is

∆Ωos (T, P ) = ∆Fhost (T ) + P [∆vp − Rg T ∆K],

(18)

where ∆K = K (lp) − K (np) is the difference in Henry constants between the lp and np structures at temperature T . The empty host free energy difference between the lp and np structures, ∆Fhost , is difficult to estimate from our experiments. From thermodynamics, ∆Fhost = ∆Uhost − T ∆Shost , and if the values proposed by Boutin et al., 17 ∆Uhost = 18.0 J g−1 and ∆Shost = 0.089 J g−1 K−1 , are adopted, we estimate that ∆Fhost = 0 at around 202 K, which falls right in the middle of the temperature range spanned in Fig. 6. Under this assumption it is possible to predict the temperature–pressure phase diagram for hydrogen adsorption in mil-53(Al) for the thermodynamic window analyzed experimentally. This is shown in Fig. 10. This contour plot should be analyzed with care for it applies only to the Henry’s law region, where eqn. (18) is valid; for simplicity the temperature dependence of ∆Fhost is also neglected. The vertical line shown in Fig. 10 is close to the temperature of 132 K at which the two Henry constants have the same value. At lower temperatures, ∆Ωos > 0 and the np-

24


Page 25 of 36

1 MIL-53lp −0.04

0.8 MIL-53np

P (bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


−0.03

0.6

−0.02

0.4

−0.01 0.2

0.01

0.05

0.0

0.02 0

80

120

160

200

240

T (K)

Figure 10: Predicted phase diagram for linear H2 adsorption (Henry’s law region) in mil53(Al),

assuming ∆Shost ≈ 0. The contour lines represent lines in the temperature–pressure

phase diagram along which ∆Ωos has a constant value. The light gray area represents the region in which the mil-53np is the more stable structure, whereas the white area represents the stable region for the lp form. The two stability regions are separated by the red isoline for which ∆Ωos = 0.0.

form is the stable conformation regardless of the applied pressure. At higher temperatures the stable conformation is the lp form at a high enough pressure. The peculiarity of this region of the phase diagram is that the term ∆vp − Rg T ∆K attains its largest negative value at ca. 170 K and then slowly increases but always with a negative value. Thus, above 170 K the lowest pressure value that makes ∆Ωos negative increases slightly with temperature. Obviously, this effect can be masked by any large enough temperature-dependence of ∆Fhost . Overall, our results can be summarized as follows. If the temperature values reported by Liu et al. 13 for the large temperature hysteresis of the structural transition in bare mil53(Al)

are also valid for our sample, the transition from the bare lp form to the bare np

form should occur around 125 K, while the transition from the bare np form to the bare lp form should happen gradually between 325 to 375 K. This is pictured in the topmost 25



(−) (LP) ΔFhost

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 36

(NP)

(NP)

(+) 75 K ΔFhost > 0

T

500 K

ΔFhost > 0

ΔFhost < 0

na

na( i )

(LP)

(LP)

(LP)

(NP)

(NP)

(NP)

(LP) (i)

Ωos (NP)

(NP) (NP) (LP)

(LP)

Pressure

Figure 11: Representative cases of H2 adsorption isotherms for mil-53(Al) derived from the experiments reported in the present work; each column of charts describes a representative type. (A fourth case not shown of a double transition would only occur if the piecewise constant temperature profile imposed on the system were obtained through progressive cooling instead of heating.) The meaning of each row of charts from top to bottom is as follows. (1) Empty host free energy difference, ∆Fhost , between the lp and np structures, as a function of temperature (adapted from ref. 13); the colored line segments represent the temperature path to which the column of graphs corresponds. (2) Representative shape of the resulting adsorption isotherm. (3) Adsorption isotherm for each of the lp and np structures. (4) Osmotic potential of each structure as a function of adsorptive pressure.

26


Page 27 of 36

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row of graphs in Fig. 11. On the other hand, the present work has shown that below ca. 130 K the Henry constants for hydrogen adsorption satisfy Knp > Klp , whereas at higher temperatures the opposite is true. However, the ordering of the saturation capacities is always (nmax )np < (nmax )lp . a a Thus, below ca. 125–130 K the np form is the more favorable bare structure and the Henry constants satisfy Knp > Klp : there will be a single np-to-lp structural transition upon hydrogen adsorption at a pressure defined by the osmotic thermodynamic theory. This case is illustrated by the graphs in the leftmost column of Fig. 11. Above ca. 375 K, the lp form is the more favorable bare structure and the Henry constants satisfy Klp > Knp : there will be no structural transition upon hydrogen adsorption and mil53(Al)

will remain in its lp form. This case is illustrated by the graphs in the rightmost

column of Fig. 11. Between ca. 125–130 K and 375 K the behavior will depend upon the temperature history of the bare material, for it can be in either the lp or np form. If the bare mil-53(Al) sample is in its lp form, there will again be no structural transition upon hydrogen adsorption, for it will remain in its lp form as in the previous case. However, if the bare mil-53(Al) sample is in its np form, there will be a single np-to-lp structural transition upon hydrogen adsorption because Klp > Knp and (nmax )np < (nmax )lp . This case is illustrated by the middle column a a of graphs in Fig. 11. The only case of structural transition in mil-53(Al) upon hydrogen adsorption not discussed here is that of a (double) lp→np→lp transition, for it would only be experimentally observed if the piecewise constant temperature profile applied to our volumetric system were generated by progressive cooling of the system instead of heating. If the system had been cooled from ambient temperature down to 15 K, mil-53lp would had been the bare stable form down to ca. 125 K. According to the osmotic potential theory it would be possible to first witness a lp-to-np structural transition when the system were being cooled below 125 K, because Knp > Klp below 130 K, and then a np-to-lp transition because (nmax )np < (nmax )lp . a a 27



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The occurrence of these events would of course depend on the amount of hydrogen introduced into the system.

Conclusions We have presented a comprehensive set of experimental sub-atmospheric adsorption equilibrium isotherms for the system H2 /mil-53(Al) at temperatures between 20 K and 260 K. Various sets of adsorption equilibrium data were generated for fixed amounts of H2 in the measuring cell by increasing the system temperature in small steps starting from 15 K while recording the equilibration pressure attained at each step. The isotherms of amount adsorbed versus pressure in the external gas phase are generated by connecting the equilibrium points obtained at the same temperature for the different fixed amounts of H2 in the system. The proposed trappe-based force field for the dispersion interactions in the H2 /mil53(Al)

system, corrected for quantum effects via a quartic approximation of the Feynman–

Hibbs variational approach, provides an accurate description of the experimental adsorption data and isosteric heats of adsorption. Much of this is due to trappe’s consistency and proven transferability of its parameters. Hydrogen interacts weakly with the mof framework, which brings about interesting features. The Henry constant Klp becomes larger than Knp at a temperature lower than that at which the dehydrated structure of the material collapses, because the pre-exponential ′ ′ factors satisfy Klp > Knp , whereas the inverse is true at lower temperatures because of the (np)

relative magnitudes of the isosteric heats, Qst

(np)

> Qst . However, if the Henry constants are

scaled by the reciprocal of the corresponding specific pore volumes, the ordering Klp > Knp prevails over the full temperature range before the material collapses. Because of mil-53(Al)’s structural bi-stability some care must be exercised when interpreting the measured adsorption data, for the phase behavior of mil-53(Al) depends not only on pressure and temperature but also on the thermal history of the material. In this

28


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Page 29 of 36

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sense, the measured adsorption data should be regarded as heat-assisted H2 desorption data partially counterbalance by pressure increase in the external gas phase. For the conditions spanned in the experiments mil-53(Al) exhibits at most a single structural transition and its phase behavior between ca. 125–130 K and 375 K depends upon the temperature history of the bare material.

Acknowledgement Financial support from the Portuguese National Science Foundation (fct/mctes), through grant ptdc/eme-mfe/66533/2006, is gratefully acknowledged. J. P. B. Mota acknowledges financial support from the Associate Laboratory for Green Chemistry and Clean Processes (laqv/requimte), which is financed by national funds from fct/mctes (uid/qui/50006/ 2013) and co-financed by the Portuguese erdf under the pt2020 Partnership Agreement (poci-01-0145-feder - 007265).

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website at DOI: . . . . • Details of molecular model, adopted force field for fluid–fluid and solid–fluid interactions, and gcmc simulation method.

References and notes (1) Férey, G. Hybrid porous solids: past, present, future. Chem. Soc. Rev. 2008, 37, 191– 214.

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(2) Rowsell, J. L. C.; Yaghi, O., M. Metal–organic frameworks: a new class of porous materials. Micropor. Mesopor. Mater. 2004, 73, 3–14. (3) Batten, S. R.; Neville, S. M.; Turner, D. R. Coordination Polymers: Design, Synthesis, and Application; Royal Society of Chemistry: Cambridge, U.K., 2009. (4) Hong, M.-C.; Chen, L. (Eds.) Design and Construction of Coordination Polymers; John Wiley & Sons: Hoboken, NJ, 2009. (5) Li, J.-R.; Kuppler, R. J.; Zhou, H.-C. Selective gas adsorption and separation in metal– organic frameworks. Chem. Soc. Rev. 2009, 38, 1477–1504. (6) Meek, S. T.; Greathouse, J. A.; Allendorf, M. D. Metal–Organic Frameworks: A Rapidly Growing Class of Versatile Nanoporous Materials. Adv. Mater. 2011, 23, 249– 267. (7) Koh, H. S.; Rana, M. K.; Hwang, J.; Siegel, D. J. Thermodynamic screening of metalsubstituted MOFs for carbon capture. Phys. Chem. Chem. Phys. 2013, 15, 4573–4581. (8) Caskey, S. R.; Wong-Foy, A. G.; Matzger, A. J. Dramatic Tuning of Carbon Dioxide Uptake via Metal Substitution in a Coordination Polymer with Cylindrical Pores. J. Am. Chem. Soc. 2008, 130, 10870–10871. (9) Horike, S.; Shimomura, S.; Kitagawa, S. Soft porous crystals. Nat. Chem. 2009, 1, 695–704. (10) Serre, C.; Millange, F.; Thouvenot, C.; Nogueès, M.; Marsolier, G.; Louër, D.; Férey, G. Very Large Breathing Effect in the First Nanoporous Chromium(III)-Based Solids: MIL-53 or CrIII (OH)·{O2 C–C6 H4 –CO2 } · {HO2 C–C6 H4 –CO2 H}x ·H2 Oy . J. Am. Chem. Soc. 2002, 124, 13519–13526. (11) Neimark, A. V.; Coudert, F.-X.; Triguero, C.; Boutin, A.; Fuchs, A. H.; Beurroies,

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I.; Denoyel, R. Structural Transitions in MIL-53 (Cr): View from Outside and Inside. Langmuir 2011, 27, 4734–4741. (12) Beurroies, I.; Boulhout, M.; Llewellyn, P. L.; Kuchta, B.; Férey, G.; Serre, C.; Denoyel, R. Using Pressure to Provoke the Structural Transition of MetalâĂŞOrganic Frameworks. Angew. Chem. Int. Ed. 2010, 49, 7526–7529. (13) Liu, Y.; Her, J.-H.; Dailly, A.; Ramirez-Cuesta, A. J.; Neumann, D. A.; Brown, C. M. Reversible Structural Transition in MIL-53 with Large Temperature Hysteresis. J. Am. Chem. Soc. 2008, 130, 11813–11818. (14) Ghoufi, A.; Benhamed, K.; Boukli-Hacene, L.; Maurin, G. Electrically Induced Breathing of the MIL-53(Cr) Metal–Organic Framework. ACS Cent. Sci. 2017, 3, 394–398. (15) Coudert, F.-X.; Jeffroy, M.; Fuchs, A. H.; Boutin, A.; Mellot-Draznieks, C., Thermodynamics of Guest-Induced Structural Transitions in Hybrid Organic–Inorganic Frameworks. J. Am. Chem. Soc. 2008, 130, 14294–14302. (16) Coudert, F.-X.; Mellot-Draznieks, C.; Fuchs, A. H.; Boutin, A. Double Structural Transition in Hybrid Material MIL-53 upon Hydrocarbon Adsorption: The Thermodynamics Behind the Scenes. J. Am. Chem. Soc. 2009, 131, 3442–3443. (17) Boutin, A.; Springuel-Huet, M.-A.; Nossov, A.; Gédéon, A.; Loiseau, T.; Volkringer, C.; F’erey, G.; Coudert, F.-X.; Fuchs, A. H. Breathing Transitions in MIL-53(Al) Metal–Organic Framework Upon Xenon Adsorption. Angew. Chem. Int. Ed. 2009, 48, 8314–8317. (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.

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(19) Férey, G.; Mellot-Draznieks, C; Serre, C.; Millange, F. Crystallized Frameworks with Giant Pores:âĂĽ Are There Limits to the Possible? Acc. Chem. Res. 2005, 38, 217–225. (20) 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. (21) Llewellyn, P. L.; Bourrelly, S.; Serre, C.; Filinchuk, Y.; Férey, G. How hydration drastically improves adsorption selectivity for CO2 over CH4 in the flexible chromium terephthalate MIL-53. Angew. Chem. Int. Ed. 2006, 46, 7751–7754. (22) Ramsahye, N. A.; Maurin, G.; Bourrelly, S.; Llewellyn, P. L.; Loiseau, T.; Serre, C.; Férey, G. On the breathing effect of a metal–organic framework upon CO2 adsorption: Monte Carlo compared to microcalorimetry experiments. Chem. Commun. 2007, 31, 3261–3263. (23) Serre, C.; Bourrelly, S.; Vimont, A.; Ramsahye, N. A.; Maurin, G.; Llewellyn, P. L.; Daturi, M.; Filinchuk, Y.; Leynaud, O.; Barnes, P.; Férey, An Explanation for the Very Large Breathing Effect of a Metal-Organic Framework during CO2 Adsorption. Adv. Mater. 2007, 19, 2246–2251. (24) Trung, T. K.; Trens, P.; Tanchoux, N.; Bourrelly, S.; Llewellyn, P. L.; Loera-Serna, S.; Serre, C.; Loiseau, T.; Fajula, F.; Férey, G. Hydrocarbon Adsorption in the Flexible Metal Organic Frameworks MIL-53(Al,Cr). J. Am. Chem. Soc. 2008, 130, 16926–16932. (25) Llewellyn, P. L.; Maurin, G.; Devic, T.; Loera-Serna, S.; Rosenbach, N.; Serre, C.; Bourrelly, S.; Horcajada, P.; Filinchuk, Y.; Férey, G. Prediction of the Conditions for Breathing of Metal Organic Framework Materials Using a Combination of X-ray Powder Diffraction, Microcalorimetry, and Molecular Simulation. J. Am. Chem. Soc. 2008, 130, 12808–12814.

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(26) Lyubchyk, A.; Esteves, I. A. A. C.; Cruz, F. J. A. L.; Mota, J. P. B. Experimental and Theoretical Studies of Supercritical Methane Adsorption in the MIL-53(Al) Metal Organic Framework. J. Phys. Chem. C 2011, 115, 20628–20638. (27) Ribeiro, R. P. P. L.; Camacho, B. C. R.; Lyubchyk A.; Esteves, I. A. A. C.; Cruz, F. J. A. L.; Mota, J. P. B. Experimental and computational study of ethane and ethylene adsorption in the MIL-53(Al) metal organic framework. Micropor. Mesopor. Mater. 2016, 230, 154–165. (28) Mayer, R. P.; Stowe, R. A. Mercury porosimetry—breakthrough pressure for penetration between packed spheres. J. Colloid Sci. 1965, 20, 893–911. (29) Khan, N. A.; Jhung, S. H. Phase-Transition and Phase-Selective Synthesis of Porous Chromium-Benzenedicarboxylates. Cryst. Growth Des. 2010, 10, 1860–1865. (30) Takaishi, T.; Sensui, Y. Thermal transpiration effect of hydrogen, rare gases and methane. Trans. Faraday Soc. 1963, 59, 2503–2514. (31) For the sake of simplicity eq. (1) does not include the gas mole number contained in a small volume (∼ 0.6 cm3 ) of SS tubing running from the reference volume at temperature TR to the measuring cell at temperature T , which is estimated considering the volume to be at the harmonic mean temperature, 2TR T /(TR + T ). Obviously, this small correction has been taken into account in the actual calculations. See also Martins, D.; Ribeiro, L.; Lopes, D.; Catarino, I.; Esteves, I. A. A. C.; Mota, J. P. B.; Bonfait, G. Sorption characterization and actuation of a gas-gap heat switch. Sens. Actuators A 2011, 171, 324–331. (32) Wick, C. D.; Martin, M. G.; J. I. Siepmann, J. I. Transferable Potentials for Phase Equilibria. 4. United-Atom Description of Linear and Branched Alkenes and Alkylbenzenes. J. Phys. Chem. B 2000, 104, 8008–8016.

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(33) Chen, B.; Potoff, J. J.; Siepmann, J. I. Monte Carlo Calculations for Alcohols and Their Mixtures with Alkanes. Transferable Potentials for Phase Equilibria. 5. United-Atom Description of Primary, Secondary, and Tertiary Alcohols. J. Phys. Chem. B 2001, 105, 3093–3104. (34) Stubbs, J. M.; Potoff, J. J.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 6. United-Atom Description for Ethers, Glycols, Ketones, and Aldehydes. J. Phys. Chem. B 2004, 108, 17596–17605. (35) Feynman, R. P.; Hibbs, A. R. Quantum Mechanics and Path Integrals; McGraw-Hill: New York, 1965. (36) Kumar, A. V. A.; Bhatia, S. K. Quantum Effect Induced Reverse Kinetic Molecular Sieving in Microporous Materials. Phys. Rev. Lett. 2005, 95, 245901. (37) Kumar, A. V. A.; Jobic, H.; Bhatia, S. K. Quantum Effects on Adsorption and Diffusion of Hydrogen and Deuterium in Microporous Materials. J. Phys. Chem. B 2006, 110, 16666–16671. (38) Buch, V. Path integral simulations of mixed para-D2 and ortho-D2 clusters: The orientational effects. J. Chem. Phys. 1994, 100, 7610–7629. (39) Frenkel, D.; Smit, B. Understanding Molecular Simulation, 2nd ed.; Academic Press: San Diego, 2002. (40) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, 1982. (41) An Ghysels, A.; Vanduyfhuys, L.; Vandichel, M.; Waroquier, M.; Van Speybroeck, V.; Smit, B. On the Thermodynamics of Framework Breathing: A Free Energy Model for Gas Adsorption in MIL-53, J. Phys. Chem. C 2013, 117, 11540–11554.

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(42) Jeffroy, M.; Fuchs, A. H.; Boutin, A. Structural changes in nanoporous solids due to fluid adsorption: thermodynamic analysis and Monte Carlo simulations. Chem. Commun. 2008, 28, 3275–3277.

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Graphical TOC Entry MIL-53(Al)lp

(−) (LP) ΔF host

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(NP)

(NP)

(+) 75 K ΔFhost > 0

T

500 K

ΔFhost > 0

MIL-53(Al)np na

Pressure

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ΔFhost < 0

Structural Transitions in the MIL-53(Al) Metal ... - ACS Publications

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