Physics Behind the Guest-Assisted Structural Transitions of a Porous

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Physics Behind the Guest-Assisted Structural Transitions of a Porous Metal-Organic Framework Material A. Ghoufi,*,† G. Maurin,*,‡ and G. F erey§ †

Institut de Physique de Rennes, UMR 6251 CNRS, Universit e Rennes 1, 263 avenue du G en eral Leclerc, 35042 Rennes, France, ‡Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, UM2, UM1, ENSCM, Universite Montpellier 2, Place Eug ene Bataillon, 34095 Montpellier cedex 05, France, and § Institut Lavoisier, UMR CNRS 8180, Universit e de Versailles Saint-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035 Versailles cedex, France

ABSTRACT MIL-53(Cr) is one of the metal-organic framework (MOF)-type materials which shows the most spectacular breathing behavior upon adsorption of various types of fluids. The previously reported thermodynamic models did not allow a subtle analysis of the factors and mechanisms that govern the structural transition of the framework in play. Here, we demonstrate that probing the interplay between the host and the guest molecules is crucial to capturing the physics behind such a transition, which has never been addressed so far. It is thus emphasized that the host/guest interactions preliminarily induce a soft mode in the host framework, which is a prerequirement for initiating the structural transition of the MIL-53(Cr) solid. It follows a displacive type of mechanism, which involves the occurrence of a new metastable phase that has been neither experimentally evidenced nor predicted. Such an observation questions the bistability of the MIL-53(Cr) solid upon adsorption reported so far in the literature. SECTION Nanoparticles and Nanostructures

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microscopic scale as it occurs too fast to be detectable. In contrast, molecular simulations are expected to bring a more subtle and conclusive analysis of the mechanism in play, considering the length and time scales sampled. The numerical investigation of this structural transition started with molecular dynamics (MD) simulations based on our newly derived classical flexible force field for the framework, which allowed successful capture of the structural transformation of this solid upon CO2 adsorption and thermal stimuli.5 It was concluded that such a structural switching is mainly governed by the intramolecular distortion term of the framework. Later, Coombes et al.6 and Dubbeldam et al.7 employed energy minimization techniques based on classical force fields to explore the evolution of the unit cell shape and size of the MIL53(Cr) solid at 0 K upon adsorption of different guests including H2O and CO2. We have further conducted a Hybrid Osmotic Monte Carlo simulation (HOMC) approach,8 which evidenced that the structural transformation of the framework is accompanied by a change of the orientational order parameter for the adsorbate. Beyond these numerical approaches, Coudert et al.9 have tackled this structural transition from a thermodynamics standpoint by comparing the grand potential (Ω) in the osmotic ensemble for both LP and NP forms in a macroscopic formulation based on experimental

ybrid porous solids represent a new class of porous materials, commonly name metal-organic frameworks (MOFs).1 Stemming from the almost infinite possibility to vary their chemistry through the metal center, organic linkers, as well as their geometry arrangements, numerous investigations which appeared during the past few years led to an explosion of new MOF structures with very promising properties for potential applications in several areas, including physics, chemistry, and biology.1 Beyond their plausible industrial interests, some of these MOFs provoke from a fundamental standpoint a great curiosity for several scientific communities due to their ability to breathe upon the action of various external stimuli, including electric field, temperature, light, and adsorption of guest molecules.1,2 The MIL-53(Cr) (MIL stands for Materials of Institut Lavoisier) solid, which shows a 3D structure defining 1D diamondshaped pores,3 is among the most spectacular breathing MOFs which correspond to a highly flexibility of its framework. This unusual phenomenon has been assigned to a reversible structural transformation between two distinct forms, namely, the large pore (LP) and the narrow pore (NP) structures. It implies a large unit cell volume contraction/ expansion up to 40% in the case of CO2.4 A great challenge consists of understanding which factors/mechanisms induce such a fascinating dynamic feature that can strongly influence their properties. Although the experimental techniques can pick out the signature of such a structural transformation, they do not provide a full picture of the transition at the

r 2010 American Chemical Society

Received Date: August 11, 2010 Accepted Date: September 3, 2010 Published on Web Date: September 10, 2010

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DOI: 10.1021/jz1011274 |J. Phys. Chem. Lett. 2010, 1, 2810–2815

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Figure 1. (a) Orientational S (green line) and translational τ (x: black; y: red; z: blue lines) order parameter of CO2 computed from eqs 1-3 as function of the MD time. The dashed line (right axis) represents the evolution of the unit cell volume of the MIL-53(Cr) framework. The inset figure represents the unit cell volume as a function of the corresponding MD time in the time interval of 0.7-0.9 ns. (b) Visualization of the highly ordered state of CO2 in the NP form using a Connolly surface representation. These calculations have been performed for the MIL53(Cr) framework loaded with three CO2 molecules/u.c.

data. They have also derived Ω to estimate a critical stress (σc) required to induce the structural transition of the MIL-53(Cr) solid.10 Although these later investigations are conclusive, there is still a need (i) to improve the models to rigorously tackle the mechanism in play by considering the microscopic behavior of the adsorbate during the transition, which has been hidden so far, and (ii) to understand the physics at the origin of this remarkable transformation, which is not addressed yet. Indeed, in this Letter, we aim at addressing these two major points on the CO2-induced structural switching of the MIL-53(Cr) structure by means of MD simulations. The interplay between the host MIL-53(Cr) and the guest molecules on the structural transition is clearly established, showing for instance a high correlation between the evolutions of the intraframework energetic contribution and the guest/ guest interaction energy. It is further demonstrated that the occurrence of a soft mode in the host framework drives a displacement progressive type structural transition, which questions the bistability of the MIL-53(Cr) solid with an abrupt transition between the LP and the NP forms reported so far. Such a mechanism implies the existence of an intermediate energetic unfavorable phase that has never been experimentally evidenced as its lifetime might be too short to be detected. As far as we know, it is the first study that brings a complete physical picture of the mechanisms and factors which govern the spectacular breathing of a MOF-type material triggered by guest molecules. MD simulations were performed in the anisotropic stress isothermal (NσT) statistical ensemble from the DL_POLY11 package, which allows both the shape and size of the framework to be changed.12 The thermostat and anisotropic barostat of Berendsen were employed (with τT = 1.0 ps and τp = 5.0 ps as relaxation times) to maintain constant pressure and temperature (p = 1 atm and T = 300 K). Equations of motions were integrated using the velocity Verlet scheme coupled with the QUATERNION, SHAKE-RATTLE algorithms.12-14 The calculations were run for at least 1 ns with a time step of 1 fs, while the configurations were stored every 200 time steps. The MIL53-(Cr) framework was described by our previously validated intramolecular and intermolecular force field,5 while the CO2 molecule was treated as a rigid model developed by Harris


and Yung.15 The simulation box consisted of 32 unit cells (u.c.) containing 2432 atoms for the LP form of MIL-53(Cr). As a typical illustration, a loading of three CO2 molecules per unit cell was considered as we have previously shown that such an adsorbed amount allows the structural switching from LP to NP.5 Electrostatic interactions were evaluated by means of Ewald summation, while the short-range interactions were calculated using a cutoff distance of 12 Å. As a first step, the orientational (S) and translational (τ) order parameters of CO2 confined within the pore of the MIL53(Cr) solid have been extracted from the analysis of the MD runs. S was calculated using eq 1 and 2, where d is the director corresponding to the highest value for the eigenvector of the inertia tensor (Q) defined by eq 2, ei is the unit vector of the atom i, N is the number of adsorbed molecules, and δRβ is the delta of Kronecker (δRβ = 1 if R = β or 0 if else). τ, which is related to the static structure factor along the direction of the director for the wave vector k = 2π/d (d corresponding to the interlayer spacing), was further evaluated using eq 3 where rj is the vector position of the atom j along the axis parallel to the director. The d value, which is not known a priori, was determined by testing a wide set of values until a maximum for τ was obtained. This translational order parameter is a measure of the onset of a translational symmetry, which results from a periodic modulation of the density correlation function. It can vary from 0 to 1 and is especially used to characterize the layered structures that occur in the smectic phase.16 S ¼

QRβ

N 1 X Æ ei dæ N i¼1

N 2 X 1 ¼ eiR eiβ - δRβ 3N i ¼ 1 3

τ ¼

N 1X jexpÆikrj æj N j¼1

ð1Þ ! ð2Þ

ð3Þ

Figure 1a reports the evolution of both orientational and translational order parameters calculated for CO2 as function of the MD time. At the LP f NP transition boundary (t ≈ 0.8 ns),

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where the unit cell volume drops suddenly from 1420 to 1050 Å3/u.c., one clearly observes a disorder f order orientational transition. The so-obtained drastic increase of S from 0.2 (LP) to 0.9 (NP) can be attributed to the high degree of confinement in the NP structure compared to that in the LP form, which tends to force the CO2 molecules to be strictly aligned along the z axis, as previously shown.4,5 An illustration of this highly ordered arrangement of CO2 in the NP form is provided in Figure 1b, where one might assume a smectic-like order with an interlayer distance of about 8.6 Å corresponding to the interpore length along the y axis. Further, the so-involved large loss of degree of freedom results in a quenched dynamics of CO2, implying an entropy decrease that is compensated by the strong host/guest interactions present in the NP form. It thus leads to a favorable free enthalpy (ΔG = ΔH - TΔS), which suggests that the structural transition is governed by an enthalpic driving force. Figure 1a also shows a significant change of the translational parameter τ along the x and y directions, leading to values of τx = 0.9 and τy = 0.7 in the NP form, while it remains almost the same along the z axis (τz = 0.05). The larger value obtained for τx can be explained by a more restricted space available for the rearrangement of the guest molecules along this direction. Indeed, the dynamics of the guest and the host are depicted below along the y axis, corresponding to the direction where the structural transition from LP to NP induces the largest modification of the cell parameter and thus the most significant physical changes of the host and the guest. Note that the conclusion drawn here remains true along the x direction, although the changes of all of the considered physical properties are less pronounced. Indeed, to highlight the interplay between the MIL-53(Cr) framework and the CO2 molecules during the structural transition, we first tried to relate the translation order parameter of the guest (τy) along the y axis to the y component of the strain tensor (ηy) of the host calculated from eq 4. η ¼ 0

a B H ¼ @ b cos γ c cos β

1 ½ðH0- 1 ÞT 3 HT 3 H 3 H0- 1 - I 2

ð4Þ

Figure 2. (a) Translational order parameter of CO2 (τy) (right axis and dotted line) and strain component of the MIL-53(Cr) framework (ηy) (left axis and red line). (b) Intraframework interaction energy (right axis and black line) and guest/guest interaction energy (left axis and red line). Tr corresponds to the transition region, while pTr is the pretransition zone. Both calculations have been performed for the MIL-53(Cr) framework loaded with three CO2 molecules/u.c. (c) Mean-square displacement (MSD) calculated for all bonds of the MIL-53(Cr) framework in the presence of one molecule (black line and right axis) and three molecules (red line and left axis) of CO2 per unit cell along the y direction.

1

b cos γ c cos β C b sin γ - c sin β cos R A 2 1=2 2 - c sin β cos R cð1 - cos β - ðsin β cos RÞ Þ 0 1 hx hxy hxz ¼ @ hyx hy hyz A hzx hzy hz

where H is the cell matrix considered as the strain tensor.17 Its expression is given by eq 4, where a, b, and c are the lengths of the cell vectors and R, β, and γ are defined as R = {b,c}; β = {a,c}, and γ = {a,b}. R* is the reciprocal angle calculated from cos R* = (cos β cos γ - cos R)/(sin β sin γ). HT is the transposed matrix of H, I the unit matrix, and H0 the reference value of H (here, we consider the cell matrix of the LP structure as a reference). H0-1 is the inverse matrix of H0. One can observe from Figure 2a, that the changes of τy and ηy are highly correlated in the region centered on 0.8 ns, labeled as Tr, when the structural transition occurs. This observation unambiguously emphasizes that the structural


switching of the framework results from a cooperative host/ guest dynamics. This conclusion is also supported by the interplay between the intraframework energetic contribution and the guest/guest interactions energy, as evidenced in Figure 2b. The correlation between these two energetic terms remains also true even below 0.8 ns in a region which we call the pretransition domain (pTr) (inset in Figure 2b), where the progressive lowering of the intraframework energy can be related to the gradual decrease of its unit cell volume (Figure 1a), which corresponds to only tiny structural relaxation of the LP structure.

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between closed and narrow pore forms upon water18 and alkane19 adsorption, corresponding also to a reopening of one every second pore of the structure. This prediction can be also consistent with the distortion of the open channels of the MIL53(Al) structure induced by the neighboring shrunken ones, evoked in a very recent study dealing with the adsorption of xenon in this solid.20 Indeed, this observation suggests a progressive dynamic of the transition rather than a strict transition between two distinct states, as one would suspect by assuming a similar behavior as those previously reported in zeolites such as silicalite-1.21 One can further note that such a magnitude of structural contraction is made possible only if the applied constraint on the host framework via the presence of CO2 is large enough to induce a soft mode in the solid. Indeed, the existence of a pretransition zone can be related to the occurrence of a soft mode. Such a mechanical constraint is consistent with the stress-based model previously reported by Neimark et al.10 However, this stress is not the real physical reason that triggers the transition but corresponds rather to a mechanical condition to reach a soft mode, a crucial prerequirement prior to initiating a displacive transition in order to switch toward the NP form. Such a concept of soft mode could explain the requirement of a critical stress threshold value10 and a given CO2 adsorbed amount5 in order to observe the structural transition. To support the occurrence of a soft mode, the MSD for the intraframework bonds was calculated along the y direction (Figure 2c). Compared to the MSD profile obtained for a loading of one CO2/u.c. which is known to induce no structural modification of the host framework,5 for the case of three CO2/u.c., one observes a significant gradual fluctuation of the bond lengths (∼0.5 Å within a range of 1 ns), which can be attributed to the occurrence of a soft mode leading to an increase of the intraframework degree of freedom. Such a phenomenon is driven by the host/guest interactions which induce structural deformations of the host. Indeed, if the guest gives rise to strong enough interactions with the framework, the soft mode will be reached more easily since the structural deformations are expected to be more pronounced. Such a mechanism can explain why the critical amount adsorbed and stress threshold are different depending on the nature of the guest molecules. Further, the rather large value of this MSD also allows confirmation that the host framework undergoes a displacivetype transition. The whole of microscopic mechanisms is summarized in Figure 4. Indeed, we have clearly evidenced that probing the interplay between the host and the guest molecules is crucial to get

The so-obtained energetic profile also suggests that both the host and guest follow a correlated trajectory through instable phases (black dashed line in Figure 2b), from which the structural transition starts from the LP structure and evolves toward a steadiest NP form. We also observe in Figure 2b the presence of a plateau in the transition zone that might be assigned to an intermediate energetic unfavorable phase, which can be associated with the change of gradient observed for the unit cell variation in the same MD time domain (Figure 1a). A further analysis shows that this metastable phase corresponds to a structure where half of the pores are open while the others remain closed, their dimensions being very similar to the ones observed for the LP and the NP structures, respectively This latter form is of triclinic symmetry with a unit cell volume intermediate between those of the NP and the LP structures, as shown in Figure 3 and Table 1. We checked that we recovered the intermediary phase from three other initial configurations, two smaller configurations (16 and 8 unit cells) and another with 64 unit cells, by considering the explicit gas/solid external interface. In the three cases, the intermediary phase has been observed with a very short lifetime. Therefore, its existence and its lifetime are independent of the size effects. The very short lifetime of this structure (less than 25 ps), which corresponds to a time scale hardly accessible by usual experimental tools, could explain why it has been never evidenced by in situ X-ray diffraction studies. However, the existence of such an intermediate species can be related to the previous experimental findings reported on the MIL-53(Fe) solid, which shows a triclinic intermediate phase here

Figure 3. Illustration of the different MIL-53(Cr) structures present during the adsorption of CO2 using Connolly surface visualization, LP (large pore), I (intermediate metastable phase), and NP (narrow pore), The unit cell volumes are reported for each structure. Table 1. Unit Cell Parameters of the Simulated LP, NP, and I Structuresa a (Å)

b (Å)

LP

17.235 (16.733)

13.035 (13.038)

6.765 (6.812)

90.00 (90.00)

90.00 (90.00)

90.00 (90.00)

1519.8 (1486.1)

Imcm

NP

19.125 (19.710)

8.660 (8.320)

6.615 (6.800)

90.00 (90.00)

98.50 (105.85)

90.00 (90.00)

1083.5 (1072.0)

C2/c

6.675

93.10

92.70

88.60

1285.0

P1

I

18.100 a

10.650

c (Å)

R (o)

β (o)

γ (o)

V (Å3)

space group

4,5

The experimental data, when available, are also reported in parentheses.


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Figure 4. Schematic picture summarizing the different “microscopic” steps that leads to the structural transition of the MIL-53(Cr) framework from the LP to NP form upon CO2 adsorption through the occurrence of the intermediate I phase.

a full picture of the structural transition mechanism of MIL53(Cr) upon CO2 adsorption. It has been demonstrated that the host/guest interactions induce first a soft mode in the host framework, which is a prerequirement for initiating the structural transition of the MIL-53(Cr) solid. It follows a displacive-type mechanism rather than the abrupt transition between two distinct structures reported so far in the literature. It implies the existence of an intermediate metastable phase, which has been neither experimentally detected or predicted so far, which might suggest a multistability of this solid upon adsorption, as was recently reported for the cobalt1,4-benzenedipyrazolate [CoBDP] MOF, which shows four different structures upon N2 adsorption.22 Finally, the structural switching between the LP and the NP forms is accompanied by a disorder/order orientational and translational transition of the guest molecules. This observation supports that the cooperative host/guest dynamics plays a crucial role in the structural transition of the framework. The whole methodology that we describe here for the MIL-53(Cr)/CO2 pair can be applied to the whole series of guest molecules that imply the breathing of the MIL-53 family and can be further transferred to treat other flexible coordination polymers which show a gate opening behavior in presence of guest molecules.

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AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: aziz.ghoufi@ univ-rennes1.fr (A.G.); [email protected] (G.M.).

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ACKNOWLEDGMENT We thank the French program ANR (SAFHS and NoMAC projects) for funding and Dr. C. Serre from the Institut Lavoisier Versailles for fruitful collaborations and many discussions.

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Analyses, Rules and Consequences. Chem. Soc. Rev. 2009, 38, 1380. (a) Horcajada, P.; Serre, C.; Maurin, G.; Ramsahye, N.; Balas, F.; Vallet-Reghi, M.; Sebban, M.; Taulelle, F.; F erey, G. Flexible Porous Metal-Organic Framewworks for a Controlled Drug Delivry. J. Am. Chem. Soc. 2008, 130, 6774. (b) Llewellyn, P. L.; Maurin, G.; Devic, T.; Loera-Serna, S.; Rosenbach, N.; Serre, C.; Bourrelly, S.; Horcajada, P.; Filinchuk, Y.; F erey, 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. (c) Ramsahye, N. A.; Maurin, G.; Bourrelly, S.; Llewellyn, P. L.; Loiseau, T.; Serre, C.; F erey, G. On the Breathing Effect of a Metal-organic Framework upon CO2 Adsorption: Monte Carlo Compared to Microcalorimetry Experiments. Chem. Commun. 2007, 10, 3261. Serre, C.; Millange, F.; Thouvenot, C.; Nogu es, M.; Marsolier, G.; Lou€ er, D.; F erey, G. Very Large Breathing Effect in the First Nanoporous Chromium(III)-Based Solids: MIL-53 or CrIII(OH) 3 {O2C-C6H4-CO2} 3 {HO2C-C6H4-CO2H}x 3 H2Oy. J. Am. Chem. Soc. 2002, 124, 13519. Serre, C.; Bourrelly, S.; Vimont, A.; Ramsahye, N. A.; Maurin, G.; Llewellyn, P. L.; Daturi, M.; Filinchuk, Y.; Leynaud, O.; Barnes, P.; F erey, G. An Explanation for the Very Large Breathing Effect of a Metal-Organic Framework during CO2 Adsorption. Adv. Mater. 2007, 19, 2246. Salles, F.; Ghoufi, A.; Maurin, G.; Bell, R. G.; Mellot-Draznieks, C.; Llewellyn, P. L.; Serre, C.; F erey, G. Molecular Dynamics Simulations of Breathing MOFs: Structural Transformations of MIL-53(Cr) upon Thermal Activation and CO2 Adsorption. Angew. Chem., Int. Ed. 2008, 47, 8487. Coombes, D. S.; Cora, F.; Mellot-Draznieks, C.; Bell, R. G. Sorption-Induced Breathing in the Flexible Metal Organic Framework CrMIL-53: Force-Field Simulations and Electronic Structure Analysis. J. Phys. Chem. C 2009, 113, 544. Dubbeldam, D.; Krishna, R.; Snurr, R. Q. Method for Analyzing Structural Changes of Flexible Metal-Organic Frameworks Induced by Adsorbates. J. Phys. Chem. C 2009, 113, 19317. Ghoufi, A; Maurin, G. Hybrid Monte Carlo Simulations Combined with a Phase Mixture Model to Predict the Structural Transitions of a Porous Metal-Organic Framework Material


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Physics Behind the Guest-Assisted Structural Transitions of a Porous

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