J. Phys. Chem. C 2010, 114, 16181–16186
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Elucidating Negative Thermal Expansion in MOF-5 Nina Lock,† Yue Wu,‡ Mogens Christensen,† Lisa J. Cameron,‡ Vanessa K. Peterson,§ Adam J. Bridgeman,‡ Cameron J. Kepert,‡ and Bo B. Iversen*,† Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus UniVersity, DK-8000 Aarhus C, Denmark, School of Chemistry, The UniVersity of Sydney, NSW 2006, Australia, and Bragg Institute, Australian Nuclear Science & Technology Organisation, Menai, NSW 2234, Australia ReceiVed: April 9, 2010; ReVised Manuscript ReceiVed: July 1, 2010
Multi-temperature X-ray diffraction studies show that twisting, rotation, and libration cause negative thermal expansion (NTE) of the nanoporous metal-organic framework MOF-5, Zn4O(1,4-benzenedicarboxylate)3. The near-linear lattice contraction is quantified in the temperature range 80-500 K using synchrotron powder X-ray diffraction. Vibrational motions causing the abnormal expansion behavior are evidenced by shortening of certain interatomic distances with increasing temperature according to single-crystal X-ray diffraction on a guest-free crystal over a broad temperature range. Detailed analysis of the atomic positional and displacement parameters suggests two contributions to cause the effect: (1) local twisting and vibrational motion of the carboxylate groups and (2) concerted transverse vibration of the linear linkers. The vibrational mechanism is confirmed by calculations of the dynamics in a molecular fragment of the framework. Introduction The vast majority of solids expands when heated because of the anharmonic nature of the chemical bond potential. This property is known as positive thermal expansion (PTE). Excitement has arisen in the materials science community over the past decade with the discovery of materials that display negative thermal expansion (NTE), that is, lattice contraction with increasing temperature. Such materials have potential applications for engineering of optical and electronic devices.1 The presence of mechanisms competing against the ubiquitous anharmonicity is required to cause an overall lattice contraction upon heating. NTE-causing mechanisms include magnetic and electronic transitions2-6 as well as atomic or molecular transverse vibrations within the crystal lattices. Such vibrational NTE compounds are open and flexible covalently bonded frameworks including oxides such as ZrW2O8 and zeolites1,7-11 as well as cyanide-based materials.12-19 The flexibility of the cyanide structures with diatomic linkers is paramount to the monatomic linked frameworks, as evidenced by reports on cyanides displaying colossal isotropic19 and anisotropic16,17 NTE. Transverse vibrations of the M-O-M′ and M-CN-M′ bridges lead to contraction of the M-M′ distances in the oxide and cyanide frameworks, respectively. These vibrations are coupled to longrange low-energy acoustic rigid unit modes (RUMs) involving rotation and translation of undistorted metal coordination polyhedra.20 Increasing the population of the transverse vibrational motions with temperature counteracts the higher energy lattice expanding longitudinal modes and results in the overall lattice contraction. Three-dimensional coordination polymers, also called metal-organic frameworks (MOFs), in which multiple atom organic linkers form bridges between metal atoms, are likely to be even more flexible than the cyanide frameworks. Recently, two experimental studies of the NTE-causing mechanisms in the coordination polymer Cu3(1,3,5-benzenetricar* Corresponding author. E-mail:
[email protected]. † Aarhus University. ‡ The University of Sydney. § Australian Nuclear Science & Technology Organisation.
boxylate)2 were reported.21,22 Local twisting vibrations around the metal centers as well as long-range translational and librational motion of the linker cause NTE in this framework. MOFs have been studied extensively because of their gas storage properties.23,24 Attention was focused on the NTE of MOFs with the discovery by Rowsell et al. of lattice contraction with temperature in a gas-loaded sample of Zn4O(BDC)3 (BDC: 1,4-benzenedicarboxylate),25 a framework also known as MOF-5 and as IRMOF-1.24,26,27 MOF-5, which is the archetype coordination polymer, has mainly been studied because of its gas absorption properties, but here it is shown experimentally to also have a very large NTE in the gas-free state. Theoretical calculations28-31 suggest different models for the mechanism behind NTE in MOF-5. One of them29 proposes a mechanism related to that found in Prussian Blue analogous materials,14,15 whereas others28,30 point to the motion of the linker as well as of the zinc centers being the origin of the NTE. Here we present a detailed atomic scale experimental investigation of the mechanism causing lattice contraction in MOF-5. This adds a new dimension to the discussion of the different computational models proposed for the MOF-5 lattice contraction. Even though the existing models provide a sophisticated picture of the NTE mechanism, the models are different, and only experiments can elucidate which models give the best description of the lattice contraction with increasing temperature. In-depth crystallographic characterization, supported by theoretical modeling of a molecular fragment of the crystal structure, suggest a mechanism in which transverse vibration of the linear linker together with a local carboxylate motion is the origin behind the abnormal thermal expansion behavior in MOF-5. Understanding the mechanism behind the observed lattice contraction is crucial for tailoring of materials possessing specific expansion properties. An example of such tailoring was very recently reported on a tetramethylammonium copper-zinc cyanide framework showing zero thermal expansion because the ammonium ion dampens the well-known lattice-contracting transverse cyanide motion.32
10.1021/jp103212z 2010 American Chemical Society Published on Web 09/09/2010
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Figure 1. (a) Temperature-dependent variation in the unit cell parameter of MOF-5 determined from powder X-ray diffraction (PXRD) data (9) and single-crystal X-ray diffraction (SCXRD) (O). The right-hand scale bar is the percentage unit cell decrease in the powder data normalized to the 80 K data. The insets show the unit cell of MOF-5 with the metal centers represented as tetrahedra and octahedra, respectively. (b) The two contributions to the absolute decrease in the unit cell relative to the 100 K value as extracted from SCXRD data are displayed. The decrease across two aromatic rings (C1 to C1′) are shown with green squares, and the decrease across two tetranuclear zinc clusters (C1′ to C1′′) are shown with red squares. The atomic labeling is given in Figure 2. The inset in part b shows that the length of the lattice parameter corresponds to twice the length of the BDC linker (C1 to C1′) indicated with green lines, plus twice the distance across the tetranuclear zinc cluster (C1′ to C1′′) indicated with red lines.
The highly symmetric cubic framework of MOF-5 (a ) 25.82 Å at room temperature, space group Fm3jm) is composed of tetranuclear Zn4O(COO)6 units that are linearly bridged by the aromatic rings to form an extended 3D simple cubic topology (Figure 1a). A central oxygen (O1) atom is coordinated to four Zn atoms in a regular tetrahedral environment. Each zinc atom forms bonds to three carboxylate oxygen atoms (O2) in addition to O1. The Zn(O1)(O2)3 tetrahedra are slightly distorted, whereas the carboxylate carbon atoms (C1) form a regular octahedron around O1. The framework with a calculated free volume of 79.2% has the useful property of accommodating guest molecules in the pores, but guest filling may influence the NTE properties. In vibrational NTE compounds, the presence of guest atoms may dampen transverse vibrations, leading to less-pronounced NTE or even PTE.19 The samples used for the present crystallographic studies therefore were desolvated and sealed under dynamic vacuum in glass capillaries, and the NTE of the MOF-5 framework is studied using evacuated crystals. Experimental Methods Single-Crystal X-ray Diffraction (SCXRD). We prepared phase pure MOF-5 by dissolving Zn(NO3)2 · 6H2O and 1,4benzenedicarboxylic acid in the stoichiometric ratio 3:1 in diethylformamide (DEF) (>99%). A glass vial containing the solution was placed in a teflon-lined stainless steel autoclave and heated from room temperature to 100 °C over 30 min. The mixture was kept at 100 °C for 16 h. In a N2-purged glovebag, DEF was exchanged with dimethylformamide (DMF), which was subsequently replaced with chloroform. Individual single crystals were packed into glass capillaries using a procedure that prevented the crystals from being directly exposed to air. The crystals were attached to the bottom of the capillaries using glass rods. The capillaries were evacuated under dynamic vacuum and flame-sealed prior to diffraction experiments. SCXRD data were collected at The University of Sydney on a Bruker Nonius FR591 Kappa APEX II diffractometer using graphite monochromated Mo KR radiation (λ ) 0.71073 Å) generated by a rotating anode. The diffractometer was equipped with a CCD detector and an Oxford Cryostream nitrogen cooling device. Synchrotron Powder X-ray Diffraction. A 10 mL DEF solution of Zn(NO3)2 · 6H2O (0.20 g) and 1,4-benzenedicarboxylic acid (0.83 g) was sealed in a glass vial and irradiated
Figure 2. (a) Rates of change of ADPs with temperature as derived from the SCXRD data. The rates are given for the three ADP axes (major: black; intermediate: dark gray; minor: light gray) in the coordinate system of the atom. No crossover of the axes was observed in the temperature range 100-500 K. The inset shows anisotropic ADPs represented by 50% thermal ellipsoids (300 K) showing a large thermal population of vibrational motion perpendicular to the plane of the aromatic ring. (b) Schematic of the C3-C3′′ distance across the benzene ring. The atoms are shown as spheres, and the black arrows indicate the librational motion (light-blue probability density function). The thermal motion is modeled with Gaussian functions corresponding to the dark-blue thermal ellipsoids with the average position marked in red. The true space and time average is marked in green, and thus the harmonic model gives an apparent shortening of the bond.38
continuously in a microwave oven for 2 min at 100 W. DEF was exchanged first with DMF and then with chloroform. The monophasic microcrystalline powder was packed in a 0.3 mm glass capillary and flame-sealed under dynamic vacuum. Synchrotron radiation powder X-ray diffraction (PXRD) data were collected using a MAR345 2D image plate detector on beamline 12-BM at the Advanced Photon Source at Argonne
Elucidating NTE in MOF-5 National Laboratory (λ ) 0.620 Å). The temperature was controlled using an Oxford Cryostream nitrogen cooling device. Theoretical Calculations. Lowest energy molecular geometries and harmonic vibrational energies were calculated using the Gaussian03 software package.33 The electron density was modeled by Gaussian-type orbitals. The B3LYP functional and the LANL2DZ basis set were used along with default settings in Gaussian03. The computational work consisted of two steps: (1) structure optimization based on input coordinates generated from a crystallographic information file (cif) and (2) calculation of vibrational frequencies. The program ChemCraft Lite34 was used to visualize the calculated vibrational modes. Results and Discussion Le Bail-fits to synchrotron PXRD data collected in the interval 80-500 K were used to determine the unit cell parameter as a function of temperature. As depicted in Figure 1a, a near-linear NTE behavior is observed in this temperature interval with a linear coefficient of thermal expansion (Rl ) da/adT) of -13.1(1) × 10-6 K-1 at 300 K, where a is the unit cell parameter at 300 K and da/dT is the average slope over the full 80-500 K interval. The Fm3jm structural model describes all observed Bragg reflections at all temperatures showing that no phase transitions occur. The unit cell parameter change shows good agreement with other experimental studies of the unit cell evolution with temperature.25,30 Conventional multitemperature SCXRD data were collected from 100 to 500 K in 20 K intervals on a desolvated single crystal. The temperature-dependent unit cell determined from the SCXRD data is included in Figure 1a. There is an overall good agreement between the powder diffraction and singlecrystal diffraction data. The unit cell derived from single-crystal data deviates less from linearity than the cell derived from powder diffraction data. We ascribe this difference to the different data collection strategies. The PXRD data were collected continuously while the temperature was changed, and this may cause the actual sample temperature to deviate slightly from the temperature of the cryostream. In contrast, the SCXRD sample was in thermal equilibrium with the cryostream at all times. The SCXRD unit cell is in general slightly smaller than the PXRD cell. This can be explained by the fact that no internal standard was used, which is, in general, required for absolute unit cell determination. However, there is good agreement between the two slopes and hence between the linear coefficients of thermal expansion obtained from the PXRD and the SCXRD data. Temperature-dependent changes of time and position averaged atomic positions and atomic displacement parameters (ADPs) were obtained from structural refinements using SHELX.35 Analysis of the size evolution and orientation of the ADPs (Figure 2a) in combination with positional changes give a comprehensive picture of the vibrational NTE mechanisms in the structure. The extended length of BDC in comparison with a mono- or diatomic linker and the fact that it is linear rather than triangular as linkages found in Cu3(1,3,5-benzenetricarboxylate)2 suggest large flexibility and multiple degrees of freedom. Consequently, this allows for several vibrational motions with different frequencies. Any aromatic ring or carboxylate group motion of transverse character potentially contributes to the framework NTE. The analysis below probes which motions of the aromatic ring and the carboxylate group are present in the structure as well as their contribution to the NTE of MOF-5. In a simple picture, the motion of the aromatic ring can be separated into rotations around its three principal axes and a
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16183 translation. Symmetry axis 1, here defined as the line that goes through the carboxylate carbons and the aromatic ring plane, is parallel to the unit cell axis (Figure 3a). Libration around axis 1 (motion A, Figure 3a) is expected to have little effect on the lattice contraction. In contrast, potential NTE motions of transverse character include a rotation around the in-plane symmetry axis 2 (motion B, Figure 3a) and a translational upand-down motion of the aromatic ring perpendicular to its plane (motion D, Figure 3a). These two motions may be considered as in-phase (D) and out-of-phase (B) transverse motions, respectively, similar to motions in cyanide-based NTE materials.36 The rates of change of the ADPs and the inset in Figure 2a clearly show that the out-of-plane vibrational states have higher populations than the in-plane states. The in-plane ADPs were expected to exceed the out-of-plane ADP if librational motion around symmetry axis 3, which is perpendicular to axes 1 and 2 (motion C, Figure 3a), had been dominant. Figure 3b shows the temperature-dependent C3-C3′′ distance. Libration around axis 1 (A) is evidenced by an apparent decrease in the space and time-averaged picture of the C3-C3′′ distance across the benzene ring as a function of temperature. We suggest that the C3 atoms in reality move on a “bananashaped” rather than ellipsoidal trajectory upon transverse thermal population. In the average picture, this motion cancels out the anharmonic increase in the distance and does not represent the actual distance between the C3 and C3′′ atom (Figure 2b). The apparent decrease in the C3-C3′′ distance with increasing temperature, nevertheless, clearly reveals the presence of the librational motion. The interatomic distance between the two C2 atoms in the aromatic ring, C2-C2′ (Figure 3b), shows zero thermal expansion, and this observation reveals that the outof-phase transverse motion (B) exactly cancels the anharmonic increase in the C2-C2′ distance. If the out-of-phase motion (B) had contributed significantly to the framework NTE, then a decrease in the C2-C2′ distance would have been observed. The in-phase transverse translational motion of the aromatic ring (D) is likely to be significant because the C1-C2 distance decreases with increasing temperature (Figure 3b). The contributions of this translational motion (D), the librational motion (A), and potentially the out-of-phase vibration (B) to the outof-plane ADP of the C3 atoms are highly correlated. Therefore, these motions are indistinguishable from the orientation of the thermal ellipsoid for C3 alone. In addition to motion of the aromatic ring, vibrational motion of the zinc carboxylate clusters also contributes to the framework NTE. The presence of transverse motion of the oxygen atoms is evidenced by the distinct Zn-O2 bond contraction (Figure 3b) and the out-of-plane orientation of the O2 ADP (Figure 2b). A similar motion has not been observed (Figure 3b) for the spatially confined isotropic O1 atom, which forms bonds to four Zn atoms. Our crystallographic data suggest that both carboxylate rotation around the C1-C2 bond and vibration of the carboxylate group perpendicular to the plane defined by the carboxylate average positions (as drawn in Figure 3a) are significant. The rotational “twisting” motion around the C1-C2 axis is evidenced by the decrease in the Bragg-averaged O2-C1-O2′ carboxylate group angle with increasing temperature (Figure 3b). The indication of a rotational motion is in good agreement with the fact that the rate of change of the transverse ADP for O2 exceeds that for C1 (Figure 2). However, a carboxylate rotation around the C1-C2 bond alone does not explain the observed preferential population of the out-of-plane ADP for C1. A vibrational motion in which C1, O2, and O2′ vibrate out of plane with the same frequency would describe
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Figure 3. (a) Sketches of possible simple motions of the benzene ring: rotation around the three principle axes of the benzene ring and a translational up-and-down motion. Axes 1 and 2 are sketched on the left-hand figure. Axis 3 is perpendicular to axes 1 and 2. The translational motion and rotation around axis 2 can be viewed as in-phase and out-of-phase transverse vibrational motions, respectively. (b) Temperature-dependent atomic distances and angles derived from the SCXRD data. Upper left: d(C2-C2′) (blue squares) and d(C3-C3′′) (red squares); lower left: d(C1-C2); upper right: d(Zn-O1) (dark blue circles) and d(Zn-O2) (dark red circles); lower right: O2-C1-O2′ angle (black circles).
this observation because such a motion would contribute to the out-of-plane ADP for C1 as well as for O2. However, in principle, a carboxylate vibration would lead to an increase in the carboxylate group angle, in contrast with a rotation resulting in a decrease, as described above. Nevertheless, both motions are likely to occur. The carboxylate and the aromatic ring motions are most likely coupled. This is evidenced, for example, in the average C1-C2 distance, which decreases with temperature (Figure 3b) because of motion transverse to axis 1 (Figure 3a). As described above, this observation can be associated with the in-phase (D) or outof-phase transverse motion (B) of the benzene ring. However, the observation is also consistent with the carboxylate group vibration. Similarly, the observed aromatic ring libration (A) can occur in tandem with the carboxylate group rotation. However, the smaller transverse ADP for O2 than for C3 suggests that the carboxylate group rotates with a smaller amplitude than the benzene ring. This makes the carboxylate rotation partially local in nature; that is, the carboxylate to some degree moves independently of the benzene ring. The present computational results support the experimentally proposed collective vibrations. Using the Gaussian software,33 the geometry and vibrational frequencies have been calculated for a molecular representative of MOF-5 consisting of two
Zn4O(COOH)5(COO) clusters linked via a benzene ring. The atoms were modeled in a harmonic potential, which makes the calculated frequencies temperature independent. Overall, the calculated vibrational dynamics are in good agreement with previous studies of the lattice dynamics of MOF-5 by Civalleri,37 a study in which NTE was not discussed. The vibrations of particular interest for this study are low-energy (
