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How Guest Molecules Stabilize the Narrow Pore Phase of Soft Porous Crystal: Structural and Mechanical Properties of MIL-53(Al)#HO 2

Mingyang Wang, Xinghua Zhang, Yunlin Chen, and Dan Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00474 • Publication Date (Web): 22 Feb 2016 Downloaded from http://pubs.acs.org on February 28, 2016

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The Journal of Physical Chemistry

How Guest Molecules Stabilize the Narrow Pore Phase of Soft Porous Crystal: Structural and Mechanical Properties of MIL-53(Al)⊃H2O Mingyang Wang, Xinghua Zhang,∗ Yunlin Chen,∗ and Dan Li Institute of Applied Micro-Nano Materials,School of Science, Beijing Jiaotong University, Beijing 100044, China E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed

1 ACS Paragon Plus Environment


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Abstract The mechanical properties of MIL-53(Al) and H2 O composite (MIL-53(Al)⊃H2 O) in the narrow pore (np) phase was addressed using density functional theory. The tensorial analysis of the elastic constants in the np phase provides a further support of adsorption induced stress mechanism of the breathing effect in MIL-53, and the practical mechanical properties of MIL-53(Al) in humidity condition. The adsorption of water molecules in MIL-53(Al) forms a reinforced wine-rack topological structure. The stable structure in the np phase eliminates the high anisotropy and anomalously low Young and shear moduli of the large pore phase. In addition, new soft modes which indicate the evolving path back to the large pore phase were found in the np phase.

Keywords: MIL-53, Metal Organic Frameworks, Mechanical Property, Guest Molecule, Structural Transition, Density Functional Theory


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1. INTRODUCTION Soft porous crystals (SPCs), a subclass of metal organic frameworks (MOFs) with remarkable flexibility, have been widely concerned due to the potential applications in sensing, catalysis, gas capture and separation. 1,2 As a prototypical material of SPCs, MIL-53(M) where M represents the metal element consists of parallel one-dimensional inorganic chains, linked together by organic ligands to form linear lozenge-shaped pores. It exhibits a reversible structural transformation triggered by adsorption of guest molecules which was first observed in MIL-53(Cr). 3,4 The wellactivated sample has a large pore (lp) structure, while in humid ambient conditions, the framework shrinks to a narrow pore (np) structure due to the adsorption of water molecules. This lp-np transition is fully reversible which is known as breathing effect. It is a common property of the MIL-53 family with different metal elements. 5–10 The mechanism of this volume transformation in crystal is not only interesting in theory but also critical to the application of flexible MOFs in application. In the hydrated condition, the guest water molecules adsorbed on the polar groups of framework induces the internal stress on the frameworks. Once the stress excesses the critical stress, the breathing transition occurs. 11–13 The mechanical responsive property is the key to understand the breathing behavior of the MIL-53 family. Recently, the full elasticity tensor of MIL-53 in lp phase without guest molecules (lpempty phase) was calculated by density functional theory. 14,15 The lpempty phase exhibits high anisotropy and anomalously low Young and shear moduli. The "soft" directions are along the diagonals of the lozenge-shaped pore (E=0.9 Gpa and 2.4 GPa). The lowest shear moduli locate in the cross section of the channels and along the organic linkers. The high Young’s modulus corresponds to the rigidity of organic linkers (E=94.4 GPa) and that of the inorganic Al(OH) chain (E=60.9 GPa). Additionally, it demonstrates both negative Poisson’s ratio and extremely high negative linear compressibility. These flexible characters from the winerack topology 16 are the key signatures of the breathing behavior and indicate the evolution path of the structural shrinking. 12 One way to get rid of the stabilize this kind of structure is to restrict the deformation topologically by forming a "reinforced" wine-rack framework. MIL-140A is a typical example of reinforced wine-rack framework. There is no soft Young’s modulus within the cross 3 ACS Paragon Plus Environment


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section of the pore and the linear compressibility is positive in all directions. In fact, the mechanical responsive property of the np phase with a few of water molecules (npwater phase) is another critical aspect to understand the breathing effect comprehensively besides the lpempty phase, since both two phases are evolved in the structural transformation. The water stability and adsorption in MIL-53 has been well reviewed by various experimental techniques including ex situ X-ray diffraction, in situ infrared spectroscopy, adsorption gravimetry, microcalorimetry, thermogravimetry analysis, differential scanning calorimetry and complex impedance spectroscopy. 6,7,17–19 The soft modes by adsorption in lpempty must be strengthened which stabilizes the np phase without further shrinking. Moreover, as a stable phase in hydrated condition, the mechanical responsive property of the npwater phase plays an important role to the application of MIL-53 in practice. In npwater phase, the guest water molecules interact with the framework through hydrogen bonds which would take important role in the mechanical responsive properties of the composite system. However, to the best of our knowledge, 20–22 there is no report on the mechanical properties of the npwater phase. In the present work, we calculated the full elastic constants tensor of the MIL-53(Al) and H2 O composite in the np phase by density functional theory using VASP package. 23,24 Based on the theoretical results, the mechanism of guest water molecules strengthen effect on the soft modes of the lpempty phase which prevent the framework from further shrinking was investigated.

2. COMPUTATIONAL METHODS In this article, empty and water are used as subscript to label MIL-53 without and with H2 O molecules, respectively. The systems, lpempty , npempty , lpwater and npwater , were studied by means of density functional theory (DFT) computation using VASP based on PBE functional. The adsorption energy per H2 O molecule on the framework can be determined by ∆E = (Ewater − Eempty − nE0 )/n,


(1)

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where n = 4 is the number of H2 O molecules in a unit cell, and E0 = −14.209 eV is the energy of a free H2 O molecule. According to the tensorial Hooke’s law, the elasticity tensors of the material were obtained (shown in Table 1). Then a full tensorial analysis was performed and some key quantities were derived that characterize the mechanical behavior of the crystal in the elastic regime. Details concerning the computational methods can be found in the 2.1-2.3. Table 1: Stiffness constants Ci j in Voigt notation.

C11 C22 C33 C44 C55 C66 C23 C13 C12 C16 C26 C36 C45

lpempty 14 90.85 33.33 65.56 7.24 8.27 39.52 12.36 20.41 54.28

lpwater 68.14 17.27 45.44 14.88 23.2 33.67 3.74 -0.58 28.24

npempty 121.3 4.59 96.05 3.96 24.95 4.85 -1.66 3.74 16.38 0.79 -0.08 -7.86 0.42

npwater 136.8 17.87 92.27 9.99 35.12 3.55 6.68 37.95 24.39 0.7 2.19 9.39 0.2

2.1 DFT calculation The DFT calculations were performed for MIL-53s under periodic boundary conditions. The structures of all materials considered were fully relaxed by optimizing both atomic positions and unit cell parameters, starting from the experimental crystallographic structure. 5–7 DFT-optimized geometries water in the np phase for the low loading obtained and given in Ref. 6. In order to compare the energy in the different phases with same water loading, 4 molecules./u.c. was chosen in both the npwater and lpwater phase. It should be noted that this loading condition corresponds to the full loading of the np form. 4 However, for the lp form, the full loading corresponds to 17 molecules/u.c. which will be investigated in the future. The Perdew-Burke-Ernzerhof (PBE) 24–26 functional was adopted. The ionic relaxation their instantaneous ground state was obtained by



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using the conjugate-gradient algorithm. For ensuring a convergence of both total energy and forces, we used a plane wave cutoff of 500 eV. The Brillouin-zone was sampled by using an equally spaced mesh provide by the Mokhorst and Pack method with 4×2×5 and 5×3×3 K-points for the lp and np phase, respectively. The accuracy of this methodology is now well established for the calculation of MOF structure, energies, and elastic constants. 27,28

2.2 Calculation of elastic constants In the tensorial Hooke’s law, the link stress σ and framework deformation ε establishes a general relationship: σi j =

∑

Ci jkl εkl ,

(2)

kl

where indices i, j, k and l run between 1 and 3. Ci jkl is the fourth-order elasticity tensor or stiffness tensor of the material. Taking advantage of the symmetries of stress and strain matrices and using the Voigt notation, Ci jkl can be expressed as a 6×6 symmetric matrix of 21 elastic constants Ci j , where reported in Table 1. The size of deformations (equals to 0.005) and total number of points sampled for each deformation mode (equals to 5) were varied to check the robustness of the method, as well as the fact that the strains imposed were within the limits of the elastic region.

2.3 Tensorial analysis of the elastic constants From the stiffness constants, a full tensorial analysis was performed and key quantities were derived that characterize the mechanical behavior of the crystal in the elastic regime: (i) Young’s modulus E(n) characterizes the uniaxial stiffness of the material in the direction of unit vector n. (ii) The linear compressibility β(n) quantifies the deformation in direction n as a response to isostatic compression. (iii) The shear modulus G(n, m) characterizes the resistance to shearing of the plane normal to m in the n direction. (iv) Poisson’s ratio ν(n, m) is the ratio of transverse strain in direction n to axial strain in direction m, when uniaxial stress is applied. The directional dependence of the above-listed properties can be calculated from the fourth-order compliance tensor S,


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which is the inverse of the stiffness tensor C, by applying to it a rotation mapping the x and y axes onto the directions of n and m to obtain a rotated tensor S0 . These properties can be expressed as functions involving the components of S and unit vectors n and m: ′

E(n) = [S1111 (n)]−1 = (ni n j nk nl Si jkl )−1 ,

(3)

β(n) = ni n j Si jkl ,

(4)

G(n, m) = (ni m j nk ml Si jkl )−1 ,

(5)

ν(n, m) = −

ni n j mk ml Si jkl . ni n j nk nl Si jkl

(6)

2.4 The soft deformation mode The softest deformation mode as the unit strain ε0 yielding the smallest energy, E(ε0 )min , can be expressed as 12

∑ E(ε0 )min = min ( Ci jkl εi j εkl ). ||ε||=1

(7)

i jkl

Thus, the soft deformation mode can be represented by the small eigenvalue and the nature of the mode can be represented by the associated eigenvector. 16

3. RESULTS AND DISCUSSION 3.1 Phase transition induced by adsorbing H2 O molecules Stable structures in hydrated and dehydrated conditions are determined by comparing the energies of DFT-optimized configurations in both the lp and np phases (shown in Figure 1(a), Fig-



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ure 1(b) and Figure S1). The detail crystal parameters and energies are list in Table 2. Because the lpempty phase (-536.709 eV) and the npwater phase (-594.658 eV) have lower energies comparing to the npempty phase and the lpwater phase, these two structures are candidates of stable structures in the dehydrated and hydrated conditions, respectively. The results consist with previous numerical and experimental results, 6 which indicates that the approximation level adopted by our numerical computation can describe the adsorption induced structural transformation at low water molecules loading or in the atmospheric environment. The nonzero energy difference between these two stable structures makes latent heat is needed to stimulate the transformation which has been observed by differential scanning calorimeter experiment. 19 The difference of cell volume between the MIL-53(Al) in hydrated and dehydrated conditions is 34.6%, which is consistent with the previous works. 29 The volume change mainly takes place in the cross section of a − b plane and the contraction along the inorganic chain can be ignored. According to Table 2, the framework shrinks in the b axis about 42.4% and expands in the a axis about 16.6%.These phase transition behaviors are the typical characters of the so-called compliant wine-rack structure. 16 Meanwhile, the framework changes from the tetragonal system to the monoclinic system. Table 2: Space group (S.G.), unit cell parameters (a, b, c, α, β and γ), volume (V) and the lowest energy of the optimized MIL-53(Al) MIL-53(Al) phase S.G. a(Å) b(Å) c(Å) α(◦ ) β(◦ ) γ(◦ ) V(Å3 ) Energy(eV) 14 lpempty Imma 16.48 13.24 6.68 90 90 90 1458 -536.709∗ lpwater Imma 16.86 13.05 6.72 90 90 90 1479 -594.658 npempty C2/c 19.85 7.85 6.7 90 109.92 90 1004 -536.087 npwater C2/c 19.76 7.63 6.67 90 104.69 90 971 -594.667 *The energy of the lpempty phase is computed in present work based on the PBE functional.

3.2 Configuration of guest H2 O molecules in the framework One superiority of theoretical work is to see the configuration of guest molecules in the host frameworks and measure the deformation of the frameworks in the real space. In the configuration of the lpwater phase, only one type of hydrogen bond exists between the oxygen atom of the water molecules (Ow ) and the hydrogen atom (HM ) of the µ2 -OH groups with the a bond length about 1.8 8 ACS Paragon Plus Environment

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Figure 1: Stable structures of MIL-53(Al) in (a) the dehydrated states or called the lpempty phase and (b) the hydrated states or called the npwater phase, respectively. Color code: C - brown, O red, H - white, Al - cyan.



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Å (Figure S1). The adsorption energy is ∆Elp = −27.66 kJ/mol which is corresponds to the energy of a hydrogen bond. In the npwater phase, besides the hydrogen bond on the µ2 -OH adsorption site, two extra hydrogen bonds (2.2 Å) are formed between H atoms of water molecules (Hw ) and the O atoms (OM ) on the [AlO4 (OH)2 ] octahedral cluster from the neighboring inorganic chain (Figure 2(b)). The formation of extra hydrogen bonds further decreases the adsorption energy per molecule, ∆Enp = −43.36 kJ/mol, which is lower than that in the lpwater phase and indicated that two extra hydrogen bonds (Hw -OM ) exist in the npwater phase and are weaker than the hydrogen bond on the µ2 -OH adsorption site. The results consists with the energy found for water adsorption in MIL-53(Cr) at low loading condition (approximately −39 kJ/mol). 4,6 This induces the np phase is more stable comparing to the lp phase in low loading condition. Moreover, the formation of these three hydrogen bonds makes the guest H2 O molecules have a preferential orientation in the channel with an angle of 36.7◦ between the plane of H2 O and the b − c plane. The configuration of guest H2 O molecules consists with that in MIL-53(Cr) obtained by DFT computation, 30 and the orientation order of H2 O was used to characterize the breathing phase transition in molecular simulation. 31 The guest H2 O molecules bridge two neighboring inorganic chains by hydrogen bonds in the middle of the pore channel, which act as the hinges of the wine-rack framework. The configuration of this host/guest system has a similar topological structure with MIL-140A which is called as a reinforced wine-rack framework. 16 However, the strength of this reinforced structure formed by the hydrogen bonds which is weaker than that reinforced by the coordinate bond in MIL-140A. The discussions in the manuscript are in the temperature of 0 K. The initial guess of the configuration is based on the XRD data from Ref. 6 and the results consistent with previous results. It is important to know the configurations of water molecules in finite temperature. However, the quantum mechanical computation is not enough. The configuration of guest molecules can be well determined by the first-principles molecular dynamics. 32 The adsorption of H2 O molecules deforms the inorganic chain as well. The deformation includes the shrinkage in c axis direction characterized by the bond angles Al-O-Al in the inorganic


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Figure 2: The configurations of (a) the inorganic chain in the dehydrated phase (lpempty ) and (b) the inorganic chain together with adsorbed H2 O molecules in the hydrated phase (npwater ). The chain is along the c axis. The O, H and Al atoms are represented by the color of red, white and magenta, respectively.



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chains and the shape of AlO4 (OH)2 octahedral cluster characterized by the rotation of the AlO4 plane. Similar with the results of MIL-53(Cr), 10 the Al-O-Al angles do not change dramatically, from 128 ◦ to 127 ◦ , which gives rise to the negligible deformation of unit cell in c axis direction. The deformation of the inorganic chain mainly takes place on the AlO4 plane. The relative angle formed between the AlO4 plane and b axis is 1.8 ◦ and that between this plane and c axis is 4.3 ◦ (from Figure 2(a) to Figure 2(b)), which makes the crystal transforms from tetragonal system to monoclinic system. Moreover, the distance between neighbouring inorganic chains is lowered by the bonded H2 O molecules which make the angles between the organic linker and the polar groups of MIL-53(Al) transform from 36.9

◦

in the lpempty phase to 6.8

◦

in the npwater phase (shown in

Figure S2).

3.3 Elastic properties of hydrated MIL-53(Al) in np phase The elasticity tensors of the lp phases and the np phases have 9 and 13 independent components, because they are orthorhombic and monoclinic lattice systems, respectively. Full elastic constants tensors of the candidate structures are provided in Table 1. It should be noted that the elasticity tensors of lpempty calculated by our work are comparable to Ref. 14 in the quantitative analysis which computed based on B3LYP hybrid density functional. The elasticity tensor is the responsive function to external mechanical stimulation. Its lowest eigenvalue corresponds to the lowest energy cost to destroy the structure. According to Born stability condition, 33 the structure becomes unstable when the relevant lowest eigenvalue becomes zero. Therefore, the linear stability analysis of the candidate structures can be performed by computing the eigenvalues of the elasticity tensor. As list in Table 3, all eigenvalues of the elasticity tensors are positive, which means these four structures can keep their structures under small deformation. In the hydrated and dehydrated conditions, the npwater and the lpempty phases have lower energies and their elasticity tensors are positive definite matrixes. Both necessary conditions ensure these two structures are stable phases in the hydrated and dehydrated conditions, respectively. On the other hand, the elasticity tensors of the lpwater and the npempty phases with higher energies in the hydrated and 12 ACS Paragon Plus Environment

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dehydrated conditions are positive definite matrixes as well, which indicates these two structures are not unstable. Therefore, the lpwater and the npempty phases are the metastable phases of MIL-53 in hydrated and dehydrated conditions. The metastability of the metastable phase is determined by the height of energy barrier which resists the crystal change from the metastable phase to the stable phase. It can be computed based on the transit state theory. As shown in Table 1, 7 out of 9 stiffness constants decrease in going from the lpempty phase to lpwater phase, which relates to the a temporary softening in the low loading regime recently reported. 34 Hereafter, we concentrate on the stable phases of MIL-53(Al) in both hydrated and dehydrated conditions, i.e., the npwater phase and the lpempty phase. Table 3: Eigenvalues λi (in GPa) of the stiffness matrix Ci j 14

lpempty lpwater npempty npwater

λ1 0.66 4.37 1.49 2.09

λ2 λ3 7.24 8.27 14.88 23.2 3.95 4.32 9.99 14.46

λ4 λ5 λ6 39.52 57 132.08 33.67 45.73 80.74 24.96 71.15 149.85 35.12 71.67 163.26

3.4 Reinforce effect of guest water molecules and hydrogen bonds The introduction of the H2 O molecule which bridges the neighbouring inorganic chains strengthens the structure in the direction along b axis. The reinforcement effect on the Young’s moduli can be concluded from the comparison between the representations of Young’s modulus for the lpempty phase (Figure S3(a) and Figure S3(b)) and the npwater phase (Figure 3(a) and Figure 3(b)). The introduction of water dramatically decreases the anisotropy of Young’s modulus which is one of key signature of the breathing phenomenon. In the npwater phase, AE = Emax /Emin = 27.5 (shown in Table 4) which is much lower than that of the lpempty phase, AE = 104.9 and similar with that of the reinforced wine-rack framework MIL-140A, AE = 31.8. 16 Although the reduction is approximately 70%, the anisotropy of elasticity tensor in npwater phase is not ignorable. In the npwater phase, as illustrated in Figure 3(c), the maximal Young’s modulus (Emax =126.4 GPa) is along n (θ = ± 38 ◦ , ϕ= ± 17 ◦ ) which corresponds to the uniaxial strain along the organic 13 ACS Paragon Plus Environment


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Figure 3: (a) Young’s modulus E representation surfaces of the npwater phase. (b) Polar plots of the cross sections of a = 0 (red lines) and b = 0 (blue lines) planes in the npwater phase (solid lines) and the lpempty (broken lines). (c) Molecular structure-stiffness property correlations, where the thickness of the lines and the size of the arrowheads represent the magnitude of the stiffness (E) in that particular orientation.

Table 4: Minimal and maximal values as well as anisotropy of Young’s modulus, shear modulus, linear compressibility, and Poisson’s ratio for the candidates studied. Anisotropy of X is denoted by AX = Xmax /Xmin . Property lpempty 14 lpwater npempty npwater

Emin Emax AE (GPa) (GPa) 0.9 94.4 104.9 21.6 75.4 3.5 1.6 70.7 44.2 4.6 126.4 27.5

Gmin Gmax AG (GPa) (GPa) 0.35 39.5 112 9.33 33.7 3.6 1.15 26.7 23 2.07 35.3 17

βmin βmax νmin −1 −1 (TPa ) (TPa ) -257.7 445.4 -2.4 -24.7 95.3 -0.33 -89.1 562.0 -3.19 -33.1 97.7 -1.53


νmax 1.9 0.58 3.87 1.65

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linkers. In fact, Emax of the lpempty phase is also from the rigidity of the organic linker. But it is lower than that in npwater phase. In the plane that are perpendicular to organic linkers, the number of the organic linkers within unit area in the npwater phase are more than that in the lpempty phase. So the energy density is enhanced after the lp-to-np transition. As a consequence, the framework becomes rigid along this direction. In order to demonstrate the mechanical effects of H2 O molecules, the Young’s moduli of the lpempty phase and the npwater phase along the direction within a = 0 and b = 0 planes are compared in Figure 3(b). In dehydrated condition, the Young’s moduli along the diagonal directions of the lozenge-shaped pore ([100] and [010]) are in the scale of 10−1 GPa which are quite flexible and close to that of rubbers. The anomalous low moduli are from the rotation of the organic linkers in the c=0 plane (the corresponding energies of the bond angles are ∼ 58 kJ mol−1 rad−2 and 121 kJ mol−1 rad−2 , respectively 35 ). These two soft modes induce the evolving path from the lp phase to the np phase. In hydrated condition, the adsorption of the water molecules topologically restricts the rotation of organic linkers. Accordingly, the uniaxial strain from this mechanism is negligible in both [010] and [100] directions and then the Young’s moduli in these two directions are strengthened. In [010] direction which appearing Emin in the lpempty phase, the Young’s modulus is increased from 0.9 GPa to 55.17 GPa, approximately 61 times. In the [100] direction, Young’s modulus is increased from 2.4 GPa to 83.44 Gpa, 35 times approximately. With the typical properties of reinforced wine-rack framework, the diagonal directions of the pore are no longer the "softest" directions and the path to shrink further has been stopped. The origins of the strengthen effects in [010] and [100] directions of the npwater phase are different. In the [010] direction, the uniaxial strain is directly restricted by the water molecules and the hydrogen bonds. The Young’s modulus in this case is from the deformation of the hydrogen bonds. On the other hand, the angle between the organic linkers and the [100] direction is restricted around 7◦ (shown in Figure S2(b)). The Young’s modulus along [100] direction is mainly from the deformation of the organic linkers instead of its rotation. This gives to the anomalously increase of Young’s modulus in [100] direction which is even larger than that of inorganic chain.



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It is interesting that the deformation of inorganic chain due to the structural transformation is ignorable, however, the modulus in [001] direction of the npwater phase, E=11.79 GPa, is much lower than that in the lpempty phase, E = 60.90 GPa. In the lpempty phase, the uniaxial stress in [001] direction has no projection on the organic linker because the organic linkers are perpendicular to the [001] axis. Therefore, only the rigidity from the deformation of the inorganic chains contributes to the whole Young’s modulus in [001] direction. After adsorbing H2 O molecule, the crystal transforms from tetragonal system to monoclinic system and the organic linkers have a 97◦ angle with respect to the c axis. Then the uniaxial strain in [001] direction includes two modes, the the deformation of the inorganic chains and the rotation of organic linkers. In fact, the energy of the organic linker tilting (∼ 136 kJ mol−1 rad−2 ) characterized by the energy of the bond angle O-C-C) is much lower than that of the deformation in the inorganic chain (∼ 672 kJ mol−1 rad−2 ) characterized by the energy of the bond angle O-C-O). 35 In principle, the Young’s modulus in a certain direction is determined by the mode with lowest energy cost. As a consequence, the Young’s modulus along [001] is dramatically decreased due to the tilting of organic linker. The most compliant direction in the npwater phase (Emin = 4.6 Gpa) is also from the tilting of the organic linker. The magnitude of the lowest modulus is in accordance with the common MOFs, i.e., MOF5 (Emin =7.5 GPa), 36 ZIF-ini (Emin =4.69 GPa) 25 and MIL-140A (Emin =2.52 GPa). 16 This new soft mode along the pore channel indicates the evolving path back to the lp phase. The 3D representation surfaces for both the maximum and the minimal shear moduli in hydrated condition are shown in Figure S5(a) and Figure 4(a), respectively. And the corresponding projection in the a= 0, b= 0, and c= 0 planes are plotted in Figure S5(b) and Figure 4(b). As list in Table 4, the introduction of water reduces the anisotropy of shear moduli and approaches that of the reinforced wine-rack framework (MIL-140A, AG = 36.2). The maximal shear modulus in the npwater phase (Gmax ) is equal to 35.3 GPa when an opposing pair of shear stresses act parallel to the softest direction, similar with that in lpempty phase (Figure S5). Anomalously low shear modulus of the lpempty phase with Gmin = 0.35 GPa is the critical reason for structural transformation. This mode originates from the shear stress acting parallel the


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Figure 4: 3D representations of (a) the minimal shear modulus Gmin for npwater . (b) Corresponding polar plots obtained via projections through the origin onto the three planes, showing the positions of minimum moduli. Axes tick labels for (a) and (b) are in GPa. (c) and (d) Four sets of normal stresses σ corresponding to the minimum stiffnesses shown in two planes.



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organic linkers plane which is the typical properties of the compliant wine-rack framework. 16 As indicated above, the energies of the angles between the neighbouring organic linkers on the same [AlO4 (OH)2 ] octahedron are quite low and susceptible to shear stress. This unstabilizing factor is eliminated by the adsorption of H2 O molecules. The shear stress with the minimal shearing modulus in the npwater phase (Gmin =2.07 GPa) is no longer along the direction with lowest shear modulus in the lpempty . Similar with the Young’s modulus, Gmin is from the tilting of organic linkers when a pair of shear stress acts on this plane. The Gmin indicates the evolving path back to tetragonal lattice system or the lp phase. The adsorption of H2 O molecules affects the shear moduli in two aspects. First, the connection between two inorganic chains by the H2 O molecules forms the so-called reinforced wine-rack structure. This structure restricts the shear strain in a − b plane which are from the rotation of the organic linkers. Second, the two hydrogen bonds between OM and Hw on the same H2 O molecule are not in the plane of the H2 O molecule and not collinear with each other (shown in Figure 4(c) and Figure 4(d)). The orientation of the adsorbed H2 O molecules and the Hw -OM hydrogen bonds are compliant to the shear stress or adsorbing more H2 O molecules. This gives rise to the subminimal shear moduli (G = 2.2 GPa) appearing along the direction of the hydrogen bonds. Its projections in the b = 0 plane can be found in Figure 4(d). Inserting extra H2 O will form new hydrogen bonds between different H2 O molecules, which will further decrease the total energy and stabilize the framework to another lp phase in high H2 O molecules loading condition. The linear compressibility of the npwater phase and the lpempty phase are compared in Figure 5(a) (z = 0 plane) and Figure 5(b) (y = 0 plane). Similar with that of the lpempty phase, the linear compressibility is anisotropic with a pair of positive lobes, a pair of quite small negative lobes normal to the positive lobes, and a small positive value along the inorganic chains direction. Although the npwater phase exhibits a much lower absolute value of linear compressibility, it still shows one contraction direction of large positive linear compressibility (βmax = 97.7TPa−1 ) and one expansion direction with negative linear compressibility (βmin = −33.1 Tpa−1 ). Similarly, the Poisson’s ratio also exhibits a negative value. The introduction of the H2 O molecule reinforces


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topology structure of the npwater phase to form a wine-rack structure. And the decrease of the unit cell volume increases the overall energy density. Both the effects dramatically decrease the absolute value of the linear compressibility. The direction of the largest linear compressibility is from the low energy of the corresponding bond angle due to the formation of monoclinic system, and is consistent with the direction of the lowest Young’s modulus and shear modulus. This is a further evidence for the existence of evolving path back to the lp phase.

Figure 5: 3D surface representation of the linear compressibility in the lpempty phase (transparent surface) and the npwater phase (non-transparent surface), as view on the z = 0 plane (a) and the y = 0 plane (b). Positive linear compressibility is indicated as blue, negative linear compressibility in red.

4. Conclusions In summary, adsorption induced structural transformation of MIL-53(Al) in low loading condition was investigated by means of density functional theory. The full elasticity tensor of the guest/host composite, MIL-53(Al)⊃H2 O, was elucidated on the approximation level of PBE functional by VASP package. In the hydrated condition, the roles of water molecules on the stability of the framework were addressed by analyzing the Young’s modulus, shear modulus, Poisson’s 19 ACS Paragon Plus Environment


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ratio and linear compressibility. The guest H2 O molecules link with MIL-53(Al) framework by hydrogen bonds forming a reinforced wine-rack framework which restrict the deformation of the pore-shape. These hydrogen bonds decrease the energy of the npwater phase which stabilize the structure. As a consequence, the anomalously low minimum values of both Young’s modulus and shear modulus and the large absolute values of linear compressibility in the lp phase are eliminated. Comparing with the lp phase, the decrease of the unit cell volume in the np phase leads to the increase of the energy density dramatically, which makes the framework becomes rigid and the maximum value of the Young’s modulus increase. Moreover, the formation of monoclinic lattice system dramatically decreases Young’s modulus and increase linear compressibility along the pore direction. These new soft modes along the pore direction make the transformation from monoclinic system to the tetragonal system easily which indicate the evolving path back to the lp phase.

ASSOCIATED CONTENT Supping Information Detals of the analysis of the lpempty phase and the metastable state. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authers *E-mail: [email protected] (Xinghua Zhang) *E-mail: [email protected] (Yunlin Chen) Author Contributions The manuscript was written through contributions of all authors Notes The authors declare no competing financial interest.


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ACKNOWLEDGEMENT This work was supported by the National Natural Science Foundation of China (NSFC) Nos. 21376026, 21304008, 21574011, NSFC-Guangdong joint special research fund (second) for application of supercomputer and National Supercomputer Center in Guangzhou, the Fundamental Research Funds for the Central Universities No.2015JBM093, start-up fund from Beijing Jiaotong University, the SRF for ROCS, SEM.

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How Guest Molecules Stabilize the Narrow Pore ... - ACS Publications

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