Effect of Defects on the Mechanical Deformation Mechanisms of Metal

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Effect of Defects on the Mechanical Deformation Mechanisms of Metal-Organic Framework#5: A Molecular Dynamics Investigation Bin Zheng, Fang Fu, Lian Li Wang, Jinlei Wang, Lifei Du, and Hui Ling Du J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10928 • Publication Date (Web): 08 Feb 2018 Downloaded from http://pubs.acs.org on February 9, 2018

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The Journal of Physical Chemistry

Effect of Defects on the Mechanical Deformation Mechanisms of Metal−Organic Framework‑5: A Molecular Dynamics Investigation Bin Zheng,*,† Fang Fu, † Lian Li Wang,† Jinlei Wang,† Lifei Du,† Huiling Du† †

School of Materials Science and Engineering, Xi’an University of Science and

Technology, Xi’an 710054, PR China

E-mail: [email protected]

TITLE RUNNING HEAD: The role of defects in the mechanical deformation of MOFs was revealed to obtain deformation mechanism and tunable mechanical properties.

ABSTRACT: Defects are likely ubiquitous in metal-organic frameworks (MOFs). Investigation on the effect of defects on the mechanical deformation of MOFs remain at a nascent stage. In this study molecular dynamics simulation was adopted to investigate the deformation mechanisms of defected MOF-5. Our results show that the defects reduce the yield strength via inducing the nucleation of dislocations. The type of dislocations depends on the defect structure, presented as a subject increased scientific interest. Also, the defected MOF-5 was deformed under different loading modes (compression, shear and tension) to understand the deformation mechanism. Revealing the 1

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mechanical deformation of defected MOFs is expected to yield considerable benefits in both controlling and tailoring the mechanical properties of MOFs.

1. INTRODUCTION Metal−organic frameworks (MOFs) are interesting as new types of organic−inorganic hybrid materials, which can incorporate a variety of metal ions/clusters and organic linkers with different chemical or physical properties, constructing a well-designed coordination to form highly ordered spatial networks and diverse porous structures. These kinds of structure and property characteristics emphasizes that MOFs can be promising choices for a variety of applications, including gas adsorption/separation,1 energy storage/conversion,2 biological processes,3, 4 chemic sensors,5 and catalysis.6 The vast majority of studies on MOFs focuses on “ideal crystals” with faultlessly arranged identical groups of atoms in space. Nevertheless, the real MOF structures always contain a significant number of various defects.7-9 One typical example is the zeolitic imidazolate framework-8 (ZIF-8), which demonstrates strong adsorption of water in laboratory test,10 contrary to the theoretical prediction of being hydrophobic.11 This constitutes the strongest evidence, which proved that the hydrophilic defects must be present in ZIF-8, even for the most precise synthesis. The ubiquitous nature of defects in MOFs establishes a critical parameter concerning the overall performance of a material. Thus, besides the composition (metal/metal-oxide nodes and organic linkers) of MOFs, the defects are also capable of tuning and tailoring the chemical and physical properties of the materials for targeted 2


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applications.7, 8 As an example, the point defects (such as metal/ligand vacancy and dangling linkers) in MOFs can drastically enhance adsorption of gases like H2, CH4, CO2 and CO.12-14 Additionally, the high accessibility of unsaturated metal ions and uncoordinated ligands structures in MOFs constitute a great source of active sites, which can act as reactive centers in many catalytic reactions.9, 15 Special attention has been paid to the stability of defected MOFs.8 Schmidt et al., 16

found that the linkers and metals vacancy in ZIF-8, impose only an insignificant

energy penalty, indicating the negligible thermodynamic effect on the framework stability. However, the challenge concerns the mechanical stability of defected MOFs commonly used in practical application. Much research has examined perfect MOFs structures, which exhibit low mechanical modulus and yield strength,17-19 while the shear-collapse mode dominated the plastic deformation.20 Thus a significant question arises concerning MOFs structure: how do defects in MOFs influence their mechanical properties? The available expertise and theories in deforming metal, ceramic and polymer materials, are not sufficient to be adopted in the mechanical deformation of MOFs. Therefore, it is essential to investigate the effect of defects on the mechanical deformation of MOFs from both theoretical and practical perspective. Experimental observation of the deformation of MOFs can be achieved using an in-situ transmission electron microscopy (TEM) technique;21,

22

however it is

ambitious to directly observe the defects in MOFs. Computational methods can be highly effective in solving these types of science problems, particularly when experimental tools are ineffective. Most of theoretical investigations on the 3



mechanical properties of MOFs have mainly focused on the elastic deformation stage of prefect MOFs.23-25 However, the study of the inelastic deformation of defected MOFs, to our knowledge, is scarce. In this study, molecular dynamics (MD) simulation was adopted to investigate the mechanical deformation of defected MOF-5. The metal/ligand vacancy, owing to its common existence in various MOFs, was chosen as the defect structure. The evolution of internal structure under loading was analyzed to reveal the effect of defects on the nucleation and propagation of dislocations. Different types of deformation modes were examined to clarify the loading dependence of the mechanical deformation mechanism in MOF-5. The understanding of mechanical deformation in defected MOFs is expected to contribute to the design and the usage of MOFs in applications related to the mechanical loading. 2. CALCULATION MODEL AND METHODS The basic unit of MOF-5 consists of tetrahedral Zn4O groups connected by 1,4-benzenedicarboxylate (BDC) ligands. Eight Zn4O groups are placed on the corner position of a simple cubic and the BDC ligands bridge neighbor groups to finally form the unit cell MOF-5 (shaded part in Figure 1). The orientation of all linkers in MOF-5 was along crystal direction. To perform the simulation, a supercell was built by replicating the cubic unit cell 6 × 6 × 6 times along x, y, and z directions. Thus, a dimension of 15.50 × 15.50 × 15.50 nm3 was formed, based on the experimental lattice parameters.26 The perfect structure consisted of 91584 atoms (left part in Figure 1). Periodic boundary conditions (PBC) were applied along the three main 4


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coordinate directions. The defect was created in the center position of the supercell (shaded part in Figure 1). In the present research, four typical point defects are presented: a) MOF-5 missing 1 linker, b) missing 8 linkers, c) missing 1 Zn4O groups and d) missing 8 Zn4O groups and 12 linkers (right part in Figure 1). The metal/ligand vacancy in MOF-5 has been observed during the experiment.27 Although other types of defect structures such as cracks, grooves, and terraces were reported in the experiment,7 this study only focused on the vacancy defect for two main reasons. First, the point defect is the basic unit constituting any complex defects. Secondly, although experimental observations of the atomic structure for MOFs defects are scarce, the atomic structure of point defects is obvious. The LAMMPS package28, 29 was used to perform the molecular dynamics (MD) simulations. Prior to deformation, an energy minimization based on the conjugate gradient (CG) algorithm was performed at zero temperature to guarantee the atomic positions during geometric optimization. Then, the system was thermally equilibrated at 300 K and zero pressure for 50 ps, using isothermal−isobaric (NPT) ensemble with a time step of 0.1 fs. The used time step is short enough to satisfy the requirement of the ReaxFF model to cope with unusually large interatomic forces. The coupling constants for the Nosé−Hoover thermostat and barostat were set to 0.1 ps and 5 ps respectively. The deformation can be induced by changing the size and/or the shape of the simulation box during a dynamics run. Six adjustable parameters (x, y, z, xy, xz, yz) can be used to change a box. The parameters x, y and z denote the dimensional size, 5



while the xy, xz, and yz parameters are the tilt factors of the simulation box. To perform the compressive (or stretching) deformation, any or all the parameters x, y, and z can be continuously decreased (or increased). The other parameters xy, xz, and yz can be used to induce the shear deformation. In this study, only uniaxial deformation was considered. Then, the box parameters of z and xy was continuously changed to realize the uniaxial compressive (or stretching) and shear deformation respectively. Other parameters were adjusted to reach zero pressure using the NPT ensemble. The linear and angular momentum of this simulation system was set to zero, avoiding the translational and rotational motion of the box during deformation. In every deformation step, the pressure along the deformation direction was collected to construct the loading-strain relation. An engineering strain rate of 3 × 109 s−1 was chosen, based on the reported results.20 The unloading dimensions of the cell during deformation were fully relaxed to zero stress using a Nosé−Hoover barostat. The VMD software30 was applied to visualize the atomic structure. The reliability of any MD simulation results mainly depends on the force field describing the atomic interactions in the materials. The typical semi-empirical force field consists of bonded (bond, angle and torsion) and nonbonded (van der Waals and electrostatic) part. This type of force field has been proved to be reliable in computing the guest adsorption and diffusion in MOF-5, and even the framework lattice dynamics.31 However, due to the bonded nature, the common semi-empirical force field cannot describe the inelastic deformation of MOFs involving bond breaking and forming.32 The reactive force field ReaxFF is also a semi-empirical force field, 6


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although it owns complicated mathematical expressions with parameters derived from quantum mechanical results.33 In particular, the bond-order dependence, which depends on the local atomic environment, was included in ReaxFF; therefore, the chemical reactions involving bond breaking and forming could be described. Aiming at MOF-5, Adri van Duin et al.34 developed ReaxFF parameters to study the stability of MOF-5 against H2O. In that study, the Zn-O interaction parameters have been confirmed by the prediction of properties of four ZnO crystal structures and their interactions with water.35 Alejandro Strachan et al.

20, 36

used the ReaxFF to

investigate the mechanical deformation and the shockwave energy dissipation of MOF-5 and obtained reliable results. Current research used ReaxFF force field and predicted lattice constant of MOF-5 (Table S1), which was insignificantly overestimated compared to experimental values. Herein, the effect of defects on the lattice constants of MOF-5 was considered negligible (Table S1). 3. RESULTS AND DISCUSSION Figure 2 illustrates the simulated compressive stress versus strain curves for the defected MOF-5. According to figure 2(a), it is noted that the yield strength of the frameworks is slightly reduced with an increasing number of missing linkers. Compared to the absence of linkers, the missing Zn4O groups can further weaken the yield strength of MOF-5 frameworks (Figure 2b). The effect of defects on Young’s modulus for the current MOF-5 samples can be considered negligible. The clear divergence of the position and the strength of the stress peaks (Figure 2b) indicates different plastic deformation behaviors. The evolution of internal atomic structure is 7



required to determine the hidden deformation mechanism. To clearly capture the structure evolution of MOF-5, the unit cell of the original framework was transformed into a simple cubic (Figure 3). The nodes and the linkages in the cubic (located right in Figure 3) denotes the Zn4O groups and the 1,4-benzenedicarboxylate (BDC) ligands, respectively. The linkage breaks if its length changes over 20% of the equilibrium value. In addition, the volume variation of the simple cubic was applied to characterize the degree of local deformation.20 Figure 4 presents the internal structure evolution of defected MOF-5 under compressive loading, employing the simple cubic model (Figure 3). In the initial structure, the strain localization (red area in Figure 4b) can be induced by the defects. The Zn4O group vacancy was found to be more likely to induce strain localization (Figure 4 and S1). External loading can result in the propagation of the strain localization (strain = 2.52% in Figure 4b). The strain localization in MOF-5 with linker vacancy requires larger driving force and scatters throughout the whole system (3.72% and 4.14% strain in Figure 4a), while, the strain localization in MOF-5 with Zn4O vacancy is concentrated in the defect position (Figure 4b). The slip along [100] was observed in the current deformation model (xz plane in Figure 4). One slip consisted of three adjacent atomic layers around the defect position and twin crystal formed as the result of the slip. By switching into the yz plane projection, no trace of a layer slip on the boundary can be observed (strain = 6.84% and 10.14% in Figure 4a and b respectively), excluding the possibility of [110] slip. A highly interesting result is that the three horizontal lines (atomic layers denoted 8


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as a, b and c in Figure 4a) curved with increasing strain. This point was absent in the MOF-5 sample with missing 8 Zn4O groups and 12 linkers (Figure 4b). Thus, different slipping mechanisms are probable to exist in the two defected MOFs samples. To reveal the slipping mechanism, the three glide layers were tracked during compression (Figure 5). For MOF-5 missing 1 linker (Figure 5a), the atomic layers partially slip along the x-axis. This movement can be traced at the strain of 4.14%. Further loading results in distinct dislocation (denoted by lines 1 and 2 in Figure 5). At strain of 5.70%, the lateral position of the atoms below the dislocation line 2 was almost unchanged, while the glide occurred between the two dislocation lines. The dislocation lines propagated under continuous compression, reaching a strain of 7.74%. The dislocation lines were always parallel to the slipping direction, which is consistent with the character of the screw dislocation. For MOF-5 missing 8 Zn4O and 12 linkers (Figure 5b), the trace of atomic layer slip can be found at a lower strain (2.52 %) compared to the 4.14% strain for MOF-5 missing 1 linker. Further loading can introduce the glide of the whole atomic layer. The dislocation line was perpendicular to the glide direction (Figure 5b), fitting the character of the edge dislocation. The above analysis indicates that the type of dislocation in MOF-5 depends on the defects. The screw dislocation is most probable to appear in MOF-5 samples missing linkers, while the absence of Zn4O groups is likely to induce the nucleation and the propagation of the edge dislocation. The videos (video-1.avi, video-2.avi, 9



video-3.avi, video-4.avi) further support this dependence between dislocations and defects in MOF-5. The appearance of different types of dislocations in the defected MOF-5 can be understood through analysis of the internal strain of dislocations and their interactions with defects (Figure 6). For the screw dislocation, the dislocation planes slide against each other via shear mode (Figure 6a). For the edge dislocation, in the region where there is no extra plane (pink area in Figure 6b), the lattice stretches, while, in the region where there is an extra plane (green area in Figure 6b), the lattice is compressed. Compared to the compressive and tensile lattice strain, the shear lattice strain can be easily induced in MOFs materials.17 Thus, the screw dislocation corresponding to the shear lattice strain prefers to appear in MOF-5. For the defected MOF-5, when only the linkers are absent the defect hardly affects the framework structure and contributes little to the formation of dislocations. For MOF-5 missing Zn4O groups, the node vacancy exists in the lattice and can effectively weaken the strain concentration due to the edge dislocation (Figure 6c). Thus, the edge dislocation becomes easy to nucleate and propagate in MOF-5 missing Zn4O groups (Figure 5 and Figure S1). Under compression, the shear-collapse linkers have been observed in MOF-5.20 Only the linkers in MOF-5, which are parallel to the loading direction, contribute to the deformation of the whole system (Figure 4). The above result was not sufficient to define the deformation in practical systems, where multiple deformation modes are involved. The following study focuses on the effect of the loading mode on the 10


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deformation mechanism. One deformation mode is the shear, where the loading directly drives the ligand-Zn4O-ligand angle torsion. When the strain reaches approximately ～20% (Figure 7 and S2), the shear strain appears to be homogeneous. This corresponds to significantly higher recoverable strain compared to that in compression (< 3%). Further loading can induce the shear strain localization in the defect position (Figure 7 and video-5.avi). The edge dislocation, instead of the screw dislocation, could be responsible for the motion of the atomic layer. It can be attributed to the shear loading which can directly drive the slipping of the whole atomic layer, fitting the character of the edge dislocation. In addition, only the linkers normal to the loading direction contribute to the whole deformation. Next, the tensile deformation mode was investigated. Figure 8 illustrates the stretching stress-strain relation and the size of the lateral section of MOF-5 that is missing 8 Zn4O groups and 12 linkers under tension, compared to that under compression. The yield stress and strain, were significantly improved, reaching values approximately 8 times and 4 times greater than those for compression, respectively (Figure 8a). Another interesting point is that the cross section of MOF-5 sharply shrinks under tension, especially in the plastic deformation stage (Figure 8b and video-6.avi). Additionally, the lateral size of MOF-5 under compression slightly changes. The evolution of the internal structure can be used to reveal the deformation mechanism under tension (Figure 9). By increasing loading, the framework lines 11



along tensile direction are stretched and broken, corresponding to the yield point (“B” in Figure 8a and 9). The breakage involved the bond linkage between BDC ligands and Zn4O groups and initially occurred at the defect position. Meanwhile, the angle variation between BDC ligands and Zn4O groups corresponded to the shear deformation. Certainly, bond stretching (tensile) was much harder than angle torsion (shear), as explained the large yield strength and strain in tension (Figure 8a). Further tensile loading resulted in enhanced bond breaking, leaving the linkers dangling and creating in the framework hexagonal units (denoted by stars in Figure 9). Consequently, bond breaking, and the vacancy defect gradually expanded (“F” and “G” in Figure 9), and the shear-collapse of the linkers along the lateral section could also be easily induced, because of the reduction of constraints (such as in the hexagonal unit). Thus, the linker shearing contributes to the large contraction of lateral section of MOF-5 during stretching (Figure 8b). 4. CONCLUSIONS MD simulation was employed to reveal the mechanisms responsible for the mechanical deformation of the defected MOF-5. The defects were found to induce the nucleation of dislocations and then to reduce the elastic yield strength in compression. It was demonstrated that the screw dislocation prefers to appear in the MOF-5 framework missing linkers, while the absence of Zn4O group easily induces the nucleation of the edge dislocation. In shear deformation, the metal-ligand-metal angle distortion was easily induced and then the homogenous tilt along the loading direction was obtained, as this contributed to a relative large elastic strain (close to 20%). Still, 12


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the strain localization mainly appears in the defect position. In tensile deformation, the linkages were stretched, which does not easily occur in shear deformation, and contributes to the improved elastic yield strength of MOF-5. The defects provide the initial position for the linker- Zn4O bond breaking, which in return can induce the expansion of defects. Furthermore, bond breaking can result in the shear-collapse of bonds perpendicular to the stretching direction, as this contributes to a severe shrinkage of the lateral section in MOF-5. The results indicated the importance of defects in the mechanical deformation of MOFs and could help to understand the experimental testing of the stiffness and ductility of MOF materials, while the suggestions obtained from the simulations can enable the design of new MOFs.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Videos showing the defect evolution in MOF-5. The lattice parameters, atomistic snapshots and stress-strain curve of MOF-5.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Notes 13



The authors declare no competing financial interest.

ACKNOWLEDGMENT. This work was supported by the Natural Science Foundation of China under grant 21503165 and 51372197, Shaanxi Province 100 plan, and the Key Innovation Team of Shaanxi Province (2014KCT-04).

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32. Ortiz, A. U.; Boutin, A.; Fuchs, A. H.; Coudert, F.-X., Investigating the Pressure-Induced Amorphization of Zeolitic Imidazolate Framework ZIF-8: Mechanical Instability Due to Shear Mode Softening. J. Phys. Chem. Lett. 2013, 4, 1861-1865. 33. van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., Reaxff: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396-9409. 34. Han, S. S.; Choi, S.-H.; van Duin, A. C. T., Molecular Dynamics Simulations of Stability of Metal-Organic Frameworks against H2O Using the Reaxff Reactive Force Field. Chem. Commun. 2010, 46, 5713-5715. 35. Raymand, D.; van Duin, A. C. T.; Spångberg, D.; Goddard, W. A.; Hermansson, K., Water Adsorption on Stepped ZnO Surfaces from MD Simulation. Surf. Sci. 2010, 604, 741-752. 36. Banlusan, K.; Strachan, A., Shockwave Energy Dissipation in Metal–Organic Framework MOF-5. J. Phys. Chem. C 2016, 120, 12463-12471.

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Figure 1. Computational model of defected MOF-5. The ball and stick display style on the right is used to emphasize the defect position.

Figure 2. Compressive stress−strain relations of defected MOF-5.

Figure 3. The process of simplifying the model for visualizing clarification. Blue gray, red and gray denote Zn, O and C atoms, respectively. All H atoms are hidden for clarity.

Figure 4. Atomic snapshots illustrate plastic deformation of defected MOF-5 during compression. The frame lines were explained in Figure 3. Colors indicate the percentage of local volume change compared to the initial value in as-equilibrated 19



systems. For visualizing clarification, the color scale bar on the right varies from 0% to 30%; however, the volume of any group of atoms can change by more than 30%. The compression is along the z axis.

Figure 5. The dislocation motion inside the defected MOF-5 under compression. The layers a, b, and c correspond to the letters in Figure 4 and are colored according to their position along z axis.

Figure 6. Illustration of (a) a screw dislocation, (b) an edge dislocation in perfect lattice and (c) the edge dislocation in lattice with point vacancy.

Figure 7. Structure evolution of defected MOF-5 under shear. The layers a, b, c and d in bottom were colored according to their position along y axis.

Figure 8. Comparison of the stretching and the compressive deformation in defected MOF-5: (a) Stress−strain relations; (b) the variation of lateral size.

Figure 9. Atomic structures of defected MOF-5 under various tensile strains corresponding to the values identified by the letters in Figure 8a. Colors indicate the percentage of local volume change, compared to the initial value in as-equilibrated systems. The linkages between the nearest neighboring nodes were broken if the length was larger than 20% of the equilibrium value. The stars denote the hexagonal 20


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units in the framework.

TOC Graphic

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Figure 1 56x26mm (300 x 300 DPI)


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Figure 4 102x81mm (300 x 300 DPI)



Figure 5 103x67mm (300 x 300 DPI)


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Figure 9 102x65mm (300 x 300 DPI)


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TOC graphic 73x110mm (300 x 300 DPI)


Effect of Defects on the Mechanical Deformation Mechanisms of Metal

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