Enhanced Framework Rigidity of a Zeolitic Metal-Azolate via Ligand Substitution

Abstract

The elastic properties of a zeolitic metal-azolate framework, Zn(mtz)₂ (MAF-7, mtz⁻ = 3-methyl-1,2,4-triazolate), have been examined from the view point of the first principles calculations and experiments. Our results demonstrate that the three independent elastic constants of MAF-7 are about 5.0–73.3% higher than those of ZIF-8, though they are isomorphic. The electron-donating effect of the nitrogen atom at the 2-position in mtz- ring dominantly accounts for such a prominent difference. The detailed analysis of the full elastic tensors reveals that the volume moduli, shear moduli, and Poisson’s ratios of MAF-7 are about 3.4% to 20.1%, 3.2% to 20.6%, and −30.3% to 12.3% higher than those of ZIF-8. The underlying structural reasons were discussed to explain the anisotropic difference of those properties. Moreover, the conclusion deduced from first-principle calculations was also been verified by nanoindentation and high-pressure synchrotron X-ray diffraction measurements.

1. Introduction

Zeolitic metal-azolate frameworks (MAFs), a subclass of porous MOFs, have been attracting particular attention due to their potential application [1] superior to traditional zeolites in many fields, such as gas storage/separation [2,3,4], catalysis [5], sensing, and drug delivery [6,7]. In practical application, the zeolitic MAFs would experience several rounds of mechanical manufacturing processes. To maintain the intrinsic properties of zeolitic MAFs during the mechanical manufacturing processes, their fundamental mechanical properties should be fully understood and, therefore, the study about the mechanical property has become one of the hottest topics in the field of MAF study. Recently, much study has revealed that significant difference exists between zeolitic MAFs and zeolites in terms of mechanical robustness [8,9,10]. In 2009, Moggach et al. performed high pressure single-crystal X-ray diffraction studies on (ZIF), Zn(mim)₂ (ZIF-8 [11], mim = 2-methylimidazolate), a zeolitic imidazolte framework, and discovered that the exertion of pressure can increase the accessible surface area and its absorption performance [12]. A follow-up high-pressure powder X-ray diffraction study reveals similar results and shows that the hydrostatic behavior of ZIF-8 also strongly depends on the size of different pressure­transmitting mediums [13]. Recently, Tan et al. reported a comprehensive nanoindentation study of ZIFs, and accordingly elaborate the structure-property relationship of its mechanical property [14]. In 2012, their another work reports the anomalously shear modulus of ZIF-8 one order lower than that of zodalite in magnitude [15].

Nevertheless, all these studies focused on zeolitic imidazolate frameworks (ZIFs), and up to now the mechanical property of zeolitic triazolate frameworks have not been investigated yet. In this work, we present a systematic study on the elastic properties of a zeolitic triazolate, Zn(mtz)₂ (MAF-7 [16], mtz = 3-methyl-1,2,4-triazolate), which is isomorphous to ZIF-8. To examine the electronic difference in elastic properties between 2-methylimidazolate and 3-methyl-1,2,4-triazolate, we performed first-principles calculations to extract the full elastic tensors of the cubic MAF-7. Our density functional theory (DFT) results elucidated that, compared with ZIF-8, the trivial electron-donating effect strongly enhance the mechanical strength of MAF-7, especially in the ability to resist uniaxial and shear stresses. Moreover, the calculated result was also testified by nanoindentation and synchrotron high-pressure powder X-ray diffraction experiments.

2. Results and Discussion

MAF-7 is isomorphous to ZIF-8 and crystallizes in the same cubic space group I-43m as reported by Zhang et al. [16]. In the structure, the Zn²⁺ ion is tetrahedrally coordinated with the triazolate ligand to form Zn(mtz)₂ open framework with zeolitic sodalite (SOD) architecture. The mtz⁻ ligand coordinates with the zinc ion via its N atoms on the 2- and 4-positions, and the N on the 1-position unbonded [16,17]. It should be emphasized the lone pair electrons of the unbonded nitrogen can donate electron to the adjacent N at the 2-position, and this effect pushes the lone pair electrons of the coordinated N to bonded with the zinc center more tightly (Figure 1). The experimentally-determined Zn-N bond length of MAF-7 (1.980(2) Å) is slightly shorter than that of ZIF-8(1.983(3) Å) at same temperature, confirming the stronger covalent interaction in the former than the latter [17].

The elastic properties of MAF-7 are listed in

Table 1. The elastic properties of MAF-7 and ZIF-8 extracted from DFT calculations.

Elastic Properties	Framework	MAF-7	ZIF-8 [15]
Stiffness coefficient, Cij (GPa)	C11	11.587	11.038
	C12	9.643	8.325
	C44	1.635	0.943
Young’s modulus, E (GPa)	Emax	E(111) = 4.659	E(100) = 3.879
		E(110) = 4.009	E(110) = 2.953
	Emin	E(100) = 2.828	E(111) = 2.736
Shear modulus, G (GPa)	Gmax	1.64	1.36
	Gmin	0.97	0.94
Poisson’s ratio, υ	υmax	$\nu <110,001>$ = 0.64	$\nu <110,1\overline{1}0>$ = 0.57
	υmin	$\nu <110,1\overline{1}0>$ = 0.23	$\nu <110,001>$ = 0.33
Anisotropy measure	Zener, A (=1 if isotropic)	1.68	0.70
	Emax/Emin	1.65	1.42
Bulk modulus K(GPa)		10.29	9.23

. Clearly, the calculated C_ij’s satisfy the fundamental elastic stability criteria for a cubic crystal, i.e., C₁₁ > |C₁₂|, C₁₁ + 2C₁₂ > 0 and C₄₄ > 0 [18,19]. It is observed that the three independent elastic constants C₁₁, C₁₂, and C₄₄, which represent the stiffness of a cubic structure, are 5.0%, 15.8%, and 73.3% larger than those of ZIF-8, indicating the overall higher rigidity of MAF-7 than ZIF-8. The larger C₁₂ and C₄₄ values [20] of MAF-7 result in its significantly different elastic properties compared with ZIF-8 as we shall discuss below. To further understand the comprehensive elastic properties of MAF-7, we performed the full tensorial analysis of the elastic constants and extracted the key mechanical index (including anisotropic Young’s moduli (E), shear moduli (G), and Poisson’s ratios (ν), as listed in Table 1 and displayed in Figure 2, Figure 3 and Figure 4) [21]. We will discuss them in details in the following sections.

We first focus on Young’s modulus, which represents the stiffness with respect to uniaxial stress. The extracted E₍₁₀₀₎, E₍₁₁₀₎, and E₍₁₁₁₎ of MAF-7 are 2.828, 4.009, and 4.659 GPa, respectively. The representation 3D and 2D surfaces of E are shown in Figure 2a,b, which indicate that the Young’s modulus exhibit strong spatial anisotropy. It can be seen that E reaches the maximum along the <111> direction, the body diagonal perpendicular to the SOD six-membered ring. The E surfaces exhibit subsidences along the cubic axes normal to the SOD four-membered ring, implying that the MAF-7 is mostly mechanical compliant along the <100> direction. It is notable that the directions of E_max and E_min of MAF-7 are reverse to those of ZIF-8. In an arbitrary direction [hkl], Young’s modulus of a cubic system is given in terms of S_ij, {E_[hkl]}⁻¹ = S₁₁ − (2S₁₁ − 2S₁₂ − S₄₄)N⁴, where N⁴ = n₁²n₂² + n₁²n₃² + n₂²n₃², n₁, n₂, n₃ are direction cosines for the direction [hkl] [19]. If 2S₁₁ − 2S₁₂ − S₄₄ > 0, E reaches the maximum and minimum in the <111> and <100> directions, as the case in MAF-7. On the contrary, if 2S₁₁ − 2S₁₂ − S₄₄ < 0, the reverse results would be obtained as in ZIF-8.

From Table 1, it is clear that the E_max and E_min of MAF-7 are about 20.1% and 3.4% higher than those of ZIF-8. Meanwhile, the E values of MAF-7 is more anisotropic than ZIF-8, characterized by the corresponding index A_E = E_max/E_min = 1.65, 16.2% higher than that of ZIF-8 (1.42). The remarkable difference in Young’s modulus between MAF-7 and ZIF-8 originate from the aforementioned electron-donating effect. Such an effect leads to the stronger Zn-N bonds in MAF-7, which resultantly strengthens its resistance to axial deformation dominantly related with the change of Zn-N bonds and rotation of Zn-triazolate-Zn bond angles compared with ZIF-8 [15].

To testify the conclusion about calculated Young’s modulus, we conducted nanoindentation experiments using non-desolvated single-crystals to extract the elastic moduli of MAF-7. The experiment was carried out in the quasi-static mode and the maximum load was set as 5000 μΝ. Representative load-indentation depth (P-h) curves obtained normal to the (100) and (110) faces are displayed in Figure 3. The smooth loading parts of both faces demonstrates that the plastic deformation occurs underneath the three-side pyramidal Berkovich tip during indentation and is relatively homogeneous in nature [22]. The average values of E₍₁₀₀₎ and E₍₁₁₀₎, extracted from the P-h curves, are 2.92(14) and 3.87(17) GPa, respectively. The good agreement between the calculated and observed values (with relative error less than 5%) confirms the high Young’s modulus of MAF-7.

Now we turn attention to the shear modulus (G). Along an arbitrary direction [hkl], the general expression for shear modulus in cubic system is {G(hkl)}⁻¹ = S₄₄ + 2(2S₁₁ − 2S₁₂ − S₄₄)N⁴, in which the direction-dependent values also depends on N⁴ [19]. The 3D representation G surface, characterized via the maximal and minimal G, is shown in Figure 4. Accordingly, the G_max and G_min are along the <100> and <110> directions, respectively, reversely to the situation in ZIF-8. As seen from Table 1, the G_min and G_max of MAF-7 are about 3.2% and 20.6% larger than those from ZIF-8, and the anisotropy in G of MAF-7 is about 15.9% higher than that of ZIF-8. For a cubic crystal, G_max (=C₄₄) characterize the ability to resist to shear strain on the (100) plane under a pair of opposing shear stresses τ exerted along the <0kl> directions, and G_min = ((C₁₁ − C₁₂)/2) represents the resistance to shear on the (110) plane under a shear along the <1–10> direction [23]. The framework of MAF-7 resists shear mostly through the cooperative bending of the N-Zn-N and rotation of Zn-mtz-Zn bond angles. Like ZIFs, MAF-7 features four-membered rings in the structure, which are most susceptible to distortion under antiparallel shear forces. For a rectangle, shearing the edges is easier than the diagonals. As such, the same pair of opposing shear stresses τ applied on the (100) or (110) plane can generate larger deformation along the <110> than <100> direction, hence, leading to G_min along <110> while G_max along <100> direction.

Now, we focus on the Poisson’s ratio (ν) which is defined as the negative ratio of the transverse strain (ɛ_j) to the longitudinal strain (ɛ_i), i.e., ν = −ɛ_j/ɛ_i [24]. Poisson’s ratio ν is expressed as $\mathsf{\nu }\left[h^{\prime }{k}^{\prime }{l}^{\prime }\right]\left[hkl\right]=\frac{S_{12}+\left(S_{11}-S_{12}-S_{44}/2\right)M^4}{S_{11}-\left(2S_{11}-2S_{12}-S_{44}\right)N^4}$ in a cubic system [19]. Therein, M⁴ = n₁²m₁² + n₂²m₂² + n₃²m₃², where m₁, m₂, and m₃ are direction cosines for the direction [$h^{\prime }{k}^{\prime }{l}^{\prime }$], respectively [19]. It can be seen that the directions of the ν_max and ν_min of MAF-7 are also closely related with the direction-dependent value of M⁴ and N⁴. The representation surfaces for Poisson’s ratios of MAF-7 are shown in Figure 5a,b, and the maximum and minimum ν values are 0.23 and 0.64 along <$1\overline{1}0$> and <001> directions. As illustrated in Figure 5c, when the structure is elongated along the <110> propelled by axial strain, ν_min and ν_max are obtained along the <001> and <$1\overline{1}0$>, respectively. The ν_max is 12.3% higher while the ν_min is 30.3% lower than ZIF-8. The large ν_max of MAF-7 coincide with its high shear modulus, which arises from the electron-donating effect as well. However, the much lower ν_min of MAF-7 than ZIF-8 implies that such an electron effect also negatively contribute to the framework stability enhancement under axial tensile or compression stresses along some directions.

We finally focus on the bulk modulus (B), which represents the resistance of a material against hydrostatic stress. The B value derived from first-principle calculated elastic constants for MAF-7 is 10.29 GPa, indicating its stiffer character than ZIF-8 (theoretical values 9.23 GPa). To further demonstrate higher volume modulus from experimental view point, the high-pressure synchrotron X-ray powder diffraction experiments were performed. As shown in Figure 6, the diffraction peaks move to high angle direction with increasing pressure from 0 to 3.755 GPa, indicating the pressure-induced contraction of the framework. It is worth mentioning that no phase-transition occurs in MAF-7 in the whole pressure range, manifesting its higher stability to resist hydrostatic pressure than ZIF-8 with (phase transition about 0.34 GPa) [13]. The function of unit cell volume and lattice parameter a with respect to pressures (shown in Figure 7) were fitted using the second-order Birch-Murnaghan equation, and the obtained bulk modulus is 10.8(15) GPa, in excellent agreement with the calculated value (10.29 GPa). As expected, the experimental B value of MAF-7 is significantly larger than that of ZIF-8 (6.52(35) GPa), which further ascertains the high mechanical strength of MAF-7.

3. Materials and Methods

3.1. Synthesis of MAF-7

All chemicals and solvents were of reagent grade and used as received. Single crystals of Zn(mtz)₂ were prepared by slow evaporation from a clear aqueous ammonia solutions according to the method of Chen et al. [16] In the procedure, 0.084 g Hmtz (Aladdin) and 0.198 g Zn(NO₃)₂·6H₂O (Alfa Aesar) were dissolved in 10 mL aqueous ammonia solutions (25%) (Sinopham Chemical Reagent Co., Ltd., Shanghai, China). The colorless crystal have precipitated from liquid after a few days. Phase identification of a ground bulk sample was confirmed by X-ray powder diffraction (see ESI).

3.2. First-Principles Calculations

The first-principles elastic constant calculations were performed by CASTEP [26,27], a total energy package based on plane-wave pseudopotential density functional theory (DFT) [28]. The functionals developed by Perdew Burke and Ernzerhof (PBE) [29] in generalized gradient approximation (GGA) form [30] were adopted to describe the exchange–correlation energy. To account for the long-range dispersion interactions, the dispersion correction in DFT + D2 form developed by Grimme [31] was included in the calculation. Optimized ultrasoft pseudopotentials were adopted to model the effective interaction between the valence electrons and atom cores [32], which allow us to adopt a relatively small plane-wave basis set without compromising the computational accuracy. The kinetic energy cutoff of 400 eV and the Monkhorst–Pack [33] k-point mesh spanning less than 0.03 Å⁻¹ were chosen.

Before the elastic constant calculation, the crystal structure with no solvent molecules at 0 GPa was firstly optimized using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) [34] minimization scheme, with the convergence criteria for energy, maximum force, maximum stress and maximum displacement set to 10⁻⁵ eV per atom, 0.03 eV, 0.05 GPa and 0.001 Å, respectively. Based on the optimized crystal structure, the elastic constants were calculated by the finite-strain method [35], in which the components of the elastic constant tensor were determined by the second-order derivative of energy with respect to specific strain and the maximum strain amplitude and the number of steps for each strain were set as 0.003 and three steps, respectively. After obtaining the calculated elastic constants, the analyses of Young’s modulus, shear modulus and Poisson’s ratio were performed using the ElAM program [21].

3.3. High-Pressure Synchrotron X-ray Powder Diffraction

The high-pressure experiments were performed on the 4W2 beam line of Beijing Synchrotron Radiation Facility with wavelength of the X-ray beam is 0.61992 Å. The gasket (300 μm in thickness) of the pre-indented stainless steel (T301) was placed on the systematic diamond anvil cells (DACs) (a culet diameter of 400 μm). The ground bulk samples were loaded in a cylindrical hole (about 150 μm in diameter), together with a few ruby chips for pressure calibration and a few drops of silicon oil used to act as pressure-transmitting medium for surrounding the samples and ensuring the uniform application of pressure. The required pressures were obtained by manually turning screws and the internal pressures were determined from measuring the shift of ruby luminescence [36]. The data were refined by using the Topas program [37].

3.4. Nanoindentation Methodology of Single Crystals

Nanoindentation experiments were performed under ambient conditions by employing a Hysitron TI 750 Ubi Triboindenter (Hysitron Corp., Minneapolis, MN, USA) in the continuous stiffness measurement mode [38]. A non-desolvated single crystal was first selected by well-defined regular dodecahedron shapes and, after face indexing, was confirmed by single-crystal X-ray diffraction using an Oxford Diffraction Rigaku XtaLAB mini^TM diffractometer (Rigaku Oxford Diffraction Ltd., Oxford, UK) with Mo-Kα radiation (λ = 0.70173 Å) at 300 K. Since any natural crystal facets were equivalent to the facet {110}, we had to polish off a certain natural facet to obtain an artificial facet (100). Crystals with {100} and {110}-oriented facets were then cold-mounted in epoxy resin and were carefully ground with emery paper up to 4000 grit, and polished with increasingly fine diamond suspensions to minimize surface roughness [15,22]. Accordingly, the indenter were aligned normal to the (100) and (110) crystal facets with a maximum surface penetration depth of 1200 nm [39]. The loading/unloading rates and the hold time at peak load, respectively, were maintained at 5000 μΝ s⁻¹ and 30 s. A fused silica standard with an elastic modulus of 72 GPa and hardness of 9 GPa was used for calibration. Young’s modulus (E_s) and indentation hardness (H) of the MAF-7 crystals were obtained from the P-h plots using the standard Oliver-Pharr method [40,41].

4. Conclusions

In summary, the elastic properties of MAF-7 were studied by first-principles calculation and experiment. Our results revealed that the elastic constant components of MAF-7 are about 5.0–73.3% higher than those of its isomorphous ZIF-8. Further analysis demonstrates that the elastic modulus, shear modulus and Poisson’s ratio values of MAF-7 are about 3.4% to 20.1%, 3.2% to 20.6% and −30.3% to 12.3% larger than those of ZIF-8, respectively. The remarkable enhancement of mechanical stiffness from MAF-7 to ZIF-8 mainly originates from the electron-donating effect of the additional nitrogen atom in the triazolate ligand. Moreover, the underlying reasons of the anisotropic difference in each property were discussed from a viewpoint of framework structure. Furthermore, the calculated high mechanical strength of MAF-7 is verified by nanoindentation and high-pressure X-ray diffraction experiment, indicating the reliability of our first principle calculations. We believe this study further deepens the understanding of mechanical properties of zeolitic azolate frameworks, and is informative for the exploration of MOF mechanics in general.