Effect of low frequency phonons on structural properties of ZIFs with SOD topology
Graphical abstract
Introduction
Any structural variations observed in the nature can be understand on the basis of direct relations between solid structure and its dynamical properties. The structural transformations are usually initiated by dynamical structural fluctuations which can be expressed in terms of mechanical excitations called phonons (or normal modes) [1]. This name, originally attributed to purely harmonic collective translational vibrations of atomic periodic solids, has been also used in the context of orientational vibrations (librations) and anharmonic vibrations [2,3]. The total phonon spectrum is very rich and contains values, where is the total number of atoms in the material. The structural properties are mostly defined by the low frequency vibrations which may exhibit a frequency reduction when a structural transformation is approached. These specific vibrations are called soft phonons [4]. The structural analysis of solid deformations and in particular the role of soft modes is an important part of the studies of structural transformation mechanisms.
Metal-organic framework (MOFs) are hybrid structures, with mixed inorganic and organic composition, i.e. metallic centers coordinated by oxygen or nitrogen atoms, and connected by linkers with (very often) aromatic rings [5]. They have recently attracted a lot of attention due to large spectra of possible applications and in particular, structural transformations which potentially allow one to modulate the framework adsorptive properties [[5], [6], [7]]. A possible role of the soft modes in the structural transformations of the MIL-53 metal-organic framework (MOF) structure has been proposed as the mechanism provoking the lattice instabilities in this structure. However, no specific soft phonons were indicated [[8], [9], [10], [11], [12]]. It was also reported that the soft acoustic phonons also contribute to the negative thermal expansion in MOFs [13,14].
Recently, it has been shown [15,16] that collective low frequency THz vibrational modes contribute to physical mechanism of pore gate-opening and breathing phenomena in a subclass of MOFs, zeolitic imidazolate framework (ZIF) structures. In this paper we show that the numerical analysis of phonon spectrum provides detailed insight into the mechanism of gate opening. This information is not accessible from the experimental data.
In the next chapter we review the concept of phonons, normal modes and their relation to the soft modes. Then, we discuss an example of the MOF structures, based on the sodalite-type ZIF-8, and show that the soft modes are the important part of the deformation mechanism. We emphasize that the phonon numerical analysis is a new methodology which can correctly identify collective low energy vibrations responsible for lattice deformations.
Section snippets
Phonon formalism: a short review
Let us consider a solid structure composed of atoms (where is on the order of the Avogadro number). If the material is ordered and periodic, its structure can be characterized by a unit cells composed of n (≪ ) atoms. Thermal fluctuations displace atoms from its equilibrium position r by an amount u. The total potential energy of any periodic structure is a function of the instantaneous positions of all atoms (index i) and the equations of motion of the lattice follow the
Structures and computational methodology
ZIFs are build up by metallic centers that are tetrahedrally coordinated by imidazole derivatives playing the role of the linkers. The prototypical framework analyzed in this work, ZIF-8, is composed of zinc centers connected by methylimidazolate molecules (Fig. 1). This material is more stable than typical MOFs: it retains its structure up to 400 °C [17]. It also shows very interesting phenomena related to adsorption. It was shown that the N2 adsorption isotherm of ZIF-8 at 77 K has a
Results
In our work we focused on the vibrations having low frequency (and hence, energy), up to 170 cm−1. First, we analyze normal modes related to the adsorption-induced deformations of the internal structure of ZIF-8, which we will consider as the reference material. The two other structures will be compared to this reference system. In our calculations we observe two types of gate-opening modes in ZIF-8: one symmetric IR-inactive mode and several IR-active asymmetric modes. Symmetric mode is
Summary
The role of phonons in the solid-state materials science has been confirmed for more than 50 years [1]. However, it is a new methodology in the field of structural studies of MOF compounds. The soft mode notion was evoked in some cases [[5], [6], [7]] in the context of adsorption-induced MOF deformations, without fundamental theoretical justification. In particular, the relation between the deformation and the symmetry properties of the soft mode was not determined.
Here, we have shown that the
Declarations of interest
None.
Acknowledgements
This work was supported by the Polish National Science Centre (NCN, grant no. 2015/17/B/ST8/00099). The calculations have been partially performed at the WCSS computer center of The Wroclaw University of Science and Technology, grant no 33. M. F. acknowledges funding by the Central Research Development Fund (CRDF) of the University of Bremen (Funding line 04 – Independent Projects for Post-Docs). A visit of F.F. to Bremen was funded by the MAPEX Center for Materials and Processes, University of
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