If we consider the ligand to be a rigid rod with no angular forces between the rod and the tetrahedra, we have the same situation as in Zn(CN)2 as analysed by Goodwin.17 In this case, the cyanide rod has 5 degrees of freedom, so that the total number of degrees of freedom per formula unit is 16. It has been shown that RUMs are responsible for properties such as displacive phase transitions10 and negative thermal expansion.13–16 If we extend the rigidity analysis to a ZIF structure, we need to consider the constraints associated with the linkages between ZnN4 tetrahedra via the imidazolate ligand. In silica and tectosilicate phases, symmetry actually generates some degeneracies amongst the constraints, which gives an additional flexibility that is seen as the existence of low-frequency vibrations of the crystal structure – phonons – in which the SiO4 tetrahedra move as rigid objects without any distortion.9 These phonons are known as Rigid Unit Modes (RUMs). Shared by 2 tetrahedra, the total number of constraint equations per tetrahedron is 4 × 3 ÷ 2 = 6, which as we noted is equal to the number of degrees of freedom. This journal is © The Royal Society of Chemistry 2016 School of Physics & Astronomy and Materials Research Institute, Queen Mary University of London, Mile End Road, London, E1 4NS, UK. Given that there are 4 vertices, and that each constraint equation is If we denote the Cartesian coordinates of the shared vertices of the two tetrahedra as (x1, y1, z1) and (x2, y2, z2) respectively, we must have x1 = x2 etc. The issue of flexibility can be initially considered using insights from rigidity theory applied to network crystal structures.9–12 If we consider any crystalline phase of silica, SiO2, in which the structure is described as a network of corner-sharing SiO4 tetrahedra, it is found that there is an exact balance between the number of degrees of freedom of the near-rigid SiO4 tetrahedra and the number of constraints associated with the linkages between neighbouring tetrahedra.10 This follows from the fact that each rigid tetrahedron has 6 degree of freedom (translation and rotation), and that there are three constraint equations per shared linkage. This paper uses computer simulation to explore the flexibility of a number of ZIF structures. Lysis based on the Rigid Unit Mode model shows considerable degree of network flexibility, including aġ Introduction Zinc-based zeolitic imidazolate framework structures (ZIFs) of formula Zn(im)2 – where im = C3N2H3− or a related ligand, and where the framework is characterised by ZnN4 tetrahedra linked together though the ligands1 – offer the prospect for applications that exploit their porous structures in areas such as catalysis, storing gases such as H2, and capture of gases such as CO2.2–8 Some of these applications will depend on the inherent flexibility of the structure, possible examples being the capacity of the structure to selectively absorb small molecules from a gas stream, and applications in catalysis. We have shown that there are instabilities of the structures of some ZIF structures at low temperatures and high pressures. Received 8th September 2015, Accepted 6th November 2015īased on ab initio calculations of clusters of ligands and metal cations. The simulations have used a force field we developed CRYSTALMAKER EXAMPLES SERIESDove* We report the results of a series of molecular dynamics simulations on a number of zinc zeolitic imidazolate framework (ZIF) structures together with some lattice dynamics calculations on ZIF-4, providing information about the flexibilities of these structures. Molecular dynamics simulation study of various zeolitic imidazolate framework structures Min Gao, Alston J. Downloaded by Gazi Universitesi on 04:07:58.
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