Flexibility in MOFs: do scalar and group-theoretical counting rules work?

Abstract

Counting rules derived from mechanical engineering and rigidity theory are applied to MOFs. Scalar versions fail to predict flexibility, but group-theoretical variant succeed. The algorithm is presented in detail and two examples are solved step-by-step.

Experimental Evidence for Vibrational Entropy as Driving Parameter of Flexibility in the Metal–Organic Framework ZIF-4(Zn)

“…The reticular chemistry approach as a successful rigid body approach intrinsically neglects topological, symmetry related and thermodynamic structural parameters that can lead to structural flexibility, 39 and modifications must be applied. For instance, once a topology (from a database) has been tested for general flexibility by applying classical counting rules or group theoretical considerations, 31,32 the next step would be the combination of the given topology with available linkers and metal nodes.…”

“…Over the past decade, there has been an intense interest in developing a thorough understanding of SPCs, with the goal being the formulation of design guidelines for the targeted synthesis of SPCs. Topological, 31 symmetry-related 32 and thermodynamic aspects 33,34 have been identified as key factors for stimulus responsive behaviour to occur, leading to numerous chemical and structural requirements that must be met at the same time.…”

Configurational Entropy Driven High‐Pressure Behaviour of a Flexible Metal–Organic Framework (MOF)

“…[4,5] A subclass of MOFs, so-called flexible MOFs, shows large structural flexibility with volume changes exceeding DV = 20 % as response to temperature and pressure variation, and guest adsorption. [5,6] Intense research efforts have shown that macroscopic parameters such as topology, [7,8] dispersion interactions and vibrational entropy [9][10][11][12] as determined by microscopic chemical interactions all contribute to structural flexibility; however, the targeted synthesis of flexible MOFs which concerns the manipulation of macroscopic thermodynamics via chemical changes on a microscopic level is still beyond our knowledge. Therefore, it is not surprising that the number of flexible MOFs [13][14][15][16] is still small when compared to the total number of existing MOFs, [17] with MOFs such as ZIF-4(Zn) (zeolitic imidazolate framework, Zn(im) 2 , with im À = imidazolate) [18][19][20] and M(bdp) (M 2+ = Fe 2+ or Co 2+ , bdp 2À = 1,4-benzenedipyrazolate) [21,22] being two of several important examples that show large structure flexibility as a function of varying temperature and (gas) pressure.…”

AFM Nanoindentation To Quantify Mechanical Properties of Nano- and Micron-Sized Crystals of a Metal–Organic Framework Material

“…[15][16][17] Design, fabrication and deployment of the foregoing applications will depend on the availability of comprehensive mechanical properties information, plus a detailed understanding of MOF mechanics which remains lacking in the literature. 1,18 There is, however, a growing body of work adopting theoretical methodologies, such as: density functional theory (DFT) to compute the full set of elastic constants of an ideal MOF crystal, [19][20][21][22] and, by implementation of group theory 23 to enable systematic studies of the structural flexibility of MOFs. Likewise, molecular dynamics (MD) [24][25] and DFT 26 calculations have been used to interrogate the possible mechanisms that could be accommodating (irreversible) plastic deformation beyond the elastic regime.…”