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

Abstract

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

“…From comparing Δ A with Δ U , it can be observed that the bistability of Cu 2 (bdc) 2 dabco is mainly driven by Δ U , and that the np form is destabilised compared to the lp form due to its unfavourable − T Δ S . This behaviour is in agreement with the general rule that the crystallographically less dense structure has a higher vibrational entropy [12, 58, 59] . This tendency has also been observed for MIL‐53(Al) [11, 60] and MIL‐53(Cr) [10] and has been explained by only considering vibrational entropy contributions.…”

“…Comparing this situation to other flexible MOFs, we here show that Cu 2 (DB‐bdc) 2 dabco represents the first example in which the physicochemical properties of the flexible MOF are governed by configurational entropy. For instance, it is established that the phase transition in ZIF‐4(Zn) is based on a delicate balance between dispersion interactions and vibrational entropy, where the lp (high temperature) phase of ZIF‐4(Zn) comes with a gain in vibrational entropy driven by a softening of low frequency modes [12] . Likewise, the np to lp phase transition in the well‐studied MOF MIL‐53 has been shown to be driven by vibrational entropy only [9, 10, 60] .…”

“…In other words, side chain modifications alter the underlying free energy landscape as determined by dispersion interactions and contributions from vibrational and configurational entropy ( cf . Figure 1 b–d), emphasising the delicate thermodynamic balance that exists in the M 2 (fu‐bdc) 2 dabco series and in flexible MOFs in general [9, 11, 12] . The response of M 2 (fu‐bdc) 2 dabco to hydrostatic pressure is yet entirely unexplored, providing us with another fascinating angle from which to probe the free energy landscape of these materials as a function of chemical changes.…”

Lattice dynamics of Pnma Sn(S1–xSex) solid solutions: energetics, phonon spectra and thermal transport

“…Again taking the x Se =0.5 model as an example, the largest difference in E n between two structures is 3.8 meV atom −1 (0.36 kJ mol −1 atom −1 ), whereas the difference in the zero point energies is 0.06 kJ mol −1 atom −1 and the difference in A n vib at 900 K is 2.06 kJ mol −1 atom −1 . Given the number of examples in the literature showing that differences in vibrational free energy-in particular the vibrational entropy-are a key driver of temperature-induced phase transitions [42,[44][45][46], and are important in the determining the stability of alloy systems [43,47,48], this finding is not surprising, but is nonetheless noteworthy.…”

Controlling multiple orderings in metal thiocyanate molecular perovskites Ax{Ni[Bi(SCN)6]}

“…22 This suggests that temperature-induced phase transitions might be uncovered with careful comprehensive variable temperature structural and calorimetric studies, as in (NH 4 ) 2 {Ni [Cd(SCN) 6 ]}, which undergoes an order-disorder transition associated with the NH 4 + cation at around 120 K. 23 Optimisation of the orientational order of A-site cations towards ferroic order might be possible through crystal-engineering, by tuning the hydrogen-bonding or introducing halogen-bonding moieties, 44 and by deepening our understanding of the role of framework entropy in NCS-perovskites. 45…”