Abstract
One of the most investigated properties of porous crystalline metal-organic frameworks (MOFs) is their potential flexibility to undergo large changes in unit cell size upon guest adsorption or other stimuli, referred to as “breathing”. Computationally, such phase transitions are usually investigated using periodic boundary conditions, where the system’s volume can be controlled directly. However, we have recently shown that important aspects like the formation of a moving interface between the open and the closed pore form or the free energy barrier of the first-order phase transition and its size effects can best be investigated using non-periodic nanocrystallite (NC) models [Keupp et al. (Adv. Theory Simul., 2019, 2, 1900117)]. In this case, the application of pressure is not straightforward, and a distance constraint was used to mimic a mechanical strain enforcing the reaction coordinate. In contrast to this prior work, a mediating particle bath is used here to exert an isotropic hydrostatic pressure on the MOF nanocrystallites. The approach is inspired by the mercury nanoporosimetry used to compress flexible MOF powders. For such a mediating medium, parameters are presented that require a reasonable additional numerical effort and avoid unwanted diffusion of bath particles into the MOF pores. As a proof-of-concept, NCs of pillared-layer MOFs with different linkers and sizes are studied concerning their response to external pressure exerted by the bath. By this approach, an isotropic pressure on the NC can be applied in analogy to corresponding periodic simulations, without any bias for a specific mechanism. This allows a more realistic investigation of the breathing phase transformation of a MOF NC and further bridges the gap between experiment and simulation.
Highlights
One of the most intriguing features of the novel class of metal-organic frameworks (MOFs), known as porous coordination polymers, is their structural flexibility combined with crystalline ordering
Since the pressure bath is a hypothetical medium, which only represents a fluid pressing on the MOF, the modeled fluid does not necessarily comply with the thermodynamic properties of natural elements, i.e., mercury
That the screened parameters were not optimized but only selected to fulfill the following criteria: 1) The parameters should be suitable to adequately trigger the pore closing starting from a completely open pore form, 2) they should not require great numerical effort, and 3) they should avoid the diffusion of pressure bath particles into the MOF pores
Summary
One of the most intriguing features of the novel class of metal-organic frameworks (MOFs), known as porous coordination polymers, is their structural flexibility combined with crystalline ordering. Modeling the Pressure Medium investigated MOF systems in this area is MIL-53, and we refer here to several reviews (Férey and Serre, 2009; Alhamami et al, 2014; Millange and Walton, 2018; Tomar and Singh, 2021) In this context, we want to note that it was Llewellyn et al who have used mercury porosimetry, usually employed to characterize mesoporous systems, to trigger the open to closed pore phase transformation by a hydrostatic external pressure Beurroies et al (2010). In the previous work, a constraining mechanical force, acting on a selected set of atoms (SBUs on opposite edges of the NC), was used to imitate the effect of pressure on the NCs (Keupp and Schmid, 2019) This allows to define a reaction coordinate for the phase transformation and to compute free energy profiles using umbrella sampling. All four conformations fulfill the zero net sum criterion proposed by Goodwin et al (Reynolds et al, 2021)
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