Mechanism of Breathing Transitions in Metal!Organic Frameworks

M frameworks (MOFs) represent a new class of porous crystals, which has attracted physicists and material scientists worldwide due to their extraordinary physicochemical and mechanical properties and potential applications in energy and biomedicine fields. Recent discovery of structural transformations between large-pore (lp) and narrow-pore (np) conformations in MOFs of MIL-53 type and others brought about a new physical phenomenon that represents a challenging problem for theoreticians.1!3 This phenomenon, called breathing, is displayed in abrupt changes of the framework volume triggered by adsorption of guest molecules that is explored to devise advanced adsorbents, drug delivery systems, sensors, and actuators. In this Letter, we suggest a multiscale cooperative mechanism of breathing transitions that involves a complex interplay of adsorption and elastic interactions on the level of the crystal. This mechanism is explored with a “primitive” stochastic model of adsorption in flexible bistable frameworks that takes into account the major physical factors with the minimum input parameters and is capable of reproducing experimentally observed features. As such, we address the topical questions of the hysteretic nature of breathing transitions and the possibility of coexistence of lp and np phases in one crystal that was highly debated in the literature recently. The most instructive examples of breathing transitions are observed in MOFs of the MIL-53 family during isothermal adsorption of Xe, CH4, CO2, and other gases. 8 The MIL-53 framework is made of parallel one-dimensional M(OH) chains (M = Al, Cr, Ga, ...), linked together by 1,4-benzenedicarboxylate (BDC) ligands to form linear diamond-shaped channels that are wide enough to accommodate small guest molecules. This structure may oscillate between lp and np phases, which have a remarkable difference in unit cell volume of up to 40% (see schematics in Figure 1). What is truly extraordinary is that the transition from the larger volume lp phase to the smaller volume np phase is not necessarily accompanied with the release of guest molecules that would be expected for the normal “exhaling”. For example, the equilibrium state of the MIL-53 crystal at 220 K in the absence of guest molecules is in the lp phase, and upon Xe adsorption, there first occurs the transition from the unloaded lp phase to the loaded np phase. This transition is associated with a sharp uptake of Xe, from a loading of ∼0.2 to ∼2.5 molecules per unit cell, and a decrease of the crystal volume by ∼25%. Upon further increase of the gas pressure, adsorption gradually proceeds in the np phase up to a certain point, when the second, now “normal”, breathing transiting occurs, from the np phase to the lp phase. The sample abruptly “inhales”, increasing the loading from ∼2.7 to ∼6.5 molecules per cell, and expands, compensating for the volume lost upon the first lp!np transition. On the desorption pass, the reverse normal lp!np and abnormal np!lp exhaling transitions take place with a prominent hysteresis. This enigmatic breathing phenomenon is engendered by guest! host adsorption interactions mediated by the elasticity of threedimensional host framework, which are currently poorly understood. The specific variations of the linker conformations in the lp and np phases during breathing transitions have been studied at the molecular level by F!erey and coauthors, both experimentally (in situ X-ray diffraction) and using molecular simulation (singlepoint DFT calculations and force-field-based dynamics). These works provide useful insight into the chemistry of the transformation of linker bonds associated with the framework deformation. However, a knowledge gap exists between this molecular understanding and the question of how the adsorption of guest molecules induces the physical forces responsible for macroscopic