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Register a new userCooperative gas adsorption without a phase transition in metal-organic frameworks
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Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.
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Diamine-appended metal{organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a firstorder phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, and point the way toward rational control, in and out of equilibrium, of cooperative adsorption in this industrially important class of materials.
We present a three-dimensional Ising model where lines of equal spins are frozen in such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this porous Ising model can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH$_4$) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.
We develop a proper nonempirical spin-density formalism for the van der Waals density functional (vdW-DF) method. We show that this generalization, termed svdW-DF, is firmly rooted in the single-particle nature of exchange and we test it on a range of spin systems. We investigate in detail the role of spin in the nonlocal-correlation driven adsorption of H$_2$ and CO$_2$ in the linear magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that spin plays a significant role during the adsorption process despite the general weakness of the molecular-magnetic responses. The case of CO$_2$ adsorption in Ni-MOF74 is particularly interesting, as the inclusion of spin effects results in an increased attraction, opposite to what the diamagnetic nature of CO$_2$ would suggest. We explain this counter-intuitive result, tracking the behavior to a coincidental hybridization of the O $p$ states with the Ni $d$ states in the down-spin channel. More generally, by providing insight on nonlocal correlation in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions.
The reentrant layering transitions found in rare gas adsorption on solid substrates have conflictually been explained either in terms of preroughening (PR), or of top layer melting-solidification phenomena. We obtain adsorption isotherms of Lennard-Jones particles on an attractive substrate by off lattice Grand Canonical Monte Carlo (GCMC) simulation, and reproduce reentrant layering. Microscopic analysis, including layer-by-layer occupancies, surface diffusion and pair correlations, confirms the switch of the top surface layer from solid to quasi-liquid across the transition temperature. At the same time, layer occupancy is found at each jump to switch from close to full to close to half, indicating a disordered flat (DOF) surface and establishing preroughening as the underlying mechanism. Our results suggest that top layer melting is essential in triggering preroughening, which thus represents the threshold transition to surface melting in rare gas solids.
The metal-organic framework (MOF) MFU-4l containing Co(II) centers and Cl- ligands has recently shown promising redox activity. Aiming for further improved MOF catalysts for oxidation processes employing molecular oxygen we present a density-functional theory (DFT) based computational screening approach to identify promising metal center and ligand combinations within the MFU-4l structural family. Using the O2 binding energy as a descriptor for the redox property, we show that relative energetic trends in this descriptor can reliably be obtained at the hybrid functional DFT level and using small cluster (scorpionate-type complex) models. Within this efficient computational protocol we screen a range of metal center / ligand combinations and identify several candidate systems that offer more exothermic O2 binding than the original Co/Cl-based MFU-4l framework.
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