Unravelling thermal stress due to thermal expansion mismatch in metal–organic frameworks for methane storage

Thermal stress is present in metal–organic frameworks undergoing temperature changes during adsorption and desorption. We computed the thermal pressure coefficient as a proxy for this phenomenon and discuss the impact of thermal expansion mismatch.Thermal stress is present in all systems undergoing temperature changes during their operation. Metal-organic frameworks (MOFs) are a class of porous, crystalline materials ideally suited for a wide range of adsorption-based technologies. The release and consumption of the heat of adsorption instigate temperature fluctuations and thermal stress in these materials that could induce disruptive volume changes. To bring these materials to engineering applications, it is of utmost importance to understand their thermal expansion behavior and the overall induced thermal stress due to thermal expansion mismatch with other components. In this work, we focus on a large group of MOFs known to have promising methane adsorption properties and predict their thermal expansion coefficients based on force field molecular dynamics simulations. Negative thermal expansion (NTE) behavior is predicted for all studied MOFs, and the magnitude of the NTE coefficients is found to be positively correlated with the degree of porosity of the frameworks. Finally, as a proxy for the thermal stress, the thermal pressure coefficient is calculated, which is found to be in the range between polymers and ceramics. Variations within the operating temperature range of MOFs are therefore expected to result in a relatively low thermal stress

Exploring the flexibility of MIL-47(V)-type materials using force field molecular dynamics simulations

The flexibility of three MIL-47(V)-type materials (MIL-47, COMOC-2, and COMOC-3) has been explored by constructing the pressure versus volume and free energy versus volume profiles at various temperatures ranging from 100 to 400 K This is done with first-principles-based force fields using the recently proposed QuickFF parametrization protocol. Specific terms were added for the materials at hand to describe the asymmetry of the one-dimensional vanadium oxide chain and to account for the flexibility of the organic linkers. The force fields are used in a series of molecular dynamics simulations at fixed volumes but varying unit cell shapes. The three materials show a distinct pressure-volume behavior, which underlines the ability to tune the mechanical properties by varying the linkers toward different applications such as nanosprings, dampers, and shock absorbers

Extension of the QuickFF force field protocol for an improved accuracy of structural, vibrational, mechanical and thermal properties of metal-organic frameworks

QuickFF was originally launched in 2015 to derive accurate force fields for isolated and complex molecular systems in a quick and easy way. Apart from the general applicability, the functionality was especially tested for metal-organic frameworks (MOFs), a class of hybrid materials consisting of organic and inorganic building blocks. Herein, we launch a new release of the QuickFF protocol which includes new major features to predict structural, vibrational, mechanical and thermal properties with greater accuracy, without compromising its robustness and transparent workflow. First, the ab initio data necessary for the fitting procedure may now also be derived from periodic models for the molecular system, as opposed to the earlier cluster-based models. This is essential for an accurate description of MOFs with one-dimensional metal-oxide chains. Second, cross terms that couple internal coordinates (ICs) and anharmonic contributions for bond and bend terms are implemented. These features are essential for a proper description of vibrational and thermal properties. Third, the fitting scheme was modified to improve robustness and accuracy. The new features are tested on MIL-53(Al), MOF-5, CAU-13 and NOTT-300. As expected, periodic input data are proven to be essential for a correct description of structural, vibrational and thermodynamic properties of MIL-53(Al). Bulk moduli and thermal expansion coefficients of MOF-5 are very accurately reproduced by static and dynamic simulations using the newly derived force fields which include cross terms and anharmonic corrections. For the flexible materials CAU-13 and NOTT-300, the transition pressure is accurately predicted provided cross terms are taken into account

Tuning the balance between dispersion and entropy to design temperature-responsive flexible metal-organic frameworks

Temperature-responsive flexibility in metal-organic frameworks (MOFs) appeals to the imagination. The ability to transform upon thermal stimuli while retaining a given crystalline topology is desired for specialized sensors and actuators. However, rational design of such shape-memory nanopores is hampered by a lack of knowledge on the nanoscopic interactions governing the observed behavior. Using the prototypical MIL-53(Al) as a starting point, we show that the phase transformation between a narrow-pore and large-pore phase is determined by a delicate balance between dispersion stabilization at low temperatures and entropic effects at higher ones. We present an accurate theoretical framework that allows designing breathing thermo-responsive MOFs, based on many-electron data for the dispersion interactions and density-functional theory entropy contributions. Within an isoreticular series of materials, MIL-53(Al), MIL-53(Al)-FA, DUT-4, DUT-5 and MIL-53(Ga), only MIL-53(Al) and MIL-53(Ga) are proven to switch phases within a realistic temperature range

Atomistic insight in the flexibility and heat transport properties of the stimuli-responsive metal–organic framework MIL-53(Al) for water-adsorption applications using molecular simulations

To exploit the full potential of metal-organic frameworks as solid adsorbents in water-adsorption applications, many challenges remain to be solved. A more fundamental insight into the properties of the host material and the influence that water exerts on them can be obtained by performing molecular simulations. In this work, the prototypical flexible MIL-53(Al) framework is modelled using advanced molecular dynamics simulations. For different water loadings, the presence of water is shown to affect the relative stability of MIL-53(Al), triggering a phase transition from the narrow-pore to the large-pore phase at the highest considered loading. Furthermore, the effect of confinement on the structural organisation of the water molecules is also examined for different pore volumes of MIL-53(Al). For the framework itself, we focus on the thermal conductivity, as this property plays a decisive role in the efficiency of adsorption-based technologies, due to the energy-intensive adsorption and desorption cycles. To this end, the heat transfer characteristics of both phases of MIL-53(Al) are studied, demonstrating a strong directional dependence for the thermal conductivity

Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta) stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible

Efficient construction of free energy profiles of breathing metal–organic frameworks using advanced molecular dynamics simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials

Thermodynamic insight in the high-pressure behavior of UiO-66: effect of linker defects and linker expansion

In this Article, we present a molecular-level understanding of the experimentally observed loss of crystallinity in UiO-66-type metal organic frameworks, including the pristine UiO-66 to-68 as well as defect-containing UiO-66 materials, under the influence of external pressure. This goal is achieved by constructing pressure-versus-volume profiles at finite temperatures using a thermodynamic approach relying on ab initio derived force fields. On the atomic level, the phenomenon is reflected in a sudden drop in the number of symmetry operators for the crystallographic unit cell because of the disordered displacement of the organic linkers with respect to the inorganic bricks. For the defect-containing samples, a reduced mechanical stability is observed, however, critically depending on the distribution of these defects throughout the material, hence demonstrating the importance of judiciously characterizing defects in these materials

On the importance of anharmonicities and nuclear quantum effects in modelling the structural properties and thermal expansion of MOF-5

In this article, we investigate the influence of anharmonicities and nuclear quantum effects (NQEs) in modelling the structural properties and thermal expansion of the empty MOF-5 metal-organic framework. To introduce NQEs in classical molecular dynamics simulations, two different methodologies are considered, comparing the approximate, but computationally cheap, method of generalised Langevin equation thermostatting to the more advanced, computationally demanding path integral molecular dynamics technique. For both methodologies, similar results were obtained for all the properties under investigation. The structural properties of MOF-5, probed by means of radial distribution functions (RDFs), show some distinct differences with respect to a classical description. Besides a broadening of the RDF peaks under the influence of quantum fluctuations, a different temperature dependence is also observed due to a dominant zero-point energy (ZPE) contribution. For the thermal expansion of MOF-5, by contrast, NQEs appear to be only of secondary importance with respect to an adequate modelling of the anharmonicities of the potential energy surface (PES), as demonstrated by the use of two differently parametrised force fields. Despite the small effect in the temperature dependence of the volume of MOF-5, NQEs do however significantly affect the absolute volume of MOF-5, in which the ZPE resulting from the intertwining of NQEs and anharmonicities plays a crucial role. A sufficiently accurate description of the PES is therefore prerequisite when modelling NQEs

The impact of lattice vibrations on the macroscopic breathing behavior of MIL-53(Al)

The mechanism inducing the breathing in flexible metal-organic frameworks, such as MIL-53(Al), is still not fully understood. Herein, the influence of lattice vibrations on the breathing transition in MIL-53(Al) is investigated to gain insight in this phenomenon. Through solid-state density-functional theory calculations, the volume-dependent IR spectrum is computed together with the volume-frequency relations of all vibrational modes. Furthermore, important thermodynamic properties such as the Helmholtz free energy, the specific heat capacity, the bulk modulus, and the volumetric thermal expansion coefficient are derived via these volume-frequency relations using the quasi-harmonic approximation. The simulations expose a general volume-dependency of the vibrations with wavenumbers above 300 cm(-1 )due to their localized nature. In contrast, a diverse set of volume-frequency relations are observed for vibrations in the terahertz region (<300 cm(-1) ) containing the vibrations exhibiting collective behavior. Some terahertz vibrations display large frequency differences over the computed volume range, induced by either repulsion or strain effects, potentially triggering the phase transformation. Finally, the impact of the lattice vibrations on the thermodynamic properties is investigated. This reveals that the closed pore to large pore phase transformation in MIL-53(Al) is mainly facilitated by terahertz vibrations inducing rotations of the organic linker, while the large pore to closed pore phase transformation relies on two framework-specific soft modes