On the intrinsic dynamic nature of the rigid UiO-66 metal-organic framework

UiO-66 is a showcase example of an extremely stable metal-organic framework, which maintains its structural integrity during activation processes such as linker exchange and dehydration. The framework can even accommodate a substantial number of defects without compromising its stability. These observations point to an intrinsic dynamic flexibility of the framework, related to changes in the coordination number of the zirconium atoms. Herein we follow the dynamics of the framework in situ, by means of enhanced sampling molecular dynamics simulations such as umbrella sampling, during an activation process, where the coordination number of the bridging hydroxyl groups capped in the inorganic Zr-6(mu(3)-O)(4)(mu(3)-OH)(4) brick is reduced from three to one. Such a reduction in the coordination number occurs during the dehydration process and in other processes where defects are formed. We observe a remarkable fast response of the system upon structural changes of the hydroxyl group. Internal deformation modes are detected, which point to linker decoordination and recoordination. Detached linkers may be stabilized by hydrogen bonds with hydroxyl groups of the inorganic brick, which gives evidence for an intrinsic dynamic acidity even in the absence of protic guest molecules. Our observations yield a major step forward in the understanding on the molecular level of activation processes realized experimentally but that is hard to track on a purely experimental basis

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

Semi-analytical mean-field model for predicting breathing in metal–organic frameworks

A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO2 and CH4, and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO2 adsorption, which was not observed for CH4. This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160–1300 Å3, which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressure model proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted

Light olefin diffusion during the MTO process on H-SAPO-34 : a complex interplay of molecular factors

The methanol-to-olefins process over H-SAPO-34 is characterized by its high shape selectivity toward light olefins. The catalyst is a supramolecular system consisting of nanometer-sized inorganic cages, decorated by Bronsted acid sites, in which organic compounds, mostly methylated benzene species, are trapped. These hydrocarbon pool species are essential to catalyze the methanol conversion but may also clog the pores. As such, diffusion of ethene and propene plays an essential role in determining the ultimate product selectivity. Enhanced sampling molecular dynamics simulations based on either force fields or density functional theory are used to determine how molecular factors influence the diffusion of light olefins through the 8-ring windows of H-SAPO-34. Our simulations show that diffusion through the 8-ring in general is a hindered process, corresponding to a hopping event of the diffusing molecule between neighboring cages. The loading of different methanol, alkene, and aromatic species in the cages may substantially slow down or facilitate the diffusion process. The presence of Bronsted acid sites in the 8-ring enhances the diffusion process due to the formation of a favorable pi-complex host-guest interaction. Aromatic hydrocarbon pool species severely hinder the diffusion and their spatial distribution in the zeolite crystal may have a significant effect on the product selectivity. Herein, we unveil how molecular factors influence the diffusion of light olefins in a complex environment with confined hydrocarbon pool species, high olefin loadings, and the presence of acid sites by means of enhanced molecular dynamics simulations under operating conditions

Protocol for identifying accurate collective variables in enhanced molecular dynamics simulations for the description of structural transformations in flexible metal-organic frameworks

Various kinds of flexibility have been observed in metal–organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal–organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters—often structural parameters—that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal–organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework

How chain length and branching influence the alkene cracking reactivity on H-ZSM-5

Catalytic alkene cracking on H-ZSM-5 involves a complex reaction network with many possible reaction routes and often elusive intermediates. Herein, advanced molecular dynamics simulations at 773 K, a typical cracking temperature, are performed to clarify the nature of the intermediates and to elucidate dominant cracking pathways at operating conditions. A series of C-4-C-8 alkene intermediates are investigated to evaluate the influence of chain length and degree of branching on their stability. Our simulations reveal that linear, secondary carbenium ions are relatively unstable, although their lifetime increases with carbon number. Tertiary carbenium ions, on the other hand, are shown to be very stable, irrespective of the chain length. Highly branched carbenium ions, though, tend to rapidly rearrange into more stable cationic species, either via cracking or isomerization reactions. Dominant cracking pathways were determined by combining these insights on carbenium ion stability with intrinsic free energy barriers for various octene beta-scission reactions, determined via umbrella sampling simulations at operating temperature (773 K). Cracking modes A (3 degrees -> 3 degrees) and B-2 (3 degrees -> 2 degrees) are expected to be dominant at operating conditions, whereas modes B-1 (2 degrees -> 3 degrees), C (2 degrees -> 2 degrees), D-2 (2 degrees -> 1 degrees), and E-2 (3 degrees -> 1 degrees) are expected to be less important. All beta-scission modes in which a transition state with primary carbocation character is involved have high intrinsic free energy barriers. Reactions starting from secondary carbenium ions will contribute less as these intermediates are short living at the high cracking temperature. Our results show the importance of simulations at operating conditions to properly evaluate the carbenium ion stability for beta-scission reactions and to assess the mobility of all species in the pores of the zeolite

The importance of cell shape sampling to accurately predict flexibility in metal-organic frameworks

In this work, the influence of cell shape sampling on the predicted stability of the different metastable phases in flexible metal organic frameworks at finite temperatures is investigated. The influence on the free energy by neglecting cell shape sampling is quantified for the prototypical MIL-53(Al) and the topical DUT-49(Cu). This goal is achieved by constructing free energy profiles in ensembles either in which the phase space associated with the cell shape is sampled explicitly or in which the cell shape is kept fixed. When neglecting cell shape sampling, thermodynamic integration of the hydrostatic pressure yields unreliable free energy profiles that depend on the choice of the fixed cell shape. In this work, we extend the thermodynamic integration procedure via the introduction of a generalized pressure, derived from the Lagrangian strain tensor and the second Piola-Kirchhoff tensor. Using this generalized procedure, the dependence on the unit cell shape can be eliminated, and the inaccuracy in free energy stemming from the lack of cell shape sampling can be uniquely quantified. Finally, it is shown that the inaccuracy in free energy when fixing the cell shape at room temperature stems mainly from entropic contributions for both MIL-53(Al) and DUT-49(Cu)

Comparison of heat flux sensors for internal combustion engines on two hot air gun test rigs and a test engine

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.The heat transfer that occurs in the cylinder of internal combustion engines has a great influence on the efficiency, power output and emissions. Development of a model that is able to predict the heat transfer is needed in order to be able to use simulations for optimization of these three properties. Prior to developing a model, the heat transfer phenomenon has to be thoroughly investigated by performing measurements inside an engine. This allows for a detailed understanding of the process and for a validation of model predictions. In previous works, a commercially available thermopile has been used to measure the heat transfer in a hydrogen combustion engine. The use of this sensor as a heat flux sensor has already been positively evaluated in a previous paper. Its dimensions, however, limit its usability for engine measurements, as it is too large to mount in production type engines. Therefore, a comparison with two alternative sensors was performed to select the best one for engine heat transfer research. Two variations of a calibration rig were used, one with a fast opening shutter and one with a chopper with adjustable speed. This paper presents a comparison of the rise time based on measurements on both test rigs. Furthermore, measurements were carried out on a test engine to evaluate the capability of the sensors to determine the heat transfer to the cylinder walls.dc201