Molecular Dynamics Simulations of the “Breathing” Phase Transformation of MOF Nanocrystallites

Chemoselectivity Inversion of Responsive Metal-Organic Frameworks by Particle Size Tuning in the Micrometer Regime

Gated adsorption is one of the unique physical properties of flexible metal-organic frameworks with high application potential in selective adsorption and sensing of molecules. Despite recent studies that have provided some guidelines in understanding and designing structural flexibility for controlling gate opening by chemical modification of the secondary building units, currently, there is no established strategy to design a flexible MOF showing selective gated adsorption for a specific guest molecule. In a present contribution it is demonstrated for the first time, that the selectivity in the gate opening of a particular compound can be tuned, changed, and even reversed using particle size engineering DUT-8(Zn) ([Zn2(2,6-ndc)2(dabco)]n, 2,6-ndc = 2,6-naphthalenedicarboxylate, dabco = 1,4-diazabicyclo-[2.2.2]-octane, DUT = Dresden University of Technology) experiences phase transition from open (op) to closed (cp) pore phase upon removal of solvent from the pores. Microcrystals show selective reopening in the presence of dichloromethane (DCM) over alcohols. Crystal downsizing to micron size unexpectedly reverses the gate opening selectivity, causing DUT-8(Zn) to open its nanosized pores for alcohols but suppressing the responsivity toward DCM.

The use of collective variables and enhanced sampling in the simulations of existing and emerging microporous materials

Microporous materials, including zeolites, metal-organic frameworks, and cage compounds, offer diverse functionalities due to their unique dynamics and guest confinement properties. These materials play a significant role in separation, catalysis, and sensing, but their complexity hinders exploration using traditional atomistic simulations. This review explores collective variables (CVs) paired with enhanced sampling as a powerful approach to enable efficient investigation of key features in microporous materials. We highlight successful applications of CVs in studying adsorption, diffusion, phase transitions, and mechanical properties, demonstrating their crucial role in guiding material design and optimisation. The future of CVs lies in integration with techniques like machine learning, allowing for enhanced efficiency and accuracy. By tailoring CVs to specific materials and developing multi-scale approaches we can further unlock the intricacies of these fascinating materials. Simulations are a cornerstone in unravelling the complexities of microporous materials and are crucial for our future understanding.

Plastic Avalanches in Metal-Organic Framework Crystals Due to the Dynamic Phase Mixing

The compressive properties of metal-organic framework (MOF) crystals are not only crucial for their densification process but also key in determining their performance in many applications. We herein investigated the mechanical responses of a classic crystalline MOF, HKUST-1, using in situ compression tests. A serrated flow accompanied by the unique strain avalanches was found in individual and contacting crystals before their final flattening or fracture with splitting cracks. The plastic flow with serrations is ascribed to the dynamic phase mixing due to the progressive and irreversible local phase transition in HKUST-1 crystals, as revealed by molecular dynamics and finite element simulations. Such pressure-induced phase coexistence in HKUST-1 crystals also induces a significant loading-history dependence of their Young's modulus. The observation of plastic avalanches in HKUST-1 crystals here not only expands our current understanding of the plasticity of MOF crystals but also unveils a novel mechanism for the avalanches and plastic flow in crystal plasticity.

Simulating the structural phase transitions of metal-organic frameworks with control over the volume of nanocrystallites

Flexible metal-organic frameworks (MOFs) can undergo structural transitions with significant pore volume changes upon guest adsorption or other external triggers while maintaining their porosity. In computational studies of this breathing behavior, molecular dynamics (MD) simulations within periodic boundary conditions (PBCs) are commonly performed. However, to account for the finite size and surface effects affecting the phase transition mechanism, the simulation of non-periodic nanocrystallite (NC) models without the constraint of PBCs is an important alternative. In this study, we present an approach allowing the analysis and control of the volume of finite-size structures during MD simulations by a tetrahedral tessellation of the (deformed) NC's volume. The method allows for defining the current NC's volume during the simulation and manipulating it regarding a particular reference volume to compute free energies for the phase transformation via umbrella sampling. The application on differently sized DMOF-1 and DUT-128 NCs reveals flexible pore closing mechanisms without significant biasing of the transition pathway. The concept provides the theoretical foundation for further research on flexible materials regarding targeted initialization of the structural phase behavior to elucidate the underlying mechanism, which can be used to improve the applications of flexible materials by targeted controlling of the phase transition.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Spatiotemporal Design of the Metal-Organic Framework DUT-8(M)

Switchable metal-organic frameworks (MOFs) change their structure in time and selectively open their pores adsorbing guest molecules, leading to highly selective separation, pressure amplification, sensing, and actuation applications. The 3D engineering of MOFs has reached a high level of maturity, but spatiotemporal evolution opens a new perspective toward engineering materials in the 4th dimension (time) by t-axis design, in essence exploiting the deliberate tuning of activation barriers. This work demonstrates the first example in which an explicit temporal engineering of a switchable MOF (DUT-8, [M₁ M₂ (2,6-ndc)₂ dabco]_n , 2,6-ndc = 2,6-naphthalene dicarboxylate, dabco = 1,4diazabicyclo[2.2.2]octane, M₁  = Ni, M₂  = Co) is presented. The temporal response is deliberately tuned by variations in cobalt content. A spectrum of advanced analytical methods is presented for analyzing the switching kinetics stimulated by vapor adsorption using in situ time-resolved techniques ranging from ensemble adsorption and advanced synchrotron X-ray diffraction experiments to individual crystal analysis. A novel analysis technique based on microscopic observation of individual crystals in a microfluidic channel reveals the lowest limit for adsorption switching reported so far. Differences in the spatiotemporal response of crystal ensembles originate from an induction time that varies statistically and widens characteristically with increasing cobalt content reflecting increasing activation barriers.

Structural phase transitions in flexible DUT-8(Ni) under high hydrostatic pressure

The behaviours of the open pore (op) and closed pore (cp) phases of the flexible Ni₂(ndc)₂(dabco) (ndc - 2,6-naphthalene dicarboxylate, dabco - 1,4-diazabicyclo[2.2.2]octane, DUT-8(Ni)) metal-organic framework under high hydrostatic pressures up to 10 GPa in isopropanol and silicone oil were studied by Raman spectroscopy. Ab initio simulations of vibrational spectra were performed for the open and closed pore phases, which allowed us to disclose the characteristic vibrational modes affected by the structural transitions under pressure. Analysis of theoretical and experimental Raman data suggests that the op-cp transition involves gateway vibrations at 25 and 67 cm^-1, corresponding to trampoline/rotational motions of aromatic linkers. The experiments reveal the formation of new distorted cp phases at pressures higher than 2 GPa, which are formed without amorphisation. The transition between the cp phase and the distorted cp phase is reversible. The experiments also reveal the pivotal role of the pressure transmitting medium on the phase transition behaviour.

Perspectives on the Influence of Crystal Size and Morphology on the Properties of Porous Framework Materials

Miniaturization is a key aspect of materials science. Owing to the increase in quality experimental and computational tools available to researchers, it has become clear that the crystal size and morphology of porous framework materials, including metal-organic frameworks and covalent organic frameworks, play a vital role in defining the physicochemical behaviour of these materials. However, given the multiscale and multidisciplinary challenges associated with establishing how crystal size and morphology affect the structure and behaviour of a material–from local to global structural modifications and from static to dynamic effects–a comprehensive mechanistic understanding of size and morphology effects is missing. Herein, we provide our perspective on the current state-of-the-art of this topic, drawn from various complementary disciplines. From a fundamental point of view, we discuss how controlling the crystal size and morphology can alter the mechanical and adsorption properties of porous framework materials and how this can impact phase stability. Special attention is also given to the quest to develop new computational tools capable of modelling these multiscale effects. From a more applied point of view, given the recent progress in this research field, we highlight the importance of crystal size and morphology control in drug delivery. Moreover, we provide an outlook on how to advance each discussed field by size and morphology control, which would open new design opportunities for functional porous framework materials.

Investigation of CO2 Orientational Dynamics through Simulated NMR Line Shapes*

The dynamics of carbon dioxide in third generation (i. e., flexible) Metal-Organic Frameworks (MOFs) can be experimentally observed by ¹³ C NMR spectroscopy. The obtained line shapes directly correlate with the motion of the adsorbed CO₂ , which in turn are readily available from classical molecular dynamics (MD) simulations. In this article, we present our publicly available implementation of an algorithm to calculate NMR line shapes from MD trajectories in a matter of minutes on any current personal computer. We apply the methodology to study an effect observed experimentally when adsorbing CO₂ in different samples of the pillared layer MOF Ni₂ (ndc)₂ (dabco) (ndc=2,6-naphthalene-dicarboxylate, dabco=1,4-diazabicyclo-[2.2.2]-octane), also known as DUT-8(Ni). In ¹³ C NMR experiments of adsorbed CO₂ in this MOF, small (rigid) crystals result in narrower NMR line shapes than larger (flexible) crystals. The reasons for the higher mobility of CO₂ inside the smaller crystals is unknown. Our ligand field molecular mechanics simulations provide atomistic insight into the effects visible in NMR experiments with limited computational effort.

Molecular Dynamics Simulations of the Breathing Phase Transition of MOF Nanocrystallites II: Explicitly Modeling the Pressure Medium

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.

Large-Scale Molecular Dynamics Simulations Reveal New Insights Into the Phase Transition Mechanisms in MIL-53(Al)

Soft porous crystals have the ability to undergo large structural transformations upon exposure to external stimuli while maintaining their long-range structural order, and the size of the crystal plays an important role in this flexible behavior. Computational modeling has the potential to unravel mechanistic details of these phase transitions, provided that the models are representative for experimental crystal sizes and allow for spatially disordered phenomena to occur. Here, we take a major step forward and enable simulations of metal-organic frameworks containing more than a million atoms. This is achieved by exploiting the massive parallelism of state-of-the-art GPUs using the OpenMM software package, for which we developed a new pressure control algorithm that allows for fully anisotropic unit cell fluctuations. As a proof of concept, we study the transition mechanism in MIL-53(Al) under various external pressures. In the lower pressure regime, a layer-by-layer mechanism is observed, while at higher pressures, the transition is initiated at discrete nucleation points and temporarily induces various domains in both the open and closed pore phases. The presented workflow opens the possibility to deduce transition mechanism diagrams for soft porous crystals in terms of the crystal size and the strength of the external stimulus.

Frustrated flexibility in metal-organic frameworks

Stimuli-responsive flexible metal-organic frameworks (MOFs) remain at the forefront of porous materials research due to their enormous potential for various technological applications. Here, we introduce the concept of frustrated flexibility in MOFs, which arises from an incompatibility of intra-framework dispersion forces with the geometrical constraints of the inorganic building units. Controlled by appropriate linker functionalization with dispersion energy donating alkoxy groups, this approach results in a series of MOFs exhibiting a new type of guest- and temperature-responsive structural flexibility characterized by reversible loss and recovery of crystalline order under full retention of framework connectivity and topology. The stimuli-dependent phase change of the frustrated MOFs involves non-correlated deformations of their inorganic building unit, as probed by a combination of global and local structure techniques together with computer simulations. Frustrated flexibility may be a common phenomenon in MOF structures, which are commonly regarded as rigid, and thus may be of crucial importance for the performance of these materials in various applications.

The micromechanical model to computationally investigate cooperative and correlated phenomena in metal-organic frameworks

Computational insight into the impact of cooperative phenomena and correlated spatial disorder on the macroscopic behaviour of metal-organic frameworks (MOFs) is essential in order to consciously engineer these phenomena for targeted applications. However, the spatial extent of these effects, ranging over hundreds of nanometres, limits the applicability of current state-of-the-art computational tools in this field. To obtain a fundamental understanding of these long-range effects, the micromechanical model is introduced here. This model overcomes the challenges associated with conventional coarse-graining techniques by exploiting the natural partitioning of a MOF material into unit cells. By adopting the elastic deformation energy as the central quantity, the micromechanical model hierarchically builds on experimentally accessible input parameters that are obtained from atomistic quantum mechanical or force field simulations. As a result, the here derived micromechanical equations of motion can be adopted to shed light on the effect of long-range cooperative phenomena and correlated spatial disorder on the performance of mesoscale MOF materials.

Configurational Entropy Driven High-Pressure Behaviour of a Flexible Metal-Organic Framework (MOF)

Flexible metal-organic frameworks (MOFs) show large structural flexibility as a function of temperature or (gas)pressure variation, a fascinating property of high technological and scientific relevance. The targeted design of flexible MOFs demands control over the macroscopic thermodynamics as determined by microscopic chemical interactions and remains an open challenge. Herein we apply high-pressure powder X-ray diffraction and molecular dynamics simulations to gain insight into the microscopic chemical factors that determine the high-pressure macroscopic thermodynamics of two flexible pillared-layer MOFs. For the first time we identify configurational entropy that originates from side-chain modifications of the linker as the key factor determining the thermodynamics in a flexible MOF. The study shows that configurational entropy is an important yet largely overlooked parameter, providing an intriguing perspective of how to chemically access the underlying free energy landscape in MOFs.

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

Insight into the heat transport and water-adsorption properties of the flexible MIL-53(Al) is obtained using advanced molecular dynamics simulations.

Influence of flexible side-chains on the breathing phase transition of pillared layer MOFs: a force field investigation

The prototypical pillared layer MOFs, formed by a square lattice of paddle-wheel units and connected by dinitrogen pillars, can undergo a breathing phase transition by a "wine-rack" type motion of the square lattice. We studied this behavior, which is not yet fully understood, using an accurate first principles parameterized force field (MOF-FF) for larger nanocrystallites on the example of Zn₂(bdc)₂(dabco) [bdc: benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)], and found clear indications for an interface between a closed and an open pore phase traveling through the system during the phase transformation [J. Keupp and R. Schmid, Adv. Theory Simul., 2019, 2, 1900117]. In conventional simulations in small supercells this mechanism is prevented by periodic boundary conditions (PBCs), enforcing a synchronous transformation of the entire crystal. Here, we extend this investigation to pillared layer MOFs with flexible side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimentally known to have different properties with the side-chains acting as fixed guest molecules. First, in order to extend the parameterization for such flexible groups, a new parameterization strategy for MOF-FF had to be developed, using a multi-structure force based fit method. The resulting parameterization for a library of fu-MOFs is then validated with respect to a set of reference systems and shows very good accuracy. In the second step, a series of fu-MOFs with increasing side-chain length is studied with respect to the influence of the side-chains on the breathing behavior. For small supercells in PBCs a systematic trend of the closed pore volume with the chain length is observed. However, for a nanocrystallite model a distinct interface between a closed and an open pore phase is visible only for the short chain length, whereas for longer chains the interface broadens and a nearly concerted transformation is observed. Only by molecular dynamics simulations using accurate force fields can such complex phenomena can be studied on a molecular level.

Single particle Raman spectroscopy analysis of the metal-organic framework DUT-8(Ni) switching transition under hydrostatic pressure

Experimental in situ observations of phase coexistence in switchable metal-organic frameworks are reported to provide a fundamental understanding of dynamic adsorbents that can change their pore structure in response to external stimuli. A prototypical flexible pillared layer framework DUT-8(Ni) (DUT = Dresden University of Technology) was studied under hydrostatic pressure by in situ Raman spectroscopy on single crystals. The closing transition of the open pore phase (op) containing DMF in the pores in silicon oil as a pressure transmitting fluid, as well as the closed pore phase (cp) to op transition under pressure in methanol, were studied. Phase coexistences during both transitions were observed.

Impact of Defects and Crystal Size on Negative Gas Adsorption in DUT-49 Analyzed by In Situ 129Xe NMR Spectroscopy

The origin of crystal-size-dependent adsorption behavior of flexible metal-organic frameworks is increasingly studied. In this contribution, we probe the solid-fluid interactions of DUT-49 crystals of different size by in situ 129Xe NMR spectroscopy at 200 K. With decreasing size of the crystals, the average solid-fluid interactions are found to decrease reflected by a decrease in chemical shift of adsorbed xenon from 230 to 200 ppm, explaining the lack of adsorption-induced transitions for smaller crystals. However, recent studies propose that these results can also originate from the presence of lattice defects. To investigate the influence of defects on the adsorption behavior of DUT-49, we synthesized a series of samples with tailored defect concentrations and characterized them by in situ 129Xe NMR. In comparison to the results obtained for crystals with different size, we find pronounced changes of the adsorption behavior and influence of the chemical shift only for very high concentrations of defects, which further emphasizes the important role of particle size phenomena.

Four-dimensional metal-organic frameworks

Recognising timescale as an adjustable dimension in porous solids provides a new perspective to develop novel four-dimensional framework materials. The deliberate design of three-dimensional porous framework architectures is a developed field; however, the understanding of dynamics in open frameworks leaves a number of key questions unanswered: What factors determine the spatiotemporal evolution of deformable networks? Can we deliberately engineer the response of dynamic materials along a time-axis? How can we engineer energy barriers for the selective recognition of molecules? Answering these questions will require significant methodological development to understand structural dynamics across a range of time and length scales.

Unraveling the thermodynamic criteria for size-dependent spontaneous phase separation in soft porous crystals

Soft porous crystals (SPCs) harbor a great potential as functional nanoporous materials owing to their stimuli-induced and tuneable morphing between different crystalline phases. These large-amplitude phase transitions are often assumed to occur cooperatively throughout the whole material, which thereby retains its perfect crystalline order. Here, we disprove this paradigm through mesoscale first-principles based molecular dynamics simulations, demonstrating that morphological transitions do induce spatial disorder under the form of interfacial defects and give rise to yet unidentified phase coexistence within a given sample. We hypothesize that this phase coexistence can be stabilized by carefully tuning the experimental control variables through, e.g., temperature or pressure quenching. The observed spatial disorder helps to rationalize yet elusive phenomena in SPCs, such as the impact of crystal downsizing on their flexible nature, thereby identifying the crystal size as a crucial design parameter for stimuli-responsive devices based on SPC nanoparticles and thin films.

Soft porous crystals hold big promise as functional nanoporous materials due to their stimuli responsive flexibility. Here, molecular dynamics simulations reveal a new type of spatial disorder in mesoscale crystals that helps to understand the size-dependency of their phase transition behavior.