Emerging concepts from scientific deep machine learning such as physics-informed neural networks (PINNs) enable a data-driven approach for the study of complex kinetic problems. We present an extended framework that combines the advantages of PINNs with the detailed consideration of experimental parameter variations for the simulation and prediction of chemical reaction kinetics. The approach is based on truncated Taylor series expansions for the underlying fundamental equations, whereby the external variations can be interpreted as perturbations of the kinetic parameters. Accordingly, our method allows for an efficient consideration of experimental parameter settings and their influence on the concentration profiles and reaction kinetics. A particular advantage of our approach, in addition to the consideration of univariate and multivariate parameter variations, is the robust model-based exploration of the parameter space to determine optimal reaction conditions in combination with advanced reaction insights. The benefits of this concept are demonstrated for higher-order chemical reactions including catalytic and oscillatory systems in combination with small amounts of training data. All predicted values show a high level of accuracy, demonstrating the broad applicability and flexibility of our approach.
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.
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.
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.
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.
The post-synthetic installation of linker molecules between open-metal sites (OMSs) and undercoordinated metal-nodes in a metal-organic framework (MOF) - retrofitting - has recently been discovered as a powerful tool to manipulate macroscopic properties such as the mechanical robustness and the thermal expansion behavior. So far, the choice of cross linkers (CLs) that are used in retrofitting experiments is based on qualitative considerations. Here, we present a low-cost computational framework that provides experimentalists with a tool for evaluating various CLs for retrofitting a given MOF system with OMSs. After applying our approach to the prototypical system CL@Cu3BTC2 (BTC = 1,3,5-benzentricarboxylate) the methodology was expanded to NOTT-100 and NOTT-101 MOFs, identifying several promising CLs for future CL@NOTT-100 and CL@NOTT-101 retrofitting experiments. The developed model is easily adaptable to other MOFs with OMSs and is set-up to be used by experimentalists, providing a guideline for the synthesis of new retrofitted MOFs with modified physicochemical properties.
For the structure prediction of MOFs and related crystalline framework materials we have proposed the Reversed Topological Approach (RTA), where the default embedding of a topology is used as a blueprint. The optimal rotational insertion of the building blocks (BBs) at the fixed vertex positions of the blueprint is performed by minimizing the target function of the average angle deviation (AAD). Here we extend this idea by pre-optimizing the maximum symmetry embedding of a topology in order to minimize the overall mean AAD for the given set of BBs. By this fast and essentially parameter-free topoFF method, the vertex positions and cell parameters of the blueprint are further optimized in order to fit the structural needs of the BBs, which speeds up the overall search for the most energetically favorable structure. In addition, different topologies can be ranked in a quantitative and intuitive way. The definition and implementation of topoFF is explained and its application for the RTA-based structure prediction of MOFs is demonstrated with a number of instructive examples.
