Phase Diagrams of Alloys and Their Hydrides via On-Lattice Graph Neural Networks and Limited Training Data.

Efficient prediction of sampling-intensive thermodynamic properties is needed to evaluate material performance and permit high-throughput materials modeling for a diverse array of technology applications. To alleviate the prohibitive computational expense of high-throughput configurational sampling with density functional theory (DFT), surrogate modeling strategies like cluster expansion are many orders of magnitude more efficient but can be difficult to construct in systems with high compositional complexity. We therefore employ minimal-complexity graph neural network models that accurately predict and can even extrapolate to out-of-train distribution formation energies of DFT-relaxed structures from an ideal (unrelaxed) crystallographic representation. This enables the large-scale sampling necessary for various thermodynamic property predictions that may otherwise be intractable and can be achieved with small training data sets. Two exemplars, optimizing the thermodynamic stability of low-density high-entropy alloys and modulating the plateau pressure of hydrogen in metal alloys, demonstrate the power of this approach, which can be extended to a variety of materials discovery and modeling problems.

Cotinuous precision separation of gold using a metal-organic framework/polymer composite.

Critical metals of environmental and economic relevance can be found within complex mixtures, such as mine tailings, electronic waste and wastewater, at trace amounts. Specifically, gold is a critical metal that carries desired redox active properties in various applications, including modern electronics, medicine and chemical catalysis. Here we report the structuring of sub-micron Fe-BTC/PpPDA crystallites into larger 250µm or 500µm granules for continuous packed bed experiments for the precision separation of gold. The Structured Fe-BTC/PpPDA is highly crystalline and porous with a BET surface area of 750 m2g-1. Further, the hybrid nanocomposite material maintains its selectivity for gold ions over common inorganic interferents. The structuring approach reported prevents excessive pressure drop and ensures stability over time and operation in a packed bed column. Further, we demonstrate that the Structured Fe-BTC/PpPDA can concentrate at least 42 wt% of gold under a dynamic continuous flow operation. These findings highlight the potential of Structured Fe-BTC/PpPDA for practical applications in industry, particularly in the selective capture of gold from complex mixtures.

Elucidating Primary Degradation Mechanisms in High-Cycling-Capacity, Compositionally Tunable High-Entropy Hydrides.

The hydrogen sorption properties of single-phase bcc (TiVNb)100-xCrx alloys (x = 0-35) are reported. All alloys absorb hydrogen quickly at 25 °C, forming fcc hydrides with storage capacity depending on the Cr content. A thermodynamic destabilization of the fcc hydride is observed with increasing Cr concentration, which agrees well with previous compositional machine learning models for metal hydride thermodynamics. The steric effect or repulsive interactions between Cr-H might be responsible for this behavior. The cycling performances of the TiVNbCr alloy show an initial decrease in capacity, which cannot be explained by a structural change. Pair distribution function analysis of the total X-ray scattering on the first and last cycled hydrides demonstrated an average random fcc structure without lattice distortion at short-range order. If the as-cast alloy contains a very low density of defects, the first hydrogen absorption introduces dislocations and vacancies that cumulate into small vacancy clusters, as revealed by positron annihilation spectroscopy. Finally, the main reason for the capacity drop seems to be due to dislocations formed during cycling, while the presence of vacancy clusters might be related to the lattice relaxation. Having identified the major contribution to the capacity loss, compositional modifications to the TiVNbCr system can now be explored that minimize defect formation and maximize material cycling performance.

Defect graph neural networks for materials discovery in high-temperature clean-energy applications.

We present a graph neural network approach that fully automates the prediction of defect formation enthalpies for any crystallographic site from the ideal crystal structure, without the need to create defected atomic structure models as input. Here we used density functional theory reference data for vacancy defects in oxides, to train a defect graph neural network (dGNN) model that replaces the density functional theory supercell relaxations otherwise required for each symmetrically unique crystal site. Interfaced with thermodynamic calculations of reduction entropies and associated free energies, the dGNN model is applied to the screening of oxides in the Materials Project database, connecting the zero-kelvin defect enthalpies to high-temperature process conditions relevant for solar thermochemical hydrogen production and other energy applications. The dGNN approach is applicable to arbitrary structures with an accuracy limited principally by the amount and diversity of the training data, and it is generalizable to other defect types and advanced graph convolution architectures. It will help to tackle future materials discovery problems in clean energy and beyond.

Challenges to developing materials for the transport and storage of hydrogen.

Hydrogen has the highest gravimetric energy density of any energy carrier and produces water as the only oxidation product, making it extremely attractive for both transportation and stationary power applications. However, its low volumetric energy density causes considerable difficulties, inspiring intense efforts to develop chemical-based storage using metal hydrides, liquid organic hydrogen carriers and sorbents. The controlled uptake and release of hydrogen by these materials can be described as a series of challenges: optimal properties fall within a narrow range, can only be found in few materials and often involve important trade-offs. In addition, a greater understanding of the complex kinetics, mass transport and microstructural phenomena associated with hydrogen uptake and release is needed. The goal of this Perspective is to delineate potential use cases, define key challenges and show that solutions will involve a nexus of several subdisciplines of chemistry, including catalysis, data science, nanoscience, interfacial phenomena and dynamic or phase-change materials.

What Lies beneath a Metal-Organic Framework Crystal Structure? New Design Principles from Unexpected Behaviors.

The rational design principles established for metal-organic frameworks (MOFs) allow clear structure-property relationships, fueling expansive growth for energy storage and conversion, catalysis, and beyond. However, these design principles are based on the assumption of compositional and structural rigidity, as measured crystallographically. Such idealization of MOF structures overlooks subtle chemical aspects that can lead to departures from structure-based chemical intuition. In this Perspective, we identify unexpected behavior of MOFs through literature examples. Based on this analysis, we conclude that departures from ideality are not uncommon. Whereas linker topology and metal coordination geometry are useful starting points for understanding MOF properties, we anticipate that deviations from the idealized crystal representation will be necessary to explain important and unexpected behaviors. Although this realization reinforces the notion that MOFs are highly complex materials, it should also stimulate a broader reexamination of the literature to identify corollaries to existing design rules and reveal new structure-property relationships.

Elucidating the Effects of the Composition on Hydrogen Sorption in TiVZrNbHf-Based High-Entropy Alloys.

A number of high-entropy alloys (HEAs) in the TiVZrNbHf system have been synthesized by arc melting and systematically evaluated for their hydrogen sorption characteristics. A total of 21 alloys with varying elemental compositions were investigated, and 17 of them form body-centered-cubic (bcc) solid solutions in the as-cast state. A total of 15 alloys form either face-centered-cubic (fcc) or body-centered-tetragonal (bct) hydrides after exposure to gaseous hydrogen with hydrogen per metal ratios (H/M) as high as 2.0. Linear trends are observed between the volumetric expansion per metal atom [(V/Z)fcc/bct - (V/Z)bcc/hcp]/(V/Z)bcc/hcp with the valence electron concentration and average Pauling electronegativity (χp) of the alloys. However, no correlation was observed between the atomic size mismatch, δ, and any investigated hydrogen sorption property such as the maximum storage capacity or onset temperature for hydrogen release.

Extracting an Empirical Intermetallic Hydride Design Principle from Limited Data via Interpretable Machine Learning.

An open question in the metal hydride community is whether there are simple, physics-based design rules that dictate the thermodynamic properties of these materials across the variety of structures and chemistry they can exhibit. While black box machine learning-based algorithms can predict these properties with some success, they do not directly provide the basis on which these predictions are made, therefore complicating the a priori design of novel materials exhibiting a desired property value. In this work we demonstrate how feature importance, as identified by a gradient boosting tree regressor, uncovers the strong dependence of the metal hydride equilibrium H2 pressure on a volume-based descriptor that can be computed from just the elemental composition of the intermetallic alloy. Elucidation of this simple structure-property relationship is valid across a range of compositions, metal substitutions, and structural classes exhibited by intermetallic hydrides. This permits rational targeting of novel intermetallics for high-pressure hydrogen storage (low-stability hydrides) by their descriptor values, and we predict a known intermetallic to form a low-stability hydride (as confirmed by density functional theory calculations) that has not yet been experimentally investigated.

Simulating Enhanced Methane Deliverable Capacity of Guest Responsive Pores in Intrinsically Flexible MOFs.

A novel computational procedure, based on the principles of flat-histogram Monte Carlo, is developed for facile prediction of the adsorption thermodynamics of intrinsically flexible adsorbents. We then demonstrate how an accurate prediction of methane deliverable capacity in a metal-organic framework (MOF) with significant intrinsic flexibility requires use of such a method. Dynamic side chains in the framework respond to methane adsorbates and reorganize to exhibit a more conducive pore space at high adsorbate densities while simultaneously providing a less conducive pore space at low adsorbate densities. This "responsive pore" MOF achieves ∼20% higher deliverable capacity than if the framework were rigid and elucidates a strategy for designing high deliverable capacity MOFs in the future.

Ab Initio Flexible Force Field for Metal-Organic Frameworks Using Dummy Model Coordination Bonds.

We present force fields developed from periodic density functional theory (DFT) calculations that can be used in classical molecular simulations to model M-MOF-74 (M = Co, Fe, Mg, Mn, Ni, Zn) and its extended linker analogs. Our force fields are based on cationic dummy models (CDMs). These dummy models simplify the methodology required to tune the parameters and improve the accuracy of the force fields. We used our force fields to compare mechanical properties across the M-MOF-74 series and determine that increasing the size of the linker decreases the framework rigidity. In addition, we applied our force fields to an extended linker analog of Mg-MOF-74 and characterized the free energy of a previously reported deformation pattern in which the one-dimensional hexagonal channels of the framework become irregular. The free energy profiles confirm that the deformation is adsorbate induced and impossible to access solely by a pressure stimulus. On the basis of our results, we conclude that the force fields presented here and others that may be developed using our methodology are transferable across metal-organic framework series that share a metal center topology. Finally, we believe that these force fields have the potential to be adapted for the study of complex problems in MOF chemistry, including defects and crystal growth, that have thus far been beyond the scope of classical molecular simulations.

Flat-Histogram Monte Carlo as an Efficient Tool To Evaluate Adsorption Processes Involving Rigid and Deformable Molecules.

Monte Carlo simulations are the foundational technique for predicting thermodynamic properties of open systems where the process of interest involves the exchange of particles. Thus, they have been used extensively to computationally evaluate the adsorption properties of nanoporous materials and are critical for the in silico identification of promising materials for a variety of gas storage and chemical separation applications. In this work we demonstrate that a well-known biasing technique, known as "flat-histogram" sampling, can be combined with temperature extrapolation of the free energy landscape to efficiently provide significantly more useful thermodynamic information than standard open ensemble MC simulations. Namely, we can accurately compute the isosteric heat of adsorption and number of particles adsorbed for various adsorbates over an extremely wide range of temperatures and pressures from a set of simulations at just one temperature. We extend this derivation of the temperature extrapolation to adsorbates with intramolecular degrees of freedom when Rosenbluth sampling is employed. Consequently, the working capacity and isosteric heat can be computed for any given combined temperature/pressure swing adsorption process for a large range of operating conditions with both rigid and deformable adsorbates. Continuous thermodynamic properties can be computed with this technique at very moderate computational cost, thereby providing a strong case for its application to the in silico identification of promising nanoporous adsorbents.

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites.

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.

Accurate Characterization of the Pore Volume in Microporous Crystalline Materials.

Pore volume is one of the main properties for the characterization of microporous crystals. It is experimentally measurable, and it can also be obtained from the refined unit cell by a number of computational techniques. In this work, we assess the accuracy and the discrepancies between the different computational methods which are commonly used for this purpose, i.e, geometric, helium, and probe center pore volumes, by studying a database of more than 5000 frameworks. We developed a new technique to fully characterize the internal void of a microporous material and to compute the probe-accessible and -occupiable pore volume. We show that, unlike the other definitions of pore volume, the occupiable pore volume can be directly related to the experimentally measured pore volumes from nitrogen isotherms.

The Influence of Intrinsic Framework Flexibility on Adsorption in Nanoporous Materials.

For applications of metal-organic frameworks (MOFs) such as gas storage and separation, flexibility is often seen as a parameter that can tune material performance. In this work we aim to determine the optimal flexibility for the shape selective separation of similarly sized molecules (e.g., Xe/Kr mixtures). To obtain systematic insight into how the flexibility impacts this type of separation, we develop a simple analytical model that predicts a material's Henry regime adsorption and selectivity as a function of flexibility. We elucidate the complex dependence of selectivity on a framework's intrinsic flexibility whereby performance is either improved or reduced with increasing flexibility, depending on the material's pore size characteristics. However, the selectivity of a material with the pore size and chemistry that already maximizes selectivity in the rigid approximation is continuously diminished with increasing flexibility, demonstrating that the globally optimal separation exists within an entirely rigid pore. Molecular simulations show that our simple model predicts performance trends that are observed when screening the adsorption behavior of flexible MOFs. These flexible simulations provide better agreement with experimental adsorption data in a high-performance material that is not captured when modeling this framework as rigid, an approximation typically made in high-throughput screening studies. We conclude that, for shape selective adsorption applications, the globally optimal material will have the optimal pore size/chemistry and minimal intrinsic flexibility even though other nonoptimal materials' selectivity can actually be improved by flexibility. Equally important, we find that flexible simulations can be critical for correctly modeling adsorption in these types of systems.

Rational Design of a Low-Cost, High-Performance Metal-Organic Framework for Hydrogen Storage and Carbon Capture.

We present the in silico design of a MOF-74 analogue, hereon known as M2(DHFUMA) [M = Mg, Fe, Co, Ni, Zn], with enhanced small-molecule adsorption properties over the original M2(DOBDC) series. Constructed from 2,3-dihydroxyfumarate (DHFUMA), an aliphatic ligand which is smaller than the aromatic 2,5-dioxidobenzene-1,4-dicarboxylate (DOBDC), the M2(DHFUMA) framework has a reduced channel diameter, resulting in higher volumetric density of open metal sites and significantly improved volumetric hydrogen (H2) storage potential. Furthermore, the reduced distance between two adjacent open metal sites in the pore channel leads to a CO2 binding mode of one molecule per two adjacent metals with markedly stronger binding energetics. Through dispersion-corrected density functional theory (DFT) calculations of guest-framework interactions and classical simulation of the adsorption behavior of binary CO2:H2O mixtures, we theoretically predict the M2(DHFUMA) series as an improved alternative for carbon capture over the M2(DOBDC) series when adsorbing from wet flue gas streams. The improved CO2 uptake and humidity tolerance in our simulations is tunable based upon metal selection and adsorption temperature which, combined with the significantly reduced ligand expense, elevates this material's potential for CO2 capture and H2 storage. The dynamical and elastic stabilities of Mg2(DHFUMA) were verified by hybrid DFT calculations, demonstrating its significant potential for experimental synthesis.

Adsorbate-induced lattice deformation in IRMOF-74 series.

IRMOF-74 analogues are among the most widely studied metal-organic frameworks (MOFs) for adsorption applications because of their one-dimensional channels and high metal density. Most studies involving the IRMOF-74 series assume that the crystal lattice is rigid. This assumption guides the interpretation of experimental data, as changes in the crystal symmetry have so far been ignored as a possibility in the literature. Here, we report a deformation pattern, induced by the adsorption of argon, for IRMOF-74-V. This work has two main implications. First, we use molecular simulations to demonstrate that the IRMOF-74 series undergoes a deformation that is similar to the mechanism behind breathing MOFs, but is unique because the deformation pattern extends beyond a single unit cell of the original structure. Second, we provide an alternative interpretation of experimental small-angle X-ray scattering profiles of these systems, which changes how we view the fundamentals of adsorption in this MOF series.

Force-Field Prediction of Materials Properties in Metal-Organic Frameworks.

In this work, MOF bulk properties are evaluated and compared using several force fields on several well-studied MOFs, including IRMOF-1 (MOF-5), IRMOF-10, HKUST-1, and UiO-66. It is found that, surprisingly, UFF and DREIDING provide good values for the bulk modulus and linear thermal expansion coefficients for these materials, excluding those that they are not parametrized for. Force fields developed specifically for MOFs including UFF4MOF, BTW-FF, and the DWES force field are also found to provide accurate values for these materials' properties. While we find that each force field offers a moderately good picture of these properties, noticeable deviations can be observed when looking at properties sensitive to framework vibrational modes. This observation is more pronounced upon the introduction of framework charges.

In silico design and screening of hypothetical MOF-74 analogs and their experimental synthesis.

In this work we present the in silico design of metal-organic frameworks (MOFs) exhibiting 1-dimensional rod topologies. We introduce an algorithm for construction of this family of MOF topologies, and illustrate its application for enumerating MOF-74-type analogs. Furthermore, we perform a broad search for new linkers that satisfy the topological requirements of MOF-74 and consider the largest database of known chemical space for organic compounds, the PubChem database. Our in silico crystal assembly, when combined with dispersion-corrected density functional theory (DFT) calculations, is demonstrated to generate a hypothetical library of open-metal site containing MOF-74 analogs in the 1-D rod topology from which we can simulate the adsorption behavior of CO2. We finally conclude that these hypothetical structures have synthesizable potential through computational identification and experimental validation of a novel MOF-74 analog, Mg2(olsalazine).

Conjugated block copolymer photovoltaics with near 3% efficiency through microphase separation.

Organic electronic materials have the potential to impact almost every aspect of modern life including how we access information, light our homes, and power personal electronics. Nevertheless, weak intermolecular interactions and disorder at junctions of different organic materials limit the performance and stability of organic interfaces and hence the applicability of organic semiconductors to electronic devices. Here, we demonstrate control of donor-acceptor heterojunctions through microphase-separated conjugated block copolymers. When utilized as the active layer of photovoltaic cells, block copolymer-based devices demonstrate efficient photoconversion well beyond devices composed of homopolymer blends. The 3% block copolymer device efficiencies are achieved without the use of a fullerene acceptor. X-ray scattering results reveal that the remarkable performance of block copolymer solar cells is due to self-assembly into mesoscale lamellar morphologies with primarily face-on crystallite orientations. Conjugated block copolymers thus provide a pathway to enhance performance in excitonic solar cells through control of donor-acceptor interfaces.