Understanding and Controlling the Dielectric Response of Metal-Organic Frameworks

Computational Modeling of Reticular Materials: The Past, the Present, and the Future

Reticular materials rely on a unique building concept where inorganic and organic building units are stitched together giving access to an almost limitless number of structured ordered porous materials. Given the versatility of chemical elements, underlying nets, and topologies, reticular materials provide a unique platform to design materials for timely technological applications. Reticular materials have now found their way in important societal applications, like carbon capture to address climate change, water harvesting to extract atmospheric moisture in arid environments, and clean energy applications. Combining predictions from computational materials chemistry with advanced experimental characterization and synthesis procedures unlocks a design strategy to synthesize new materials with the desired properties and functions. Within this review, the current status of modeling reticular materials is addressed and supplemented with topical examples highlighting the necessity of advanced molecular modeling to design materials for technological applications. This review is structured as a templated molecular modeling study starting from the molecular structure of a realistic material towards the prediction of properties and functions of the materials. At the end, the authors provide their perspective on the past, present of future in modeling reticular materials and formulate open challenges to inspire future model and method developments.

Impact of Host-Guest Interactions on the Dielectric Properties of MFM-300 Materials

Metal-organic framework (MOF) materials are attracting increasing interest in the field of electronics due to their structural diversity, intrinsic porosity, and designable host-guest interactions. Here, we report the dielectric properties of a series of robust materials, MFM-300(M) (M = Al, Sc, Cr, Fe, Ga, In), when exposed to different guest molecules. MFM-300(Fe) exhibits the most notable increase in dielectric constant to 35.3 ± 0.3 at 10 kHz upon adsorption of NH3. Structural analysis suggests that the electron delocalization induced by host-guest interactions between NH3 and the MOF host, as confirmed by neutron powder diffraction studies, leads to structural polarization, resulting in a high dielectric constant for NH3@MFM-300(Fe). This is further supported by ligand-to-metal charge-transfer transitions observed by solid-state UV/vis spectroscopy. The high detection sensitivity and stability to NH3 suggest that MFM-300(Fe) may act as a powerful dielectric-based sensor for NH3.

Materials Quest for Advanced Interconnect Metallization in Integrated Circuits

Integrated circuits (ICs) are challenged to deliver historically anticipated performance improvements while increasing the cost and complexity of the technology with each generation. Front-end-of-line (FEOL) processes have provided various solutions to this predicament, whereas the back-end-of-line (BEOL) processes have taken a step back. With continuous IC scaling, the speed of the entire chip has reached a point where its performance is determined by the performance of the interconnect that bridges billions of transistors and other devices. Consequently, the demand for advanced interconnect metallization rises again, and various aspects must be considered. This review explores the quest for new materials for successfully routing nanoscale interconnects. The challenges in the interconnect structures as physical dimensions shrink are first explored. Then, various problem-solving options are considered based on the properties of materials. New materials are also introduced for barriers, such as 2D materials, self-assembled molecular layers, high-entropy alloys, and conductors, such as Co and Ru, intermetallic compounds, and MAX phases. The comprehensive discussion of each material includes state-of-the-art studies ranging from the characteristics of materials by theoretical calculation to process applications to the current interconnect structures. This review intends to provide a materials-based implementation strategy to bridge the gap between academia and industry.

Structure-Property Relationship of Piezoelectric Properties in Zeolitic Imidazolate Frameworks: A Computational Study

Metal-organic frameworks (MOFs) are a class of nanoporous crystalline materials with very high structural tunability. They possess a very low dielectric permittivity ε_r due to their porosity and hence are favorable for piezoelectric energy harvesting. Even though they have huge potential as piezoelectric materials, a detailed analysis and structure-property relationship of the piezoelectric properties in MOFs are lacking so far. This work focuses on a class of cubic non-centrosymmetric MOFs, namely, zeolitic imidazolate frameworks (ZIFs) to rationalize how the variation of different building blocks of the structure, that is, metal node and linker substituents affect the piezoelectric constants. The piezoelectric tensor for the ZIFs is computed from ab initio theoretical methods. From the calculations, we analyze the different contributions to the final piezoelectric constant d₁₄, namely, the clamped ion (e₁₄⁰) and the internal strain (e₁₄^int) contributions and the mechanical properties. For the studied ZIFs, even though e₁₄ (e₁₄⁰ + e₁₄^int) is similar for all ZIFs, the resultant piezoelectric coefficient d₁₄ calculated from piezoelectric constant e₁₄ and elastic compliance constant s₄₄ varies significantly among the different structures. It is the largest for CdIF-1 (Cd²⁺ and -CH₃ linker substituent). This is mainly due to the higher elasticity or flexibility of the framework. Interestingly, the magnitude of d₁₄ for CdIF-1 is higher than II-VI inorganic piezoelectrics and of a similar magnitude as the quintessential piezoelectric polymer polyvinylidene fluoride.

Water-Driven Structural Transformation in Cobalt Trimesate Metal-Organic Frameworks

We report on the synthesis and the characterization of a novel cobalt trimesate metal-organic framework, designated as KCL-102. Powder X-ray diffraction pattern of KCL-102 is dominated by a reflection at 10.2° (d-spacing = 8.7 Å), while diffuse reflectance UV-Vis spectroscopy indicates that the divalent cobalt centers are in two different coordination geometries: tetrahedral and octahedral. Further, the material shows low stability in humid air, and it transforms into the well-known phase of hydrous cobalt trimesate, Co3(BTC)2·12H2O. We associated this transition with the conversion of the tetrahedral cobalt to octahedral cobalt.

Investigation on the optical nonlinearity of the layered magnesium-mediated metal organic framework (Mg-MOF-74)

The wavelength-related optical nonlinearities of few-layer Mg-MOF-74 nanosheets were investigated in the wavelength region around 1.08, 1.94, and 2.85 μm by the closed aperture Z-scan, open aperture Z-scan and I-scan method. Under the excitation of 100-μJ laser pulses, the nonlinear refractive index (n₂) of -7.7 ± 2.6, -131 ± 5 and 4.9 ± 0.2 cm²/W were obtained, respectively. The wavelength-related optical nonlinearity of the Mg-MOF-74 nanosheet was also investigated. In 2.85 μm wavelength region, the Mg-MOF-74 nanosheets shows a stable saturable absorption property with a modulation depth of 8% and a saturation intensity of 170 mJ/cm². In the 1.08 and 1.94 μm wavelength regions, we can observe that the Mg-MOF-74 transits from saturable absorption regime to reverse saturable absorption regime with the increasing incident laser intensity. Employed as a saturable absorber in a Er:Lu₂O₃ laser, Mg-MOF-74 nanosheet shows a thickness-related laser modulation performance. The shortest laser pulse of 284-ns was achieved under a repetition rate of 116 kHz with a 6-nm-thick Mg-MOF-74 nanosheet, which corresponds to a pulse energy of 3.2 µJ and a peak power of 11.4 W.

Strongly Bound Excitons in Metal-Organic Framework MOF-5: A Many-Body Perturbation Theory Study

During the past years, one of the most iconic metal-organic frameworks (MOFs), MOF-5, has been characterized as a semiconductor by theory and experiments. Here we employ the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation to compute the electronic structure and optical properties of this MOF. The GW calculations show that MOF-5 is a wide-band-gap insulator with a fundamental gap of ∼8 eV. The strong excitonic effects, arising from highly localized states and low screening, result in an optical gap of 4.5 eV and in an optical absorption spectrum in excellent agreement with experiments. The origin of the incorrect conclusion reported by past studies and the implication of this result are also discussed.

Detailed total scattering analysis of disorder in ZIF-8

This work investigates the X-ray scattering signatures of disorder in the zeolitic imidazolate framework ZIF-8. Two layer disorder models are examined in reciprocal space and compared with conventional Rietveld analysis. Stacking faults along the [001] direction of the cubic lattice are in poor agreement with experimental powder diffraction data, consistent with previously reported density functional theory studies showing that these defects are energetically unfavorable compared with amorphization. Meanwhile, fluctuation of layer position along the [110] direction of the cubic lattice shows a significant agreement with experimental data. This result is interpreted analogously to an anisotropic strain mechanism, suggesting links between elastic anisotropy and crystallographic imperfections found in metal–organic framework materials. In direct space, it is demonstrated that models accounting for the static position disorder amongst the linker and metal sublattices are required to fit the experimental pair distribution function data.

Engineering entangled photon pairs with metal-organic frameworks

The discovery and design of new materials with competitive optical frequency conversion efficiencies can accelerate the development of scalable photonic quantum technologies. Metal-organic framework (MOF) crystals without inversion symmetry have shown potential for these applications, given their nonlinear optical properties and the combinatorial number of possibilities for MOF self-assembly. In order to accelerate the discovery of MOF materials for quantum optical technologies, scalable computational assessment tools are needed. We develop a multi-scale methodology to study the wavefunction of entangled photon pairs generated by selected non-centrosymmetric MOF crystals via spontaneous parametric down-conversion (SPDC). Starting from an optimized crystal structure, we predict the shape of the G (2) intensity correlation function for coincidence detection of the entangled pairs, produced under conditions of collinear type-I phase matching. The effective nonlinearities and photon pair correlation times obtained are comparable to those available with inorganic crystal standards. Our work thus provides fundamental insights into the structure-property relationships for entangled photon generation with metal-organic frameworks, paving the way for the automated discovery of molecular materials for optical quantum technology.

Metal-Organic Frameworks: Synthetic Methods and Potential Applications

Metal-organic frameworks represent a porous class of materials that are build up from metal ions or oligonuclear metallic complexes and organic ligands. They can be considered as sub-class of coordination polymers and can be extended into one-dimension, two-dimensions, and three-dimensions. Depending on the size of the pores, MOFs are divided into nanoporous, mesoporous, and macroporous items. The latter two are usually amorphous. MOFs display high porosity, a large specific surface area, and high thermal stability due to the presence of coordination bonds. The pores can incorporate neutral molecules, such as solvent molecules, anions, and cations, depending on the overall charge of the MOF, gas molecules, and biomolecules. The structural diversity of the framework and the multifunctionality of the pores render this class of materials as candidates for a plethora of environmental and biomedical applications and also as catalysts, sensors, piezo/ferroelectric, thermoelectric, and magnetic materials. In the present review, the synthetic methods reported in the literature for preparing MOFs and their derived materials, and their potential applications in environment, energy, and biomedicine are discussed.

Tuning the Electric Field Response of MOFs by Rotatable Dipolar Linkers

Recently the possibility of using electric fields as a further stimulus to trigger structural changes in metal-organic frameworks (MOFs) has been investigated. In general, rotatable groups or other types of mechanical motion can be driven by electric fields. In this study we demonstrate how the electric response of MOFs can be tuned by adding rotatable dipolar linkers, generating a material that exhibits paraelectric behavior in two dimensions and dielectric behavior in one dimension. The suitability of four different methods to compute the relative permittivity κ by means of molecular dynamics simulations was validated. The dependency of the permittivity on temperature T and dipole strength μ was determined. It was found that the herein investigated systems exhibit a high degree of tunability and substantially larger dielectric constants as expected for MOFs in general. The temperature dependency of κ obeys the Curie-Weiss law. In addition, the influence of dipolar linkers on the electric field induced breathing behavior was investigated. With increasing dipole moment, lower field strengths are required to trigger the contraction. These investigations set the stage for an application of such systems as dielectric sensors, order-disorder ferroelectrics, or any scenario where movable dipolar fragments respond to external electric fields.

Electron Density and Dielectric Properties of Highly Porous MOFs: Binding and Mobility of Guest Molecules in Cu3(BTC)2 and Zn3(BTC)2

Two isostructural highly porous metal-organic frameworks, the well-known {Cu₃(BTC)₂} _n (BTC = 1,3,5-benzenetricarboxylate), often appointed with the name HKUST-1, and {Zn₃(BTC)₂} _n, have been investigated as models for the buildup of dielectric properties, differentiating the role of chemi- and physisorbed guest molecules and that of specific intraframework and framework-guest linkages. For this purpose, electron charge density analysis, impedance spectroscopy, density functional theory simulations, and atomic partitioning of the polarizabilities have been exploited. These analyses at different degrees of pores filling enabled one to observe structural and electronic changes induced by guest molecules, especially when chemisorbed. The electrostatic potential inside the pores allows one to describe the absorption mechanism and to estimate the polarization of guests induced by the framework. The dielectric constant shows very diverse frequency dependence and magnitude of real and imaginary components as a consequence of (I) capture of guest molecules in the pores during synthesis, (II) MOF activation, and (III) water absorption from the atmosphere after activation. Comparison with calculated static-dielectric constant and atomic polarizabilities of the material has allowed for evaluating building blocks' contribution to the overall property, paving the way for reverse crystal engineering of these species.

Interpenetration Isomerism in Triptycene-Based Hydrogen-Bonded Organic Frameworks

We describe an example of "interpenetration isomerism" in three-dimensional hydrogen-bonded organic frameworks. By exploiting the crystallization conditions for a peripherally extended triptycene H₆ PET, we can modulate the interpenetration of the assembled frameworks, yielding a two-fold interpenetrated structure PETHOF-1 and a five-fold interpenetrated structure PETHOF-2 as interpenetration isomers. In PETHOF-1, two individual nets are related by inversion symmetry and form an interwoven topology with a large guest-accessible volume of about 80 %. In PETHOF-2, five individual nets are related by translational symmetry and are stacked in an alternating fashion. The activated materials show permanent porosity with Brunauer-Emmett-Teller surface areas exceeding 1100 m²  g^-1 . Synthetic control over the framework interpenetration could serve as a new strategy to construct complex supramolecular architectures from simple organic building blocks.

Dielectric Properties of Zeolitic Imidazolate Frameworks in the Broad-Band Infrared Regime

The field of metal-organic framework (MOF) materials is rapidly advancing toward practical applications; consequently, it is urgent to achieve a better understanding and precise control of their physical properties. Yet, research on the dielectric properties of MOFs is at its infancy, where studies are confined to the static dielectric behavior or lower-frequency response (kHz-MHz) only. Herein, we present the pioneering use of synchrotron-based infrared reflectivity experiments combined with density functional theory (DFT) calculations to accurately determine the dynamic dielectric properties of zeolitic imidazolate frameworks (ZIFs, a topical family of MOFs). We show, for the first time, the frequency-dependent dielectric response of representative ZIF compounds, bridging the near-, mid-, and far-infrared (terahertz, THz) broad-band frequencies. We establish the structure-property relations as a function of framework porosity and structural change. Our comprehensive results will pave the way for novel ZIF-based terahertz applications, such as infrared optical sensors and high-speed wireless communications.