Weak Relaxation Research Articles

Magnetic-field coils for metastability-exchange optical pumping, spectroscopy, and magnetic resonance of helium.

Optical pumping on the 23S-23P transition (1083nm) of metastable 3He or 4He atoms is used for science and applications. Gas is usually enclosed in elongated cells with lengths ranging from several centimeters to several meters for efficient absorption. Good magnetic-field homogeneity is needed for weak diffusion-induced relaxation and long nuclear magnetic resonance (NMR) signal lifetimes. A compact coil system is designed using a target-oriented numerical optimization method. It provides a suitably uniform field over cell volumes, with characteristics depending on the chosen optimization parameters. Additional pairs of coils can be used to generate transverse field components with contributions to the total field inhomogeneities that are discussed.

Road network, landing location, and routing optimization for forest smallholders landscapes

AbstractWe present two mixed integer linear programming (MILP) formulations for a well‐known integrated network, timber landing location, and routing problem that arises in forest management. The models seek to jointly optimize the construction and maintenance schedule of forest road networks with landing site selection and transportation routing for timber production. This problem is, in general, difficult to solve as it contains the so‐called fixed charge network flow problem, which is known to be NP‐hard. One of the proposed MILP formulations considers 3‐index continuous variables to represent timber flows on road segments in each period. The presence of Big‐M constraints leads to weak linear relaxation bounds. Disaggregating flow variables, according to timber origin, results in a novel 4‐index formulation with very tight linear relaxation bounds. Nevertheless, the number of variables increases prohibitively. This research makes use of spatial constraints common to Smallholding Forested Landscapes to develop a solution approach that reduces the number of flow variables in the new 4‐index model. Results from a real‐world case study located in Northwest Portugal show that, with the 4‐index formulation, the proposed solution approach makes it possible to obtain optimal solutions in a short computational time.

Dislocations in twistronic heterostructures

Long-period moiré superlattices at the twisted interface of van der Waals heterostructures relax into preferential stacking domains separated by dislocation networks. Here, we develop a mesoscale theory for dislocations in networks formed in twistronic bilayers with parallel (P) and antiparallel (AP) alignment of unit cells across the twisted interface. For P bilayers we find an exact analytical displacement field across partial dislocations and determine analytic dependences of energy per unit length and width on the orientation and microscopic model parameters. For AP bilayers we formulate a semi-analytical approximation for displacement fields across perfect dislocations, establishing parametric dependences for their widths and energies per unit length. In addition, we find regions in the parametric space of crystal thicknesses and Moiré periods for strong and weak relaxation of the Moiré pattern in multilayered twistronic heterostructures.

A novel exact formulation for parallel machine scheduling problems

Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations.

Crystallization kinetics of (S)-4'-(1-methylheptyloxycarbonyl)biphenyl-4-yl 4-[4-(2,2,3,3,4,4,4-heptafluorobutoxy)but-1-oxy]-2-fluorobenzoate.

Chiral liquid crystalline compounds belonging to the homologous series of (S)-4'-(1-methylheptyloxycarbonyl)biphenyl-4-yl 4-[m-(2,2,3,3,4,4,4-heptafluorobutoxy)alk-1-oxy]-2-fluorobenzoates show various behaviors on cooling depending on the length of the CmH2m chain. The homologue with m = 2 crystallizes, while for m = 5, 6, 7, and presumably also for m = 3, the glass of the anticlinic smectic CA* phase is formed. The previous results for m = 4 suggest that this homologue may also be a glassformer. This paper presents the study of the crystallization kinetics for the compound with m = 4 in isothermal conditions (by polarizing optical microscopy) and for the 5-40 K min-1 cooling rates (by differential scanning calorimetry). Microscopic observations enable estimation of the energy barrier for nucleation, which equals 409 kJ mol-1. The threshold cooling rate necessary for complete vitrification of the smectic CA* phase, obtained by extrapolating the enthalpy change during crystallization to zero, is equal to 81 K min-1 or 64 K min-1 for the linear and parabolic fits, respectively. The structural studies by X-ray diffraction show that crystal phases have lamellar structures both in the pristine sample and after crystallization from the melt but with different layer spacing. A weak relaxation process is detected in the sample after melt crystallization, revealing the presence of the conformational disorder. The dynamic glass transition temperature of the SmCA* phase, estimated from the relaxation time of the PH process (as the α-relaxation time could not be registered in a wide enough temperature range), is 244 K.

The mechanism of ferroelectric phase transformation in Gd2O3 modified BCZT ceramics: Experimental studies and first-principles calculations

Lead-free (Ba0.85Ca0.15)(Ti0.90Zr0.10)O3 (BCZT)-based piezoelectric ceramics have attracted considerable interest due to their excellent piezoelectric properties and abundant phase structures. However, there is a serious lack in the theoretical calculations for the ferroelectric phase transition behavior. Here, the experimental and first-principles calculations were utilized to analyze the ferroelectric phase transition process of (Ba0.85Ca0.15)(Ti0.90Zr0.10)O3-xGd2O3(BCZT-xGd, x = 0, 0.02, 0.04, and 0.05) ceramics. The incorporation of Gd2O3 has induced a transformation from tetragonal to rhombohedral phase due to the decrease in the dislocation energy with A-site cations and the attenuation of the bonding energy between B-site cations and the planar O atoms. Moreover, the hybridization between the d orbitals of B-site atoms and the O 2p orbitals, coupled with the reduction of the polarization vector along the [001] axis, leads to enhanced weak coupling relaxation. This work provides a theoretical basis for the ferroelectric phase transition behavior of other piezoelectric systems.

Inzhektsiya spina dvizhushcheysya domennoy stenkoy na granitse razdela antiferromagnitnogo izolyatora s dvumernym metallom

A domain wall (DW) which moves parallel to a magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional (2D) metal can pump spin polarization into the metal. It is assumed that localized spins of a collinear AFMI interact with itinerant electrons through their exchange interaction on the interface. We employed the Keldysh formalism of Green’s functions for electrons which experience potential and spin-orbit scattering on random impurities. This formalism allows a unified analysis of spin pumping, spin diffusion and spin relaxation effects on a 2D electron gas. It is shown that the pumping of a nonstaggered magnetization into the metal film takes place in the second order with respect to the interface exchange interaction. At sufficiently weak spin relaxation this pumping effect can be much stronger than the first-order effect of the Pauli magnetism which is produced by the small nonstaggered exchange field of the DW. It is shown that the pumped polarization is sensitive to the geometry of the electron’s Fermi surface and increases when the wave vector of the staggered magnetization approaches the nesting vector of the Fermi surface. In a disordered diffusive electron gas the induced spin polarization follows the motion of the domain wall. It is distributed asymmetrically around the DW over a distance which can be much larger than the DW width.

Dielectric behavior and impedance spectroscopy of Niobium substituted Lanthanum based orthovanadates at high temperatures

We present the detailed study of the temperature dependent dielectric properties, impedance spectroscopy and electrical conductivity of LaV1−xNbxO4 (x=0–1) samples prepared by the solid-state reaction method. The dielectric constant (ϵr′) increases (decreases) with increase in the temperature (frequency); while, the magnitude of ϵr′ remains almost invariant (order of 104 at 100 Hz and 600 °C) with x. The single phase x=0 (monoclinic-monazite, P21/n) and x=1 (monoclinic fergusonite, I2/a) samples show the lower values of loss factor [tanδ= (4–8)] as compared to the x=0–0.8 samples [tanδ= (12–18)] having mixed tetragonal and monoclinic phases, which indicates the strong correlation between the crystal structure and the dielectric properties. The real part of impedance (Z′) decreases with both temperature and frequency, and the observed weak relaxation remains almost unaltered with x. The imaginary part of impedance (Z′′) shows strong relaxation peaks shifting towards higher temperatures with frequency, which is attributed to the effect of grains, grain boundaries, and electrodes in the samples. The activation energy of the relaxation process is estimated to be 0.8–1.0 eV for the x=0–0.6 samples, and ≈1.4 eV for the x=0.8; whereas the x=1 sample shows two values (≈0.5 eV and ≈1.0 eV) in the higher and lower temperature range, respectively. Further, the change in total conductivity with the angular frequency, which found to be in the range of 10−3 to 10−5 S/m, is fitted using the Jonsher power law. The analysis suggests the overlapping large polaron tunneling (OLPT) model for all the samples, whereas the x = 1 sample exhibit a transition near 480 °C and at higher temperatures it shows non-overlapping small polaron tunneling (NSPT) and quantum mechanical tunneling (QMT). This transition is corroborated by the tangent loss curves and may be associated with the change in structure.

High‐performance poly(methylsilane arylether arylacetylene) resins with low curing temperatures and weak secondary relaxations

AbstractA series of poly(methylsilane arylether arylacetylene) (PSEA‐H) resins were synthesized from methyldichlorosilane and isomeric arylether arylacetylenes, and characterized by 1H‐NMR and FT‐IR spectroscopies. The effect of reactive Si‐H groups and the linking positions of benzene rings in the arylether arylacetylene units on the properties of the resins were investigated. The results show that PSEA‐H resins possess good processability with processing windows of over 80°C. The introduction of Si‐H groups reduces the curing temperatures for PSEA‐H resins and weakens the secondary relaxation for the cured PSEA‐H resins. The cured resins and T300 carbon fiber (T300CF) reinforced composites display high mechanical properties. The flexural strengths of a cured PSEA‐H resin and its T300CF composite at room temperature reach 64.2 and 426.5 MPa, respectively. The flexural properties depend on the linking positions of benzene rings. The cured PSEA‐H resins show excellent heat resistance with a temperature of 5% weight loss (Td5) above 500°C.

Polymer architecture effect on rheology and segmental dynamics in poly (methyl methacrylate)-silica nanocomposite melts.

Architecturally different polymer chains lead to fundamentally different rheological responses and internal dynamics, which can be utilized to rationalize advanced thermoplastic nanocomposites with tunable mechanical behavior. In this work, three model poly (methyl methacrylate) (PMMA) polymers with linear, bottlebrush, and star architectures with the same total molar mass were investigated in their neat form, and nanocomposites with well-dispersed silica nanoparticles using rheology and broadband dielectric spectroscopy (BDS). The master curves of the dynamic moduli obtained by time-temperature superposition (TTS) over the entire range from the Rouse regime to the terminal flow and a sequence of significantly different relaxation modes were observed for the samples with linear and branch chains. While linear chains form an entangled polymer network, the branched bottlebrush, and star chains show a viscoelastic response with no sign of rubbery entanglement plateau and a weak arm relaxation regime between Rouse and terminal flow, akin to other branched polymers. Moreover, branched chains showed a higher fragility index (m = 3.46 for the bottlebrush and 5.36 for the star) compared to linear chains (m = 3.29) due to dynamical heterogeneities induced by arm relaxation. The addition of nanoparticles affects only the terminal relaxation regime, where the whole chain motion is hindered by the attractive nanoparticles. The dynamics of the polymer segment were investigated by performing broadband dielectric spectroscopy (BDS) at a frequency range from 10-2 Hz to 107 Hz. The results revealed more than 10 times slower segmental relaxation for the star homopolymers and a slowdown in the α-relaxation process for all three architectures in their composite form. The dynamical slowdown in the composites is temperature dependent and more pronounced at low temperatures (leading to approximately equal to 80 times slower dynamics for nanocomposite with bottlebrush PMMA at 150 °C) due to prolonged relaxation of the interfacial polymer compared to the matrix chains. The results from this study have practical applications in fields such as gas separation and polymeric electrolyte membranes, where simultaneous improvement of segmental mobility and mechanical moduli is highly desired.

Hybrid organic/inorganic interface: in situ and ex situ characterization in terms of structure, morphology, electronic and magnetic properties

Organic conjugated molecules are promising media to host spin-polarized carriers, due to their weak spin relaxation mechanisms. Here, we fabricated a metal–hybrid organic–inorganic complex oxide heterostructure made of Fe–Phthalocyanine (FePc): Co(0.5 nm)/FePc(0; 0.5; 1 nm)/La0.67Sr0.33MnO3/SrTiO3 and investigated the interface structure and chemical bonding, and overall magnetic properties. Details about the Co/FePc and FePc/LSMO interfaces were obtained through X-ray photoelectron and absorption characterizations. The combined in-situ and ex-situ magnetic measurements of the heterostructure indicates the contribution of FePc and Co moments to the overall magnetic response. Moreover, these measurements indicate that the LSMO bulk magnetic properties were not canceled out by the surface treatment, but favored the formation of a magnetic dead layer. The hybrid heterostructure presents a modification of the saturation magnetization attributed to the contribution of the molecular layer. The present results are a step forward in the engineering of hybrid organic/inorganic interfaces.

Reliable network design considering endogenous customers’ choices under probabilistic arc failures

We consider a reliable network design where the facility location and road ban decisions are jointly optimized to minimize the total expected costs and risks against uncertain exogenous arc-dependent failures and customers’ endogenous interactions. We formulate endogenous customers’ choices by incorporating an expressive measure, Cumulative prospect theory, into the widely used multinomial logit model. Additionally, we use a well-known downside measure, Conditional value-at-risk, for the designer to control integrated risks from exogenous arc failures and endogenous customers’ choices. Accordingly, a mixed-integer trilinear program is developed. To solve the model, we first transform it into a class of mixed-integer linear programs based on the separable structure. Then, a customized branch-and-Benders-cut algorithm is proposed to solve these mixed-integer linear programs. We devise a set of novel valid inequalities based on the endogenous transition of choice probability to strengthen the weak relaxation of the master problem. Moreover, by aggregating the grouping and dual iterations shrinking techniques for solving sub-problems, the branch-and-Benders-cut algorithm can converge within 30 seconds and the whole problem can be solved within 15 minutes for a network with 90 nodes and 149 road segments. Some managerial insights for balancing risk and cost are finally extracted.

Enhancement of Sphingomyelinase-Induced Endothelial Nitric Oxide Synthase-Mediated Vasorelaxation in a Murine Model of Type 2 Diabetes.

Sphingolipids are important biological mediators both in health and disease. We investigated the vascular effects of enhanced sphingomyelinase (SMase) activity in a mouse model of type 2 diabetes mellitus (T2DM) to gain an understanding of the signaling pathways involved. Myography was used to measure changes in the tone of the thoracic aorta after administration of 0.2 U/mL neutral SMase in the presence or absence of the thromboxane prostanoid (TP) receptor antagonist SQ 29,548 and the nitric oxide synthase (NOS) inhibitor L-NAME. In precontracted aortic segments of non-diabetic mice, SMase induced transient contraction and subsequent weak relaxation, whereas vessels of diabetic (Leprdb/Leprdb, referred to as db/db) mice showed marked relaxation. In the presence of the TP receptor antagonist, SMase induced enhanced relaxation in both groups, which was 3-fold stronger in the vessels of db/db mice as compared to controls and could not be abolished by ceramidase or sphingosine-kinase inhibitors. Co-administration of the NOS inhibitor L-NAME abolished vasorelaxation in both groups. Our results indicate dual vasoactive effects of SMase: TP-mediated vasoconstriction and NO-mediated vasorelaxation. Surprisingly, in spite of the general endothelial dysfunction in T2DM, the endothelial NOS-mediated vasorelaxant effect of SMase was markedly enhanced.

Structure, morphological and dielectric properties of BZT-BST ceramics

Barium zirconate titanate (BZT), a relaxor ferroelectric ceramic based on barium titanate (BT), has received substantial research. In this study, Ba(Zr0.2Ti0.8)O3 and Ba0.85Sr0.15TiO3 were separately prepared by solid state method and thereafter they were mixed in the following ratio (1-x){Ba(Zr0.2Ti0.8)O3} – x{Ba0.85Sr0.15TiO3} (x = 0, 0.1, 0.2) (BZT-BST) to make ceramic composite using high energy ball mill. The structure, morphology, and dielectric properties of these composites have been systematically studied. The crystal structure of the BZT-BST composite was determined by X-ray diffraction technique. The XRD pattern shows a well-developed tetragonal perovskite crystal structure. Without a second phase, all samples exhibit the perovskite structured BZT diffraction peaks. Permittivity measurements show that the relative permittivity (εr) of the composite increases as the amount of BST increases from × = 0 to × = 0.1, but then decreases at × = 0.2, indicating a broad transition in dielectric constant. The observed Curie temperatures (Tc) for all the compositions mentioned are 31 °C, 36 °C, and 43 °C, of ​​which the dielectric maximum for each composition is found to be ∼ 5000, 6100, and 3810 at the frequency of 1 kHz. It can be seen that the relative permittivity (εr) of all three BZT-BST compositions decreases gradually with increasing frequency. At low frequency, there are several different polarizations mechanisms. However, at high frequencies, only electronic displacement polarization exists. Morphological analysis of the sintered samples by Field emission scanning electron microscopy (FESEM) shows that the pure BZT ceramics have numerous pores. The compactness of BZT-BST ceramics was significantly enhanced by the addition of BST. The grain size of BZT-BST ceramics increases with increasing BST content. Pure BZT ceramics exhibit ferroelectric diffusion phase transition characteristics with weak relaxation behaviour. BZT-BST composites exhibit increasing relaxation behaviour with increasing BST content. These may be the most promising candidate materials for capacitor applications.

Investigations of axioms of twist grain boundary phases (TGBPs) in binary mixture of liquid crystals

In this paper, the investigated mixture of liquid crystals shows a spacious range of twist grain boundary phases (TGBPs). Thermo dynamical, optical and dielectric measurements confirmed the presence of TGBPs in the mixtures of nematic and cholesteric liquid crystals. In the heating cycle, differential scanning calorimetry (DSC) thermogram shows the mixed different TGBPs at the high scanning rate. Cylindrical and cone-like textures with brushes of TGBA* is observed under the optical investigation. The grain boundaries and blocks of smectic phases are twisting two times around an axis. Wide-ranging dielectric investigation of nematic and cholesteric liquid crystal mixture have been performed in the 50 Hz–10 MHz range of frequency for the homogeneous conditions. In the absence of direct bias, TGBA* phase exhibits two dielectric relaxation processes, soft mode (SM) and process in the grain boundaries (PGBs). In the presence of electric field, grain boundaries steadily demolished the phases. Whereas the weak dielectric relaxation processes have been distinguished in the presence of the electric field in the TGBPs.

A branch and bound algorithm for robust binary optimization with budget uncertainty

Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due to its weak linear relaxation. To overcome the problems arising from the weak formulation, we propose a bilinear formulation for robust binary programming, which is as strong as theoretically possible. From this bilinear formulation, we derive strong linear formulations as well as structural properties for robust binary optimization problems, which we use within a tailored branch and bound algorithm. We test our algorithm’s performance together with other approaches from the literature on a diverse set of “robustified” real-world instances from the MIPLIB 2017. Our computational study, which is the first to compare many sophisticated approaches on a broad set of instances, shows that our algorithm outperforms existing approaches by far. Furthermore, we show that the fundamental structural properties proven in this paper can be used to substantially improve the approaches from the literature. This highlights the relevance of our findings, not only for the tested algorithms, but also for future research on robust optimization. To encourage the use of our algorithms for solving robust optimization problems and our instances for benchmarking, we make all materials freely available online.

Spin dynamics in a Heisenberg weak antiferromagnetic chain of an iodide-bridged Cu(II) complex.

[CuII(chxn)2I]I (chxn = 1R,2R-diaminocyclohexane) has been synthesized, which is the first report of an iodide-bridged Cu(II) chain structure. This chain compound shows S = 1/2 Heisenberg weak antiferromagnetism (J = -0.3 cm-1) and magnetic relaxation (τ = 43 ms at 1.8 K) with a Raman process in a static field.

Structural, rheological and functional properties of extruded mozzarella cheese influenced by the properties of the renneted casein gels

Renneted casein gels, often named cheese curds, are traditionally pre-heated by immersion in water before stretching, which influences cheese functional properties. This work aims to understand the effect of pre-heating (cooking) on extrusion process of cheese curds at 80 and 90 °C in a lab twin-screw, co-rotating extruder, and consequences for composition, microstructure and functional properties of the extrudates. The cooking significantly enhanced curd meltability and oiling-off, resulting in faster extrusion, higher exit temperature and lower specific mechanical energy. Microscopic observations at different length scales, combining confocal laser scanning microscopy and X-ray micro-tomography, showed that cooking caused extensive fat coalescence and cracks in protein matrix, resulting in extrudates with less fibrous structure, lower elasticity and tensile strength. The extrusion process induced significantly increased of calcium bridges in extrudates, which may replace weak water-protein interactions and increase relaxation time of the more mobile water fraction (T2.2). The specific mechanical energy was less influenced by the extrusion temperature in cooked than uncooked curds, likely due to a more extensive oiling-off during extrusion of the cooked curd. In agreement with the microscopic observations, extrudates obtained at 80 °C differ from 90 °C specially regarding fat content respectively 23.8–24.8% and 29.5% (w/w) and fat globule size and distribution, influencing fiber formation. In general curds extruded at 90 °C had higher elasticity and tensile strength, which was related to the well-elongated fat domains. This study provided knowledge about extrusion process of curds generating new ideas to improve cheese processing and design customized cheese products.

Phase Sequence, Kinetics of Crystallization and Molecular Dynamics of the Chiral Liquid Crystalline Compound Forming a Hexatic Smectic Glass

The vitrification of the antiferroelectric hexatic smectic XA* phase and cold crystallization are reported for (S)-4′-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[5-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]benzoate. The kinetics of isothermal cold crystallization and melt crystallization are investigated, revealing that both are controlled mainly by diffusion, as indicated by decrease in the characteristic crystallization time with increasing temperature of crystallization, with an activation energy of 114 kJ/mol. A weak relaxation process is detected in a crystal phase, with an activation energy of 38 kJ/mol, implying the conformationally disordered crystal phase. The estimated fragility parameter of the investigated glass former is equal to 94.5, which indicates rather high fragility.

Stable Lanthanide Metal-Organic Frameworks with Ratiometric Fluorescence Sensing for Amino Acids and Tunable Proton Conduction and Magnetic Properties.

Four new isostructural lanthanide metal-organic frameworks (MOFs), namely {[Ln(DMTP-DC)1.5(H2O)3]·DMF}n [H2DMTP-DC = 2',5'-dimethoxytriphenyl-4,4″-dicarboxylic acid; LnIII = EuIII (1), GdIII (2), TbIII (3), and DyIII (4)], have been synthesized and characterized. Single-crystal structure analysis reveals that 1-4 are three-dimensional Ln-MOFs with rich H-bonding of coordinated H2O molecules in the network channels. The X-ray diffraction patterns indicate that Ln-MOF 1 displays good stabilities in organic solvents and aqueous solutions with distinct pH values. Both 1 and 3 show characteristic emission of LnIII ions. Ln-MOF 1 can be used as a ratiometric fluorescence sensor for arginine and lysine in aqueous solution, and the detection limits are 24.38 μM for arginine and 9.31 μM for lysine. All 1-4 show proton conductivity related to relative humidity (RH) and temperature, and the maximum conductivity values of 1-4 at 55 °C and 100% RH are 9.94 × 10-5, 1.62 × 10-4, 1.71 × 10-4, and 2.67 × 10-4 S·cm-1, respectively. The value of σ increases with the decrease in ionic radius, indicating that the radius of the LnIII ions can regulate the proton conductivity of these MOFs. Additionally, 2 exhibits a significant magnetocaloric effect (MCE) with a magnetic entropy change (-ΔSm) of 18.86 J kg-1 K-1 for ΔH = 7 T at 2 K, and 4 shows weak field-induced slow relaxation of magnetization. The coexistence of good fluorescence sensing capability, attractive proton conductivity, and relatively large MCE in Ln-MOFs is rare, and thus, 1-4 are potentially multifunctional MOF materials.