A Computational and Experimental Approach Linking Disorder,High‐Pressure Behavior,and Mechanical Properties in UiO Frameworks

Whilst many metal–organic frameworks possess the chemical stability needed to be used as functional materials, they often lack the physical strength required for industrial applications. Herein, we have investigated the mechanical properties of two UiO‐topology Zr‐MOFs, the planar UiO‐67 ([Zr₆O₄(OH)₄(bpdc)₆], bpdc: 4,4′‐biphenyl dicarboxylate) and UiO‐abdc ([Zr₆O₄(OH)₄(abdc)₆], abdc: 4,4′‐azobenzene dicarboxylate) by single‐crystal nanoindentation, high‐pressure X‐ray diffraction, density functional theory calculations, and first‐principles molecular dynamics. On increasing pressure, both UiO‐67 and UiO‐abdc were found to be incompressible when filled with methanol molecules within a diamond anvil cell. Stabilization in both cases is attributed to dynamical linker disorder. The diazo‐linker of UiO‐abdc possesses local site disorder, which, in conjunction with its longer nature, also decreases the capacity of the framework to compress and stabilizes it against direct compression, compared to UiO‐67, characterized by a large elastic modulus. The use of non‐linear linkers in the synthesis of UiO‐MOFs therefore creates MOFs that have more rigid mechanical properties over a larger pressure range.     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.     

A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip

This paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically use a non‐physical equation of state in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi‐component systems containing gases of differing molecular masses. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. The new model developed for multi‐component gases avoids the pitfalls of some other LB models. A single computational grid is shared by all the species, and the diffusivity is independent of the viscosity. The Navier–Stokes equation for the mixture and the Stefan–Maxwell diffusion equation are both recovered by the model. Diffusion slip, the non‐zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one‐dimensional model for channel flow. To increase the accuracy of the scheme, a second‐order numerical implementation is needed. This may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright © 2011 John Wiley & Sons, Ltd.     

Measurement of k 0 values for caesium and iridium

The OPAL research reactor in Australia has been used to determine k ₀ values for ^134mCs, ¹³⁴Cs, ¹⁹²Ir and ¹⁹⁴Ir. Values for ²⁴Na have also been measured for quality control. The neutron flux at the irradiation positions was very highly thermalised (f > 2,000), resulting in almost negligible activation by epithermal neutrons. As a consequence, the contribution to the total uncertainty of the k ₀ values from epithermal-related factors such as Q ₀ and $ \bar{E}_{\text{r}} $ was very small. The measured caesium k ₀ values have been compared with the library values as well as with recent measurements by St Pierre et al. and Farina Arboccò et al. While there are k ₀ values for ¹⁹⁴Ir in the library, no ¹⁹²Ir values have been measured previously. Despite ¹⁹²Ir having a higher sensitivity than ¹⁹⁴Ir, k ₀ values were not measured during the establishment of the k ₀-method because the nuclear data available at the time indicated that the activation cross-section of ¹⁹¹Ir deviated significantly from 1/v behaviour (g(T _n ) ≠ 1), which would result in unacceptable errors if k ₀ analysis were to be carried out using the Høgdahl convention. However later nuclear data compilations showed that ¹⁹¹Ir has better 1/v behaviour than previously reported, making it suitable for k ₀ analysis using the Høgdahl convention. For completeness, k ₀ values have been determined using both the Høgdahl and modified-Westcott conventions and these have been compared with library (¹⁹⁴Ir) and calculated values.     

Microporated PEG Spheres for Fluorescent Analyte Detection

Poly(ethylene glycol) (PEG) hydrogels have been used to encapsulate fluorescently labeled molecules in order to detect a variety of analytes. The hydrogels are designed with a mesh size that will retain the sensing elements while allowing for efficient diffusion of small analytes. Some sensing assays, however, require a conformational change or binding of large macromolecules, which may be sterically prohibited in a dense polymer matrix. A process of hydrogel microporation has been developed to create cavities within PEG microspheres to contain the assay components in solution. This arrangement provides improved motility for large sensing elements, while limiting leaching and increasing sensor lifetime. Three hydrogel compositions, 100% PEG, 50% PEG, and microporated 100% PEG, were used to create pH-sensitive microspheres that were tested for response time and stability. In order to assess motility, a second, more complex sensor, namely a FITC-dextran/TRITC-Con A glucose-specific assay was encapsulated within the microspheres.     

Formation and emission of tetraalkylammonium salt molecular ions sputtered from a gelatin matrix

A gelatin matrix was simultaneously doped with nine equimolar, homologous, tetraalkylammonium salts ranging in mass from 210 to 700 Da. Bombardment of the sample with kiloelectronvolt ions resulted in a nonidentical distribution of relative cation intensities with a maximum at m/z 242 for samples with a total salt concentration of 0.004 g of salt/g of gelatin. A rapid increase in relative intensities with increasing mass is observed for the low mass salts and is believed to be linked to changes in the ionization efficiencies. The changes in ionization efficiencies are likely related to decreasing coulombic attractive forces between the organic cation and the counterion. Disappearance cross-sections, determined from decay curves, indicate that sputter-induced damage increases with increasing mass of the cation. Fragment-to-intact cation ratios also suggest that damage accumulates fastest in the heaviest salts. These observations indicate that desorption yields of the organic salts in a gelatin matrix decrease with increasing mass. In addition, suppression of lower mass tetraalkylammonium salt intact cation intensities was observed for salt-in-gelatin concentrations greater than 10⁻³ g/g.     

Iodine stabilised 640 nm helium-neon laser

The wavelength of a helium-neon laser operating at 640 nm coincides with two strong absorption lines in the spectrum of iodine-127 when the gain tube is filled with neon-22. The absorption lines have been identified by measuring their hyperfine structure and the performance of the laser has been investigated. The beat frequency pair variance between two similar lasers was 7.6 kHz for a 10-second averaging time and the wavelength of component g of the 8-5 P(10) line was measured as 640.2834686 nm.     

Low temperature elastic constants and Debye temperature of NbO2

The transit times of ultrasonic waves have been measured in single crystal NbO₂ from 295 K down to 1.5 K for quasilongitudinal and shear waves propagating in the [100] direction and down to 160 K for eight other waves. Values are obtained for the C₄₄ elastic constant and for an elastic constant combination which is approximately equal to C₁₁ for temperatures down to 1.5 K and for C₁₁, C₁₂, C₁₃, C₁₆, C₃₃, and C₆₆ down to 160 K. These results are used to deduce 0 K values for the elastic constants and an elastic Debye temperature of 596 ± 7 K at 1.5 K. The acoustic mode heat capacity calculated from the latter is significantly smaller than the heat capacity measured by Wenger and Keesom at low temperatures. Following Wenger and Keesom, the difference is attributed to phasons (excitations involving the phase modulation of charge density waves). An average velocity is deduced for the phasons.