Water transport on infinite graphs

If the nodes of a graph are considered to be identical barrels – featuring different water levels – and the edges to be (locked) water‐filled pipes in between the barrels, consider the optimization problem of how much the water level in a fixed barrel can be raised with no pumps available, that is, by opening and closing the locks in an elaborate succession. This model is related to an opinion formation process, the so‐called Deffuant model. We consider the initial water profile to be given by i.i.d. unif(0,1) random variables, investigate the supremum of achievable water levels at a given node – or to be more precise, the support of its distribution – and ask in which settings it becomes degenerate, that is, reduces to a single value. This turns out to be the case for all infinite connected quasi‐transitive graphs, with exactly one exception: the two‐sided infinite path

Survey of classical density functionals for modelling hydrogen physisorption at 77 K

This work surveys techniques based on classical density functionals for modeling the quantum dispersion of physisorbed hydrogen at 77 K. Two such techniques are examined in detail. The first is based on the "open ring approximation" (ORA) of Broukhno et al., and it is compared with a technique based on the semiclassical approximation of Feynman and Hibbs (FH). For both techniques, a standard classical density functional is used to model hydrogen molecule-hydrogen molecule (i.e., excess) interactions. The three-dimensional (3D) quantum harmonic oscillator (QHO) system and a model of molecular hydrogen adsorption into a graphitic slit pore at 77 K are used as benchmarks. Density functional results are compared with path-integral Monte Carlo simulations and with exact solutions for the 3D QHO system. It is found that neither of the density functional treatments are entirely satisfactory. However, for hydrogen physisorption studies at 77 K the ORA based technique is generally superior to the FH based technique due to a fortunate cancellation of errors in the density functionals used. But, if more accurate excess functionals are used, the FH technique would be superior

Functionalised metal-organic frameworks: a novel approach to stabilising single metal atoms

We have investigated the potential of metal-organic frameworks for immobilising single atoms of transition metals using a model system of Pd supported on NH2-MIL-101(Cr). Our Transmission Electron Microscopy and in-situ Raman spectroscopy results give evidence for the first time that functionalised metal-organic frameworks may support, isolate and stabilise single atoms of palladium. Using Thermal Desorption Spectroscopy we were able to evaluate the proportion of single Pd atoms. Furthermore, in a combined theoretical-experimental approach, we show that the H-H bonds in a H2 molecule elongate by over 15% through the formation of a complex with single atoms of Pd. Such deformation would affect any hydrogenation reaction and thus the single atoms supported on metal-organic frameworks may become promising single atom catalysts in the future

Hausdorff spectrum of harmonic measure

For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding harmonic measure is comparable with Hausdorfff measure on the boundary. Moreover, we introduce one parameter family of probability measures which interpolates a Patterson-Sullivan measure and the harmonic measure, and establish a formula of Hausdorff spectrum (multifractal spectrum) of the harmonic measure. We also give some finitary versions of dimensional properties of the harmonic measure

How to functionalise metal–organic frameworks to enable guest nanocluster embedment

We report on the development and verification of an enhanced computational model capable of robust predictions and yielding a single descriptor to the successful embedding of guest nanoclusters into the pores of functionalised metal-organic frameworks. Using the predictions of this model, we have been able to embed Pd nanoclusters in the pores of Br-UiO-66 and show that the embedding of Pd nanoclusters in both (OH)2-UiO-66 and (Cl)2-UiO-66 is not successful. Also, using various independent methods, we identified the strong host-guest interactions that anchor the guest nanoclusters inside the Br-UiO-66 framework which result in the surface modification of said nanoclusters. We demonstrated that the level of this surface modification is a direct function of the framework functional groups. This new approach for the rational design of nanocluster-metal-organic framework systems, and a demonstrated tool box for their characterisation, will promote the exploitation of surface modification of nanoclusters via their embedding into functionalised metal-organic framework pores

Interplay of Linker Functionalization and Hydrogen Adsorption in the Metal–Organic Framework MIL-101

Functionalization of metal–organic frameworks results in higher hydrogen uptakes owing to stronger hydrogen–host interactions. However, it has not been studied whether a given functional group acts on existing adsorption sites (linker or metal) or introduces new ones. In this work, the effect of two types of functional groups on MIL-101 (Cr) is analyzed. Thermal-desorption spectroscopy reveals that the −Br ligand increases the secondary building unit’s hydrogen affinity, while the −NH2 functional group introduces new hydrogen adsorption sites. In addition, a subsequent introduction of −Br and −NH2 ligands on the linker results in the highest hydrogen-store interaction energy on the cationic nodes. The latter is attributed to a push-and-pull effect of the linkers

Developments in the Ni–Nb–Zr amorphous alloy membranes

Most of the global H2 production is derived from hydrocarbon-based fuels, and efficient H2/CO2 separation is necessary to deliver a high-purity H2 product. Hydrogen-selective alloy membranes are emerging as a viable alternative to traditional pressure swing adsorption processes as a means for H2/CO2 separation. These membranes can be formed from a wide range of alloys, and those based on Pd are the closest to commercial deployment. The high cost of Pd (USD *31,000 kg-1) is driving the development of less-expensive alternatives, including inexpensive amorphous (Ni60Nb40)100-xZrx alloys. Amorphous alloy membranes can be fabricated directly from the molten state into continuous ribbons via melt spinning and depending on the composition can exhibit relatively high hydrogen permeability between 473 and 673 K. Here we review recent developments in these low-cost membrane materials, especially with respect to permeation behavior, electrical transport properties, and understanding of local atomic order. To further understand the nature of these solids, atom probe tomography has been performed, revealing amorphous Nb-rich and Zr-rich clusters embedded in majority Ni matrix whose compositions deviated from the nominal overall composition of the membrane

Entwicklung und Untersuchung eines 100-kV-Elektronen-Feldemissionsstrahlers fuer die Rastermikroskopie

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