Numerical Stability of Lanczos Methods

The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form $\psi^\dagger g(A) \psi$. We show that this quadrature evaluation is numerically stable and explain how the numerical errors which are such a fundamental element of the finite precision Lanczos tridiagonalisation procedure are automatically and exactly compensated in the Bai, Fahey and Golub algorithm. In the process, we shed new light on the mechanism by which roundoff error corrupts the Lanczos procedureComment: 3 pages, Lattice 99 contributio

Tuning palladium selective oxidation catalysts via mesoporous supports

Surfactant templating provides a facile route to mesoporous materials with tuneable architectures, whilst simultaneously allowing control over complementary macro and micro porosity. The impact of these varying physical properties, on both catalyst synthesis and during catalytic reactions, was one principal area of investigation. Catalyst series were prepared on mesoporous SBA-15, SBA-16 and KIT-6, meso-macroporous SBA-15, true liquid crystal templated SBA-15 and a commercial low surface area silica support. Additionally two mesoporous alumina series, with mesoporosity akin to SBA-15, were produced. The catalytic activity of the materials was screened for the selective oxidation of allylic alcohols, which represents a class of industrially relevant chemical upgrading reactions. Nanoparticulate palladium is widely recognised as an able catalytic species, although the active site nature is still debated with both metallic and oxidic surfaces proposed. Further insight into the active species was another major area of investigation. Extensive characterisation confirmed successful support synthesis and mesopore stability after palladium impregnation. Irrespective of support, decreasing metal loading elevates dispersion (particles sizes are typically less than 2nm), which correlates with the increase of surface PdO content. In relation to the silica supports these trends escalate via support transition in the order of: Pd/low surface area commercial silica < Pd/true liquid crystal templated SBA-15 < Pd/SBA-15 < Pd/mesomacroporous SBA-15 < Pd/KIT-6 ≈ Pd/SBA-16. Initially increasing support surface area is critical and later rising mesopore accessibility dictates. Catalytic activity, for cinnamyl and crotyl alcohol selective oxidation, reveals significant rateenhancements with PdO content, with turnover frequencies providing compelling proof of a PdO active species. Alumina supports, even with lower surface areas than equivalent silicas, allow further gains in metal dispersion, surface oxidation state and resulting catalytic activity. In conclusion, tuning the physical and chemical properties of the support is paramount if highly active catalysts are to be produced.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Highly selective hydrogenation of furfural over supported Pt nanoparticles under mild conditions

The selective liquid phase hydrogenation of furfural to furfuryl alcohol over Pt nanoparticles supported on SiO₂, ZnO, γ-Al2O₃, CeO₂ is reported under extremely mild conditions. Ambient hydrogen pressure, and temperatures as low as 50 °C are shown sufficient to drive furfural hydrogenation with high conversion and >99% selectivity to furfuryl alcohol. Strong support and solvent dependencies are observed, with methanol and n-butanol proving excellent solvents for promoting high furfuryl alcohol yields over uniformly dispersed 4 nm Pt nanoparticles over MgO, CeO₂ and γ-Al₂O₃. In contrast, non-polar solvents conferred poor furfural conversion, while ethanol favored acetal by-product formation. Furfural selective hydrogenation can be tuned through controlling the oxide support, reaction solvent and temperature

Tuning palladium selective oxidation catalysts via mesoporous supports

Surfactant templating provides a facile route to mesoporous materials with tuneable architectures, whilst simultaneously allowing control over complementary macro and micro porosity. The impact of these varying physical properties, on both catalyst synthesis and during catalytic reactions, was one principal area of investigation. Catalyst series were prepared on mesoporous SBA-15, SBA-16 and KIT-6, meso-macroporous SBA-15, true liquid crystal templated SBA-15 and a commercial low surface area silica support. Additionally two mesoporous alumina series, with mesoporosity akin to SBA-15, were produced. The catalytic activity of the materials was screened for the selective oxidation of allylic alcohols, which represents a class of industrially relevant chemical upgrading reactions. Nanoparticulate palladium is widely recognised as an able catalytic species, although the active site nature is still debated with both metallic and oxidic surfaces proposed. Further insight into the active species was another major area of investigation. Extensive characterisation confirmed successful support synthesis and mesopore stability after palladium impregnation. Irrespective of support, decreasing metal loading elevates dispersion (particles sizes are typically less than 2nm), which correlates with the increase of surface PdO content. In relation to the silica supports these trends escalate via support transition in the order of: Pd/low surface area commercial silica < Pd/true liquid crystal templated SBA-15 < Pd/SBA-15 < Pd/mesomacroporous SBA-15 < Pd/KIT-6 ≈ Pd/SBA-16. Initially increasing support surface area is critical and later rising mesopore accessibility dictates. Catalytic activity, for cinnamyl and crotyl alcohol selective oxidation, reveals significant rateenhancements with PdO content, with turnover frequencies providing compelling proof of a PdO active species. Alumina supports, even with lower surface areas than equivalent silicas, allow further gains in metal dispersion, surface oxidation state and resulting catalytic activity. In conclusion, tuning the physical and chemical properties of the support is paramount if highly active catalysts are to be produced

Extending the range of liquids available for NMR cryoporometry studies of porous materials

Nuclear magnetic resonance (NMR) cryoporometry, although well established, can be limited by the inability of any one liquid to probe a broad range of pore sizes, a relatively small number of commonly-used probe liquids and the requirement to match the probe liquid to the chemistry of the material being studied. Here we demonstrate, for the first time, the use of menthol and t-butanol as probe liquids in NMR cryoporometry measurements. Using appropriate estimates for the values of the melting point depression constant, kc, and the non-freezing surface layer, 2sl, NMR melting data was converted into pore size distributions. The melting point depression constant for t-butanol is similar to that of cyclohexane; however due to its functionality, t-butanol may be the preferred liquid used to study the porosity of hydrophilic materials. Menthol, having a larger value of kc, can accurately analyze larger pore sizes up to 100 nm. This represents the first use of menthol and t-butanol to accurately probe pore dimensions in NMR cryoporometry

NMR cryoporometric measurements of porous silica:A method for the determination of melting point depression parameters of probe liquids

Nuclear magnetic resonance (NMR) cryoporometry is a non-invasive method for determining the pore size distributions of materials such as porous silica. Cryoporometry has several advantages over other porometric techniques. It is able to measure the melting process in a series of discrete steps, whereas transient heat flow techniques, such as differential scanning calorimetry (DSC), have a minimum rate of measurement, and, secondly, NMR cryoporometry can analyze pore shapes with any geometry, where nitrogen porosimetry is complicated for samples with spherical pores with narrow necks. However, one key drawback of the method is that, for any one liquid observed in any one material, there is a lack of consensus in the two parameters, kckc andView the MathML source2sl , used to convert experimental NMR melting point depression data into a pore size distribution. By considering two decades worth of literature data, values for both were obtained for water in porous silica supports, in particular an estimate of a non-freezing layer between the solid ice and the inner surface of the pore. These values were used to produce pore size distributions for three silica materials, SBA-15 and KIT-6, both with cylindrical pores but possessing different structures, and SBA-16, which has spherical pores. This represents the first time KIT-6 has been characterized by the NMR method. Furthermore, this work demonstrates a general method for obtaining values for kckc and View the MathML source2sl which can be applied to any liquid for which suitable literature data is available

Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction

We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.Comment: 18 pages, 19 figures, 1 tabl

Alkali-Free Zn–Al Layered Double Hydroxide Catalysts for Triglyceride Transesterification

Zn–Al layered double hydroxides (LDHs) of general formula [Zn2+(1−x)Al3+x(OH)2]x+(CO32−)x/2·yH2O are promising solid base catalysts for the transesterification of lipids to biofuels. However, conventional synthetic routes employ alkali hydroxide/carbonate precipitants which may contaminate the final LDH catalyst and biofuel. The use of (NH3)2CO3 and NH3OH as precipitants affords alkali-free Zn–Al-LDHs spanning a wide composition range. The hydrothermal reconstruction of calcined Zn–Al-LDHs offers superior solid basicity and catalytic activity for the transesterification of C4–C18 triglycerides with methanol, compared with cold liquid phase or vapour phase reconstruction. Hydrothermally activated Zn3.3–Al-LDH was stable towards leaching during transesterification

Tailored mesoporous silica supports for Ni catalysed hydrogen production from ethanol steam reforming

Mesoporous silica supported Ni nanoparticles have been investigated for hydrogen production from ethanol steam reforming. Ethanol reforming is structure-sensitive over Ni, and also dependent on support mesostructure; three-dimensional KIT-6 possessing interconnected mesopores offers superior metal dispersion, steam reforming activity, and on-stream stability against deactivation compared with a two-dimensional SBA-15 support