Parallel and totally geodesic hypersurfaces of non-reductive homogeneous four-manifolds

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.     

Unusual chain length dependent adsorption of linear and branched alkanes on UiO-66

In this work, the zero coverage adsorption properties of C₅–C₁₀ n- and iso-alkanes on the UiO-66, UiO-66-Me and UiO-66-NO₂ metal–organic frameworks are studied by gas phase pulse chromatography. Analysis of enthalpy values, entropy values, Gibbs free energies and Henry constants reveals unusual chain length dependent adsorption behaviour of linear and branched alkanes, caused by the complex structure of the zirconium metal–organic framework UiO-66. The UiO-66 structure consists of a small, tetrahedral and large, octahedral cage. It is shown that at specific carbon chain lengths (e.g. C₆–C₇ for n-alkanes), distinctive jumps in adsorption enthalpy, entropy values and Henry constants occur. This chain length dependent effect is even more pronounced for 2- and 3-methyl alkanes and double branched alkanes. This distinctive shift in adsorption behaviour occurs at a molecular size that coincides with the cavity dimensions of the smallest, tetrahedral cage. The resulting selective adsorption arises from confinement effects and is function of both the molecular shape and size.     

Higher Order Parallel Surfaces in Bianchi–Cartan–Vranceanu Spaces

We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e., in the so-called Bianchi–Cartan–Vranceanu family. This gives a positive answer to a conjecture formulated in [2]. As a partial result, we prove that totally umbilical surfaces only exist if the ambient Bianchi–Cartan–Vranceanu space is a Riemannian product of a surface of constant Gaussian curvature and the real line, and we give a local parametrization of all totally umbilical surfaces. Received: December 20, 2006. Revised: March 15, 2007.     

Sequences of harmonic maps in the 3‐sphere

We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold . As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.     

Experimental investigation of the difference in B-term dominated band broadening between fully porous and porous-shell particles for liquid chromatography using the Effective Medium Theory

The difference in B-term diffusion between fully porous and porous-shell particles is investigated using the physically sound diffusion equations originating from the Effective Medium Theory (EMT). Experimental data of the B-term diffusion obtained via peak parking measurements on six different commercial particle types have been analyzed (3 porous and 3 non porous). All particles were investigated using the same experimental design and test analytes, over a very broad range of retention factor values. First, the B-term reducing effect of the solid core (inducing an additional obstruction compared to fully porous particles) has been quantified using the Hashin-Shtrikman expression, showing that the presence of a solid core can account for a reduction of about 11% when the core diameter makes up 63% of the total particle diameter (Halo and Poroshell-particles) and a reduction of 16% when the core diameter makes up 73% (Kinetex). Remaining differences can be attributed to differences in the microscopic structure of the meso-porous material (meso-pore diameter, internal porosity or relative void volume). The much lower B-term diffusion of Halo and Kinetex particles compared to the fully porous Acquity particles (some 20-40% difference, of which about 10-15% can be attributed to the presence of the solid core) can hence largely be attributed to the much smaller internal porosity and the smaller pore size of the meso-porous material making up the shell of these particles.     

Activation of the metal-organic framework MIL-47 for selective adsorption of xylenes and other difunctionalized aromatics

The capacity and selectivity of the metal-organic framework MIL-47 for liquid phase adsorption are shown to heavily depend on the pretreatment of the material, as illustrated in detail by the particular case of selective xylene adsorption. By totally removing the uncoordinated terephthalic acid from the pores and simultaneously avoiding oxidation to nonporous V(2)O(5), pore volume and uptake of xylenes can be maximized. The presence of uncoordinated terephthalic acid in the pores improves the selectivity between p- and m-xylene. Calcination bed thickness and oven geometry influence the optimal calcination procedure. The physicochemical modifications of MIL-47 during its activation are investigated in detail with XRD, SEM, nitrogen physisorption, TGA and diffuse reflectance UV-Vis spectroscopy. Using optimally pretreated MIL-47 as adsorbent for xylene, ethyltoluene, dichlorobenzene, toluidine or cresol isomers, the para-isomer is in each case preferred over the meta-isomer in pulse chromatographic and batch experiments. The role of stacking in the selective adsorption of these isomers is discussed. In the case of the dichlorobenzenes, the meta- and para-isomers can be separated in a breakthrough experiment with a selectivity of 5.0.     

Pore-filling-dependent selectivity effects in the vapor-phase separation of xylene isomers on the metal-organic framework MIL-47

Vapor-phase adsorption and separation of the C8 alkylaromatic components p-xylene, m-xylene, o-xylene, and ethylbenzene on the metal-organic framework MIL-47 have been studied. Low coverage Henry adsorption constants and adsorption enthalpies were determined using the pulse chromatographic technique at temperatures between 230 and 290 degrees C. The four C8 alkylaromatic components have comparable Henry constants and adsorption enthalpies. Adsorption isotherms of the pure components were determined using the gravimetric technique at 70, 110, and 150 degrees C. The adsorption capacity and steepness of the isotherms differs among the components and are strongly temperature dependent. Breakthrough experiments with several binary mixtures were performed at 70-150 degrees C and varying total hydrocarbon pressure from 0.0004 to 0.05 bar. Separation of the different isomers could be achieved. In general, it was found that the adsorption selectivity increases with increasing partial pressure or degree of pore filling. The separation at a high degree of pore filling in the vapor phase is a result of differences in packing modes of the C8 alkylaromatic components in the pores of MIL-47.     

Length exclusion in the adsorption of chain molecules on chabazite type zeolites

In the adsorption of linear C1-C8 alkanes, alkenes and alcohols on zeolite chabazite, molecules smaller than 6.7 A are adsorbed in significant amounts, whereas longer chains are almost fully excluded from the micropores.     

Experiments with Organic Modifiers in Reversed-Flow MEKC

Reversed-flow MEKC, i.e. MEKC at low pHs to suppress the electroosmotic flow, was evaluated for the separation of some homologous series. At low pHs compared to MEKC, the elution order reverses and normal phase type migration is obtained. Moreover, the elution window is nearly infinite. Efficiencies are very high and reproducibilities in absolute migration times are acceptable (%RSD < 5). The influence of a series of alcohol modifiers was investigated.