By taking advantage of a conformal mapping technique, we propose designs for various optical elements such as directional antennas, flat lenses, or bends. In contrast to most of the existing design approaches, the elements can be implemented with isotropic materials, thus strongly facilitating their fabrication. We furthermore generalize the concept and show that under certain conditions previously suggested devices consisting of anisotropic materials may be replaced by isotropic ones using an appropriate transformation. The designs are double-checked by full-wave simulations. A comparison with their anisotropic counterparts reveals a similar performance.

Dispersions of crystalline nanoparticles with at least one sufficiently large unit cell dimension can give rise to Bragg reflections in the small-angle scattering range. If the nanocrystals possess only a small number of unit cells along these particular crystallographic directions, the corresponding Bragg reflections will be broadened. In a previous study of phospholipid stabilized dispersions of β-tripalmitin platelets [Unruh, J. Appl. Crystallogr. 40, 1008 (2007)], the x-ray powder pattern simulation analysis (XPPSA) was developed. The XPPSA method facilitates the interpretation of the rather complicated small-angle x-ray scattering (SAXS) curves of such dispersions of nanocrystals. The XPPSA method yields the distribution function of the platelet thicknesses and facilitates a structural characterization of the phospholipid stabilizer layer at the solid-liquid interface between the nanocrystals and the dispersion medium from the shape of the broadened 001 Bragg reflection. In this contribution an improved and extended version of the XPPSA method is presented. The SAXS and small-angle neutron scattering patterns of dilute phospholipid stabilized tripalmitin dispersions can be reproduced on the basis of a consistent simulation model for the particles and their phospholipid stabilizer layer on an absolute scale. The results indicate a surprisingly flat arrangement of the phospholipid molecules in the stabilizer layer with a total thickness of only 12 Å. The stabilizer layer can be modeled by an inner shell for the fatty acid chains and an outer shell including the head groups and additional water. The experiments support a dense packing of the phospholipid molecules on the nanocrystal surfaces rather than isolated phospholipid domains.

ZnO nanoparticles (NPs) have great potential for their use in, e.g., thin film solar cells due to their electro-optical properties adjustable on the nanoscale. Therefore, the production of well-defined NPs is of major interest. For a targeted production process, the knowledge of the stabilization layer of the NPs during and after their formation is of particular importance. For the study of the stabilizer layer of ZnO NPs prepared in a wet chemical synthesis from zinc acetate, only ex situ studies have been performed so far. An acetate layer bound to the surface of the dried NPs was found; however, an in situ study which addresses the stabilizing layer surrounding the NPs in a native dispersion was missing. By the combination of small angle scattering with neutrons and X-rays (SANS and SAXS) for the same sample, we are now able to observe the acetate shell in situ for the first time. In addition, the changes of this shell could be followed during the ripening process for different temperatures. With increasing size of the ZnO core (d(core)) the surrounding shell (d(shell)) becomes larger, and the acetate concentration within the shell is reduced. For all samples, the shell thickness was found to be larger than the maximum extension of an acetate molecule with acetate concentrations within the shell below 50 vol %. Thus, there is not a monolayer of acetate molecules that covers the NPs but rather a swollen shell of acetate ions. This shell is assumed to hinder the growth of the NPs to larger macrostructures. In addition, we found that the partition coefficient μ between acetate in the shell surrounding the NPs and the total amount of acetate in the solution is about 10% which is in good agreement with ex situ data determined by thermogravimetric analysis.

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Aqueous suspensions of platelet-like shaped tripalmitin nanocrystals are studied here at high tripalmitin concentrations (10 wt % tripalmitin) for the first time by a combination of small-angle X-ray and neutron scattering (SAXS and SANS). The suspensions are stabilized by different lecithins, namely, DLPC, DOPC, and the lecithin blend S100. At such high concentrations the platelets start to self-assemble in stacks, which causes interference maxima at low Q-values in the SAXS and SANS patterns, respectively. It is found that the stack-related interference maxima are more pronounced for the suspension stabilized with DOPC and in particular DLPC, compared to suspensions stabilized by S100. By use of the X-ray and neutron powder pattern simulation analysis (XNPPSA), the SAXS and SANS patterns of the native tripalmitin suspensions could only be reproduced simultaneously when assuming the presence of both isolated nanocrystals and stacks of nanocrystals of different size in the simulation model of the dispersions. By a fit of the simulated SAXS and SANS patterns to the experimental data, a distribution of the stack sizes and their volume fractions is determined. The volume fraction of stacklike platelet assemblies is found to rise from 70% for S100-stabilized suspensions to almost 100% for the DLPC-stabilized suspensions. The distribution of the platelet thicknesses could be determined with molecular resolution from a combined analysis of the SAXS and SANS patterns of the corresponding diluted tripalmitin (3 wt %) suspensions. In accordance with microcalorimetric data, it could be concluded that the platelets in the suspensions stabilized with DOPC, and in particular DLPC, are significantly thinner than those stabilized with S100. The DLPC-stabilized suspensions exhibit a significantly narrower platelet thickness distribution compared to DOPC- and S100-stabilized suspensions. The smaller thicknesses for the DLPC- and DOPC-stabilized platelets explain their higher tendency to self-assemble in stacks. The finding that the nanoparticles of the suspension stabilized by the saturated lecithin DLPC crystallize in the stable β-tripalmitin modification with its characteristic platelet-like shape is surprising and can be explained by the fact that the main phase transformation temperature for DLPC is, as for unsaturated lecithins like DOPC and S100, well below the crystallization temperature of the supercooled tripalmitin emulsion droplets.