An Implicit Function Theorem for One-sided Lipschitz Mappings

Implicit function theorems are derived for nonlinear set valued equations that satisfy a relaxed one-sided Lipschitz condition. We discuss a local and a global version and study in detail the continuity properties of the implicit set-valued function. Applications are provided to the Crank–Nicolson scheme for differential inclusions and to the analysis of differential algebraic inclusions.     

Diode-pumped efficient slab laser with two Nd:YLF crystals and second-harmonic generation by slab LBO

We demonstrate a diode-pumped electro-optical Q-switched slab laser with a high optical efficiency, high pulse energy, and short pulse width with two Nd:YLF crystals inside one resonator. The single compact slab resonator can generate a 1D top-hat beam at both the far field and the near field. With a slab-geometry-design lithium triborate (LBO) crystal, efficient critical phase-matching second-harmonic generation for a 1D top-hat beam with multiple transverse modes is achieved.     

First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions

The investigation of electron transport processes in nano-scale architectures plays a crucial role in the development of surface chemistry and nano-technology. Experimentally, an important driving force within this research area has been the concurrent refinements of scanning tunneling microscopy (STM) techniques. The theoretical treatment of the STM operation has traditionally been based on the Bardeen and Tersoff-Hamann methods which take as input the single-particle wave functions and eigenvalues obtained from finite cluster or slabs models of the surface-tip interface. Here, we present a novel STM simulation scheme based on non-equilibrium Green’s functions (NEGF) and Wannier functions which is both accurate and very efficient. The main novelty of the scheme compared to the Bardeen and Tersoff-Hamann approaches is that the coupling to the infinite (macroscopic) electrodes is taken into account. As an illustrating example we apply the NEGF-STM method to the Si(001)-(2×1):H surface with sub-surface P doping and discuss the results in comparison to the Bardeen and Tersoff-Hamann methods.     

In situ static and dynamic light scattering and scanning electron microscopy study on the crystallization of the dense zinc imidazolate framework ZIF-zni

The kinetics and mechanism of crystallization of the dense zinc imidazolate framework with zni topology, from comparatively dilute methanol solutions containing Zn(NO(3))·6H(2)O and imidazole with variation of the zinc-to-imidazole ratio, were followed in situ by time-resolved static and dynamic light scattering. The light scattering data revealed that metastable primary particles of about 100 nm in diameter form rapidly upon mixing the component solutions. After a lag time that is dependent on the imidazole concentration, the primary particles aggregate into secondary particles by a monomer addition mechanism with the primary particles as the monomers. Complementary scanning electron microscopy revealed that further evolution of the secondary particles is a complex process involving polycrystalline intermediates, the non-spherical morphologies of which depend on the initial zinc-to-imidazole ratio. Time and location of the first appearance of crystalline order could so far not be established. The pure-phase ZIF-zni crystals obtained after 240 min are twins. The aspect ratio of the tetragonal crystals can be controlled via the zinc-to-imidazole ratio.     

Partitioning of dual-lipidated peptides into membrane microdomains: lipid sorting vs peptide aggregation

The lateral membrane organization and phase behavior of the lipid mixture DMPC(di-C(14))/DSPC(di-C(18))/cholesterol (0-33 mol %) with and without an incorporated fluorescence-labeled palmitoyl/farnesyl dual-lipidated peptide, BODIPY-Gly-Cys(Pal)-Met-Gly-Leu-Pro-Cys(Far)-OMe, which represents a membrane recognition model system for Ras proteins, was studied by two-photon excitation fluorescence microscopy. Measurements were performed on giant unilamellar vesicles (GUVs) over a large temperature range, ranging from 30 to 80 degrees C to cover different lipid phase states (all-gel, fluid/gel, liquid-ordered, all-fluid). At temperatures where the fluid-gel coexistence region of the pure binary phospholipid system occurs, large-scale concentration fluctuations appear. Incorporation of cholesterol levels up to 33 mol % leads to a significant increase of conformational order in the membrane system and a reduction of large domain structures. Adding the peptide leads to dramatic changes in the lateral organization of the membrane. With cholesterol present, a phase separation is induced by a lipid sorting mechanism owing to the high affinity of the lipidated peptide to a fluid, DMPC-rich environment. This phase separation leads to the formation of peptide-containing domains with high fluorescence intensity that become progressively smaller with decreasing temperature. As a result, the local concentration of the peptide increases steadily within the confines of the shrinking domains. At the lowest temperatures, where the acyl-chain order parameter of the membrane has already drastically increased and the membrane achieves a liquid-ordered character, an efficient lipid sorting mechanism is no longer supported and aggregation of the peptide into small clusters prevails. We can conclude that palmitoyl/farnesyl dual-lipidated peptides do not associate with liquid-ordered or gel-like domains in phase-separated bilayer membranes. In particular, the study shows the interesting ability of the peptide to induce formation of fluid microdomains at physiologically relevant cholesterol concentrations, and this effect very much depends on the concentration of fluid vs ordered lipid molecules.     

Novel μ-membrane module for online determination of the free fatty acid content in the dispersed phase of oil-in-water emulsions

Monitoring the dispersed phase of an oil-in-water (O–W) emulsion by means of Fourier transform infrared (FTIR) spectroscopy is a challenging task, restricted to the continuous phase that is in contact with the FTIR probe. Nonetheless, real-time measurement and kinetic analysis by FTIR, including analysis of the dispersed, often non-polar phase containing substrates and/or products, is desirable. Enzymatic hydrolysis of sunflower oil was performed in an O–W emulsion. After separation of the oil phase by use of a newly developed μ-membrane module, infrared spectra were collected using an attenuated total reflectance (ATR) cell. Different chemometric models were calibrated using the partial least squares (PLS) algorithm. Online application of a chemometric model based on the FTIR spectra enabled real-time monitoring of free fatty acid concentrations in the oil phase.

NMR studies of carbon dioxide and methane self-diffusion in ZIF-8 at elevated gas pressures

Self-diffusion measurements with methane and carbon dioxide adsorbed in the Zeolitic Imidazolate Framework-8 (ZIF-8) were performed by ¹H and ¹³C pulsed field gradient nuclear magnetic resonance (PFG NMR). The experiments were conducted at 298 K and variable pressures of 7 to 15 bar in the gas phase above the ZIF-8 bed. Via known adsorption isotherms these pressures were converted to loadings of the adsorbed molecules. The self-diffusion coefficients of carbon dioxide measured by PFG NMR are found to be independent of loading. They are in good agreement with results from molecular dynamic (MD) simulations and resume the trend previously found by IR microscopy at lower loadings. Methane diffuses in ZIF-8 only slightly slower than carbon dioxide. Its experimentally obtained self-diffusion coefficients are about a factor of two smaller than the corresponding values determined by MD simulations using flexible frameworks.     

Measurements of fast fluctuations of viscoelastic properties with the quartz crystal microbalance

The quartz crystal microbalance (QCM) was used to study the variability of acoustic properties of living cells on the sub-second time scale. A confluent cell layer of rat cardiac myocytes was grown onto the electrode of quartz crystal resonator. The cell layer performed periodic, synchronous contractions at a rate of about 1.5 Hz. In order to monitor these rather fast changes in the state of the cells, the QCM was operated in a "fast mode", which allows sampling of the shift of the resonance frequency and energy dissipation with a rate of up to 100 Hz. The contractions were clearly reflected in periodic variations of the resonance frequency and the bandwidth. The rate of the contractions, in particular, could be easily detected in this way. Building on the rate of contraction, the setup can be used to monitor the response of the cell layer to heart stimulating drugs like isoproterenol. Depending on the concentration of isoproterenol, the beat rate was found to increase by up to a factor of two.