A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorder

We study a colloidal model system where disorder can be continuously tuned from no disorder --corresponding to a system that can crystallize-- to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.     

Dynamics of semi-flexible tethered sheets : a simulation study using stochastic rotation dynamics

The dynamics of a semi-flexible sheet or tethered membrane in a solvent is studied using the method of stochastic rotation dynamics. Hydrodynamic interactions between different parts of the sheet are naturally included in this method. We confirm the scaling law for the radius of gyration versus sheet size predicted for a self-avoiding tethered membrane. The mean-square displacement shows both sub-diffusive and diffusive behavior similar to linear polymers. In the intermediate scattering function the sub-diffusive behavior appears as stretched exponential which we reproduce in our simulations. Thereby, we confirm an early prediction between the roughness and the sub-diffusion exponent derived from Zimm dynamics (E. Frey, D.R. Nelson, J. Phys. I 1, 1715 (1991)). Finally, we show that the diffusion coefficient of the square sheet is inversely proportional to the edge length of the sheet again in good agreement with theoretical predictions.     

Triphilic Ionic‐Liquid Mixtures: Fluorinated and Non‐fluorinated Aprotic Ionic‐Liquid Mixtures

We present here the possibility of forming triphilic mixtures from alkyl‐ and fluoroalkylimidazolium ionic liquids, thus, macroscopically homogeneous mixtures for which instead of the often observed two domains—polar and nonpolar—three stable microphases are present: polar, lipophilic, and fluorous ones. The fluorinated side chains of the cations indeed self‐associate and form domains that are segregated from those of the polar and alkyl domains. To enable miscibility, despite the generally preferred macroscopic separation between fluorous and alkyl moieties, the importance of strong hydrogen bonding is shown. As the long‐range structure in the alkyl and fluoroalkyl domains is dependent on the composition of the liquid, we propose that the heterogeneous, triphilic structure can be easily tuned by the molar ratio of the components. We believe that further development may allow the design of switchable, smart liquids that change their properties in a predictable way according to their composition or even their environment.     

Immobilized β-cyclodextrin on surface-modified carbon-coated cobalt nanomagnets: reversible organic contaminant adsorption and enrichment from water

Surface-modified magnetic nanoparticles can be used in extraction processes as they readily disperse in common solvents and combine high saturation magnetization with excellent accessibility. Reversible and recyclable adsorption and desorption through solvent changes and magnetic separation provide technically attractive alternatives to classical solvent extraction. Thin polymer layered carbon-coated cobalt nanoparticles were tagged with β-cyclodextrin. The resulting material reversibly adsorbed organic contaminants in water within minutes. Isolation of the immobilized inclusion complex was easily carried out within seconds by magnetic separation due to the strong magnetization of the nanomagnets (metal core instead of hitherto used iron oxide). The trapped molecules were fully and rapidly recovered by filling the cyclodextrin cavity with a microbiologically well accepted substitute, e.g., benzyl alcohol. Phenolphthalein was used as a model compound for organic contaminants such as polychlorinated dibenzodioxins (PCDDs) or bisphenol A (BPA). Fast regeneration of nanomagnets (compared to similar cyclodextrin-based systems) under mild conditions resulted in 16 repetitive cycles (adsorption/desorption) at full efficiency. The high removal and regeneration efficiency was examined by UV-vis measurements at chemical equilibrium conditions and under rapid cycling (5 min). Experiments at ultralow concentrations (160 ppb) underline the high potential of cyclodextrin modified nanomagnets as a fast, recyclable extraction method for organic contaminants in large water streams or as an enrichment tool for analytics.     

Electronic coupling and scaling effects during dielectric barrier electrospray ionization

The mechanism of the previously published technique of dielectric barrier electrospray ionization (DB-ESI) was investigated in more detail. Two independent current signals occurring during the DB-ESI could be explained and allocated to sub-processes. The modulated shape of the HV signal, the applied frequency as well as the inner diameter of the emitter capillary have a big impact on the spray. Furthermore, there exists a cut-off frequency which depends on the electronic properties of the DB-ESI interface. Comparable mass spectra for lysine employing both conventional ESI and DB-ESI show a good analytical potential of the new technique.     

The Edge Correlation of Random Forests

The conjecture was made by Kahn that a spanning forest F chosen uniformly at random from all forests of any finite graph G has the edge-negative association property. If true, the conjecture would mean that given any two edges ε₁ and ε₂ in G, the inequality \mathbbP(e₁ ? F, e₂ ? F) ￡ \mathbbP(e₁ ? F)\mathbbP(e₂ ? F){{\mathbb{P}(\varepsilon_{1} \in \mathbf{F}, \varepsilon_{2} \in \mathbf{F}) \leq \mathbb{P}(\varepsilon_{1} \in \mathbf{F})\mathbb{P}(\varepsilon_{2} \in \mathbf{F})}} would hold. We use enumerative methods to show that this conjecture is true for n large enough when G is a complete graph on n vertices. We derive explicit related results for random trees.