Influence of interfacial properties on Ostwald ripening in crosslinked multilayered oil-in-water emulsions

The influence of interfacial crosslinking, layer thickness and layer density on the kinetics of Ostwald ripening in multilayered emulsions at different temperatures was investigated. Growth rates of droplets were measured by monitoring changes in the droplet size distributions of 0.5% (w/w) n-octane, n-decane, and n-dodecane oil-in-water emulsions using static light scattering. Lifshitz-Slyozov-Wagner theory was used to calculate Ostwald ripening rates. A sequential two step process, based on electrostatic deposition of sugar beet pectin onto fish gelatin or whey protein isolate (WPI) interfacial membranes, was used to manipulate the interfacial properties of the oil droplets. Laccase was added to the fish gelatin-beet pectin emulsions to promote crosslinking of adsorbed pectin molecules via ferulic acid groups, whereas heat was induced to promote crosslinking of WPI and helix coil transitions of fish gelatin. Ripening rates of single-layered, double-layered and crosslinked emulsions increased as the chain length of the n-alkanes decreased. Emulsions containing crosslinked fish gelatin-beet pectin coated droplets had lower droplet growth rates (3.1 ± 0.3 × 10⁻²⁶ m³/s) than fish gelatin-stabilized droplets (7.3 ± 0.2 × 10⁻²⁶ m³/s), which was attributed to the formation of a protective network. Results suggest that physical or enzymatic biopolymer-crosslinking of interfaces may reduce the molecular transport of alkanes between the droplets in the continuous phase.     

Ruthenium(II)‐Catalyzed C?H Alkenylations of Phenols with Removable Directing Groups

Cationic ruthenium(II) complexes enabled oxidative alkenylations of phenols bearing easily cleavable directing groups. The optimized catalytic system allowed twofold C? H bond activations with excellent chemo‐, site‐, and diastereoselectivities. The double C? H functionalization process proceeded efficiently in an aerobic fashion under an atmosphere of ambient air. Detailed mechanistic studies were performed and provided strong support for an initial reversible C? H bond activation by the formation of six‐membered ruthenacycles as the key intermediates.     

Quantum walk with jumps

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi-ports can connect not to their nearest neighbor but to another multi-port at a fixed distance – we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping a universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.     

A posteriori error estimates for FEM with violated Galerkin orthogonality

This article investigates Petrov‐Galerkin discretizations of operator equations with linearly stable operators, where the residual does not belong to the annihilator W of the discrete test space W_h. Conforming and nonconforming methods are considered separately, and for the treatment of the nonconforming situation the concept of elliptic lifting is introduced. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 241–259, 2002; DOI 10.1002/num.1005     

Homogeneous ZnO Nanoparticles by Flame Spray Pyrolysis

Zinc oxide (ZnO) nanoparticles were made by flame spray pyrolysis (FSP) of zinc acrylate–methanol–acetic acid solution. The effect of solution feed rate on particle specific surface area (SSA) and crystalline size was examined. The average primary particle diameter can be controlled from 10 to 20nm by the solution feed rate. All powders were crystalline zincite. The primary particle diameter observed by transmission electron microscopy (TEM) was in agreement with the equivalent average primary particle diameter calculated from the SSA as well as with the crystalline size calculated from the X-ray diffraction (XRD) patterns for all powders, indicating that the primary particles were rather uniform in diameter and single crystals. Increasing the solution feed rate increases the flame height, and therefore coalescence and/or surface growth was enhanced, resulting in larger primary particles. Compared with ZnO nanoparticles made by other processes, the FSP-made powder exhibits some of the smallest and most homogeneous primary particles. Furthermore, the FSP-made powder has comparable BET equivalent primary particle diameter with but higher crystallinity than sol–gel derived ZnO powders.     

The Poisson Voronoi Tessellation II. Edge Length Distribution Functions

This paper presents a method for the determination of the distribution function of the length of the 'typical' edge of the Poisson Voronoi tessellation. The method is based on distributional properties of the configuration of the centres in the neighbourhood of the 'typical' vertex. The distribution and density functions of the edge lengths are given in double integral form for various dimensions. Analogous characteristics are considered for two-dimensional sections through higher-dimensional Poisson Voronoi tessellations.