Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures

In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1–204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally, we illustrate the behavior of the model with various numerical simulations.     

Zur Aequivalenz bilinearer alternierender Formen

Ohne Zusammenfassung     

Synthesis of arborescent polystyrene‐g‐[poly(2‐vinylpyridine)‐b‐polystyrene] core–shell–corona copolymers

Arborescent copolymers with a core‐shell‐corona (CSC) architecture, incorporating a polystyrene (PS) core, an inner shell of poly(2‐vinylpyridine), P2VP, and a corona of PS chains, were obtained by anionic polymerization and grafting. Living PS‐b‐P2VP‐Li block copolymers serving as side chains were obtained by capping polystyryllithium with 1,1‐diphenylethylene before adding 2‐vinylpyridine. A linear or arborescent (generation G0 – G3) PS substrate, randomly functionalized with acetyl or chloromethyl coupling sites, was then added to the PS‐b‐P2VP‐Li solution for the grafting reaction. The grafting yield and the coupling efficiency observed in the synthesis of the arborescent PS‐g‐(P2VP‐b‐PS) copolymers were much lower than for analogous coupling reactions previously used to synthesize arborescent PS homopolymers and PS‐g‐P2VP copolymers from the same types of coupling sites. It was determined from static and dynamic light scattering analysis that PS‐b‐P2VP formed aggregates in THF, the solvent used for the synthesis. This presumably hindered coupling of the macroanions with the substrate, and explains the low grafting yield and coupling efficiency observed in these reactions. Purification of the crude products was also problematic due to the amphipolar character of the CSC copolymers and the block copolymer contaminant. A new fractionation method by cloud‐point centrifugation was developed to purify copolymers of generations G1 and above. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1075–1085     

Instrumentation, standards, and procedures used at the National Research Council of Canada for high-accuracy fluorescence measurements

This paper describes the two-monochromator reference spectrofluorimeter, calibration standards, and procedures used at the National Research Council of Canada for performing high-accuracy fluorescence measurements over the spectral range 250–1050 nm. The basic measurement principles of the two-monochromator method and the calibration procedures used to determine the instrument spectral characteristics are described in detail. The instrumental set-ups, data acquisition procedures, and representative results for the measurement of reflected and bispectral luminescent radiance factors and calculation of total radiance factors are graphically illustrated in a step-by-step fashion for a typical red fluorescent material. The measurement performance of this instrument is demonstrated for several applications, including customer-supplied source data, paper, paint and textile samples.     

Structural rigidity control in arborescent graft polymers

Successive chloromethylation-anionic grafting sequences on polystyrene have led to well-defined hyperbranched macromolecules. Polymers with branching functionalities f > 5000 and molar masses over 10⁷ g/mol were thus prepared while maintaining a ratio of mass- to number-average molar masses M_w/M_n = 1,1-1,3. Three series of styrene polymers were prepared by varying the density of grafting sites along the chain, resulting in controllable stiffening of the molecular structure. Characterization of the branched molecules by size-exclusion chromatography/low-angle laser light scattering and light scattering confirmed a geometric increase in molar mass for successive generations, and a low ratio of mass- to number-average molar masses. Static and dynamic light scattering experiments showed that the molecules behave like hard spheres in dilute solutions. Measurements in the semidilute range, however, showed a progressive structural stiffening effect as the branching density increases.     

Water transfer in mixed water-in-oil emulsions studied by differential scanning calorimetry

Water transfers are observed within complex systems containing aqueous phases separated by a membrane or an oil phase, such as biological cells or multiple emulsions. In order to better understand water transfer mechanism, a system made of a mixed water-in-oil (W/O) emulsion containing two kinds of aqueous droplets — pure water and a 30 % urea solution — was developed. Water transfer from pure water droplets to urea solution droplets was evidenced by Differential Scanning Calorimetry (DSC). Finally the mixed emulsion contains one kind of droplets made of a diluted urea solution which composition is in agreement with formulation and data obtained from experiments performed on single W/O emusions which dispersed phase is a diluted urea solution of the same composition. These mixed emulsions have been pictured as a three-fluid phases system containing two aqueous phases separated by a plane oil membrane. From a homogeneous solubility-diffusion model applied to a quasi-stationnary regime, the water intra-diffusion coefficient has been obtained and compared to the value calculated from the Stokes-Einstein equation. A factor ten makes the discrepancy between the two values, the value deduced from the model being the highest. A possible influence of the emulsifier molecules has been evoked.     

An STM study of the adsorption of Pb on Cu(100): formation of an ordered surface alloy

The adsorption of Pb on Cu(100) from 0 to 1 ML was investigated by UHV scanning tunneling microscopy. We obtained atomic resolution images of the different superstructures which appear at 300 K with increasing coverage (c(4 × 4), c(2 × 2) and c( √2)R45°). We confirm recent results and propose, partly on the basis of low temperature studies, new arguments in favour of an incorporation of lead atoms in the surface layer of copper for low coverage. We demonstrate that the c(4 × 4) superstructure corresponds to an ordered surface alloy of Pb₃Cu₄ composition, by investigating separately the alloying and de-alloying transitions. De-alloying occurs during the first-order transition between the c(4 × 4) and c(2 × 2) superstructures.