Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

Propriétés viscoélastiques linéaires de solutions de polybutadiène en régime semi-dilué et concentré

Résumé L'évolution des propriétés viscoélastiques linéaires de polymères en solution est caractérisée par l'étude des variations des trois paramètres caractéristiques de la viscoélasticité linéaire (viscosité limite ₀, complaisance limiteJ _e ⁰ et module de plateauG _N ⁰ ) en fonction de la concentration dans différents solvants. Les polymères étudiés sont des polybutadiènes linéaires et branchés en étoile, à distribution étroite de masses moléculaires. Les solvants étudiés ont des températures de transition vitreuse inférieure, égale ou supérieure à celle du polybutadiène (respectivement le tétradécane, un polybutadiène de faible masse moléculaire et une huile commerciale). Les résultats obtenus ( ₀ c ^4,0,G _N ⁰ c ^2,25 etJ _e ⁰ c ^–2,25) sont en désaccord avec le comportement conforme aux modèles de champ moyen généralement admis, et semble partiellement en accord avec les modèles récents de la relaxation et de la thermodynamique des longues chaînes flexibles.

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Summary The linear viscoelastic properties of polymer solutions are studied through the concentration dependence of the three characteristic parameters of linear viscoelasticity (zero-shear viscosity ₀, limiting complianceJ _e ⁰ and plateau modulusG _N ⁰ ) in various solvents. The polymers are narrow-distribution linear and starbranched polybutadienes. The glass transition temperatures of the solvents are below, equal to, and above, theT _g of polybutadiene (respectively tetradecane, low molecular weight polybutadiene, and a commercial oil). The results ( ₀ c ^4.0,G _N ⁰ c ^2.25 andJ _e ⁰ c ^–2.25) do not agree with the usual mean field behavior assumed for the viscoelastic properties of polymer solutions, and seem to agree partly with recent models for the relaxation and thermodynamics of long chains.

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Zusammenfassung Das linear-viskoelastische Verhalten von Polymerlösungen wird anhand der Abhängigkeit der drei charakteristischen Parameter (Nullviskosität ₀, NullkomplianzJ _e ⁰ und PlateaumodulG _N ⁰ ) von der Konzentration in verschiedenen Lösungsmitteln untersucht. Bei den Polymeren handelt es sich um lineare und sternförmig verzweigte Polybutadiene mit enger Molmassenverteilung. Die Glasübergangstemperaturen der Lösungsmittel (Tetradecan, niedermolekulares Polybutadien bzw. ein kommerzielles Ol) sind niedriger, gleich oder höher als diejenigen des Polybutadiens. Die Ergebnisse ( ₀ c ^4,0,G _N ⁰ c ^2,25 undJ _e ⁰ c ^–2,25) stimmen nicht mit den Voraussagen der üblicherweise zugrundegelegten, durch Mittelwertbildung gekennzeichneten Theorien überein, sondern scheinen zumindest zum Teil denen neuer thermodynamischer bzw. Relaxationstheorien langkettiger Polymerer zu entsprechen.

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Avec 13 figures et 6 tableaux     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.     

Photosensitized Thymine Dimerization via Delocalized Triplet Excited States

A new mechanism of photosensitized formation of thymine (Thy) dimers is proposed, which involves generation of a delocalized triplet excited state as the key step. This is supported by chemical evidence obtained by combining one benzophenone and two Thy units with different degrees of freedom, whereby the photoreactivity is switched from a clean Paternò–Büchi reaction to a fully chemo‐, regio‐, and stereoselective [2+2] cycloaddition.     

Translocation versus cyclisation in radicals derived from N-3-alkenyl trichloroacetamides

Under radical reaction conditions, two different and competitive reaction pathways were observed for N-(α-methylbenzyl)trichloroacetamides with a N-3-cyclohexenyl substituent: 1,4-hydrogen translocation and radical addition to a double bond. However, for radicals with an acyclic alkenyl side chain, the direct cyclisation process was exclusively observed. The dichotomy between translocation and direct radical cyclisation in these substrates has been theoretically studied using density functional theory (DFT) methods at the B3LYP/6-31G** computational level.     

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.     

Resonant inelastic x-ray scattering at the limit of subfemtosecond natural lifetime

We present measurements of the resonant inelastic x-ray scattering (RIXS) spectra of the CH(3)I molecule in the hard-x-ray region near the iodine L(2) and L(3) absorption edges. We show that dispersive RIXS spectral features that were recognized as a fingerprint of dissociative molecular states can be interpreted in terms of ultrashort natural lifetime of ～200 attoseconds in the case of the iodine L-shell core-hole. Our results demonstrate the capacity of the RIXS technique to reveal subtle dynamical effects in molecules with sensitivity to nuclear rearrangement on a subfemtosecond time scale.