Averaging rheological quantities in descriptions of soft glassy materials

Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate procedure in mechanics than in more classical situations such as phase transitions in magnetic systems. This leads us to modify the predictions of the recently proposed SGR model for soft glassy materials, for which we suggest that the viscosity should diverge at the glass transition temperature $T_g$ with an exponential form $\eta \sim \exp(\frac{A}{T-T_g})$.Comment: 4 pages, Latex, 1 eps figur

The Saint-Venant principle for columnar discotic liquid crystals

We compute the high frequency elastic distortion of a columnar discotic single crystal submitted to a longitudinal dilation. The ends of the columns are assumed to be clamped and anchored perpendicularly to two infinitely rigid glass plates, on a width L. The local strain close to the plates relaxes to the homogeneous distortion of an unclamped sample on a characteristic length £ ∼ (Lm)1/2, where m is a molecular length. £ is much shorter than L, the usual damping length in standard solids. This results from the mixed (displacement and curvature) elasticity of columnar discotic materials, analogous to the one of smectic materials. The apparent Young modulus of an ideal short discotic single crystal should be length dependent. The free relative glide of columns allows also the conservation, along the columns, of any transverse non-uniformity of the longitudinal strain or stresses. We reformulate the Saint-Venant principle for these anisotropic materials. In practice, permeation and plasticity should prevent these non-uniform distortions from existing permanently.Nous calculons la déformation d'un monocristal discotique colonnaire soumis à une traction longitudinale. Les extrémités des colonnes sont supposées encastrées perpendiculairement à deux lames de verre infiniment rigides, sur une largeur L. La déformation locale près des plaques relaxe vers la déformation homogène d'un échantillon non encastré, sur une longueur caractéristique £ ∼ (Lm)1/2, où m est une longueur moléculaire. C est très inférieure à L, la distance d'atténuation pour les solides usuels. Ceci s'explique par l'élasticité mixte (déplacement et courbure) des matériaux discotiques colonnaires, analogues aux matériaux smectiques. Le module d'Young apparent d'un monocristal idéal et court de discotique devrait dépendre de sa longueur. Le libre glissement des colonnes entre elles permet d'autre part la conservation, le long des colonnes, de n'importe quelle non-uniformité transversale des contraintes ou déformations longitudinales. Nous reformulons le principe de Saint-Venant pour ces matériaux anisotropes

Linear viscoelasticity of incompatible polymer blends in the melt in relation with interfacial properties

A quite general characteristic of the rheology of incompatible polymer blends in the melt is their highly elastic behaviour at low fiequencies, corresponding to long-time relaxation processes. For emulsions of Newtonian liquids, this property can be readily connected to interfacial tension α : in a macroscopic flow, suspended droplets of radius R are subjected on the one hand to a viscous drag related to the viscosity µm of the matrix liquid and tending to deform their shape, and on the other hand to an elastic force of the order of α/R opposing the deformation. From a rheological point of view, the emulsion shows viscoelastic behaviour with characteristic relaxation times of the order of µmR/α. Blends of incompatible uncrosslinked polymers in the molten state can also be considered as emulsions, but the behaviour of the phases becomes viscoelastic by itself. A recent model, which accounts for the viscoelasticity of the phases, the polydispersity in size of the droplets and their hydrodynamic interactions, allowed us to explain the linear viscoelasticity of some selected polymer blends