Molar mass dependence 317 entangled network

Secondly, since U/RTc vanishing positive second virial coefficient as it is indicative for a good solvent. The third observation is that, in the limit of high concentrations, the molar mass dependence of U vanishes. This occurs when the polymer chains interpenetrate each other and an entanglement network builds up. The observation tells us that, once the entanglement network has formed, the single chain properties become irrelevant. 

The simplest explanation is that there is a rubber-like network present and that this has a maximum extensibility due to the degree of entanglement, which is constant for a given grade of polymer and depends on its molar mass and method of polymerisation. This limiting extensibility is not to be confused with the limit of applicability of the affine rubber model for predicting orientation distributions discussed in section 11.2.1 because the limiting extension can involve non-affine deformation. 

A reversible crosslinked system forms a transient network that when placed under a macrodeformation shear rate exhibited shear flow. The properties depended on disruption and recombination of the reversible network. The linear response to oscillatory deformations has been determined for the reversible network with uniform chains with reversible crosslinking at end groups. Where molar mass (M) was less than the critical M for entanglements the dynamic moduli were related to temperature, M and crosslink bond... 

Non-linear viscoelastic properties were observed for fumed silica-poly(vinyl acetate) (PVAc) composites, with varying PVAc molar mass and including a PVAc copolymer with vinyl alcohol. Dynamic mechanical moduli were measured at low strains and found to decrease with strain depending on surface treatment of the silica. The loss modulus decreased significantly with filler surface treatment and more so with lower molar mass polymer. Copolymers with vinyl alcohol presumably increased interactions with silica and decreased non-linearity. Percolation network formation or agglomeration by silica were less important than silica-polymer interactions. Silica-polymer interactions were proposed to form trapped entanglements. The reinforcement and nonlinear viscoelastic characteristics of PVAc and its vinyl alcohol copolymer were similar to observations of the Payne effect in filled elastomers, characteristic of conformations and constraints of macromolecules. ... 

The semi-dilute regime constitutes a sizeable concentration range vl V2 1, where u is the volume fraction corresponding to the concentration c. The semi-dilute solution case is in fact the simplest to describe. Molar mass effects are highly suppressed but still the solution is diluted. The solution activity and the osmotic pressure are independent of molar mass but dependent on the distance between the entanglement points in the loose network. The latter is controlled simply by the volume fraction of polymer V2), and the osmotic pressure is given by des Cloiseaux law ... 

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