An estimation of the tube radius in the entanglement effect of concentrated polymer solutions

MOLECULAR TREATMENT OF RUBBER-LIKE ELASTICITY FOR ACTIVE FILLER–LOADED NETWORKS

Prior comparison of experimental observations and model predictions for natural rubber/styrene–butadiene rubber carbon black–filled systems has indicated a need for further development of tubelike constraint-based entropy models. In particular, systems incorporating active fillers introduce constraints whose effects should be considered. This contribution extends the finite-extension single-chain model proposed originally by Teramoto, via consideration of the bound rubber layer surrounding a filler particle as well as filler-cluster breakup and strain-amplification effects. The resulting model includes descriptors of the entropy state of the polymer matrix, the affine and phantomlike chain deformation, and tube diameter. The model produced a more accurate prediction of the shape of observed stress–strain curves, particularly at moderate and high strains.

The quantification of entanglement effects in polymer melts

The entanglement of polymers in a melt or concentrated solution can be measured by the plateau modulus and takes the form c x where c is the effective concentration of polymer and 2 < x < 3. Different arguments exist in the literature for x . It is shown in this paper that x may be directly calculated and that the value 3 comes from purely random walks as noted by Doi in a scaling argument, x = 2.25 from semidilute scaling theory, and x = 2 from a direct calculation of the entanglement by a cage of rectilinear molecules. Physical reality is reasonably placed between these limits. The whole analysis is based on the Gauss topological invariant.