Comparison of Dielectric and Viscoelastic Relaxation Functions of cis-Polyisoprenes: Test of Tube Dilation Molecular Picture

Within the context of the generalized tube model, the tube representing the entanglement constraint is not necessarily fixed in space but moves with time. This tube motion results in constraint release (CR) as well as dynamic tube dilation (DTD) for the chain trapped in the tube. For monodisperse systems, the DTD molecular picture leads to the normalized relaxation modulus μ( t ) (= G ( t )/ G N ) being proportional to square of the surviving fraction of the dilated tube. In contrast, the normalized dielectric relaxation function Φ( t ) of the chain having noninverted type-A dipoles is proportional to this fraction. Thus, the viscoelastic and dielectric relaxation functions satisfy a relationship μ( t ) = [Φ( t )] 2 if the tube dilates in time scales of the chain relaxation. The validity of this relationship was examined for linear cis -polyisoprene (PI) chains having those type-A dipoles. The relationship was approximately valid, and thus, the tube dilated for the PI chains with M / M e = 10−30 in their bulk state, although these chains did not necessarily reptate in the dilated tube with their intrinsic curvilinear diffusion coefficient. On the other hand, the relationship reformulated for blends was not valid for dilute PI probe chains in entangling matrices of much shorter polybutadiene (PB) chains. The probe fully relaxed via the CR mechanism during the DTD process and did not obey this relationship. The lack of DTD was also confirmed for the same probe in a much longer, CR-free PB matrix.