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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)/GN) 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/Me ) 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.

For concentrated polystyrene solutions, the effect of varying strain on the relaxation modulus can be described with the tube-model theory of Doi and Edwards at times longer than a certain characteristic time rk determined for each sample. The characteristic time is proportional to the second power of the number of entanglements per molecule and has been conjectured to define the complete equilibration of the fluctuation of the primitive path length. Here, we see that rk is about 4.5 times as large as the configurational relaxation time of an isolated (unentangled) polymer molecule in a hypothetical viscous medium that exerts the same frictional force to polymer segments as the polymer solution does. We also see that the same holds true for polystyrene solutions of relatively low concentrations if the entanglement molecular weight Me is assumed to be proportional to the -1.4 power of the concentration in this case.

Rheological and dielectric behavior was examined for concentrated solutions of a styreneisoprene-styrene (SIS) triblock copolymer in monomeric and polymeric I-selective solvents, n-tetradecane (C14) and a low-M homopolyisoprene (I-1; M ) 1.4K). The I blocks had symmetrically once-inverted dipoles along the block contour, and their midpoint motion was dielectrically detected. The SIS solutions exhibited rubbery, plastic, and viscous behavior at low, intermediate, and high temperatures (T). Dielectric and viscoelastic data strongly suggested that the S and I blocks were more or less homogeneously mixed in the viscous regime. In the rubbery and plastic regimes, the S blocks were segregated to form spherical domains, and the I blocks took either the loop or bridge conformation. In these regimes, the inverted dipoles of the I blocks enabled us to dielectrically estimate the loop fraction, φ1 = 60% in C14 and I-1. These loops, having osmotically constrained conformations, strongly affected the rheological properties of the SIS solutions. A strong osmotic constraint in C14 resulted in almost equal contributions of the loops and bridges to the equilibrium modulus. The loop contribution became less significant in I-1 that (partly) screened this constraint. Similarly, the yield stress σy in C14 was essentially determined by dangling (noninterdigitated) loops at relatively high T where the S/I mixing barrier was rather small, while the bridges and interdigitated loops had a large contribution when this barrier was enhanced, i.e., at lower T and/or in I-1 (a poorer solvent for the S blocks than C14).

Dielectric behavior was examined for solutions of a styrene-isoprene-styrene (SIIS) triblock and SI diblock copolymers in an I-selective solvent, n-tetradecane (C14). The SI copolymer had noninverted type-A dipoles in the I block while the SIIS copolymer, a head-to-head coupled dimer of SI, had once-inverted dipoles in the I block. At a low temperature (5 °C) where the S blocks formed glassy, spherical microdomains, the I blocks of SIIS had either the bridge or loop configurations. The loop fraction φl in these I blocks was estimated from the dielectric losses of the SIIS and SI solutions at low frequencies. The φl was found to increase (from 0.6 to 0.8) with decreasing SIIS concentration (from 50 to 20 wt %). This increase of φl was attributed to stretching and destabilization of the bridge configuration on dilution. The equilibrium elasticities of the bridge and dangling loop, estimated from the φl values and rheological data of the concentrated SIIS/C14 solutions, were comparable in magnitude. This significant elasticity of the dangling loops reflected the strong osmotic constraint on the I block conformation in the concentrated I/C14 matrix phase.