Viscoelastic and Dielectric Relaxation of a Cayley-Tree-Type Polyisoprene: Test of Molecular Picture of Dynamic Tube Dilation

Abstract

For an entangled Cayley-tree-type cis-polyisoprene (CT-PI) composed of two classes of arms, trifunctionally branched inner arms each carrying two outer arms (Mi = 24.7 × 103 and Mo = 12.3 × 103 for each inner and outer arm, respectively), the molecular picture of dynamic tube dilation (DTD) was examined through viscoelastic and dielectric data. The global motion of the arms was dielectrically active because they had the so-called type A dipole parallel along their backbone. The dielectric relaxation function Φ(t) thus measured for CT-PI enabled us to experimentally evaluate the survival fraction of the dilated tube φ′(t), a key quantity in the DTD picture. In the conventional picture of full-DTD, relaxed portions of the arms are regarded as a simple solvent, thereby allowing the number of mutually equilibrated entanglement segments per dilated segment, β(t), to fully increase to that in a corresponding solution, βf-DTD(t) = {φ′(t)}−d with d = 1.3 for PI. The corresponding full-DTD relationship between φ′(t) and the normalized viscoelastic relaxation function μ(t), μf-DTD(t) = {φ′(t)}1+d, did not hold for the φ′(t) and μ(t) data of CT-PI. In contrast, in the molecular picture of partial-DTD, β(t) is determined through competition of the constraint release (CR) motion of the focused chain and the motion of surrounding chains, the former determining the maximum possible βCR(t) value in a given time scale, t. In this picture, the length and time scales are consistently coarse-grained on the basis of the CR mechanism. The partial-DTD relationship, μp-DTD(t) = φ′(t)/β*(t) with β*(t) = min[βf-DTD(t), βCR(t)], was found to hold for the φ′(t) and μ(t) data satisfactorily. In addition, analysis of the φ′(t) data unequivocally indicated that the inner arm hardly relaxed until the outer arm relaxation completed; i.e., the hierarchical relaxation occurred through partial-DTD. These results suggested the importance of the consistent coarse graining in molecular description of the dynamics of branched chains in general.