Dielectric and Viscoelastic Behavior of Star-Branched Polyisoprene: Two Coarse-Grained Length Scales in Dynamic Tube Dilation

Abstract

<i>cis</i>-Polyisoprene (PI) chain has the type A dipole parallel along the backbone so that its large-scale (global) motion results in not only viscoelastic but also dielectric relaxation. Utilizing this feature of PI, this paper examined dielectric and viscoelastic behavior of star PI probe chains (arm molecular weight 10^–3<i>M</i>_a = 9.5–23.5, volume fraction υ₁ = 0.1) blended in a matrix of long linear PI (<i>M</i> = 1.12 × 10⁶). The constraint release (CR)/dynamic tube dilation (DTD) mechanism was quenched for those dilute probes entangled with the much longer matrix, as evidenced from coincidence of the frequency dependence of the dielectric and viscoelastic losses of the probe in the blend. Comparison of the probe data in the blend and in monodisperse bulk revealed that the star probe relaxation is retarded and broadened on blending and the retardation/broadening is enhanced exponentially with <i>M</i>_a. This result in turn demonstrates significant CR/DTD contribution to the dynamics of star PI in bulk. The magnitude of retardation was quantitatively analyzed within the context of the tube model, with the aid of the dielectrically evaluated survival fraction of the dilated tube, φ′(<i>t</i>), and the literature data of CR time, τ_CR. In the conventional molecular picture of partial-DTD, the tube is assumed to dilate <i>laterally</i>, but not <i>coherently</i> along the chain backbone. The corresponding <i>lateral</i> partial-DTD relationship between φ′(<i>t</i>) and the normalized viscoelastic relaxation function μ­(<i>t</i>), μ­(<i>t</i>) = φ′(<i>t</i>)/β­(<i>t</i>) with β­(<i>t</i>) being the number of entanglement segments <i>per</i> laterally dilated segment (that was evaluated from the φ′(<i>t</i>) and τ_CR data), held for the μ­(<i>t</i>) and φ′(<i>t</i>) data of star PI in bulk. Nevertheless, the observed retardation of the star probe relaxation on blending was <i>less significant</i> compared to the retardation expected for the arm motion (retraction) along the laterally dilated tube in bulk PI. This result suggests that the relaxation time of the probe in bulk is governed by the <i>longitudinal</i> partial-DTD that occurs <i>coherently</i> along the chain backbone. In fact, the magnitude of retardation evaluated from the φ′(<i>t</i>) and τ_CR data on the basis of this <i>longitudinal</i> partial-DTD picture was close to the observation. These results strongly suggest that the star PI chains in monodisperse bulk have two different coarse-grained length scales: the diameter of laterally dilated tube that determines the modulus level and the diameter of longitudinally dilated tube that reflects the path length for the arm retraction and determines the relaxation time. Thus, the star PI chains in bulk appear to move along the longitudinally dilated tube that wriggles in the laterally dilated tube. This molecular scenario is consistent with the previous finding for bulk linear PI [Matsumiya et al. Macromolecules 2013, 46, 6067]