Dielectric and viscoelastic investigation of segmental dynamics of polystyrene above glass transition temperature: Cooperative sequence length and relaxation mode distribution

摘要

Atactic polystyrene (PS) has the type-B dipole perpendicular to the chain backbone so that its local, segmental motion activates the dielectric relaxation. For monodisperse oligostyrene (OS) and PS samples of various molecular weights M, details of this motion were examined at temperatures T well above T_g through comparison of the complex modulus, G* = G′ + iG″, and the complex dielectric permittivity, ε* =ε′ - iε″, measured as functions of the angular frequency ω. For the OS samples, G*(ω) and ε*(ω) fully relaxed through the segmental dynamics thereby exhibiting respective terminal relaxation tails (low-frequency tails), G′(ω) ~∝ ω~2, G″(ω) ~∝ ω, Δε′ (ω) ≡ ε′(0) - ε′(ω)~∝ ω~2, and ε″(ω) ~∝ ω, at ω below the segmental relaxation frequency ω_s. For the PS samples, G*(ω) relaxed partly through the segmental dynamics and then exhibited the polymeric full relaxation characterized by the Rouse-like behavior followed by the terminal flow behavior (with/without intermediate entanglement plateau depending on M). In contrast, ε*(ω) of the PS samples still relaxed completely through the segmental dynamics. For respective samples, the G*(ω) and ε*(ω) data in the segmental relaxation zone exhibited very similar relaxation mode distribution and had the same time-temperature shift factor. Nevertheless, a ratio of the dielectrically and viscoelastically detected segmental relaxation times, r(M) = ω_(s,G)/ω_(s,ε), and the dielectric relaxation intensity, Δε(M), decreased with increasing M up to M* ? 2 × 10~3 and then became insensitive to M on a further increase of M. The viscoelastic segmental relaxation reflects the cooperative torsion of the repeating units along the molecular backbone (as noted from rheo-optical data), while the dielectric segmental relaxation detects reorientational motion of those units affected by both intra- and intermolecular cooperativity (as noted from the basic dielectric expression). The observed decreases of r(M) and Δε(M) suggested that the dimension Ξ_m of the whole OS molecule (over which the cooperative torsion occurs) is smaller than the length scale Ξ_c for the intermolecular cooperative motion and that Ξ_m approaches Ξ_c on an increase of M up to M*. Consequently, the high-M PS molecules having Ξ_m > Ξ_c exhibited the M-insensitive r(M) and Δε(M). Thus, the M value for the crossover between these two regimes, M* ? 2 × 10~3, can be taken as the molecular weight of the cooperative sequence along the PS backbone. Furthermore, the quantitative similarity of the viscoelastic and dielectric mode distributions suggests that the cooperative torsion of the repeating units along the molecular backbone is governed by the cross-correlation of the units belonging to different molecules.