Entanglement Length in Miscible Blends ofcis-Polyisoprene and Poly(p-tert-butylstyrene)

Abstract

The entanglement length a, being equivalent to the plateau modulus G N (∝M e –1 ∝ a –2), is one of the most basic parameters that determine the slow dynamics of high molecular weight (M) polymers. In miscible blends of chemically different chains, the components would/should have the common a value. However, changes of a with the blend composition have not been fully elucidated. For this problem, this study conducted linear viscoelastic tests for miscible blends of high-M cis-polyisoprene (PI) and poly­(p-tert-butylstyrene) (PtBS) and analyzed the storage and loss moduli (G′ and G″) data in a purely empirical way, considering the very basic feature that unentangled and entangled blends having the same composition exhibit the same local relaxation. (From a molecular point of view, this local relaxation reflects the chain motion within the length scale of a.) On the basis of this feature, a series of barely entangled low-M PI/PtBS blends having various component molecular weights and a given composition were utilized as references for well-entangled high-M PI/PtBS blends with the same composition, and the modulus data of the reference were subtracted from the data of the high-M blends. For an optimally chosen reference, the storage modulus of the high-M blends obtained after the subtraction (G ent′ = G high‑M blend′ – G ref′) exhibited a clear plateau at high angular frequencies ω. The corresponding loss modulus G ent″ decreased in proportion to ω–1 at high ω, which characterized the short-time onset of the global entanglement relaxation: A mischoice of the reference gave no plateau of G high‑M blend′ – G ref′ and no ω–1 dependence of G high‑M blend″ – G ref″ at high ω, but a survey for various low-M PI/PtBS blends allowed us to find the optimum reference. With the aid of such optimum reference, the entanglement plateau modulus G N of the high-M PI/PtBS blends was accurately obtained as the high-ω plateau value of G ent′. G N thus obtained was well described by a linear mixing rule of the entanglement length a with the weighing factor being equated to the number fraction of Kuhn segments of the components, not by the reciprocal mixing rule utilizing the component volume fraction as the weighing factor. This result, not explained by a mean-field picture of entanglement (constant number of entanglement strands in a volume a 3), is discussed in relation to local packing efficiency of bulky PtBS chains and skinny PI chains.

Dynamic dilution exponent in monodisperse entangled polymer solutions

“…This is illustrated in Figure 7, which shows the storage modulus corresponding to G d for the two blends, and compares this value to the real plateau modulus 8 9 determined by removing the contribution of the high frequency Rouse relaxation as well as the CR-Rouse modes (see Eq. 14) from the theoretical curves [46][47][48] . It is seen that, due to the overlap between Rouse relaxation and CR-CLF process, the minimum of the tand curve is found at a rather low frequency w d (see the X symbols), at which the sample has already partially relaxed by tension equilibration.…”

“…defined as the value of the storage modulus at the frequency w d where the tand curve (= G" / G') shows a minimum 45,46. G d is usually used to approximate the value of the plateau modulus8 9 .…”

Nonlinear Stress Relaxation of Miscible Polyisoprene/Poly(p-tert-butylstyrene) Blends in Pseudomonodisperse State

“…Further detail of the blend preparation was described in the previous paper. 41 For comparison, a chemically homogeneous PI 321/PI 99 blend with the PI 321 content w PI 321 = 75 wt % was also examined. The blend was prepared by dissolving prescribed masses of the PI 321 and PI 99 samples in benzene and then casting the solution into a film.…”

“…For the blends containing PtBS 729, PtBS 442, and PtBS 219 samples, the linear viscoelastic storage and loss moduli, G′(ω) and G″(ω), were measured at those temperatures in the previous work. 41 For the newly prepared PI 321/PtBS 91 blend, G′(ω) and G″(ω) were measured in this study with ARES-G2.…”

“…In contrast, a is common for PI and PtBS in the blend. Recent experiments revealed that changes of a with w PI are well described by a linear mixing law weighed with the number fraction n of the component Kuhn segments in the blend,41 …”