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京都大学0048新制・課程博士博士(工学)甲第9543号工博第2129号新制||工||1232(附属図書館)UT51-2002-G301京都大学大学院工学研究科分子工学専攻(主査)教授 尾崎 邦宏, 教授 吉﨑 武尚, 教授 田中 文彦学位規則第4条第1項該当Doctor of EngineeringKyoto UniversityDFA

Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

For flexible polymers, the deviatoric parts of the stress and optical anisotropy tensors, with the latter reflecting the orientational anisotropy of the monomeric segments, are proportional to each other. This proportionality, known as the stress-optical rule (SOR), is valid not only in the linear viscoelastic regime but also in the moderately nonlinear regime, given that the chain is not highly stretched and is free from the finite extensible nonlinear elasticity (FENE) effect. On start-up of flow in such a moderately nonlinear regime, the chain exhibits an overshoot of the shear stress and thus of the shear component of the segmental orientational anisotropy. Nevertheless, it was not clearly understood whether this overshoot is associated with an overshoot of chain stretch. This study revisited SOR to conduct a simple analysis for this problem. It turned out that the orientational anisotropy of subchains overshoots but the subchain stretch (identical to the chain stretch) does not when the shear stress overshoots in the moderately nonlinear regime

Primitive chain network simulations for asymmetric star polymers

For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and/or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers

Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

For flexible polymers, the deviatoric parts of the stress and optical anisotropy tensors, with the latter reflecting the orientational anisotropy of the monomeric segments, are proportional to each other. This proportionality, known as the stress-optical rule (SOR), is valid not only in the linear viscoelastic regime but also in the moderately nonlinear regime, given that the chain is not highly stretched and is free from the finite extensible nonlinear elasticity (FENE) effect. On start-up of flow in such a moderately nonlinear regime, the chain exhibits an overshoot of the shear stress and thus of the shear component of the segmental orientational anisotropy. Nevertheless, it was not clearly understood whether this overshoot is associated with an overshoot of chain stretch. This study revisited SOR to conduct a simple analysis for this problem. It turned out that the orientational anisotropy of subchains overshoots but the subchain stretch (identical to the chain stretch) does not when the shear stress overshoots in the moderately nonlinear regime

Primitive chain network simulations for comb-branched polymer under step shear deformations

The damping of the relaxation modulus under step shear deformation is weaker for multi-branched polymers such as comb polymers than for linear polymers. This weak damping has been related to the hierarchical relaxation, the branched arm relaxation occurring prior to the backbone relaxation and dilating the entanglement network for the backbone relaxation/contraction. A corresponding model has been proposed and favorably compared with the data for the damping function. However, the enhancement of dilation due to large deformation, known to occur for linear polymers to affect the chain contraction rate, was not considered in the model. Thus, in this paper, we investigated the dilation for a comb polymer under deformation with the aid of a 3D multichain sliplink simulation that naturally accounts for the dilation due to the constraint release through the many chain dynamics. The simulation was confirmed, to the first time, to reproduce the linear and nonlinear viscoelastic data for a comb polyisoprene (Kirkwood et al., Macromolecules 42:9592–9608, 2009). A magnitude of dilation under deformation was examined for the survival probability of the sliplinks. It turned out that the dilation for the comb backbone activated by the arm relaxation is enhanced by the deformation at short times but not at long times where the backbone relaxes and the damping function is defined. This result lends support to the conventional model

Component Relaxation Times in Entangled Binary Blends of Linear Chains: Reptation/CLF along Partially or Fully Dilated Tube

Recent dielectric analysis suggested that entangled linear cis-polyisoprene (PI) chains in monodisperse bulk exhibit, in the terminal relaxation regime, reptation/contour length fluctuation (CLF) along a partially dilated tube with its diameter being determined by the constraint release (CR) activated tension equilibration along the chain backbone (Matsumiya et al. Macromolecules 2013, 46, 6067). In relation to this finding, we re-examined the dielectric and viscoelastic terminal relaxation times of components in linear PI blends having various component molecular weights and volume fractions, Mi and υi (i = 1 and 2 for the short and long components). In entangling blends with M2 ≫ M1 and large υ2 (>critical volume fraction υ2e for the onset of long−long entanglement), the relaxation time τ2,b of the long chain decreases with decreasing υ2 but stayed considerably larger than τ2,soln of the same long chain in a solution having the same υ2. This result suggested that the CR-activated tension equilibration retards the reptation/CLF motion of the long chain in such blends. A simple “solution model” considering this retardation due to the CR relaxation of short−long entanglements was formulated. Utilizing data for the CR relaxation time τdil‑2,CR of dilute long chains (with υ2 υ2e very well. Nevertheless, this model could not apply to the cases where M2 and M1 are rather narrowly separated and the short−long entanglements considerably survive in the time scale of the long chain relaxation. For this case, a “blend model” was formulated to consider self-consistently, though in an approximate way, the CR relaxation of all species of entanglements (short−short, short−long, long−short, and long−long entanglements) thereby mimicking coupled relaxation of the long and short chains. The component relaxation times deduced from this model (again on the basis of the τdil‑2,CR data) were surprisingly close to the data, not only for the PI/PI blend having narrowly separated M2 and M1 but also for those with M2 ≫ M1 (the latter being described satisfactorily also with the solution model), suggesting that reptation/CLF of the components in the terminal relaxation regime occurs along partially dilated tube with the diameter being determined by the CR-activated tension equilibration. Furthermore, the “blend model” worked satisfactory also for literature data for polystyrene blends having various M2/M1 ratios. These results demonstrate the importance of CR-activated tension equilibration in the blends, which is consistent with the finding for monodisperse bulk

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

For miscible pair of polyisoprene (PI) and poly­(<i>p</i>-<i>tert</i>-butylstyrene) (PtBS), the component molecular weights, composition, and temperature were tuned to prepare PI/PtBS blends in the <i>pseudomonodisperse</i> state where the component PI and PtBS chains had the same terminal relaxation time, τ₁. These pseudomonodisperse blends had the linear viscoelastic moduli indistinguishable from the moduli of entangled monodisperse bulk homopolymers of particular molecular weights, and satisfied the time-strain separability in their nonlinear stress relaxation behavior under large step strains. The damping function <i>h</i>(γ) of those blends was close to <i>h</i>_DE(γ) calculated from the Doi–Edwards model and classified to be the so-called type-A damping function, even though the major component (PI) in the blends had a large entanglement number <i>per</i> chain (<i>N</i> ≥ 50). Highly entangled monodisperse homopolymers having similarly large <i>N</i> are known to exhibit the so-called type-C damping characterized by <i>h</i>(γ) ≪ <i>h</i>_DE(γ), and this damping behavior was indeed confirmed for high-<i>M</i> bulk PI utilized as the blend component. Thus, the nonlinear damping behavior was different for the pseudomonodisperse PI/PtBS blends and high-<i>M</i> bulk PI, despite the similarity in the entanglement number <i>N</i> for PI therein. This difference was discussed within the molecular scenario of Marrucci and Grizzuti in relation to the topological hindrance for PI segments due to PtBS segments having a much larger friction. This hindrance retarded the Rouse equilibration of the PI backbone in the blends, which possibly provided the highly entangled PI with a slow contour length fluctuation mechanism that competed with reptation. Such a competing mechanism smears the elastic instability underlying the type-C damping as suggested from the Marrucci–Grizzuti scenario, which possibly allowed the pseudomonodisperse PI/PtBS blends containing highly entangled PI to exhibit the type-A damping. Furthermore, the type-A damping was observed also for a chemically homogeneous, highly entangled PI/PI blend being free from the topological hindrance for PI segments. In this PI/PI blends, the partial constraint release of the high-<i>M</i> component, activated by the relaxation of the low-<i>M</i> component, appeared to compete with reptation of the high-<i>M</i> component thereby smearing the instability and suppressing the type-C damping. Thus, the smearing of instability could be a rather universal feature occurring irrespective of the detail of the competing mechanisms