Hiroshi Watanabe

Dielectric and viscoelastic behavior was examined for a styrene-isoprene diblock copolymer, SI 11-60, and its head-to-head dimer, SI2S 11-(60)2-11 triblock copolymer, with the sample code numbers representing the block molecular weights MS, MI, and MI2 in the unit of kg mol–1. SAXS data showed that the copolymers formed a bcc lattice of spherical S domains and patches of those lattices were randomly oriented to form a polygrain structure. The I and/or I2 blocks were well entangled in their matrix phase embedding those spherical S domains. The I block had the type-A dipole parallel along its backbone, whereas the I2 block had the type-A dipole once inverted at the block midpoint. Thus, the slow dielectric relaxation of SI 11-60 and SI2S 11-(60)2-11 exclusively detected the end-to-end vector fluctuation of the I block and the end-to-center vector fluctuation of the I2 block, respectively, without being contributed from the viscoelastically detected (but dielectrically inert) slow dynamics of the polygrain structure. Comparison with a reference material, 6-arm star homopolyisoprene 6(I-59) having the arm molecular weight almost identical to MI of the I block, revealed that SI 11-60 and 6(I-59) exhibited very similar dielectric relaxation except for the relaxation intensity moderately smaller for SI 11-60 by a factor of 0.65. In contrast, SI2S 11-(60)2-11 showed the dielectric relaxation much weaker, by a factor of 0.1, compared to 6(I-59). These results suggested that the motion of the I block anchored on the S domain was similar to the arm retraction of the 6(I-59) star in a dilating entanglement network (as considered in the standard tube model) but was constrained by a thermodynamic requirement of preserving a constant mass density without the motion of the S–I junction. In contrast, the motion of the I2 block having its two ends fixed on the S domains appeared to occur just through the Rouse fluctuation along an array of the trapped entanglements under the requirement of preserving a constant mass density, and thus much less significant compared to the motion of the I block.

Dendritic hyperbranched poly(methyl acrylate)s (HBPMAs) with controlled molecular weight and low dispersity (Đ ≤ 2) were synthesized by radical copolymerization of MA and a branch-inducing monomer, evolmer 2b, in the presence of organotellurium chain transfer agent (CTA) 1, by targeting theoretical generation (G_n) of 3-5 and branch molecular weight (M_BL) of 0.25M_e-2.0M_e, with M_e (= 11,000) being the entanglement molecular weight of PMA. The control of the self-similar branch layer structure in HBPMAs thus synthesized was examined by measuring their linear viscoelastic moduli (G* = G' + iG″). For all G_ns having M_BL = 0.25M_e, the storage modulus G' was lower than the loss modulus G″ at all ω examined. This unentangled feature was observed even when the portion of the chain spanning the two outmost ends of the branches had a molecular weight of 2.0M_e, possibly because of a lack of deep penetration among those G_n chains. In contrast, for M_BL ≥ M_e, G' was higher than G″ in a given range of ω, and this range became wider and the relaxation mode distribution therein became broader on an increase of M_BL, which is characteristic of entangled branch polymers. For the entangled HBPMA chains having the same M_BL but different G_n, hierarchically self-similar relaxation based on the branch retraction mechanism was confirmed for the G' and G″ data: The data for higher G_n agreed with the data for lower G_n after a shift along the ω axis according to this self-similarity. For the unentangled BPMA chains of different G_n, the G' and G″ data obeyed the Rouse-type relationship based on the self-similarity but without the hierarchy. These results support good control of the dendritic branch structures of the HBPMAs synthesized with the current method.

Deviation of kinematic viscosity ν (square) and dielectric time τ_ε (circle) from respective high-T asymptotes noted for 5CB/DMT mixtures. Red curves/asterisks show the deviation of τ_ε resulting from that of ν deduced from free energy analysis.

Dendritic hyperbranched poly(methyl acrylate)s (HBPMAs) with controlled molecular weight and low dispersity (Đ ≤ 2) were synthesized by radical copolymerization of MA and a branch-inducing monomer, evolmer 2b, in the presence of organotellurium chain transfer agent (CTA) 1, by targeting theoretical generation (Gn) of 3-5 and branch molecular weight (MBL) of 0.25Me - 2.0Me, with Me (= 11,000) being the entanglement molecular weight of PMA. The control of the self-similar branch layer structure in HBPMAs thus synthesized was examined by measuring their linear viscoelastic moduli (G* = G' + iG"). For all Gns having MBL = 0.25 Me, the storage modulus G' was lower than the loss modulus G" at all ω examined. This unentangled feature was observed even when the portion of the chain spanning the two outmost ends of the branches had the molecular weight of 2.0Me, possibly because of a lack of deep penetration among those Gn chains. In contrast, for MBL ≥ Me, G' was higher than G" in a given range of ω, and this range became wider and the relaxation mode distribution therein became broader on an increase of MBL, which is characteristic of entangled branch polymers. For the entangled HBPMA chains having the same MBL but different Gn, hierarchically self-similar relaxation based on the branch retraction mechanism was confirmed for the G' and G" data: The data for higher Gn agreed with the data for lower Gn shifted according to this self-similarity. For the unentangled BPMA chains of different Gn, the G' and G" data obeyed the Rouse-type relationship based on the self-similarity but without the hierarchy. These results support good control of the dendritic and branch structure of the HBPMAs synthesized with the current method.

For an unentangled four-arm star chain having long-lived associative groups (stickers) at the arm ends, a bead-spring analysis was conducted to examine nonlinear stress relaxation behavior under single-step strain. In the analysis, some stickers were disrupted by the strain to activate very fast intrinsic motion of the star chain, and the disrupted and undisrupted stickers, respectively, were treated as mobile and immobile beads during this fast process. This intrinsic motion leads the chain to average/equilibrate its conformation to an extent allowed by the constraint from the immobile beads, and the disrupted stickers are reformed after the intrinsic motion. Thus, the star chain is affinely deformed by the strain but this deformed conformation is further tuned on the strain-induced sticker disruption followed by the conformational averaging and the sticker reformation. For this tuned initial conformation, the bead-spring analysis of the slow relaxation process (governed by intact/reformed stickers) combined with a free energy analysis suggested that the star chain exhibits time-strain separable damping of its relaxation modulus under moderate strain whereas some instability of uniform deformation (possibly resulting in the yielding of the system) emerges under large strain. These results of the analyses were favorably compared with a preliminary experiment made for a transient gel of end-associative tetra-poly(ethylene glycol) star chains. Furthermore, the analyses were extended to a transient gel of associative linear chains to discuss differences/similarities of the transient gels of star and linear chains having topologically different backbones.

For an unentangled four-arm star chain having long-lived associative groups (stickers) at the arm ends, bead-spring analysis was conducted for the nonlinear stress relaxation under double-step strain. The analysis considered strain-induced sticker disruption activating the fast intrinsic motion and partial equilibration of the chain, as in the case of the relaxation under the single-step strain examined in the accompanying paper (Ref. 1 of this paper). However, under the double-step strain, the conformation of a given arm keeps its memory from the first step strain γ1 (imposed at time −tw) when the second step strain γ2 is imposed at a later time 0. Namely, the conformation just before imposition of the second strain is different for the arms that carry the stickers having or not having been disrupted by the first strain, so that the analysis needs to be conducted for a whole cascade of the conformational memory, from the conformations on imposition of the first strain to those on imposition of the second strain. For the star chain having four arms, the conformational distribution in this cascade was still manageably narrow, and the bead-spring analysis allowed us to formulate the stress σ(t; γ1, γ2) at time t > 0 (after imposition of the second strain). It turned out that σ(t; γ1, γ2) thus deduced from the analysis captures the features of preliminary data obtained for tetra-PEG chains associating at the arm ends, confirming the importance of the cascaded memory and the isochronal cross-correlation of the arm conformations for those chains. In addition, for the case of γ2 ≅ −γ1/2, differences were found between the data and σ(t; γ1, γ2) deduced from the widely adopted BKZ constitutive equation, which further demonstrated the importance of the cascaded memory and cross-correlation not incorporated in this equation.