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In the linear viscoelastic regime, multiarm star chains having more than 24 arms bound by a soft core exhibit fast relaxation due to motion of individual arms and slow relaxation related to motion of the soft cores (structural rearrangement in a liquidlike order). In this regard, the multiarm stars are qualitatively similar to randomly dispersed polystyrene−polyisoprene (PS−PI) and polybutadiene−polystyrene (PB−PS) copolymer micelles, the former having rigid (glassy) PS cores and the latter with soft (rubbery) PB cores. However, the multiarm star PB chains and the copolymer micelles were found to exhibit significant rheological differences in the nonlinear regime possibly because of the differences in their core−arm (core−corona) compatibility and core softness. In long time scales, the nonlinear damping of the relaxation modulus measured for the multiarm star PB was much weaker than that for the micelles and somewhat similar to the damping of a critical gel. In contrast, the damping in short time scales was moderately stronger for the multiarm stars. A corresponding difference was observed for the viscosity under fast flow. These differences may be attributed to a strain-induced elastic coupling of the multiarm star chains:  The soft core of the multiarm star, chemically identical to the arms, may become scarcer on application of large deformation to suck in some segments of neighboring star arms so as to preserve the segment density therein. Then, the multiarm star chains are elastically coupled/connected through these cores to form a huge transient network under large deformation, thereby increasing and decreasing the relaxation intensities in long and short time scales, respectively. This mechanism, being absent for the PS−PI and PB−PS micelles because of lack of the core−corona compatibility (as well as the core rigidity for the PS−PI micelles), would have led to the observed weakening and enhancement of the damping for the slow and fast processes of the multiarm stars.

Rheological properties were examined for polybutadiene−polystyrene (PB−PS) diblock copolymer micelles that had soft PB cores and were dispersed randomly in a matrix of low-M homopolystyrene (hS) plasticized with dibutyl phthalate. In the linear viscoelastic regime, the micellar dispersions exhibited fast and slow relaxation processes attributed to the orientational relaxation of individual corona blocks and the relaxation of the Brownian stress (occurring through the micelle diffusion), respectively. Under large step strains, the fast and slow processes exhibited nonlinear damping in their relaxation moduli, and the damping was much stronger for the slow process than for the fast process. Under fast flow, two-step thinning of the viscosity corresponding to this damping behavior was observed. All these linear and nonlinear rheological features were quantitatively similar to those of PS−polyisoprene (PI) copolymer micelles having glassy PS cores. Analysis based on the emulsion model suggested that the interfacial relaxation of the soft PB cores of the PB−PS micelles occurred rapidly (almost together with the corona relaxation) because the PB cores had only small diameters (<40 nm). Thus, in long time scales after this interfacial relaxation, the PB core effectively behaved as a rigid core (keeping its spherical shape due to the segregation power/surface tension against the hS matrix), thereby exhibiting the above similarities with the PS−PI micelles having glassy PS cores.

The nonlinear relaxation modulus was examined for styrene−isoprene (SI) diblock copolymer micelles having rigid (glassy) S cores and flexible I corona blocks. These micelles, being dispersed randomly in entangling and/or nonentangling matrices of homopolyisoprene (hI), exhibited fast and slow relaxation processes. The fast process reflected the orientational relaxation of the corona I blocks, and the slow process detected the relaxation of the Brownian stress σB. This σB reflected the anisotropy of micelle distribution and relaxed through the micelle diffusion. The fast and slow processes exhibited the nonlinear damping of the modulus under large step strains (γ), and the time-strain separability was observed for both processes in either the entangling or nonentangling matrices. For the fast process, the damping function hf(γ) hardly changed with the SI micelle concentration CSI and matrix molecular weight Mmatrix and was close, in magnitude, to h(γ) of homopolymers. The nonlinearity of the corona relaxation characterized with this hf(γ) was attributed to retraction of the strain-elongated corona blocks occurring prior to their rotational motion (orientational relaxation). The damping function hs(γ) of the slow process, being smaller than hf(γ), decreased with increasing CSI. This nonlinearity of the slow process, similar to that of Brownian suspensions, reflected the γ-insensitivity of the micelle distribution anisotropy for large γ, and the strong CSI dependence of hs(γ) was attributed to relative rotation of concentrated micelles colliding with each other under large strains. (This rotation is similar to random mixing, thereby reducing the anisotropy and enhancing the damping.) Interestingly, the damping of the slow process was weaker in the entangling matrices than in the nonentangling matrices. This effect of the corona−matrix entanglement, observed for both the concentrated and dilute micelles with and without corona−corona entanglement, was attributed to the elasticity of the entangling matrices that disturbed the relative rotation of the mutually colliding micelles. A similar elastic effect of the corona−corona entanglement on the damping behavior was also noted.

The molecular picture of dynamic tube dilation (DTD) was tested for viscoelastic and dielectric data for two series of entangled binary blends of linear cis-polyisoprenes (PI) having 10^-3M2 = 308 and 10^-3M1 = 94.0 or 21.4. The volume fraction υ2 of the high-M chains was varied from 0.005 to 0.5. The Struglinski−Graessley parameter rSG (= M2Me²M1^-3), specifying the constraint release (CR) contribution to the relaxation of high-M chains at small υ2, was quite different for the two series of blends (rSG = 0.0093 and 0.79). For large υ2 (= 0.5), the full-DTD picture treating the relaxed portions of the chains as a simple solvent held satisfactorily in the entire range of time t irrespective of the rSG value. However, on a decrease of υ2, this picture began to fail at intermediate t and further at long t (in the terminal regime of the high-M chains), and the failure was more significant for the blend with small rSG. This failure occurred when the number βCR(t) of the entanglement segments equilibrated through the Rouse−CR dynamics was smaller than the equilibration number assumed in the full-DTD picture, βf-DTD(t) = {ϕ‘(t)}^-d with ϕ‘(t) and d (= 1.3) being the dielectrically determined tube survival fraction and the dilation exponent, respectively. A test was made also for the partial-DTD picture incorporating the maximum number of the segments that can be CR-equilibrated under the given ϕ‘(t) value. The behavior of the blends of various υ2, including the low-υ2 limit, was considerably well described by the partial-DTD picture, although nonnegligible differences still remained between this picture and experiments. Thus, the partial-DTD picture (including the full-DTD picture as an extreme case) was quite tempting, and a brief discussion was made for a possible improvement of existing molecular models on the basis of this molecular picture.

Viscoelastic and dielectric experiments were conducted for entangled binary blends of linear cis-polyisoprenes (PI) having widely separated molecular weights, M1 = 21.4 × 10³ ≅ 4Me and M2 = 308 × 10³ ≅ 62Me with Me (≅5 × 10³) being the entanglement molecular weight. The PI chain had type-A dipoles and its global motion (end-to-end vector fluctuation) was dielectrically active. The volume fraction of the high-M chain, υ2, was varied from 0.005 to 1. The Struglinski-Graessley parameter for the blends, M2Me²/M1³ = 0.79, was larger than a threshold value ≅0.5 necessary for the thermal constraint release (CR) mechanism to dominate the relaxation of the dilute high-M chains. Indeed, the Rouse-like CR relaxation was experimentally detected for the blends with small υ2 ≤ 0.01. For large υ2 (≥0.05), the high-M chains were entangled with each other (as well as with the low-M chains) and exhibited solution-like relaxation behavior at long times in their terminal regime. Comparison of viscoelastic and dielectric data suggested that the molecular picture of the dynamic tube dilation (DTD; with the dilation exponent d ≅ 1.3) incorporating the tube-edge fluctuation effect was valid in this regime. However, at intermediate times that were still longer than the relaxation time of the low-M chains, the moduli of the high-M chains were larger than the DTD prediction. In this intermediate regime, the CR equilibration of the entanglement segments in a dilated tube segment (the prerequisite of DTD) could not occur in time, thereby resulting in this failure of the DTD picture. In addition, the viscoelastic mode distribution of the high-M chains in the blends (with υ2 ≥ 0.05) agreed with that in the corresponding solutions only in time scales longer than the time required for the CR equilibration over the whole contour of the chain. These results demonstrated the importance of the CR equilibration in the entanglement dynamics.

For poly(ethylene oxide) (PEO) melts containing lithium perchlorate (LiClO4), angular frequency ω dependence of the dynamic dielectric properties under steady shear flow was measured using a rheodielectric instrument. The instrument also enabled measurements of the dielectric properties in the quiescent state as well as the linear and nonlinear rheological properties. A significant increase in the zero-shear viscosity η0 was observed upon addition of LiClO4 to PEO, and this increase was attributed to Li⁺-mediated intermolecular bridging of the PEO chains formed in the quiescent state. Significant shear thinning of the steady-state viscosity η(&ggrdot;) was observed with increasing shear rate &ggrdot;, suggesting the flow-induced breakup of these bridges. The presence of liberated ions was detected directly by dielectric experiments under steady shear flow. The dielectric dispersion (due to the electrode polarization of the ions) shifted to higher ω with increasing &ggrdot;, indicating an increase in the ionic conductivity σ. The dispersion curves for different &ggrdot; values collapsed onto a single master curve when plotted against a reduced frequency, {λ(&ggrdot;)}^-1ω, where λ(&ggrdot;) was a &ggrdot;-dependent shift factor representing the increase of σ. This result strongly suggested that the increase of σ under shear flow was due to an increase in the ionic mobility μ by the factor of λ(&ggrdot;) and not due to a change in the number density of ions. Furthermore, excellent agreement was found between the η(&ggrdot;)/η0 ratio and {λ(&ggrdot;)}^-1. This agreement reflected a strong motional cooperativivity between the PEO chain segment and ion (Li⁺).

Rheological and structural properties were examined for a 30 wt % solution of a 1,4-butadiene−styrene−1,4-butadiene (BSB) triblock copolymer (MS = 108 × 10³, MB = 13.3 × 10³ for each B block) in an S-selective solvent, dibutyl phthalate (DBP). At equilibrium at 25 °C, a bcc lattice of the unsolved, soft (rubbery) B domains connected by the middle S blocks (a lattice-type network) was formed to exhibit the elastic behavior against small strains. This lattice-type network was disrupted under steady shear to lose its elasticity, and the strongest disruption occurred at an intermediate shear rate (&ggrdot;) close to a frequency of B/S concentration fluctuation. This disruption behavior was similar to that of a BS/DBP diblock micellar lattice system. However, for the BSB/DBP system, an order of magnitude increase of &ggrdot; resulted in a minor change (by a factor <30%) of a time tr^∞ required for the full recovery of the elasticity during a quiescent rest after the preshear. This result, quantitatively different from that seen for the BS/DBP diblock system, was related to the bridge-type configuration of the middle S blocks of BSB:  Under the steady shear, a large fraction of the bridges in the flowing defect region would be converted into loops. Thus, the re-formation of the bridges in this region (a process absent in the BS/DBP system) should be required for the full recovery of the elasticity of the BSB/DBP system. This bridge re-formation, leading to a recovery of the order of the B domain arrangement and allowing the coexisting loops to exhibit the elasticity, should be accompanied by a transient mixing of the B and S block and thus gave the very weakly &ggrdot;-dependent tr^∞ determined by the mixing enthalpy.

In a nonpolar solvent such as benzene (Bz), living anionic chains having Li as the countercations generally aggregate with each other through Li at their ends. Specifically, the bianionic chains having Li at both ends form an aggregated network. For investigation of the dynamics of the aggregates, polybutadienyl dilithium (PBLi2) bianionic chains were polymerized in Bz, and their viscoelastic behavior was examined in a vacuum with a magnetically floating ball rheometer. This rheometer magnetically kept a position of a steel ball in a flowing liquid contained in a glass cell (test tubing) and measured a force acting on the ball, and the viscosity was obtained from this force. The viscoelastic relaxation after cessation of the flow was also detected as a decay of the force. In the experiment for the living PBLi2/Bz solution, the deactivation of the PB bianions was avoided by coating the steel ball with a nonreactive polyethylene film and by rinsing the cell with a Bz solution of diphenylethylenyllithium before the PBLi2/Bz solution was vacuum-sealed in it. The zero-shear viscosity η0^(anion) and terminal relaxation time τ1^(anion) of the living PB bianionic chains of the molecular weight = 14 × 10³ and concentration = 2.2 wt %, measured at several temperatures T ≤ 30 °C, were orders of magnitude larger than those of the same chains deactivated with methanol. This result confirmed that the PB bianionic chains aggregated into a transient network. Thus, the viscoelastic τ1^(anion) was assigned as the lifetime of the Li aggregates sustaining the network. The lifetime independently estimated from ⁷Li NMR data was close to τ1^(anion), lending support to this assignment of τ1^(anion). Furthermore, the analysis of the viscoelastic relaxation intensity suggested that only a small fraction (≅2%) of the PB chains formed the large transient network and the majority of the chains formed smaller aggregates.

For highly entangled cis-polyisoprene (PI) star polymers having more than 10 entanglements in each arm, dielectric and viscoelastic properties were examined within a context of the generalized tube model incorporating the dynamic tube dilation (DTD) mechanism. The star PI had the type A dipoles parallel along the arm backbone, and the global motion results in the viscoelastic as well as dielectric relaxation. The DTD relationship between the dielectric and viscoelastic relaxation functions Φ(t) and μ(t), μ(t) ≅ [Φ(t)]² (derived under an assumption of random displacement of the entanglement segment in the dilated tube edge), was not valid for the star PI. Furthermore, the DTD model (Milner−McLeish model) excellently described the viscoelastic data, but considerable differences were found for the dielectric data, even if an effect of the segment displacement in the tube edge was considered in the model. These results indicated a failure of the DTD molecular picture for a few entanglement segments near the branching point. Thus, these segments near the branching point appeared to fully relax via the constraint release (CR) mechanism before the expected tube dilation was completed. On the basis of this result, the DTD model was modified by explicitly incorporating this CR process (though in a crude way). This modification moderately improved the model prediction, suggesting a possible direction of further refinement of the model.

Structure−property relationships of aligned block copolymer lamellae in the vicinity of the order−disorder transition are studied by a combination of optical birefringence and rheology. Minimizing defect density was a crucial part of our experiments. The organization of block copolymer chains into aligned lamellae leads to a reduction in both zero shear viscosity and compliance relative to the disordered state. The frequency dependencies of the storage and loss shear moduli of the aligned lamellae are close to the Rouse prediction. In addition, the measured value of the compliance of the ordered and aligned state is within a factor of 2 of the Rouse prediction (agreement obtained with no adjustable parameters). In contrast, large differences between the experiments and the Rouse model are seen in the disordered state due to the presence of concentration fluctuations.

Rheological properties were examined for a butadiene−styrene (BS) diblock copolymer dissolved in an S-selective solvent, dibutyl phthalate (DBP). This copolymer was composed of a deuterated B block (MB = 13.3 × 10³) and a protonated S block (MS = 53.9 × 10³), and the microdomain structure in the quiescent state as well as under steady shear was detected with small-angle neutron scattering (SANS). At 25 °C, a quiescently equilibrated BS/DBP system of the BS concentration = 28 wt % exhibited elastic behavior under slow, small-amplitude oscillatory shear. This elasticity reflected a bcc lattice of BS micelles with B cores and S corona. Although the B cores were in the liquid state, the thermodynamic power of segregation from the S/DBP phase forced these cores to be arranged on the lattice at equilibrium. Under steady shear, the BS/DBP system exhibited significantly non-Newtonian flow behavior. At low shear rates (&ggrdot;), the steady state was attained after a significant stress overshoot followed by a thixotropic stress decay, and the viscosity η in this state was proportional to &ggrdot;^-1. This plastic behavior reflected mild disruption of the micellar lattice (decrease of the grain size) under slow shear. In contrast, at higher &ggrdot;, the lattice was massively disrupted to exhibit weaker &ggrdot; dependence of η. Corresponding to this massive disruption, the BS/DBP system just after cessation of the fast pre-shear exhibited full relaxation (with no equilibrium elasticity) attributed to the B/S concentration fluctuation. This pre-sheared system reformed the micellar lattice to recover its elasticity when kept quiescently, and the slowest reformation/recovery was observed at the pre-shear rate being comparable to the frequency ωf of the concentration fluctuation. Thus, the pre-shear at &ggrdot; ≅ ωf disrupted the lattice most efficiently (thereby resulting in the slowest lattice reformation). These rheological features and structures of the BS/DBP system were discussed in relation to the softness of the micellar B cores.

In current tube models for entangled polymer chains, the tube representing the topological constraint is considered to move with time. This tube motion results in constraint release (CR) as well as dynamic tube dilation (DTD), the latter occurring as a result of CR-equilibration of the chain. For the DTD process of type-A star chains, a particular relationship between the normalized dielectric and viscoelastic relaxation functions, Φ(t) and μ(t), can be derived under an assumption that a fluctuation amplitude of the star-branching point (BP) is smaller than the diameter of the dilated tube. This DTD relationship, μ(t) ≅ [Φ(t)]², does not hold for the terminal relaxation of the stars (Watanabe et al. J. Polym. Sci. B Polym. Phys. 2000, 38, 1024). This result, suggesting failure of the DTD molecular picture, might have been also attributed to breakdown of the assumption utilized in the above derivation. Under this background, this study examined dielectric and viscoelastic properties for a series of type-A cis-polyisoprene (PI) star chains having the same arm molecular weights (Ma ≅ 7Me) but different arm numbers q (= 4−15). The BP fluctuation should be suppressed, and thus, the DTD relationship should become valid with increasing q if the breakdown of the above assumption was the main reason for the observed failure of the DTD relationship. Nevertheless, for the series of star PI, this relationship was found to fail to nearly the same extent irrespective of the q value. This result indicated that the assumption of short-ranged BP fluctuation was not responsible for the observed failure of the DTD molecular picture. Thus, this failure was attributed to incomplete CR-equilibration for the portion of the star arms near BP. Analyses of the Φ(t) data suggested that this incompleteness was intrinsically related to the broad motional modes of the star arm.

We have examined the forces of interaction between opposing polystyrene brushes of various molecular weights in cyclohexane near the Θ temperature. The force−distance profiles and structural information obtained from surface forces experiments are compared to those of brushes in the good solvent, toluene. In both solvents, the chains are stretched a few times their free solution radii of gyration, though we find that when the solvent quality is decreased from good to near-Θ, the brush chains contract more than would free coils in solution undergoing the same solvent change. This shrinkage of the brushes measured from surface forces experiments agrees with hydrodynamic measurements of the layer thickness and theoretical predictions. A mean-field model successfully coalesces the surface forces data of different brushes in the near-Θ solvent to a single universal profile; however, this master curve is distinct from the universal profile formed by brushes bathed in a good solvent. We also show that in near-Θ cyclohexane the osmotic free energy that swells the tethered layer is more than an order of magnitude higher than the corresponding homopolymer solution of the same concentration. Although such a difference was seen for well-solvated brushes, here the magnitude for near-Θ conditions is considerably greater. We assert that the extra repulsion arises because the cyclohexane is a marginal solvent for the tethered chains (similar to the situation for branched chains in solution) and show, by superposing the force−distance data from brushes in both toluene and near-Θ cyclohexane, that ν > 0.5, where ν is the exponent relating the radius of gyration to molecular weight. Additionally, we report the results of experiments using a bimodal brush and discuss how its arms of different length affect its structural behavior.

Large deformation, nonlinear stress relaxation behavior was examined in the molten state for two types of ABS polymers, with one type containing well-dispersed rubber particles and the other, agglomerated rubber particles. These different morphologies were accomplished by adjusting the chemical composition of poly(styrene-co-acrylonitrile) (SAN) grafted on the rubber particles, such that the acrylonitrile content of the grafted SAN is equal to or different from that of the matrix SAN. The time-strain separability was found for the nonlinear relaxation of the matrix/grafted SAN chains in those ABS polymers. In the ABS polymer containing randomly dispersed rubber particles, the damping function h(γ) of the SAN chains was more strongly dependent on the strain γ than h(γ) of the pure matrix SAN chains. This difference was attributed to the filler effect in that ABS polymer. In contrast, in the ABS polymers containing networks of the agglomerated rubber particles, the SAN chains exhibited less γ-dependent h(γ) that is close to the pure matrix chains, possibly due to lack of the filler effect in large pockets formed in this network.

Dielectric behavior was examined for solutions of a styrene-isoprene-styrene (SIIS) triblock and SI diblock copolymers in an I-selective solvent, n-tetradecane (C14). The SI copolymer had noninverted type-A dipoles in the I block while the SIIS copolymer, a head-to-head coupled dimer of SI, had once-inverted dipoles in the I block. At a low temperature (5 °C) where the S blocks formed glassy, spherical microdomains, the I blocks of SIIS had either the bridge or loop configurations. The loop fraction φl in these I blocks was estimated from the dielectric losses of the SIIS and SI solutions at low frequencies. The φl was found to increase (from 0.6 to 0.8) with decreasing SIIS concentration (from 50 to 20 wt %). This increase of φl was attributed to stretching and destabilization of the bridge configuration on dilution. The equilibrium elasticities of the bridge and dangling loop, estimated from the φl values and rheological data of the concentrated SIIS/C14 solutions, were comparable in magnitude. This significant elasticity of the dangling loops reflected the strong osmotic constraint on the I block conformation in the concentrated I/C14 matrix phase.

Solidlike and liquidlike linear viscoelastic responses were observed at low and high temperatures (T) for polystyrene−polyisoprene−polystyrene (SIS) triblock copolymers dissolved in an I-selective solvent, n-tetradecane (C14). These SIS systems behaved as thermoreversible physical gels, with the microphase-separated S domains working as the cross-links at low T. Linear responses of those systems were examined in the vicinity of the sol−gel transition temperature Tgel. For the systems fully equilibrated in an isothermal state at Tgel, the power-law behavior, G‘(ω) ~ G‘ ‘(ω) ~ ωⁿ, was observed only at high frequencies ω, and a separate slow relaxation mode was observed at low ω. For the system quenched from high T (>Tgel) to low T (<Tgel), no power-law behavior was found during the transient gelation process. The power-law behavior should have been observed if the system had a self-similar, fractal network structure at Tgel. Thus, the observed lack of this behavior indicated that the structural self-similarity vanished over large length scales, possibly due to dynamic compositional fluctuation of the copolymer chains that dominated slow viscoelastic responses at Tgel (≅TODT). Similar features were observed also for a SI diblock copolymer in C14.

Dielectric relaxation spectroscopy and computer simulations have been used to elaborate on the loops/bridges population ratio in ordered poly(styrene-block-cis-isoprene-block-styrene), PS−PI−PS, triblock copolymer lamellae. The dynamics of the PI blocks are examined dielectrically for a PS−PI−PS copolymer having symmetrically inverted dipoles along the midblock backbone together with its diblock PS−PI precursor; the present work is an extension of a previous attempt (Watanabe, H. Macromolecules 1995, 28, 5006) addressing the loop/bridge ratio on the basis of a difference in the dynamics of these chains. The experiments indicate that the relaxation of the PS−PI−PS triblock lamella at T < %@mt;sys@%%@ital@%T%@rsf@%%@sx@%%@ital@%g%@rsf@%%@be@%PS%@sxx@%%@mx@% is significantly affected by preannealing at T > %@mt;sys@%%@ital@%T%@rsf@%%@sx@%%@ital@%g%@rsf@%%@be@%PS%@sxx@%%@mx@% , whereas the relaxation of the PS−PI lamella is insensitive to this annealing. These results as well as changes in the data for the triblock lamella with the sample preparation method should be related to structural changes occurring only for the triblock lamella, i.e., changes in the loop/bridge population distribution as well as formation of mutually knotted loops/bridges on annealing/sample preparation. In the computer simulations, equal mobilities are assumed for the PS and PI blocks, and thus, the PS−PI junctions are allowed to move rather freely under the segregation potential. The equilibrium bridge fraction is estimated and, in agreement with theoretical predictions, is found in the range of 0.50−0.37 as the molecular weight increases. The computer simulations suggest that the relaxation intensity of loops is almost twice that of bridges with both, however, having similar relaxation rates. The dynamics of loops and bridges are found not very different from that of the diblocks (except for the lowest molecular weight); however, the total intensity for the triblocks at equilibrium is much larger than that for the respective diblocks, which may be related to the observed increase of the intensity of the triblock lamella on annealing. However, the dielectric behavior of the diblock and triblock lamellae observed for T < %@mt;sys@%%@ital@%T%@rsf@%%@sx@%%@ital@%g%@rsf@%%@be@%PS%@sxx@%%@mx@% was not explained from the simulation. These results, indicating an important influence of the junction mobility on the block dynamics, in turn suggest that the (unknotted) loops and bridges can be dielectrically distinguished only when the junction motion is essentially frozen in order to enhance the thermodynamic effect on the block motion due to the density-preserving requirement.

Three blends were prepared from a high molecular weight of poly(vinyl chloride) (PVC) (Mw = 173 000, Mw/Mn = 2.0) and a low molecular weight PVC (Mw = 39 400, Mw/Mn = 1.7). Dynamic viscoelastic properties of these PVC blends in bis(2-ethylhexyl) phthalate (DOP) were measured at 40 °C as a function of polymer concentration, and the effect of long chains on gelation has been studied. The scaling exponent n at the gel point was found to be constant (=0.75), independent of molecular weight and molecular weight distribution. The critical concentration cg for the sol−gel transition still followed the relation cg ∝ Mw^-1, which was unchangeable with the molecular weight distribution and was also in good agreement with the previous results. As a result, cg was well expressed by a mixing rule, 1/cg = w1/cg1 + w2/cg2, where wi is the weight fraction of the component polymer i. The gel strength Sg at the gel point did not obey the relation Sg ∝ Mw^-1, but scaled as Sg ∝ Mz^-1 to show the effect of long chains on gelation. In the postgel state, the gel elasticity determined by the quasi-equilibrium modulus Ge still followed the scaling law, Ge ∝ ε^z, where ε is the relative distance to the gel point and z = 2.6 for the (PVC blend)/DOP samples, but the Ge values at the same ε were observed to be dominated by the long chains of PVC.

For a series of cis-polyisoprene (PI) chains having nearly the same molecular weight (M ≅ 50000) but differently once-inverted dipoles parallel along the chain backbone, dielectric behavior was examined in homogeneous blends in an entangling polybutadiene (PB) matrix with M = 263 000. In the blends, the PI chains (5 vol %) were entangled only with the matrix chains. The constraint release (CR) mechanism made a negligible contribution to the global relaxation of those PI chains. The series of PI chains exhibited quite different dielectric losses ε‘‘. These differences, reflecting the different location of the dipole inversion point in the chain backbone, were utilized to experimentally determine the eigenfunctions fp(n) and relaxation times τp defined for a local correlation function, C(n,t;m) = (1/a²)〈u(n,t)·u(m,0)〉 = (2/N)∑pfp(n) fp(m) exp(−t/τp) with u(n,t) being the bond vector for the nth segment at time t. The fp(n) and τp/τ1 ratio (p = 1−3) evaluated for the PI chains in the high-M PB matrix were found to be close to those determined in a low-M entangling matrix (M = 9240) as well as in the monodisperse bulk state of the same PI chains. The PI relaxation was dominated by the CR mechanism in this low-M matrix, while this mechanism made a moderate contribution to the PI relaxation in the monodisperse bulk state. Thus the close coincidence of fp(n) and the τp/τ1 ratio (p = 1−3) in the three environments indicated that the distribution of the slowest three eigenmodes was hardly affected by the CR mechanism. In contrast, for higher eigenmodes, modest CR effects were observed through differences in the shape of the ε‘‘ curves at intermediate frequencies for respective dipole-inverted PI chains in the three environments.

For cis-polyisoprene (PI) chains having dipoles parallel along their backbone, viscoelastic relaxation reflects orientational anisotropy of subchains (stress-generating units) at respective times while the dielectric relaxation reflects orientational correlation of the subchains at two separate times. This difference between viscoelastic and dielectric relaxation processes enables us to examine the short-time coherence of subchain motion in individual chains through comparison of these processes. Specifically, for the two extreme cases of perfectly coherent or incoherent subchain motion, viscoelastic moduli %@mt;sys@%%@ital@%G%@rsf@%%@sx@%coh%@be@%*%@sxx@%%@mx@%[S_EL2;space] and %@mt;sys@%%@ital@%G%@rsf@%%@sx@%incoh%@be@%*%@sxx@%%@mx@% are explicitly calculated from the relaxation times τp and eigenfunctions fp defined for a local correlation function describing fundamental features of the dielectric relaxation. On the basis of these backgrounds, the %@mt;sys@%%@ital@%G%@rsf@%%@sx@%coh%@be@%*%@sxx@%%@mx@% and %@mt;sys@%%@ital@%G%@rsf@%%@sx@%incoh%@be@%*%@sxx@%%@mx@% were calculated for a PI chain (M = 48800) dilutely blended in a high-M entangling polybutadiene (PB) matrix (M = 263000). (The τp and fp data necessary for this calculation were obtained dielectrically in Part 1 of this series of papers.) The %@mt;sys@%%@ital@%G%@rsf@%%@sx@%coh%@be@%*%@sxx@%%@mx@% was in excellent agreement with the G* data of the PI chain while %@mt;sys@%%@ital@%G%@rsf@%%@sx@%incoh%@be@%*%@sxx@%%@mx@% was significantly different from the data, meaning that the subchain motion was highly coherent for the PI chain in the high-M PB matrix. In contrast, the subchain motion of the same PI chain was found to be incoherent in an entangling PB matrix of smaller M (=9240). The constraint release mechanism made a negligible contribution to the global dynamics of the PI chains in the high-M matrix while it dominated the dynamics in the low-M matrix. These results indicate that the constraint release is an important factor that determines the degree of coherence of the subchain motion.

Nonlinear stress relaxation after imposition of step strain γ (≤2) was examined for blends of styrene−isoprene (SI) diblock copolymers in a homopolyisoprene (hI) matrix. The blends contained spherical micelles with S cores and I corona. For most cases, the blends had no plasticity and exhibited complete relaxation. Fast and slow relaxation processes characterizing the linear viscoelastic behavior of the micelles (part 1) were observed also for nonlinear relaxation moduli G(t,γ). For sufficiently small γ, G(t,γ) agreed with the linear relaxation moduli evaluated from the G* data of part 1. However, G(t,γ) decreased for larger γ (mostly for γ > 0.1). This nonlinear damping was much more significant for the slow process than for the fast process. For quantitative analysis of the damping behavior, the linear viscoelastic relaxation time τ* of the fast process was utilized to successfully separate the G(t,γ) data into contributions from the fast and slow processes, Gf(t,γ) and Gs(t,γ), in the following way:  At t > 6τ* where the fast process had negligible contribution to G(t,γ), Gs(t,γ) were taken to be identical to G(t,γ). By extrapolating those Gs(t,γ) data to shorter time scales, Gs(t,γ) were evaluated at t < 6τ*. Gf(t,γ) were evaluated as G(t,γ) − Gs(t,γ). For both Gf(t,γ) and Gs(t,γ), the terminal relaxation times were insensitive to γ and the time−strain separability held in respective terminal regions. This separability enabled us to define damping functions in those regions, hx(γ) = Gx(t,γ)/Gx(t) (x = f, s). For the fast process of the SI micelles, hf(γ) exhibited only modest γ dependence that was in good agreement with the dependence for homopolymer chains. This result indicated that the fast process corresponded to relaxation of individual corona I blocks, giving a strong support for the discussion of part 1. On the other hand, hs(γ) of concentrated micelles exhibited very strong γ dependence that was comparable, in both magnitudes and sensitivities to the I block concentration and molecular weight, with the dependence of the damping function hC14(γ) obtained for solutions of SI in an I-selective solvent, n-tetradecane (C14). Those solutions exhibited plasticity due to macrolattices of the micelles, and their nonlinearity was attributed to strain-induced changes in the micelle position. Thus, the similarity of hs(γ) and hC14(γ) suggested that the slow process of the concentrated micelles in the SI/hI blends was related to the changes in the micelle position and the subsequent micelle diffusion, again supporting the discussion of part 1.

Linear viscoelastic and dielectric relaxation behavior was examined for blends of styrene−isoprene (SI) diblock copolymers in a nonentangling homopolyisoprene (hI) matrix. The copolymers formed spherical micelles with S cores and I corona. The I blocks had type-A dipoles, and their global motion induced dielectric relaxation. The micelles exhibited fast and slow relaxation processes for both dielectric loss ε‘‘ and viscoelastic moduli G*. For the fast process, a nearly universal relationship was found for reduced moduli Gr* = [MbI/cbIRT]G*SI and reduced frequencies ωτ*, where G*SI was the contribution of the SI micelles to G*, MbI and cbI were the molecular weight and concentration for the I block, and τ* was a relaxation time that increased exponentially with cbI for large cbI. Similar behavior was found also for ε‘‘SI (SI contribution to ε‘‘). These features were qualitatively the same as those for the relaxation of star chains, indicating that the fast process corresponded to starlike relaxation of individual I blocks tethered on the S cores. Effects of the S cores on τ* were discussed within the content of the tube model. For the slow process of the concentrated micelles entangled through their I blocks, a relaxation time τs was close to the Stokes−Einstein (SE) diffusion time τSE evaluated from the viscosity associated with the fast process. Thus, the slow process of those concentrated micelles was attributed to their SE diffusion governed by the relaxation of individual corona I blocks. On the other hand, for dilute micelles in the nonentangling matrix, τs was significantly shorter than τSE but close to the SE diffusion time evaluated from the matrix viscosity. This result suggested that the slow process of those micelles corresponded to the SE diffusion in the pure matrix.

The shear relaxation modulus, G(t,γ), of entangled polymers decreases with increasing magnitude of shear, γ. A damping function defined as h(t,γ) = G(t,γ)/G(t,0) decreases with time and approaches a finite value, h(γ), at long times. In the tube model theory, the relaxation of G(t,0) is attributed to the reptation process and that of h(t,γ) is attributed to the retraction along the tube of a chain extended according to the large deformation of the material. We examine, in view of experimental results, an expression h(t,γ)/h(γ) = [1 + A(t,γ)]² derived from a theory of Doi. Here, 1 + A(t,γ) is an average elongation ratio of a chain contour in the tube. At γ less than about 7, the function A(t,γ) was factorizable into functions of t and γ, respectively:  the reptation process and the retraction process are not coupled in this case. At higher strains, A(t,γ) is not factorizable and is dominated by modes of shorter relaxation times. Possibly the limited extensibility of chain portions of the order of the entanglement spacing changes the nature of the tube at large deformations. For branched polymers, the fast relaxation modes become dominant even at γ = 5. This may be in accord with the well-established theory for branched polymers that stress relaxation at vanishing γ requires the retraction of the chain end along the contour of the chain. This process is essentially the same as the retraction process at large strain, and these two relaxation processes cannot occur independently of each other.

The complex strain-optical ratio, O*(ω), and the complex Young's modulus, E*(ω), of four vinyl polymers, atactic polypropylene, 1,2-polybutadiene, poly(ethylethylene), and poly(4-vinylbiphenyl), were measured from the rubbery plateau to the glassy zone to investigate the origin of the birefringence and the chain orientation in the glassy zone. The data, including those for polystyrene and poly(vinyl naphthalene), were analyzed through a modified stress-optical rule:  The rule states that O*(ω) and E*(ω) are described as a sum of two component functions (denoted by R and G) and that a proportional rule similar to the ordinary stress-optical rule holds well for each of the R and G components with different stress-optical coefficients. The R and G components have been interpreted to be respectively related to the orientation of the main chain axis toward the stretch direction and tilting of the structural units by a rotational orientation about the main chain axis. According to this interpretation, the stress-optical coefficients for the R and G components are predicted to decrease and increase, respectively, with increasing size of the side chain. The present study shows the validity of this prediction. In addition, it is suggested that the degree of the rotational orientation responsible for the G component becomes larger with increasing size of the side chain.