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Complex dynamic shear moduli, shear and normal stresses in steady shearing flow, and complex moduli with superposed steady shear are investigated in both theoretical and experimental aspects. Firs) it summary of phenomenological and molecular theories is given. Experimental tests of phenomenological theory are made by comparing dynamic (linear viscoelastic) data and steady shearing flow (nonlinear viscoelastic) data. It is found that the recent theory of memory fluids is quite satisfactory and also the results show that the action of normal stress in steady shearing flow is mainly pull in the direction of the flow line. The behavior of dilute polymer solutions (near A condition are best approximated by the molecular theory of Zimm, particularly at very low shear rates. At higher shear rates, the Zimm theory fails in predicting the appearance of non-Newtonian viscosities and nonquadratic normal stresses. Various proposed modifications of the theory are examined experimentally. The behavior of concentrated polymer solution does not seem to fit any of the existing molecular theories; therefore, some typical features of the experimentally observed behavior of concentrated solutions are simply summarized. The results of the measurements of complex moduli with superposed steady shear show that in the low-frequency region the effect of superposed shear rate results in a much larger decrease in the real part of the complex modulus that in the imaginary part, while in the higher-frequency region the real part is again decreased but the imaginary part is increased with the increase of superposed shear rate.

The complex Young's modulus and the complex strain-optical coefficient of two series of polycarbonate derivatives were measured around the glass transition zone to investigate the molecular structure-property relationships. The data were analyzed with the modified stress-optical rule: The complex Young's modulus was separated into two component function, R and G. Main chain flexibility and the intrinsic birefringence were estimated from the R component. It was found that the main flexibility was insensitive to the substitution on phenylene groups or propylene groups while the intrinsic birefringence could be significantly reduced.

The complex shear modulus, G*, was studied for polystyrene solutions in dioctyl phthalate (DOP); temperature = 22 °C (ϑ) ∼ 50 °C; concentration = 59 kg m-3; molecular weight range 200−20 000 kg mol-1. The data were compared with those for PS in a good solvent, tricresyl phosphate (TCP). The solvent viscosity of the two neat solvents was found to be the same within experimental accuracy in the range of studied temperatures. For high-M samples, the rubbery plateau modulus of the two systems, in ϑ and good solvents, agrees with each other. This result is inconsistent with the prediction of the original scaling theory, which predicts a lower rubber plateau modulus in a ϑ solvent, but agrees well with the two-parameter scaling theory by Colby and Rubinstein [Macromolecules 1990, 23, 2753]. The location of the terminal flow region was almost the same for low-M samples, M < Me. However, with increasing M, the terminal flow region in DOP was located at lower frequencies than in TCP. These results indicate that G*...

The significance of linear density equilibration time, 2τR, of a polymer chain in Doi−Edwards (DE) tube model theory was investigated for the relaxation modulus, G(t,γ), at various magnitudes of sh...

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τRZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τL > τRZ) and a high-frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ1) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K-BKZ) equation with the damping function h(γ) = (1 + 0.2γ2)−1/2, where γ is the magnitude of shear. Contributions to η and Ψ1 from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τst = τ + (τRZ − τ)/(1 + 0.35τRZ γ˙) instead of τRZ. Here, γ˙ is the rate of shear, and τ is the τRZ value at the infinite dilution limit. η and Ψ1 at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol−1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002

Nonlinear viscoelasticity was studied for a polystyrene solution in tricresyl phosphate; molecular weight = 5480 kg mol-1; concentration = 49 kg m-3. The longest Rouse relaxation time, τR, was estimated by fitting the Rouse theory to dynamic modulus at high frequencies. The Doi−Edwards tube model theory presumes that 2τR is the characteristic time for equilibration of chain contour length; (2τR)-1 is the rate for an extended chain to shrink back to equilibrium. The τR value was much lower than that evaluated with more widely accepted methods. However, the shear stress (σ) and the first normal stress difference (N1) in the start-up of shear flow with low rate of shear ( 8(2τR)-1), the maxima of σ and N1 were located at t = 2τR and 4τR, respectively, in accord with the interpretation that 2τR is the characteristic time for chain shrink. The strain-dependent relaxation modulus, G(t, ...

Dynamic birefringence and dynamic viscoelasticity of polystyrene/tricresyl phosphate solutions were measured over a wide reduced frequency region from the rubbery to the glassy zone for concentrations ranging from 0.20 g cm-3 to bulk. The rubbery (polymeric) component of the modulus whose molecular origin is attributed to the segment orientation was separated from solvent contribution with aid of the modified stress−optical rule. The size of the Rouse segment was calculated from the limiting modulus of the rubbery component at high frequencies. The stress−optical coefficient, which is a measure of size of the optical segment, was found to be insensitive to polymer concentration. This result indicates that the main chain orientation created by the unit stress is insensitive to polymer concentration, implying that statistical nature of polymer chain is not affected by the presence of solvent. This result is in accord with a conformational study, which indicates that the radius of gyration of PS chains is al...

The equilibrium modulus G e of the poly(vinyl chloride) (PVC)/bis(2-ethylhexyl) phthalate (DOP) gels was examined at temperatures T ≥ 40 °C. Near the sol-gel transition temperature, G e decreased rapidly with increasing T. The normalized moduli G e M/cRT of the gels at different M, T, and/ or c were universally dependent on the relative distance from the gelation point, ∈, with c and M being the PVC concentration and molecular weight, respectively, and R being the gas constant. This result suggested that the mesh size of the gel network near the gelation point was universally determined by ∈ and M. The normalized moduli were smaller than unity, i.e., G e < cRT/M at low ∈. This result suggested that the average mesh size near the gelation point was larger than the PVC chain size. Thus, several PVC chains appeared to be connected at cross-linking crystal domains to form a larger, effective mesh strand.

Viscoelastic behavior of PVC gels/sols in a wide range of PVC concentration c was examined in various plasticizers having different solubility toward PVC. The gel point c g decreased with decreasing solubility, possibly due to enhanced formation of PVC crystallites (crosslinking points in the gels) in poorer plasticizers. The exponent characterizing the power-law behavior of the critical gel (G'~G''~ωn), n = 0.75, was insensitive to the plasticizer solubility. The exponent z (= 2.52 ± 0.14), characterizing the equilibrium modulus Ge of the well developed gels (Ge~ez with e =|c - cg |/cg) was also insensitive to the plasticizer solubility. However, the magnitude of the normalized modulus c-1Ge was smaller in poor plasticizers, suggesting some heterogeneity in the gel network structure therein. The other exponent γ characterizing the viscosity η of the sols (η~ eγ) moderately increases from 1.2 to 1.9 with increasing solubility. Comparison of the normalized viscosity and compliance in different plasticizers suggested that the sol structure was heterogeneous and this heterogeneity sensitively increased with decreasing solubility.

Estimation methods for the longest Rouse relaxation time (τR) of an entangled polymer in a semidilute solution were examined. We evaluated τR by fitting the dynamic modulus (G′) with the Rouse model theory in the power law range, where G′ was proportional to the square root of the angular frequency (ω). The τR values thus obtained for polystyrene (PS) solutions in tricresyl phosphate (TCP) were employed to derive an empirical formula for the evaluation of τR from the viscosity (η): M is the molecular weight, and c is the mass of polymer per unit volume; Me = cRT/GN is the entanglement molecular weight, where GN is the G′ value at the inflection point of the graph of log G′ versus log ω. The subscript η indicates that τR is derived from η data. The proposed equation was also applicable to bulk PS and bulk polyisoprene. Discrepancies among reported τR values in semidilute solutions seem to be mostly due to discrepancies in Me values. For PS solutions in dioctyl phthalate, a Θ solvent, the τR value derived from η was much larger than that from the G′ curve. Apart from the evaluation method of τR, we observed for PS that Me was independent of temperature for good solvent systems and melts, that Me for solutions in TCP agreed with that for solutions in another good solvent, and that Me for a Θ-solvent system was equal to that for good solvent systems with the same M and c values. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1704–1712, 2001

Some topics in nonlinear rheology are discussed for polymeric systems: constitutive equation for dilute solutions; strain hardening in elongational flow; chain retraction in entangled systems; stress overshoot of non-entangled systems; entanglement molecular weight.

Dynamic viscoelasticity and dynamic birefringence were investigated for a series of polyesters with various combinations of dimethyl decalin 2,6-carboxylate, DMHN and dimethyl terephthalate, DMT as acid component and 9,9-bis[4-(2-hydroxy-ethoxy)phenyl]fluorene, BPEF and ethylene glycol, EG as diol component. The lowering of the stress-optical coefficient was achieved by the displacement of phenylene (DMT) with a hydrogenated naphthylene ring (DMHN) in the main chain and by the introduction of BPFE in the place of EG. The former choice lowered the intrinsic birefringence but did not affect the chain flexibility. The latter enhanced the flexibility but did not affect the intrinsic birefringence. The systematic result clearly revealed the importance of two different factors, the anisotropy of structural units and the chain flexibility, in molecular designs for polymers with low stress-optical coefficient.

The dynamic birefringence and the dynamic viscoelasticity of an oligostyrene, A1000, whose molecular weight (Mw = 1050) was comparable to the Kuhn segment size, MK, were examined near and above the glass-transition temperature in order to characterize polymeric features of very short chains with M ∼ MK. The complex shear modulus, G*(ω), was similar to that for supercooled liquids: No polymeric modes such as the Rouse mode were detected at low frequencies of viscoelastic spectrum. On the other hand, the strain-optical coefficient was found to be negative in the terminal flow zone and positive in the glassy zone. Because the negative birefringence of polystyrene is originated by polymeric modes associated with chain orientation, the present results indicate that polymeric modes exist and become dominant for birefringence in the terminal flow. The data were analyzed using a modified stress-optical rule: The modulus and the strain-optical ratio were separated into polymeric (rubbery) and glassy components. The total modulus, G*(ω), was mostly due to the glassy component, GG*(ω), resulting in the positive birefringence. GG*(ω) for A1000 agreed with that for high M polystyrenes when compared at a comparable reduced frequency scale. The polymeric component, GR*(ω), giving rise to the negative birefringence was lower than GG*(ω) over the whole frequency range but its contribution to the birefringence exceeded that of the glassy component at low frequencies because of the larger optical anisotropy and longer characteristic relaxation time of the former. The limiting modulus of GR* at high frequencies was about 3 times lower than that for high M polystyrenes, indicating that the main-chain orientation of the oligostyrene on instantaneous deformation was reduced compared with that of high M polystyrenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 954–964, 2000

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 sig...

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type-A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]2 if the tube actually dilates in the time scale of the star relaxation. For 6-arm star cis-polyisoprene (PI) chains (having those type-A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight Ma. However, in the range of Ma examined, Ma ≤ 8Me (Me = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of Ma, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000

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 ...

Overshoot of shear stress, σ, and the first normal stress difference, N1, in shear flow were investigated for polystyrene solutions. The magnitudes of shear corresponding to these stresses, γσm and γNm, for entangled as well as nonentangled solutions were universal functions of γ˙τeq, respectively, and γNm was approximately equal to 2γσm at any rate of shear, γ˙. Here τeq = τR for nonentangled systems and τeq = 2τR for entangled systems, where τR is the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. Only concentrated solutions exhibited stress overshoot at low reduced rates of shear, γ˙τeq 1, γσm and γNm were approximately proportional to γ˙τeq. At very high rates of shear, the peak of σ is located at t = τR, possibly indicating that the polymer chain shrinks with a characteristic time τR in dilute solutions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1917–1925, 2000

Dynamic viscoelastic behavior was investigated for solutions of polystyrene in tricresyl phosphate, a good solvent, at concentrations, c, less than the coil-overlapping concentration, c*. At the infinite dilution limit, the behavior was in accord with the theory of Doi and Edwards involving the excluded volume potential and hydrodynamic interaction (HDI). Thus, the viscoelastic functions were completely derived from the intrinsic viscosity–molecular weight relation. At finite c, the complex modulus was represented by the sum of two terms. One was a Rouse–Zimm (RZ) term conveniently represented by the Zimm theory with an arbitrarily chosen value of the HDI parameter. The other was a term with a single relaxation time, longer than the longest RZ relaxation time, and with a high-frequency modulus proportional to the square of c [the long-time (LT) term]. The behavior of the RZ term indicated the stronger screening of HDI with increasing c. Using the experimental c dependence of the longest RZ relaxation time to get the relevant parameter, we compared the RZ viscoelastic function with the Muthukumar–Freed theory. The agreement was good at low concentrations, c < c*. The contribution of the LT term, which was not included in the theory, was quite significant at low frequencies; about 60% of the Huggins coefficient was attributable to this term. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 211–217, 2001

The overshoot of the shear stress (σ) and the first normal stress difference (N1) in the shear flow was investigated for polystyrene solutions in tricresyl phosphate. The magnitudes of the shear (γσm and γNm) corresponding to the maxima of σ and N1 were compared with the theory of Pearson et al. (J Polym Sci Part B: Polym Phys 1991, 29, 1589), a modification of the tube model theory of entanglement including the possible elongation of polymer chains in a fast flow. The results for the entangled systems were in excellent agreement with the theory if the equilibration time of the chain contour length (τe) was equated with 2τR, in accord with the dynamics of the tube model chain. Here, τR was the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. The results for the nonentangled systems were fitted with the same theoretical function, with τe = 1.2τR. This result may indicate that at the same concentration, nonentangled chains contract faster than entangled chains. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3271–3276, 2000

Viscoelasticity and morphology of polycarbonates being multi block copolymers composed of bisphenol A polycarbonate, PC, and polydimethylsiloxane, PDMS, were investigated as a substitute for soft poly (vinyl chloride). Mechanical properties of the soft polycarbonates were found to be well stable for temperature compared with soft poly (vinyl chloride). Modulus of the polycarbonates could be controlled by varying PDMS content. Small angle X-ray scattering experiment and electron microscope revealed that the sort polycarbonates formed microdomain structures.

Overshoot of shear stress, σ, and the first normal stress difference, N1, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γσm and γNm, corresponding to the peaks of σ and N1 lay on the universal functions of γ˙τR, respectively, proposed for dilute solutions in pure solvent. Here τR is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γσm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τR < 10−2. This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γσm and γNm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000

Within the context of the generalized tube model, the tube representing the entanglement constraint is not necessarily fixed in space but moves with time. This tube motion results in constraint release (CR) as well as dynamic tube dilation (DTD) for the chain trapped in the tube. For monodisperse systems, the DTD molecular picture leads to the normalized relaxation modulus μ(t) (=G(t)/GN) being proportional to square of the surviving fraction of the dilated tube. In contrast, the normalized dielectric relaxation function Φ(t) of the chain having noninverted type-A dipoles is proportional to this fraction. Thus, the viscoelastic and dielectric relaxation functions satisfy a relationship μ(t) = [Φ(t)]2 if the tube dilates in time scales of the chain relaxation. The validity of this relationship was examined for linear cis-polyisoprene (PI) chains having those type-A dipoles. The relationship was approximately valid, and thus, the tube dilated for the PI chains with M/Me = 10−30 in their bulk state, although...

The structure of a colloidal suspension under shear flow was studied by in situ small angle neutron scattering (SANS). This suspension exhibited shear thinning at low shear rates and shear thickening at high shear rates. Under quiescent conditions, the SANS profiles were azimuthally symmetric and contained a well-defined scattering maximum. This is due to local, liquidlike correlations between neighboring particles. Increasing shear rate lead to changes in the interparticle correlations. These changes are quantified by obtaining the anisotropic structure factor of the suspension under shear flow. We found an increased probability for the formation of inter-particle clusters in the gradient-vorticity plane. This results in an increase in the low angle scattering intensity in the flow direction, and the scattering peak, observed under quiescent conditions, is reduced to a shoulder. We found no evidence for a shear-induced phase transition in our experimental window. At low shear rates (γ), the microstructu...

Rheo-dielectric behavior was examined for 4−4′−n-octyl-cyanobiphenyl (8CB) having large dipoles parallel to its principal axis (in the direction of the C≡N bond). In the quiescent state at all temperatures (T) examined, orientational fluctuation of the 8CB molecules was observed as dielectric dispersions at characteristic frequencies ωc>106 s−1. In the isotropic state at high T, no detectable changes of the complex dielectric constant ɛ*(ω) were found under slow flow at shear rates ˙γ≫ωc. In the nematic state at intermediate T, the terminal relaxation intensity of ɛ*(ω) was decreased under such slow flow. In the smectic state at lower T, the flow effect became much less significant. These results were related to the flow-induced changes of the liquid crystalline textures in the nematic and smectic states, and the differences of the rheo-dielectric behavior in these states are discussed in relation to a difference of the symmetry of molecular arrangements in the nematic and smectic textures.

Nonlinear rheology was examined for concentrated suspensions of spherical silica particles (with radius of 40 nm) in viscous media, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture and pure ethylene glycol. The particles were randomly and isotropically dispersed in the media in the quiescent state, and their effective volume fraction φeff ranged from 0.36 to 0.59. For small strains, the particles exhibited linear relaxation of the Brownian stress σB due to their diffusion. For large step strains γ, the nonlinear relaxation modulus G(t,γ) exhibited strong damping and obeyed the time-strain separability. This damping was related to γ-insensitivity of strain-induced anisotropy in the particle distribution that resulted in decreases of σB/γ. The damping became stronger for larger φeff. This φeff dependence was related to a hard-core volume effect, i.e., strain-induced collision of the particles that is enhanced for larger φeff. Under steady/transient shear flow, the particles exhibited thinning and thickening at low and high γ˙, respectively. The thinning behavior was well described by a BKZ constitutive equation using the G(t,γ) data and attributable to decreases of a Brownian contribution, σB/γ˙. The thickening behavior, not described by this equation, was related to dynamic clustering of the particles and corresponding enhancement of the hydrodynamic stress at high γ˙. In this thickening regime, the viscosity growth η+ after start-up of flow was scaled with a strain γ˙t. Specifically, critical strains γd and γs for the onset of thickening and achievement of the steadily thickened state were independent of γ˙ but decreased with increasing φeff. This φeff dependence was again related to the hard-core volume effect, flow-induced collision of the particles enhanced for larger φeff.

Dynamic viscoelasticity and dynamic birefringence measurements were performed on a quenched amorphous sample of a syndiotactic polystyrene, sPS. The measurements were carried out at temperatures where crystallization did not occur above the glass transition temperature. The data were analyzed with a modified stress-optical rule: The complex Young's modulus was separated into two components, designated with subscripts R and G, for which the ordinary stress-optical rule held well individually. A comparison with the results for a conventional amorphous atactic polystyrene has shown that the stereoregularity of sPS enhances the stiffness of main chain and then increases the optical anisotropy of segments. This conclusion is in accord with theoretical calculation on coil dimension and optical anisotropy. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 399–404, 1999

The complex shear modulus was measured for four low molecular-weight polystyrenes (Mw = 10,500, 5970, 2630, and 1050) near and above the glass transition temperature. For the lowest molecular weight sample, the method of reduced variables, the time–temperature superposition principle, was applicable, while it was not applicable for the higher M samples. For these higher M samples, it was assumed that the complex modulus is composed of two components (R and G components). The R component was estimated by subtracting the G component, which was assumed to be the same as the modulus of the lowest molecular weight sample. The time–temperature superposition principle was applicable to each of the R and G components, and the shift factors were different from each other. The contribution of the R component to the total complex modulus decreased with decreasing M. Anomalous temperature dependence of the steady-state compliance for low M polymers as Plazek reported could be attributed to difference in temperature dependence of the two components. The estimated complex modulus for the R component was in accord with that calculated by spring-bead model theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 389–397, 1999

From a simple calculation considering no thermodynamic requirement of maintaining uniform density, we estimated the effects of spatial confinement on the dielectric relaxation of model block copolymer chains having type-A dipoles. The results were utilized to discuss the relative importancc of these requirement and confinement in the block chain dynamics. For a tail (tethered) chain composed of N segments as well as for loop/bridge chains composed of 2N segments, all confined in a lamella of thickness L=N1/2b (b=segmental step length), the terminal relaxation was moderately faster, its mode distribution was slightly broader, and the dielectric intensity was considerably smaller than those of the same chains in free space. These effects of the spatial confinement were identical for the bridge and loop (either in the knotted or unknotted configuration) and nearly the same also for the tail. The dielectric behavior expected from this calculation was quite different from the behavior of actual type-A blocks. This result strongly suggests that the block chain dynamics is affected much moer significantly by the requirement of maintaining uniform density than by the spatial confinement.

For a wide variety of systems, structures under flow have been investigated with rheo-optical techniques. It is of particular interest and importance to examine the flow effects on structures and dynamics with different techniques. A rheo-dielectric technique, that detects dynamic dielectric responses under flow, is complementary to rheo-optical techniques and provides us with a very useful method of investigating these effects. This article gives a brief review of rheo-dielectric features of some model systems revealed in recent studies to demonstrate the applicability of the rheo-dielectric technique.

Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions in their complex dielectric constant e*(ω) at characteristic frequencies ω c above 106 rad s–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of e*(ω) under flow at shear rates \(\). In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of e*(ω) as well as the static dielectric constant e′(0) decreased under flow at \(\). This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution) and anisotropy in motion of individual molecules with respect to the director.

Nonlinear rheological features were investigated for an aqueous solution of tetraethylammonium perfluorooctyl sulfonate (C8F17SO3–N+(C2H5)4; abbreviated as FOSTEA). In the solution (c=0.045 mol/l; 28.3 g/l), spherical micelles of FOSTEA were connected with each other to form threads of pearl-necklace shape. These threads were further organized into a transient network to exhibit linear relaxation characteristic of living polymers, single-mode terminal relaxation widely separated from faster relaxation processes. Nonlinear relaxation experiments against large step-strains γ(≤8) revealed that the terminal relaxation mode had a γ-insensitive relaxation time but its relaxation intensity exhibited significant damping (much stronger than that for entangled polymers). In contrast, the relaxation time and intensity for the fast relaxation modes first increased and then decreased with increasing γ. Under shear flow, the FOSTEA threads exhibited strong thinning of the viscosity. These nonlinear features of the FOSTEA threads were compared with those of other threadlike micelles, analyzed on the basis of an empirically introduced constitutive equation, and discussed in relation to strain/low-induced scission of the living threads.

Strain-induced birefringence, Δn, was measured at wavelengths 400nm

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 G * coh and G * incoh are explicitly calculated from the relaxation times τ p and eigenfunctions f p defined for a local correlation function describing fundamental features of the dielectric relaxation. On the basis of these backgrounds, the G * coh and G * incoh were calculated for a PI chain (M = 48800) dilutely blended in a high-M entangling polybutadiene (PB) matrix (M = 263000). (The τ p and f p data necessary for this calculation were obtained dielectrically in Part 1 of this series of papers.) The G * coh was in excellent agreement with the G * data of the PI chain while G * incoh , 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.

The tensile stress and the birefringence of polystyrene were measured under elongation at a constant rate up to the elongation ratio of 4 at 115, 105, and 100 °C. The tensile stress was separated into two component functions, designated with subscripts R and G, through a modified stress−optical rule, MSOR, considering the effect of finite extensibility of the polymer chain on the stress dependence of the stress-optical coefficient. The R component represents the stress attributed to the polymer segment orientation and the G component to the twist of the polymer chain. At 115 °C, the time dependence of the viscosity growth function of the two components, ηER+ and ηEG+, can be described in the framework of linear viscoelasticity except for a steep increase of ηER+ at times longer than 1/(2e), where e is the rate of elongation. It is well-known that this type of steep increase is due to the strong increase of strain measured under elongation at a constant rate. At lower temperatures, ηEG+ decreased with incr...

Nonlinear rheology was examined for a critical gel of poly(vinyl chloride) in dioctyl phthalate (PVC/DOP). PVC crystal domains worked as the cross-linking domains in this physical gel. In the linear regime, the gel exhibited power-law dependence of storage and loss moduli on frequency ω, G‘(ω) ∝ G‘‘(ω) ∝ ωn with n ≅ 0.7. In stress relaxation experiments the gel exhibited nonlinear damping of the relaxation modulus G(t,γ) with increasing step-strain γ, but the magnitude of damping was much smaller than that for homogeneous homopolymer liquids. In addition, for the gel, the G(t,γ) data for the largest strain examined (γ = 5) were in close agreement with the linear G(t) measured after imposition of this strain. On start-up of shear flow at a rate γ, the viscosity growth function η+(t,γ) of the gel followed the linear η+,L(t) at a short time scale, deviated downward from η+,L(t) but still increased gradually at an intermediate time scale, exhibited an apparent plateau (pseudo-steady-flow behavior) over a long...

In hard-sphere suspensions of solid particles, the stress has the Brownian (thermodynamic) and hydrodynamic components σB and σH, the former reflecting the anisotropy of the particle distribution while the latter being determined by the hydrodynamic interaction between the particles. These two components exhibit nonlinearities under steady shear flow with different mechanisms. The nonlinearity of σB results from the particle distribution insensitive to the shear rate, while σH becomes nonlinear due to flowinduced clustering of the particles. These structural origins of the nonlinearities were confirmed from flow-SANS experiments.

The stress-birefringence relationship was examined for amorphous poly(ethylene terephthalate) films under uniaxial stretching in the temperature range 80–95°C at various stretch speeds in order to study the effect of strain-induced crystallization. At high temperatures, the ordinary stress-optical rule (SOR) held well at low draw ratios; the birefringence was proportional to the stress. However, at a certain draw ratio, the birefringence started to increase more rapidly than the stress and the SOR did not hold thereafter. D.s.c. measurements for films quenched at various stages of stretching supported the breakdown of the SOR being due to strain-induced crystallization. At still higher draw ratios, the stress suddenly began to increase. This is attributed to the non-Gaussian nature of the highly extended chains. The stress-optical coefficient has to be assumed to decrease with stress in order to estimate the crystallinity from the birefringence of films under high stress. At very low temperatures or at very high stretch speeds, the SOR was invalid even at low draw ratios due to the contribution of glassy stress. Even for such cases, the onset of strain-induced crystallization may be determined from the stress-birefringence relationship provided that the crystallization starts at relatively high draw ratios where the contribution from the glassy stress is small.

Non-Newtonian flow behavior was examined for a styrene−isoprene (SI) diblock copolymer (MS = 13.9K, MI = 28.8K) in a low-M homopolyisoprene matrix (I-4; M = 4.1K) at −20 °C where the copolymer formed spherical micelles with glassy S cores and soft I corona. Those micelles (15 wt % in the system) were isotropically dispersed in the I-4 matrix at equilibrium, and the corona blocks were entangled neither among themselves nor with the short matrix. The viscosity η of this micellar dispersion exhibited two-step shear-thinning behavior. Molecular origin of this behavior was examined in relation to previously investigated linear and nonlinear relaxational features of the SI micelles. In the linear regime (for small strain), the micelles exhibited fast and slow relaxation processes. The fast process was due to the relaxation of the micellar corona, while the slow process was related to the thermodynamic (Brownian) stress that reflected a strain-induced anisotropy in the spatial distribution of the micelles. This ...

Rheological and dielectric behavior was examined for concentrated solutions of a styrene−isoprene−styrene (SIS) triblock copolymer in monomeric and polymeric I-selective solvents, n-tetradecane (C14) and a low-M homopolyisoprene (I-1; M = 1.4K). The I blocks had symmetrically once-inverted dipoles along the block contour, and their midpoint motion was dielectrically detected. The SIS solutions exhibited rubbery, plastic, and viscous behavior at low, intermediate, and high temperatures (T). Dielectric and viscoelastic data strongly suggested that the S and I blocks were more or less homogeneously mixed in the viscous regime. In the rubbery and plastic regimes, the S blocks were segregated to form spherical domains, and the I blocks took either the loop or bridge conformation. In these regimes, the inverted dipoles of the I blocks enabled us to dielectrically estimate the loop fraction, φ1 ≅ 60% in C14 and I-1. These loops, having osmotically constrained conformations, strongly affected the rheological prop...

Dynamic birefringence and dynamic viscoelasticity of poly(4-methyl styrene) and poly(4-t-butyl styrene) were measured to investigate the molecular origin of viscoelasticity around the glass transition zone. The data were analyzed with a modified stress-optical rule: The birefringence and the stress were separated into two component functions of different molecular origins. One component is related to the orientation of the main chain axis and the other one to the rotation of the repeating units about the main chain axis. The strain dependence of the two characteristic orientation functions in the glassy zone was estimated and the orientation mechanism of repeating units was discussed.

The complex strain-optical ratio and the complex Young's modulus of a polyarylate with a low molecular anisotropy, PAr1, were measured around the glass-to-rubber transition zone. The polyarylate was synthesized from 2,2′-dicarboxy biphenyl and 4,4′-dioxydiphenyl-2,2′-propane. The data were analysed with a modified stress-optical rule: The Young's modulus and the complex strain-optical ratio were separated into two component functions (denoted by G and R) for which the ordinary stress-optical rule held well individually. A comparison of the component functions was made with a conventional amorphous polyarylate (UP) and bisphenol A polycarbonate (PC). The limiting modulus of the R component at high frequencies for PAr1 was about two times higher than that for UP and PC. This result suggested that PAr1 had a highly flexible main-chain structure. This high flexibility was in accord with a zigzag structure of 2,2′-dicarboxy biphenyl unit of the main chain. The stress-optical coefficient for the R component of PAr1 was 9.0 × 10 −10 Pa −1 , and approximately five times smaller than that for UP. Conversely, the intrinsic birefringence for PAr1 was estimated to be 2.5 times smaller than that for PC. This result indicates that reducing stiffness of main chain with flexible junctions and also optical anisotropy are effective in decreasing C R . The stress-optical coefficient for the G component of PAr1 was 3.1 × 10 −11 Pa −1 . This value agreed well with that for the polymers containing phenyl rings in their repeating unit.

The dynamic birefringence and viscoelasticity were measured for poly(ethylene naphthalene-2,6-dicarboxylate), and the contributions from the main chain orientation and the rotational orientation of repeating unit to the strain-induced birefringence were evaluated. The values, together with published ones for other glassy polymers, were compared with the anisotropy of polarizability tensor of the repeating units. The contribution from the main chain orientation for various polymers was in accord with that evaluated from the excess polarizability of the unit in the main chain direction assuming a quasi-affine orientation of the unit. The contribution from the rotation was well correlated with the anisotropy in the plane perpendicular to the chain axis. The degree of the rotational orientation was similar among the polymers. The rotational orientation was high for vinyl polymers with large side-groups.

Time-dependent nonlinear flow behavior was investigated for a model hard-sphere suspension, a 50 wt% suspension of spherical silica particles (radius = 40 nm; effective volume fraction = 0.53) in a 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The suspension had two stress components, the Brownian stress σ B and the hydrodynamic stress σ H After start-up of flow at various shear rates $$\dot \gamma $$ , the viscosity growth function η+ (t, $$\dot \gamma $$ ) was measured with time t until it reached the steady state. The viscosity decay function η− (t, $$\dot \gamma $$ ) was measured after cessation of flow from the steady as well as transient states. At low $$\dot \gamma $$ where the steady state viscosity η ( $$\dot \gamma $$ ) exhibited the shear-thinning, the η− (t, $$\dot \gamma $$ ) and η+ (t, $$\dot \gamma $$ ) data were quantitatively described with a BKZ constitutive equation utilizing data for nonlinear relaxation moduli G (t, γ). This result enabled us to attribute the thinning behavior to the decrease of the Brownian contribution η B = σ B / $$\dot \gamma $$ (considered in the BKZ equation through damping of G (t, γ)). On the other hand, at high $$\dot \gamma $$ where η ( $$\dot \gamma $$ ) exhibited the thickening, the BKZ prediction largely deviated from the η+ (t, $$\dot \gamma $$ ) and η+ (t, $$\dot \gamma $$ ) data, the latter obtained after cessation of steady flow. This result suggested that the thickening was due to an enhancement of the hydrodynamic contribution η H = σ H / $$\dot \gamma $$ (not considered in the BKZ equation). However, when the flow was stopped at the transient state and only a small strain (

Dynamic viscoelasticity of α,ω-dihydroxyl polybutadiene/p-xylene system is studied through gelation process by end-crosslinking reaction with crosslinker which has three isocyanate groups. The gel point is determined as the reaction time t=t c 1 at which the storage and the loss shear moduli, G'(ω) and G(ω), become both proportional to ω over the whole ω range measured, where ω is the angular frequency and n is a critical exponent at the gel point. The relative extent of chemical reaction p(t) is estimated from a decrease in the absorption peak of the isocyanate residue by FT-IR measurement to estimate precisely e=(p(t)-p|/p c 1 the relative distance from the gel point (p=p c ). Effects of polymer concentration C on the increase of zero shear viscosity η o before the gel point and on the increase of equilibrium modulus G eq after the gel point are examined in terms of critical exponents of k and z for power laws, η o ∼ e -k and G eq ∼ e z , respectively. The exponents n and z are found to take universal values of n=0.67±0.02, and z= 2.5 ± 0.1 independent of C in the lower concentration of C

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: A...

For blends of styrene−butadiene (SB) diblock copolymers in entangling, high-M homopolybutadiene (hB) matrices, two-step viscoelastic relaxation behavior found in a previous study (Watanabe, H.; Kotaka. T. Macromolecules 1984, 17, 342) was reexamined to elucidate features of the fast process on the basis of recently accumulated knowledge for relaxation of homopolymer blends. The SB/hB blends contained spherical micelles with S cores and B corona. For the fast process, the micelles exhibited nearly universal dependence of reduced moduli, Gr* = [MbB/cbBRT]G*SB, on reduced frequencies, ωτ*, with cbB and MbB being the concentration of the B blocks in the hB matrix and the B block molecular weight, respectively, and τ* being the relaxation time of the fast process. Behavior of τ* changed with MbB, cbB, and the matrix molecular weight MhB. For dilute micelles with cbB < ce (entanglement threshold for the B blocks), the B blocks were entangled only with the hB matrix and τ* were found to be close to constraint re...

ガラス転移領域付近での複屈折と応力の関係は, 修正応力光学則 (MSOR) によって記述することができる. この法則は, 応力と複屈折がRとGの二っの成分の和で記述することができ, さらにそれぞれの成分には, 普通の流動域での応力光学則と類似の関係が成立することを示す. MSORの分子論的解釈を述べ, R成分が主鎖の配向に, G成分は構成単位が主鎖軸を中心回転して生じる配向に対応していることを示す. この解釈の是非を調べるため, RとG成分の配向機構に関するモデルについて説明し, 実験と比較する. さらに, 成分関数の強度, 時間依存性などの特徴と分子構造との関係について考察し, 二つの成分関数が主鎖の屈曲性と関連していることを示す. 他の研究者による応力光学則との関係について調べ, また2D-IR法との関係についても記述する.