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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.

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

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.

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

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

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

Linear viscoelastic behavior was investigated for aqueous solutions of perfluorooctyl sulfonate (C8F17SO− 3; abbreviated as FOS) micelles having a mixture of tetraethylammonium (N+(C2H5)4; TEA) and lithium (Li+) ions as the counter-ions. The solutions had the same FOS concentration (0.1 mol l−1) and various Li+ fractions in the counter-ions, φLi = 0−0.6, and the FOS micelles in these solutions formed threads which further organized into dendritic networks. At T ≤ 15 °C, the terminal relaxation time τ and the viscosity η, governed by thermal scission of the networks, increased with increasing φLi up to 0.55. A further increase of φLi resulted in decreases of τ and η and in broadening of the relaxation mode distribution. These rheological changes are discussed in relation to the role of TEA ions in thermal scission: Previous NMR studies revealed that only a fraction of TEA ions were tightly bound to the FOS micellar surfaces and these bound ions stabilized the thread/network structures. The concentration of non-bound TEA ions, CTEA *, decreased and finally vanished on increasing φLi up to φLi * ≅ 0.6, and the concentration of the bound TEA ions significantly decreased on a further increase of φLi. The non-bound TEA ions appeared to catalyze the thermal scission of the FOS threads, and the observed increases of τ and η for φLi 0.55 (where CTEA * ≅ 0), were related to destabilization of the FOS threads/networks due to a shortage of the bound TEA ions and to the existence of concentrated Li+ ions. Viscoelastic data of pure FOSTEA and FOSTEA/FOSLi/TEACl solutions lent support to these arguments for the role of TEA ions in the relaxation of FOSTEA/FOSLi solutions.

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

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.

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.

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.

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 (

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), were measured for polyisobutylene (PIB) over a wide temperature range near and above its glass transition temperature. The master curves could be constructed well for each function with the method of reduced variables. The shift factor, aT, for E*(ω) is the same as that for O*(ω). The ratio of the imaginary parts of O*(ω) and E*(ω), O″(ω)/E″(ω), takes an extremum, which has never been observed for other polymers. The relation between O*(ω) and E*(ω) cannot be described by a modified stress-optical rule (MSOR) which has been found valid for various polymers. The basic concept of the MSOR. i.e., the chain orientation and the orientation of flat monomer units in the stretch direction, is not sufficient to describe the behavior of PIB and another origin of stress, presumably due to the fluctuation of local stress, should be included. This term does not contribute to the birefringence. The main maximum of tan δ is ascribed to the relaxation of the chain orientation in contrast with many other polymers, such as polyisoprene and polycarbonate, for which the maximum of tan δ is ascribed to the rotational relaxation of monomer units. © 1995 John Wiley & Sons, Inc.

Published data of dynamic birefringence and viscoelasticity of amorphous polymers were compared with the molecular expression of stress proposed by Gao and Weiner. The theory states that the stress is composed of contributions from the chain orientation (orientation term), the monomer orientation around the chain axis (rotation term), and the fluctuation of the local stress tensor (fluctuation term); the birefringence is composed of only two terms corresponding to the first two of the stress. The experimental data indicate that in the glassy zone and the high-frequency region of the glass-to-rubber transition zone the stress is attributable to the rotation and the fluctuation terms and the degrees of contribution vary with polymer species. For polymers with flat units (like polycarbonate), the fluctuation term is negligible and the relaxation spectrum in the glassy zone is low. For polymers with thin axisymmetric units (like polyisobutylene) or bulky irregular units (like poly(2-vinylnaphthalene)), the relaxation spectrum in the glassy zone is enhanced by the fluctuation term. It is also argued that, for polymers with thin axisymmetric units, the relaxation spectrum for the rotation term resembles that of a dilute solution; the role of rotational barrier along the chain is relatively enhanced since the rotational barrier from the surrounding is low because of the symmetry of the unit and because of the high fluctuation of the local stress. Some experiments are proposed to verify the statements

A network model has been investigated to understand the rheological characteristic of complex fluids which form certain structures depending on thermodynamic or deformation history. The creation and loss rates of the crosslinks are given as an exponential function of effective strain, which is defined as a ratio of the first normal stress difference and the shear stress. Two empirical parameters are introduced in the model. Depending on the parameter values, the model predicts various cases including both shear thickening and shear thinning. A special case predicts the rheological properties of a real fluid very well; an aqueous poly(vinyl alcohol) solution containing sodium borate. By considering as many cases as possible which are mathematically feasible, characteristics of each class have been studied and explained in terms of network parameters. The origin of shear thickening as well as the change of relaxation time and fluid elasticity have also been clarified with the help of network parameters. Even though this model does not cover all the real fluids and the description of the microscopic process is not sufficient, it helps us to increase our understanding of the characteristics of complex fluids as well as the mechanism of shear thickening.

Dynamic light scattering measurements are made on viscoelastic networks formed by threadlike micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at three temperatures T of 25, 33, and 40 o C. Dynamic shear moduli of the same samples are also measured in the angular frequency range from 1×10 -2 to 1×10 2 rad s -1 at T=25, 33, 40, 50, and 60 o C. The surfactant concentration C D of the samples is fixed at 0.1 M and a ratio of the salt concentration C S to C D is varied from 0.8 to 6. The time correlation function A q (t) of light intensity scattered from the solutions with 0.8≤C S /C D ≤4 exhibits the bimodal distribution of the decay rate Γ. The fast and the slowly decaying components are assigned as the diffusive gel mode and the relaxation mode, respectively, from the scattering vector dependences of the first cumulant Γ i (i=f, s) estimated from respective time profiles of the decay curves at short and long times. The dynamical correlation length ξ H calculated from D c =Γ f /q 2 is found to take a constant value of 10.5±1.5 nm irrespective of C S /C D and T for 1≤C S /C D ≤6. The characteristic relaxation time τ s (≡Γ s -1 ) for the slow mode agrees with the mechanical relaxation time τ M which is obtained by a fit of the dynamic shear modulus data of the same solutions to a Maxwell model with the single relaxation time τ M . The results demonstrate that concentration fluctuation in the micellar network decays by local cooperative diffusion of network strands at the short time as well as by the slow relaxation of elastic stress generated by the network deformation due to the mass flow

The studies on dynamic birefringence of amorphous polymers are reviewed. The birefringence in oscillatory deformation is related to the viscoelasticity through the stress-optical rule (SOR) in the rubbery and the terminal flow zones. The deviation from the SOR in the glassy and the glass-to-rubber transition zones can be described with a modified SOR, based on the assumption that the stress is a sum of two components associated with respective stress-optical coefficients. Experimental results are reviewed for 14 polymers: polystyrene, poly(α-methyl styrene), poly(2-vinyl naphthalene), polyisobutylene and 10 polymers for engineering plastics. The nature of various parameters is discussed in relation to the molecular structure.

The shear stress, σ, and the first normal stress difference. N 1 , at the start of shear flow with various rates of shear, γ, were measured for a 2% aqueous poly( vinyl alcohol) solution containing 1% sodium borate (PVA/B). Reduced stresses, σ/γ and N 1 /γ 2 , increased slightly with γ and leveled off to steady values when γ was less than a certain critical value, γ c . At very high rates of shear, the reduced stresses increased significantly with γ and kept on increasing with time until the flow became unstable. At moderate γ just above γ c , the reduced stresses exhibited a tendency to level off over quite a long period and then started to increase again. At any rate of shear, the stress relaxed rapidly on cessation of the flow. This observation may be interpreted by the assumption of enhanced rate of Borax-ol complex formation in highly oriented PVA chains in flow, and the slowing down of the relaxation of chain orientation trapped in the temporarily crosslinked network formed by the complex of finite lifetime.

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), of a polystyrene (PS)/bisphenol A polycarbonate (PC) blend and a graft copolymer were studied in the glass-to-rubber transition zone at frequencies ranging from 1 to 130Hz at various temperatures between 102°C and 182°C. The relaxation behaviors in E*(ω) and O*(ω) of two alloys were compared with each other in relation to the relaxation behaviors of constituents, PS and PC. It was clarified that for the blend in the mechanical spectrum two isolated relaxation peaks are detected at frequencies apart from each other, which means that the consitituents relax independently. For the copolymer two relaxation peaks of constituents were almost merged giving rise to about a single peak which indicates cooperating relaxation of the two components.The optical relaxation spectra, O*(ω), of two alloys showed distinct difference in quality and it also made us predict their compatibility to some extent. For both alloys, the stress-optical coefficient, CR, in the rubbery zone was reduced to 1/4-1/6 of the absolute value of components polymer as a result of compensation of the opposite-signed birefringences of constituent polymers. The photoelastic coefficient, Cd, for two alloys and the component polymers, PS and PC, exhibited a strong correlation with the stress-optical coefficient, CR.

Rheological properties were studied for aqueous solutions of poly(vinyl alcohol) containing sodium borate. The solution exhibited a marked shear thickening at a certain critical rate of shear, γ c and the flow was unstable at higher rates of shear. The loss modulus exhibited a maximum and the angular frequency corresponding to the maximum, ωMAX, was approximately equal to $$\dot \gamma _C $$ . These features were common to several measurements including various molecular weights and concentrations of polymer and various temperatures. Possible mechanism of shear thickening was discussed based on a temporary network model composed of crosslink points of a finite lifetime.

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G N . Two time constants, τs and τ1, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant τ k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios τ1/τ s and τ k /τ s were determined solely by N for each polymer species. The ratio τ1/τ s was proportional to N 4.5 and N 3.5 for PMMA and PS solutions, respectively. The ratio τ k /τ s was approximately proportional to N 2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants τ s and G N are known.

The complex Young’s modulus, E*(ω), and the complex strain‐optical coefficient, O*(ω), of poly(α‐methyl styrene), PMS, and Bisphenol A polycarbonate, PC, were measured over the frequency range of 1–130 Hz around the glass‐to‐rubber transition point. The real part of O*(ω), O’, of PMS is negative over the entire temperature range considered and the imaginary part, O‘, changes its sign from negative to positive with decreasing temperature. Both O’ and O‘ of PC are positive over the entire temperature range used. These results are qualitatively different from those for polystyrene. The data were analyzed with a modified stress‐optical rule and the complex modulus was separated into two components (denoted by R and G). The G component, which is located in the glassy zone, is related to the high glass modulus, and the shapes of the G components of PMS, PC, and PS are very similar to each other. The R component, located at the long time end of the glass‐to‐rubber transition zone of PC, is quite different from t...

The birefringence of polystyrene in the oscillatory elongation and in the stress relaxation process under constant elongation is compared in order to examine if the modified stress-optical rule can be consistently extended to deformation histories other than oscillation and to investigate the glass-to-rubber transitionzonebased on the data obtained at different times and temperatures

Viscoelastic and forced Rayleigh scattering measurements were made on mixtures of PS and PVME over the wide range of temperature and PS molecular weight. The temperature dependence of the tracer diffusion coefficient D of PS in PVME was well described by the shift factor aT obtained from time‐temperature superposition of the dynamic shear modulus data of PVME in bulk. The dependence of D on PS molecular weight was described by the free‐draining Rouse chain model in the low M region where the coil size of the diffusing PS chain is smaller than the mesh size of the PVME entanglement network. In the high M region, on the other hand, D did not decrease in proportion to M−2, being in disagreement with the prediction of the reptation model, but took a constant value nearly equal to the calculated Ds value of the PVME molecule in bulk at the high M end. Two conjectures were proposed for interpretation of the above anomalous diffusion behavior.

Dynamic birefringence and dynamic viscoelasticity of bisphenol A polycarbonate were simultaneously measured over a wide range of temperature from -150 to 180°C. Large γ dispersion observed for the complex Young's modulus was found to be inactive for the complex strain-optical coefficients, which is the ratio of birefringence to the strain. The present result indicates that γ dispersion cannot be attributed to the reorientation of any atomic groups, but to the relaxation of internal strain by translational motions. Dynamic birefringence was anticipated to be a new experimental method for the subrelaxation of glassy polymers.