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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 stress relaxation and simultaneous birefringence variation were measured for bisphenol A polycarbonate over the glassy to the rubbery plateau regions. The measurements were performed at various temperatures of 142–156 °C over the time range of 0.4 to 2000 s. Results of relaxation measurements were consistent with those of dynamic measurements with respect to the birefringence as well as the stress in the framework of linear viscoelasticity. A modified stress‐optical rule was applied to the results of relaxation measurements. This rule was earlier proposed to replace the stress‐optical rule which was suitable only in the rubbery and the terminal flow regions. The relaxation modulus, E(t), was separated into two component functions, ER(t) and EG(t). In constructing master curves of ER(t) and EG(t) with the method of reduced variables, their shift factors were found to have different temperature dependence. This result can account for the break down of time‐temperature superposition principle for E(t) reported by several investigators. The present modified stress‐optical rule was more convenient in several ways compared with the similar modifications proposed earlier by Priss et al. and Read.The stress relaxation and simultaneous birefringence variation were measured for bisphenol A polycarbonate over the glassy to the rubbery plateau regions. The measurements were performed at various temperatures of 142–156 °C over the time range of 0.4 to 2000 s. Results of relaxation measurements were consistent with those of dynamic measurements with respect to the birefringence as well as the stress in the framework of linear viscoelasticity. A modified stress‐optical rule was applied to the results of relaxation measurements. This rule was earlier proposed to replace the stress‐optical rule which was suitable only in the rubbery and the terminal flow regions. The relaxation modulus, E(t), was separated into two component functions, ER(t) and EG(t). In constructing master curves of ER(t) and EG(t) with the method of reduced variables, their shift factors were found to have different temperature dependence. This result can account for the break down of time‐temperature superposition principle for E(t) re...

The stress‐optical rule (SOR) does not hold valid in the glassy and the glass‐to‐rubber transition zones of amorphous polymers. The birefringence and stress can be related through a modified SOR: The stress is composed of two components each of which contributes to the birefringence with different degree of effectiveness. Studies of Read [Polym. Eng. Sci. 23, 835 (1983)] and of the present authors [Macromolecules, 24, 5670 (1991)] are based on different methods of assignment of the stress‐optical coefficients for the two components. We show that the two component viscoelastic functions derived from the latter method are thermorheologically simple but those from the former are not.

Complex Young’s modulus, E*(ω), and complex strain‐optical coefficient, O*(ω), of Poly (2‐vinylnaphthalene) (P2VN) were studied in the glass‐to‐rubber transition zone at frequencies ranging from 1 to 130 Hz at various temperatures between 145 and 200 °C. In comparing the master curves of E*(ω) and O*(ω), we apply the modified stress‐optical rule to deliberate the glass transition modulus attributable to different relaxation mechanisms. The characteristics of master curves are also compared with those of polystyrene (PS), poly (a‐methylstyrene) (PMS), and polycarbonate (PC) in view of their chemical structures. The stress‐optical coefficient, CR, determined in the rubbery zone, is −8.3×10−9 Pa1, which is 1.6 times larger than that of PS. The large negative value may be due to the large optical anisotropy of naphthyl side group. In the glassy zone, the relative rate of decrease of E‘(ω) with ω is lower compared with the other polymers. This behavior is believed to be attributed to β relaxation of large naph...

Dynamic viscoelasticity is measured for threadlike micelles from cetyltrimethyl‐ammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at temperatures T=25, 33, 40, and 50 °C. The CTAB concentration of the solutions is fixed at CD=0.01 M and a ratio of NaSal concentration CS to CD, CS/CD, is varied from 1 to 41. Effects of both CS/CD and T on frequency dependence of storage and loss shear moduli, G’(ω) and G‘(ω), are described in this paper in detail. Characteristic features of this micelle system may be summarized as (1) at 25 and 33 °C, the steady viscosity η and the mechanical relaxation time τM both show a minimum at CS/CD∼4 that is followed by a maximum at CS/CD∼10 as CS/CD increases. (2) The η and τM monotonically decrease with increasing T in the range of CS/CD from 1 to 20, but the maximum itself gradually disappears as T increases. (3) The steady state compliance Je is independent of T and decreases at lower CS/CD. A rapid increase in Je is observed at higher T and CS/CD ends. (4)...

Pigment dispersibility was studied for resins with various numbers of carboxyl groups at the chain end. The resins were synthesized by ring‐opening polymerization of e‐carprolactone. G‐type resin had a carboxyl group at one end of each molecule. S‐type resin was a mixture of molecules with 0, 1, or 2 carboxyl groups at the end of molecules. P‐type resin was a tetrafunctional resin terminated with carboxyl groups. L‐type resin was without carboxyl groups. Dispersed pastes of Cu‐phthalocyanine blue using G‐type resin revealed a higher degree of dispersion and a lower structural viscosity than pastes using S‐type resin. TiO2 dispersed pastes were prepared using mixtures of G‐type resin and L‐type resin at various mixing ratios. As the amount of G‐type resin increased, the degree of dispersion was enhanced and the yield value decreased. L‐type resin showed almost no effect on the yield values of TiO dispersed pastes. TiO2 dispersed pastes using P‐type resin showed a lower degree of dispersion and a higher structural viscosity than those using G‐type resin. The resin molecules with no carboxyl groups did not affect the dispersibility or the structural viscosity of pigment dispersed pastes. The resin molecule with more than two carboxyl groups built up a structure among pigment particles and caused aggregation.

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.

Diffusion of rod‐like micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions were studied by varying CTAB concentration CD and NaSal concentration CS. For solutions with CD=0.01 and 0.1 M, a ratio CS/CD ranged from 1.0 to 41 and from 0.70 to 6.0, respectively. For measurement of the diffusion coefficient D, the forced Rayleigh scattering technique was employed at 25 °C. Plots of D against CS/CD gave very complicated behavior such that D took a maximum and afterward took a minimum with increasing CS/CD. CS/CD values of the maximum and minimum for solutions with CD=0.01 M was very different from that for CD=0.1 M. But the magnitude of D was of the same order of 10−9 cm2 s−1 for both solutions. Diffusion data could be reduced to one master curve by plotting D against the concentration CS* of free salicylate ion Sal− in the low CS* region. The CS* dependence of D at low CS* was found to roughly correspond to that of the relaxation time τ obtained in earlier investigat...

An apparatus was constructed for simultaneous measurements of the dynamic birefringence and the complex Young’s modulus. The frequency range was 1–200 Hz. The instrument was calibrated with a polybutadiene film, for which the stress‐optical law was expected to hold well. The stress‐optical coefficient estimated by dynamic birefringence measurement was consistent with the result of the static measurement. The stress‐optical law did not hold valid for a polystyrene film containing 5 wt. % dibutyl phtalate in the glass‐to‐rubber transition region.

This paper summarizes recent works in which the entanglement effect on diffusion and viscoelasticity was mainly studied on solutions of narrow‐distribution polystyrene (PS) in dibutylphthalate (DBP) over a wide range of temperature T, concentration C, and molecular weight M. The temperature dependence of the self‐diffusion coefficient Ds and the tracer diffusion coefficient Dtr was described by the WLF equation with values of the WLF coefficients the same as found for the solution viscosity η. The effects of entanglements on the self‐diffusion behavior and the viscoelastic behavior were examined from data analysis in terms of the two parameters, the effective friction coefficient of a segment ζ and the molecular weight between entanglements Me. The product Dsη/C was close to the theoretical prediction based on the free Rouse chain up to M/Me∼1 and, for M/Me≳10, showed universal behavior characterized by the linear proportionality to M/Me. The ratio of the two characteristic times for viscoelasticity and d...

The strain‐induced birefringence of amorphous polymers can be described with the stress‐optical rule in the rubbery plateau and the terminal flow zones. This is not the case in the glassy and the glass‐to‐rubber transition zones. When the stress or the strain is sufficiently small, the birefringence may be described in terms of the linear response theory similar to the linear viscoelasticity theory. In this paper, we present some new relations among the response functions such as the time‐dependent stress‐optical coefficient and strain‐optical coefficient. The birefringence in the following processes were considered: the stress relaxation at constant strain, the creep, the oscillatory deformation, the strain of constant rate, and the subsequent elastic recoil.

The viscoelasticity and self‐diffusion were investigated for aqueous solutions of cetyltrimethylammonium bromide (CTAB) containing sodium salicylate (NaSal). The concentration of CTAB, CD, was equal to that of NaSal, CS. This system contains thread‐like micelles and exhibits pronounced viscoelastic behavior. The storage modulus G’ and loss modulus G ‘ could be fitted with the Maxwell model of one relaxation time when CD

Experimental tests of a few constitutive models were performed on the basis of time‐dependent stress data for an 8% polystyrene solution in chlorinated biphenyl. The strain‐dependent relaxation modulus G was measured with a cone‐and‐plate relaxometer. The shear stress σ and the first normal stress difference ν1 at the start and on the cessation of shear flow were evaluated from previous results of flow birefringence measurement. The BKZ model consistently described the relation between σ and ν1 on the cessation of shear flow. A BKZ relation, corresponding to the van Es‐Christensen relation for the rate‐dependent constitutive model, held good for the stresses at the start of shear flow. The BKZ model calculation starting from G gave σ and ν1 slightly different from those observed at high rates of shear. The deviation may be removed by allowing a slight rate dependence of the memory function as was done by Macdonald. The model of Acierno‐La Mantia‐Marrucci‐Titomanlio gave a too marked overshoot of ν1. The m...

The time‐dependent flow birefringence was measured on application of a step‐shear strain for an 8% polystyrene solution in chlorinated biphenyl. Measurements were performed with an apparatus of coaxial cylinder type at various shear strains γ ranging from 0.913 to 7.56. The amount of birefringence was in agreement with that evaluated from the shear stress with the use of the stress‐optical law. The extinction angle χ was independent of time and satisfied a relation 2 cot 2χ=γ. This result combined with the stress‐optical law indicates that the Lodge‐Meissner relation holds valid for the polystyrene solution, i.e., the first normal stress difference is equal to the shear stress multiplied by the shear strain in the stress relaxation process following an application of step‐shear strain.

The shear stress σ and normal stress difference ν3, the sum of the first and the second normal stress differences, were measured for a concentrated polystyrene solution in double‐step shear deformations: a shear strain γ1 was applied at time t=−t1, another shear strain γ2 was added at t=0, and the stresses were measured for t>0. When t1 and t were larger than a certain characteristic time τk, the observed results for σ and ν3 were in accord with the prediction of the tube‐model theory of Doi and Edwards for various combinations of γ1 and γ2. Here the characteristic time τk, previously determined from the strain‐dependent relaxation modulus, gives the measure of the equilibration time of the contour length of polymer chain. The results for t>τk≫t1 were well described with the phenomenological BKZ model. The success of this model for t>τk≫t1 can be accounted for with the concept of tube model.

The viscoelastic properties of dilute solutions of comb‐shaped branched polymers have been calculated from the bead‐spring model, following the Zimm and Zimm‐Kilb theories, with exact numerical evaluation of eigenvalues by the method of Lodge and Wu. Eigenvalues, relaxation times, and frequency dependence of the reduced intrinsic shear moduli [G′]R and [G″]R have been obtained for various combinations of number of branch points (f) 1 to 10, beads per branch (Nb) 1 to 37, backbone beads between branches (Na) 1 to 22, and the reduced hydrodynamic interaction parameter (h*) 0 to 0.25. Since the total number of beads (f+1) Na+fNa+fNb−1 is restricted to an unrealistically small value of 111 by computer limitations, attention is focused on the low‐frequency behavior where this restriction will have the least influence. Here, the behavior is characterized by the reduced steady‐state shear compliance. This quantity is quite sensitive to f when the mass backbone fraction λ is small (approaching starshaped geometry...

An apparatus was developed for measurements of the flow birefringence of polymer solutions in time‐dependent flow, such as the start and the sudden cessation of steady shear flow. A linearly polarized light beam was led through the sample held in the gap between two coaxial cylinders in relative rotation, and then through an analyzer. The intensity of the transmitted light was measured as a function of time. The birefringence Δn and the extinction angle χ were evaluated from light intensities for which the angles between the direction of flow and the direction of polarization of the incident beam were −22.5°, 0°, 22.5°, and 45°, respectively. Measurements were performed at 35°C on an 8% solution of polystyrene of weight average molecular weight 3.0×106 in chlorinated biphenyl. The stress‐optical law was applicable to the solution at the start and on the cessation of steady shear flow over the range of rate of shear, from 6.6×10−3 sec−1 to 2.14×10−1 sec−1, studied. The stress‐optical coefficient obtained w...