This paper summarizes a phenomenological relaxation theory of polarization reversal in ferroelectric polymers developed by the present author and his coworkers. The relaxation time τ is assumed to be a function of both electric field E and polarization P. The functional form of τ against E is taken from the experimental law in switching and the form against P is deduced from the depolarization field effect. The theory can explain both polarization reversal switching and polarization-electric field hysteresis from a unique simple relaxation equation.
This paper describes rheological properties of model ABS polymers together with those of mechanical blends of ABS resins and an acrylonitrile-styrene (AS) copolymer. Samples having different structural factors, namely, acrylonitrile (AN) content of grafted AS copolymers, grafting degree, and size of rubber particles with sharp particle-size distribution, were prepared, and dynamic viscoelastic and steady-flow properties were measured using a coaxial cylinder-type rheometer in the temperature region from 130 to 245°C. Difference in morphologies of samples was reflected strongly on the rheological properties, and two typical features were observed. With samples in which rubber particles agglomerated and formed three-dimensional network structure, the second-plateau region appeared in plots of storage modulus G′ against frequency. At low frequencies, the plots exhibited the pseudo-equilibrium modulus being independent of frequency. While, the second-plateau region was not observed with samples in which rubber particles were finely dispersed, and values of G′ decreased with lowering frequency. For model ABS polymers, the difference in AN content between grafted and matrix AS copolymers caused the morphological change of samples. When the difference was small, rubber particles were finely dispersed. Large differences caused agglomeration of rubber particles, and the second-plateau region appeared in the G′ vs. frequency plots. In the long-time region, viscoelastic functions, e. g. G′, depended strongly on grafting degree of the polymer. With increasing grafting degree, the functions first decreased and then increased. The minima of the functions located at the grafting degree of about 45% for the ABS polymers having the average size of rubber particles of 170 nm. When the grafting degree was lower, or higher, than 45%, the second-plateau region in G′ plots and yield stress in flow curves were observed in the long-time region. Effects on viscoelastic functions of the size of rubber particles in the ABS polymers were studied employing samples in which rubber particles were dispersed finely without agglomeration. Dependences of flow curves on the rubber content and on the particle size were discussed in terms of a layered structure model of the particles.
The relation between the properties and the structure of two sorts of rubber vulcanizates was studied. Here, two sorts of rubber vulcanizates are that cured by a normal method which is called DC-sample and that cured by a special method, or a solution cured one which is called SC-sample. The latter sample is considered to have less entanglements than the former one, and then this seems to be an approximate phantom network rubber vulcanizate. The difference between both samples was remarkably observed by following measurements (a physical stress relaxation in N2 at room temperature, a stress-strain behavior, X-ray diffraction patterns, a birefringence-extension experiment, Mooney-Rivlin plots, and a chemical stress relaxation). It is known that the parameter h in eq. (1) is unity for a phantom network rubber, while h is zero for an affine network rubber. G=(n-hμ)κT(1) Here, G: shear modulus, n: the number of main chains between crosslinks per unit volume (crosslinking density), μ: the number of crosslinks, κ: Boltzmann constant, T: absolute temperature, h: an index of the degree of fluctuation of crosslink site. For DC-sample, h was found to be approximately a half. This indicates that the degree of fluctuation is approximately medium between affine deformation and phantom deformation for DC-sample. The simple relation f(t)/f(0) (relative stress)=n(t)/n(0) (relative network chain density) was established for SC-sample, while the complicated relation was found for DC-sample.
Granulation of natural rubber (NR) after breaking of blocks in an oval-type twinrotor mixer is analyzed based on the flow behavior of model materials in a parallel plate rheometer. The surface of NR sheet was coated with a film of styrene-butadiene rubber (SBR) to simulate the effect of a thin layer of melted NR. In the parallel plate rheometer, the NR sheet was granulated first in a ring region along the periphery on the surface in contact with SBR. The granulated region increased its thickness and finally filled the gap from one surface to the other of the rheometer. The inner radius of the ring depended on thickness of the film. The melt fracture zone in the parallel plate rheometer formed also a ring. Radii of the two types of rings were the same and so granulation of NR is related to the melt fracture of film. The result was used in the analysis of NR mixing in the mixer, and it was clarified that granulation of NR is originated from the melt fracture in a thin layer of NR melted by higher temperature on the inner surface of the mixing chamber.
Reduction in Mooney viscosity of natural rubber (NR) of the early stage of mixing in an oval-type twin-rotor mixer was measured during three periods characterized by block breaking, granulation, and viscous flow. The reduction rate was constant in each period, and depended on mechanical design and operating condition for the first two periods. The result shows that Mooney viscosity reductions during the two periods are mainly caused by elastic breaking of NR, and molecular break is closely related to elastic deformation. Dispersion of carbon black (CB) into NR was observed in detail. The granulated particles of NR were coated with fine CB particles, which formed striated layers during viscous flow of NR. Styrene-butadiene rubber (SBR) was also examined for comparison. The striation thickness in SBR was larger than in NR, because SBR was not granulated during mixing. Both energy efficiency and final level of CB dispersion in NR was higher than in SBR. The result shows that granulation during mixing is effective for CB dispersion.
Linear viscoelaticity was investigated for solutions of the mixture of polystyrene (PS) and poly (vinyl methylether) (PVME) in dibutyl phthalate. Concentrations of PS and PVME were 0.076 g cm-3 and 0.774 g cm-3, respectively. Molecular weight of PVME was 6.0×104; molecular weights of PS samples were 4.39×104, 1.90×105, 9.5×105 and 1.26×106. The solution formed a single phase at low temperatures and became turbid at about 80°C. The storage modulus, G′, and the loss modulus, G″, were measured at several temperatures ranging from 4 to 60°C. The results could be reduced to a reference temperature, 30°C, through the frequency-temperature superposition principle. When PS molecular weight was 4.39×104 or 1.90×105, the viscoelastic properties of blend solution were similar to those of narrow-distribution polymer. The plateau modulus was independent of the PS molecular weight. The maximum relaxation time increased as the molecular weight of PS increased. When PS molecular weight was 9.5×105 or 1.26×106, a second plateau region appeared at lower frequencies. The modulus of the second plateau region was lower than that of the first one and coincided with the plateau modulus of the 0.076 g cm-3 solution of PS in an ordinary solvent, and its maximum relaxation time increased as the molecular weight of PS increased. The first plateau region may be originated by PVME-PVME and PVME-PS entanglments and the second plateau by PS-PS entanglements.
Ultrasonic relaxations of poly (vinyl chloride) dilute solutions were measured in the range of frequency from 1 to 95 MHz and of temperature from 0 to 40°C. Solvents used were tetrahydrofuran (THF) and methyl ethyl ketone (MEK). Results were described by a single relaxation process. The ultrasonic single relaxation process of the polymer solution is interpreted in terms of a local mode associated with localized rotational isomerism of a diad part of the backbone chain. Thermodynamic parameters of a diad part were determined on the basis of the two state model. In the good solvent (MEK), the energy difference was ΔH0=2.8±0.2 kcal/mol, and the equilibrium constant was K≅0.03. In THF (in I phase near I-I'phase transition point in Daoud's phase diagram), ΔH0=1.2~1.7, kcal/mol and K≅0.06~0.13. These results indicate that the polymer-solvent interaction affects energy differences in energy levels of possible rotational isomers, in the alteration of relative energies of the several conformations
Dielectric relaxation in steady shear flow was studied at 297 K and in the range of frequency f from 1 to 1000 kHz for bulk cis-polyisoprene (cis-PI) with the weight average molecular weight of 16,200. At zero shear rate γ, the loss maxima due to the normal and segmental mode processes were found at log f=3.2 and 7.6, respectively. At 1 kHz near the loss maximum frequency for the normal mode process, ε′ and ε″ were independent of shear flow. In the range satisfying γ>10 s-1 and log f>4, ε′ increased but ε″ decreased with increasing γ. The results were inconsistent with the theory proposed by Peterlin and Reinhold.