Shigeharu Onogi

Non‐Linear Behavior of Viscoelastic Materials. I. Disperse Systems of Polystyrene Solution and Carbon Black

To determine non‐linear viscoelasticity parameters for disperse and high‐polymeric systems, some fundamental relations have been derived between these parameters and the experimental quantities by viscoelastometry, particularly with a torsionally oscillating rheometer, on the basis of the general theory presented by Green and Rivlin. The non‐linear viscoelasticity of several disperse systems consisting of polystyrene solutions and carbon black has been measured by means of the torsionally oscillating rheometer at various temperatures ranging from 100 to 170°C, and in a frequency range from 2×10−3 to 0.5 cycle per sec. As a result of harmonic analysis of the experimental results, it has been revealed that the resultant torque consists of the fundamental component and odd harmonics, and that the energy dissipated during one cycle is the same as that calculated from the fundamental component alone. Frequency dependence curves at various temperatures for G1′ and G1″, which correspond to G′ and G″ for linear v...

Rheological Properties of Disperse Systems of Spherical Particles in Polystyrene Solution at Long Time‐Scales

The dynamic and steady flow properties of disperse systems of styrene–divinylbenzene copolymer particles in a polystyrene solution have been measured over wide ranges of frequency, shear rate, and strain amplitude by means of a cone‐and‐plate type rheometer. The main results may be summarized as follows. 1) These systems show Newtonian behavior at extremely low rates of shear, that is, the apparent viscosity is approximately constant. This fact indicates that the systems have no yield stress, although they appear to show one if only the behavior at high shear rates is considered. 2) They show linear viscoelastic behavior at strain amplitudes less than 0.5%, but striking nonlinearities at larger strains. However, at very long time‐scales, these systems are linearly viscoelastic and independent of the strain amplitude. 3) The nonlinear viscoelastic functions G1′ and G1″ decrease with increasing strain amplitude, but they are almost independent of strain for strains larger than 50%, over the entire frequency...

Nonlinear Behavior of Viscoelastic Materials. II. The Method of Analysis and Temperature Dependence of Nonlinear Viscoelastic Functions

The nonlinear viscoelastic functions G1′, G1″, G3′, and G3″ were evaluated for disperse systems of polystyrene solution and styrene‐divinyl benzene copolymer particles at various temperatures ranging from 10 to 70°C over the frequency range from 12 to 1/256 Hz. In general, frequency dependence curves of all the functions are rather flat and become less sensitive to temperature as the temperature rises. To the curves at different temperatures, the so‐called time‐temperature superposition can be applied; the shift factors determined in the course of horizontal shifts of curves for various functions are quite the same and are independent of the strain amplitude. Master curves of the nonlinear functions manifest plateaus in the low frequency region, where the polymer solution itself shows rapid changes in G′ and G″. The height of the plateaus increases very rapidly with increasing particle content. All the moduli G1′, G1″, G3′, and G3″ decreases first rapidly and then slowly with increasing strain amplitude u...

Forced Vibration of Reed as a Method of Determining Viscoelasticity

The motion of a clamp‐free reed excited by a sinusoidal displacement of the clamped end was analyzed by rigorously solving the fundamental equation for vibration. The real and imaginary parts of the modulus are given in terms of resonant frequency and band width of the frequency curves. The results are compared with those of Nolle which were obtained in an approximate manner by introducing an equivalent electric circuit. As long as the mechanical loss tangent is smaller than 10−1, as is the case in most high polymers, the practical error caused by the approximation is estimated to be insignificant. Nolles network was interpreted from a purely mechanical standpoint by means of the fundamental equation for vibration.

Rheological properties of polymethyl methacrylate and polyvinyl acetate in the molten state

SummaryDynamic viscosityη′, dynamic rigidityG′ and apparent viscosityηa of fractions and blends of polymethyl methacrylate and of polyvinyl acetate having different molecular weight and distribution have been measured at high temperatures by means of a concentric cylinder-type rheometer which enables us to measure not only dynamic but also steady-flow properties. The values ofη′ andG′ as functions of frequency for each sample at different temperatures can be superposed according to the usual time-temperature superposition principle, giving master curves covering a wide range of frequency. The absolute value of complex viscosity as a function of angular frequency coincides very well with the apparent viscosity as a function of rate of shear, indicating that the empirical law byCox andMerz holds well with the experimental results. The dynamic viscosity curves for various samples unite in one curve aboveω=1000 sec−1, and this united portion corresponds to the transition region. The effects of branching and bimodal distribution of molecular weight and the variation of frequency dependence of viscosity-molecular weight relation have been discussed, and emphasis has been placed on the significance of intramolecular motion to the flow properties of polymer melts at higher rates of shear or frequency.ZusammenfassungDie dynamische Viskositätη′, der dynamische SchermodulG′ und die scheinbare Viskositätηa von Fraktionen und Gemischen des Polymethacrylsäuremethylesters und Polyvinylacetat mit verschiedenem Molekulargewicht und verschiedener Verteilung wurden bei hohen Temperaturen mit einem Rotationsrheometer vom konzentrischen Zylindertyp gemessen, das nicht nur dynamische, sondern auch stationäre Fließeigenschaften zu messen gestattet.η′, undG′ können als Funktionen der Frequenz für jede Probe bei verschiedenen Temperaturen nach dem üblichen Zeit-Temperatur-Superpositionsprinzip überlagert werden und liefern Masterkurven, die einen großen Frequenzbereich überstreichen. Der Absolutwert der komplexen Viskosität als Funktion der Drehfrequenz stimmt gut mit der scheinbaren Viskosität als Funktion der Schergeschwindigkeit überein, was zeigt, daß die empirische Beziehung vonCox undMerz die Versuchsergebnisse gut wiedergibt. Die Kurven für die dynamische Viskosität verschiedener Proben vereinigen sich oberhalbω=1000 sec−1 zu einer Kurve, und dieser gemeinsame Teil entspricht dem Umwandlungsbereich. Der Einfluß von Verzweigungen und bimodalen Molekulargewichtsverteilungen sowie die Änderung der Frequenzabhängigkeit der Viskositäts-Molekulargewichtsbeziehung werden diskutiert und die Bedeutung der intramolekularen Bewegung für die Fließeigenschaften von Polymerschmelzen bei höherer Schergeschwindigkeit oder Frequenz betont.

Rheological Properties of Dispersions of Spherical Particles in Polymer Solutions

The steady flow and dynamic viscoelastic properties of disperse systems consisting of polystyrene copolymer particles of different sizes in polystyrene solutions were measured by means of rotating cylinder type rheometers over wide ranges of temperature, rate of shear, and frequency. The yield values, evaluated by use of the modified Casson equation for disperse systems, were found to be independent of temperature. Time‐temperature superposition was applied to the flow curves and the frequency dependence curves of the dynamic properties, giving identical shift factors which obeyed the WLF type equation and were almost independent of the size and content of the particles. The yield value increased with increasing particle content and polymer concentration in the disperse medium. The smaller the particle size, the larger the yield value. The frequency dependence curves of the storage shear modulus G′ and the loss modulus G″ showed second plateaus lower than the rubbery plateau at lower frequencies. The correlation between the yield value and the complex shear stress is discussed.

The diffusion coefficient for the nylon 6 and water system

Abstract The diffusion of water vapor in nylon 6 film has been measured by means of quartz microbalance and weighing bottle methods at penetrant concentrations ranging from about 1 to 8 (wt. %) or (%) and at temperatures ranging from 15° to 60°C. From the sorption-desorption data the average diffusion coefficient D a as a function of penetrant concentration, and the apparent activation energy for diffusion processes as a function of temperature have been determined. The mutual diffusion coefficient D as a function of penetrant concentration has been determined from the steady-state behavior, and compared with D a . D a is almost independent of the penetrant concentration, especially at higher temperatures, whereas D increases with increasing concentration, even at temperatures higher than the transition temperature of the sample. This difference might be attributed to the fact that chain molecules need a long time to change their configurations when the concentration changes.

Dynamic Measurements of Physical Properties of Pulp and Paper by Audiofrequency Sound

The dynamic Youngs moduli of various types of paper were measured by the vibrating reed method. The Youngs modulus of paper increases statistically at a rate approximately proportional to the square of its density. The modulus and density of paper increase with the degree of beating. The sulfite and sulfate fibers behave differently during beating. The angular dependence of Youngs modulus, tensile strength, and elongation at break was analyzed mathematically; and the results were verified by experiments. According to this theory, the mean value of Youngs modulus and tensile strength of machine‐made paper should be expressed by the geometrical mean of the values of the machine and cross directions, whereas the mean value of elongation can be given by the arithmetical mean. The removal of parenchyma cells is very effective in reducing the Youngs modulus of dissolving pulp. The viscoelastic properties of paper were observed within the frequency range from 20 to 180 cps. The dynamic modulus and mechanica...

Nonlinear Viscoelastic Properties of Semisolid Emulsions

The dynamic viscoelastic properties of semisolid emulsions (commercial cosmetic creams) at 25°C were measured by means of a Weissenberg rheogoniometer at frequencies ranging from 1.582×10−3 to 1.582 Hz. In general, these emulsions manifested remarkable nonlinear viscoelasticity even at very small strains; when sinusoidal strains were applied to the emulsions, the resultant stresses were not sinusoidal, in marked contrast to the case in ordinary linear viscoelastic materials. Such nonsinusoidal stresses were analyzed by the method proposed by Onogi et al. to give nonlinear viscoelastic functions. The frequency dependences of these nonlinear functions for the emulsions were quite different from those of the viscoelastic functions for polymer solutions or melts, especially in the low frequency range; the viscoelastic functions for the semisolid emulsions showed second plateaus lower than the so‐called rubbery plateau. Some considerations concerning the origin of the nonsinusoidal stresses were given, and it ...

Viscoelastic Properties of Concentrated Solutions of Polyvinyl Alcohol

The dynamic viscosity and rigidity of concentrated solutions of polyvinyl alcohol samples having different molecular weights have been measured by means of a torsionally oscillating rheometer and an electromagnetic transducer within the ranges of frequencies from 0.08 to 400 cps and the temperature range from 20° to 55°C. The solutions behave almost as Newtonian liquids at lower frequencies; however, at the frequencies around 1 to 10 cps the viscosity of solutions begins to decrease while the rigidity increases rapidly. The frequency at which the rather abrupt change in dynamic viscosity and rigidity takes place is lower the higher the concentration, the higher the molecular weight, and the lower the temperature. The effects of the concentration, temperature, and molecular weight on the zero shear (frequency) viscosity have been examined quantitatively, and some of characteristic features observed on other high polymers have also been found. Comparison of the dynamic voscosity with the steady‐flow viscosi...