In order to gather information on viscoelastic properties of crystalline high polymers, stress relaxation of polyvinyl alcohol (PVA) films were studied. The original films were casted from concentrated solutions of PVA having the viscosity average degree of polymerization (DP) of 2180, 1600 and 600, and had no orientation in the plane of the film. Some of them were heated at 160°and 200°C for 10 minutes to vary the crystallinity from about 20% of the original film to 36.0% and 47.3%, respectively. The degree of crystallinity were evaluated from density measurements. The measurements of the stress relaxation were carried out by employing an Instron Tensile Tester of table model. In order to measure at various temperatures (20°∼120°C) and relative humidities (0%∼75%), a particular cell was inserted between two jaws of the tester and the sample film was tested in this cell at controlled temperature and humidity.
The results obtained are summerized as follows:
1) Original films having DP 2180 and 1600 showed quite the same behavior at 0% and 60% R.H. at 20°C, while the film having DP 600 did somewhat different behavior from the others, though it had almost the same degree of crystallinity. This discrepancy may be attributed to the difference in its fine structure from the others.
2) Original films of DP 2180 and 600 were tested at 20°C over a wide range of relative humidity, and a notable dispersion was found near 50% R.H. for both of the films. Relaxation modulus against logarithm of time at various R.H. can be superposed by horizontal shift of the curves along the log time axis to give a composite curve at any reference humidity. The relaxation spectrum calculated from the composite curve referred to 0% R.H. ranged from 0 to 10¹⁵sec, and showed good agreement with that obtained by Kawai et al. from the dynamic data over a range of 10³ to 10⁸sec. Although our spectrum ranged to very long time, any flow region was not observed.
3) Heat-treated film having DP 2180 and degree of crystanity 47.3% was tested in a temperature range from 20°C to 120°C. The time-temperature superposition principle was not valid for the result. Qualitatively speaking, it seemed that for PVA film there appeared many dispersions in glassy state differing from the cases of amorphous polymers.
4) The effect of crystallinity on sterss relaxation were studied with two samples having the degree of crystallinity of 36.0% and 47.3%, respectively. Although the phehomena observed were too complicated to discuss quantitatively, it was clear that the effect appeared only in the dispersion regions.

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In an attempt to clarify the mechanism of the deformation process of the crystalline polymers, measurements were carried out on the stress relaxation, the dead weight creep, and the two-dimensional extension of polyethylene films up to the range of large deformation.
In the stress relaxation within 5% extension, the anisotropy of Young's modulus was measured and it was found that the modulus in the direction parallel to the molecular chain orientation was lower than the modulus in the perpendicular direction, and that the modulus decreased with increasing initial elongation.
On the other hand, in the dead weight creep test, it was found that the specimen film could be extended more easily in the direction perpendicular to the chain orientation than in the parallel direction. These facts snggest a difference exhisting between the mechanism operating in the small deformation process (as in the stress relaxation) ahd that in the large deformation process (as in the creep).
The difference can also be seen directly on the inspection of the creep curves with various loads: With a load lower than a certain critical value the elongation remains within several per cent, while with a larger load the specimen elongates in definitely up to the break point.
It may be conceivable that the small deformation process results from the rubber-like elongation of the amorphous chains as well as from the orientation and the plastic deformation of the crystallites. On the other hand the large deformation process may be due to the long range rearrangement of the crystallites resulting in the transformation of the spherulite structure to the fibre structure.
Creep test on sevesal high density polyethylene (Marlex 50) were also performed. They, in general, exhibited different features compared with the low density polyethylene. It was found that the specimen with lower melt indices manifested larger creep.
Two-dimensional stress-strain measurements were made by the inflation of the polyethylene film hydrostatically. Elongation at the break was much lower in the two-dimensional case than in the one-dimensional case. This fact can be interpreted as that the large deformation through the rearrangement of crystallites will be hindered in the case of two-dimensional extension.

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In general, fiber-forming substances are composed of long chain molecules linked together by bonds of secondary nature such as strong Van der Waal's and dipole-dipole bonds, etc. These cross linking bonds between polymer chains form an effective network structure. When these substances are deformed, the strong bonds act as junction points of the network, while the weak bonds will cause a viscous resistance to the relative motion of the segments. As a crystalline poltymer is cooled through its transition temperature region, certain degrees of freedom characteristic of rubbery solids are “frozen in” and at the same time the distribution of the cross bonds become dense, so the segmental motion (Brownian motion) of the molecular chain will be restricted. In fact, many of the crystalline polymers exhibit a sufficiently large elastic modulus in the lower temperature region, indicating that only the energy component of force and not the entropy component is important in this region.
To illustrate this mechanism the following model is adopted. Strong intermolecular bonds divide a molecular chain into a number of submolecules. Furthermore each submolecule is divided into two equal rodlike segments. As a result of the intermolecular interaction, the frictional force is applied to each molecule as it moves relative to the surroundings. For simplicity it is assumed that each submolecule interacts only through the linking point of the two component segments.
Based on this model the theoretical stress-strain cusves have been derived and compared with the observed stress-strain curves for the synthetic fibers subjected to a constant rate extension. It is found that a new yield point observed at low stress-strain region for shrinked synthetic fiber will be related to slackening of stretched molecular chain and regeneration of weak bonds on it. Some interesting informations are obtained upon the correlation between the characters of the stress-strain relation (stress, strain and magnitude of the viscous flow at the yield point) and the molecular constants (the rigidity of the molecular chain and strength of the intermolecular interaction).
It is obvious that this model should be improved by taking into account (1) the large deformation process for a folded molecular chain involving more than two rodlike segments, and (2) the entropy force caused by the thermal motion of the segments in the higher temperature region.

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The remarkable difference in rheological properties between the crystalline polymers and the amorphous ones is represented by the relaxation time spectra H(τ), τ being the relaxation time. In amorphous polymers it is well known that the intrachain relaxation gives rise to the wedge type spectrum with the slope of -1/2 in the log H-logτ plot. Here is discussed about the molecular characteristics in case of the crystalline polymers. We consider in the linear viscoelastic range and at temperatures above the glass transition point.
The peculiarities in crystalline polymers, such as the rotation of crystallites, the slipping of chain segments in or on the surface of crystallites, and the spacial heterogeneity in friction constants for chain segments do not change the spectrum in amorphous polymers significantly.
The crystalline polymers owe their crystallinity intrinsically to the high regularity in the molecular structure and the strong intermolecular interaction. Therefore, even in the amorphous region of the crystalline polymer, we can expect many crystalline nuclei or physical secondary bonds, under frequent dissociation and reconstruction. Then the movement of a molecular chain is inevitably accompanied by the cooperative movement of neighbouring chains. It is a main aim of this paper to study how these characteristics influence the above mentioned wedge type spectrum.
Accordingly, in treating a molecular chain by the normal coordinate method for Bueche's vibrating string model, it is suggested to assume that the normal mode with the longer wave length suffers the larger frictional resistance. Under the assumption, it can be shown that the spectrum in crystalline polymer has a smaller slope and a larger spread than in amorphous polymers.
To proceed more quantitatively, a tentative assumption is made such that, in order to excite a normal mode, a constant fraction of the secondary bonds should be cut off within a sphere, say the cooperative sphere, with radius equal to a quarter of the wave length characterisitic of the mode. Then we have in fact log H=const. -(1/4)logτ, being in qualitative accord with the spectrum for Teflon.
The theoretical viewpoints at present, however, are far from the final stage, and the critical review on the experimental situations is much desired, especially as to whether the rheological properties are studied experimentally at temperature higher than the glass transition point.

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The relaxation time spectrum of crystalline polymers for α transition was obtained by the use of reduced variables logE_r=logE+logT₀/T-logΛ/(1-Λ)+logΛ₀/(1-Λ₀) and logt_r=logt+logT₀/T-(ε'/k)(1/T-1/T₀). Where E is Young's modulus, t is time, T is temperature, Λ is crystallinity, ε'/k is the quantity related to the activation energy of viscosity and (T₀, Λ₀) is the standard (T, Λ).
The difference of relaxation time spectrum between amorphous and crystalline polymers is caused by the irregulality of the network structure which is formed by crystalline regions in polymer. The effect of this irregulality to the relaxation time spectrum of crystalline polymers was estimated by perturbation method. The relaxation time of crystalline polymer is given by 1/τ=kΣs=0C_sP^2s(p=1, 2, ……, N), where N is the number of segments of a polymer molecule. This relaxation time spectrum is modified from the one of amorphous polymers at the region for short relaxation time.

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The relaxation time spectrum of the so-called Rouse chain is examined from the viewpoint of statistical thermodynamics of irreversible processes, and two ways of approach to explain the flat shape of the spectrum obtained for crystalline polymers, one way is to modify the elastic character of the original Rouse chain and the other is to modify the internal frictional character, are indicated to be equivalent. The former way of approach seems to be more comprehensible than the latter, because the latter way in general inevitably introduces multiple activation energies and this makes the Ferry's reduction rule invalid, while recent experimental results for crystalline polymers demonstrate the validity of this rule. As the well-known -1/2 slope of the wedge-shaped part of the spectrum for amorphous polymers is in the former way of approrch shown to be connected with one dimensional distribution of normal modes in the chain taken for an elastic body, so the flat shape of the spectrum for crystalline polymers would correspond to some relaxation mechanism where more-than-one dimensional distribution of normal modes play a rôle. Taking account of the anisotropy for the intersubmolecular elastic force owing to the presence of crystalline regions, we can obtain a nearly flat shape of the spectrum in the range of large relaxation time under suitable conditions.

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While recently many attentions have been paid to the temperature characteristics of elastic modulus in crystalline high polymers, especially from the point of view that they reflect the variations of the fine structure such as chemical constitution, crystallinity or orientation, only the limited qualitative knowledges about them are obtained. In this paper, quantitative analysis of the temperature dispersion curves was tried with regard to the primary dispersion (α-dispersion), and more profound meaning of it was pursued.
If it is assumed that the relaxation spectrum (logH vs. logτ) concerning to the primary dispersion takes the shape of wedge with negative slope of β(<1/2), and its intensity, H₀, at τ=1sec., the temperature dependence of dynamic modulus, E', is expressed by the following equation,
logE_W=log(E'-E_B)=logH₀+βloga_T+βlogω-logβ,
where a_T is the shifting factor, taking unity at the second-order transition temperature T_g, E_B is the contribution to the modulus E' from the relaxation spectrum corresponding to the intermolecular relaxation mechanism (box-type distribution corresponds to this for amorphous polymers), which exists in the far longer time region than the observation time for crystalline polymers, and E_W is the contribution to E' from wedge-type distribution. According to the above equation, logE_W vs. T curves corresponding to the various values of ω can be reduced to a single curve by shifting them along logE_W-axis by βlogω. The shape of logE_W(T) curves is described by βloga_T. When the observation time exists on the shorter time region than the lower limit τ_l of wedge-type spectrum, the modulus levels off to the ω-independent constant value towards the lower temperature. The typical example for this can be found in the case of polyethylene terephthalate reported by Thompson and Woods.
When the time, t, always exists in the region of wedge-type spectrum irrespective of temperature, the inflexion point of logE_W(T)-curve corresponds to the maximum apparent activation energy for relaxation process and is considered to agree with T_g. This fact is supported by the experimental results on several fibers. Moreover it should be noted that the position of T_g remains on the same point on the T-axis irrespective of ω. If the observation time exists on the shorter time region than τ_l, the temperature dispersion of modulus occurrs at the higher temperature than T_g and depends remarkably on ω.
According to the analyzing method described above, it was concluded that the values of C₁' and C₂' in the WLF-equation must increase in crystalline high polymers due to the existence of crystalline region.

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For polyethylene terephthalate, relationships between the dielectric properties and the dynamic mechanical properties have been studied. And effects of crystallinity and crystallization temperature on anomalous dispersions (absorptions) in the dielectric properties have been surveyed. Dielectric measurements have been carried out over the frequency range of 0.1 to 10⁶c/s and temperature range of -35 to 110°C. Amorphous polyethylene terephthalate have been crystallized at 118°C (series 1) or 202°C (series 2) and 10 samples having different degree of crystallinity have been prepared. If partially crystallized samples of series 1 and 2 are compared at the same degree of crystallinity, as judged by density, the spherulites in the sample of series 2 are larger in size but smaller in number. The dynamic mechanical data have been adopted from Thompson and Woods' paper.
For all samples, two dielectric disperions (absorptions) are observed. A main absorption (α) locates in high temperature and low frequeucy range and another absorption (β) locates in low temperature and high frequency range. For amorphous samples as well as highly crystalline sample, position and apparent activation energy ΔH^* of the dielectric α absorption are nearly identical with those of the mechanical α absorption. In both dielectric and mechanical properties, α absorption of the crystallized sample shifts towards higher temperature and lower frequency and has smaller ΔH^* than that of the amorphous sample. Distribution of dielectric relaxation time τ or mechanical retardation time for α loss process of the crostallized sample is broader than that of the amorphous sample. ΔH^* for the dielectric, β absorption which is independent of crystallinity is nearly equal to that for the mechanical, β absorption.
In series 2 as well as series 1, increase of crystallinity has many effects upon α absorption, such as decrease of the magnitude, shift of the position towards higher temperature and lower frequency, decrease of ΔH^* and ΔS^* (but ΔF^* is independent of crystallinity) and broadening of the distribution of τ. These effects are more remarkable in series 1. Therefore it is suggested that molecular motions in amorphous region are strained more markedly in series 1. The magnitude of α absorption for samples of series 2 changes linearly with crystallinity and may become zero at 100% crystallinity. However that for samples of series 1 does not change linearly with cystallinity. On the other hand, the position, ΔH^*, ΔS^*, ΔF^* and the distribution of τ for β absorption are independent of crystallinity and only the magnitude decreases with increase of crystallinity. From the magnitude and quantitative analysis of end groups of the polymer chains, mechanism of β absorption is discussed.

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As the simplest and common model accounting for the mechanism of the cold-drawing of crystalline high polymeric substances, the usual theory for the rubber elasticity of vulcanized rubber was applied. The theoretical relationships between tensile strength or elongation at break and drawing ratio of drawn fibers were introduced. For example, tensile strength increases proportionally and elongation at break decreases inversely to drawing ratio. These theoretical results were in relatively good agreement with the experimental ones obtained from the drawn fibers of Phillips polyethylene. The increase of tensile strength by heat-treatment of drawn fibers seems to be attributed to the crystallization of oriented molecular chains. This fact was elucidated from the measurement of density change of both drawn and heat-treated fibers.

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The rheological properties of crystalline high polymers are discussed in contrast with those of amorphous polymers.
The mixture of hard particles and amorphous polymer gives the simplest model of crystalline polymers. Some considerations in changes of structure of mixing state, gives a good interpretation for the change of Young's modulus with increasing crystallinity by this simple mixture model. Although this approach can not give the interpretations of time-dependent phenomena, the author believes that this simple model has still some possibility of progresses.
The time dependent mechanical properties of high polymers must be expressed as a function of time and temperature. The most elabolate method, which measures the dynamical properties as a function of both time and temperature is developed by Fitzgerald. Very recently, it is revealed by Fitzgerald's transducer, that the crystalline polymers show some resonance-type dispersions at audio frequencies. This phenomenon has an important meaning which connects the polymer rheology with dislocation theory of crystal plasticity.
Relations between mechanical loss factor and temperature under nearly constant frequency for various crystalline polymers are obtained by Schmieder and many other researchers.
On the contrary, the measurement under constant temperature and variable frequencies need a high technique. Fujino and Kawai, and Tokita have measured the mechanical responses of several crystalline polymers covering six decade of frequencies by the use of several different apparatus.
The time-temperature reduction method, which has played an important role in the progress of rheology of amorphous polymers, is found to be also applicable for crystalline polymers. By the application of reduction method and of its modification by Takemura, the author and his coworkers have succeeded to determine the relaxation time spectra of Nylon-6, Teflon, Kel-F and Polyethylene over a wide range of relaxation time. As is seen in Fig. 3, these spectra for crystalline polymers seem to have some common features. And it is found that these spectra give successful interpretation for many of rheological properties of crystalline polymers.
The investigations of non-linear behavior, and mechanical properties of anisotropic polymers, which are most interesting for crystalline polymer, will need more accumulations of systematic experimental works not only by rheological methods but also by colaboration of structure analysis, dielectric and NMR measurements.

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In order to measure the temperature dependence of the dynamic modulus in crystalline high polymers at definite frequency, an apparatus was constructed, which was found to be very useful for analysis of temperature-dispersion curve of dynamic modulus, due to its high accuracy and rapid operation for measurements, adding to the advantage of constant frequency.
Both ends of sample fiber or high polymer film are fixed to two strain gauges of unbonded type, one of which is used to transform the sinusoidal displacement into electrical quantity proportional to the displacement and the other is transducer of generated force. Absolute values of these electrical vectors representing force and displacement are adjusted to unity (full scale of voltmeter) and vector reduction are conducted by changing the connection of the output circuit of two strain gauges. By this operation the value of tanδ can be directly read off by the voltmeter. Regulation of the magnitude of vector is conducted conveniently by controling the input of strain gauges. Dynamic modulus, G', can also be calculated from the ratio of the input voltages of strain gauges, E₂/E₁, when the output voltages of them are regulated to be equal,
G'=K(E₂/E₁),
where K is a constant relating to the dimensions of samples and strain gauges.
The main structural feature of this apparatus exists in that the vector reduction is conducted without amplifying the respective electrical output from two strain gauges proportional to force and displacement respectively. By this method the possibility of introducing experimental error based on the phase shifting effect from amplifier could be avoided. However, in order to make this possible, it was necessary to amplify very small output voltage (less than one micro volt) by using selective amplifier of the highest sensitivity.
Another advantage of this apparatus must be cited: the reading of the output voltages of strain gauges is not necessary in absolute values but the relative values of them are satisfactory for determination of both values of tanδ and G'. This makes the measuring operation so rapid that the long time stability of the amplifier is not so serious, and high reproducibility of data can be realized.
The measurements of tanδ and G' at one temperature need only several tens seconds. The temperature characteristics of viscoelasticity of several fibers over a wibe temperature range were measured with heating rate of 1°C/min., with high precision and reproducibility.

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It is generally agreed that in the flow of viscoelastic fluids not only tangential stress but also normal stresses may be generated. This fact raises the necessity of the developement of the goniometry of flow. To satisfy this purpose, Roberts¹ has developed a series of instruments named“Weissenberg Rheogoniometer.”The instrument reported here is also the one devoted to this purpose. The schematic arrangement and two examples of main assemblies for torque and thrust measurments of this instrument are shown in Figs. (1) to (3), respectively.
As is well known, the shear stress and strain velocity relation in laminar shear flow is determined from the data of torque and rotational velocity by the use of Eq. (1) in coaxial cylinders and by Eq. (3) in parallel discs.
For the measurements of normal stresses, we adopted an instrument of a parallel plate type, with which the pressure distribution and the total thrust on a stationary disc of radius R are measured under known rotational velocity and gap spacing. Relations between normal stresses and strain velocity are obtained from those data by the use of Eqs. (4) to (9) with the assumptions that the influence of the centrifugal force may be neglected and complexities arising from the edge of bob and the side boundary may be simply replaced by an isotropic term p'.
In the sense of phenomenological theory, ¹ stresses are correlated to so-called“recoverable strain”and to an over-all rigidity of a fluid in sheared state as shown in Eqs. (12) and (13). The time-dependent features of rigidity may be known by oscillatory laminar shearing tests. The dynamic complex viscosity is determined by Eq. (10) in the coaxial cylinder and by Eq. (11). in the parallel discs. It is of interest to perform the test in which an oscillatory motion is superimposed on the steady shear, for such tests may reveal a fine structure of the rigidity of a fluid in the sheared state. In the present instrument a superimposer of rotational and oscillatory motions is also furnished for this purpose.

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The conventional Hottenroth index (H.I.) method for determining the degree of ripeness of viscose is very useful for viscose industries, but has a few inevitable shortcomings. In order to avoid these shortcomings and to control the ripening process more easily, an automatic tester was developed by one of us (S.O.). The principle of the tester is to record automatically the change in consistency of viscose sample during titration with salt solution; the change in torque required for stirring the sample viscose at constant velocity is converted to the change in electrical potential by means of a differential transformer device.
Employing this tester, some rheological properties of viscose with added various salt solutions, especially ammonium chloride solution, were studied, and it was concluded that the conventional H.I. method did not always determine a volume of 10% NH₄Cl solution by which coagulation of sample viscose just set in. On the oher hand, it was found that viscose with added ammonium chloride solution manifested thixotropic nature, and that the H.I. by the usual method represented a volum of 10% NH₄Cl solution by which a viscose sample became notably thixotropic.
Further studies were carried out for the practical application of this tester to the viscose industry, because it was desirable to correlate the H.I. with the characteristic point in coagulating curve obtained by this tester. It was found that when higher concentrations of viscose (viscose 30g: water 20ml) and ammonium chloride solution (13.5%) were chosen the plot of the logarithm of torque against the volume of NH₄Cl solution added gave a broken straight line and the break point coincided very well with the H.I. given by the conventional method.

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In spite of the great requirements of a self-recording viscometer for industrial use, any suitable one has not been available. For several years our efforts have been made to develop viscometers which automatically record the viscosity and enable us to control processes in various chemical industries, especially in high polymer industries.
According to the results of our studies on rheological properties of concentrated high polymer solutions, it is clear that viscosity at low rate of shear (or frequency) is not only more sensitive to temperature, concentration and molecular weight of solute polymer but also more significant of the solutions than that at high rate of shear, and that the dynamic type of rheometer operating at low frequencies is not suitable for our present purpose. And hence, viscometers of the steady flow type such as rotaing cylinder and cone-plate types have been produced by way of experiment. They are devided into three classes: the first is suitable for a liquid in a open vessel, the second for a lquid in a closed vessel, and the last for a liquid flowing in a pipe. The change in torque exerted to the inner cylinder or plate is converted to the change in electrical potential by means of a differential transformer device and is recorded after being amplified. Instead of the torsion wire or spring used in the ordinary viscometers, a torsion pipe is employed in our viscometers.
One of the viscometers was subjected to continuous tests of practical purpose with about 50% solutions of polyvinyl acetate in methanol-vinyl acetate mixture. The results showed that the accuracy of the viscometer was fairly satisfactory and would be further improved by changing the electrical circuit and by providing for a jacket to control temperature of the liquid to be tested.

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For the purpose of studying the molecular conditions in aqueous solutions of biologically important macromolecules, we frequently measure the viscosity of their dilute solutions. Since the mean shear rate in an Ostwald type viscometer is usually over 1000sec^-1, the results cannot be treated with Simha's equation. Therefore a viscometer with a long capillary tube was designed to reduce the shear rate down to about 100sec^-1.
Recently we designed a coaxial cylinder type (Couette type) viscometer to measure viscosity at lower shear rates for studying large molecules having small rotary diffusion coefficients.
The outer and inner cylinders are made of“Carbate”. The inner cylinder is hollow so as to make the apparent density slighty smaller than water, and is supported by small pivot bearings at the top and the bottom. The pivot is made of iridosmine alloy to avoid any corrosion due to the solution to be measured. The cup bearing was made of synthetic saphire. The outer cylinder is supported by precision preloaded ball bearings, and immersed in oil, the temperature of which is kept constant. The outer cylinder has a pulley which is made to rotate through a rubber belt by the motor. The motor is a shunt type controlled by thyratrons. When the voltage of the power supply was kept constant, the speed of the motor is constant within 0.2% at any speed between 30 to 3000 r.p.m.
The gap between the inner and the outer cylinders is 1mm. The bottom part is designed as a cone-and-plate type so as to make the shear rate uniform all over the gap between both cylinders. The total volume of the gap is about 4ml. For measurements, however, 7ml. of solution is used in order to minimize the interaction between the upper surface of the inner cylinder and the free surface of the solution.
An aluminum disk is on the axis of the inner cylinder and rotates with it. The edge of the disk is in the gap of a permanent magnet, and receives braking torque when the inner cylinder rotates. The strength of the torque is proportional to the rotational speed of the disk, and the value may be calibrated by placing liquid of known viscosity in the gap.
In order to measure the viscosity of a solution, the solution is placed in the gap, and while rotating the outer cylinder at various speeds, the rotational speed of the inner cylinder and the difference of the rotational speed of the inner and the outer cylinders are measured. In this way viscositty of the solution may be measured at various points over a wide range of shear rate.
We have measured non-Newtonian viscosity of myosin-B, tobacco mosaic virus, nucleic acid, collagen, polyacrylic acid, etc. over the shear rate range of 1 to 100sec^-1. The upper limit for the shear rate is due to the method of measuring the rotational speed. If the rotational speed should be measured by a suitable electronic method instead of the present naked eye and a stopwatch method, the upper limit would be raised considerably. In order to lower the lower limit, we are trying to reduce the bearing friction.

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A coaxial cylindrical rheometer was developed for measuring viscoelastic properties of liquid by rotational and/or oscillational method. A feature of this apparatus is the fully automatic recording system which is achieved by means of the electric driving and detecting units.
A torque-motor, instead of a torsion wire, is connected to inner cylinder and the deflection is measured by a special electromagnetic detector.
A specially constructed sinusoidal voltage generator, of very low frequency below 1cps, is used for giving the oscillatory torque to inner cylinder.

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The study of dynamic mechanical properties of materials is well recognized to be of both practical and theoretical value. But few works have been reported on the elastic properties of the molten polymers, although engineers encounter a number of difficult problems caused by the properties. In the present paper, a new device of cup-bob-rod system, particularly designed for the molten polymers, is reported torgether with the experimental data on the end-effect obtained by the trially produced dynamic phase contrast co-axial cylinder viscometer shown in Photo. 1 and diagramatically in Fig. 1.
In the system, as illustrated in Fig. 2, the cup is electrically heated with nichrome wire. By the use of this cup in combination with such a plunger as shown in Fig. 3, samples may be easily preformed into cylindrical tablets closely fitted to the cup dimensions. The most essential characteristic of the system is that the centering of bob both at the immersion of itself into the test specimen and at the rotation is achieved by the narrower clearance indicated in Fig. 4. To gain the smooth rotational simple vibration, it is desirable to introduce silicone oil into the clearance. This heat-resistant oil also prevents the rapid oxidation of the specimen through cutting off the diffusion of fresh air.
It has been well known that in static co-axial cylinder viscometer the compensation of the end-traction both on the top and bottom of bob accounting it in terms of increased bob length is necessary. In the dynamic viscometer, however, none has been reported concerning to the practical magnitude of this effect. In this research multiple-bob method is adopted and Phillipps' Polyethylene Marlex 50 is exclusively used for the test specimen. The testing is carried out at 160±0.3°C, unless otherwise noted, over the low frequency range from 0.015 to 0.8 cycles per second. The essential dimensions of bob, cup and rod used are shown in Table 1. The effects of restoring torque of rod and separation between bottom of bob and cup are shown in Tables 2 and 3, and effects of the volume of test specimen flowed over the bob in Fig. 5. The plots of apparent dynamic viscosity and rigidity against reciprocal of bob length give stratght lines as shown in Figs. 6 and 7, where the slope gives the product of the additional bob length Δh₁ for the end correction and the true viscosity or rigidity given by the ordinate intercept, respectively. The conclusions are as follows:
(1) As well as in static viscometer, the end-effect in the dynamic co-axial cylinder viscometer can be expressed in terms of additional length of bob which remains constant radius. The end correction term Δh₁ computed from viscosity coincides with that from rigidity.
(2) Variation of the end correction term with frequency can scarcely be observed.
(3) The end correction term increases with clearance, and shows somewhat lower value than that reported by Lindsley-Fischer obtained with Newtonian liquid of lower viscosity. The magnitudes with 1cm cup radius are found to be approximately 0.25 and 0.35cm for the 0.1 and 0.2cm clearances, respectively.

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The dynamic viscosity of liquid can be measured by inserting an oscillating metal plate into the liquid and measuring its mechanical impedance by an electronic means. The merit of this device is the convenience for the continuous recording of viscosity, but difficulties lie in securing the good stability of apparatus. The main causes are the fluctuaion of gain in electronic circuits, the dissipation of oscillation energy through the support of plate, the time variation of the mechanical damping of metal plate etc. These difficulties are diminished by the adequate device as employing the zero method, but they are principally eliminated by taking the resonance width instead of the resonant amplitude as the measure of viscosity.
When the resonance amplitude is employed as the measure of viscosity, the equation connecting the product of density ρ and viscosity η of liquid to the reading of output meter E, which is proportional to the resonance amplitude or velocity of oscillating plate, is
ρη=K₁(E_A/E-1)²
where E_A corresponds to the resonance amplitude or velocity of plate in the air and K₁ is a constant determined by the mechanical design.
A mechanical damping Q^-1 of the oscillating system is expressed by (f₁-f₂)/f_r, where f_r is the frequency at resonance and f₁ and f₂ are the frequencies at which the amplitude of oscillation is 1/√2 times the resonance amplitude. The variation of Q^-1 can be followed by measuring the resonance frequency width (f₁-f₂) if f_r does not change. When the mechanical damping Q^-1 is employed as the measure of viscosity the following equation stands,
ρη=K₂(Q^-1-Q^-1_A)²
where Q^-1_A is the mechanical damping of oscillating plate in the air and K₂ is a constant of apparatus.
The fluctuation of Q^-1_A is so small compared to Q^-1 that the reproducibility of measurement is improved. The sensitivity of the instrument becomes better in a range of the lower viscosity in the former method, but of the higher viscosity in the latter method. The most sensitive range can be brought into various values of viscosity by the appropriate design of the mechanical impedance of oscillating plate.
The determination of frequencies f₁, f₂, and f_r is easily carried out by measuring the phase angle between exciting voltage and receiving voltage of the oscillating system. In the proposed scheme of apparatus, the electric signal comes out from the phase sensitive detector at the phase angle of 45, 90 and 135 degrees, each corresponding to f₂, f_r and f₁ respectively and indicates these frequencies on the recording paper.

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In this paper, the authors discuss rheological aspects of rheometers. The rheological classification of the dynamic behavior of materials is shown in Table 1. The features of the dynamic behaviors of non-thixotropic, nonlinear visco-elastomers are shown in Tables 2, 3, 4 and 5. The neccessary testing performances of rheometer for measuring the rheological properties of non-thixotropic, nonlinear visco-elastomers and of thixotropic materials are discussed.

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