The explanation of rheological properties of paper and pulp sheets in terms of their structure has hitherto been considered to be very difficult, seeing that they are composed of a lot of macroscopic elements or fibers, though it seems rather easier than those of other materials composed of microscopic elements or molecules. Therefore, rheological studies in this field have not been very actively made in spite of practical importance of these materials. In this article, the rheological studies by the author, especially those on non-destructive elastic and viscoelastic properties, have been reviewed along with the related studies by other investigators.
There are two distinct lines in the theories relating the rheological and other physical properties of paper to its structure. Nissan's works are typical of the first of the two. He assumes that the strain of paper under stress is derived from the extension of hydrogen bonds. The author and several others, assuming that paper consists of randomly arranged three-dimensional array of fibers, have put forward theories for elastic and other properties, assuming also that the deformation of paper arises from the bending, stretching and shearing of the fiber segments between the bond sites. The latter theories can presuppose many important facts, some of which have been known experimentally or empirically, though imperfectly yet.
Paper is a typically orthotropic material, and its Young's modulus and tensile strength in an arbitrary direction are well represented by the Horio-Onogi equations (8) and (9), which describe a peculiar elastic property of paper, as was pointed out by Campbell and Craver and Tayler. The correlation between the density and modulus of elasticity, the effects of humidity and several manufacturing variables such as beating, wet press, screening and drying on rheological properties of papers and pulp sheets are also discussed. The viscoelastic data reported by the author reveal that paper has essentially the same viscoelastic properties as cellulosic fibers such as viscose and Bemberg rayons if, and only if, they are corrected for the density. This indicates that the junctions between the constituent fibers are very strong and similar to those between the cellulose molecules as was assumed in the above theories, while the macroscopic structural factor should also be taken into account.

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An experimental result is reported in the present report of the plastic and viscoelastic properties of the Kanto loam and the hedoro. The Kanto loam is composed of allophane mineral, and the hedoro is deposit clay, composed of montmorillonite mineral. They are both nearly saturated with water in natural state. Their rheological properties can be explained mainly by the concept of the state of water respecting its energy in the soil pF.
From the results of three-dimensional stress relaxation test in the soil unsaturated with water in Fig. 3, it is shown that the stress σ₃ decreases with time, while the stress σ₁ increases nearly to be equal to σ₃. The elasticity of the undisturbed sample of the Kanto loam increases irreversibly with temperature.
The strength of soil S is defined by the state of stress applied to the soil particles. The state of stress p is the sum of the internal pressure p_i and the external pressure p_e. The internal pressure p_i is decided by the physico-chemical properties of the particles of the soil. Then, the state of stress in the soil water system can be determined by the thermo-dynamic treatment. And the relations among the strength and chemical potential of the water and the suction of clayey soil have been clarified.

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The hydrogel of Wyoming bentonite shows characteristic slip patterns under critical stress σ₀, i.e. the shear strength for slip fracture. The shear strength of the bentonite gels is related to the shear modulus G, as shown by the E_q. (1). G varies depending upon the concentration, and the ptoportional constant γ₀ takes values ranging from 1/10 to 1/30, which depend on the strain rate.
In this report, the dependence of σ₀, G, γ₀ and viscosity η on the temperature and the relation between σ₀ and η were observed by the cone and plate method. The experimental results in Table I show the dependence of viscoelastic properties of bentonite gels on the concentration at 25°C, Over the wide range of concentration examined, a linear relation (2) is obtained between σ0 and η, as shown in Fig. 1. A proportional constant R in this equation is approximately equal to 5×10^-5sec^-1, which is the lower critical rate of strain for the slip fracture. These facts suggest that γ₀ is proportional to η/G. σ₀ and G increase with the increasing temperature between 3-50°C, but take almost constant values at the temperature between 50-70°C, as shown in Fig. 2. Fig. 3 shows the facts that η and η/G decrease with the increasing temperature between 3-70°C. Over the whole range of temperature examined, the linear relation (1) holds between σ₀ and G, and then γ₀ is independent of temperature, as shown in Fig. 4 and Table II.

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The flow properties of the suspension of titanium dioxide in cane sugar salution were investigated using the following viscometers; a coaxial cylinder viscometer for the lower shearing rate range, the M.K.S. (Maron, Krieger and Sisko) type capillary viscometer for the middle shearing rate range and the NBS (National Bureau of Standard) type capillary viscometer for higher shearing rate range. The volume fraction of the titanium dioxide examined ranged from 20 to 40vol%.
In the higher shearing rate range, the linear relations between the shearing rate and the shearing stress were obtained. This rate range can be called the Newtonian range.
The region where apparent viscosity increases with the shearing rate can be called the dilatant range. On the other hand, dilatancy can he defined by the differential viscosity, because the apparent viscosity has little physical significance in non-Newtonian range.

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Observations were made of the dielectric properties of water film adsorbed on silica and alumina gels to investigate the structural conditions of adsorbed water films which may cause non-Newtonian behaviour and thixotropic characteristics in these dispersions.
The following results have been obtained
When the amount of water in the adsorbed film was increased:
(1) Contribution to the dielectric polarization of dissolved and adsorbed ions in the moisture film decreased
(2) The relaxation time of interfacial polarization due to the adsorbed ions decreased
(3) The width of the distribution of relaxation time became a little narrower. When the compression was applied to the gels:
(4) The interfacial polarization due to the adsorbed ions in the adsorbed moisture layer increased.
(5) The relaxation time decreased to a small extent
(6) Little variation of width has been detected in the distribution of relaxation time.
From these results investigated, it can be concluded that the water molecules in the adsorbed water layers have different properties from those of free water molecules. The adsorption forces on the surface of gel powder decrease with the distance from the powder surface. When the electrical field is applied, the adsorbed ions have a tendency to move through the outer layers where the adsorption forces are small.

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The stickiness between a stainless steel plate and several kinds of hydrogenated oils and their mixtures for margarine was measured by the use of an improved high sensitive stickiness meter.
On the range between 10g/cm² and 50g/cm² of compressive stress, the rate of separation of the plate does not affect the stickiness of hydrogenated cotton seed oil, but the stickiness of mixing oil for margarine increases up to 60% at the rate of 5mm/min. It is noticeable that the values of the hesion force of oils and fats are somewhat scattered in the range of separation rate between 0.5 and 50mm/min.
The hesion force of hydrogenated oil increases in general with temperature, but margarine oil of soft type decreases remarkably its hesion force with temperature over 15°C. Between the peeling time t_b and the hesion force f_b, Eley's relation t_b ∝ f_b^-n, is established the n of oils and fats being in the range from 1 to 3.
The solid fat content of oils and fats is an important characteristic in connection with the variability of the hesion force.
Under the standardized conditions of the two peeling rates, 1mm/min and 5mm/min, the maximum peak of hesion force was found at solid fat content of about 22%. It will be concluded, therefore, that the adhesive force to steel reaches an equilibrium with the cohesive force of oils due to their structural characteristics.

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In a system of polymer blends, which is composed of n kinds of component polymers, free volume fraction of i component (f_i) is assumed to be by E_q. (1).
(1)
where suffixes i, j and k mean components i, j and k respectively, and the suffix 0 means the value before blend. V is a volume fraction of component and a_i^j is a coefficient, which becomes zero when i equals j and b_i^jk a coefficient which becomes zero when i equals j or when i equals k. The relationships between the glass transition temperature T_g and the composition for various types of polymer blend were derived from E_q. (1) for the two component system.
The relationships for perfectly miscible system, random copolymer system and microheterogeneous system are expressed as follows;
(2)
where Δα is the expansion coefficient of free volume fraction and B, C, B' and C' are constants including a_i^j and b_i^jk of E_q. (1). The values of a_i^j for various kinds of polymer blend were obtained from T_g values observed as a function of composition and the physical meanings of a_i^j were discussed.
Assuming that the blend system is composed of many cells with different value of free volume, we newly defined a distribution function of free volume fraction F(f), to explain the behavior of actual polymer blend. The function F(f) could be obtained from the specific volume-temperature curve. By using it, we could express the mixing state of polymer blends and explain their viscoelastic behavior near glass transition temperature. These results can be applied to the various types of copolymers.

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The dynamic modulus and dynamic viscosity of a potato starch solution in 1N KOH were measured in concentrations from 2.0 to 7.0g/100ml by using a forced torsional vibration rheometer of various frequencies at temperature 25°C. The similar measurement was applied to the starch solutions irradiated by gamma ray. The master curves of the reduced dynamic modulus and reduced dynamic viscosity were derived in fairly good single lines, according to Ferry's time-concentration reduction principle.
The concentration dependence of the dynamic modulus G'∝C^m, the dynamic viscosity η_d∝C^n', and of the zero angular frequency viscosity η/η₀∝Cⁿ were respectively determined. The authors' m values suggest that the network structure in the starch solutions is formed by some trifunctional crosslinkages. The n value generally indicates the degree of intermolecular interaction. The authors' n values lie between that of the gelatin solution and that of the collagen solution.
The relaxation spectra of the starch solutions were obtained in curves of nearly linear shapes, and those of the irradiated starch solutions shifted to shorter relaxation time with steeper inclinations in accordance with increasing total dose. It was suggested from the range of logτ observed that the relaxation spectra were in the flow region of the whole relaxation spectra, and that they were attributable to the relaxation mechanism caused by the macro-brownian movements of the starch molecules. It is to be noted that the relaxation spectra derived from the time-concentration reduction principle agree well with those derived from the time-temperature reduction principle which were reported for the solutions in formamide in the previous paper. This proves that the starch solutions in formamide and 1N KOH are thermorheologically simple, and that they can be treated as linear viscoelastic fluids. Moreover, the similarity in the relaxation spectra for both kinds of solvent may be due to the good solubility of the starch in these solvents.

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In this paper are presented some reports of theoretical studies made on hemorheology which is the rheology of blood and blood vessels. The first problem is concerning the influence of the plasmatic zone upon the apparent viscosity of blood in capillaries. If the central core is treated as a Bingham body with the plastic viscosity η_B and the yield value τ_f, the volume of flow per unit time is obtained as follows.
with γ=1-δ/R> and ξ=2L_τf/PR. Here R is the radius, P is the pressure difference between the two cross sections at a distance L, η_p is the viscosity of plasma, and δ is the thickness of the plasmatic zone.
If we neglect small terms of order (δ/R)², then the above equation becomes modified as follows.
It is pointed out that the formula obtained by Bayliss
is not correct.
If we consider that the central core obeys Casson's equation, we get
with ξ=2L τf/PR. η_c is the Casson viscosity and τf is the yield value. If we neglect small terms of order (δ/R)², the above formula is reduced to that derived already by the author.
The second problem is concerned with the elastic tension in thick-walled blood vessels in relation to the law of Laplace. Since some doubts have been expressed in physiological literature about the applicability of the law of Laplace to blood vessels, we have examined closely the elastic tension in the wall from the physical point of view. Let a thick-walled vessel be in equilibrium under the internal pressure p₁ and the external pressure p₂ and let the inner and the outer radius be denoted by r₁', and r₂', respectively. Then the circumferential tension T_c is exactly given by T_c=p₁r₁'-p₂r₂'.
This relationship holds quite well generally, irrespective of whether the blood vessel wall has Hookean or rubber-like elasticity, whether the vessel wall is homogeneous or inhomogeneous, and whether the vessel wall is isotropic or anisotropic. Our formula is reduced to the law of Laplace for thin-walled blood vessels.

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The steady flow viscosity of blood and plasma during the early stage of coagulation was measured by a coaxial cylindrical viscometer in a range of shear rate from 2 to 100sec^-1. The relation between stress and shear rate observed for clotting blood was well represented by Casson's equation. The plastic viscosity and yield value increased as the coagulation proceeded appreciably.
To measure the dynamic viscoelastic moduli, the blood or plasma was poured into a gap between the two coaxial cylinders, which were connected to two strain gauges respectively. The outer cylinder was vertically oscillated at a frequency of 10c/s and with an amplitude of 60 microns to cause the shear strain to the sample. The alternating stress given to the inner cylinder due to viscoelastic properties of the sample was detected by the strain gauge and dissolved into two components, one with the same phase with strain and the other being 90 degree out of phase with strain. The former gave dynamic elastic modulus E′ and the latter dynamic loss modulus E″.
In a few minutes after adding coagulant to the sample, E′ first began to increase, followed by the rise of E′. The earlier increase of E″ would indicate the onset of polymerization of fibrinogen into fibrin. Rapid increase of both E′ and E″ in succession was observed, which suggested the formation of networks of fibrin fibers. The time required for E′ and E″ to reach the saturated values was several hours for whole blood and less than 1 hour for plasma. When the plasma was diluted with water, keeping the hematocrit unchanged, the saturated values of E′ and E″ decreased. The presence of blood cells largely increased the saturated values of E′ and E″ in whole blood.

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It is the aim of this paper to examine experimentally the fitness of Bagley's method for the end correction of capillaries. The experiments were performed with the silicone fluid of 6×10³ degree of polymerization as materials by using capillaries and reservoirs of various dimensions.
Even in case the linearity of P-l</r relation of a given capillary, at constant shear rate, (P as applied pressure, l as capillary length, and r as capillary radius) is perfect, should capillary radius be varied, the end corrections will cease to agree between them.
The above disagreement is well illustrated by introducing the effect of pressure loss resulting fromflow through the reservoir into the total pressure loss.

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The general theory of steady slow motion of non-Newtonian fluids through a tapered tube is presented in the present paper.
The general formulae for shear stress, velocity and flow have been obtained for a straight tube, a rotating coaxial cylinder viscometer, a cone and plate viscometer, and a double cone viscometer. However, no similar formula in general for non-Newtonian fluid through a tapered tube has yet been available.
It is assumed that the fluid is characterized by a time-independent flow curve f(τ), and that the tapering angle α is very small. It is further assumed that the coefficient of viscosity η which appears in the relationship between the stress and the strain rate of non-Newtonian fluid is not constant, but a function of the velocity gradient. Under these assumptions the following formulae for the shear stress, velocity, and flow have been obtained, which will be taken in general.
τ_a being the shear stress on the wall. These formulae, quite similar to those for a straight tube of uniform cross section, are applied to the following particular fluids: Newtonian fluid, power law fluid, Bingham body and the fluid obeying Casson's equation.

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The double cone viscometer consists of two coaxial cones. The generator of the external cone makes an angle γ with the horizontal plane, and the generator of the internal cone makes an angle γ+α with the horizontal plane. We shall consider that the angle α is very small. The wedge-like spacc between the two cones is filled with a liquid to be investigated. Either of the cones, internal or external, is rotated. In the present treatment, the external cone has been rotated with a constant angular velocity Ω around the axis of the cone.
We shall first find general relationship between the torque M and the angular velocity Ω for a time-independent non-Newtonian liquid specified by an arbitrary flow curve. Then we shall show how to determine the flow curve from the experimental relationship between M and Ω for some special cases.
With regard to the motion of the liquid, the following assumptions are made: (1) the liquid is incompressible; (2) the motion of the liquid is laminar; (3) the motion is steady; (4) there is no force acting on the liquid; (5) the motion has an axial symmetry; (6) each liquid particle moves in a circle on the horizontal plane perpendicular to the axis of rotation; (7) there is no relative motion between the walls and the liquid in immediate contact with the walls; (8) the edge-effect is negligible. The assumption (6) corresponds to neglect of centrifugal forces. For small values of Ω, this assumption as well as the assumption (2) may be allowed.
We shall take a spherical coordinate system r, θ, and φ whose origin is at the vertex of the cone. If we assume that the angular velocity ω of a liquid particle around the axis of the cone is a function of θ alone, then the shear stress τ_θφ is given by τ_θφ=c/sinsin²θ, where c is a constant. For a non-Newtonian liquid specified by an arbitrary flow curve f(τ), we get
The constant c is related to the torque M on the internal cone by the relationship M=c·2πa³/3. For a non-Newtonian liquid obeying a power law flow curve f(τ)=kτn the following formula has been obtained:
For the special case where n is equal to unity, the above formula is reduced to the well-known formula for a Newtonian liquid:
Here η=1/k is the coefficient of viscosity. We have also examined other special cases: (1) non-Newtonian liquid whose flow curve is expanded into power series, (2) Bingham body and (3) non-Newtonian liquid obeying Casson's equation.

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Fluid fracture processes were considered from time, temperature and concentration dependence of the ultimate property during the course of an investigation of fracture processes of polymeric liquids, rubberlike and hard plastic polymers. The samples were liquid polybutadiene (PBD)-benzen solutions with six different volume fractions of PBD (v₂) ranging from 0.374 to 0.782. The method and an apparatus used for the experiment are described in a previous report.¹⁾ The drop weight W and the breaking time t_b were measured with various drop sizes at four different temperatures from 25°C to 40°C for each sample. The results may be summarized as follows:
(1) Time and temperature dependence; (i) Weight vs. time curves a_t different temperature for each sample can be superposed into an almost unified master curve by the horizontal shift along the time axis. (ii) The shift distance loga_T seem to follow the prediction of the Arrhenius equation. (iii) The apparent activation energy for the viscoelastic process from a plot of loga_T against l/T systematically increases with decreasing v₂.
(2) Time and concentration dependence; (i) Time-concentration superposition is possible on a plot of W vs. logt_b at each temperature, but it is impossible on a plot of W(ρ_s/ρ) vs. log t_b, where ρ is weight of PBD per unit volume of the solution, ρ_s is a ρ selected arbitrarily as reference. (ii) The shift distance loga_c was examined from the following two equations; -1/loga_c=f(v_s)+[f(v_s)]²/γ(v₁-v_s)…(1), loga_c=log(η/η_s)={b(v₂-v_s)+c(v₂²-vs²)}/RT…(2), where v₁=1-v₂, v_s is a reference volume concentration, b, c are constants. The Eq. (1) has been presented by Fujita and Kishimoto³⁾, and corresponds to WLF equation. The E_q. (2) was lead from Andrade's viscosity equation η=A exp (U/RT), where U is replaced by interaction energy between polymer chain elements and solvent molecules in the from U=a+bv₂+cv₂² which was obtained form thermo-dynamical consideration of polymer solution. The present temperature-concentration region may be divided into three parts where loga_c obtained from experiment follow approximately the Eq>. (1) only, the Eq. (2) only, and both the Eqs.

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Two theories of fracture of viscoelastic materials are hereunder proposed, the one based on a simple model and the other generalized thereupon, and an attempt is made to explain the dependence of stress and strain at break on temperature and strain rate as particularly was called the failure envelope by T.L. Smith.
The model of the first simple theory consists of two Maxwell elements (system 1 and 2) connected in parallel and the following criteria for fracture are introduced.
(1) Fracture occurs first at the system 1, and then at the system 2 where the whole load is applied.
(2) Fracture of the system 1 occurs either when the spring reaches the critical strain ε_11c (in the case of large strain rate) or the dashpot does so to ε_12c (in the case of small strain rate).
For the deformation of constant rate R, the following results are obtained, which explain the experimental behaviors well at least qualitatively.
at larger strain rates
at smaller strain rates
where σ, ε, G and τ follow the ordinary use and suffices 1 and 2 mean system 1 and 2 respectively and the suffix b does so "at break".
Next the above model theory is so extended to the generalized Maxwell bodies as to read that the stress of deformation at constant rate is expressed by the equation
In this case the storage energy W_st and the dissipation energy W_dis of deformation are calculated after Landel, and the following criterion is introduced, that is, the sample breaks either when the elastic part with its own modulus G₀ (the instantaneous modulus) reaches the critical strain ε_1c or the viscous part with its steady flow viscosity η₀ reaches the critical strain ε_2c.
The results are given as
at larger strain rates
at smaller strain rates
where G' and η' are dynamic modulus and viscosity respectively. Considering the dependence of G' and η' on shear rate and temperature, the failure envelope can be explained with these equations.

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Studies have been made of the dynamic viscoelastic properties of copolymers of styrene (S) and butadiene (B) in toluene (good solvent for both components) at 30.0°C. The polymers were prepared by the "living polymer" method with the same monomer feed ratio of S 61mol % and B 39mol %. The two were block copolymers with three sequences of B-S-B (BSB 1101) and S-B-S (SBS 1102), and the one was a random copolymer (SB 1103). The complex rigidities and the steady shear viscosities were measured by means of torsional crystals at the frequencies of 19.6kc, 39.2kc or 40.15kc, and 117.7kc, and a Ubbelohde dilution type viscometer respectively. The intrinsic rigidities and the generalized limiting relaxation times were obtained by extrapolation to zero concentration.
The dimensionless functions of intrinsic rigidities were plotted logarithmically against the generalized angular frequencies together with the theoretical curves of Rouse (free-draining case) and Zimm (non-draining case). In these plots, the experimental points lie between the Rouse and the Zimm theory for the two block copolymers and closely on the Zimm theory for the random copolymer. It means that the random copolymer is nearly non-draining, and the block ones are partial-draining; BSB 1101 seems to exhibit the stronger draining effect than SBS 1102 in toluene at 30.0°C. Since the draining effects correlate with the volume expansion, it may be suggested that the random copolymer has more compact conformation than the block sorts in such good solvent as toluene.

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The time and concentration dependences of yield stress were examined for poly (vinyl chloride) (PVC) plastisized with small amount of di-2-ethylhexyl phthalate (DOP), over concentration range of 0.270 to 0.125 in volume fraction of DOP, which is a part of studying the transformation from fluid fracture to ductile fracture, and from ductile fracture to brittle fracture, with sample liquidlike rubber-like and hard plastic polymers.
Tensile yield stress σ_y was measured at room temperature and at strain rates ε varying from 0.020min^-1 to 20.0min.^-1 The resultant yield stress was plotted in the form log (σ_yρ_s/ρ) against ε, where ρ is weight of PVC per unit volume of the sheet, and ρ_s is aρ selected arbitrarily as reference. These data for the samples with various concentrations have been shifted laterally along the strain rate axis to construct a yield stress muster curve.
The dependence of shift distance loga_c on volume fraction of plastisizer v₁, or that of polymer v₂ (=1-v₁), seems to be represented approximately by the relation log a_c=b (v₂-v_2s) at high v₂ range, where b is constant. This expression is obtained from Andrade's viscosity equation, η=A exp (U/RT) and the relation a_c=η/η_s, whereU is replaced by cohesive energy of chain segment-solvent molecule; U=a+b_v2.
The yield strain data and birefringence data observed in ruptured specimens were also shifted laterally along the strain rate axis by the same distance that was used for superposition of yield stress data. The shifted yield strain data did not form a curve but gave a domain. The birefringence data form a muster curve at v₂=0.73. This curve seems to increase rapidly at a shifted strain rate 1.00min^-1. In the test of the strain rate mentioned above, clear necking was observed in the specimens.

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The curing process of urea resin adhesive was studied by the change of fluidity measured with Koka Flow Tester.
The flow test was operated under the fixed testing conditions of pressure (10kg/cm²), orifice dimensions (0.2mmφ×1mm), and temperature (20°C). The volumetric flow rate was calculated at several points on the auto-recorded flow curves. And the relative fluidity-decay curves were obtained by plotting in the form Q(t)/Q(0), where Q(t) was the efflux rate at time t, and Q (0) the initially measured efflux rate, versus log t for each sample.
In order to express the character of fluidity in curing urea resin as a function of time and hydrogen ion concentration, experiments were made with resins adjusted to various pH's. It seems that the change in pH removed the fluidity-decay curve horizontally along the logarithmic time axis. The slope of the curve, however, was affected by the condensation degrees of the resin.
To find any possible influence of chemical components of resin in the shape of the fluidity-decay curve, further experiments were carried out by using several different resins.
As the resins used were prepared under different conditions, they were subjected to analysis to determine the amounts of free and combined formaldehyde (methylol, methylene, and dimethylene ether groups). The results revealed that the shape of the fluidity-decay curve was remarkably varied with the amount of the aldehyde groups. It seems that the fluidity-decay curve represents the condensation process of the urea resin.

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Piezoelectric properties of elongated films of cellulose diacetate and cellulose triacetate were investigated in a temperature range from -160°C to +160°C. The sinusoidal stress was given to a film specimen cut at 45 degrees obliquely to the orientation axis at frequency 20c/s, and measurement was taken of the electrical polarization that appeared on the faces of the film. Not only the absolute value of piezoelectric constant but also the phase difference between the stress and the polarizatian was detected. Defining the complex piezoelectric modulus as d^*=d'-id", d' and d" were quantitatively determined as a function of temperature.
In cellulose diacetate, d' increased with the rise of temperature accompanied by a peak of d" with a positive sign, indicating that the polarization lagged behind the stress. On the contrary, in cellulose triacetate, d' decreased with the rise of temperature, accompanied by a trough of d" with a negative sign, indicating that the polarization overreached the stress. Such results may be called as piezoelectric dispersion and absorption with temperature.
Dynamic viscoelastic and dielectric measurements were also carried out for the same specimens. Comparison of the results indicated that piezoelectric, elastic, and dielectric absorptions took place over the same range of temperature, and that the piezoelectric absorption was the sharpest among them.
The oriented polar molecules or oriented crystallites are supposed to be the units responsible for the piezoelectric polarization in the elongated polymer films. Distribution of mechanical stress and dielectric shielding around these units and even piezoelectric moduli of units themselves can be altered by the thermal variation of the molecular motion in polymers.

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The H_v small angle light-scattering from polyethylene films gives a sort of diffraction pattern like a four-leaf clover type. This suggests that there might be a kind of regularity for the presence of optical heterogeneity within the films.
The change in distribution of scattered intensity with static elongations was observed in two kinds of polyethylene films, a slowly cooled film of medium density polyethylene, Lupolen KR 1051, and the same irradiated by electron bombard using a high-tension electron microscope. Moreover, the dynamic response to the distribution of scattered intensity with sinusoidal tensile strain was observed by the photographic method using stroboscope technique.
The dynamic response to scattered intensity at given scattering and azimuthal angles was usually in advance of the dynamic strain by the phase angle γ and represented by
where I_s is the static level of the scattered intensity and I_d is its dynamic amplitude. The amplitude can be represented by the in-phase and out-of-phase components, ΔI' and ΔI", with respect to the dynamic strain, and the phase angle γ may be defined by ΔI"/ΔI'=tanγ.
The frequency dependence of these parameters, I_s, ΔI', ΔI" was investigated at temperatures, both room and elevated near 60°C, over the frequency range from 0.05 to 10cps. A frequency dispersion of I_s was definitely found around 0.7cps, which shift to higher frequencies with increase of temperature, whereas those of ΔI' and ΔI" were not definite because of much scattering of the data.

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The two relaxation mechanisms of low and high activation energy (α₁ and α₂) which underlie the socalled α relaxation of bulk crystallized polyethylene are re-examined on the relaxation map, taking into account the following facts reported in the literature:
(1) The α₁ (grain-boundary) relaxation sometimes appears as twin peaks on the loss modulus vs. temperature curve.
(2) The time required for the α₂ (intra-crystalline) relaxation of the specimens grown from the solution (single crystals) is relatively shorter, and is made longer by a heat treatment.
(3) The relaxation time determined by the rheo-optical methods is by no means correlated with the twisting oscillation of the folded molecular chains, that is, the α₂ relaxation.

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In our previous paper¹⁾ of this series the properties of styrene-butadiene rubber vulcanizates in tensile fracture was discussed. In this paper the properties of three copolymer vulcanizates in tensile fracture are studied, namely isoprene-butadiene, styrene-isoprene and methyl methacrylate-isoprene, and the following conclusions have been obtained.
(1) The fracture in the vulcanizates of these copolymers compounded with carbon black is mainly due to scission in the molecular chains of polymer, and there is almost no scission in the bonds between the rubber molecules and the surface of the carbon black.
(2) The temperature which affords the maximum value of ultimate elongation depends entirely on the transition temperature T_g, though the rubbers used may vary in average molecular weights per piece, in the network chain densities and in the combined sulfur structure.
(3) The ultimate elongation at reduced temperature is little affected by the composition of two copolymers that do not differ markedly in T_g of homopolymer, as in the isoprene-butadiene system, while the elongation is thought to be decreasing with the increasing variance between the two component copolymers in T_g of homopolymer. For instance the elongation of styrene-isoprene copolymer decreases with increased content of styrene.

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It is well known that in amorphous polymer the distribution curve of relaxation time of stress is depicted as a continuous spectrum of the "wedge" part and the "box" part. The "box" part is dependent on such factors as molecular weight and its distribution, branching, composition etc. We have attempted, therefore, to study the relation between the structure of polymer and its viscoelastic properties.
The master curve obtained and relaxation spectra calculated from it changed remarkably with the composition of random copolymers. In the "wedge" part, this is due to the flexibility of the polymer chain, and the slope approaches 1/2 with increase in the composition of MMA. Of the "box" part, the values of various kinds of parameter from Procedure X (for example, τ_m, η_t, Je etc.) were calculated. The relation between τm, ηt and polymer composition showed remarkable phenomena. This seems to be due to the inter-molecular dilution effect by the MA that constitutes the other side of the random copolymers. The relaxation time was observed to have a tendency of shifting to the side of MA.

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The equation of Casson (1957) and that of Goodeve (1939) have been presented for interpreting flow characteristics of disperse systems; the former particularly for suspensions and the latter for suspensions and emulsions. Although these two equations have been established on different theoretical models, they have similar forms in relating shear stress (or pressure) and rate of shear (or rate of flow), and they differ from each other only at a point where the equation of Casson has an additional term containing the square root of rate shear. From this formal difference the equation of Casson appears to have a wider applicability than that of Goodeve, especially in the range of greater rate of shear or in the range of smaller concentration of dispersed phase.
This consideration is examined in this paper by applying these two equations for experimental data obtained by the present author on the following systems: bentonite-water suspensions, benzenewater emulsions containing bentonite and oleic acid as emulsifiers, nitrobenzene-water emulsions containing amylalcohol and sodium dodecylsulfate as emulsifiers, and also for the data on blood obtained by Copley and his collaborators.
It is shown that the equation of Casson has certainly a wider applicability than that of Goodeve for both suspensions and emulsions, while the latter seems to have a favorable applicability for systems showing thixotropy and particularly for systems (emulsions) containing spherical particles.

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A new type of biaxial tensile tester for flat plates has been produced, which can make uniform extention of a square plate in biaxial directions. The tensile mechanism of this tester consists of two servomechanism for the control of the position of the two travelling beams on which cramp chacks are mounted. These chacks are capable of easy travelling on the beam surface by means of ball bearings. By the use of this tester it is made possible to perform such testing as tensile testing, stress relaxation measurement, creep testing and fracture strength testing, under homogeneous biaxial stress states.
In this paper the mechanism of this tester is described, and the results of elastic property measurements of BR, SBR, and IR rubber sheets using this tester are reported. The load-elongation diagrams are obtained by this tester and energy function are calculated from it as a function of invarients I₁, I₂ of deformation tensor.

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Under the uniaxial tensile deformation of viscoelastic materials the values of break stress σ_B or break elongation λ_B of the materials are scattered even at the same mode of deformation. On the other hand, if the mode of deformation is changed, both the mean tesile strength and the distribution of the strength are also varied in each mode of deformation.
The mechanical properties of the viscoelastic materials, that is, the relations of stress and strain, can be estimated by calculations if the material constants are given. Similarly it may be possible to estimate the failure properties in different mode of deformation under some given material constants on failure.
We have used the following equation derived by Kawabata and Blatz for the distributions of time to break, t_B, under comparatively simple assumptions.
(1)
where t_B is the break time, P(t_B) is the probability density function of the break time and V is the volume of the sample. m_c is a function of stress state denoted by φ and can be defined by
(2)
From (1) and (2)
(3)
The distribution of the break time t_B is shown in Eq. (3) in which two failure constants n and C are included.
In this study these failure constants n and C have been determined by creep rupture experiment and using these constants, we estimated the distributions of break strain of SBR vulcanizate under constant rate of strain testing at the various cross-head speeds and at two stages of temperature 40°C and 55°C.
A series of experimental data agreed very well with those of theoretical calculations.

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A rheometer was designed to measure the viscoelastic behavior of polymer melts and concentrated solutions at high temperature under high pressure. By means of this apparatus, the dynamic viscoelastic properties were measured of concentrated solution (20wt%) of polyisobutylene which had a viscosity-average molecular weight of 6.5×10⁵ in decalin. Measurements were made at 40°C, frequencies being varied from 0.025 to 6.3 sec^-1, under the pressure in the range from 0 to 1000kg/cm².
With the increase of pressure, both the dynamic viscosity and rigidity increased to the same extent as had been shown in the case of polymer melts. The time-pressure superposition, similar to the usual time-temperature superposition, was made to give a smooth master curve. In order to know how the shift factor depends on pressure, the iso-thermal compressibility of the same sample was determined at 40°C.
From the above experiments the following conclusions can be made.
(1) The specific volume of the solution can be related to the gauge pressure by Tait's equation,
(1)
where V_p and V₀ are the specific volumes at gauge pressures P and 0kg/cm² respectively. B and C are constants independent of pressure, and have the values of 760.7kg/cm² and 0.1829 for the solution studied. Assuming that the relative free volume is defined as the ratio of the free volume to the occupied volume, the relative free volume of the solution was derived from Eq. (1),
(2)
where f_p, f_s and f₀ are the relative free volumes of the solution at gauge pressures P, P_s (reference pressure) and 0kg/cm², respectively.
(2) Combining Eq. (2) with Doolittle's equation, the expression for the dependence of the shift factor on pressure can be derived as follows:
(3)
This expression shows satisfactory agreement with experimental results.

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