This paper describes a general theory on the rheological dispersion caused when substances of different sorts are mixed. In rheological researches, it is usual that experimental results are directly connected to molecular structure. The present theory suggests that such a method is premature, because measured dispersions may have been possibly caused by the mixing.
As an example, a case of series mixture is treated here. The new dispersion appeared in this case corresponds to the Maxwell-Wagner dispersion in the problem of dielectrics. To discuss the case of a general mixture, the electrical circuit theory is applied.
First of all, equivalent circuit model of the general mechanical system is shown. This circuit was already obtained by G. Kron, but as some errors are found in it, they are corrected in this paper. The circuit is composed of ideal transformers and two kinds of elements with admittances of 2μ^*Δl and λ^*Δl (where μ^* and λ^* are complex Lamé moduli, and Δl is an elementary length). Assuming that the sample body is noncompressible, the elements of the circuit are reduced to only one kind (2μ^*Δl). If the sample is made of binary mixture of such substances, the equivalent circuit for the sample are to imply only two kinds of elements. General form of the appearent complex modulus of the mixture is obtained as a function of the moduli of the components, applying the Cauer's theory on 2-terminal impedance of the electrical network composed of two kinds of elements.
In the light of the circuit theory, the relaxation frequency of the modulus is equal to the coordinates of the pole of the modulus devided by -2π, provided that the pole means the point where the denominator of the modulus as a function of p(=iω) is equal to zero. The zero of the modulus means the zero point of its numerator. The zero of the modulus is, therefore, the pole of the compliance, which is proportional to the relaxation frequency of the compliance. Considering the moduli of the components to be given as functions of p, the modulus of the mixture which is known above as a function of the moduli of the components is obtained eventually as a function of p. As a result, there are obtained laws on the relative position between zeros and poles of the moduli of components and those of the mixture. The main points of the laws are as follows:
If the whole negative real axis of p is divided into sections by the zeros and poles of the moduli of the components, newly produced zeros and poles find themselves in the section at the most right side or in the alternate sections to it. The other sections become prohibited bands. The number of new zeros and poles increases as the mixing becomes more complicated.

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The rheological behavior in viscose industry (especially, in rayon industry) is discussed to obtain the fundamental knowledges related to the manufactural processes.
(1) Viscose (Spinning Solution)
The properties of viscose rayon are influenced essentially by the network structures which are constructed in the initial spinning step and relate to the internal structure in viscose solution. It is appropriate by measuring structural viscosity, dynamic viscoelasticity, spinnability and tensile viscosity of viscose in order to detect the internal structure of viscose, which widely changes with conditions and components of viscose. It was found that there exists the considerable relation between these measuring data and maximum draft of spinning and properties of rayon, then we can explain the internal structure of viscose by a distinct conceptions.
(2) Coagulation and Regeneration of Viscose (Gelation and Orientation with Spinning)
At the spinning of viscose, it takes place the coagulation, orientation and regeneration of cellulose xanthate by physical and chemical reaction in contacted with spinning bath, then these transition processes are first step to fix the fiber structure and important step effecting to fiber properties. In these view point, it is possible to obtain the some suggestions for stretch spinning technics by measuring of stretching form, stress and stress relaxation, birefringence change in connection with these spinning processes.
(3) Internal Structure Changes of Regenerated Cellulose Fibers
Fiber structure is completely fixed through washing, refining and drying of regenerated fresh cellulose gels. Then, it is considered that crystallization (corning) and shrinkage of cellulose molecules take place on the several types correspond to the deswelling conditions, and reflect sharply upon the dyeability, feeling etc. From the experiments of stress relaxation, it could be estimated these slight effects of deswelling process upon the many properties of rayon fibers. And, by the measurements of both stress relaxation and stress recovery, it was found that regenerated cellulose fiber has a interesting properties, particularly in stress recovery, which shows the stress increase after returning the strain.

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The dielectric studies of six kinds of vinylidene chloride copolymers (VC-VD copolymers) were studied over the wide range of frequency and temperature.
For the samples I, II and III, we observed one dispersion and for the samples IV, V and VI, we observed two kinds of dispersions. The higher-frequency dispersion (β-dispersions) which appeared in the case of IV, V and VI could not be observed in the polymer containing vinylidene chloride more than 70%, that is, in the case of I, II and III.
The variation of the magnitude of the α-dispersion which is related to the glass transition has been investigated.
From the dielectric point of view the glass transition temperature is lowered with increasing content of vinylidene chloride.
The values of Cole's parameter α for the vinylidene chloride and vinyl chloride copolymer decreased with increasing temperature and increasing vinylidene chloride content.
From the temperature dependence of dielectric dispersion, the activation energy for orientation of dipole for samples I, II, III, IV, V and VI, were calculated to be 34, 35, 40, 46, 64 and 92kcal/mole, respectively.
The activation energy decreased with increasing content of vinylidene chloride.

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The apparent viscosity of a concentrated high polymer solution decreases with increasing velocity gradient. This is called the structural viscosity. This is due to the dispersion of highly associated polymer molecules into molecules of smaller degree of association, by the effect of the velocity gradient. The structure change like this should obviously affect the dynamic viscosity and the dynamic elasticity of the high polymer solution.
The Rouse theory on the viscoelastic properties of high polymer solutions does not sufficiently explain all the experimental results. The theory can not show the existence of the structural viscosity either. The existence of the structural viscosity and some anomalous viscoelastic properties may, however, be explained, if the Rouse theory is extended and applied to a mixture of highly associated polymer molecules and single polymer molecules (or, of lower degree of association), and if it is assumed that the ratio of these two components varies with the frequency or velocity gradient.
By introducing three parameters α, β and F defined by
α(ωτ_N)=2√2/π√ωτ_N∑^N_p=1p²/p⁴+ω²τ_N² (4)
β(ωτ_N)=2√2/π1/√ωτ_N∑^N_p=1ω²τ_N²/p⁴+ω²τ_N² (5)
and F=σ√kT/4√3√Bn_NN (6)
the Rouse equations for the dynamic viscosity η_N and dynamic elasticity G_N of a solution of high polymer molecules composed of N segments can be rewritten into the equations:
η_N=(F/√ω) α(ωτ_N)
G_N=F√ωβ(ωτ_N)} (7)
where n_N is the number of the N segment molecules, τ_N is the longest relaxation time (τ₁ in the original paper by Rouse), σ is the average length (root-mean-square of end-to-end distance) of the segment (or the submolecule), and B is the mobility of the one end of the segment. The points to be emphasized here are, first, that the parameter F is proportional to the total number of segments in a unit volume of the solution, or to the weight concentration, irrespective of the degree of molecular association; and, second, that α and β are functions of ωτ_N only, whose values approach to zero when ωτ_N is small, and approach to unity when ωτ_N is large, as shown in Table 1 and Fig. 1.
Now, in order to consider a mixture of molecules of N₁ segments and molecules of N₂ segments, the dynamic viscosity η and the dynamic elasticity G of the mixture may be assumed to be:
η=(x₁α₁+x₂α₂)(F/√ω) (8)
G=x₁(G₀+β₁F√ω)+x₂β₂F√ω (9)
where x₁ is the weight fraction of the molecules of higher association degree.
By analizing rotary oscillation of the inner cylinder of a concentric cylinder apparatus containing potato starch paste, the frequency dependence of the dynamic viscosity (Fig. 2) and of the dynamic elasticity (Fig. 3) was measured. Variation of x₁ with the circular frequency ω was then estimated by using equations (8) and (9).

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The apparent viscosity η_a of concentrated solutions of polyvinyl alcohol (PVA) samples having different molecular weight have been measured within the ranges of rates of shear from 0.5 to 1000 and the temperature range from 20° to 55°C. The instrument employed here is a capillary viscometer with continuously varying pressure head as described by Maron, Krieger and Sisko. Some data have been supplemented for polyvinyl acetate obtained by acetylation of PVA.
The important results are summerized as follows:
1) The apparent-viscosity data can been superposed as satisfactorily as dynamic-viscosity data according to the method of reduced variables. Shift factors obtained agree well with those obtained from the dynamic data.
2) Log-log plot of the zero shear viscosity against concentration consists of two straight lines that intersect at one point (critical concentration c_c). The slopes of the lines are about 6 above c_c and 4.4 below c_c, respectively. Critical concentration in volume fraction of polymer in soluton, v_2c, multiplied with the chain length Z increases with increasing chain length and ranges from 130 to 280. The product v_2cZ^1/2 is almost constant and independent of the chain length.
3) The reductions of viscosity curves referring to concentration as reported by Ferry and DeWitt et al. are not applicable to our data. But when log-log plot of the apparent viscosity against the rate of shear are shifted along a straight line having slope-1 or higher, they can be superposed fairly well in the concentration region above c_c. By such a reduction, rheological properties of pure polymer can be expected, but they are quite different from those measured actually with PVA films.

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A molecular theoretical investigation of the viscoelastic properties of amorphous polymeric substances in the range of long relaxation time has been made using the temporarily cross-linked network-structure-model. The origin of the energy dissipation is ascribed to the slipping of chains and the change of number of chains induced by deformation.
When the network structure is deformed each chain will slip since the network structure does not return to its initial state when the deformation is taken off. As the chains slip the deformations of chains do not coinside with that of the network structure. Then we introduce the two kinds of deformation tensor, one is the observable deformation tensor of the netwok structure and the other is the inner deformation tensor of each chain. Assuming that the deformation of all chains can be characterized by a single average inner deformation tensor, we obtain Eq. (7) which expresses the relation between the observable and the inner deformation tensors.
We can also obtain Eq. (31) expressing the change of the number of chains which depends upon the time and the deformation. Eq. (31) has the same form to that of the chemical reaction as expected by the theory of rate process.
The strain free energy of each chain is assumed to depend only on the end-to-end distance of each chain and the free energy of whole system is assumed to be given by the sum of the said strain free energy of each chain and the free energy depending on the density of segments which corresponds to the inner pressure of the system.
Accordingly the stress is obtained by Eq. (17) as the function of the inner deformation tensor. Using the relation between the observable and the inner deformation tensors, Eq. (7), we obtain the stress- time-deformation relation Eq. (20), which is the natural generalization of equation of Maxwell model. In small deformation the tensors are automatically symmetrized and we obtain Eq. (33) which is just the same formula with that of Maxwell model. As we assume the average inner deformation tensor, namely the average slipping of each chain we have only a single relaxation time which is the average relaxation time in the range of box type relaxation time spectrum. In this formalism, as the average inner deformation is assumed we can not explain that the system must have the box type relaxation time spectrum in the range of the long relaxation time.
The energy dissipation expressed by Eq. (37) has two terms, one is due to the slipping of chains and the other for the change of the number of chains.
Some applications of the theory are made in last section. We define the stationary state by the state of constant inner deformation tensor. In stationary state the number of chains are kept constant and the origin of the energy dissipation is ascribed to the slipping of chains only. First, we treat the stationary simple elongation, the stress and the energy of dissipation are expressed by Eq. (42) and Eq. (43) respectively and the tensile viscosity coefficient η^* is expressed by Eq. (45) in case of no volume change. Secondly, we treat the stationary simple shear, in this case the normal stress effect appears as is shown by Eq. (47) and we have Eq. (49) as the relation between the tensile and the shear viscosity coefficients, which is known as Trouton's law. Lastly we treat the instantaneous simple elongation, as is shown by Eq. (50) and Eq. (51) the stress shows nearly exponential decay since the number of chains changes slowly with time. The inner deformation decreases monotonously and tends to return to its initial state, on the other hand the number of chains decreases at first and passes a minimum value then increases again and tends to approach to the equilibrium value.

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A phenomenological theory of the non-linear viscoelasticity of three dimensional bodies is treated. The two elementary models of the classical theory of linear viscoelasticity, that is the Maxwell and the Voigt model, are extended to three dimensional non-linear cases. In addition to the observable (external) deformation tensor a and the stress tensor σ, we define the two internal deformation tensors and the stress tensors: The internal elastic deformation tensor, α_E and stress tensor σ_E correspond to the energy stored mechanism while the internal viscous deformation α_η and stress σ_η represent the state of the energy dissipative mechanism. They are just the three dimensional analogues of these of the spring and the dashpot in the mechanical model of the classical theory of viscoelasticity.
The three dimensional Maxwell model is defined by the condition
σ=σ_E=σ_η. (1)
On the other hand, the three dimensional Voigt model is characterized by the restriction
a=α_E=α_η. (2)
From the energy consideration, we find the fundamental equations of the three dimensional Maxwell model in such the forms
dα/dt=da/dt·a^-1·α+(dα/dt)^*, (3)
σ=P1+Qλ+Rλ·λ, (4)
λ=α·α⁺, (5)
(dα/dt)^*=-β(α-1), (6)
where α is the rewriting of the internal elastic deformation α_E, and (dα/dt)^* corresponds to the deformation production due to the dissipative mechanism. Equation (6) is merely a assumption for the dissipative term, and β represents the reciprocal of the so-called relaxation time, τ=1/β. P, Q and R may be the scalar functions of the three invariants associating to the internal (elastic) deformation, α.
On the other hand, the fundamental equations of the three dimensional Voigt model are as follows:
σ≡σ_E+σ_η (7)
σ_E=P'1+Q'ε+R'ε·ε (8)
σ_η=p1+qε+rε·ε (9)
ε=a·a⁺ (10)
ε=da/dt·a^-1+a^+-1·da⁺/dt (11)
where P', Q' and R' and p, q and r are the scalar functions of the three invariants associating to the strain tensor ε and the strain-rate tensor ε, respectively.
Our models are shown to be successful in analysing the so-called normal stress effects, i.e., the Weissenberg effect for elasticoviscous liquids (in the case of Maxwell model) and the Poynting effect for viscoelastic solids (Voigt model).
Non-linearities in viscoelastic properties are classified into three cases: elastic, viscous or relaxational, and geometrical ones. Elastic non-linearity corresponds to the non-ideality of the stress-deformation relation of the energy stored mechanism, and viscous non-linearity represents nothing but the kinetic character of the energy dissipative mechanism. An essential feature of the three dimensional bodies is the geometrical non-linearity. The typical examples of this are the said normal stress effects which arises from the cross effect between the shearing deformation and the normal stress components.

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Phenomenological equation relating a non-linear response function to a time-dependent excitation function is presented, starting from the assumptions of causality, convergence and stationariness. When the excitation and the response are denoted by σ(t) and ε(t), respectively, the equation is
ε(t)=∫^∞₀σ(t-τ₁)J₁(τ₁)dτ₁+∫^∞₀∫^∞₀σ(t-τ₁)σ(t-τ₂)J₂(τ₁, τ₂)dτ₁dτ₂+∫^∞₀∫^∞₀∫^∞₀σ(t-τ₁)σ(t-τ₂)σ(t-τ₃)J₃(τ₁, τ₂, τ₃)dτ1dτ2dτ3+………,
where J₁, J₂, J₃, …… are a series of the decay functions which characterize the excitation-response system. Fourier representation of the above equation (Eqs. (11) and (12) in the text) as well as several transformation relations (Eq. (13)) are derived. Applications of the theory to the case of a sinusoidal excitation and to the case of a step function-like excitation, especially with exponential decay functions, are developed. Finally, a critical examination of the adopted assumptions and a remark on the difference between a creep function and a recovery function are made.

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A few subjects on the relation of viscoelastic behavior of polymers to their dielectric and NMR behavior are discussed. The validity of temperature-time reduction rule is doubtful except for α-dispersion region of the amorphous polymers. The complicated relaxation mechanisms in polymers require the distributions of relaxation times, connected with the correlation function ‹F(t)F(0)_av› of respective quantities F, which vary according as viscoelasticity, dielectricity or NMR is concerned, and respective spectra are so different in shape but are reflecting parts of the same molecular motion. The box shape of correlation time spectrum for PIB is the only spectrum known at pressent in NMR. The activation energies obtained from NMR data are often much smaller than those obtained from viscoelastic and dielectric data. As NMR data are corresponding to the temperature dependence data under constant frequency in viscoelastic and dielectric measurements, the neglect of correlation time distribution in NMR causes the underestimation of activation energy. We can show the apparent activation energies of viscoelasticity and dielectricity recalculated from the temperature dependence data only, assuming a single relaxation time, are much nearer to those of NMR, which are illustrated for PMMA, PIB and PTFMCE. If the temperature reduction rule is invalid, not only the shape of the correlation time spectrum but also its temperature variation play a rôle, so far as the temperature-dependent behavior is concerned.

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Rubber-styrene resin is a new type of polymer alloy, which can be polymerized at 60-90°C for several hours from viscous mixtures of styrene monomer, rolled rubber and divinyl benzene catalysed by benzoyl peroxide, and cured at 120-150°C for several hours after the shrinkage of the reacting system ended.
This is a new type of cast resin which has a very low dielectric loss tangent, comparable to that of NBS type, and low cost and wider uses available in the field of electrical parts.
Low frequency dynamic modulus and loss tangent of this resin were measured from -80°C to 100°C, relating with the composition and after cure time.
The effects of composition (styrene: 70-85%; rubber 12-18%; DVB 2-8%; BPO 1%) on the dynamic mechanical properties show that DVB elevates the softening temperature, but rubber lowers it and increases mechanical loss. Measurements below room temperature reveal the remarkable mechanical absorption at -40--50°C which should be contributed from rubber molecules. The temperature at which the loss tangent has its maximum, did not seen to shift appreciably by changing composition of this resin.
Secondly, for the constant composition, cure condition and after cure temperature, it has been shown that the high temperature mechanical loss decreases with increasing after cure time, but the low temperature mechanical loss increases with increasing after cure time. This fact may suggest some possibility of chain scission in rubber molecule kept at high temperature for long time.
Our results have thrown some lights into the internal structure of this resin. Although the existence of some graft or network structure between rubber and polystyrene molecules cannot entirely be neglected, the results could be fairly well explained as “mixture”, that is, rubber could exist as blend in polystyrene-DVB network structure.

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Analyzing mechanical elongation of polymer films having water-sensitive functional group such as hydroxyl group under the diffusion controlled condition, we intended to study the mechanism of diffusion of water into polymer films at various temperatures and under various relative humidities. While one of us has already reported a work on polyvinyl alcohol and in its formalized films, this is to be presented our measurement in the creeps and the adsorption for uncoated cellophanes.
Although a report on the theoretical treatments of the results has been made, the following brief account is given.
It is assumed that crystalline region and amorphous region in polymer films are evidently distinguishable, and that a elastomer characteristically corresponds to the network and to the network-chain in vulcanized rubber. When stress is applied, the hydrogen bonds, water-sensitive and resistive to elongation, are partially broken and the resultant strains, in the form of elongation, appear.
The displacement length of the chains are calculated here on the assumption that, although each network-chain interacts with hydrogen bonds, the total number of configurations of network-chains is to be approximately computed according to the Gaussian distribution law. Furthermore, considering the orientation of crystalline parts in the samples, the elongation of polymer films at equilibrium adsorption of water, γ_∞, is expressed by the following equation,
γ_∞=fκa₀/6ν^5/3kT·Nn/N+n,
where N is the number of OH-radicals per unit volume of the sample, n the total number of the water molecules, ν the number of network-chains per unit volume of sample, f the stress, k Boltzmann constant, T absolute temperature, and a₀ and κ constants related to potentials among the network-chains. Since the process involves the diffusion of water into the samples, n is a function of time, whereas, as non-Fickian type of diffusion into such uncoated cellophanes is to be expected here, n, as a function of time, is expressed by the following equation,
n=n_s(1-e^-αt)²,
where n_s is the number of water molecules in the samples at equilibrium, and α a parameter for the rate of diffusion process of water molecule into the samples.
Furthermore, it is assumed that the elongations, when the constant amounts of water is absorbed, are given by the simple Voigt model of network-chains, and that the elongations attending the adsorption process are given by the accumulation of each small successive elongations, Δγ,
Thus, following the simple Voigt model, a differential equation for elongation, γ_∞, is obtained,
γ+kγ=kγ_∞,
where γ is any elongation of sample, and k a parameter for the rate of deformation (of course, a function of time). Conveniently we regard as the average quantity depending exclusively upon the final amounts of adsorption. Now, α and k, having, in above equations, an analogous meaning for the both processes, are assumed equal in later computations. Finally, we obtained an equation concerning the length at any time,
γ=γ_∞/s+1{(s+1)(1-e^-kt)-2kte^-kt-se^-kt(1-e^-kt)²+(1-s)e^-kt(1-e^-kt)},
where s-represents n_s/N.
The equation thus obtained shows a creep-curve having a point of inflection, t_i, at which the following equation is derived

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In the case of dry spinning or melt spinning, the extruded liquid-thread from the spinneret are coagulated rapidly or slowly by drying or cooling depending on the system. The spinnability of the extruded liquid-thread under such conditions are different as compared with the spinnability of ordinary means, but it has important meaning at the stand point of industrial spinning process.
It has been tried to analyse the deformation process of extruded liquidthread under simple assumptions, i.e., there is no drying or cooling of liquid-thread during the deformation process. Under such special conditions, the following behavior is recognized.
1. Keeping the diameter of spinneret hole and the viscosity of spinning liquid constant, a small rate of extrusion brings a small rate of deformation.
2. Keeping the rate of extrusion and the viscosity of spinning liquid constant, a large diameter of spinneret hole brings a small rate of deformation.
3. Keeping the rate of extrusion and the diameter of spinneret hole constant, a large viscosity of spinning liquid brings a small rate of deformation.
From the behavior mentioned above, some interesting suggestions about the practical spinning process will be obtained. In the case of melt spinning, the extruded liquid-thread is cooled by heat conduction only, and the coagulating speed is rather slow as compared with the dry spinning of volatile spinning solution. Then rather large diameter of spinneret hole is suitable for melt spinning, because a small rate of deformation provides a sufficient time for coagulation. From another view point, the extruded liquid-thread will be drafted enough during the long coagulating time, so a fine denier filament is obtainable by using even a large diameter spinneret hole.
A spinning of slow coagulating liquid should take a spinning condition of small rate of deformation in order to get a suitable coagulating time, but an extremly small rate of deformation brings some difficulties, that is, the position of the maximum stress in the extruded liquid-thread shifts upwards by smaller rate of deformation and uncoagulated liquid-thread receives a large stress, it becomes a cause of breaking of liquid-thread in actual spinning process.
In the case of dry spinning of cellulose acetate, the spinning solution is very volatile and the coagulation of extruded liquid-thread is rapid. Then it is rather difficult to get a long drafting time, so small diameter of spinneret hole is suitable to get a fine denier filament.
From above considerations, we can choose an optimum spinning condition for getting suitable coagulating time by changing the diameter of spinneret hole, the rate of extrusion, and the viscosity of spinning liquid.
There are another characteristics having influence on the spinnability, for instance, the shear dependence of viscosity, the balooning of extruded liquid-thread and the surface tension of the spinning liquid.
The spinning liquid having large shear dependence of viscosity will not suitable for slow coagulating spinning conditions, because a large shear dependence brings an acceleration of deformation, and it is difficult to control the spinning condition without breaking of liquid-thread. The influences of the balooning and the surface tension are not described in this paper.

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The dielectric properties of five crystalline polymers and four amorphous polymers have been measured over the frequency range of 10^-1cps (or 10^-4cps for four polymers) to 10⁶cps and the wide temperature range. Two or three dielectric absorptions which have been designated as α, β and γ absorption with descending temperature have been observed for each polymer and all absorptions are due to the molecular motions in the amorphous region.
In the crystalline polymers, mechanisms of these absorptions have been discussed using results of the studies of the crystall growth processes. In vinylidene chloride copolymer, polychlorotri-fluoroethylene, polyoxymethylene and polyhexamethylene adipamide, the crystall growth has been detected by the density or X ray measurement in the temperature range where only the β absorption can be observed and the α absorption cannot be observed. Moreover the β absorption is related to the glass transition. Consequently it is concluded that the β absorptions of the four polymers are due to the motions of the main chains in the amorphous region. Supposing that the α absorptions of the four polymers are due to the motions of the main chains in strained amorphous region, the region has been searched by the dielectric measurements of polychlorotri-fluoroethylene samples having different degree of crystallinity. If two samples having different size of crystallites are compared at the same degree of crystallinity, the magnitude of the β absorption of the sample having larger crystallites is greater than that of the sample having smaller crystallites but the magnitude of the α absorption of the former is less than that of the latter. Moreover the positions of the α and the β absorption may be coincide with each other at the melting temperature. Consequently it is conjectured that the strained amorphous region is the surroundings which extend to a definite distance from crystallites and the amorphous region is the region between the strained amorphous regions.
In four amorphous polymers and a crystalline polymer, polyethylene terephthalate whose degree of crystallinity is nearly zero, the α absorption is related to the glass transition and may be due to the motions of the main chains. Generally the magnitudes of the β absorptions of these five polymers are considerably smaller than those of the four crystalline polymers mentioned above. The β absorption of an amorphous polymer, polymethyl methacrylate, is due to the motions of the side chains. It is uncertain whether the mechanisms of the β absorptions of the remaining four polymers and γ absorption of polyhexamethylene adipamide are the same as that of polymethyl methacrylate.
The temperature dependences of the dielectric relaxation times have been analized in terms of the apparent activation energy ΔH^*. For several absorption processes, ΔH^* increases with decreasing temperature and decreases after arrival at the maximum value. This anomalous phenomenon is related to dielectric transition that the magnitude of the absorption decreases sharply with decreasing temperature. The origin of the phenomenon is discussed. On the other hand, ΔH^* increases with decreasing temperature and not shows maximum for the absorption processes in which the dielectric transition is not observed.

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Viscosities of five poly-(dimethylsiloxane) samples of molecular weights ranging from 6.1×10⁴ to 23.5×10⁴ were determined by using capillary pipette, falling sphere and cone-and-plate viscometers. The molecular weights were estimated from intrinsic viscosities in toluene at 25°C., using Kolorelov et al.'s equation, instead of Barry's equation employed by previous investigators.
The melt viscosities measured at low shear rates were related to molecular weight M by the eqation, logη40°C=3.5logM-14.88.

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When a rubber vibration insulator of tread type is given, for many hours, a torsional vibration with a fairly large strain amplitude, the observed amplitude of torsional moment, in the beginning, decreases nearly in proportion to the logarithm of the number of strain cycles and, after 4-9×10⁶ cycles, it becomes keep about constant value. Furthermore, in the intermittent test which repeats the driving and cessation, the amplitude of torsional moment shows some recovery during cessation and especially after the second driving, these decrease and recovery appeares about the same extent. These facts are also attentioned as phenomena in the early stage of fatigue process. While the gum type stock, which does not contain any carbon black, does not show such phenomena.
The dynamical model used for the analysis of the dynamical behavior of rubber vibration insulator was already proposed by the one of the authors. The differences in the models between tread type and gum type stocks consist in the slider mechahism, so that the above thixotropic phenomena also arise from the characteristic change of the slider. Perhaps, it is due to the breakdown of the rubber-carbon bond. From our experiments, the rate of above decrease changes by the variation of the frequency of vibration, but the temperature does not affect upon it.
In this paper, we considered on such thixotropic phenomena and derived the empirical formulas between the amplitude of torsional moment and number of strain cycles, fitting for both cases of the virgin and the intermittent driving.
We assume, for the virgin state, on the life of the slider mechanism
N=N₀e^αn,
where n is the total number of the slider breakdown before the number of strain cycles N. By calculating the decrease of the stress produced by the above breakdown, we obtain the desired formula as follows:
T=A-BlogN+C(logN)².
For the driving after the second, the characteristic change of the slider mechanism which recombines during the term of the cessation, is slightly different from the former case, so that we assume to use a small quantity ζ as follows:
dn/dN=1/αN^1+ζ.
By the similar operation as the proceeding, we get the formula:
T=P-QN^-ζ+RN^-2ζ.
Thus, after the second driving, the curves of the amplitude of torsional moment with number of strain cycles deviate a little from the linear relationship with respect to the logarithm of N. The quantity ζ, which is zero in the virgin state, becomes a small finite value subsequent to the second driving and then it keeps to hold almost constant value through each driving.

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Equations describing force-temperature characteristics at constant length with constant rate of cooling are derived in two ways from the theory of linear viscoelasticity.
The first method based upon the relaxation time spectrum and the time-temperature superposition principle gives Eq. (8). Secondly, Eq. (9) is deduced from the approximate consideration that the stress relaxation due to the contraction of original length with descending temperature is estimated by step-wise cooling approximation and use of relaxation modulus corresponding to the time of each step.
Force-temperature measurement and its analysis are conducted on unoriented crystalline polyethylene terephthalate.
The first and the second theoretical deductions are successfully applied to these results as shown in Figs. (3) and (4). While verifications of the first method are confined to the temperature range only above the second-order transition temperature (95°C, Fig. (1)) due to the limitation of the applicability of time-temperature superposition principle, those of the second method are done over the whole temperature range of measurements.

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The mechanical behavior of wool fiber in water is studied by the free damped vibrational method at low frequency (period=4∼5sec) and large amplitude (maximum amplitude=2% extension) under various static strains and temperatures. In order to measure the stationary viscoelasticity, the logarithm of double amplitude must be decreased linearly with the vibration. In the case of wool in water, these straight lines (plots of logarithm of the double amplitudes (A_N) against successive vibration numbers (N)) are concave or convex about the axis of the successive vibration number (N). There are three types of logA_N∼N curves: Straight line and concave or convex against N-axis. The above three types are assumed as follows:
(1) Straight line:
The breaking and reformation of the secondary bonds are in equilibrium and a stationary state is attained.
(2) Convex curve:
The reformation of the secondary bonds exceeds the breaking during the vibration.
(3) Concave curve:
The breaking of the secondary bonds exceeds the reformation during the vibration.
The above hypothesis may explain the mechanical behavior of wool in water at various conditions. This is shown as follows:
1. The wool fiber is extended in the state where the breaking of the secondary bonds exceeds the reformation of the bonds, but during retraction the reformation exceeds. The change of the viscoelasticity under extension and retraction is reversible within 0∼30% extension region (Fig. 2∼3).
2. During the stress relaxtation at 10% extension, the breaking of the secondary bonds exceeds and a stationary state is attained with the elapse of time (Fig. 4).
3. When the vibration contains the yield point, the reformation of the bonds exceeds the breaking under large double amplitude, and the breaking exceeds the reformation under small double amplitude (Fig. 5).
4. Under rising temperature at 10% extension, the breaking of the bonds exceeds and under falling temperature, the formation of the bonds exceeds (Fig. 6).
The temperature dependency of the relative Young's modulus is compared with the data of Meredith and Feughelman. The temperature coefficient of Young's modulus at Hookean region derived by some workers are as follows:

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The relation between the fine structure of the fibers and their mechanical properties is much interesting. Depending on the utility, there are many chances for the fibers to be placed in high temperature and in the wet state. To obtain a fundamental knowledge of this, it is necessary to do the measurement of the viscoelastic behaviour of the fibers in the wet state at various temperatures. There are many researches of Clark etc., on the physical properties of the regenerated cellulose fibers in the wet state at various temperatures, and that of Wakeham etc., on the relation between tension and temperature. In this research the mesurement has been performed in water at low freqency by varying temperature and the dependency of longitudinal dynamic modulus, longitudinal viscosity, and tan delta with temperature and their relation with the fine structure of the fibers have been investigated. Fortisan, bemberg, viscose rayon, high tenacity rayon, cellophane, and gel-cellophane were used as samples. The aggregate state of these samples were estimated by Maeda's method and to determine the relation between the aggregate state and the orientation of the part, which has much influence on the effect of mechanical properties, the measurement of swelling and contraction was performed. When the relation between the orientation and the aggregate state is determined, it is observed that Fortisan possesses a good orientation in the state of high order and high tenacity rayon possesses orientation in low order. Although viscose rayon and bemberg possess little orientation, bemberg has orientation up to high order. The fine structure and the viscoelastic properties of these fibers were compared. The method of measuring dynamic properties was that wire strain gauge was used for the measurement of tension and strain and each wave was recorded in the oscillograph. Lissajous' figure of the relation between stress and strain was drawn from these wave forms. The speed of the cycle was 9.8 second and the applied strain was 0.4%. The shape of the hysteresis loop satisfies the linearity approximately. Gel-cellophane shows the lowest value for the longitudinal elastic modulus and cellophanes of lateral and longitudinal directions follow it. The influence of temperature in cellophane is small and there was not much large difference. The effeect of orientation on the elastic modulus is the most large one. The degree of change of modulus in high tenacity rayon is considerably large and it shows the large temperature dependency in the place of low aggregate state. The temperature dependency of the modulus of Fortisan was simple and there was no change point. The temperature dependency and sample dependency of the energy loss derived from hysteresis loop resemble well with the temperature dependency of the longitudinal elastic modulus. The energy loss of Fortisan was most large and was minimum in the case of gel-cellophane. It may be that tan delta varies with the aggregate states rather than orientation. The difference due to direction in cellophane was not observed. With the increase of water content in the regenerated cellulose fibers, the temperature dispersion of tan delta shifts gradually towards low temperature or it may be that the dispersion of tan delta exists below those temperatures. This tendency was approximately same for every regenerated cellulose fibers. The dynamic longitudinal viscosity was determined from the width of the loop and its temperature dependency was observed. At low temperature the effect of hydrogen bond between the cellulose molecules may be dominating, and at high temperature the effect of more weak secondary bond force of the amorphous parts of cellulose fiber may be perceived. The temperature dependency of dynamic behavior of heat treated Fortisan appears some change to untreated case and for H.T. rayon the effect is little.

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Recently we have designed a new type of rotational viscometer to study the non-Newtonian flow of the dilute polymer solutions. With our viscometer we can obtain the relative viscosity without measuring viscosities of solvent and solution separately.
The viscometer is constructed with two sets of concentric cylinders of the same size, one of which is placed on the other on the same vertical axis. The lower inner cylinder and the upper outer one are connected with a thin rod. This connection part is supported and slightly floated by an air bearing, and can be rotated freely. The upper inner cylinder is fixed to the support. The lower outer cylinder is rotated at a constant speed by a synchronous motor through precision gears. The gap in the lower cylinders is filled with solution, and the gap in the upper one is filled with solvent. The floating part is rotated continuously with the torque owing to the viscosity of the solution, and receives braking torque at the upper outer cylinder owing to the viscosity of the solvent. Then, the rotational speed of the floating part is determined by the viscosity difference between the solution and the solvent. Therefore, if no friction exists in the air bearing, the relative viscosity can be formulated as follows:
η_r=η/η₀=ω/ω₀-ω.
η: viscosity of the solution,
η₀: viscosity of the solvent,
ω: angular velocity of the floating part,
ω₀: angular velocity of the lower outer cylinder.
But actually, a small friction is inevitable in the air bearing owing to the viscosity of air so that correction must be applied to the preceding formula.
The cylinders are made of 18-8 stainless steel to avoid any corrosion. The gap between the inner and the outer cylinders is 0.5mm. The bottom of the inner cylinders has a conical hollow to minimize the effect of shear at the bottom. The total volume of the gap is 4ml. For measurement, however, 10ml of the liquid is used in order to avoid the effect of surface tension.
The rotational speed of the lower outer cylinder is variable from 1/16 to 256rpm by thirteen steps. Then, in the case of dilute solutions the velocity gradient at the gap of the lower cylinders is about 0.1 to 300sec^-1. The rotational speed of the floating part is measured visually or photoelectrically.
Experimental data obtained by this viscometer will be reported in later communications.

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The variation of viscosity, rigidity and yield value of butter due to working has been measured. The working of butter has been performed by kneading the specimen in a duplicate roller which is composed of two cylinders with the same diameter and rotating in the opposite direction.
The diameter of cylinder was 7.6cm and the gap between two cylinders were varied in three steps i. e. 0.55mm, 1.65mm and 4.05mm. The temperature at working was 25°C to 27°C. The small specimen of butter was taken up from the roller at a fixed time interval during working and the viscosity and rigidity of the specimen were measured by a vibration-plate viscometer. The viscosity and yield value of the worked specimen after setting at constant temperature of 16°C for 20 hours, 8 days and 10 days respectively have been measured by a parallel plate plastometer. The formula used in the calculation was that derived by Oka et al.
Both the viscosity and rigidity of butter decrease rapidly with the amount of working and approach to the saturated values which are determined by the distance of gap between two cylinders. The smaller gap produced the more amount of working, hence the lower saturated values of viscosity and rigidity were obtained. The viscosity and yield value measured after setting for 20 hours decreased also with the working time. The remarkable recovery of these values were observed after setting for 8 days or 10 days but the harder working resulted in the smaller recovery.
The effect of working is considered to destruct the network structure of fat crystals formed in butter as well as to decrease the size of each fat crystals. The recovery of the viscosity and yield value due to setting may be associated with the recrystallization of fat crystals.
A clear pattern of stripes parallel to the direction of rotation was observed in the butter during working. The number of peaks appearing in the pattern increases with the decrease of viscosity. Denoting D as the distance between two peaks of stripes, the following relation between D and the viscosity η has been determined experimentally, η=η₀e^-C/D-D₀, where η₀, C, D₀ are constants.

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The parallel-plate plastometer is a simple and important instrument to investigate rheological behavior of matter. Especially, it is very useful for materials which have yield values. But there is only Scott's theory for this case and he made rather rough assumptions in the beginning of the calculation, so it is not sure whether the final result is reasonable or not. We have made calculation starting from the general equation of motion for the Bingham solid and obtained the relationship between the thickness of the specimen h and the time t when a constant force is applied perpendicular to the plates. Calculations have been made for the two cases: (a) The specimen is larger than the plates; thus the area under compression is constant. (b) The plates are larger than the specimen; thus the volume of the specimen is constant. Our final results (34) and (40) enable us to determine the yield value and the coefficient of plastic viscosity η. And our results reduces to the equations derived by Stefan and Healey when the yield value f is neglected.

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The flow properties of O/W type emulsions (liquid-paraffin in water) have been investigated, covering both Newtonian and non-Newtonian flow range. The combinations of emulsifier are; Tween 60 (polyoxyethylene sorbitan monostearate)-G.M.S. (glyceryl monostearate), Tween 60-Arlacel 60 (sorbitan monostearate) and Tween 60-fatty alcohols (n-C₁₈OH and n-C₁₆OH).
These emulsions generally show Newtonion flow in the range of relatively low dispersion concentration. The stability of emulsion and its viscosity coefficient depend on kind and concentration of the emulsifying agents contained in oil phase.
In the system of Tween 60-G.M.S., flow unit is considered to be the dispersed particle with a number of hydration layers, and Einstein's theoretical equation concerning the suspension of spherical particles has been applied present emulsions, neglecting the influence of emulsifying agents. A linear relationship has been obtained for log ηrel-φ curve and its slope has been found to be proportional to G.M.S. concentration in oil phase.
Mesurements for Tween 60-Arlacel 60 and fatty alcohol systems, in the dispersion state in which Newtonian flow is observed, can not be accurate because of instability of the emulsions. Their dispersed particles have a tendency to be hydrophobic and form aggregate and the flow unit has been found to be an aggregate of several dispersed particles.
With increasing dispersion concentration, the emulsion becomes to show non-Newtonian flow. In the systems of Tween 60-G.M.S. and Arlacel 60, the flow curves take the shape of shear-rate thinning flow, while in the fatty alcohol system, remarkable hysteresis is observed, and the dispersion state varies considerably depending on the kind of emulsifying agents contained in oil phase. However, each equilibrium flow curve can be still expressed by Dahlgren's formula.
Fluidity of emulsion depends on dispersion state, and dispersion state is strongly influenced by the surface structure of dispersed particle. But, in general, in the case where dispersed particle is hydrophilic, the emulsion shows viscous flow in spite of high emulsion concentration. This may be understood as an effect of hydration layers surrounding dispersed particle, by which particles are kept to be comparatively independent of each other. On the other hand, in the case where dispersed particle is hydrophobic and emulsion concentration is high, the emulsion becomes to show thixotropy. This may be interpreted by the formation of the secondary structure of particles.
In the case of the state so-called “cream”, similar discussions to the above may be allowed.

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The change in the tensile force of several kinds of blown asphalts was recorded at various temperatures and rates of extension. The critical velocity for brittle fracture, V_B, was defined by discontinuous break-down of the tensile force followed by no deformation. The relation between V_B and the temperature, T, was given empirically by a relation as follows:
V_B=Ae^-E_B/RT, (1)
where A is an experimental constant, E_B the apparent activation energy and R the gas constant.
It was assumed that brittle fracture occurs when the viscous resistance exceeds the cohesion of the viscous materials locally. Following the rate process theory of viscous flow and from the relation (1), we have
E_B-RTlnA=ΔF^*-RTlnK, (2)
where ΔF^* is the free energy of activation for flow and K a constant which depends upon the shear stress, the temperature and the vibrational frequencies of the liquid molecules concerned. Though neither ΔF^* and K can be evaluated directly, the left side of the relation (2) can be estimated experimentally and it may give the measure relative to ΔF^*. It was shown that the linear relations between logV_B and 1/T shift according to values of (E_B-RTlnA) at a certain temperature which depend upon the composition of the asphalts used.
Effects of colloidally fine fillers on the flow properties of asphalts were observed. It was found that carbon black reduces V_B remarkably in comparison with colloidal silica and calcuim carbonate.

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One can easily solve the differential equations for viscoelastic materials
∂ε/∂t=σ₀/η and cρ∂θ/∂t=ασ₀/Jη∂ε/∂t+k∂²θ/∂x²
simultaneously with the initial condition of the temperature rise
δ(x)=q₀/2π∞∫-∞exp(iωx)dω
in such the simplest case that σ₀ is a constant tensile stress and 1/η is approximated by a linear function of temperature increase, θ. The first term in the right-hand side of the second equation, representing the heat source, is derived from the work done by the stress per unit of volume per unit time. α is a factor less than (but differing little from) unity and J the mechanical equivalent of heat.
Our object in solving the equations is this: linear polymer may increase in temperature by some chance in the neighbourhood of a certain section of the material before break and the coefficient of viscosity may decrease there. It facilitates the subsequent extension of the same part, and finally leads to melting and then to breaking. We have good reason for the existence of the pattern of such an origin among several fracture patterns appearing on the fracture surface.
Thus, the fracture energy is expected to be estimated as the work done on the fracture surface layer of finite depth subjected to large local flow, and obtained as
W_B=Jcρ/αx_Bθ_B,
where x_B and θ_B are the thickness of fracture surface and the mean temperature rise there respectively.
This approach is regarded as worthy of further consideration, because of the identity of the order of magnitude of the calculated energy with those of the current data and because of the deduced reasonable relationships between the depth of the fracture surface and the thermal properties of the materials, the temperature dependency of the coefficient of viscosity and the acting stress.

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One of the present authors (B. T.) previously made studies on the colloid-chemical and rheological properties of the concentrated suspension of sericite, one of the common clay minerals produced in Japan, in water, aqueous salt solution and organic solvent (Ref. 2). The present paper reports a study of flow properties, namely, viscosity and streaming double refraction under various velocity gradients, of the dilute suspension of the same mineral in water and aqueous salt solution. For the viscosity measurement a COUETTE-type rotational viscometer is used and for the measurement of streaming double refraction an EDSALL-type apparatus is applied.
The suspension of the mineral in water or in aqueous salt solution exhibits anomalous viscosity as shown in Fig. 1 and Fig. 2. The relative viscosity is remarkably increased by adding salt. Moreover, a hysteresis phenomenon is observed in the course of the viscosity measurement for the suspension in salt solution. The angle of extinction is found to be indendent of the sericite concentration in the range of 0.001-0.03% as shown in Fig. 3 and Fig. 4, while the double refraction increases with the concentration and it becomes almost constant for each concentration, when velocity gradient reaches the value of 500sec^-1, as indicated in Fig. 5.
These experimental results suggest that the sericite particles behave almost independently to each other and orientate in the direction of the shear force in the above concentration range. However, the effect of the added salt is very remarkable, and for the suspension in salt solution a regular relation between angle of extinction and velocity gradient can not be obtained as shown in Fig. 6. This may be due to a partial aggregation of the particles.
From electron microscopic measurement the sericite particle is known to have a blade-like shape (Photo. 1). Assuming an oblate ellipsoide model for the particle, the rotational diffusion coefficient and accordingly, the longer axis of the particle is calculated from the value of d_χ/dG. The result obtained is found in good agreement with that of the electron microscopic measurement.
The flow properties determined for dilute sericite suspensions are further discussed in relation to the rheological properties of concentrated suspensions. The rheological properties of the sericite suspension are compared with those of suspensions of other clay minerals (Table 1).

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The mechanism of chip formation is studied in order to find the optimum cutting condition for high polymers. The orthogonal machining operation was adopted to observe the phenomena of chip formation, and to measure the cutting force and the deformation of work material during cutting process for PTFE under machining conditions; cutting speed: 0.02-762m/min, depth of cut: 0.023-1.0mm, rake angle of tool: -30°-40° having straight cutting edge. We choose as work materials Teflon No. 1 and No. 5 which are du Pont's products.
We found the peculiarities fall within cutting phenomena:
(1) Types of chip: Two types of chip, continuous and discontinuous, appeared in whole range of our experiments (Photo. 1 & 2), and they were influenced by the cutting conditions. Chips formed at high cutting speed were varied from continuous to discontinuous due to decrease of rake angle (Fig. 2), and chips at low speed were always continuous.
(2) Deformation of work materials: The patterns of deformation of work material around the cutting edge were influenced by the rake angle as shown in Photo. 3 and Fig. 3. The amount of deformation were very large as compared with that in the case of metal cutting.
(3) Cutting force required in machining: The larger the rake angle the smaller the cutting force and the more it turns from downward to upward (Fig. 5 & 6). In the lower range of cutting speed, the cutting force decreases with decreasing cutting speed, but in the higher range, it decreases with increasing cutting speed (Fig. 7). These phenomena may be explained by the time and thermal effects on the strength of work material in machining process.
(4) Critical rake angle: The authors named the rake angle which makes the thrust force F_t=0 as “Critical rake angle”, it depends upon the depth of cut as shown in Fig. 8. Using these relations, we may machine under the optimum condition in which the residual strain will be the smallest.
(5) Friction on tool rake face: Friction force between chip and rake face was very small due to the low shear strength of work material, and coefficient of frictions less than 0.2 (Fig. 9). The so-called “shear plane” or “shear zone” is not recognized in these cases.
It should be re-emphasized that the following matters were observed in PTFE cutting.
(1) When the cutting speed is high (few hundred meter per minute), high polymers behaves in the same way as metals, so the work material to be cut can be assumed as a perfectly plastic material.
(2) When the cutting speed is very low (below one meter per minute), the elastic deformation being large, friction force on the rake face is small, and shearing in the so-called “shear plane” can not be observed. Therefore, the mechanism of chip formation in these cases will be considered to be rather tearing and large compressive strain, than shearing.

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