Online ISSN : 1880-7488
Print ISSN : 0514-5163
ISSN-L : 0514-5163
12 巻 , 116 号

• 1963 年 12 巻 116 号 p. 263
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
• 柴田 徹
1963 年 12 巻 116 号 p. 264-266
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Changes in volume of soils are a function of changes both in normal stresses and shearing stresses. Development of mathematical expressions for the change in volume would be of aid for the understanding of the failure criteria for clays and would permit more reliable estimates for the settlement of structures founded on massive clay deposits.
This paper describes an investigation of the stress-volume change characteristics of a normally-consolidated clay. The test procedure was similar to that in the case of drained compression test, except that the loading was arranged so that the mean principal effective stresses might be maintained constant throughout the test.
The nomenclature used in this paper is as follows: C: coefficient of compressibility. D: coefficient of dilatancy. V0: initial volume corresponding to σ0'. ΔV: total volume change. ΔVc: change in volume due to the change in mean principal stress. ΔVd: change in volume due to the change in shearing stress. σ1' σ3': principal effective stress. σm': mean principal effective stress. σ0': pre-consolidation pressure. σc: critical stress, below which dilatancy is zero. σm'-const.-test: drained compression test in which the mean principal effective stress is maintained constant.
The analysis of the test data shows that the volume change behaviour can be adequately described by the following conclusions:
1) The volume of normally-consolidated clays decreases when the mean principal effective stress is increased, and vice versa. The virgin branch of a semi-logarithmic plot of the consolidation diagram is usually straight (Fig. 1) and can be expressed by the equation
ΔVc/V0=C·logσm'/σ0'
2) The volume decreases when normally-consolidated clays are subjected to an increase in shearing stress. Fig. 6 shows that the volume change during a σm'-const.-test ΔVd/(V0Vc) is a unique function of (σ13)/σm' and correlations between them can be established.
ΔVd/(V0-ΔVc)=D{(σ13)-σcm'}
3) The total volume change ΔV of normally-consolidated clays is ΔVVcVd, then ΔV is given by the expression
ΔV/V0=C·logσm'/σ0'+D(1-C·logσm'/σ0'){(σ13)-σcm'}
• 赤井 浩一
1963 年 12 巻 116 号 p. 267-270
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Some experimental studies have been performed to investigate the deformation characters of undisturbed fully-saturated clays. It has been well-known that the secondary compression proceeds even after the dissipation of water from clay specimens has ceased, which cannot be explained by the famous Terzaghi's theory. From the author's point of view, it seems there exists a common tendency in the conventional approaches to investigate the secondary compression of clay that the phenomenon has been treated through somewhat formal model analyses.
In the one-dimensional consolidation one should consider the anisotropy of stresses applied to soil specimens, which causes the shear creep by movement of the relative position of clay particles.
Considering the stress and strain relation during the oedometer test, one can recognize that the coefficient of lateral earth pressure (K31) is equal to unity at the beginning of consolidation. With the time elapses a lateral displacement (-δ) due to the volume change occurs which compensates the lateral shear displacement (+δ), the lateral pressure σ3 decreasing steadily. Thus K becomes smaller than unity with time. This mechanism has been confirmed by the triaxial consolidation test controlled lest any lateral strain should occur (see Fig. 5 (c)). The change of the coefficient K during consolidation can be represented on the Rendulic's stress plane (Fig. 1 (a), (b)) and the stress locus in terms of the effective stress should be determined by the behaviour of the pore pressure in the specimen.
It has been found from the test result indicating the correlation between the volume change ΔV/V and σm', the mean effective stress that ΔV/V increases rapidly at the end of 100%-primary consolidation for any value of K (Fig. 2).
A series of long-term oedometer test (for 13 weeks) using an undisturbed fully-saturated silty-clay (Fig. 3) shows:
(1) the rate of the secondary compression does not depend on the sample thickness, the change of void ratio being taken as the ordinate,
(2) the time of the end of primary consolidation t100 is exactly porportional to the square of the sample thickness,
(3) the time of the end of secondary compression is about 2 weeks for the standard sample of 2cm height, and
(4) the secondary and primary compression ratio increases with decreasing the sample thickness.
On the other hand, a series of triaxial consolidation test under anisotropic stress condition shows the fact that the rate of the secondary compression increases with decreasing the effective principal stress ratio (K'=σ3'/σ1') (see Fig. 4).
As a result it can be concluded that the rheological parameters of clay have to be determined by the triaxial consolidation test in which no lateral strain is permitted, under the same stress condition at the site where the settlement of clay layer is to be estimated.
• 阪上 信次
1963 年 12 巻 116 号 p. 271-275
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Petroleum asphalt is a so-called viscoelastic material. In this paper, the dynamic properties of some kinds of straight asphalts, which are residual materials obtained in a vacuum distillation process of crude oil, have been investigated by means of a method which has been effective in studying the linear viscoelasticity of many kinds of amorphous polymers. Furthermore, the viscoelasticity of straight asphalt with crystal paraffin or some kinds of stearates has been also examind.
The results obtained are as follows:
(1) Straight asphalt is a thermorheologically simple material, the temperature dependence of the shift factor aT reduced to the standard temperature Ts obeys the WLF's equation and this material has a glass transition point Tg and the difference between Ts and Tg is about 50°C.
(2) The dynamic viscoelasticity of asphalt with crystal paraffin varies rapidly at temperature where the crystallization or melting of the paraffin occurs.
(3) The dynamic viscoelasticity of asphalt with Al-stearate does not differ so much from that of one without it, but that of the asphalt with Ca-stearate or Na-stearate clearly differs from that of one without them. Namely, that dynamic viscosities of these materials vary remarkably depending upon frequencies.
• 内田 一郎, 藤本 広
1963 年 12 巻 116 号 p. 276-280
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Recently, with development of soil engineering, when we stand on a view-point that the soil is also one of the engineering materials such as the high polymer or metal, and wish to explain unificatively the complicated mechanical behaviour of soils, it is methodologically necessary that we must consider an introduction of thermo-dynamics and statistical mechanics based on the molecular theoretical investigation.
In this case, however, we cannot avoid facing a difficulty which is due to that the deformations of soils are irreversible in general, because the thermo-dynamical analysis is confined to considerations of reversible process of deformation only.
Then, in order to overcome the above difficulty, the authors have established several assumptions as follows:
(1) The authors have adopted a network structure of“card-house”presented by T. K. TAN1) for the skeletal structure of clay. However, we cannot mathematically express a formal distribution of the skeletal structure merely by this network structure. Therefore, a pattern showed in Fig. 2(a) was presented by the authors anew, which was a cross section of the clay network structure. In Fig. 2(b), a broken line turned at random was called“imaginary chain”of the clay network by the authors, further the mutual contact between the clay particles (i.e., the turning point of the imaginary chain) was denominated“unit mechanism of deformation”. The bonding force at this contact point, of course may be due to Coulomb attraction force between the positively charged edges and negatively charged flat sides of the clay particles, van der Waals forces, bonding by cations, and dipole hydrogen bridges.
(2) For the deformation process, we have assumed that a micro elastic deformation may occur at the instant of loading, and a retarded deformation that is due to slipping of the clay particles follows on the instantaneous elastic deformation. The macro plastic deformation consists of these two deformations. The micro irreversible deformation at the contact point occurs only when the stress component acted to the unit mechanism of deformation becomes greater than the bonding energy of the contact point.
(3) For a thermo-dynamical expression of the micro reversible deformation process of the clay, we have assumed that the external force is composed of the energy elasticity and the entropy elasticity, and the former is proportional to the latter.
By the above hypotheses, the authors have accomplished the introduction of thermo-dynamics and statistical mechanics to soil mechanics. As a result of the theoretical investigation, the authors have obtained a unificative equation (12) that is of the same type as Maxwell's equation. However, by the simple Maxwell's equation, it is not yet enough to explain the complicated rheological properties of clay, and so the authors introduce the structural viscosity of clay by applying Eyring's viscosity theory to the double water layer of clay particles. Consequently we have been able to explain molecular theoretically the rheological behaviour of clay.
• 田中 一彦, 田沢 栄一, 橋本 博和
1963 年 12 巻 116 号 p. 281-287
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The qualities necessary for the grouting paste for prestressed concrete are faculty of smooth flow, little bleeding and change of volume, high strength (compressive and bond) and resisting power for freezing. But those qualties, excepting the faculty of flow, are improved by the minimum use of water.
The current apparatus for measurement of fluidity of grouting paste are such as shown in Fig. 1∼Fig. 3, either of which is used, according to the enquête undertook by the Dutch Grouting Committee, in various foreign countries except in Holland.
The“International Recommendation”arranged by the same Committee has recently stated that“The water-cement-ratio must be as low as possible for a good workability. The fluidity of the grout may be measured with every kind of apparatus that gives reproducible results. Every type of apparatus must be calibrated in poises.”
But no apparatus has been calibrated in poise so far.
It is partly due to the thixotropic property of cement paste but mainly to the assumption that cement paste is nothing but a Newtonian liquid. The experiments which the writers have made with his coworkers on an assumption that cement paste is Bingham body clearly show that the measurements done with those apparatus can be expressed in terms of absolute unit.
The measurement has been done by means of BH type rotation viscometer (Photo. 1) at various rates of shear, that is, its number of rotation of rotor.
Investigation has also been made as to the change which the charactaristic values of ηpl and ν undergo by taking into consideration various conditions necessary for the presstressed concrete grouting, that is, mix proportion, types and numbers of rotation of mixer, mixing time and the fineness of cement.
Several results are shown in the following figures. From these experiments some conclusions have been obtained as follows:
(1) Cement paste behaves as Bingham body, and the fluidity of grouting paste is represented both by ηpl and ν.
(2) The values of these rheological properties are influenced by mixproportion, types and numbers of rotation of mixer, mixing time and the fineness of cement etc..
(3) The current apparatus for measurement of fiuidity of paste which are shown in Fig. 1∼ Fig. 3 will not be sufficient for measurement of ηpl and ν.
• 松本 幸雄
1963 年 12 巻 116 号 p. 288-291
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
(1) Flow properties of emulsions containing from 10 to 60vol. % of liquid-paraffin in water, stabilized with SDS or Tween 60, have been investigated using Maron and Belner's capillary viscometer at 32°C.
Viscosities of SDS system do not depend on the rate of shear at dispersion concentrations below 40vol. %. Tween 60 system shows non-Newtonian flow over the range of dispersion concentrations at relatively low rate of shear. At higher shear rate, flow of the Tween 60 system tends to show Newtonian behavior and the values of the relative viscosities of the system agree with those of SDS system at the same dispersion concentrations.
These differences in flow behavior of the two systems may be attributed to the difference in the dispersion state, which is remarkably influenced by the nature of the surface layer on the dispersed particle.
(2) Flow properties of surface active agent (emulsifier) aqueous solutions containing n-octanol or n-hexane have been studied at 32°C.
In n-octanol system, values of viscosity increase with the increasing amount of solubilized n-octanol and pass through a maximum value in the neighborhood of the concentration of the limit of solubilization and decrease again with the further addition of n-octanol. In n-hexane system, the values of viscosity increase with the increasing amount of n-hexane in a fairly normal way.
These differences in flow behavior of the two system may be attributed to the difference in polarity between n-octanol (polar liquid) and n-hexane (non-polar liquid).
• 奥田 聡
1963 年 12 巻 116 号 p. 292-294
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The author has measured the rheological properties of time-independent suspensions (MgCO3-water slurry and Ca(OH)2-water slurry)by means of a rotational viscometer and pipe flowing.
First he observed that the viscosity of suspension depends largely on the aggregative state of suspended solid in the liquid by the rotational viscometer (Fig. 1).
From the results of the experiment of pipe flow where the range of rate of shear is very wide (Fig. 4), he found that the rheological behavior of suspension is not always constant, but, according to the magnitude of shear rate, that is the degree of aggregation of suspended solid, varies its form from Bingham plastic (Fig. 6) to psuedo-plastic (Fig. 2, Fig. 3) and further to Newtonian fluid (Fig. 5).
• 福島 正義, 曽根 敏麿, 深田 栄一
1963 年 12 巻 116 号 p. 295-299
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The non-linear behavior of dynamic viscoelasticity of plastic materials (e.g., plastic fat, butter, margarine, paraffin etc.) were investigated by means of a rotating rod method. The results were analyzed by using two phenomenological theories, i.e., Eyring's theory of rate process for non-Newtonian liquids and a mechanical model with slider element.
In the former analysis the hole volume and activation energy of flow were calculated. It was found that the smaller value of the hole volume is accompanied by the larger values of the activation energy and of the stress at which the non-linear effect appears.
In the latter analysis, the magnitudes of characteristic constants of spring, dashpot and slider were numerically determined. The model consists of two circuits of mechanical elements: the one is a parallel combination of a spring and a dashpot for describing the elasticity and viscosity in the range of linear deformation, and the other is a parallel combination of a spring, a dashpot and a slider for describing the elasticity, viscosity and yield value in the range of non-linear deformation.
The tested materials contain fine crystalline particles which in amorphous medium, form a kind of network structure by the interlinkages. The observed non-linear deformation is probably caused by slippage between these interlinked crystalline particles.
• 種谷 真一, 曽根 敏麿
1963 年 12 巻 116 号 p. 300-303
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
In the previous paper we reported that the internal friction of powder is related to the variation of void during tapping or the powder constant of Nutting's equation. And it was seen that the shearing stress increases pulsatively with the increase of shearing displacement and saturates gradually.
In this study we carried out determination of pulsative vibration of the shearing stress during flowing of powder by the use of modified Green's rotational cylindrical viscometer. The stress of inner cylinder in response to the shearing stress of powder due to the rotation of outer cylinder represented pulsative vibration at early period and got to the constant of amplitude at the later period of rotating time.
From the results of the recording of pulsative flow patterns obtained employing various kinds of powder, it was found that the amplitude of vibration is related inverse proportionally to the cohesive property of powder.
From the analysis of flow pattern could be derived two types of mechanism of flow properties, i.e. the random flowing of each particles and the flowing of the block of powder. Both types of flowing of particles are attributed to the variation of void during flowing.
An empirical dependence of the mean torque on the duration of the experiment can be satisfactorily represented by the relation;
|(T-T)/(T-T0)|=expKN
where T is the mean torque at any time, T0 the torque at the initial time of the experiment and T the equilibrium torque after long time. N is the number of rotation and K is a constant relating to the speed of rotation and depending on the packing rate of powder. Subsequently the above equation agree to Roller's equation which was obtained from the relation between the variation of density of powder due to tapping and the number of tapping.
• 奥山 政高, 広瀬 達三
1963 年 12 巻 116 号 p. 304-307
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The present authors consider that both shear flow and volume change are ascribed to the appearance and disappearance of holes. Number of holes decreases with increasing pressure and increases with decreasing pressure.
When pressure on liquid is anisotropic, time rate (frequency) of appearance of hole becomes also anisotropic.
From this point of view, a general relation between stress and deformation of liquid is derived.
[Ur]=vh/v0kT/hF≠/F0exp(-εjh/kT)[exp(-prvh/2kT)]-(pm/K2-θ)kT/hF≠/Fhexp(-εj/kT)[exp(prvh/2kT)]-1/3K2[pr]
[Ur]: tensor of time derivative of strain. Bracket means tensor. Subscript r means principal axes x, y, z of strain. v0, vh: volumes of a molecule and a hole, respectively. εj: activation energy for collapse of a hole. εh: energy for creation of a hole. F0, Fh, F≠: partition functions. pr: time derivative of pressure pr along each principal axis of strain. pmr=x, y, zpr/3. θ: bulk strain both by the appearance and disappearance of hole and by the change of inter-molecular distance. K2: bulk elasticity only by the change of inter-molecular distance. Further from the relation, complex shear viscosity and complex bulk viscosity can be derived. So present theory comprises Hirai-Eyring theory on bulk viscosity (1958) as a special case. If the mechanisms of shear viscosity and bulk viscosity are the same (i.e. the appearance and disappearance of hole), the empirical rule that their activation energies are much the same becoms self-evident.
• 岡野 光治
1963 年 12 巻 116 号 p. 308-310
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Based upon the phenomenological theory of non-linear responses of many variable systems (K. Okano and O. Nakada, J. Phys. Soc. Japan, 16, 2071 (1961)) the non-linear constitutive equations for isotropic viscoelastic materials are presented.
Let σ(t) denote the stress tensor at an instant of time t, and D(t) be the displacement gradient ∇S (S being the displacement vector) or velocity gradient ∇V (V being the velocity vector) according as the material concerned is a viscoelastic solid or a viscoelastic liquid, then we have (K. Okono, Japanese J. Appl. Phys., 1, 302 (1961)) the following non-linear constitutive equation (up to the second order terms in D) for an isotropic viscoelastic material:
σ(t)=∫t-∞[a(1)(t-τ)D(0)(τ)+b(1)(t-τ)D(2)(τ)]dτ+∫t-∞t-∞[a(2)(t-τ1, t-τ2)D(0)1): D(0)2)I
+b(2)(t-τ1, t-τ2)D(2)1): D(2)2)I+c(2)(t-τ1, t-τ2)D(0)1)·D(2)2)
+d(2)(t-τ1, t-τ2){1/2D(2)1)·D(2)2)+1/2D(2)2)·D(2)1)-1/3D(2)1): D(2)2)I}
+e(2)(t-τ1, t-τ2){1/2D(1)1)·D(2)2)-1/2D(2)2)·D(1)1)}]dτ12
+higher order terms.
In the above equation I is the unit tensor and
D(0)≡1/3∇·SI or 1/3∇·VI
D(1)≡1/2(D-D)
D(2)≡1/2(D+D)-D(0)
and a(1)(t), b(1)(t), a(2)(t1, t2), ect. are the scalar material functions characterizing the viscoelastic response of the system concerned. The third order terms in D are given in the text. (eq. 2.5).
If the material concerned is incompressible the terms on the right hand of the above constitutive equation which are connected with a dilatational deformation (the terms containing a(1), a(2), b(2), c(2)) should be replaced by an indeterminate hydrostatic pressure: -pI
• 岡 小天
1963 年 12 巻 116 号 p. 311-313
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The purpose of this paper is to present a theory of the steady flow of Newtonian liquid through a conical nozzle. The equation of motion of viscous liquid has been treated on the following assumptions: i) the liquid is incompressible; ii) the motion of liquid is not turbulent; iii) the motion is steady; iv) no body force acts on the liquid; v) the motion has an axial symmetry; vi) there is no slip at the wall; vii) the stream lines are the straight lines passing through the vertex of the cone, that is, the end effect is neglected; viii) the motion is so slow that the inertia term can be neglected.
We have taken a spherical coordinate system r, θ, and φ whose origin is at the vertex of the cone. Then the velocity is given by
vr=3A(cos2θ-cos2α)/4r2,
where α is the semi-angle of the cone, and A is a constant. The expression for the pressure is obtained as follows:
p=p0+3/2Aη[cos2θ+1/3/r3-cos2α+1/3/r13],
where η is the coefficient of viscosity, and p0 the atmospheric pressure. Thus the average pressure gradient taken over the spherical surface of radius r is given by
(∂p/∂r)=-3/2Aη/r4(2+cosα+cos2α).
On the other hand, the volume of flow in unit time is given by
Q=-πA(1-cosα)2(1+2cosα).
Eliminating A from the above two equations, we get
Q=π/8R4/η(∂p/∂r)F(α),
where R is equal to rα, and F(α) is given by
F(α)=16/3(1-cosα)2(1+2cosα)/α4(2+cosα+cos2α).
Since limα→0F(α)=1, the above equation may be reduced to Poiseuille's equation for a tube of uniform cross section.
From the expression for the velocity vr we can calculate stress components of the fluid. Especially, the tangential stress σ is given by
σ=-3/2Aηsin2θ/r3.
For a given value of r, σ varies as sinθ does in contrast with the case of a tube of uniform cross section where tangential stress decreases linearly from a maximum to zero with decreasing distance from the axis of the tube.
• 岡 小天
1963 年 12 巻 116 号 p. 314-316
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The purpose of this paper is to show how to determine yield velue f and plastic, viscosity η of a Bingham body by means of a parallel plate plastometer. The material under test in the form of a cylinder is placed between parallel circular plates. A constant force F is applied perpendicularly to one plate, the other plate being fixed. From the meaurement of the displacement of the other plate, the rheological behavior of the specimen may be determined.
We have treated the problem under the following assumptions: i) the material is incompressible; ii) no body force acts on the material; iii) the motion is very slow; iv) there is no relative motion between the plates and the material in immediate contact with the plates; v) the distance h between the plates is so small compared to the radius R of the sample that the velocity component in the perpendicular direction is negligible.
Then it is found that the pressure p is a function of time t or h and the distance r from the axis of the sample and satisfies the following equation,
6ηr(p'r+p)3h=p'{h(p'r+p)-fr}{h(p'r+p)+2fr}2. (1)
Since p may be regarded as a function of r, h and f, we developed p with regard to h and f and neglected second order terms. Then the pressure is given by
p=p0-3ηh/h3(R2-r2)+(R-r)f/h, (2)
where p0 is the atmospheric pressure.
Since the applied force F together with πR2p0 is in equilibrium with the pressure in the material, We get
-3πR4η/2h3h+πR3f/3h=F. (3)
We then treat the following two arrangements: i) the specimen is larger than the plates; thus the area under compression is constant. ii) the plates are larger than the specimen; thus the volume V of the specimen is constant.
i) We may take R=a, and eq. (3) can be written as
D=(τ-f)/η (4)
with D=-9ah/2h2 and τ=3hF/πa3. Thus if D is plotted against τ, a straight line of slope tan-1 (1/η) is obtained. From the intercept on the abscissa, the yield value f can be obtained.
ii) If we express eq. (3) in terms of V, we have the same relation as (4) with D=-3V1/2h/ 2π1/2h5/2 and τ=3π1/2h5/2F/V3/2.
Eq. (3) may be integrated in the special case πa3f/3Fh<<1. Thus we have
3πa4/4(1/h2-1/h02)+πa7f/6F(1/h3-1/h03)=F/ηt. (5)
Similarly we get
3V2/8π(1/h4-1/h04)+fV7/2/13π3/2F(1/h13/2-1/h013/2)=F/ηt (6)
in the special case where V3/2f/3π1/2h5/2F<<1. If we put f=0 in eqs. (5) and (6), these reduce to the well-known formulate for Newtonian liquids.
• 山本 三三三
1963 年 12 巻 116 号 p. 317-321
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
In previous papers1) we studied on the phenomenological theory of the non-linear viscoelasticity of three dimensional bodies. Since that time a criticism has been given to it that our stress-strain relation for the three dimensional Maxwell model is not invariant for the rigid rotation of the sample and for the coordinate transformation.2) In this paper a reformed theory is treated for the model. We define the observable displacement (deformation) tensor a and the internal elastic displacement tensor α as
Δr=a·Δr0andΔξ=α·Δξ0, (1)
respectively, with the lengths of a line element in the sample at initial state, Δr0 and at deformation state, Δr, and those of the internal elastic mechanism, Δξ0 and Δξ.*** Instead of the fundamental equation of the previous paper for the time derivative of internal elastic displacement tensor, we consider the time derivative of the Cauchy-Green's left internal strain tensor λ=α·α+ (+ denotes the transposed tensor). That is,
dλ/dt=da/dt·a-1·λ+λ·a+-1·da+/dt+(dλ/dt)* (2)
assuming the dissipation term of the form
(dλ/dt)*=-β(λ-1). (3)
The stress tensor is written as ∞
σ=Rλ·λ+Qλ+P1=σe+P1. (4)
We can get the stress-strain relation from Eqs. (2) and (4):
e/dt=da/dt·a-1·σee·a+-1·da+/dt+Rλ[da/dt·a-1+a+-1·da+/dt]λ+Rλ·λ+Qλ+(dσe/dt)* (5)
where
(dσe/dt)*=Q(dλ/dt)*+R[λ·(dλ/dt)*+(dλ/dt)*·λ]. (6)
The Cauchy-Green's right internal strain tensor λ'=α+·α has a relation similar to Eq. (2) with the modified displacement tensor a'=R+·a, where R is the orthogonal tensor representing the rotation of the sample as a whole.
Denoting the additional rigid rotation of the sample by an orthogonal tensor T(t), the displacement tensor and the left internal strain tensor should be transformed to
a=T·a and λ=T·λ·T+, (7)
respectively. The relation between a and λ is just similar to Eq. (2), that is, this relation is invariant for the rigid rotation of the sample.
On the other hand, due to the coordinate transformation T(t), the displacement tensor and the left internal strain tensor become
a=T·a·T+and λ=T·λ·T+ (8)
respectively. The time derivative of λ has, besides the terms similer to those of Eq. (2), the additional term
-[a·T·dT+/dt·a-1·λ+λ·a+-1·dT/dt·T+·a+]. (9)
This term arises from the change of the reference coordinate system for the initial line element of the sample, and if the coordinate transformation is independent of time, this term vanishes.
As an example of our theory, the so-called Barus effect is treated based on the consideration of Metzner et al7).
1963 年 12 巻 116 号 p. 322-325
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
• 平井 西夫
1963 年 12 巻 116 号 p. 326-328
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
In order to study the mechanical properties of high polymer on the basis of their molecular structure, it is necessary to know the elemental structure of polymeric substances. Recently it was found that the single crystal is a fundamental structure in addition to the original fringe micell model. Here the growing process and the structure of the single crystals are discussed briefly, on the basis of which the elastic properties, the viscoelastic absorption and the drawing processes are explained.
Screw dislocations with a spiral structure often grow on a single crystal. The Burgers vector of the screw dislocation in the crystal of metal is of the order of atomic distance, while that of polymer single crystal is equal to the thickness of the crystal itself, that is about 100A. This may be due to the much lower elastic modulus of single crystal of high polymer. In metal and other inorganic salts, the plastic properties as well as the growth mechanism are explained in term of the screw dislocation. On the other hand, in the case of polymer, the roles played by dislocation on their mechanical properties are not yet clear.
The fold conformation of the polymer chain induces a stress in the surface layer of the lamellae and this stress can be released by twisting the lamellae. The critical stress inducing the twisting and the period of the twist are represented in terms of the thickness, the width, the rigidity, the Young's modulus of the lamellae, the strain in the surface and the thickness of the strain layer.
The elasticity of polymer along the main chain in crystalline part is calculated to be about 2.5×109g/cm2 from the measurement of the change in X-ray diagram of a polymer sample under stress. This value is several times as large as those of extended fibers and about one hundred times as large those of unoriented crystalline polymers. The elasticity of the direction normal to the molecular chain is determined to be about 2×107g/cm2. This is very close to those obtained by the direct measurement of unoriented crystalline polymers, and suggests that the elasticity of unoriented crystalline polymers is the value correspond to the van der Waals force in the direction normal to the main chain folded in the lamellar structure in solid polymers.
The best way of illustrating the relation between the fringe micell model and the new concept of the folded conformation model may be to observe the process by which the fold molecules in a single crystal are reoriented into a drawn fiber. Some electron micrographs obtained seem to illustrate such processes. This may be called the“necking”of a single crystal. The fold plane (110) cleaved sharply when the crystal was torn along it, while molecules are drawn into a fiber when the crystal was torn along a plane crossed with a large angle to (110) plane.
• 1963 年 12 巻 116 号 p. 329
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
• 荒川 泓, 窪田 一成, 長島 義久
1963 年 12 巻 116 号 p. 330-334
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
An ultrasonic pulse technique was applied to the rheological study of aqueous solutions of polyvinyl alcohol in the ultrasonic frequency region.
Two samples of polyvinyl alcohol were used. The average degree of polymerization of sample A and sample B was 1800 and about 2000, respectively. The content of residual acetyl groups was smaller than 0.7% by mole for sample A and was 12.2% by mole for sample B. The molecular weight distribution curve of sample A was obtained by the successive precipitation method proposed by Spencer.
Ultrasonic velocity and absorption were measured over the temperature range of 3∼70°C for the solutions in the concentration range of 5∼15% by weight. The frequency of ultrasound was 1.42Mc/s throughout the experiment.
The following results were obtained:
In sample A, the temperature dependence of ultrasonic velocity has similar characteristics on the whole to that observed in pure water, and the ultrasonic velocity increases with the increase of concentration. In sample B which contains acetyl groups by 12.2% by mole, however, the behavior is fairly different. In the low temperature region no remarkable difference between A and B is found, but above 40°C it is clearly seen that sound velocity is smaller than that for the solutions of sample A which have the same concentration. The tendency of smaller sound velocity becomes more evident in high temperature region, and the velocity decreases with increase of polymer concentration in sharp contrast to the case of sample A. The velocity-temperature curve of solutions of sample B has a broader peak than in pure water, and the peak becomes lower, and the peak temperature shifts to lower temperature side. For example, in the case of the 10wt.% solution of sample B the peak temperature is about 50°C, whereas the value for pure water is 74°C.
The average absorption coefficient in the temperature range of the present experiment increases with increase of concentration in both samples. The data for solutions of sample B are seen to be larger than those for solutions of sample A of the same concentration.
The longitudinal elastic modulus M1 and the longitudinal loss modulus divided by angular frequency M2/ω are obtained from the data of sound velocity and absorption.
• 鈴木 邦夫, 深田 栄一
1963 年 12 巻 116 号 p. 335-338
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Theories on normal force effect have been proposed by several workers since Weissenberg's first investigation. In experiments, however, data on this effect are not enough to verify these theories in generality.
Two kinds of silicon oil were taken up as samples, one 104 centi stokes, the other 105 centi stokes. These samples were irradiated with a variety in radiation dose by γ ray from Co60. Normal force (σ1122), steady flow viscosity over a range of shear rate from 10-2 to 102sec-1 and dynamic modulus and viscosity over a range of angular frequency between 5×10-2 and 3×10sec-1 were measured by a Weissenberg Rheogoniometer at 20°C. The variation of dynamic modulus and viscosity with the shear rate of superposed steady flow was also measured.
Silicon oils with more radiation dose have larger viscosity and normal force. It is found that the normal force of more irradiated specimen was larger than that of less irradiated ones though their viscosities were in the same magnitude. This is considered to be due to cross linkages in the materials.
Two kinds of molecular weight were determined: one according to the relation between molecular weight and viscosity which was treated as a linear molecule, the other according to the relation between molecular weight and radiation dose treated as cross linked materials.
The recoverable shear s was calculated from the values of shearing stress σ12 and normal force σ1122 in steady flow. It was found that these silicon oils follow “Hooke's low in shear” from the linearity of plots in s against σ12.
The comparison of curves of dynamic viscosity against angular frequency and the steady flow viscosity against shear rate was made, and approximate equality of shear rate and angular frequency was seen.
The elastic modulus G and relaxation time τ in the sense of Maxwell model were calculated from both steady flow and dynamic experiments, making use of the equality of shear rate and angular frequency. The values of G and τ agreed in the order of magnitude in the range where normal force experiments were done.
• 尾崎 邦宏, 田村 幹雄, 倉田 道夫, 小高 忠男
1963 年 12 巻 116 号 p. 339-340
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
• 上野 弥, 大野 育造
1963 年 12 巻 116 号 p. 341-346
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Creep of gelatin-water system was studied covering a wide range of concentration at several different temperatures. The sample studied is unfractionated and photographically inert alkali-processed hide gelatin with isoelectric point of pH4.8. Creep at higher concentrations was measured with automatically extension-recording apparatus or travelling microscope at definite humidities and definite temperatures, and that at lower concentrations with special gel elastometer. The strain values were limited to be less than 1%.
The result of the measurements suggests the existence of three concentration regions showing deformation with different mechanisms in mechanical behavior.
First, glassy state above 85% in concentration at 20°C. It is reasonable to surmise that water molecules are present at hydration centers of the amorphous region of gelatin. Creep compliance curves at various concentrations are superimposed on each other, and compose a smooth curve through usual horizontal shift along time axis.
Second, dispersion region. The concentration range at 20°C is from about 40 to 83%. Young's modules and creep compliance depend remarkably on concentration, and the dependency seems not very simple. The upward shift of creep compliance curves for gelatin at pH 4.8 maintaining its shape was found when concentration decreased, therefore, the composite curve was obtained through vertical shift along creep compliance logJ axis. Horizontal shift as well as vertical shift was necessary to superimpose creep compliance curves at pH6.5, but the former reducing factors were smaller than the latter one. Increasing amount of water saturates all available hydration centers in amorphous region of gelatin, then induces disturbance of crystallites, and then is supposed to decrease the degree of crystallinity remarkably. The large vertical shift above-mentioned is considered to relate with crystallinity changes according to the recent research on synthetic, crystalline polymers. The crystallites in this region may be micelle-like.
Third, the square law region. Elasticity modulus of gelatin gel is proportional to the square of gelatin concentration up to about 30% but from that to 40% the modulus is less than the value predicted from the square law. To superimpose the creep compliance curves, vertical shift along logJ axis was necessary. Here, the gel is essentially rubber-like, and the cross-linkages may be formed between two chain segments, caused by secondary bonds. Since the cross-linkages are evidently dissociated by decreasing gelatin concentration or arising temperature, vertical superposition may become possible.
In conclusion, the viscoelastic properties of gelatin not in glassy state are characterized by vertical shift of the curves denoting them concerning with concentration or temperature, and horizontal reducing factor log b is null or nearly null, otherwise not null but always smaller than vertical reducing factor. The different mechanisms of viscoelastic deformation in three regions in concentration above-mentioned result from the structural difference of gelatin.
• 後藤 廉平, 吐山 尚美
1963 年 12 巻 116 号 p. 347-350
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The elongation or the creep of Du Pont's Maylar film (0.0065×25×100mm) in the aqueous solution of phenol was recorded automatically by means of a linear variable differential transformer (Fig. 1) at various concentrations and temperatures under a constant load (50g).
The elongation of the film (Δlt) increased exponentially with time at the initial stage and attained a limiting value (Δl) according to the concentration (c) of phenol at a constant temperature (Fig. 2). Δl increased almost linearly with the increasing concentration, while it decreased with the increasing temperature (Fig. 3).
The logarithm of the time for half elongation (log t1/2) decreased linearly with increasing log c; the higher the temperature, the smaller the inclination was (Fig. 4).
After unloading, the film shrank instantly at first and then recovered slowly to a limiting length, Δl being about a half of Δl (dotted lines in Fig. 2). This elongation of the unloaded film means swelling by phenol. The change in the weight of the film during the process of swelling increased with the increasing concentration (Fig. 7). The infrared absorption measurement suggested that the phenol molecules absorbed by the film combine with the polyester molecules by hydrogen bonding.
The creeping of Maylar film in the phenol solution was accelerated by neutral salts, i.e. sodium chloride, sodium acetate and sodium sulfate, but was retarded by potassium carbonate (Fig. 8). Surface active agents accelerated slightly the creep at low concentrations, but retarded considerably at high concentrations.
These results suggest that the swelling effect of phenol is closely related to its carrier effect in the dyeing process of polyesters.
• 祖父江 寛, 村上 謙吉, 星野 祐幸, 井手上 英斗
1963 年 12 巻 116 号 p. 351-354
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
One of the elastomers recently developed is ethylene-propylene co-polymer which was first synthesized by Natta and his co-workers using organo-metallic catalysts. The structure of this polymer is amorphous, or partially crystallitne, depending upon its ratio of co-polymers.
The characteristics of this polymer are high-resistance to high temperature, degradation, and chemicals. The chemorheology, one of the new research fields, was here thought to be one of the effective means to elucidate the changes of the structure of ethylene-propylene co-polymers under a given condition. The elastomer whose ratio of ethylene to propylene is 70 to 30 was offered to us by Prof. Tobolsky at Princeton University by his courtesy. This elastomer was then irradiated at 1.26MeV electron by the apparatus of Van de Graaf for 15sec., 30sec., and 150sec., respectively, under the room temperature (25°C) in the air. As the results, three kinds of elastomers with different initial densities, n(0) were obtained. Such initial densities, the mole numbers of total network chains in a unit volume were calculated from the stress relaxation measuremet as shown by Table 1.
When n(0) is plotted against the radiation time, EPR-2, EPR-1, and EPR-3 are all on the same straight line exactly. From these data, the G value in this case was calculated to be 1.34.
(I) In the case where the cross-linking chains cut alone or prior to the main chains, the relation between f(t)/f(0) and log t is independent of the initial densities n(0), but that between q(t) and t is dependent on the initial densities n(0).
These tendencies are shown by Fig. 2 (a).
(II) In the case that the main chains cut alone or preferably to the cross-linking chains, the relation between f(t)/f(0) and log t is dependent on the initial densities n(0), but that between q(t) and t is independent of the initial densities n(0).
The basic theory through the above results is described in the recent textbook by Prof. Tobolsky.
The stress relaxation of the ethylene-propylene co-polymer was studied at the elongation 15%, and 140°C. Fig. 3 shows that the relation between f(t)/f(0) and log t for three samples indicate the same tendency. On the other hand, the relation between q(t) and t for three samples shows different curves as indicated by Fig. 4. From the above results obtained, the change of the structure of the samples due to the mechanism (I) seems to occur, in another words, the chanis of cross-linking cut alone or preferably to the main chains for the ethylene-propylene co-polymer.
As the facts that when natural rubbers by irradiation cure are exposed to the oxidation under the air of high temperature, the scission of the main chains occurs preferably to the cross-linking chains have been observed by A.V. Tobolsky and his co-workers, our results are quite noticeable when compared with their results.
The stress decay curves by the intermittent and continuous method for ethylene-propylene co-polymer are shown by Fig. 5, Fig. 6 and Fig. 7. It is clear that for the sample of EPR-2 of which initial density n(0) is the lowest among the three samples, the interval between the curves by both methods is increasing gradually with the length of the time. In another words, the amounts of cross-linking chains are gradually increasing.
In EPR-1, whose density is the midst among the three, the amounts of cross-linking chains created are increasing with increasing of the time at first, then they are decreasing gradually with further increasing of the time. In EPR-3, whose initial density is the highest among the three, the amounts of cross-linking chains created by the oxidation are not so remarkable as in the other two samples, and the two curves by both methods become overlapped in the long time range
• D. NARAYANAMURTI, R.C. GUPTA, JAGRAJ SINGH
1963 年 12 巻 116 号 p. 355-357
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
• 林 静男
1963 年 12 巻 116 号 p. 358-361
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
A molecular theoretical investigation of the viscoelastic properties of amorphous polymeric substances in the range of long relaxation time has been pursued by using a temporarily crosslinked network model, in which crosslinkages are created by secondary valence of segments or by entanglement of linear polymer molecules.
Consider a single polymer molecule in the system. The deformation of the molecule is different, in general, from that of the system since the polymeric substances do not return to its initial state even though the deformation is removed. Therefore the concept of slipping of molecules or chains is acceptable.
In the present consideration, a part of polymer molecule between two adjacent crosslinkages is termed“chain”, and the chains, each having the same length, are considered to be Gaussian-chain-springs. The friction of chain is replaced by a bead moving in a medium which is the assembly of polymer molecules excepting the said molecule. Therefore a polymer molecule is equivalent to the so-called Rouse model which corresponds to the macro-Brownian motion of molecule contrary to the micro-Brownian motion in the ordinary Rouse model. The medium in this model is viscoelastic medium, since polymer molecules are crosslinked to one another. Therefore one chain in a molecule has elastic and viscous effects on other chains through the agency of the medium. The evaluation of the two effects are made by using the above model and on the following two assumptions. One is the assumption determining the viscous effect and is expressed as “The slipping of a chain is influenced by the contractive force of the chain and by the forces given by the nearest chains”, and the other is the assumption relating to the elastic effect and is written as“In such a motion of polymer molecule that k chains move in a group, the elastic effect is caused by k chains”.
From the above model and two assumptions, the slipping equation is obtained in the form of Eq. (26) or Eq. (26') and the stress is expressed by Eq. (28) or Eq. (28'), these two relations show that our model corresponds to the parallel combination of the generalized three dimensional Maxwell model. The relaxation spectrum is of the box type as is given by Eq. (41), in which ν is the number of chains in unit volume, n is the number of chains in a molecule, and τβ and τα are the maximum and minimum relaxation times of the spectrum. The steady flow viscosity is given by Eq. (43), in which X and q are the number of repeating unit in a molecule and in a chain respectively. Eq. (43) shows that the steady flow viscosity is proportional to the 3.4 power of molecular weight. For a system with polydispersed molecular weight distribution, the relaxation time is expressed by Eq. (45), and the“box”is out of shape in the range of long relaxation time.
• 柴山 恭一
1963 年 12 巻 116 号 p. 362-366
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
All solid polymers are present in three dimentional network structure because their molecular chains aggregate with various junctions e.g. chemical crosslinking, chain entanglement and other intermolecular couplings. It is probable that the macroscopic properties of polymers are dependent on the nature of the network structure even when no regularity exists in the mode of the aggregation and the system is completely amorphous. Descriptions of the network structure so far presented has been done solely in terms of the network density. However, the network structure may also depends on local packing geometry of molecular chain which includes many junctions. An essential feature of network structure is the restriction of segmental motion by the network junction. In the case of flexible chain molecule, this restriction may be effective in certain length of chains around the junction point. Segmental mobilities are then distributed along a molecular chain which passes through several junctions. To characterize the network structure, a new concept of the distribution of segmental mobilities is introduced. This concept will be found to be valid so as to apprehend systematically the volume effect of network density and some aspects of viscoelasticity.
A simple relation between specific volume v and the network density ρ is deduced assuming that the restriction is localized near the junction point,
v=βalnρ0/ρ (1)
ρ0 being a constant. The parameter β is unity above the glass temperature Tg, and a depends on the decrement of free volume accompanied by an increase in ρ. In several crosslinked polymers, a takes a value ranging 0.02 to 0.04 which is in reasonable agreement with the previous estimation of fractional free volume of polymers. Below the glass temperature, β depends on the distribution of free volume along the chain taking values between zero and unity according to the uniform distribution and the extreme localization, respectively. Assuming that the segmental mobilities are a function of free volume alone, β can be regarded as a measure of distribution of segmental mobilities. Dependence of β on the structure of chain unit is studied on crosslinked styrene copolymers. It is found that β takes a lower value in the case of higher styrene content, reflecting the rotation hindrance of the rigid styrene sequence. From equation (1) one can derive an expression of the dependence of Tg on ρ.
Tg-a/Δα(1-β)lnKρ (2)
where K is a constant and Δα is the difference of the thermal expansion coefficient above and below the glass temperature. Equation (2) is found to hold for several crosslinked systems.
As for the viscoelasticity, response of a modified ladder model is studied by an analog computer. Larger resistive values are assinged to terminal elements according to the concept of distribution of segmental mobilities. The shape of tanδ curve becomes mare symmetric when the localization of restriction due to network junction is pronounced. Since experimental tanδ curves of polymers are usually symmetric, it can be concluded that the localization of the restriction is a universal feature of network polymers provided the model was an adequate one. The ratio of the resistive values of terminal elements to that of middle elements has a marked effect on the steepness of viscoelastic dispersion. The dispersion becomes much steeper, increasing this ratio which is considered to correspond to increasing β. Practical examples may be found in copolymer systems of two components, one of which is more flexible having a higher value of β. Tobolsky has reported that the slopes of relaxation modulus become steeper when the concentration of butadiene is increased in styrene butadiene copolymers
• 祖父江 寛, 村上 謙吉, 星野 祐幸
1963 年 12 巻 116 号 p. 367-370
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
It is widely known that the“box”type curve is depicted in the rubbery region of the relaxation spectrum of a linear amorphous polymer. Three parameters, τl, τm and E0 are defined as the minimum relaxation time, the maximum relaxation time, and the height in the “box”curve function respectively.
One of these characterizing factors, τm was shown to be the function of molecular weight and temperature in a quantitative form for polymers by Tobolsky and Andrews, and later by Tobolsky and Murakami in a more refined form. The method of obtaining the value of τm suggested previously by Tobolsky and Andrews, is less natural than those proposed by Tobolsky and Murakami, which is so-called Procedure X. In the previous papers, the possibility of measuring the molecular weights by Procedure X was briefly described for some amorphous polymers such as polyisobutylene, polyvinyl acetate, and polystyrene.
This paper deals with such a new procedure for polymethyl methacrylate with more details.
The relation among τm, a maximun relaxation time, nw, weight-average chain length, T temperature and Tg, glass transition temperature, or Ts, WLF temperature, or Td, Tobolsky's temperature is indicated as follows:
logτm(sec.)=logAi-C1T-Ti/C2+T-Ti+3.4lognw
The value of i is g, s or d, changing the values of the constants C1 and C2 in each case.
The samples of polymethyl methacrylate whose monomers were purified by means of vacuum distillation under the nitrogen currents were prepared in the presence of varying concentration of the initiator 2-azobis isobutyronitrile at 60°C, using lower conversion around 10%. The radical-initiated polymers thus obtained were found to have a heterogeneity index of 1. 9.
If the values of logτm are plotted against that of logPn, the lines consisting of two straight lines are obtained, in which the slope has a value of 3.4 in the ranges of more than logPn=3.4, or about Pn=2500, and has a value of approximately unity in the ranges of less than logPn=3.4.
It is interesting to consider that the knick point by two straight lines may have a close relation with the critical molecular weight Mc, though this point looks located at the place somewhat higher than Mc of polymethyl methacrylate.
If the value of {logτm+17.44T-Tg/51.6+T-Tg} is plotted against that of log nw beautiful straight lines are obtained for the data including polyisobutylene, polyvinyl acetate, and polystyrene.
Finally, the dependency of τm on temperatures is studied for polymethyl methacrylate whose slope is unity. For this polymer whose slope is unity, the following equation is obtained.
logτm/nw·As'+C1=C1C2/C2+T-Ts
It is found that the experimental relation between τm and temperature can be on the theoretical line shown by the above equation almost exactly.
• 佐藤 良泰
1963 年 12 巻 116 号 p. 371-375
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
A theory of filler-reinforcement more precise than the previous one1)4)is presented here, based upon the same model and by means of more accurate internal deformation1). Suppose just the same dispersed system with the one of the previous theory where M spherical rigid particles with a radius d are uniformly dispersed in a vulcanized rubber-like substance whose volume is Vr. Then the volume V of the system, the volume ratio X of the filler to the rubbery medium and the volume fraction Y of the filler are given by
V=Vr+M(4π/3)d3, X=M(4π/3)d3/Vr and Y=M(4π/3)d3/V,
respectively.
Let the system be considered as a double network system constructed both from the ordinary network chains spatially distributed in the rubbery medium with volume density gr and from the adhered network chains over the particle surfaces with surface density gf, and let it be considered as our model for the filled vulcanized rubber-like specimens.
The following assumptions used in the previous theory are used here again:
(a) Spherical rigid particles are uniformly disperesed in the rubbery medium.
(b) The movements of the center of each particle under the external deformation accords to the requirment of proportionality (: an affine deformation).
(c) The one-body approximation in terms of“D-sphere”is adopted.
(d) The adhesion state is represented by the“mixing”approximation.
(e) The shape off the surface of cavity assumes the ellipsoid of revolution.
(f) The volume of rubbery medium is kept constant under the external deformation.
(g) The network chains accord to the“deformation theorem”derived from the“internal deformation”.
(h) The assumptions in the ordinary theory of rubber elasticity3) are adopted here except the requirement of proportionality; especially
(α) The network chains are ideal Gaussian.
(β) The free energy of the system consists of two parts: the energy due to entropy of individual chains and the liquid like interaction energy U among the chain segments.
Against the external deformation α which is uniformly in appearance the internal deformation αR is defined as transformation matrix in formally by which any point P of the rubbery medium with a position vector R with respect to the center in the D-sphere transforms to the point P' with a vector R':
R'=αRR. (0)
It is clear that the internal deformation αR must satisfy at least the following conditions:
i)αR=α over the D-sphere,
ii)αR=γ over the d-sphere(: particle is sometimes called the d-sphere),
iii)αR→ α as Y→0,
iv)αR minimizes the deformation energy of the system for the given α.
Here γ represents the deformation of the surface of the cavity occurred around each particle and is assumed as the ellipsoid of revolution of such a shape thatγ12=1, γ3=γ, when the external deformation α is the simple elongation such that α12=β, α3=α(cf. Eq.(6)in the main discourse), and γ is an undecided function of α. Taking differential ΔR' of. R' in Eq. (0) for increment ΔR in R and rewriting asΔR=r, ΔR'=r', the“deformation theorem”of the network chain with end-to-end vector r located at P is derived. as in Eq.(4).
• 関口 直度, 佐藤 良泰, 古川 淳二
1963 年 12 巻 116 号 p. 376-379
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
In the previous paper we compared the mechanical and optical measurement data with the theory concerned with filled vulcanized rubber. Since, in higher concentrated specimens, the isochromatic lines were not clear and moreover the transparency was poor, the optical data could not be analysed in the foregoing study.
In this paper, more transparent specimens have been used and Sato's new theory (which is shown in this issue) based on the more accurate internal deformation is made use of and examined.
The specimens used here are: MgCO3-NR (X=0, 0.052, 0.103, 0.210, 0.318, and 0.415), SiO2-NR and SiO2-SBR (in the latter two X=0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35), where X is the volume ratio of filler to rubber.
The tension σ and the strain birefringence Δn were measured simultaneously, and the apparatus used and the conditions were the same as those in the previous report.
According to the analysis of both data of σ and Δn by means of Sato's theory, the degree of adhesion (1-ζ) decreases from the second time of loading, and also the decrease tends to be saturated in repeated elongations. Since the values of measurement of Δn for the specimens containing SiO2 do not always bear out the theory, we are going to make more accurate and detailed measurement and analysis in future.
• 河合 弘迪, 宮本 喜八郎, 前田 宏, 鈴木 康夫
1963 年 12 巻 116 号 p. 380-384
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
For all numerous studies, the mechanical properties of crystalline polymers have not been well-understood when compared with those of amorhous polymers which have been much clarified theoretically and experimentally. For example, such a fundamental problem as which phase in crystalline or non-crystalline phases contributes to what extent to the deformation processes of crystalline polymers, has been left unsolved.
In this paper, the elastic recovery of a low density polyethylene stretched to various degree of % elongation is explained quantitatively in terms of the response of internal structures manifested by the changes of orientation factors of crystalline and non-crystalline phases and of degree of crystallinity, which are evaluated from simultaneous measurements of X-ray diffraction and of optical birefringence in the stretched and released states.
The sample polymer used is a low density polyethylene (Mitsubishi Yukalon K-3202) having melt index of 3.5 and branched degree of 2.0 CH3/100 carbon atoms, and the original test specimen has been cast from melt into thin film of about 0.2mm thick by a hot press and annealed. The original specimen thus prepared is of a random nature without any preferential orientation of crystal axis.
Within the elastic limit, the elastic recovery of test specimen is accompanied by the complete recovery of orientation factors to 0 either in crystal or in non-crystal phase. From the plastic region just beyond the yielding point, the recovery of orientation factors of three crystallographic axes is not complete, especially, showing such a peculiar behavior of b-axis orientation factor as going from negative to positive value, and not to 0, which might be explained in terms of some preferential collapse of crystal texture. From the plastic region near the beginning of necking the recovery of orientation factors of the three crystallographic axes is still fairly good, from the plastic region near the end of necking (complete of fibre-structure) the recovery becomes very poor, and from the region of strecthed fibre-structure the recovery is somewhat improved, again.
From the plastic regions as classified above the recovery of non-crystalline phase evaluated from the change of the orientation factor of methylene unit is generally better than that of crystalline phase, while from the stretched fibre-structure the recovery is extremely superior.
The elastic recovery of test specimen is also accompanied by the change of degree of crystallinity, usually showing the decrease of the degree with the elastic recovery, except for the regions within the yielding point and of stretched fiber-structure where the degree increases with the elastic recovery in contrast to the above.
• 石田 陽一, 山藤 馨, 島田 晃二, 高柳 素夫
1963 年 12 巻 116 号 p. 385-388
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The relaxation time spectrum of the αa-absorption of the semi-crystalline polymer is broader than that of the amorphous high polymer, which seems not to have been so satisfactorily explained by many theoretical attempts made so far. The assumptions of these theoretical attempts seem not to be supported by the experimental evidence. We, therefore, attempted to find out experimentally the main cause of this phenomenon.
Three possibilities might be considered for the main causes of this phenomenon. The first possibility is the characteristic features of the molecular chain of the semi-crystalline polymer, e.g., the regularity or stiffness of the molecular chain. The second is the network-like structure of the molecular chains in the amorphous part of the semi-crystalline polymer due to the existence of the crystalites. The third is the alteration of the values of the frictional coefficients and the force constants of the molecular chains in the amorphous part owing to the existence of the crystalline part.
The first possibility is, however, not so effective in this phenomenon because the amorphous polyethylene terephthalate, for example, shows the dielectric αa-absorption curve nearly as sharp as that of the usual amorphous polymer. In order to test the second possibility, the molecular chains of polychloroprene were cross-linked by the γ-ray. As a method for testing the third possibility, the effect of blending was investigated. Since polychloroprene and polyvinyl chloride are considered to be nearly amorphous and their glass transition temperatures are far apart from each other, they were respectively adopted as the testing samples. As the segmental micro-Brownian motions of polyvinyl chloride are frozen at the temperature where the αa-absorption of polychloroprene is observed, the frozen chains of polyvinyl chloride are expected to serve as a crystalline-like part to the molecular chains of polychloroprene.
The αa-absorption of polychloroprene was measured with a mutual inductance bridge.
As the result of the dielectric observations, the shape of the αa-absorption of polychloroprene became considerably broader by the blending of polyvinyl chloride although it became not so broad by the cross-linking. We could, therefore, conclude that the first and the second possibilities seem not to be so effective for broadening of the shape of αa-absorption. The third possibility may, therefore, give a proper model for explanation of this phenomenon. Further investigations, however, will be necessary in order to establish a more detailed model for explaining this phenomenon.
• 高柳 素夫, 針間 浩, 岩田 安弘
1963 年 12 巻 116 号 p. 389-394
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
Methods for evaluation of viscoelastic behavior of blends of amorphous polymers from those of component polymers were investigated by model experiments and the limitations of the methods were examined.
It is possible in principle to calculate the properties of polymer blends from those of component polymers for the system consisting of two separate phases. In order to establish the description method for this system, model specimens were prepared by bonding together the films of component polymers of known size, and dynamic modulus E' and loss modulus E" were measured at 138c/s over a temperature range from -170°C to 120°C. The film of polyvinyl chloride (PVC) and that of nitrile-butadiene rubber (NBR) were used as materials of the model specimens. The results of measurements were compared with the values calculated from dynamic properties of component polymers.
Close agreement was obtained between the observed values of E' and E" of various types of model specimens and the values calculated by the equation, in which the volume fraction and the construction form were taken into consideration.
As an example of the two phase system, Cycolac H of Marbon Chem. Co. was studied. Its temperature dispersion curve resembles closely to that of model specimen, which was constructed by putting the rubber phase (NBR) into the plastic phase (PVC). The location of the higher temperature dispersion of Cycolac H, 115°C, accorded with that of the dispersion of a styrene-acrylonitrile copolymer separately measured. The lower temperature dispersion at -185°C was found to correspond to that of polybutadiene. The dispersion curves of Cycolac H were successfully calculated by employing those of the component polymers based upon the two phase simple model.
As an example of molecularly mixed system, the measurements were performed on the specimens prepared from PVC and NBR of various compositions by the solvent casting method with tetrahydrofuran. Of all the compositions, only one main absorption was found at the temperature region between the absorptions of PVC and NBR. The shape of absorption becomes most broad at the intermediate compositions. This broadness is considered to be due to the microheterogeneity in segmental size, corresponding to the varieties of segmental environment. The general expression for this case was presented.
The shape of temperature dispersion curve for the partially miscible system showed an intermediate form between those of the typical two phase system and the molecularly mixed system. The behavior of blends of a styrene-acrylonitrile copolymer and NBR belongs to this type. Observed values for this system were compared with the values calculated on the basis of the typical two phase system of the same compositions. Definite deviations from calculated values were found, which were duly ascribed to the portion of molecularly mixed phase. Broadening of absorptions of both rubber and plastic phases could not be interpreted from the typical two phase model, but only from the consideration of the effect of molecularly mixing.
This circumstances were ascertained by the behavior of the model specimen specifically prepared for this purpose.
• 高橋 勇蔵, 田中 広司, 世良田 弘治
1963 年 12 巻 116 号 p. 395-399
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The tensile stress relaxation behavior of the phenol resin-polyvinyl butyral (PVB) system, varying the PVB content in the system, was investigated at various temperatures above the glass transition temperature of PVB in order to compare it with the dielectric relaxation behavior. Mechanical and dielectric relaxation spectra were obtained from the so-called master relaxation curve found by shifting relaxation curves measured at various temperatures over to reference temperature 131°C, on the basis of the hypothesis of time-temperature superposition.
Applicability of the two shift factors, i.e. aT for tensile stress relaxation and bT for dielectric relaxation, to the WLF-equation was checked by means of a straight-line relationship between (T-T0)//logaT and T for all the specimens employed herein.
When checking the results on the tensile stress relaxation process, existence of two segments of straight lines were observed at the temperature ranges from 110 to 130°C and from 135 to 151°C respectively. Moreover, the temperature dependence of the apparent activation energy during the relaxation process evaluted from the shift factor aT showed two peaks at the foregoing temperature ranges. The peak at the lower temperature range, which may be due to the second transition of PVB contained in the system, corresponds to the dielectric dispersion in α range from 90 to 140°C.
The two shift factors are identical for the specimens of the PVB contents ranging from 60 to 80%, but the mechanical and dielectric relaxation spectra are of very different shape. In addition, the maximum in the mechanical relaxation spectrum is, for each specimen, at a much longer time than the maximum in the dielectric one.
From the results of the check mentioned above, the WLF-equation holds fairly well for the specimens of the PVB contents ranging from 20 to 80% in the case of the dielectric relaxation process, but it does not hold for the specimens under 40% PVB content in the case of the mechanical relaxation process.
It is therefore concluded that mechanical and dielectric relaxation behavior of polymers must be related, since they involve configurational changes of flexible molecules, and also that mechanical relaxation behavior may be strongly influenced by a distribution of effective chain length, whereas dielectric one would not be so much.
• 藤野 清久, 小川 靖雄, 河合 弘迪
1963 年 12 巻 116 号 p. 400-403
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
The mechanical properties of polymer blends depend on the degree of mixing of the blended components. If the blended polymers are poorly compatible or incompatible, which is oftener met in actual and is more significant in modifying the mechanical properties of a single polymer component in a practical point of view, it presents a sort of physically blending rather than a sort of solvation. This common type of blending usually shows the existence of two glass-transition temperatures which correlate, more or less, to the original glass-transition temperatures of each component and suggest that the physically blending leaves homogeneous regions of each polymer component.
In this paper, it is intended to relate the viscoelastic properties of this type of physically blended system of two polymer components to the degree of mixing by using a generalized model representation, as shown in Fig. 2, consisted of n elements coupled in parallel by the volume fraction λ, in which the ith element consists of two polymer components coupled in series by the volume fraction φi.
Considering λi as a function of φi and n as infinite, then the following mathematical relations will be obtained:
E(T)=∫10E(T, φA)λ(φA)dφA (2')
1=∫10λ(φA)dφA (3')
VA=∫10λ(φAAA (4')
and
1/E(T, φA)=φA/EA(T)+(1-φA)/EB(T) (1')
where E(T) is temperature dependence of Young's modulus of the whole blended system; E(T, φA) is that of the element having the volume fraction of A component φA; and VA, EA and EB are volume fraction of A component in the whole system, temperature dependence of Young's modulus of A component and that of B component, respectively.
The degree of mixing, λ(φA) is obtained by solving the integral equation (2') under the additional conditions of Eqs. (3') and (4'), since E(T), EA(T) and EB(T) are measurable functions and thereby E(T, φA) is a known function. It is, however, difficult to solve Eq. (2') analytically, and the equation must be solved numerically.
The degree of mixing λ(φA) of the blended systems of 30/70 butadiene-styrene copolymer and polystyrene varying VA from 0 to 100% is determined from the temperature dependence of E(T) of the blended systems given by Tobolsky. λiAi) determined by the numerical method shows maxima at the extremes of φAi, i.e., near φA=0 and 1, and reveals gradual increase of λiAi≅1) or decrease of λiAi≅0) with increase of VA.
• 白樫 侃, 石川 欣造, G.K. JOARDER
1963 年 12 巻 116 号 p. 404-408
発行日: 1963/05/15
公開日: 2009/08/20
ジャーナル フリー
High speed impact testing is important and necessary, because materials tested at static speed show quite different behaviour in case of high speeds. The impact machine used in this study is a rotary disk type impact tensile testing machine. The diameter of the disk is 1800mm and the thickness is 100mm. The disk is a Ni-Mo-V steel forging, which weighs 2300kg and rotates up to 1450rpm. The speed of the disk reaches 140m/sec when it rotates at 1450rpm, and the sample of the fiber or high polymer is pulled by the jaw at the same speed. The tensile load is measured and detected by strain gauge fixed on the sample holder and the output of the strain gauge is led to the vertical axis of the synchroscope. The horizontal axis of this synchroscope is time axis and is drawn by a single sweeper driven by an outside circuit containing 45 volt.
Various plasticizers such as n-dioctyl phthalate, dioctyl adipate, tricresyl phosphate were added to study their effect on the impact behaviour of polyvinyl chloride sheet. The rolling of the mixture was done in 100-180°C for 10 minutes and the pressing was done for 5 minutes in 105-165°C under a load of 150kg/cm2. The sheet was punched in to the shape of dumbell and used as sample. The effect of degree of polymerization and added amount of vinyl acetate was also studied. The breaking stress of polyvinyl chloride decreases with the increase of the amount of plasticizer and the effect of strain rate is not clear in this case. The breaking stress increases a little while the degree of polymerization rises and decreases when the added amount of vinyl acetate increases. These tests were done at various impact speed from static speed to 2200000%/min. The sample containing different amount of vinyl acetate (8%, 15%) goes through at 1000000%/min, but the sample containing less amount of vinyl acetate shows this maximum at a little higher speed. Young's modulus was determined from the slope of the stress-strain curve. The value of the modulus goes through a maximum at a certain speed and then possesses an equilibrium value. The breaking energy of P.V.C. containing large amount of plasticizer is much greater at static speed, but the sample containing no amount of plasticizer shows a greater value at high impact speed. At impact speeds all the crossections of the broken samples are perpendicular in respect to the main axis of the sample. The extension of the sample was measured by giving standard marks at an interval of 1.28mm and the distance between these marks were read after impact tests. The result shows that the sample containing less and no amount of plasticizer do not extend at different speeds but the sample containing more amount of plasticizer extend more at static speed and less at high speed. This shows easiness of plastic flow at high speed. At a certain speed the value of extension drops sharply and this speed shifts toward higher value when the amount of plasticizer increases. The decrease of cross-sectional area is less in case of high speed. The critical velocity measured from the stress-strain curve drawn at impact speed shows that it increases with the addition of plasticizer and its value was compared with that of textile fiber. The propagation of plastic wave was also determined.
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