Hereunder is presented a resume of the author's recent work on hemorheology. The problem concerns in the first place the influence of the plasmatic zone upon the relationship of the quantity of blood and its pressure flowing through minute vessels. When blood is regarded as a Bingham body with plastic viscosity ηB and yield value fB, the pressure-flow relationship is given in eq. (6) as P>pB/γ and in eq. (8) as P<pB/γ, where ξ=pB/P, pB=2LfB/R and γ=1-(δ/R). Here δ is the thickness of the plasmatic zone, R is the radius of the vessel, and P is the difference in pressure between two cross-sections at distance L. Similar pressure-flow relationships (11) and (13) were also obtained of the blood obeying Casson's equation with Casson viscosity ηc and Casson yield value fc. The problem concerns in the second place the flow behavior of blood in capillaries with permeable walls. Blood is regarded, for simplicity, as an incompressible Newtonian fluid with viscosity η, and an approximate solution of Navier-Stokes equation was obtained under the boundary conditions u=0 and v=k(p-α) at the wall. Here u and v are respectively the axial and radial component of velocity, p is the hydrostatic pressure, k is the permeability coefficient and α is a constant. Starling's law was assumed with regard to filtration and reabsorption of water. The streamlines are shown in Fig. 9. It is shown that the flow Q becomes minimum at a distance LΔα/Δp from the arterial end of the capillary, where L is the length of the capillary, Δα=pa-α and Δp=pa-pv. Here pa and pv are respectively the pressure at the arterial and venous end of the capillary. In case where filtration and reabsorption of water balance, Δα/Δp must be equal to 1/2, that is, α=(pa+pv)/2. The problem concerns lastly the circumferential tension T in a thick-walled blood vessel. The tension is given in T=p1r1'-p2r2', where r1' and r2' are respectively the inner and the outer radius of the vessel under the internal pressure p1 and the external pressure p2. The formula holds quite generally, irrespective of whether the wall is homogeneous or inhomogeneous, whether the wall is isotropic or anisotropic, whether the elasticity of the wall is Hookean or nonlinear. The distribution of the circumferential stress τ in the wall with Hookean elasticity was discussed in detail on the basis of classical theory of elasticity. It is shown that τ is not always positive throughout the wall even if p1 is greater than p2. Three cases actually occur: (a) τ is always positive throughout the wall, (b) τ is positive in the inner region, while it is negative in the outer region, and (c) τ is always negative throughout the wall. Introducing non-dimensional parameters difined by k=p1/p2 and s=r2/r1, sk-plane (s>1, k>1) can be divided by two curves k=(1+s2)/2 and k=2s2/(1+s2) into three regions A, B and C which correspond to the cases a, b and c, respectively. It is clear that the circumferential tension T is not always positive in more general cases.
We have been studying rheological properties of crystalline high polymers under high pressure for several years. Among the results of these studies the following topics will be worth attention: (1) The finding of the crystalline dispersion, of the grain-boundary dispersion and of the main dispersion in polytetrafluoroethylene. (2) The rheological properties of phase transition in polytetrafluoroethylene and trans-1, 4-polybutadiene. (3) The rheological properties of high pressure phase in polytetrafluoroethylene.
The necessity as well as possibility of application of polymer rheology to rubber technology was first discussed, mainly occasioned by the research for development of new rubber products. The most effective and economical testing methods and standards were suggested therein as workable in practice. Adopting the theory of linear viscoelasticity, the time-temperature superposition principle, the factorization of the time-and strain-dependences of stress at large deformations, the qualitative similarity between the dynamic and the steady-flow viscosities, the qualitative similarity between the failure envelope and the isochronal stress-strain curve and others as the working hypotheses, a set of material functions was newly proposed. Those were the relaxation spectra, the nonlinear factor for the elasticity, the strain-at-break vs. temperature diagram and the shift factor as a function of temperature, and they are tabulated in Table I in the text. The analytical expressions of those material functions are here presented, listed also in Table II. Twelve material parameters involved in those expressions are summarized in Table III, and this rheological model is named as the "JSR 12 constant model." An approximate method of formulating each item listed in the present testing standards as a function of those material parameters and the parameters describing the excitation factor is recommended, and the significance of this type of study is stressed. The expression of the heat buildup with a Goodrich flexometer is given as an example and the result of the application of this expression to the experimental data on various sample specimens is illustrated in Fig. 1. The importance of correlating quantitatively the material parameters with the parameters characterizing the internal structure of the material is emphasized herein from an industrial point of view and also in consideration of the present situation. An illustration is given in Fig. 2 of the relationship between the two material parameters, n and λbmax, which are supposed to have the same molecular structural origin. Finally, the estimation of optimum values of rubber products including unvulcanized synthetic rubbers are discussed with respect to the material parameters of each species. After reviewing the history of rubber industry, it will be expected that the optimization of products in quality in the market at present in general will proceeds to a considerably high degree. This expectation is experimentally verified when the commercial products from different factories are compared with respect to the shapes of the material functions of particular species where all their curves fall within a band of fairly narrow width irrespective of their chemical composition or of any other physical factors. The results of this experimental verification are demonstrated graphically in the relaxation spectra of various commercial synthetic rubbers in Fig. 3 and also in the strain-atbreak vs. temperature diagrams of the tread portions of automobile tires (Passenger car) from different factories in Fig. 4.
A supplementary calculation is hereunder presented which was made to the preceding investigations5)-7) treating the hydrodynamic behaviour of rod-like particles in Poiseuille flow by using the Oseen-Burgers formula. It has been theoretically shown that the particles are to migrate radially from the tube axis to the wall, due to its bending deformability. There remain some problems, however, that must be made clear in these treatments. The two outstanding problems are as follows: (1) An approximation used to solve the Burgers-type integral equation is mathematically too rough. (2) The direction of the migration is against what is observed in the laboratory. The first problem can be overcome by regarding the particles as prolate spheroid instead of cylinder. In this case the integral equation is to be solved to the extent of the error of the square of the short-/long-axis ratio of the spheroid. For the second problem, a study has been made on the effect which may have been caused when the curvature becomes large for an infinitely thin rod. It seems to be more important, however, to take the deformation velocity of the particles into account.
When blood flows through capillaries, exchanges of various substances, particularly of water, take place across the capillary wall. It is interesting to consider the influence of the exchange of the fluid across the wall upon the motion of the fluid within the capillary. A hydrodynamical theory of steady slow motion of blood through capillaries with permeable walls is hereunder presented. It is assumed that the exchange of fluid across the capillary wall obeys Starling's hypothesis, M=k(p-α), that is, the rate of flow M per unit area of the wall surface is proportional to the difference between the pressure of the fluid within and that outside the capillary. It is further assumed that the filtration constant k is very small, that is, ε=kη/R<<1, where η represents the coefficient of the viscosity of blood and R the radius of the capillary. Blood is regarded as homogeneous Newtonian fluid. The following expressions have been obtained for the velocity and pressure distributions within the capillary and the volume of the fluid flowing per unit time across the cross section of the capillary. with where u and v represent respectively the longitudinal and the radial component of the velocity and L the length of the capillary. The constants pa and pv represent respectively the arterial and the venous pressure.
With a view to obtaining mathematical bases for microcirculation of plasma with filtration or reabsorption the Stokes equations for steady, axisymmetric creeping flow have been applied to a Newtonian fluid flowing through a straight, uniform tube of circular section with permeable walls. As a boundary condition Starling's law is adopted, which states in mathematical version that the velocity component normal to the wall is assumed to be a linear function of the local hydrostatic pressure. It is required that if a dimensionless parameter ε=2ηκ/R (η: viscosity of the fluid, R: radius of the tube, κ: filtration constant) vanishes, the solution will be reduced to the basic Poiseuille flow with a constant pressure gradient. In fact, ε is so small that the radial component of the fluid velocity veries linearly with the axial distance, as is seen from the boundary condition. The solution of the Stokes equations to meet this requirement can be derived in a simple form. The relation between the volume flux through each section of the tube and the pressure gradient is also easily obtained. Although this solution yields a flow pattern with non-vanishing velocity component tangential to the wall, this slip flow is understood to occur in consequence of the penetration.
Hereunder is presented a consideration on the theory of distribution of vertical stress in powder piled in a cylindrical vessel in a state of equilibrium. The same problem was treated by Janssen, but his theory was based on the assumption that vertical stress was constant on a horizontal plane. On the other hand, experimental studies show that vertical stress in powder in equilibrium in a cylindrical vessel does not remain constant on a horizontal plane, but changes according to the distance from the axis of the cylinder. As far as we are informed, no theory has yet been developed dealing with the variation of vertical stress with the distance from the axis of the cylinder. We have developed a theory on distribution of vertical stress, taking into account its variation with the distance from the axis of the cylinder. It is assumed that both the vertical stress and the horizontal stress are connected by Rankine's law. But in the theory proposed under this assumption the possible effect of compression is neglected. From the condition of powder in equilibrium an equation has been derived to determine the vertical stress as a function of both the distance h from the free surface of powder and the distance ξ=r/R from the axis of the cylinder. A solution has been found in taking the vertical stress as expressed in Taylor's series in ξ. The boundary condition at the free surface is so chosen that the total pressure over the free surface is equal to zero. It is shown that our theory agrees fairly well with the experimental data by taking the product of Rankine's coefficient and the frictional coefficient of the wall as appropriate value.
Extrusion of high density polyethylene (PE) in solid state was carried out successfully with a cylinder-and-ram type device at the temperatures from 70°C up to 110°C, which corresponded with the temperatures of the region of viscoelastic crystalline dispersion. Large plastic deformation proceeded smoothly, and the cross sectional area of the extrudate was 1/16 of the original. The factor of 16 can not be realized by ordinary cold or hot drawing process of PE in solid state. Polymer crystals in the extrudate and also in the sample chips in the die hole were highly oriented. The crystal c-axis are in parallel with the extrusion in its direction. The degree of orientation was uniform in the cross section, suggesting that the movement of the solid polymer in the die hole was almost at the same velocity at the center of the hole as at the wall side. The dimensional stability of the extrudate against temperature change was remarkably high compared with the ordinary drawn PE. The extrudate did not shrink below 100°C, whereas the ordinary drawn sample highly shrank at 60°C. Another feature of the extrudates was its being highly transparent in appearance.
The following is the report of the studies that were made of applicability of Graessley's theory for the Non-Newtonian viscosity to polythyelenes and polypropylenes which have very broad logarithmic-normal distributions of the molecular weight. The relationships between the viscosity and the shear rate of the samples were measured by a cone-and-plate viscometer and a gas operated extrusion type rheometer for about four decades of shear rate, at 190°C. The functions of molecular weight distribution were determined by the column fractionation technique. Considering a maximum molecular weight for the distribution function, the experimental relationship between the viscosity and the shear rate for polymers having a wide range of molecular weight distribution including a fruction showed on excellent agreement with the theoretical prediction of Graessley. The molecular relaxation time of entanglement was found to be proportional to the product of the zero shear viscosity and the weight average molecular weight which justified the use of the Rouse-Bueche type relaxation time for the entanglement relaxation time, although the absolute value of the latter seemed to be about one decade smaller than the former.
By means of a high pressure rheometer designed to study the viscoelastic behaviour of polymeric liquids under high pressure, the viscosity of polystyrene (Mv; 1.88×105) solutions in toluene was measured over a wide range of concentration (c: 0.03-0.50) under various pressures up to 900 kg/cmcm2. The effects of pressure on the viscosity and critical concentration were discussed. The effect of pressure on the viscosity (logηp/ηo) above critical concentration cc was shown to increase with the increase of the concentration. Below cc, this effect was similar to that with the solvent and independent of the concentration. The log(ηp/ηo) was proportional to Pn. It is evident that these results can be described by combining the empirical equation and the viscosity equation proposed by Onogi. It is found also that cc is slightly shifted to lower concentrations with the elevation of pressure.
In recent years the finite element method is more and more frequently being used in the analysis of elasticity, of plasticity, of elastoplasticity and of structure. In the analysis of viscoelasticity, however, the time required for the purpose and temperature dependency make it difficult to use the method. It is the purpose of this paper to show that the correspondence principle can be applied to the solution of problems concerning linear viscoelasticity by using the finite element method. But there are many problems in connection with solution of elasticity that are algebraically too complicated to be readily inverted by the formal inversion method. R. Bellman proposed a method for approximate inversion of the Laplace transform which involves the idea of dynamic programming. The method was partially adopted in this paper with necessary modification, and considerably accurate numerical solution has been achieved.
The stress relaxation properties of SBR vulcanizates, those unfilled and those filled with carbon, under orthogonal-biaxial deformation, were subjected to observation in a region from 3.4 to 10 of I1 values where I1 was invariant of deformation tensor, and the contour maps of ∂W/∂I1 and ∂W/∂I2 were obtained as functions of time t. The following results have been obtained. The time dependence of both ∂W/∂I1 and ∂W/∂I2 of the unfiilled SBR vulcanizate are very similar within experimental error, but in the case of the filled SBR, those are quite different. In the filled SBR, the relaxation rate of ∂W/∂I1 decreases with increase in I1, and on the contrary, the rate of ∂W/∂I2 increases with increase in I1. The shape of ∂W/∂I1 surface of the filled SBR is similar to that of the unfilled SBR, but the former is on a considerably higher level than the latter, while the shape of ∂W/∂I2 surface of the filled SBR is different from that of the unfilled SBR. The values of ∂W/∂I1 and ∂W/∂I2 in the uniaxial deformation are obtained by the extrapolating method using the biaxial data. It is shown that the values of ∂W/∂I1 and ∂W/∂I2 in the uniaxial deformation decrease with increase in deformation. In this fact is suggested that strain energy function W cannot be estimated by Mooney-Rivlin plot, and that the constants C1 and C2 obtained from the plot are almost of no significance.
From the phenomenological theory of finite deformation, a stress-strain relation was obtained with a second order approximation to the stored energy function w with higher degree accuracy than that shown by L.R.G. Treloar or R.S. Rivlin. In the phenomenological theory of large elastic deformation, the stored energy function w can be written in terms of three strain invariantes I1, I2 and I3, and one way of expressing this is in terms of power series: (1) where I1=α12+α22+α32, I2=α12α22+α22α32+α12α32, I3=α12α22α32 and αi, (i=1, 2, 3) are the principal extension ratios. If the principal extension ratios α1, α2 and α3 are small and assumed to be nearly in unity, the second order approximation to the expression (1) for w will be given as follows, in the case of incompressible materials (2) because the squared term (I>1-3)2 is equivalent to the term (I2-3) through the principal extension ratios, from the view-point of the second order approximation. From this type of the stored energy function, the following stress-strain relation has been obtained (3) for the case of simple extension or uniaxial compression defind by the extension ratio or the compression ratio α, where A≡2(c100-6c200), B≡2(4c200+c010), C≡4c200. Upon comparing the resulting stress-strain relation with the experimental stress-strain behavior, it seems that this relation is valid for rubber vulcanizates, and even for larger deformations to which the assumption that deformations are small (α«2) is inapplicable, and that this relation almost coincides with the observed stress-strain relation in the extension range wider than that predicted by Mooney-Rivlin equation.
In the preceding paper1), a report was made of the study enactted by one of the authors of the stress-strain relation that was obtained from the phenomenological theory of finite deformation. So far as the incompressible materials were concerned, the relation was written as follows: (1) where f denoted the tension at extension ratio α, A, B, and C were constants. In this paper, the applicability of the Eq. (1) to the stress-strain behavior of styrene-butadiene rubber (SBR) and butadiene rubber (BR) was tested, and the temperature dependences of the values of A, B, C were examined. This is, however, only a preliminary examination, because the data discussed in this paper were determined while making the study of fracture phenomena, and little attention was paid to attaining equilibrium state in obtaining the data. SBR and BR were both cured with tetramethyl thiuram disulfide and contained 5 parts of zinc oxide and 2 parts of stearic acid per 100 parts of rubber. The stress-strain data were determined by means of an Instron type tester at various temperatures between-40 and 120°C at a crosshead speed 50mm/min. It was found that at temperature over 30°C, fracture occurred at low extensions (α>3) and Mooney-Rivlin equation (Same tipe equation as Eq. (1) where C=0) was in agreement with the data over 30°C, and that at temperatures below 30°C, the experimental stress-strsin relations almost coincided with the relation of Eq. (1) in the extension range α<4.5, while Mooney-Rivlin equation coincided with the data only in the extension range α<3. It was found also that the values of A for SBR and BR showed almost linear increase with temperature above 30°C, the values of B and C decreased with increase of temperature and C were almost 0 for the data above 30°C.
For the purpose of investigating the mechanical properties of vulcanized rubbers under finite deformation, three kinds of NBR (Butadien-Acrylonitrile copolymer) vulcanizates of different degree of crosslinking were prepared, and their stress relaxation behavior under orthogonal biaxial deformation was observed. The results were compared with those of NR (Natural rubbuer). The results are as follows. (1) It has been ascertained that engineering stress f1 and f2 under single step biaxial deformation (λ1, λ2) at t=0 can be expressed in such a simple form as, and consequently It has been found that the above relations are not valid in strict sense and that fi should be written as and that φi depends on λi more than λj(i, j=1, 2., i≠j). (2) The contour maps of ∂W(I1, I2, t=1.0min.)/∂Ii have been drawn by the method mentioned previously1). The nature of the slope of the surfaces are similar to those of NR at relatively small deformation region in (I1, I2) plane. But, with increase of I1+I2, the contour lines of ∂W/∂I1 and ∂W/∂I2 are respectively oriented in the directions of I1 axis and I2 axis more sharply than those of NR. On the other hand, the dependency of ∂W/∂Ii surfaces on the degree of crosslinking has a typical property in that the surfaces come down with vertical shifting by decrease in the degree of crosslinking. This dependency is different from that of NR as mentioned previously. (3) A postulation for W[W=w(λ1)+w(λ2)+w(λ3)] proposed by Valanis and Landel2) are found to be satisfactory in predicting the true stress σ11-σ23 and σ22-σ33 by using ∂W/∂λ which can be determined by strip-biaxial data with the use of the above postulation. However the values of ∂W/∂Ii have not been predicted with reasonable accuracy from the ∂W/∂λ. This results are discussed in detail in this paper.
The molecular theory of filler reinforcement which was previously proposed by one of the authors (Y.S.) has been applied by extension to the analysis of the mechanical properties of polymer blends. Almost the same model has been used in the present experiment of the theory of filler reinforcement as those which were used in the previous experiment of the theory of the same, and almost the same assumptions are made for the present theory as was made for the previous theory, except that the dispersed spherical particles are rigid, because the spherical particles dispersed in polymers as demonstrated in the present theory are no longer to be necessarily designated rigid, but only deformable bearing the rigidity G0. Of the blend of two kinds of polymers with rigidity G and G0, the stress-strain relation of simple extension is obtained as follows where σ denotes the tension at extension ratio α, Y and (1-ζ) denote the volume fraction of the dispersed polymer and the degree of adhesion, respectively, and K is the ratio of the surface modulus to the volume modulus and is a parameter expressing the surface effects, φ is the ratio of the volume of the sample before and after deformations, γ1 and γ represent the deformation of the inner surface of the medium facing the dispersed particles in the direction of extension in a perfect adhesion state and an actual adhesion state, respectively, γ1' and γ' represent the deformation perpendicular in the direction of extension in perfect adhesion state and an actual adhesion state, respectively. Upon this relation, it has been examined theoretically how Y or X (Volume ratio of two polymers), (1-ζ) and K will affect the stress-strain behavior of polymer blends. The two cases of blend system have been considered; the system composed of two kind of polymers in which a polymer medium with rigidity of 2.5 includes softer polymer particles with rigidity of 1.25, and harder polymer particles with rigidity of 5.0. The results show that in the case of a perfect adhesion state, the calculated tension σ for both the systems increased with increasing α and X, while in the case of a perfect non-adhesion state, σ increased with α but the rate of increase changed at an extension ratio of about 1.5 or 2.0 and decreased with increasing X. It was also found that σ was fairly sensitive to the change in the value of K.
To determine non-linear viscoelasticity parameters for disperse and high-polymeric systems, the fundamental relations have been derived between these parameters and the experimental quantities by viscoelastometry, particularly with a torsionally oscillating rheometer, on the basis of the general theory presented by Green and Rivlin. The non-linear viscoelasticity of several disperse systems consisting of polystyrene solutions and carbon black has been measured by means of the torsionally oscillating rheometer at various temperatures ranging from 100 to 220°C and in a frequency range from 4×10-3 to 0.5 cycle per second. As a result of the harmonic analysis of the experimental results, it has been revealed that the resultant torque consists of the fundamental component and odd harmonics, and that the energy dissipated during one cycle is the same as that calculated from the fundamental component alone. The frequency dependence curves at various temperatures for G1' and G1", which correspond to G' and G" for linear viscoelastic materials, can be superposed into master curves by horizontal and vertical shifts. The master curves manifest a plateau lower than the ordinary rubbery plateau on the low frequency side.
It is shown that anisotropic absorption or dichroism due to molecular orientation can be discussed in terms of optical rotation recorded by means of a spectropolarimeter. When a polyvinyl chloride (PVC) film containing anthracene is stretched, an optical rotatory dispersion curve is obtained at various degrees of elongations corresponding to the absorption spectrum of anthracene (Fig. 2 and 5). The optical, rotatory power α° at the characteristic absorption frequency is related to the anisotropic optical densities, A// and A⊥, respectively in parallel with and perpendicular to the line of stretching as follows, (1) where D is called “dichroic difference”. Taking θ as an average angle between the stretching direction and the transition moment of the absorption band, the orientation function F is given by the relation, (2) Thus the values of F and θ can be estimated from the experimental values of α and A// or A⊥; the latter two are obtained by the polarized spectra of the stretched film. The orientation function of PVC is obtained by the polarized infrared spectra and compared with that of anthracene at respective degrees of elongation.
The strain-optical coefficient and relaxation modulus were simultaneously measured of high density polyethylene at various temperatures ranging from 12 to 100°C. Not only the horizontal but also the vertical shifts Were necessary to obtain smooth master curves by application of time-tem perature superposition. However, the relaxation modulus decreases with rising temperature, While the strain-optical coefficient increases, indicating that the variation of the relaxation modulus and the strain-optical coefficient with time can not be explained by decrease in crystallinity With rising temperature, since decrease in crystallinity usually causes decrease in the strain-optical coefficient. It is required that some other explanation will be sought for the vertical shift in the time-temperature superposition of the time-dependence curves of the relaxation modulus and the strain-optical coefficient at various temperatures. The master curve of the strain-optical coefficient or the optical distribution function of relaxation times determined from it serves to distinguish the type and thermal history of the polyethylene.
To find out the true causes for the increase in birefringence and the decrease in relaxation modulus for high density polyethylene with rising temperature, measurements were made of the changes in its crystalline structure as well as in its thermal, viscoelastic, and rheo-optical properties with temperature, employing several techniques such as DSC, DLI, infrared dichroism, X-ray diffraction, NMR, and so on. The values in degree of crystallinity obtained from the DSC fusion curve, density, and IR absorbances coincide very well, and show almost no divergence till about 80°C. The optical vertical shift factor pT can be related to the ratio of the orientation function for the crystal c-axis at an arbitrary temperature to that at the reference temperature, fε/fε0. The mechanical vertical shift factor bT, on the other hand, is associated with the variation with temperature, not of the degree of crystallinity, but of the mobility of molecular chains as determined by the NMR technique.
Temperature change of polycarbonates under tensile loads was measured, respectively in static tension and in pulsating tension. In the former case, the specimen began to rise in temperature when viscoelastic strain became appreciable on the stress-strain diagram. The rise θV could be formulated as a function of the viscoelastic strain εV, In fatigue tests, the average temperature began to rise immediately after the decrease due to thermoelastic effect. The amount of the heat generation, α, was constant for each cycle throughout the fatigue process and has a relation to the fatigue life, Nf, where a is another adjustable constant. From the rheological aspect of dissipation energy, the equation is transformed to a relation between the viscoelastic strain and the fatigue life as which is similar to the one for metals given by Coffin and Manson. The temperature rise in fatigue was also related to the viscoelastic strain. The relation was of the same form as in static tension but with value of the factor one order less.
In order to investigate the interaction between the ingredients of toothpaste, we measured the rheological properties of toothpaste using the Brookfield Synchro Lectric Viscometer. And we found that: (1) At low shear rate, the relation of shear stress versus shear rate in toothpaste has been obtained in general form of the well-known Williamson's empirical equation for pseudoplasticity. Here G is the shear rate. η* represents the limiting viscosity of toothpaste at G→∞. η* does the viscosity of toothpaste at G. The C1 and C2 are the constants. As can be seen from the equation form, the viscosity of toothpaste consists of sum of the first term which is independent of shear rate and the second term which decreases with increasing shear rate. The second term indicates the viscosity by structure. We take C1 to be the magnitude of contribution to the structural viscosity. So we attach no small importance to C1. (2) The rheological properties of suspensions are generally determined by the property of dispersing medium and the volume of concentration of the dispersed phase. We varied the property of the dispersing medium by varying the concentration percentage and kinds of Na-CMC. We varied also the volume concentration of the dispersed phase by varying the volume fraction of Dicalcium phosphate dihydrate (DCPD). First we measured C1 with modified Na-CMC in concentration percentage and kind. When C1/N is plotted as a function of concentration of Na-CMC (N), a straight line is obtained. Thus we have obtained the following empirical equation a, b are constant. The constant a is greatly variable according to the kinds of Na-CMC used. We think that it has been caused by the nature of Na-CMC. We think also that it is based on the difference between D.P. and D.S. Na-CMC is difficult to dissolve in water with increasing D.P. and decreasing D.S.. We have introduced D. P./D. S. to know the solubility of Na-CMC, and found that the constant a is proportional to D.P./D.S.. We have also determined the constant a by varying the concentration percentage of glycerine. We have found that the constant a indicates the measure of interaction between the Na-CMC molecules, because the entanglement of Na-CMC is proportional to the solubility of Na-CMC. (3) We have measured C1 by varying the volume fraction of powder (φ). When log C1 is plotted as a function of the volume fraction of (φ), two straight lines of volume concentration are obtained, locating the critical point with the larger slope of the straight line beyond it than below it. When the concentration percentage of Na-CMC increases, the position of the critical point is shifted to enlarge the side of the higher concentration of φ. It is thought that the structural viscosity of toothpaste is mainly the result of the network of Na-CMC below the critical point, and is as mainly the result of interaction of the powder beyond the critical point.
A sensitive rotational viscometer with concentric double cylinders has been constructed, which makes it possible to measure the viscosity of blood at very low shear rates below 1sec-1. An outer cylinder is rotated by a d.c. motor coupled with a reduction gear. The speed of rotation of the cylinder is detected by a tachometer and is led to an X axis of an XY recorder which indicates the shear rate in the liquid. The torque due to the viscosity of liquid is detected by the deflection of a mirror attached to the suspended inner cylinder. The voltage induced in the phototube is amplified and the resulting d.c. current is introduced to the coil, placed in a magnetic field and attached to the inner cylinder, in order to balance the defection of the inner cylinder to null. The output current from the d.c. amplifier is led to a Y axis in the XY recorder, which indicates the shear stress in the liquid. The flow curve of the liquid is thus recorded in a few seconds with gradual increase or decrease of shear rate. The limit of measurable torque was approximately 0.1 dyne-cm. With ascending and descending shear rate in a range below 1sec-1, a hysteresis curve of blood with hematocrit 79% was observed as illustrated in Fig. 2. The descending curve indicated a steady flow curve and yield value was observed to exist at zero shear rate. If the rotation of liquid was raised in about a second up to a very low shear rate below 1sec-1 and sustained at that shear rate, the torque gradually increased to that indicating the shear stress in the steady flow condition, after passing through a maximum during the transient period. The gradual increase of the shear stress has been probably caused by the occurrence of viscous flow following the initial elastic deformation of liquid, which takes place under a stress below the yield value. The transient maximum of shear stress may be produced by the nonuniform packing of blood cells subjected to shear stress. When the disturbing vibration was given to the outer cylinder without affecting the sensitivity of torque measurement, both yield value and steady flow viscosity of blood decreased. The coagulative structure of blood cells must have been disrupted by the vibration. No hysteresis was observed in Newtonian liquids such as water, oil and glycerin. A marked hysteresis and a transient variation of shear stress were observed in aqueous dispersions of cocoa. It is considered that this kind of phenomenon is commonly observed in coagulative dispersions.
The ultrasonic absorption of polymer solution was measured by the pulse method over 5Mc-45 Mc within the temperature range from -45°C to 30°C. Samples were prepared of polyvinylacetate, polymethylacrylate, and polyvinylchloride. Polyvinylacetate samples were mostly the subject of discussion in this paper. The solvents were 1, 2-dichloroethane, cyclohexanone, toluene, acetone, and methanol. The concentration of solution was from 1g/100c.c. to 7g/100c.c., From the curve which was plotted of absorption coefficient divided by square of frequency (This quantity is represented by α/f2, where α is absorption coefficient and f is frequency.) against the logarithm frequency, the relaxation phenomena were observed in all the solutions. When α/f2 was plotted against temperature, this curve exhibited a maximum in various P.V. Ac. solution. The position of this peak does not depend on the concentration. But the peak of the curve shifts toward the higher temperature at higher frequency. It is thought that the relaxation means thermal relaxation. Then temperature-frequency superposition is to be discussed. Shift factor at was determined by the usual method. The curve of shift factor versus temperature was compared with W.L.F. equation. The result of the experiment is in good agreement with the theory. Next, the concentration dependence of α/f2 was discussed. Using the assumption of additivity of α/f2 between solvent and solute, the quantity α2/f2 (Apparent ultrasonic absorption of polymer) was calculated from the slope of the curve of α/f2 versus concentration. From the results, it is concluded that α2/f2 is independent of solvent within the error of experiment. Finally, the assumption of single relaxation was discussed as was made in the conclusion by Bauer et al. and Miyahara et al. in the polystyrene solution. The relaxation frequency, used in the assumption of single relaxation theory, was determined by the I.B.M.-1620 computor. The temperature dependence of hypothetical relaxation frequency was divided into two parts of P.V. Ac. solution. One part was like a single relaxation (0°C-20°C). The other part did not depend on temperature (-40°C-0°C). It is considered that the relaxation observed in P.V. Ac. solution was multi-relaxation.
The theory of elasticity of vulcanized rubber treats its network as statistically homogeneous. It should be noticed that the vulcanizates with the same crosslink density show different mechanical strength when different vulcanizing agents and conditions are used. This fact is often interpreted as due to the difference in the chemical structure of the crosslink or that in the distribution of the crosslink density. In this paper, we have taken up the latter problem. The observation of the texture was made with electron microscope, and the measurement of viscoelasticity in its primary absorption was made to discuss the effect of the microheterogeneity on the absorption shape. The samples are natural rubber (NR) and cis-1, 4-Polybutadiene (BR). Electron micrographs were taken on the ultrathin sections of the rubber vulcanizates embedded in PMMA and stained with osmic acid. Electron micrographs of sulfur vulcanizates of NR showed homogeneous texture independent of the cure time of 40-120min. In the case of BR, 40min sulfur vulcanizate showed comparatively homogeneous texture, but 120min vulcanizate showed remarkably heterogeneous texture. About 50Å diameter particles of highly crosslinked regions appeared as an aggregate with a few hundred Å composed of. With increasing cure time, the contrast of the image increased in BR. With increasing sulfur content, highly crosslinked regions of about 200Å diameter were dispersed like filler. In contrast to the sulfur vulcanizates, the γ-ray irradiated BR showed remarkably homogeneous texture in its electron microscope image. The viscoelasticity in the primary absorption regions was measured by Vibron DDV-II. The curve of tanδ vs. temperature was analyzed under the assumptions that the lower temperature side of tanδ peak was expressed by single relaxation model and the temperature dependence of relaxation time was represented by Arrhenius type equation. According to these assumptions, tan δ vs. 1/T curves of sulfur vulcanized rubber were divided into absorption I and II from the lower temperature side. The tanδ vs. 1/T curve of BR showed an unsymmetrical shape broadened more than that of NR. The shape of tanδ curve of absorption I was analyzed to agree with that predicted by the single relaxation time model. The magnitude of absorption II of BR increased with increasing cure time and sulfur content, but that of NR did not increase with cure time. The γ-ray irradiated BR showed only absorption I and its shape was perfectly symmetrical. Absorption II was concluded as characteristic of sulfur vulcanizate and its appearance was closely related to the microheterogeneity of the vulcanized texture revealed by the electron microsope.
Hereunder is presented a report of an experiment made of polymethyl methacrylate films that were stretched to a predetermined length at 140°C in a silicone oil bath, and kept at the temperature, until the stress relaxed adequately. The temperature was then lowered stepwise, leaving the films at certain fixed length. At each temperature the sample was kept for about 30 minutes. Observations were enacted of various specimens with different extensions with respect to their reversible stress vs. temperature relations; the glass-rubber transition temperature decreased linearly with increasing extension (102°C and 98°C for 16% and 120% extension, respectively). The volume of the specimens increases slightly with stretching, and this could be interpreted reasonably by considering that the configurational entropy should be frozen at a constant value in glassy state; it relates to the number of 'holes' in the system. The film held at constant length was cooled to room temperature below Tg, then the stress was removed; its length almost remained unchanged. The specimen thus obtained was heated in the bath, and the length vs. temperature relation was measured. It began to shrink abruptly at the transition temperature and the length changed irreversibly to an equilibrium value. The transition point varied more rapidly with extension than that in the reversible stress vs. temperature relation (106°C and 97°C for 16% and 120% extension, respectively, at a heating rate of 1°C per minute). It depends on the heating rate; the slower the heating, the lower the temperature is. The time effects on the recovery were measured at various temperatures in the transition region for 5% and 40% extended samples. The isotherms were closely superposable by horizontal shifts. Temperature dependence of the logarithmic shift factors (logaT) was in fair accord with the WLF equation for the temperature range below 115°C, but diverged from the equation at higher temperatures. In case the specimen with previous history was fixed at constant length and heated, no stress was observed in the temperature range below Tg. The stress due to thermal shrinkage was observed, however, at several degrees above the transition temperature; the value increased and the temperature where it appeared decreased with increase in the extension. The time effects were also measured of various extensions in this case, but they behaved in very complicated manner. The mechanism of the thermal stress could be explained qualitatively based on a thermodynamic consideration.