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Viscoelastic properties of concentrated solutions of a mixture of three- and four-branched polystyrenes were measured by means of a concentric cylinder type rheometer. The Vogel parameters, αf and T0, were calculated from the temperature dependence of viscosity and the shift factor aT. From the frequency dependence of the storage shear modulus G′ and the loss modulus G″, the characteristic parameters in the terminal zone such as zero-shear viscosity η0 and steady-state compliance Je0 were evaluated. The dependence of these parameters on concentration was compared with that of concentrated solutions of linear polystyrenes. The concentration dependence of η0 for star polymers is very similar to that for linear ones. However, Je0 for the mixture of three-and four-branched polystyrenes showed unusual behavior that was quite different from that of linear polymer and monodisperse star polymer. The entanglement compliance is also discussed.

New criteria for testing integral constitutive equations are proposed. The constitutive models studied are generalized models with stress‐, strain‐, and rate‐dependent memory functions, as well as the BKZ and Bogue‐White (BW) models. On the basis of these models, the critical relations for the test of constitutive equations are derived for five types of experiments: single‐ and double‐step stress relaxation under finite shear strain, stress overshoot, interrupted flow, and stress relaxation after cessation of steady shear flow. Among the models examined in this study, the predictions as to the time‐dependent stress or relaxation modulus in single‐ and double‐step stress relaxation are quite different, and therefore these relaxation experiments are very useful for testing the models. The Van Es‐Christensen function is monotone increasing in time for strain‐dependent models as well as for rate‐dependent models. On the other hand, it is possible that the function overshoots for the stress‐dependent model. Ne...

A new kinetic theory has been proposed in which the formation of structure is assumed to take place in two processes. Combining structural parameters of the model with the viscosity, the variation of shearing stress with time for rheopectic suspensions has been described. A good agreement was obtained between theoretical predictions and experimental results obtained for suspensions of titanate fibers in a polymer solution. Rate constants for both the formation and breaking of network structure were evaluated as functions of rate of shear. The theory was also applied to a suspension of polystyrene particles investigated by Gadala‐Maria and Acrivos to evaluate rate constants. The dependence of the rate constants on rate of shear was found to be different from that for suspensions of titanate fibers.

Molecular weight M and concentration c dependencies of the zero-shear viscosity (η) were measured over wide ranges of M and c for concentrated solutions of linear and branched poly(vinyl acetate) as well as of polystyrene under θ conditions. The log η versus log M and log η versus log c curves for a given system can be superposed by the horizontal shift along the abscissa, giving smooth master curves. From the shift factors the ratio of two exponents β and α, which appear in the following equation, can be evaluated: η = K′(cρ)αMβ, where ρ is the density of the solution and K′ is a constant at constant temperature. The evaluated values of β/α for the systems under θ conditions are equal to or very close to 0.50 as was anticipated from the previous work. The above superposition method was also applied to available viscosity data, and it was found that β/α had a good correlation with a in [η] = KMa. This indicates that the individual molecules in concentrated solutions maintain the same individuality as in dilute solutions, and might be a positive support to the packed sphere model proposed previously by the authors. The effect of solvent on the molecular weight and the concentration dependencies of viscosity was also discussed.

Viscoelastic Properties of Concentrated Solutions of Poly(methyl methacrylate) in Diethyl Phthalate

Recent work with binary blends of narrow-distribution polystyrenes has shown that the elastic properties depend on the molecular weight distribution in a complex way when the molecular weights are both above the entanglement point. In particular the steady-state compliance Je0 becomes proportional to w2−2 when w2, the weight fraction of the higher molecular-weight species, approaches unity. These results led to the suggestion that a high-order (nonlinear) blending law might be required above the entanglement point.In the present work the general problem of modelling the molecular weight dependence in the transition, rubbery plateau, and terminal flow regimes is discussed, including models for the juncture points between these regions. A general mathematical framework is presented which includes the Rouse spectrum and a linear blending law for low molecular weights (and also for the short-time portion of the spectrum generally); a network spectrum and a quadratic blending law for the higher molecular weights; and a mixture of these models for intermediate cases. Also, results for wide-distribution mixtures and for n-th order blending laws are stated.

高分子溶融物は,合成繊維の紡糸,プラスチックの成形などの加工に使われ,その流動性は加工性を直接支配する要因である。一方,溶融物や濃厚溶液を学問的に考えれば,希薄溶液や結晶のような理想状態とはちがって,理論的に取り扱うことのむずかしい状態であり,分子構造と溶融高分子の性質との関係は,高分子科学の中でも最も解明の遅れた分野の一つであるといえよう。しかし最近の研究は, 高分子の分子構造, たとえば分子の大きさ, 分子量分布,枝分れなどと溶融物のレオロジー的性質との関係を明らかにしつつある。特に分子量分布の均一な単分散試料について得られたデータが集積され,高分子の構造と溶融状態における流動性との関係を帰納する上に大きく貢献している。この記事は,このような溶融物に関する最近の研究を,著者らの研究を中心として概観しようとするものである。

The viscoelastic properties of concentrated solutions of linear and randomly branched polystyrenes were measured and compared with each other. From the frequency dependence of the storage shear modulus G′ and the loss modulus G″, the characteristic parameters in the terminal zone, such as zero-shear viscosity η0 and steady-state compliance Je0, were evaluated. The dependence of these parameters on the molecular weight and concentration were discussed. The zero-shear viscosity and its dependence on molecular weight for the solution of randomly branched polystyrene are lower than those of linear polystyrene. The steady-state compliance is proportional to Mw0.84 for the branched samples, while it does not depend on molecular weight for the linear polymer. These results lead to the suggestion that the maximum relaxation time is proportional to Mw2.3 and Mw3.5 for branched and linear polystyrene solutions, respectively. The concentration dependence of the steady-state compliance for the branched polymers is also much less than that of the linear ones. Comparing the frequency dependence curves of G′ for the randomly branched and linear polystyrenes, there seems to be a significant difference in the shape of the relaxation spectra in the region associated with entanglement coupling. This behavior is considered to be due to the difference in the two chain structures.

同心円筒型粘度計を使用して, 数種の懸濁液の流動特性を,せん断速度5×10-1～1.6×103sec-1の範囲で測定した。用いた分散媒は流動パラフィンおよびポリスチレンのフタル酸ジエチル溶液であり, 分散させた固体粒子はカーボンブラック(CB), ベントナイト(B), カオリナイト(K)およびパーマネントレッド4R(PR)である。得られたおもな結果はつぎのとおりである。(1)ニュートン媒体からなる系においてはCassonの式, S1/2=ko+k1D1/2, がよく成立する。ここでSはせん断応力, Dはせん断速度, ko,k1は定数である。非ニュートン媒体の系においてはS1/2対D1/2曲線はDが非常に低くないかぎり直線にならない。(2)koから求められる降伏応力Syは,分散媒の粘度に依存せず,粒子の種類だけに依存する。(3)せん断速度が低くなるにつれて, 塑性粘度ηp1=(S-Sy)/Dは増加し,一定値を与えない。(4)粒子による非ニュートン流動は高分子による非ニュートン流動よりも明らかに低いせん断速度で現われる。(5)粒子濃度に対するη∞(せん断速度無限大のときの粘度)のプロットは,各粒子についてかなり高い濃度まで直線となる。(6)以上の結果を総合すれば, 粒子による非ニュートン流動は, 高分子溶液や融解物の示す非ニュートン流動とはその機構および流動形式をまったく異にする。

To determine non‐linear viscoelasticity parameters for disperse and high‐polymeric systems, some 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 170°C, and in a frequency range from 2×10−3 to 0.5 cycle per sec. As a result of 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. Frequency dependence curves at various temperatures for G1′ and G1″, which correspond to G′ and G″ for linear v...

プチルゴムの流動パラフィン溶液に,粒子径の異なった2種類のカrボンブラックを分散させた系のレオロジー的性質について研究した。分散系の塑性粘度ηP1.降伏値Sy,動的粘性率η',動的剛性率G'を2種類の回転円筒型レオメータ.一によって測定した。えられたおもな結果はつぎのとおりである・(1)Cassonの式S1/2=K0+KD1/2(ここでS はせん断応力,Dはせん断速度,K0,K1は定数)はニュートン液体を分散媒とする分散系においてはよく成立するが,非ニュートン液体を分散媒とする分散系においては,Dが非常に低くないかぎり成立しない。(2)Cassonの式から求めた降伏値Syが分散媒の粘度や測定温度に依存しない系もあるが,それらに依存する系もある。その事情は測定条件,すなわち分散媒や粒子の種類,測定温度によって変化する。(3)分散系特有の非ニュートン流動は低せん断速度領域あるいは低せん断応力領域において顕著である。この点は高分子溶液あるいは溶融物の非ニュートン流動と非常に異なる・(4)降伏値が温度に依存しない系においては,塑性粘度ηP1に対して時間一温度の重ね合わせの原理がタイムスケールの全領域にわたって適用できるが,降伏値が温度に依存する系においては,時間一温度の重ね合わせの原理ほ適用できない。(5)時間一温度の重ね合わせが可能ならば,著者らの実験範囲において,移動係数αTは粒子濃度に無関係である。(6)分散系の塑性粘度ηP1と分散媒自身の粘度ηmの比は,高せん断速度領域で一定値になる。この一定値は分散系中の高分子濃度約0.3%で極大をもつ.(7)今回の研究においては,降伏値の値と粒子の大きさの間に相関関係が認められなかった。

The viscoelastic properties of molten blends of poly(methyl methacrylate)s having different molecular weights were measured, and several characteristic parameters resulting from these measurements were determined.The Vogel temperature T0, plotted against the weight fraction of the high molecular-weight component, w2, has a minimum at about w2=0.2, while the temperature coefficient of the fractional free volume, αf, is almost constant in the entire range of w2. The steady-state compliance Je0 of the blends is inversely proportional to w22, when w2 is near unity, but it decreases with decreasing w2 after passing through a maximum at about w2=0.2. At this point the higher molecular-weight component shows a shoulder rather than a clear peak on the molecular weight distribution curve for the blend.The horizontal and vertical shift factors aM and cM obtained from the time-composition superposition proposed in our previous papers are respectively related to the interaction parameter λ2 in the Ninomiya theory and to the steady-state compliance Je0. Further, aM is proportional to M1.2–2.5, and cM to M−2.5−–2.8, where M is the calculated weight-average molecular weight of the blend.

異なった分子量をもつ線状および分岐ポリ酢酸ビニル(PVAc)ならびにポリスチレン分別物の濃厚溶液について,分子量および濃度の広い範囲にわたって,零せん断粘度ηoの分子量および濃度依存性を測定し,流動性におよぼす分岐と溶媒の影響を研究するとともに,これらの実験結果および同様の既存のデータを解析して,粘度を決定する要因である分子量と濃度との関係を求め,理論の結果と比較した。得られた結果および結論のおもなものを要約するとつぎのとおりである。1)等価球模型を採用し,球の半径がZe(Zは鎖長, e は系によって定まる定数)に比例するものと仮定すると, 球の体積分率が一定であるとき,つぎの関係が得られる。cρZ3e-1=const.ただし,cは重量パーセントで表わした濃度,ρ は溶液の密度である。この式は,eの大きさを適当に変えることによって,分子鎖間のからみ合いを決定する分子量と濃度との間に従来から知られている関係のすべてを表わすことができる。以前,小野木らによって与えられた関係は,上式のeが0.50の場合で,それ以外の場合にはeは0.50より大きい。eの最大値は2/3である。2)PVAcおよびPSの濃厚溶液について得られたlog M 曲線およびlog ηo-log cρ 曲線は,水平移動によって全部が重なり合い,一つのなめらかな合成曲線を与える。 重ね合わせを行なうときの粘度曲線の移動量から,粘度式ηo=K'(cρ)αMβに現われるα とβ の比を決定することができる。ただし,上式のK'は定数,α およびβ は,それぞれlogηo-logcρ および109ηo-logM曲線の勾配である。特定の粘度値について考えるときには,β/α が上の(3e -1)に等しい。3)β/α は分岐の有無とは無関係に一定であることが,線状および分岐PVAcの実験結果からわかる。一方,β/α は溶媒の溶解力に強く依存し,溶媒が貧溶媒であるほど,その値は小さく,θ 溶媒中において下限値0.50をとる。4)上記の粘度曲線の重ね合わせは,他の研究者による既存のlog ηo-log cρ およびlogηo-logM曲線に対しても適用可能である。多くの系について求められたβ/α の値は,θ 状態における値0.50から0.74にまでわたり,いずれも小野木らの以前の理論値0.50とBuecheらの理論値0.83の間にある。またβ/α のこれらの値は,同じ系について求められた[η]=KMαのα の値と密接に関係している。この事実は,濃厚溶液や溶融物中で分子が希薄溶液申におけると同程度の拡がりをもって,比較的丸まった形で密集しているという,著者らの以前からの見解を支持するものと考えられる。

Hereunder a report is presented of measurement made of the viscoelastic properties of concentrated solutions of star-shaped polystyrenes. From the frequency dependence of the storage shear modulus G' and loss modulus G" the characteristic parameters in terminal zone, such as zero-shear viscosity η0 and steady-state compliance Je0, have been evaluated. The dependence of these parameters on the concentration have been discussed and compared with those of concentrated solutions of linear polystyrenes.For the star polymers, the zero-shear viscosity reduced to the iso-free volume state, f=0.0608, is proportional to (w2ρ)6 and (w2ρ)1 at higher and lower concentrations, respectively, than the critical concentration, where w2ρ is the concentration in g/ml. The critical concentration for entanglement was evaluated to be 0.23g/ml for the star-shaped polystyrene having the molecular weight of 407000. The concentration dependence of steady-state compliance of the solutions of star polymer can be divided into three parts. The steady-state compliance is proportional to (w2ρ)-1 at low concentrations below 30wt%and to (w2ρ)-2 in the concentration range from 30 to 70wt%. In both the regions, Je0 is proportional to the molecular weight. At higher concentrations, Je0 increases rapidly passing through the minimum at about 70wt% but is independent of molecular weight. The molecular weight dependece of Je0 in the entanglement region and its rapid increase at extremely higher concentrations for the star polymers are quite different from those for linear polymers described in our recent papers. The entanglement compliance JeN0 of the solution of star polymers is proportional to (w2ρ)-2 above the critical concentration, which is similar to that of linear polymer.

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.

Dynamic viscosityη′, dynamic rigidityG′ and apparent viscosityη a of fractions and blends of polymethyl methacrylate and of polyvinyl acetate having different molecular weight and distribution have been measured at high temperatures by means of a concentric cylinder-type rheometer which enables us to measure not only dynamic but also steady-flow properties. The values ofη′ andG′ as functions of frequency for each sample at different temperatures can be superposed according to the usual time-temperature superposition principle, giving master curves covering a wide range of frequency. The absolute value of complex viscosity as a function of angular frequency coincides very well with the apparent viscosity as a function of rate of shear, indicating that the empirical law byCox andMerz holds well with the experimental results. The dynamic viscosity curves for various samples unite in one curve aboveω=1000 sec−1, and this united portion corresponds to the transition region. The effects of branching and bimodal distribution of molecular weight and the variation of frequency dependence of viscosity-molecular weight relation have been discussed, and emphasis has been placed on the significance of intramolecular motion to the flow properties of polymer melts at higher rates of shear or frequency.

The viscoelastic properties of poly(methyl methacrylates) obtained by anionic polymerization were measured in the molten state by means of a concentric cylinder type rheometer over wide ranges of frequency and temperature. From the frequency dependence of the storage modulus G′ and the loss modulus G″, the characteristic parameters in the terminal zone, such as zero-shear viscosity η0 and steady-state compliance Je0 were evaluated, and the dependence of these parameters on the molecular weight M was discussed, η0 and Je0 for samples having molecular weights higher than the critical molecular weight MC were respectively proportional to M4.4 and M. The quasi-equiliblium modulus GeN0 and the average molecular weight between entanglement coupling loci, Me, were also evaluated. Me was found to increase gradually from 6760 to 13100 with increasing molecular weight. The ratio Mc/Me was not constant but varied from 6 to 2, being larger than the value of 2 obtained by previous authors, both theoretically and experimentally. The parameters for this material are discussed in connection with molecular structure, together with those for anionic polystyrene published in the previous paper.

The dynamic viscoelastic properties for binary blends consisting of an isotactic polypropylene (i-PP) and an ethylene-1-hexene copolymer (EHR) were investigated in both solid and molten states to reveal the relation between miscibility in the molten state and the morphology in the solid state. In this study, two types of EHRs were employed: “ethylene-rich” EHR and “1-hexene-rich” EHR. The blend of i-PP and EHR of 30 mol % 1-hexene content shows a very long time relaxation due to the phase separation in the molten state. The blend film shows two separate glass-relaxation processes associated with those of the pure components. These indicate that the blend shows phase-separated morphology in the solid state as well as in the molten state. On the other hand, dynamic moduli in the molten state of the blends of i-PP and EHR of 57 mol % 1-hexene were found to be intermediate between those of individual pure components. Furthermore, the apparent activation energy of the blends is constant and is identical with those of i-PP and the EHR. The blend films show a single glass-relaxation process at the temperatures between those of the pure components, indicating that the EHR molecules are incorporated in the amorphous region of i-PP in the solid state. Accordingly, it was found that the polymer miscibility in the molten state for the i-PP/EHR blends directly affects the morphology in the solid state. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 467–474, 1997

Lymph node metastasis to the iliac or inguinal region of colon cancer is extremely rare. We experienced a case of ascending colon cancer with synchronous isolated right external iliac and inguinal lymph node metastases but without any regional lymph node metastasis. An 83-year-old woman was admitted to our hospital due to anemia. Colonoscopy and computed tomography revealed an ascending colon cancer and also right external iliac and inguinal lymph node swelling. Further examination by F-deoxyglucose positron emission tomography strongly suggested that these lymph nodes were metastatic. Right hemicolectomy with lymph node dissection along the superior mesenteric artery, and right external iliac and inguinal lymph node dissection were performed. Histological examination revealed that both lymph nodes were metastasized from colon cancer, and there was no evidence of regional lymph node metastasis. The patient has shown no sign of recurrence at 27 months after surgery.