Stress prediction for polymer blends with various shapes of droplet phase

Okamoto

2007

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After application of a large step shear strain, a polymer droplet in an immiscible polymer matrix takes rod-like and spheroidal shapes before returning to the spherical shape. Change in semi axes of those droplets is calculated based on the Cohen-Carriere theory and the extension of the theory by Okamoto et al. From comparison with experimental data, it has been found that retraction of semi axes is well described by the theory using a hydrodynamic factor for the droplet associated with the viscous resistance of the matrix. The excess shear stress for rod-like and spheroidal droplets is predicted based on the Doi-Ohta theory by evaluating the interface tensor from the semi axes calculated. The predicted excess shear stress for the deformed droplet is close to experimental data of a polymer blend with narrow distribution of droplet size after normalization per one droplet with the volume-averaged radius. The effects of polydispersity and interaction with adjacent droplets in the blend are suggested for the remaining difference between the prediction and the data.

Section: Introductionmentioning

confidence: 99%

Retraction of Rod-like and Spheroidal Droplets and Stress Relaxation after Step Shear Strain in Polymer Blends

Okamoto

2007

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“…E-mail: mdt@kit.ac.jp, Tel/Fax: +81-75-724-7835 the effect of the droplet size distribution, and revealed that the droplet size distribution has significant influence on the excess first normal stress difference of polymer blends in start-up of shear flow. Takahashi et al 10) also reported that the experimental results of the stress relaxation for a hydroxypropylcellulose aqueous solution/polydimethylsiloxane (PDMS) blend agree with the stress calculated by the Laplace pressure term only when the droplet size distribution is considered. In addition, Takahashi and Okamoto 11) speculated that the droplet size distribution affects the strain dependence of the stress relaxation for a polyisobutylene (PIB)/PDMS blend especially for the retraction of spheroidal droplets.…”

Section: Introductionmentioning

confidence: 86%

“…This r V /r n value is chosen since the value is close to roughly estimated value of r V /r n for the PIB/PDMS blend. 10) We plot the calculated results only at t ≥ t s (r max ), where r max denotes the radius for the largest droplet, since the largest droplet is not spheroidal shape at t < t s (r max ), and thus the calculations at those times are out of the scope of the present paper.…”

Section: Effects Of Droplet Size Distributionmentioning

confidence: 99%

“…For the stress relaxation of polymer blends with K < 1 under large step shear strains, the Laplace pressure term evaluated from the shape recovery data of isolated droplets agrees fairly well with experimentally obtained stress relaxation data. [9][10][11] Recently, the interface velocity term is taken into account in some theories. [12][13][14] The total stress including the interface velocity and the Laplace pressure terms is compared with literature data of dynamic moduli, steady shear flow and startup of shear flow for polymer blends.…”

Section: Introductionmentioning

confidence: 99%

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Effects of Interface Velocity on the Stress Tensor in Immiscible Polymer Blends: Retraction of Spheroidal Droplets and Stress Relaxation

Okamoto

2008

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The total stress tensor for immiscible polymer blends is calculated based on the theoretical expression by Batchelor (1970), andMellema andWillemse (1983) in the last stage of the stress relaxation under large step shear strains. In this stage, the shape of droplets is spheroid and the retraction of isolated droplets is calculated according to the theory developed by . The calculated results are compared with experimental data for a polyisobutylene/ polydimethylsiloxane blend. Contribution of the motion of the interface (the interface velocity term) to the total stress tensor in the theoretical expression for the isolated droplets is 37 % − 50 %, which cannot be neglected compared with the contribution of the pressure difference beyond the interface (the Laplace pressure term). The summation of both terms agrees well with the experimental data at step strain γ = 1, in which effects inherent in multiple droplet systems are the smallest. The γ dependence of the reduced stress appearing in the experimental data, which cannot be predicted by the theoretical calculation for the isolated droplets, is qualitatively explained by considering droplet size distribution in the theoretical calculation.

“…[1][2][3][4][5] The average size and sizedistribution of dispersed phases after steady flow have been studied in detail, and then the average size can be predicted and controlled. It has been shown by our series of studies on droplet deformation [6][7][8][9][10][11] and stress [7][8][9][10][11][12][13] after application of step shear strains that the shear stress due to the interface in polymer blends with the droplet/matrix structure can be predicted rather well based on the Doi-Ohta theory 14) from observed shapes and dimensions of the deformed droplets.…”

Section: Introductionmentioning

confidence: 93%

Creep Behavior of a Polymer Blend Melt and 3D Observation of the Deformed Bicontinuous Structure by a High-contrast X-ray CT

Hatakeyama

Nishikawa

2016

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Dynamic viscoelastic, creep and steady shear flow measurements are made on a polymer blend melt with a phaseseparated bicontinuous structure. 3D structures at quiescent, constant-stress and constant-shear-rate states are observed by a high-contrast X-ray computerized tomography (CT) after quick quenching of each sample. At the quiescent state, the frequency dependence of the storage modulus at 200 o C shows a power law behavior with the exponent of 0.84. In the shear rate range (at the small shear stress s = 100 Pa) where partial relaxation of the interface of the blend is possible, a peculiar plate-like pattern in the deformed bicontinuous network is observed in the through view of the X-ray CT image. At higher shear rates (at the higher shear stress s = 1000 Pa) where the interface relaxation is suppressed, another peculiar short plate-like pattern appears in the edge view. When the shear rate in the steady shear flow is equal to the average shear rate in the creep test, a very similar deformed pattern of the interface is observed.At the macroscopic shear strain of 3.2 in the creep test at 100 Pa, the observed strain of the deformed bicontinuous network has a distribution and the majority are much smaller than the strain expected from the affine deformation assumption. An average orientation angle of the deformed network at the shear strain of 3.2 corresponds to the angle given by the affine deformation of the shear strain 1.35.