Experimental Appraisal of the Doi-Edwards Theory for Polymer Rheology Based on the Data for Polystyrene Solutions

Osaki, Kunihiro; Kurata, Michio

doi:10.1021/ma60075a036

Cited by 146 publications

(103 citation statements)

References 12 publications

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“…This function was found to be a universal function for various polymeric systems, 17 and its strain dependence was well described with the tube model theory; in short, it represents the decrease of stress due to the shrink of highly extended chains in the equilibration process of the fluctuation of chain contour length. 8 We add an obvious extension of eq 18.…”

Section: Nonlinearity At Long Timesmentioning

confidence: 78%

Birefringence of a Block Copolymer Solution in the Stress Relaxation Process

Osaki

Takatori

Kurata

et al. 1986

Polym J

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ABSTRACT:The birefringence, !'J.n, and the shear stress, u, were measured after an instantaneous shear deformation for a 10.5% solution of triblock copolymer, poly(methyl methacrylate)-block-polystyrene-block-poly(methyl methacrylate), in polychlorinated biphenyl. Hereafter M stands for methyl methacrylate and S for styrene. The mole fraction of S of the copolymer was 0.4. Measurements were performed at various magnitudes of shear, y, ranging from 0.4 to 3 and !'J.n was measured with a light led perpendicularly to the shear plane. Under assumptions that the !'J.n and u are sums of independent contributions from M and S blocks and that the stress-optical law holds good for the contribution from each block, the stresses, uM and u8, attributable to theM and S blocks, respectively, were separately evaluated. The result at short times was consistent with the assumption that the chain is uniformly deformed on instantaneous deformation of the material. The ratio u8lu increased with time. For small y, the result was consistent with the tube model theory if the ratio· u8lu was regarded as the fraction of stress attributable to the central portion of chain. At large deformations, the increase with time of the ratio was much less than expected from the theory.KEY WORDS Birefringence I Stress Relaxation I Nonlinear Viscoelasticity I Block Copolymer I Poly(methyl methacrylate-styrene-methyl methacrylate) I Entanglement I Tube Model I

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Section: Nonlinearity At Long Timesmentioning

confidence: 78%

Birefringence of a Block Copolymer Solution in the Stress Relaxation Process

Osaki

Takatori

Kurata

et al. 1986

Polym J

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“…This might be due to the fact that the elongation is here 4.6, while it was only 3 in the previous work. This will be discussed elsewhere [30] [31][32][33]. This contraction should also lead to a decrease in the radius of gyration in the same time; however, our detailed measurement of that radius [8,9,10,40] failed to observe the contraction.…”

Section: Introductionmentioning

confidence: 76%

Loss of affineness in gels and melts

1985

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Résumé. 2014 (ii) A gel, crosslinked in solution, deformed by drying (deswelling of 10, leading in one direction to a deformation of 10-1/3 ~ 0.46 too). The long chain was crosslinked with the other non-deuterated chains. We believe that a direct comparison of the two form factors is interesting for the times here involved (« rubbery plateau ») : the chain is a labelled path which is obliged, for the gel, to pass across numerous crosslinks and, for the melt, to pass through numerous entanglement points (meshes are comparable in the two cases).In addition to this direct comparison, we compare the two classical models of rubber elasticity (affine and phantom), for which we have calculated the form factor.In spite of some differences, data for the two systems agree more between them than they do with classical models : the disagreement with those suggests a loss of affineness at larger scales than the mesh.

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“…Generally the strain and the time are not separable in shear modulus. For polymer solutions and melt, it is often found that when time is larger than a critical value, timestrain separability can be observed (120) and the shear modulus can be expressed as…”

Section: Standard Test Methods Of Shear Flowmentioning

confidence: 99%

Rheological Measurements

2013

Encyclopedia of Polymer Science and Technology

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Rheology is the science to study the flow and deformation of matter. It becomes an important field in material science and engineering, food, biotechnology, and so on. The objects in rheological study are not the ideal solid and ideal fluid, which can be described by the Hookean elastic model and the Newtonian viscous model, respectively. Instead, the rheological study often focuses on materials that can exhibit viscous, elastic, and plastic behavior under different flow conditions. They are often termed as complex fluids or soft matter, which include polymers, gels, suspensions, emulsions, biofluids, foods, inks (1). In contrast to hydrodynamics, which often accounts for the complex flow behavior of simple fluids, simple geometry is utilized in rheological measurements to understand the rather complicated relationship between the mechanical input and output of complex fluids. The real flow fields encountered in many applications (such as polymer extrusion, injection molding, blow molding, fiber spinning, inkjet printing, coating) are rather complicated (2). It becomes a problem whether the rheological measurements that performed under simple flow fields are useful in understanding the complicated flow behaviors of complex fluids. Fortunately, it has been proved in many examples that the properties determined from simple rheological measurements are sufficient to quantify the material parameters in various constitutive equations, which have been used widely and successfully to simulate the flow behaviors in polymer processing (3-11). The most frequently used simple flow fields are simple shear flow and simple extensional flow.The simplest geometry that defines the simple shear is two infinite parallel plates separated by a distance h. The liquid is set between two plates with one plate moving parallel to the other (Fig. 1). In reality, when the length L and the width B are much larger than the gap h, the flow in the center regime resembles the flow between two infinite plates. It means that the edge effects are ignored in most experimental shear geometries. In rheological measurements, the flow between two plates should be laminar. Moreover, it is usually assumed that the velocity across the gap satisfies a linear profile. As shown in Fig. 1, if the bottom plate is fixed and the upper plate moves horizontally with the velocity V, the fluid velocity varies linearly from 0 at the bottom plate to V at the upper plate if the no-slip boundary condition is satisfied. The linear velocity profile generates a constant velocity gradient, which is known as the shear rate. Then, the flow field between two parallel plates is homogeneous in the shear rate. The homogeneous assumption is nontrivial in the rheological tests since the actual velocity

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Experimental Appraisal of the Doi-Edwards Theory for Polymer Rheology Based on the Data for Polystyrene Solutions

Cited by 146 publications

References 12 publications

Birefringence of a Block Copolymer Solution in the Stress Relaxation Process

Birefringence of a Block Copolymer Solution in the Stress Relaxation Process

Loss of affineness in gels and melts

Rheological Measurements

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