Volume 11, Issue 1, March 1967
Index of content:
11(1967); http://dx.doi.org/10.1122/1.549087View Description Hide Description
In the hydrostatic theory of liquid crystals, we characterize those orientation patterns which may occur, in the absence of externally applied body forces, no matter what the form of the stored energy function may be. It turns out that there are three types of such patterns. In one, the orientation vector is perpendicular to a family of concentric spheres. Another results from replacing these spheres by concentric circular cylinders. In the third, the orientation vector is constant in each of a family of parallel planes, the direction changing continuously with distance measured normal to these planes.
Dynamic Intrinsic Viscosity of Macromolecules with Internal Viscosity. III. Effect of Molecular Weight, Excluded Volume, and Hydrodynamic Interaction11(1967); http://dx.doi.org/10.1122/1.549086View Description Hide Description
The frequency dependence of the complex intrinsic viscosity and elastic modulus of a macromolecule with internal viscosity is calculated for the Gaussian coil and the coil with excluded volume in a wide range of molecular weight and hydrodynamicinteraction. Due to limitations in eigenvalues and because of coil rotation in laminar flow the results obtained are sufficiently accurate only for a large number of coil segments and for small internal viscosity.Hydrodynamicinteraction enhances the effect of internal viscosity so that the macromolecule seems to be stiffer than in the free‐draining case. The non‐Gaussian character of intrachain distances has a very small effect. Finite internal viscosity yields a nonvanishing limiting viscosity at which at sufficiently large M increases as The relative limiting viscosity as a function of molecular weight hydrodynamicinteraction (h), non‐Gaussian character of the coil (ε), and internal viscosity (φ) can be well represented by a single master curve if plotted against The eigenvalue is unity for the free‐draining coil and asymptotically increases as a linear function of h and ε. Molecular weight enters the abscissa of the master curve implicitly through and explicitly through Z.
11(1967); http://dx.doi.org/10.1122/1.549070View Description Hide Description
Viscoelasticflows with a type of small controlled deviation from viscometricity are investigated. The calculations provide a basis for exploring the use of simple constitutive equations in some steady flows. The two‐dimensional flow of a low‐order Rivlin‐Ericksen fluid through a channel of slowly varying width is worked out. Inversion formulas enabling the deduction of material functions from experimental observations are also given, which may provide a new means of measuring one normal stress difference.
11(1967); http://dx.doi.org/10.1122/1.549071View Description Hide Description
Extensions of the Sokolovsky‐Malvern theory of strain‐rate‐dependent plasticity are proposed. These extensions are based on concepts of strain‐dependent viscosity and of hereditary integral viscosity, and are based on both the linearly viscoplasticconstitutive equation and on the exponentially viscoplastic one. The basic tests, creep,relaxation, and constant strain rate, are examined and the application of the theories to wave propagation is discussed.
11(1967); http://dx.doi.org/10.1122/1.549088View Description Hide Description
We compare experimental results for tube flow of polymer melts with those computed from Pao's theory. We further present a correlation scheme for the behavior of bulk polymer melts in steady flow and dynamic oscillatory experiments. The correlation is not limited to low shear rates, but is theoretically valid for all frequencies and shear rates. The steady flow shear viscosity is expected to equal or exceed the dynamic viscosity at all frequencies and shear rates. Similarly, the correlation predicts that G exceeds or equals over the entire frequency range. At low shear rates should correlate with and is given by Limited agreement between the experimental results and computed curves for tube flow is observed. The correlation scheme appears to represent the behavior of certain polymer solutions very well but quantitative agreement is not obtained for a linear polyethylene melt. We propose that changes in the relaxation spectrum of the polymer melt subjected to steady shearing can account for the discrepancies.
11(1967); http://dx.doi.org/10.1122/1.549072View Description Hide Description
The melt flow of a variety of poly(vinyl chloride) (PVC) samples was studied at shear rates of in a constant‐load capillary rheometer. Pronounced differences were observed in apparent viscosity, post‐extrusion swelling, and extrudate roughness, depending upon sample preparation and previous history. These differences could not be correlated with molecular weight, molecular weight distribution, or other parameters of molecular structure. A possible explanation was suggested by certain correlations between flow behavior and particle structure or state of fusion. Fracture‐surface electron photomicrographs of molded or extruded PVC samples provided clear evidence that resin particles, as formed during polymerization, can maintain their identity and shape during melt flow processes. The melt flow of PVC under some conditions thus must involve the slippage of resin particles past one another, rather than a homogeneous deformation of the melt. Thermal and mechanical history severe enough to obliterate particle identity in fracture‐surface photos also shifts melt flow behavior toward higher apparent viscosity and greater melt elasticity, due to a reduction of particle slippage and a more homogeneous flow process. Particle boundaries may be viewed as discontinuities in an entanglement network, and elimination of boundaries as an extension of the network by molecular diffusion. On this basis, our results demonstrate the important contribution of entanglement distribution to polymer melt rheology.
11(1967); http://dx.doi.org/10.1122/1.549073View Description Hide Description
While the concept of the complex modulus is based on a forced vibration experiment it is a frequent practice to perform instead a much simpler free damped oscillation test from which an approximate value of the modulus is then evaluated. The validity of this approach and the ensuing errors are discussed and illustrated on a multielement generalized Maxwell body. It is shown that with modifications the method is applicable even for highly damped materials.
11(1967); http://dx.doi.org/10.1122/1.549074View Description Hide Description
Flow behavior of a 3% solution of polyisobutylene (Vistanex L‐100) dissolved in decalin was studied in helical flow between concentric cylinders. Shear rate in the fluid ranged between approximately 30 and A flow visualization technique was developed which permitted quantitative measurement of velocity profiles in the helical flow field. Results indicate that the correspondence between helical flow and Poiseuille flow which is predicted for simple fluids in viscometric flows is in fact observed to a close approximation. One concludes that the spatial variation of flow direction which exists in helical flow does not have an important effect on the flow of polyisobutylene solution under conditions studied in these experiments, a result consistent with the theory of simple fluids. Velocity profile measurements at two axial positions in the helical flow field indicate that a fully developed velocity profile was readily established.