Index of content:
Volume 47, Issue 3, May 2003
47(2003); http://dx.doi.org/10.1122/1.1567753View Description Hide Description
Tensile creep tests, tensile relaxation tests and a tensile test with a constant strain rate are performed on injection-molded isotactic polypropylene at room temperature. A constitutive model is derived for the time-dependent behavior of semicrystalline polymers. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The network is modeled as an ensemble of passive mesoregions (with affine junctions) and active mesodomains (where junctions slide with respect to their reference positions with various rates). The distribution of activation energies for sliding of junctions in active mesoregions is described by a random energy model. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. It is demonstrated that the concentration of active mesodomains monotonically grows with strain, whereas the average activation energy for sliding of junctions and the standard deviation of energies suffer substantial down jumps in the vicinity of the yield point. With reference to the concept of dual population of lamellae, these changes in material parameters are attributed to transition from breakage of subsidiary (thin) lamellae in the subyield region to fragmentation of dominant (thick) lamellae in the postyield region of deformations.
47(2003); http://dx.doi.org/10.1122/1.1567752View Description Hide Description
In this contribution correlations between the type of strain hardening of long-chain branched polyethylenes and the level of their zero shear-rateviscosities in comparison to linear polyethylenes are described. For polyethylenes of various branching structures four different types of strain hardening can be observed. Type I: strain hardening is approximately independent of elongational rate. Type II: strain hardening decreases with increasing elongational rate. Type III: strain hardening increases with increasing elongational rate. In addition to that, materials are found which do not show strain hardening within the experimental window (type IV). Qualitative correlations with the dependence of the zero shear-rateviscosity on the weight average molecular mass can heuristically be deduced. Polyethylenes of type IV fulfill the well-established relationship samples of types I and II give higher zero shear-rateviscosities than the linear products. Type III samples generally exhibit zero shear-rateviscosities lower than the linear relationship. As the dependence of the zero shear-rateviscosities on the molecular mass offers some insight into the branching structure of a polyethylene the differences in strain hardening can heuristically be related to the molecular structure. These correlations can be transferred to different types of long-chain branched polypropylenes giving some hint to their molecular structure.
Simultaneous dielectric and dynamic mechanical measurements on PVDF in the molten state: Study of the linear/nonlinear viscoelastic transition47(2003); http://dx.doi.org/10.1122/1.1562157View Description Hide Description
Simultaneous dielectric and dynamic mechanical measurements on PVDF in the molten state have been performed by a dynamic rheometer equipped with an electrical cell. This device permits the evolution of the dielectric and mechanical properties to be recorded both inside and outside the linear viscoelastic domain (LVD). Dielectric properties during shear experiments inside the LVD are not dependent on the shear rate, according to linear viscoelastic theory and Brownian motion considerations. The linear/nonlinear transition is depicted by a fall of conductivity as well as the presence of a maximum of the real part of the permittivity. The decrease of specific conductivity results from modification of the conductive paths, which demonstrates ionic mobility that is different in the direction along and normal to the chain, whereas the maximum of real permittivity is correlated to anisotropic dielectric properties. Stopping the dynamic mechanical strain causes a return of the dielectric parameters to a level close to the one obtained inside the linear viscoelastic domain.
47(2003); http://dx.doi.org/10.1122/1.1562479View Description Hide Description
Dilute solutions of worm-like micelles exhibit shear thickening caused by microstructural changes under specific flow conditions. In this work, for the first time, shear thickening in parallel plate and Poiseuille flows is investigated using simultaneously particle image velocimetry(PIV) and rheometry. Four distinctive zones of flow behavior are identified in parallel plates as the shear rate increases, namely, a Newtonian region, a transition regime where inhomogeneous nucleation of the shear-induced structures (SIS) is followed by homogeneous nucleation of SIS, and an apparent second-Newtonian regime at high shear rates, where rapid temporal fluctuations of the viscosity are smoothed out by inertia of the moving plate. In pipe pressure flow,PIV results reveal a flow pattern consisting of a superposition of two parabolic regions of the velocity profile located near the center and close to the pipe walls, and a transition region where again strong fluctuations in the velocity profile are observed. The experimental results are compared with predictions of a convected Maxwell constitutive equation coupled to a kinetic equation that accounts for an increase in dissipation of the system due to the presence of the SIS. The model accounts for the average steady values of the viscosity in the structured thickened state.
47(2003); http://dx.doi.org/10.1122/1.1562152View Description Hide Description
A model is developed to predict the transient shape evolution of an ellipsoidal Newtonian droplet with interfacial tension, suspended in another Newtonian fluid with a different viscosity. Using the Eshelby equivalent inclusion theory [Eshelby (1957)], this model adds an approximate interfacial tension term to the exact deformationmodel of Wetzel and Tucker (2001) for droplets with zero interfacial tension. The model can predict large deformations and rotations of the ellipsoid, it allows any value of viscosity ratio, and it admits arbitrary far-field flows. The model does not incorporate breakup or coalescence. At viscosity ratios less than 0.1, the model blends the Eshelby model (for compact shapes) with a classical slender-body model (for thread-like shapes), providing a smooth transition between these two limits. The model accurately matches many experimental results from the literature, including steady shapes in simple shear, transient shapes during shear reversal, widening in simple shear, relaxation after step shear, and the critical capillary number for breakup in both shear and planar elongation. The model also compares favorably to the ellipsoidal dropletmodel of Maffettone and Minale (1998).
47(2003); http://dx.doi.org/10.1122/1.1562156View Description Hide Description
A high-density polyethylene (HDPE), a poly(dimethylsiloxane) (PDMS), and an oxetane based alternating block thermoplastic elastomer (TPE) were subjected to steady torsional and capillary flows. HDPE and PDMS exhibited wall slip in steady torsional flow. The shear stress ranges at which wall slip became apparent during steady torsional flow for HDPE and PDMS coincided with the wall shear stress ranges in capillary flow at which distortions of the extrudates emerging from capillary die were first noted. In contrast, TPE did not exhibit wall slip in steady torsional flow (for shear rates up to 200 s−1 and strains up to 25). None of the three polymers exhibited any overshoots of shear stress or first normal stress difference under steady flow conditions, indicating that the often-reported stress overshoots could be artifacts of wall slip. Furthermore, the extrudates of the TPE were relatively smooth and exhibited only minor and nonperiodic surface blemishes. The absence of extrudate distortions under the presumed no-slip condition for TPE emphasizes the intimate link between wall slip and the development of extrudate distortions and strengthens the premise that extrusionflow instabilities can be eliminated under conditions of stable wall slip or stick.
47(2003); http://dx.doi.org/10.1122/1.1562153View Description Hide Description
This study is aimed at characterizing the nonlinear viscoelastic behavior of hard cheeses using mild cheddar and gruyere as examples. The constitutive model consists of the Van der Waals hyperelastic function and the Prony series. The material constants were calibrated using data from monotonic compression and stress relaxation tests. Based on these constants, finite element simulations of three point bend and wire cutting tests were performed. The finite element predictions were compared with experimental data and good agreement was observed. In addition, successful predictions of the steady-state cutting force in the wire cutting tests have been made through the use of a critical strain failure criterion.
Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenes47(2003); http://dx.doi.org/10.1122/1.1567751View Description Hide Description
The effects of sparse (<1 branch per chain) long-chain branching (LCB), molecular weight (MW), and molecular weight distribution on the shear rheological properties of commercial polyethylenes are often convoluted. In this paper a method for separating the effects of sparse LCB in metallocene-catalyzed polyethylenes (mPE) from those of molecular weight and its distribution based on time–molecular weight superposition is proposed. Four metallocene polyethylenes with degrees of long-chain branching [i.e., M of the arm is greater than that for the onset of entanglements, as determined from dilute solutionmeasurements ranging from zero (linear) to along with a conventional Ziegler–Natta polymerized linear low-density polyethylene (LDPE), and a tubular free-radical polymerized LDPE are investigated. In general, it is observed that sparse LCB (for levels increases the zero shear viscosity, (e.g., by a factor of 7) and decreases, but even to a greater degree, the critical shear rate for the onset of shear thinning (e.g., by a factor of 100). The breadth of the molecular weight distribution just affects but not for the range of data used in this study. Furthermore, the dynamic storage modulus shows similar enhancement at low frequencies as viscosity does, while the primary normal stress difference coefficient, exhibits a greater dependence on long-chain branching than that predicted from the zero-shear viscosity enhancement. The results for the mPEs are consistent with recent molecular theories for randomly branched molecules in that it is the spacing between branch points and not the number of branches at a point that is important. Furthermore, the results are consistent with the idea that the branches are located on the longest chains, and hence, have the greatest effects on the longest relaxation modes.
47(2003); http://dx.doi.org/10.1122/1.1562154View Description Hide Description
Sharkskin-type melt fracture is generally produced by a discontinuous boundary condition at a die exit. In order to investigate this flow instability, a shear flow having a negative pressure gradient at the exit was generated by a wedge-shaped slider. A high-resolution differential interference contrast microscope was used for simultaneous observation of the inside and outside of the flow cell, which employed linear PDMS. At the cell exit, the spatial distribution and the temporal change in velocity were measured under sharkskin-like instability by use of a particle tracking method and laser Doppler velocimetry. A slip flow and a stick flow appeared alternately at the exit of the sliding plate; the slip flow is associated with cavity penetration from the cell exit. This inner instability was found to be associated with the formation of valleys and ridges on the outer free surface. At the cell exit, a slip flow appeared with a valley, and a stick flow appeared with a ridge. The penetration length of the cavity increases with sliding-plate speed, and this increase in penetration length induces flow stagnation upstream of the cavity. This stagnation relaxes high shear upstream of the cavity and suppresses the increase in penetration length of the cavity. Except for incipient instability, the penetration length has a linear relation with the wavelength of the outer ridges. A close relationship is found to exist between free surface roughness and inner flow instability.
47(2003); http://dx.doi.org/10.1122/1.1566034View Description Hide Description
We employ a particle-level simulation technique to investigate the rheology of non-Brownian, flexible fiber suspensions in simple shear flow. The model incorporates a variety of realistic features including fiber flexibility, fiber deformation, and frictional contacts. The viscosity of fiber suspensions is strongly influenced by the fiber equilibrium shape, interfiber friction, and fiber stiffness. The viscosity of the suspension increases as the fiber curvature, the coefficient of friction, or the fiber stiffness is increased. The yield stress of fiber suspensions scales with the volume fraction in a manner similar to that observed experimentally. Fiber suspensions that flocculate exhibit a shear thinning regime that extends to shear rates lower than those observed for homogeneous suspensions.
Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model47(2003); http://dx.doi.org/10.1122/1.1562155View Description Hide Description
The elongational viscosity of three tubular and five autoclave low-density polyethylene (LDPE) melts is analyzed, and quantitative comparison of the strain-hardening characteristics is made by using the molecular stress function model. This is based on a new strain-energy function, which assumes that the total strain energy of a branched section of a macromolecule is given by the addition of the strain energies of the individual chain segments contained in this section. The model employs only two nonlinear material parameters: one parameter describes the average number of crosslinked chain segments, which occupy the same tube section, and determines the slope of the elongational viscosity after inception of strain hardening. The second parameter indicates the maximum relative stretch of the chain segments and determines the steady-state (plateau) value of the elongational viscosity. Both parameters depend on the complex branching topology of LDPE melts. While quantitative relationships between branching structure and the two nonlinear parameters are not yet available, the results of this comparison seem to indicate that the more tree-like structure of autoclave LDPE leads to a higher density of crosslinked chain segments in the same tube section than in the case of LDPE polymerized in tubular reactors.
47(2003); http://dx.doi.org/10.1122/1.1566035View Description Hide Description
Interfacial slip between high density polyethylene (HDPE) and polystyrene (PS) melts was studied. The HDPE/PS layered structure was subjected to steady shear in a Cambridge shearing system. Through thickness melt velocities of the HDPE/PS layered structure were measuredin situ by a confocal microscope. Velocity profiles of both HDPE and PS layers were obtained. Velocity discontinuity was observed at the HDPE/PS interface from the velocity profiles and indicated interfacial slip. The slip velocity obtained from velocity discontinuity is in good agreement with that deduced by independent rheological measurements.
47(2003); http://dx.doi.org/10.1122/1.1567750View Description Hide Description
Numerous papers have recently appeared in the literature presenting quantitative comparisons of experimental linear viscoelastic data to the most recent versions of “tube” models for entangled polymer melts and solutions. Since these tube models are now being used for quantitative, rather than just qualitative, predictions, it has become important that numerical prefactors for the time constants that appear in these theories be evaluated correctly using literature data for the parameters (i.e., density, plateau modulus, etc.) that go into the theories. However, in the literature two definitions of the entanglement spacing in terms of plateau modulus have been presented, and confusion between these has produced numerous errors in the recent literature. In addition, two different definitions of the “equilibration time,” a fundamental time constant, have also appeared, creating additional potential for confusion. We therefore, carefully review the alternative definitions and clarify the values of the prefactors that must be used for the different definitions, in the hope of helping future authors to avoid such errors.