Volume 40, Issue 1, January 1996
Index of content:
40(1996); http://dx.doi.org/10.1122/1.550785View Description Hide Description
The theory developed by Doi and Ohta was evaluated for its ability to predict the rheology of an immiscible polymer blend. The theory describes the additional stresses arising as a consequence of interfacial tension in two phase systems in which the constituents consist of Newtonian fluids and have equal viscosities. The blend considered in this paper consisted of an immiscible mixture of poly(ethylene terephthalate) (PET) and nylon 6,6 at a composition ratio of 25/75 w/w PET/nylon 6,6. The rheological properties of this blend were found to be stable for the time frame required for the rheological experiments used in this work (e.g., <5 min). The Doi–Ohta theory was found to be capable of qualitatively predicting the extra stresses arising as a result of the interfacial tension as observed in the steady state viscosity and steady state first normal stress difference. The transient shear stress and first normal stress difference at the start up of steady shear flow were qualitatively predicted by the Doi–Ohta theory while the recovery of the initial overshoot observed experimentally was not. The overshoot observed experimentally during step‐up experiments and the undershoot observed during step‐down experiments were not predicted by the theory in which it was predicted that the stresses change monotonically with a stepwise change of the shear rate to the final steady state value. While the shear thinning behavior observed for this blend was not predicted by the theory, the scaling relation for the transient stresses predicted by the theory was found to hold for the blend using stepwise changes of shear rate at a constant step ratio.
A numerical study of the flow of a low‐density‐polyethylene melt in a planar contraction and comparison to experiments40(1996); http://dx.doi.org/10.1122/1.550736View Description Hide Description
The flow of a low‐density polyethylene (LDPE) melt in a 10:1 slit‐die contraction at 150°C is simulated by using a two‐dimensional finite element program, and comparisons are made with the experiments of Kramer (1993) who used laser Doppler velocimetry to measure the velocity field at several flow rates. The LDPE melt is modeled by a Rivlin‐Sawyers integral constitutive equation with a spectrum of relaxation times where the parameters were determined from shear and elongational data. Evaluation of the general performance of our model and simulation at several flow rates shows that the simulation accurately predicts the vortex size but underpredicts the velocity overshoot along the centerline. Repeating Kramer’s particle tracking analysis of the flow field at one flow rate for a given set of streamlines we find good quantitative agreement for the elongation rates and relative stretch ratio, but we find our simulation generally underpredicts the shear rates and relative shear strain.
40(1996); http://dx.doi.org/10.1122/1.550790View Description Hide Description
Reversing double‐step strains provide a severe test of constitutive equations and have often been used to test the Doi–Edwards (DE) model with and without the independent alignment approximation. We report measurements of the full stress tensor in a concentrated monodisperse polystyrene solution subjected to reversing double‐step strains using flow birefringence. Shear stress and first normal stress difference results agree with previous studies. In flows where the second strain is half the magnitude of the first (‘‘specialized type‐B’’), certain rheological models predict that normal stresses should be independent of time between strains (t 1), and equal to those measured in single‐step strain. Both first and second normal stress differences follow this behavior at long times, but deviations are found at short times, where chain retraction is occurring. In flows with equal and opposite step strains (‘‘type‐C’’), the ratio N 1/σ is found to be equal to the strain. In both of these flows, the DE model predicts the normal stress ratio −N 2/N 1 to be independent of t 1. In specialized type‐B flows, the experimental normal stress ratio is nearly independent of t 1, while in type‐C flows the ratio depends strongly on t 1 and is found to be substantially larger than that predicted by the DE model or observed in single‐step strains. DE calculations for more general flow protocols predict that the normal stress ratio may depend on t 1 and on the time following the second deformation. Experiments show qualitative agreement with both forms of the DE model for these other flows, where the major influence of the independent alignment approximation is on the magnitude of the predicted normal stress ratio.
40(1996); http://dx.doi.org/10.1122/1.550784View Description Hide Description
In order to interpret the time dependence of the measuredtorque in a steady shear experiment on an aggregating dispersion, a microrheological model has been used in which two existing models are integrated. In this microrheological model, a theory for fractalaggregation in shear flow is combined with a theory for the sedimentation and resuspension of non‐colloidal hard spheres. The former theory describes the viscosity as a function of shear rate, while the latter predicts the stress increase in a Couette device due to sedimentation. The connection between the two theories is made by identifying the aggregate parameters with the hard sphere parameters (size and volume fraction). The parameters of the aggregates as a function of shear stress are obtained by measuring a flow curve before sedimentation effects become significant and fitting this curve with the fractalaggregation theory. During the sedimentation, the aggregate size and volume fraction become a function of both time and position in the rheometer. Taking this into account, the predicted stress increase as a function of time is found to describe the experiments rather well. This result corroborates both of the existing theories.
40(1996); http://dx.doi.org/10.1122/1.550789View Description Hide Description
We present a complete, self‐consistent set of thermodynamic constitutive equations for viscoelastic solid and fluid materials which can be applied during arbitrary, three‐dimensional deformations and thermal processes. Deformational and thermal histories are measured using a fading memory norm in a material time which provides a quantitative indication of the constitutive models’ ability to represent the dynamic response. The free energyconstitutive equation is a Frechet expansion about the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time. The kinetic relationship between the laboratory and material time scales does not depend on equilibrium considerations. This approach greatly extends the applicability of low‐order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, entropy,enthalpy, and heat capacity are derived. All the required material properties can be evaluated unambiguously by independent experiments via equilibrium and linear thermomechanical tests. Example predictions illustrate (i) the isobaric volume relaxation as a rubber is cooled into the glassy state, (ii) the yielding of a glassy solid polymer in uniaxial extension, (iii) non‐Newtonian shear thinning during steady shear of fluids, and (iv) stress overshoot of a polymer fluid in transient shear.
The relaxation of shear and normal stresses of nematic liquid crystalline polymers in squeezing and shear flows40(1996); http://dx.doi.org/10.1122/1.550733View Description Hide Description
The growth and relaxation of the shear and normal stresses in squeezing and simple shear flow are studied in this article for the nematic thermotropic liquid crystalline polymer Vectra A900. The shear stresses are found to relax very quickly to low values as soon as the flow stops, showing a long tail which is slow to die out. The normal stress never relaxes completely after a shear flow or a squeezing flow. There is good scaling agreement with strain in the case of the shear stress, whereas the agreement is less for the normal stress. The steady state values of the viscosity at 310 °C form the three‐region curve characteristic of liquid crystalline polymer fluids. Apparently the relaxation behavior of the normal stress is connected to the development of certain structures in the melt. The structures depend on the type of flow and change slowly during the relaxation. This change can also be observed by the gradual increase of the dynamic moduli, G′ and G″, measured as a function of time after the cessation of the shear flow.
40(1996); http://dx.doi.org/10.1122/1.550737View Description Hide Description
It is shown that chemically derived ultrafine zirconia powders (mean particle size ≤100 nm) can be processed at up to 60 vol % in a wax‐based organic vehicle by the selection of suitable dispersants and addition levels. These suspensions have been injection molded, and the resulting components sintered. This article describes the effects of two dispersants on the rheological behavior of suspensions. For the more effective dispersant, a high apparent maximum packing fraction correlates with a low yield stress, the appearance of a Newtonian plateau at low shear rate and volume fraction, and a high flow behavior index. Conversely, a less effective dispersant provides a higher yield stress, lower maximum packing fraction, and lower flow behavior index. In identical compositions of fluid, a coarse powder displays the same effects and also, when well‐stabilized, presents a dilatant transition which is ceramic volume fraction dependent. These behaviors are consistent with current interpretations of suspension rheology based on particle interactions.
40(1996); http://dx.doi.org/10.1122/1.550796View Description Hide Description
External flow is known to induce anisotropic growth of concentration fluctuations in polymer solutions close to the phase boundary. In this article, scattering dichroismmeasurements are used to investigate the structural dynamics of flow‐enhanced concentration fluctuations in a near‐critical, semidilute polymer blendsolution subjected to small‐amplitude oscillatory shear flow. Our measured frequency response reveals that the behavior of the shear‐induced fluctuations is governed by the relaxation time of the concentration fluctuations. Predictions from a hydrodynamic model, in good agreement with the experimental results, also indicate that the dynamics are dominated by a single relaxation time. In addition, relaxation times of the concentration fluctuations at various temperatures are calculated from dichroism data and are found to agree with those previously obtained from small‐angle light scattering experiments.
Sliding plate rheometer studies of concentrated polystyrene solutions: Large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate40(1996); http://dx.doi.org/10.1122/1.550738View Description Hide Description
A very high molecular weight, narrow molecular weight distribution polystyrene, having a molecular weight of 8.42×106, was investigated using a sliding plate rheometer. The solvent was diethyl phthalate. The solution exhibited wall slip during steady shear, even at very low shear rates and exhibited a marked normal‐stress‐driven secondary flow at high shear rates. However, there was no evidence of slip during the oscillatory shear tests. Using fast Fourier transformanalysis, the results of the oscillatory shear tests on this solution are presented in terms of response surfaces in a space based on a Pipkin diagram (strain‐rate amplitude versus frequency). These reveal the linear and nonlinear regimes and the approach to a purely elastic regime at high frequencies. Wagner’s constitutive equation predicts the major trends in the experimental data but does not provide quantitative predictions over the entire range of experimental parameters.
The effect of added triblock copolymer on the nonlinear rheology of ordered diblock copolymer mesophases40(1996); http://dx.doi.org/10.1122/1.550734View Description Hide Description
We present a phenomenological theory for the rheological behavior of ordered mesophases of mixed diblock and triblock copolymer under shear. This theory is based on a coupled multilayer model for mesophase dynamics, and represents the extension of an earlier theory [Doi et al., Macromolecules26, 4935 (1993)] for pure diblock copolymer mesophases. We show that added triblock copolymer suppresses yielding behavior in copolymer mesophases. We discuss the possible relevance of our model to experimental rheological and structural studies of microphase‐separated diblock+triblock copolymer solutions in selective solvents.