Elastic properties of polyethylene melts at high shear rates with respect to extrusion

Rheology and microstructure of magmatic emulsions: theory and experiments

The viscosities of a number of monodisperse polystyrene melts have been measured using a capillary rheometer. The materials covered a molecular weight range of 43,000–460,000. Shear rates of 1.54–1540 sec.−1 and temperatures of 350–450°F. were studied. The effect of molecular weight distribution of polydisperse polystyrene was also measured. It was found that while low shear viscosity was dependent on Mw, higher shear melt viscosities depended on averages between Mw and Mn until at 1000–2000 sec.−1, Mn controlled viscosity. Agreement with the 3.4‐power dependence of zero shear viscosity was good. Similar exponential relationships were found, with higher rates of shear, corresponding to smaller values of the exponent. Constant values of the exponent were found at constant shear stress but not at constant shear rate. Agreement with the constancy of the activation energy for viscous flow for various molecular weights and distributions at constant shear stress was good. However at constant shear rate, ΔE decreased as the molecular weight average increased and as the distribution broadened. Viscosity versus shear rate master curves were constructed by using the Buehe‐Harding procedure. All monodisperse polystyrenes showed excellent fit with the master curve. Other molecular weight distributions did not. Master curves also were constructed for measurements of dynamic viscosity versus frequency for monodisperse polystyrene. These curves when compared to steady state viscosities failed to confirm the correspondence of ηa to either |η*| or to η′.

The rate of breakage of duplex DNA molecules by laminar flow through a capillary has been studied. For λb2b5c DNA (molecular wt., M = 25 × 106) the point at which breakage occurs is normally distributed around the center of the molecule with a standard deviation of 12.5% of the molecular length. At constant shear stress or shear rate, the breakage rate is independent of ionic strength. Thus, shear induced local denaturation is not a rate limiting, preliminary step in breakage. In experiments at constant temperature with varying solvent viscosity (controlled by added sucrose) the breakage rate is a function of shear rate, not of shear stress. The rate of opening of hydrogenbonded circles into linear molecules by hydrodynamic shear is also shown to be a function of shear rate and not of shear stress. The breakage rate at constant shear rate is not greatly dependent on temperature. The shear rate required to achieve breakage is inversely proportional to M1,2. The breakage rate constant, k varies as a very high power of the shear rate; at 25°C, d In k/d In Gm ∼ 15; at 10°C, d In k/d In Gm ∼ 26, where Gm is the maximum shear rate at the capillary wall. The unexpected result that breakage rate is mainly dependent on shear rate, not shear stress, supports a model in which the DNA molecule is distorted with a driving force which depends on the hydrodynamic shear stress, ηG, but the rate limiting step is segment diffusion into a highly extended configuration. The characteristic time to achieve this configuration is proportional to solvent viscosity, η, hence the breakage rate is dependent on ηG/η or G, the shear rate.

The effects of long‐chain branching and of temperature on the melt elasticity in shear of polyethylene were investigated using die swell measurements and relating them to recoverable shear strain, normal stress, and shear modulus. Die swell measurements, as a function of shear rate, were obtained for high‐ and low‐density polyethylenes at temperatures ranging from 130° to 225°C. The samples were characterized by GPC and intrinsic viscosity for molecular weight distributions and degrees of long‐chain branching. The importance of annealing the extrudates at temperatures above the polymer melting temperature to achieve equilibrium, or strain‐free, values of die swell was demonstrated. The effect of long‐chain branch was to decrease elastic deformation. At constant shear stress, the melt elasticity of both high‐ and low‐density polyethylene was found to be essentially independent of temperature. Thus, at constant shear rate, elastic deformation decreased with increasing temperature, and it was demonstrated that this decrease could be quantitatively defined in terms of previously determined shear rate–temperature viscosity superposition shift factors.

By means of a cone and plate rheometer the relaxation of the shear stress and the first normal stress difference in polymer liquids upon cessation of a constant shear rate were examined. The experiments were conducted mostly in a high shear rate region of relevance for the processing of these materials. The relaxation behavior at these shear rates can only be measured accurately under extremely precise specifications of the rheometer. To determine under which conditions the integral normal thrust is a convenient measure for the relaxing local first normal stress difference the radial distribution of the pressure in the shear gap was measured. The shape of relaxation of both the shear stress and the first normal stress difference could be closely approximated for the entire measured shear rate and time range by a two parameter statistical function. In the range of measured shear rates, one of the parameters, the standard deviationS, is equal for the shear and the normal stress, and is independent of the shear rate within the limit of experimental error. The second parameter, the mean relaxation timet′50,τ of the shear stress andt′50,σ of the first normal stress difference, can be calculated approximately from the viscosity function and only a single relaxation experiment.

Vinyl ester resins with varied acid values (11, 22, 32, 38, and 48 mg KOH/g solid) were prepared by reacting epoxy-novolac resin with methacrylic acid. The rheological behavior of these synthesized vinyl ester resin (VER) samples containing styrene as reactive diluent was studied using a Haake Rotovisco RV 20 viscometer. The apparent viscosity was found to be inversely proportional to the square root of the acid value in the temperature range of 25–40°C and at shear rates ranging from 100–800 sec−1. The zero-shear viscosity of these VER samples containing styrene (40% w/w) as reactive diluent decreased linearly with temperature. The activation energies for flow at constant shear stress (25–100 Pa) for a particular sample were found to be constant. The activation energy at constant shear rate decreases with the increase in the shear rate (50–400 sec−1). The activation energy at constant shear rate and shear stress decreased with the increase in the acid value. The viscosity of vinyl ester resin containing styrene as reactive diluent decreased almost 50 times with the increase in the concentration of reactive diluent from 30% to 100% (w/w of the resin).

Apparent flow activation energies evaluated from viscosity changes with temperature can be calculated in the non‐Newtonian region at either constant shear rate, E, or at constant shear stress, E. For many linear, amorphous polymere, it can be shown that E is independent of stress over the full range for which shear stress data tire reported. This conclusion also holds for solutions of several polymer types. Anomalous results are documented only for branched polyethylene. E decreases with shear in the non‐Newtonian region approaching a lower limit corresponding to the “power law” region. The relative changes in E with shear rate can be expressed in terms of reduced variables. The absolute change in E with shear rate can he used as a measure of polymer molecular weight distribution.

The variation with shear of the concentration dependence of the reduced viscosity was studied in the system polystyrene‐toluene at 20, 40, and 60°C. The slope constant k′ was determined at constant shear stress k′T and at constant shear rate k′D; k′T was found to increase, k′D to decrease, with increasing shear. Alternatively, the concentration dependence was expressed in terms of Peterlin's effective viscosity. For this system the effective viscosity at constant shear stress was independent of shear but the effective viscosity at constant shear rate decreased with shear. The decrease in k′D, and in effective viscosity at constant shear rate with shear are attributed to molecular entanglement and an explanation is proposed for the observed differences in behaviour at constant shear stress and constant shear rate. In appendices a new formula for the calculation of viscosity ratios from the relative flow times is derived, and a procedure is outlined to compute intrinsic viscosities and limiting slope constants that will be free from absorption effects.

The theological properties of nematic liquid crystalline polymers are strongly affected by the dynamic behavior of the molecular alignment. Starting from a closed nonlinear inhomogeneous relaxation equation for the five components of the alignment tensor which, in turn, can be inferred from a generalized Fokker-Planck equation, it has recently been demonstrated (G. Rienacker, M. Kroger, and S. Hess, Phys. Rev. E 66, 040702(R) (2002); Physica A 315, 537 (2002)) that the rather complex orientation behavior of tumbling nematics can even be chaotic in a certain range of the relevant control variables, viz. the shear rate and tumbling parameter. Here the theological consequences, in particular the shear stress and the normal stress differences, as well as the underlying dynamics of the alignment tensor are computed and discussed. For selected state points, long-time averages are evaluated both for imposed constant shear rate and constant shear stress. Orientational and theological properties are presented as function of the shear rate. The transitions between different dynamic states are detected and discussed. Representative examples of alignment orbits and theological phase portraits give insight into the dynamic behavior.

The stress-optical properties of aluminum dilaurate-toluene solutions were investigated over a wide range in shear rates, D. Flow curves of 1, 2, and 3 wt-% of the aluminum soap dispersed in toluene displaced the type of behavior previously reported by Weber and Bauer: i.e., Newtonian behavior at low shear rates, pronounced shear thinning at D greater than 10−2 sec−1, and dependence of apparent shear stress, τ, on length-to-radius ratio, L/R, of the capillary tubes used at high shear rates. Flow birefringence behavior was similar. For example, at low shear rates the degree of birefringence, Δn, increased in proportion to D and the extinction angle, χ, was nearly 45°. Above a critical shear rate, Δn, increased overproportionally, finally leveling out at a high value. Simultaneously χ decreased equally rapidly to about 1°. Despite these dramatic changes in dependence of τ, Δn and χ on D, the stress-optical coefficient remained constant over the entire range of variables. Elastic recoverable shear strains, or simply “recoverable shears,” s, were calculated from the variance of τ with L/R. These were found to be in good agreement with data obtained from normal stress measurements in a Weissenberg Rheogoniometer. At low shear stress s increased linearly with τ. Above a critical shear stress the recoverable shear increased rapidly with small increases in τ finally leveling off at a value of approximately 300 shear units and remaining constant with additional increases in shear stress. This behavior is similar to that observed with polyethylene in the region where melt fracture occurs. In these experiments, however, the transition takes place in a rotational instrument under continuous shear in which no “entrance effects” can be postulated as causing melt fracture. During the progress of this investigation it was ascertained that the rotational viscometer could be used to determine elasticity in aluminum soap solutions under dynamic conditions. Quantitative evaluation of the results produced data which correlated with dynamic test data obtained by a variety of techniques. The authors believe that this is a unique and novel method for measuring the dynamic rheological properties of viscoelastic materials.

Cardiovascular blood-recirculating devices provide life saving cardiopulmonary support to critically ill populations. Unfortunately, common device-related thrombotic complications continue to result in significant mortality, neurological morbidity, and limb loss. Past studies have shown that increased wall shear stress from blood-recirculating devices activates circulating monocytes and platelets. Less well studied is the enhancement of thrombosis by platelet-derived (PMPs) and monocyte-derived microparticles (MoMPs). These are small (0.1-1 micron) cell-derived membrane vesicles released from activated cells. Studies using a biological stimulant demonstrate that MoMPs initiate clotting whereas PMPs enhance clotting. Few if any studies have defined the contributions of device-produced microparticles (MPs) to changes in thrombotic potential. Our hypothesis is the increased dynamic or constant shear stress generated by a blood-recirculating device promotes release of prothrombotic MPs. Using an Anton Paar MCR Rheometer we exposed whole human blood in vitro to both dynamic (70 dynes/cm 2 at 0.05hz) and constant (70 and 35 dynes/cm 2 ) shear stress conditions for two minutes. After shear, MPs were collected with dual centrifugation and then quantified using a BD FACS Canto II flow cytometer with forward scatter photomultiplier tube (resolution=200nm). Then we pelleted and washed MPs to measure changes in thrombin generation with a Calibrated Automated Thrombogram (CAT). Dynamic shear stress generated 3841±1171 PMPs/μL and 3522±1090 MoMPs/μL, (MEAN±SE, n=6). Constant shear stress at 70 dynes/cm 2 and 35 dynes/cm 2 generated PMPs/μL of 4937±1655 and 1880±389 and MoMPs/μL of 6935±2029 (n=3) and 2262±1041 respectively (MEAN±SE, n=3 for each). All shear conditions generated an increase in MP concentration over static conditions of 644±120 PMPs/μL and 538 MoMPs/μL (p<0.01). Dynamic and constant sheared MPs increased the estimated thrombin potential and peak thrombin generation by at least 30% compared to static (p<0.05). This study is the first to demonstrate that device relevant constant and dynamic shear stresses can generate PMPs and MoMPs that promote thrombosis.

Complex fluids exhibit time-dependent changes in viscosity that have been ascribed to both thixotropy and aging. However, there is no consensus for which phenomenon is the origin of which changes. A novel thixotropic model is defined that incorporates aging. Conditions under which viscosity changes are due to thixotropy and aging are unambiguously defined. Viscosity changes in a complex fluid during a period of rest after destructuring exhibit a bifurcation at a critical volume fraction ϕc2. For volume fractions less than ϕc2 the viscosity remains finite in the limit t →∞. For volume fractions above critical the viscosity grows without limit, so aging occurs at rest. At constant shear rate there is no bifurcation, whereas under constant shear stress the model predicts a new bifurcation in the viscosity at a critical stress σB, identical to the yield stress σy observed under steady conditions. The divergence of the viscosity for σ≤σB is best defined as aging. However, for σ > σB, where the viscosity remains finite, it seems preferable to use the concepts of restructuring and destructuring, rather than aging and rejuvenation. Nevertheless, when a stress σA(≤σB) is applied during aging, slower aging is predicted and discussed as true rejuvenation. Plastic behaviour is predicted under steady conditions when σ > σB. The Herschel-Bulkley model fits the flow curve for stresses close to σB, whereas the Bingham model gives a better fit for σ >> σB. Finally, the model’s predictions are shown to be consistent with experimental data from the literature for the transient behaviour of laponite gels.

Primary normal stress difference data of some 32 different polymer solutions have been examined and correlated to the shear stress by a simple power‐law model. The normal stress at constant shear stress is shown to increase with the molecular weight of the polymer, but decreases with the polymer concentration. The method proposed by Abdel‐Khalik, et al. , for predicting the primary normal stress difference from viscosity data for these polymer solutions is inadequate. The FENE‐P dumbbell model is used to obtain master curves combining normal stress and viscosity data as a function of a dimensionless shear rate. It is found that this presents several drawbacks. It predicts shear‐thinning effects with a power‐law slope of −2/3, which is found to be too restrictive. The model fails to predict shear‐thinning effects for dimensionless shear rates λ E γ lower than approximately 0.5. It also fails to predict satisfactorily the low shear rate value of the dimensionless combination of viscosity and first normal stress coefficient Ψ 1 /λ E (η − η s ). An empirically modified correlation is proposed. The fit for a series of polyacrylamide (Dow Separan AP‐30) solutions is very good. In the case of a series of monodisperse polystyrene solutions, the fit is not as good, as the data show a more pronounced effect of polymer concentration at high shear rates.

Melt rheology and extrudate swell properties of talc filled polyethylene compounds

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.