Melt rheology and extrudate swell properties of talc filled polyethylene compounds

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 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 rheological properties of a sodium tallow-coconut oil soap (15% water) have been determined using a high pressure capillary extrusion viscometer over shear rates of 14.7 to 2560 sec−1 and temperatures of 70–103°C. Capillary flow measurements were also made on sodium stearate (25% water) at 90°C. The data indicated shear thinning characteristics and were fitted to an equation of the form: $$\log \tau _R = \log A + n\log \dot \gamma _R $$ over the above shear rate range. The flow indices (n) of 0.337–0.437 were comparable to those obtained from polyethylene data in the literature. A zero shear activation energy of 57.2 Kcal/mole was calculated for the tallow-coconut soap. The activation energy at constant shear stress was greater than that at constant shear rate and decreased with increasing shear stress and shear rate. The soap flow unit was estimated to contain about 2 · 104 molecules.

The viscosity of polymer melts is dependent on various factors such as shear rate, temperature, pressure and molecular structure. High-pressure capillary rheometery (HPCR) can be used to determine viscosity as a function of shear rate and temperature in the shear rate range relevant for injection molding and extrusion processing. Conventional HPCR measurements cannot determine the pressure dependence of viscosity so that it is typically neglected. Particularly at high pressures and low shear rates, the viscosity is therefore underestimated. However, it is possible to determine the pressure dependency using a counter pressure chamber or actively controlled counter pressure viscometer. Nevertheless, these devices are rarely available, and the measuring effort is high compared to conventional measurements. In order to be able to represent the pressure-dependent material behavior and thus improve the accuracy of process simulations in a cost-effective way, the aim of this paper is to use the free volume approach via the coupled equations of state according to Simha and Somcynsky1 to link the temperature and pressure dependence of the melt density to the viscosity. The model was extended according to Utracki and Sedlacek2–4 and applied to true viscosity data at constant shear stresses in the process relevant apparent shear rate range from 1 to 5000 1/s. The necessary viscosity data for the investigated PP and PC at different temperatures in the typical processing range were determined using a conventional HPCR, and a pvT measuring device was used to determine the melt density. The hole fraction as a measure for the free volume is calculated at each shear stress through the coupled equations of state and linked to the true viscosity through error square minimization at the mean pressure in the capillary. This allows for the recalculation of an isobaric viscosity curve at different pressure and temperature levels. For validation of the model viscosities were also measured at various pressure levels using a counter pressure chamber to determine an experimental pressure coefficient. The model results for the investigated materials show a high agreement with the experimentally determined pressure coefficients

Properties modification by blending polymers has been an area of immense interest. In this work, rheological and mechanical properties of poly(lactic acid)/polystyrene (PLA/PS) blends were investigated. PLA/PS blends in different ratios were prepared using a laboratory scale single screw extruder to obtain (3 mm) granules. Rheological properties were studied using a capillary rheometer and the Bagley’s correction was performed. True shear rate (γr), true shear stress (τr), and true viscosity (ηr) were determined, the relationship between true viscosity and (1/T) was studied for PLA70 blend and the flow activation energy at a constant shear stress (Eτ) and a constant shear rate (Eγ) was determined. The mechanical property measurements were performed at room temperature. Stress at break and strain at break were determined. The results showed that PLA/PS blend exhibited a typical shear-thinning behavior over the range of the studied shear rates, and the viscosity of the blend decreased with increasing PLA content. Also it was found that no equal-viscosity temperature exists between PLA and PS. The mechanical results showed immiscibility between PLA and PS in the blend.

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).

At high shear rates a steady state of shear flow with constant shear rate, constant shear stress, and constant recoverable shear strain is observed in the short-time sandwich rheometer after some few shear units already. The melt exhibits rather high elastic shear deformations and the recovery occurs at much higher speed than it is observed in the newtonian range. The ratio of first normal stress difference and twice the shear stress, being equal to the recoverable strain in the second-order fluid limit, significantly underestimates the true elastic shear strains at high shear rates. The observed shear rate dependence of shear stress and first normal stress difference as well as of the (constrained) elastic shear strain is correctly described on the basis of a discrete relaxation time spectrum. In simple shear a stick-slip transition at the metal walls is found. Necessary for the onset of slip is a critical value of shear stress and a certain amount of elastic shear deformation or orientation of the melt.

The melt viscosities of three low density polyethylenes of widely varying melt indices were studied as a function of temperature over a broad range of shear rates and shear stresses. Apparent viscosities at constant shear stress could be fitted adequately to a simple Arrhenius equation over the entire temperature range studied. However, pronounced curvature of the log ηa–1/T curves was observed for apparent viscosities at constant shear rate. The apparent activation energies for viscous flow at constant shear stress were found to decrease slowly with increasing shear stress and also to decrease with decreasing molecular weight. A temperature‐shear rate superposition was demonstrated to hold, and the shift factor dependence on temperature was determined.

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 influence of calcium carbonate and kaolin fillers on the viscosity of HDPE and PP melts with various melt viscosities was investigated by capillary viscometry. Two regions of flow behaviour could be distinguished. In region I, at low shear stresses, the relative viscosity at constant shear stress η rτ is stress-dependent and the flow is strongly influenced by the presence of aggregates or structures formed by the filler. In region II, at high shear stresses, η rτ is independent of τ and the influence of the filler is predominantly hydrodynamic due to separate filler particles. In both flow regions the relative viscosity at constant shear rate \({\eta _{r\dot \gamma }}\) is a function of the shear rate and the matrix viscosity.

Relative hydraulic resistance, shear rate, and pressure in a vascular network integrate the network's architecture via fluid flow, and determine vein dynamics, with a time delay, in the prototypical organism Physarum polycephalum.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross-linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt%, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt%, and after that shows a maximum at a gel fraction of about 25 wt%, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40wt%. The flow activation energy at a constant shear rate, ΔHγ, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70wt%.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt. %, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt. %, and after that shows a maximum at a gel fraction of about 25 wt. %, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end-correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40 wt. %. The flow activation energy at a constant shear rate, ΔHγ̇, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70 wt. %.

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.

Melt viscosity of a polypropylene (PP) resin was measured in a capillary rheometer between 220 and 260°C. The melt viscosity showed a power law behavior with strong shear rate dependence. The effects of temperature and shear rate on the degradation were studied in the rheometer by heating at 260 and 280°C, and extruding at shear rates up to 10000 sec −1 . Melt flow index (MFI) of samples after shearing and heating treatment was measured to characterize the molecular weight change. An increase in MFI was found for PP sheared at high temperature. Heating for longer time also increased MFI. Increase of shear rate had a small effect on increasing MFI at 260°C but produced a larger effect at 280°C. A constant increment in MFI was observed in PP subjected to high temperature processing and was attributed to degradation due to oxygenated products.