Temperature dependence of polymer viscosity. The influence of shear rate and stress

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.

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.

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.

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).

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.

Melt rheology and extrudate swell properties of talc filled polyethylene compounds

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.

The investigations about the steady shear viscosity of non-Newtonian flow in concentrated polymer solutions have been reported by Porter et al. and Ozaki et al. Log viscosity versus log molecular weight relations obtained by Porter et al. and by Ozaki et al, are those at constant shear stresses and at constant rates of shear, respectively.In the results obtained by Porter et al., the slope of log η"log M relation becomes smaller as the shear stress increases in the region of molecular weight higher than a critical value Mc as is shown in Fig. 1.On the other hand, the slopes of log η"log M relation obtained by Ozaki et al. are 3.4 in the region of molecular weight lower than a second critical value M'c (>Mc) which depends on shear rate γ0 and <3.4 (nearly 2) in the region of molecular weight higher than M'c as is shown in Fig. 2.Since the concentrated polymer solution spreads a network structure crosslinked temporarily by the entanglement of polymer molecules, it is desirable to make clear the viscosity versus molecular weight relations by making use of the theory of network structure.In § 2 the linear theory of viscoelasticity of network structure is reported in a reformed formalism. When we consider a polymer molecule in the network structure, the aggregation of the remaining molecules could be considered to be a sort of viscoelastic medium. When a part of polymer molecule between the adjacent crosslinkages termed chain, a chain in a molecule has the viscoelastic effects on other chains in the same molecule through the viscoelastic medium, so that the system corresponds to a model composed of interacting Rouse model. The viscoelastic interactions between the chains in a, molecule. though they seems intra-molecular interactions, are due to the average inter-molecular interactions induced by the motion of the viscoelastic medium. By using the above model we obtain the slip equation (2.17) and the stress (2.2'), where <γi> and <Di> contained in τi are viscous and elastic effects in the i-th normal coordinate and are given by (2.19). For continuous distribution of relaxation times, the slip equation and the stress are written as (2.21), which are the expressions in the linear theory.In order to investigate the non-Newtonian effect on viscosity, the linear theory is extended by introducing the parameters depending on the shear stress or rate, and we assume the phenomenological relations (3.1), where α and β are parameters characterizing the elastic and the viscous effects and functions depending only on the shear stress. In non-Newtonian flow, the stress and the slip equation are given by (3.2) and (3.3), respectively. τα is the critical relaxation time corresponding to the movement of molecule having molecular weight Mc, τβ being the maximum relaxation time.For steady flow the stress is given by (4, 2), where γo is the shear rate and ν is the number of chains in the unit volume. The log η-log M relation at constant shear stress is given by (4.3'), where Ms (=Mc) is the molecular weight of chain. From (4, 3'), β is determinable as a parameter depending on shear stress from the experimental results obtained by Porter et al. The experimental data show that as the shear stress increases β decreases from 2.5 to 0.On the other hand β is a function of shear rate and molecular weight, since the shear stress is a function of molecular weight M and shear rate γo.

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 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 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 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.

The plastic deformation kinetics of 95.5Sn4Cu0.5Ag solder joints were determined in monotonic loading shear over the temperature range of 25°–150°C using three types of tests: (a) constant shear rate, (b) constant shear stress (creep), and (c) differential tests (changes in shear rate or temperature during an otherwise isothermal constant shear rate test). The deformation kinetics were evaluated in terms of the Dorn high temperature plastic deformation equation γ˙p=A(μb/kT)D(b/d)P(τ/μ)n where γ˙p is the shear rate, μ the shear modulus, b the Burgers vector, D the appropriate diffusion coefficient, d the grain size and τ the shear stress. A, p, and n are constants whose values depend on the rate controlling mechanism. It was found that n increased with stress from ~4 at 2 MPa to ~20 at 25 MPa, relatively independent of temperature. The activation ΔH was determined to be 21.1 ± 2 kcal/mole. The constant A, however, decreased with temperature from a value of ~1018 at 25°C to ~1010 at 150°C. The values of n and ΔH suggest that dislocation glide and climb is the rate controlling mechanism and hence that p ≈ 0. It is speculated that the large decrease in A with temperature may be the result of an effect on the microstructure.

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.

A capillary rheometer equipped with a pressure chamber is used to measure the pressure-dependent viscosity of polymethylmethacrylate (PMMA), poly-α-methylstyrene-co-acrylonitrile (PαMSAN), and low-density polyethylene (LDPE). Data analysis schemes are discussed to obtain pressure coefficients at constant shear rate and at constant shear stress. It is shown that the constant shear stress pressure coefficients have the advantage of being shear stress independent for the three polymers. The constant shear rate pressure coefficients, on the other hand, turn out to depend on shear rate, which makes them less suitable for use, e.g., in process simulations. In addition to the commonly used superposition method, a direct calculation method for the pressure coefficients is tested. Values obtained from both methods are equivalent. However, the latter requires less experimental and calculational efforts. From the obtained pressure coefficients, it is clear that PMMA and PαMSAN have a very similar pressure dependence, while LDPE is less sensitive to pressure.