Relation between kneading behavior and flow instability of a high molecular weight high density polyethylene,applications to extrusion

Non-monotonic continuous curves of torque as a function of shaft speed, M(N), have been obtained for a high molecular weight high density polyethylene (HDPE) from measurements obtained with a torque rheometer (Haake Rheocord). Previous papers have given theoretical demonstration of the non-monotonic character of the shear stress-shear rate function, s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}), which makes it possible to explain the extrusion behavior of a high molecular weight HDPE. In capillary rheometry, it is not possible to obtain the values of s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) into the “well zone” of this function because the compressibility of the polymer creates a phenomenon of oscillation in the barrel affecting the die output flow rate and the pressure loss. The M(N) function measured by the Haake Rheocord is a complete representation of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function, although the capillary rheometer only gives a partial representation of this function. The transformation of the M(N)function into s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) is quite difficult because of the complex geometry of the Haake Rheocord measuring head. The “critical points” of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function in the capillary rheometer (appearance of oscillations), can be correlated to the maximum points of the M(N) function in the Haake Rheocord at constant temperature. The non-monotonic aspect of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function provides an important technological application: extrusion of a high molecular weight HDPE at an increased flow rate at low temperatures.     

The Radiation Chemistry of Cytochrome c

The literature on the reaction of cytochrome c with the radiolytically generated radicals \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm e}_{{\rm eq}}^ -,^. {\rm OH,}^{\rm .} {\rm H,CO}_2^ -,{\rm O}_{\rm 2}^ -,{\rm Br}_{\rm 2}^ - $\end{document} and various organic radicals is reviewed. It would appear that negatively charged radicals, aided by the electric field of cytochrome c, react at the exposed haem edge. Uncharged organic radicals also react at this site. \documentclass{article}\pagestyle{empty}\begin{document}$ ^. {\rm H} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ ^. {\rm OH} $\end{document} are likely to reduce the prosthetic group indirectly by a tunnelling mechanism.     

The stress-strain behavior of materials exhibiting andrade creep

The stress-strain behavior of a material exhibiting Andrade creep (for which the creep compliance is linear in the cube-root of time) has been calculated for loading at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm \varepsilon}\limits^{\rm .} $\end{document} and at constant stress rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for the limiting case of linear viscoelastic behavior and at constant \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for one type of nonlinear viscoelastic response. The recoverable strain after the stress has been removed has also been calculated for these three cases. The results of the calculations are compared with experiment.     

Characterization of polyvinyl chloride part II. The unperturbed end to end distance values obtained from a new GPC method and viscometry

A new gel permeation chromatography (GPC) method is proposed for determining the unperturbed end-to-end distance, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document}, of polymers of known molecular weights, Mn and Mw. This method requires the value of \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} _{{\rm ps}} $\end{document} of polystyrene which was determined through viscometry to be 0.735 \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{{\rm {\AA}}^2-{\rm mole}}}{{gm}}} \right)^{0.5} $\end{document} Polyvinyl chloride (PVC) was chosen to illustrate the method and \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} was found to be 0.99 from GPC data which is in agreement with the result obtained from viscometry, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} = 1.01. All \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document} values were determined at 30°C. The advantage to this method lies in its speed and economy of materials.     

Zur kinetik der acrylnitril-polymerisation

The heterogeneous bulk polymerization of acrylonitrile initiated by AIBN has been studied by means of an improved dilatometric technique and a new method of analysis, where the initial reaction rate (v_w)₀ results from the intercept of a straight line in a \documentclass{article}\pagestyle{empty}\begin{document}$ \frac {\ln \left( 1 \hbox{---} {\rm U} \right)} {{\rm e}^{{- 0,5} {\rm k}_{\rm s}{\rm t} \hbox{---} 1}}$\end{document} versus t plot. It has been found that the initial reaction rate is proportional to the square root of the initial catalyst concentration S₀. The ratio of the rate coefficients of propagation and termination\documentclass{article}\pagestyle{empty}\begin{document}$\frac { {\rm k}_{\rm a} } { {\rm k}_{ {\rm w}^{2} } } $\end{document} could be calculated from the slope of a straight line passing through the origin in a plot of (v_w)₀ versus \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt { {\rm S}_{0} }$\end{document} and yielded a value of 280 mol 1^?1.     

Empirical correlation of flow properties of poly(vinyl chloride)

Empirical correlations of flow properties of poly(vinyl chloride) were made using data reported by a number of investigators. Correlation was made by plotting the reduced variable viscosity η/η₀ versus \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w )/(_\rho RT) $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w ^{0.5} )/(_\rho RT) $\end{document} for unplasticized PVC and versus \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w ^{0.5} )/(_\rho RTW_2 ^a ) $\end{document} with polymer concentration, W₂, for PVC containing plasticizer.     

Kinetic study of the hydrolysis of cellulose acetate in the pH range of 2–10

A kinetic study of the hydrolysis of 39.8 wt.-% acetyl cellulose acetate has been made as a function of pH and temperature over the pH range of 2.2–10 and temperature range of 23–95°C. The hydrolysis reaction was carried out on highly porous membranes under quasihomogeneous conditions and the data have been treated as a pseudo-first-order reaction in acetyl concentration. The reaction can be represented by the equation \documentclass{article}\pagestyle{empty}\begin{document}$k_1 {\rm = }\;k_{\rm H ^ +} \left[ {{\rm H^+}} \right]{\rm +}k_{\rm OH^-}\left[ {{\rm OH}^ - } \right] + k_{\rm H_2O} $\end{document}, and where \documentclass{article}\pagestyle{empty}\begin{document}$k_{\rm H} ^ + {\rm = 5}{\rm .24}\;{\rm x 10}^{\rm 5} {\rm exp }\left\{ {{\rm ‐ 16}{\rm .4 x 10}^{\rm 3} /RT} \right\},{\rm }k_{{\rm OH}} ^ ‐ {\rm = 1}{\rm .55}\;{\rm x 10}^{\rm 4} {\rm exp }\left\{ {{\rm ‐ 8}{\rm .1 x 10}^{\rm 3} /RT} \right\}$\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$k_{\rm H_2O} {= 4.25\;\times 10}^{- 2} {\rm exp }\left\{ {{- 11.5 \times 10^3 /RT}} \right\}$\end{document} (where the quantities in brackets are activities of the ions shown).     

Zum Einfluß von Lösungsmitteln auf das VIS-Spektralverhalten von 4′-Dialkylamino-α-cyano-stilben-4-diazoniumsalzen

Solvatochromism of 4′-Dialkylamino-α-Cyano-Stilbene-4-Diazonium-Salts 4′-Dialkylamino-stilbene-4-diazonium-salts are deep coloured compounds and give strong solvatochromism. 4′-Diethylamino-α-cyano-stilbene-4-diazonium-tetrafluoroborate was investigated in 52 different solvents and 3 binary solvent mixtures. With increasing solvent basicity the longest wave lenght absorption maximum (\documentclass{article}\pagestyle{empty}\begin{document}$ \nu^{\hspace{-5pt}\sim}_{\rm max} $\end{document}) decrease. Complex formation by crown ethers causes a decrease of \documentclass{article}\pagestyle{empty}\begin{document}$ \nu^{\hspace{-5pt}\sim}_{\rm max}$\end{document}, too. In solvents with dielectricity constants higher than about 15 dissociation effects superpose solvatochromism. The summary of experimental dates support the approach of specific nucleophilic solvatation of diazonium ions.     

Influence of electrolytes on the absorption of nitrogen oxide components N2O4 and N2O3 in aqueous absorbents

The influence of electrolytes, which are dissolved in the aqueous absorbent and do not react with nitrogen oxides, on the absorption kinetics of both these components was investigated experimentally. In addition to demineralized water, various salt solutions of different concentrations as well as sodium hydroxide solution were used as absorbents. The term H \documentclass{article}\pagestyle{empty}\begin{document}$ H\sqrt {k_1 D} $\end{document} for N₂O₄ and N₂O₃, which is important for the design of industrial absorbers, was determined as a function of composition and concentration of the absorbents. In the case of N₂O₄, the chosen measuring and evaluation methods permitted a separate determination of the rate constant k of the pseudo first order reaction and of the solubility H. The diffusion coefficient D of the gas in the absorbent can be obtained only by calculation. Experimental results showed that \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 4} } $\end{document} decreases with increasing ionic strength I, however, without a clear indication of any ion-specific effects. This decrease does not appear to be caused simply by a reduction in solubility (salting out effect), or in diffusion coefficient, but at least, to the same extent, through a decrease of the rate constant k with increasing electrolyte content in the absorbent. The measurements permitted the determination of the gas-based salting out parameter for N₂O₄. The investigations on the absorption of N₂O₃ in water and in an Na₂SO₄ solution showed no experimentally detectable influence of dissolved salts on \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 3} } $\end{document}. The numerical value of \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 3} } $\end{document} is six times that of \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 4} } $\end{document}.     

The rheology and spin coating of polyimide solutions

The rheological properties of five types of concentrated polyamic acid and polyimide solutions are characterized by non-Newtonian shear viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) and primary normal stress coefficient Ψ₁(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) measurements over a wide range of shear rates. Onset of non-Newtonian flow of the polyamic acid solutions was observed in the shear rate range 30 to 400s^?1 and of the fully imidized polyimide solution at below 3 × 10^?2s^?1. Significant viscoelastic properties exemplified by normal stresses were observed in all the solutions. The solution rheology results are discussed in the context of spin coating for the deposition of thin films. The relative magnitude of effects of non-Newtonian flow on the dynamics of spin coating is assessed with a Deborah number characteristic of the flow.     

Characterization of polyvinyl chloride. Part III. An alternative GPC method for measuring the radii of gyration,and the degree of long-chain branching of polydispersed polymers

A method for measuring the unperturbed radius of gyration and the degree of long-chain branching in Gaussian-distribution polymers is proposed. Polyvinyl chloride (PVC) and polyvinyl acetate (PVAc) were selected to illustrate the method. It was observed that PVC samples prepared by homogeneous and heterogeneous polymerizations exhibit the same degree of long-chain branching. This conclusion is supported by viscometric data. The polydispersity ratios (M_w/M_n) indicate that both types of polymerizations would yield a very small amount of total branching (long chain and short chain.) The calculated unperturbed radius of gyration of linear PVC samples was found to be 0.185 \documentclass{article}\pagestyle{empty}\begin{document}$ \left( {\frac{{{\rm \dot A}^{\rm 2} {\rm mole}}}{{{\rm gm}}}} \right) $\end{document}, and that of PVAc was determined to be 0.107 \documentclass{article}\pagestyle{empty}\begin{document}$ \left( {\frac{{{\rm \dot A}^{\rm 2} {\rm mole}}}{{{\rm gm}}}} \right) $\end{document}. The value obtained for PVC is shown to be in agreement with the value determined from the viscometric method as described in our previous work.     

Polymer melt elongation—methods,results, and recent developments

For film blowing of polyethylene it has been shown previously that melt elongation is very powerful for polymer characterization. With two types of rheometers, simple (also called “uniaxial”) elongational tests as well as creep tests can be performed homogeneously. In simple elongation, the melts of branched polyethylene show a remarkable strain hardening. With respect to their advantages and disadvantages, these rheometers complement each other. For multiaxial elongations the various modes of deformation can be performed by means of the rotary clamp technique. With the strain rate components ordered such that \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ ? \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂ ≥ \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₃₃, the ratio m = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂/\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ characterizes the test mode. The Stephenson definition of the elongational viscosities makes use of the linear viscoelastic material equation and proves to be very efficient because the linear shear viscosity (t) (“stressing” viscosity) can act as the reference for the nonlinear behavior in elongation. Results are given for polyisobutylene measured not only in simple, equibiaxial, and planar elongations, but also in new test modes with a change of m during the deformation. This allows one to investigate the consequences of a deformation-induced anisotropy of the rheological behavior.     

Die Wahl des optimalen Verfahrens für die Bestimmung des Primärradikalabbruchs aus Geschwindigkeitsdaten

The various plots for estimating the ratio of rate constants characteristic for primary radical termination, k₅/k₁k₂, have been examined systematically. Apart from the special case d ≡ k₃k₆/k₅² = 1 there is no exact linear relationship between the general quantity \documentclass{article}\pagestyle{empty}\begin{document}${\rm Y \equiv (\sqrt {c_S} c_{M}/v_{Br})^{n}}$\end{document} and the general variable \documentclass{article}\pagestyle{empty}\begin{document}${\rm X \equiv (\sqrt {c_S} /c_M)^{s} (v_{Br}/c_M^{2} )^{1 - s}}$\end{document}. In any case, however, Y can he expressed as a power series of X. Therefore the best way to obtain the most favourable linear representation of Y as a function of X is to choose s and n according to the condition that the coefficient of the term quadratic in X has to disappear (n ? 2 s + d = 0) and the coefficient of the X³-term also equals 0 or is at least close to 0. Under these conditions even those data can be represented in an almost perfect linear form which show variations of the quantity \documentclass{article}\pagestyle{empty}\begin{document}$({\rm \sqrt{c_{s}}c_{M}/v_{Br})}$\end{document} by a factor of \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt{2}$\end{document} or more for different initiator concentrations c_s. If additionally allowance is made for the consumption of monomer by the initiation process the desired ratio of rate constants, k_s/k₁k₂, is obtained from the plot of Y vs. X according to the equation The application of this method is illustrated using an example from literature.     

Yield stress and flow measurements in ABA block copolymer melts

A parallel-plate constant-stress rheometer is used to measure the yield stress τ_y, and the post-yield flow curve T(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}), where τ is shear stress and \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is shear rate, for microphase-separated triblock copolymer melts. Five polymer samples, all styrene-butadiene-styrene but with differing composition ratios and molecular weights, are tested at 125°C. Specimens are prepared by casting sheets from solutions made with different solvents. The τ(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}) is found usually to be sigmoidal, for the range 10^?5 < \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} < 10^?3 s^?1, representing different stages of microstructural degradation in flow. Measurements indicate that a true τ_y exists, with values in the range 100 < τ_y < 500 Pa for these melts. A general trend is detected for τ_y to decrease as the casting solvent solubility parameter increases. A scheme for correlating the dependence of τ_y, on composition and molecular weight is proposed for the various polymers. For selected samples, the effect of mechanical history (sequence of stress application) and a temperature variation that crosses T_s (110 to 150°C) are also explored.     

Dynamic stress intensity factors during viscoelastic crack propagation at various strain rates

Dynamic stress intensity factors K_D were measured by the caustic method and crack propagation velocity ? by the velocity gauge techniques for PMMA [poly(methyl methacrylate)] during dynamic crack propagation at various strain rates \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} . No definite applied strain rate effects on the dynamic stress intensity factor were observed for applied strain rates ranging from 8.33 × 10^?4 to 30/sec; however, the test results do show crack propagation velocity dependency in K_D ～ ? relations. The high local strain rate region may be realized at the running crack tip even under the quasi-static loading case of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} = 8.33 × 10^?4/sec, since all the crack propagation velocities obtained were greater than 50 m/sec even up to 450 m/sec.     

Light-scattering studies on solutions of high and low molecular weight polystyrene mixtures used as models of microgel-containing solutions

Diluted solutions of linear polystyrene (PS) in toluene and dioxane were studied by the light-scattering method. The solutes were mixtures of high-M?_w and low M?_w PS. The dissolved PS mixtures were regarded as polymer solutions containing microgels, the high-M?_w PS being looked upon as the microgel counterpart. The calculation method as proposed by Strazielle¹ and Burchard² was used to evaluate the microgel percentage and particle size, whereby the method could be verified against mixtures with well-known weight composition and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document}. The \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values evaluated for the mixtures from the experimental data were compared with those estimated from the molecular weights of the components, their weight concentrations, and their \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values. The method^1,2 was found to be useful for evaluating the microgel content in a sample, but not for \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values as calculated by Guinier's procedure nor those calculated by Zimm's procedure; the former were low and the latter were even incongruous. A comparative analysis of the theoretical function P^?1(θ)-versus-sin² (θ/2) and experimental (Kc/R(θ))_c=0-versus-sin² (θ/2) curves allowed to discuss the effect of the course of these curves at samll angles from 0° to 30° on M?_w and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} as determined for the high and low molecular weight polystyrene mixtures in toluene as solvent.     

Polymerization of olefins through heterogeneous catalysis. II. Kinetics of gas phase propylene polymerization with Ziegler–Natta catalysts

Propylene was polymerized in gas phase over a \documentclass{article}\pagestyle{empty}\begin{document}${\rm TiCl}_3 \cdot \frac{1}{3}{\rm AlCl}_3$\end{document} (Stauffer Type AA) Catalyst with AlEt₂Cl cocatalyst both with and without H₂ present. The effects of polymerization temperature, monomer concentration, catalyst composition, and hydrogen were investigated. The experiments were carried out at operating conditions approaching industrial practice.     

Elongational behavior of short glass fiber reinforced polypropylene melts

The Rheometrics Elongational Rheometer was employed to study the uniaxial extensional flow of glass fiber filled polypropylene melts, in which the fiber concentration, c, varied between zero and 40 weight percent. The constant strain rate mode was used for strain rates, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document}, between 0.003 and 0.6 s⁻¹. Steady state elongational viscosities were observed in most cases for fiber filled polypropylene melts, even at rates at which the stress continued to increase for unfilled polypropylene. The rate of relative stress growth increased with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and was affected by the addition of fibers. The steady elongational viscosity of the fiber reinforced melts was found to decrease with increasing \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and to increase with increasing c. Yield stresses were observed in elongational flow at high concentrations, although there was no clear evidence of yield in steady shear.     

Melt rheology and extrudability of polyethylenes

Commercial high density polyethylene (HDPE), low density polythylene (LDPE), and linear low density polyethylene (LLDPE) resins were tested at 150, 170, and 190°C in steady state, dynamic, and extensional modes. Within the low rates of deformation \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω ≤ 0.3, the steady state and dynamic functions agreed: η = η′ and N₁ = 2G′; at the higher rates, the steady state parameters were larger. The elongational viscosity, η_e, was measured under a constant rate, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}, or stress, σ, condition. In the first case for LLDPE, the transient η reached an equilibrium plateau value, η_e. For HDPE, η increased up to the break point. For LDPE, stress hardening was recorded. Under constant stress the η_e, could always be determined; its value, within experimental error, agreed with the maximum value of η determined in a constant \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document} experiment. The maximum strain at break was only ε = 1.5 for HDPE and 3, to 4 for LDPE and LLDPE. The rate of deformation dependence of the η (or η′) and η_n may be discussed in terms of the Trouton ratio, R_T = η_e/3η at \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document}: R_T ≤ 1.2 for LLDPE, R_T ≤ 2.5 for HDPE, and R_T ≤ 15 for LDPE. The PE resins were extruded at 190°C through a laboratory extruder equipped with a slit or rod die. The rotational speed of the screw varied from 0 to 90 rpm. Extrusion pressure, output, and energy were measured and correlated with the rheological parameters of the resins.     

Application of a constitutive equation to polymer melts

Yamamoto's integral constitutive equation in which the memory function is dependent on the second invariant of the rate of deformation tensor at past times has been found to be successful in predicting many of the nonlinear viscoelastic functions from the linear viscoelastic data for melts of linear polyethylenes, polypropylenes, and polystryene but not for those of branched polyethylenes with high level of long-chain branching. A specific functional form for the rate-dependent relaxation spectrum is used and is based on the physical meaning resulting from the molecular entanglement theory of Graessley on steady shearing flow. No arbitrary constant is involved in such an interconversion scheme. The data examined are dynamic storage modulus and loss modulus, steady flow viscosity, first normal stress difference, and parallel superimposed small oscillations on steady shear flow. The theory predicts that in such parallel superimposed experiments, storage modulus G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) divided by the square of frequency shows a maximum under finite shear and that G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) would itself become negative at a frequency whose value is about one third the superimposed rate of shear. The experiments are in line with such predictions. Possible reasons for the failure of the theory for branched polyethylenes are considered, and a possible approach is suggested so that the interconversion scheme may be successful for such resins.