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.     

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 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.     

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.     

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.     

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.     

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.     

A simplified theory for generalizing results from a radiant panel rate of flame spread apparatus

Experimental results on the rate of lateral flame spread and time for piloted ignition under an externally imposed radiant flux were analyzed with a simple theroretical model. The data were developed from a radiant panel apparatus that considers a wall mounted sample with a flux distribution \documentclass{article}\pagestyle{empty}\begin{document}$ (\dot q_{\rm e} ^{\prime \prime } ) $\end{document} of 5 W cm^?2 at the ignited end to 0.2 W cm^?2 at the other end. It is shown that after an appropriate preheating time (flux exposure time before sample is ignited) the rate of flame spread (V_f) results can be correlated by \documentclass{article}\pagestyle{empty}\begin{document}$ V_{\rm f} - {\textstyle{1 \over 2}} = C\left( {\dot q''_{{\rm o,ig}} - \dot q_{\rm e} ^{\prime \prime } } \right) $\end{document} where C is a material ‘constant’ and \documentclass{article}\pagestyle{empty}\begin{document}$ \dot q''{\rm }_{{\rm o,ig}} $\end{document} is minimum flux for piloted ignition—also a material (and configuration) constant. An extension of this model demonstrates that V_f can also be expressed in terms of an ‘ignition temperature’ and the surface temperature of the material. Both correlations are derivable from a single flame spread experiment. Results are presented for a number of typical wood and plastic materials.     

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.     

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).     

Mass transfer between solid spheres and oscillating fluids — A critical review

Relative oscillatory motion between solid particles and a fluid increases the rate of interphase mass transfer due to the establishment of secondary flows (acoustic streaming). A critical survey of published data shows that mass transfer is well correlated by a theoretically founded dimensionless relation of the form where K, a, b and d depend on the Schmidt number. The equation successfully correlates experimental data for both gases and liquids over a range of frequencies F < 1 Hz to F ～ 10⁶ Hz, provided the amplitude to diameter ratio A/D is below 0.75. At higher values of this parameter, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar N_{Sh} $\end{document} is better predicted by a quasi-steady model which no longer depends on A/D.     

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.     

Thermal decomposition of potassium persulfate in aqueous solution at 50°C in the presence of ethyl acrylate

Potassium persulfate modes of thermal decomposition and reactions with ethyl acrylate in aqueous solution at 50°C in nitrogen atmosphere have been investigated. It has been found that the rate of persulfate decomposition may be expressed as ?d(S₂O)/dt ∝ (S₂O)^{1.00 ± 0.06} × (M)^0.92±0.05 while the steady state rate of polymerization (R_p) is given by R_p ∝ (S₂O)^{0.50 ± 0.50} × (M)^{1.00 ± 0.06} in the concentration ranges of the persulfate, 10^?3?10^?2 (m/L), and monomer (M), 4.62?23.10 × 10^?2 (m/L), i.e., within its solubility range. In the absence of monomer, the rate of persulfate decomposition was slow and first order in persulfate at the early stages of the reaction when the pH of the solution was above 3.0. The separating polymer phase was a stable colloid at low electrolyte concentrations even in the absence of micelle generators. It has been shown that the oxidation of water soluble monomeric and oligomeric radicals by the S₂O ions in the aqueous phase, viz., \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm M}_j^ \cdot + {\rm S}_2 {\rm O}_8^{2 - } \to {\rm M}_j - {\rm O} - {\rm SO}_3^ - + {\rm SO}_4^{ \cdot - } $\end{document} is not kinetically significant in this system. It has been found that the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm M} + {\rm S}_2 {\rm O}_8^{2 - } \rightarrow{k}{\rm M} - {\rm O} - {\rm SO}_3^ - + {\rm SO}_4^{ \cdot - } $\end{document} would also lead to chain initiation at the outset of the polymerization reaction. k has been estimated as 5.41 × 10^?5 (L/m/s) at 50°C. Taking k_p as 10³ (L/m/s), k_t has been estimated as 0.168 × 10⁶ (L/m/s). The partition confficient (β) of the monomer between the polymer phase and the aqueous phase was found to be 16 ± 2, at 50°C. The rate constant for persulfate ion dissociation has been found as 1.40 × 10^?6 s^?1 at 50°C.     

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.     

Effect of entrance geometry on the capillary flow of cellulose acetate–acetone solution

Capillary flow data were obtained for a 27.5% solution of cellulose acetate in acetone. The solution temperature was 50°C, and the range of apparent shear rates investigated was 1.7 × 10⁵ to 1.7 × 10⁶ sec^?1. Capillaries having tapered entrance angles of 37.88° to 120.63° were used. A power-law model was adequate to describe the shear stress at the wall (τ_w) and the corrected shear rate \documentclass{article}\pagestyle{empty}\begin{document}$(\dot \gamma )$\end{document} relationship. Entrance angle affected the entrance pressure drop corrected for kinetic energy, (ΔP_0,c); ΔP_0,c increased as the angle widened. Treating the entrance flow as an elongational flow situation facilitated superposition of the Delta;P_0,c data on a single curve. Estimated elongational viscosities decreased with increasing applied stress.     

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.     

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.     

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.     

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.     

Graft polymerization of methyl methacrylate onto wool initiated by a hydrogen peroxide-sodium thiosulphate redox system. Part II kinetics and mechanism of the grafting reaction

Methyl methacrylate was grafted onto wool in the presence of an aqueous dioxane solution with a hydrogen peroxide-sodium thiosulphate initiator system, using the optimum conditions found in our previous paper¹⁹. It was stated that up to 90% conversion for the rate of reaction the following equation holds: \documentclass{article}\pagestyle{empty}\begin{document}${\rm R}_{\rm p} = - \frac{{{\rm d}\left[ {\rm M} \right]}} {{{\rm dt}}} = {\rm K} \cdot \left[ {\rm M} \right]^{1.5}$\end{document} where R_p is the overall rate of the graft polymerization, and [M] is the monomer concentration at the time t. The degree of polymerization of the isolated poly(methyl methacrylate) was found to be linearly proportional with the monomer concentration [M]. Investigations of the effect of the ratio of solvent to monomer concentration [S]/[M] on the reciprocal of the degree of polymerization showed that there was no chain transfer caused by the solvent dioxane. The number average molecular weight M?_n of the polymer separated from the grafted wool was found to be within the range of 3–15.9 × 10⁶ as determined by viscosimetry. The molecular weight distribution of the isolated poly(methyl methacrylate) samples was determined by turbidimetric titration. The following relationship was established between the volume fraction of the non-solvent, γ and the number average molecular weight M?ⁿ. of poly(methyl methacrylate): \documentclass{article}\pagestyle{empty}\begin{document}$\gamma = - 0.0285 + \frac{{50.54}}{{\sqrt[3]{{\overline M _n }}}}. $\end{document} The molecular weight distribution curves were found to be rather homogeneous indicating approximately the same chain length of the grafted poly(methy1 methacrylate) on the wool backbone. It was stated before³³ that the number average molecular weight could be determined from the inflection point of the turbidimetric curves. This method can be used for determining the molecular weight of all kinds of poly(methy1 methacrylate) occurring in practice.