Stress relaxation behaviour of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

The stress relaxation behaviour of liquid crystal-forming ethyl celllulose (EC) solutions in m-cresol was determined by means of a cone-plate type viscometer at 30°C. The effect of molecular weight (MW) on the behaviour was also determined. The relaxation behaviour could be fitted with the following equation: where σ_i and σ_f are steady-state shear stresses at shear rate $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, σ(t) is time- dependent stress, A₁ and A₂ are constants, τ₁ and τ₂ are relaxation times, t is time, and t_c is a characteristic time. When log σ* was plotted against time, one straight line was obtained for isotropic solutions, whereas anisotropic solutions yielded two straight lines. This suggests that the liquid crystalline solutions have two separate relaxation processes: Process 1 has a relatively short relaxation time, and process 2 has a long one. The parameters τ₁, τ₂, and A₂ were greatly dependent on polymer concentration, combination of $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, and MW, whereas A₁ was independent thereof and was close to unity. The process 1 was supposed to be valid for individual molecules, and process 2 for liquid crystalline domains or randomly aggregated or entangled molecules.     

Elongational flow studies of hinged rodlike molecules

Poly(amino acid) in an intermediate state of its helix-coil transition is known to be in a hinged rodlike conformation. In this work, the responses of poly(amino acids) in the hinged rodlike conformation against an elongational flow field were investigated by monitoring their flow-induced birefringence. Poly(L-glutamic acids) (PGA) and poly(γ-benzyl-L-glutamate) (PBLG) were examined as polyelectrolyte and noncharged poly(amino acids), respectively, and the results were compared. In the plots of flow-induced birefringence, Δn, against strain rate, $ {\dot \varepsilon } $, for hinged rodlike PBLG, there was a critical strain rate, $ \dot \varepsilon_0 $, below which Δn was not observed. Over $ \dot \varepsilon_0 $, the birefringence pattern observed was identical with that of rodlike molecules. The Δn vs. $ {\dot \varepsilon } $ plot for hinged rodlike PGA had characteristics of a rigid rod at any strain rate and there was no $ \dot \varepsilon_0$ observed. The rotational diffusion coefficient, D_r, of PBLG in the hinged rodlike conformation was larger than that for its helical conformation, while D_r, for the hinged-rodlike PGA was smaller than that for its helical conformation. It is concluded that the hinged-rodlike PGA molecule is in an extended form and that the hinged-rodlike PBLG is hydrodynamically more compact and rigid than that in its quiescent state. It is deduced that at $\dot \varepsilon_0$ hinged rodlike PBLG molecules collapse to a conformation optically anisotropic and mechanically rigid. © 1996 John Wiley & Sons, Inc.     

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.     

The kinetics and mechanism of the chloride-chlorate reaction

The kinetics of the reaction have been studied at 25°C. in strong acid solution; the effects of acidity, chloride, chlorate and chlorine are reported. A mechanism is postulated to interpret the peculiar features of this reaction as well as the stoichiometry and some of the kinetics of the parallel reaction The mechanism involves HClO₂ and HOCl as intermediates General rate expressions are derived for the formation of chlorine dioxide and chlorine, and the individual rate constants are calculated. An expression is obtained for the relationship between the ratio of chlorine dioxide to chlorine produced and the ratio of chlorate to chloride.     

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.     

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.     

Shear rate dependence of the viscosity of cellulose nitrate solutions in the dilute concentration regime revisited

A detailed rheological study of cellulose nitrate in ethylacetate had been carried out in the dilute concentration (c) regime, covering a degree of polymerization (DP) range between 300 < DP_η < 7000 and shear rates ($ \dot \gamma $) between 100 s^?1 < $ \dot \gamma $ < 2000 s^?1. The results show a strong dependence of the transition Newtonian to non-Newtonian behavior on the three variables $ \dot \gamma $, DP, and c, similar to that found recently on solutions of synthetic polymers. Emphasis has been put on the critical concentrations corresponding to the standard shear rate 1000 s^?1 to correspond to the standard conditions ($ \dot \gamma $ ? 1000 s^?1; 0.3 < [η] · c < 0.6; DS = 2.90 ± 0.02) proposed for the determination of the intrinsic viscosity [η] of cellulose nitrates. It is shown that solutions with concentrations adjusted according to the above given conditions still exhibit Newtonian behavior, up to the highest range of DP. It follows, therefore, that applying the standard conditions, an extrapolation to $ \dot \gamma $ = 0 as has been proposed often for the intrinsic viscosity determination of cellulose nitrate is not advisable and results in considerable error. Considering the relationship between [η] and DP, the present results indicate that the decrease of the exponent ( a ) from a = 1.0 to a = 0.76, taking place above a DP ? 1000, is not a consequence of the applied shear rate but rather of the molecular properties of the solutes themselves.     

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.     

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.     

Viscosity of bead suspensions in polymeric solutions

Viscosity measurements made by a cone-plate viscometer on polyisobutylene in decalin solutions at different concentrations and their corresponding glass bead suspensions with filler loadings up to 40% by volume are reported. The range of shear rate $ \dot \gamma $ investigated is between 0.1 and 1000 sec^?1. The solutions show shear-thinning behavior, and the relative viscosity η_r of the slurries generally decreases with increasing shear rate. The results indicate two different types of mechanism, respectively at high and low shear rates. At low $ \dot \gamma $, the relative viscosity can be correlated extending relations already well known for suspensions in Newtonian liquids which are based on the mechanism of aggregate disruption. The behavior at high $ \dot \gamma $ values is believed to be due to the influence of the filler on the flow properties of macromolecules, in particular on relaxation time. Through a shifting procedure, an increase in relaxation time which depends on filler content and not on polymer concentration is shown.     

Simulation and optimal design of seeded continuous emulsion polymerization process

Simulation and optimal design of the reactor for the seeded continous emulsion polymerization process have been done in this work. An internal mixer (Toray Hi-Mixer) as seeder connected with a stirred tank is designed to correlate conversion, molecular weight, and MWD with the model simulation proposed. An optimal mean residence time of seeder \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _s)_c$\end{document} is found to lie between \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _1)$\end{document} and t_in, where \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _1)_{{\rm opt}} = (3aS_0 /2r\eta N_a \alpha)^{3/5}$\end{document} and t_in = 1.57(aS₀/r_iηN_A)^3.5. The optimal design of the process is performed according to the above relations under several polymerization conditions. In general, the increase in number of stages inside the seeder can reduced the volume of CSTR for a required production. Molecular weight of products is increased by increasing the number of stages inside the seeder, by decrasing the concentration of the initiator, and by increasing the concentration of the emulsifier under the optimal conditons.     

A corresponding states treatment of saturated density,surface tension and capillary constant of cryogenic liquids and refrigerants

Using a new set of energy (kT) and length (σ) parameters, a corresponding states treatment is applied to the calculation of some thermophysical properties in a generalised non-dimensional form. The saturated density is well represented by the following equation: for all the liquids studied here. The surface tension correlations are $ \gamma _r^* = 2.055\left({1.219 - T_r^*} \right)^{1.240} $ for cryogenic fluids and hydrocarbons and $ \gamma _r^* = 2.322\left({1.228 - T_r^* } \right)^{1.244}$ for refrigerants. An interpretation of the index in the density equation and the constants in the surface tension equations is given. Using these correlations, an equation is also proposed for the capillary constant.     

Esterification of styrene–maleic anhydride copolymer by mixed alcohols

A copolymer (MW = 1800) of styrene (St) and maleic anhydride (MAn) was esterified with an excess amount of an alcohol mixture, and then the relation between the esterification rates of the individual alcohols and the contents of the esters in the esterific copolymer was examined. At first, the rate constant of an individual esterification was obtained for four different alcohols (n-butanol, i-amylalcohol, and benzylalcohol) in a noncatalyst system. Then, the mixed esterification of n-butanol and i-amylalcohol was carried out; from the analysis of the ester contents, the following equation was obtained: From this result, it was concluded that, in esterification with alcohols involving n species, the content of the individual ester can be expressed by the following equation: where [P] = concentration of esters in the copolymer, [B]₀ = initial concentration of alcohols, and k = rate constant of esterification (i,j = 1,2…,n).     

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.     

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.     

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.     

Jet penetration measurements in a venturi scrubber

The maximum centreline penetrations, l^**, of cross-current liquid jets in a Venturi scrubber were measured for orifice diameters, d, of 1.397, 2.108, 2.565 and 3.860 mm. The data are correlated by for the range of conditions, 36 ≤ gas throat velocity V_g ≤ 125 m/s; 1.2 ≤ liquid injection velocity V_j ≤ 18 m/s; 0.06 ≤ liquid to gas ratio      

Mixing rules for predicting the viscosity of bitumens saturated with pure gases

Mixing rules are developed and evaluated for predicting the viscosity of Alberta bitumens saturated with each of N₂, CO, CH₄, CO₂ and C₂, H₆. The viscosity-temperature variation for all bitumens and gases is expressed as [log(μ + 0.8) = ± 10 T]. A linear cross-correlation between parameters b₁ and b₂ in the above relationship is identified and used subsequently to derive a one-parameter viscosity equation: [log(μ + 0.8) = θ(ΦT)^b]. where θ = 160, Φ = 0.008 for all bitumens and θ = -0.1, Φ = 0.015 for all gases. The two mixing rules examined in this study are: $ \log \left( {\bar \mu + 0.8} \right) = \sum v_i \,\log \left( {\mu _i + 0.8} \right) $ and $ \log \left( {\bar \mu + 0.8} \right) = \sum v_i \,\log \left( {\mu _i + 0.8} \right) + \sum \sum v_i v_j B_{ij} $, where v represents the geometric mean of mass and mole fractions and B_ij is a binary viscous interaction term. Predictions for the viscosity of gas-saturated bitumens are validated with over 400 experimental data points for five Alberta bitumens at temperatures from 12 to 120°C and pressures up to 10 MPa.     

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.     

Drop size distribution in a graesser contactor

An investigation was conducted of drop size distribution in a Graesser contactor, employing five liquid – liquid systems, viz., kerosene/water, benzene/water, xylene/water, hexane/water and n–butyl acetate/water. A 100 mm (4 inch) diameter Graesser contactor was used for this purpose It was found that the drop size distribution in a Graesser contactor obeys the upper – limit distribution expressed as: where A correlation was developed relating the Sauter mean diameter (d₃₂) to other effective groups