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.     

In‐Line Monitoring and Control of Conversion and Weight‐Average Molecular Weight of Polyurethanes in Solution Step‐Growth Polymerization Based on Near Infrared Spectroscopy and Torquemetry

Summary: It is well known that the weight‐average molecular weight ( ) is strictly dependent on conversion in step‐growth polymerizations performed in batch and that the is very sensitive to impurities and molar imbalance. This makes the work of controlling a non trivial job. In this paper a new methodology is introduced for in‐line monitoring and control of conversion and of polyurethanes produced in solution step‐growth polymerizations, based on near‐infrared spectroscopy (NIRS) and torquemetry. A calibration model based on the PLS method is obtained and validated for monomer conversion, while the weight‐average molecular weight is monitored indirectly with the relative shear signal provided by the agitator. Control procedures are then proposed and implemented experimentally to avoid gelation and allow for maximization of . The proposed monitoring and control procedures can also be applied to other step growth polymerizations.

Proposed control scheme.     

The apparent rate constant model for kinetics of radical chain copolymerization: Chemical-controlled process

In this article the kinetics of chemical-controlled radical-chain copolymerization have been reduced to pseudohomopolymerization kinetics by introducing the apparent rate constants, The methods for the determinations of the values of the apparent rate constants, mode of termination, and the methods for the calculation of molecular weights and distributions are proposed. The data required for these determinations and calculations are simply obtained by the usual steady-state method. According to the traditional kinetics along with the definitions of the apparent rate constants, these apparent rate constants as functions of traditional rate constants, monomer compositions, and copolymer compositions are derived. Further utilizing the theoretical expressions obtained, we show that the apparent rate constants are the general rate constants for both radical chain homo- and copolymerizations. The bulk radical copolymerizations of methyl methacrylate and styrene at various monomer feed compositions at 60°C are used to test the proposed model. The empirical apparent rate constants obtained are described well, by the following expressions, and and the mode of termination on the combination termination is where K and K denote the apparent rate constants of propagation and termination, respectively. The term f₁(= 1 ? f₂) stands for the mole fraction of styrene in the monomer solution fed. F₁ is the copolymer composition produced at f₁. β is the mode of termination.     

Surface energy mapping of Kevlar® fibers by inverse gas chromatography

The surface energy characteristics of three Kevlar® fibers have been systematically studied using two inverse gas chromatography (IGC) techniques, i.e., at an infinite probe dilution and at a finite probe concentration, with the latter allowing a unique mapping of the surface energy levels, which complements greatly the more traditional characterization of the highest energy sites. The standard thermodynamic parameters, such as the free energy −Δ , and the adsorption enthalpy and entropy (Δ and −Δ ), as well as the dispersive and the specific component ( and ΔG^sp/I^sp) of the fiber surface energy, were determined from the retention behavior at zero coverage of selected molecules of various polarity. The values are between 49–58 mJ m⁻² for the three fibers at 50°C. The polar components, ΔG^sp or I^sp, calculated by three different methods, reveal the polar feature of the fiber surface. It is interesting to note that the adsorption enthalpies Δ for the short chain alkane probes are nearly the same as their liquefaction energies. Using the second IGC approach, i.e., at finite concentration, the isotherms for the adsorption of n-octane and n-hexylamine on the three selected Kevlar® fibers were constructed by the one-peak method. These are shown to be instrumental to establish the corresponding energy distribution functions. The results may indicate that, unlike the alkane probes, the polar molecules interact strongly with the Kevlar® fiber surfaces, which appear, in this case, energetically heterogeneous. The resulting energy distribution mapping opens new avenues towards the surface characterization of the global surface without the restriction of the averaging imposed by other bulk analysis techniques. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 487–500, 1998     

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.     

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.     

Viscoelasticity of some engineering plastics analyzed with the modified stress-optical rule

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), of poly(ether sulfone) (PES), polysulfone (PSF), and polyethermide (PEI), were measured over the frequency range 1 to 130 Hz. The data were analyzed with a modified stress-optical rule: The Young's modulus was decomposed into two complex functions, E(ω) and E(ω); the modified stress-optical coefficient, C_R and C_G, associated with the rubber (R) and glass (G) components, respectively, were determined. The results for six polymers, including polystyrene, poly(α-methyl styrene), and bisphenol A polycarbonate were compared with each other. One of the coefficients, C_R, equivalent to the stress-optical coefficient in melts, mainly depended on the way in which phenyl groups were connected to the chain. The other, C_G, was in the range of 20 to 40 Brewsters, and did not strongly depend on the details of polymer structure. The component function, E(ω), which was located in the glassy region and originated from the high glassy modulus, was almost the same in shape when plotted against ω with double logarithmic scales. The R component, E(ω), located at the long time end of the glass-to-rubber transition zone, was slightly sensitive to the molecular structure of polymers.     

Kinetics of ion exchange in monodisperse resin

Ion-exchange kinetics within a conventional strong base resin, Dowexl-8X®, and a resin with uniform particle size, Dowex® Monosphere® Tough Gel® TG550A®, were investigated using neutron activation analysis and radio-tracer techniques. The kinetics of ion exchange were measured in a batch and in a “shallow-bed” flow system. The experimental data were compared with the results of model computations. The diffusivities of several anions within TG550A and Dowexl-8X were deduced. It was found that at 25°C Br^-, Cl^-, OH^-, and Na⁺ diffuse within TG550A with the diffusion coefficients = 6.0 × 10^-7 cm²/s, = 1.2 × 10^-6 cm²/s, = 7.0 × 10^-8 cm²/s, and = 5 × 10^-7 cm²/s. Diffusion of anions within a conventional resin, Dowexl®, was slower: = 3.5 × 10^-7 cm²/s, = 6 × 10^-7 cm²/s, = 2.7 × 10^-8 cm²/s, and = 5 × 10^-7 cm²/s. A higher rate of ion diffusion and the bead-size uniformity may make monodisperse Dowex Monosphere Tough Gel TG550A resin attractive for analytical applications. The difference in properties between conventional and monodisperse resins is not sufficient to affect the large volume applications of resins. © 1997 John Wiley & Sons, Inc. J Appl Polm Sci 65:1271–1283, 1997     

Intrinsic birefringence of nylon 6

Different values are reported in the literature for the intrinsic birefringence of the crystalline (Δn) and the amorphous (Δn) phases in nylon 6. Mostly, these values have either been determined by extrapolation (and then it is assumed that Δn = Δn) or calculated theoretically. In this study, intrinsic birefringence values Δn and Δn for nylon 6 were determined using the Samuels two-phase model which correlates sonic modulus with structural parameters. Three series of fiber samples were used: (1) isotropic samples of different degrees of crystallinity for estimation of E and E moduli at two temperatures. The following modulus values were obtained: 1.62 × 10⁹ and 6.66 × 10⁹ N/m² for 28.5°C, and 1.81 × 10⁹ and 6.71 × 10⁹ N/m² for ?20°C; (2) anisotropic, amorphous fiber samples for estimation of Δn = 0.076 and E = 1.63 × 10⁹ N/m² at 28.5°C; (3) semicrystalline samples of various draw ratios for estimations of Δn = 0.089 and Δn = 0.078. All measurements were carried out with carefully dried samples to avoid erroneous results caused by moisture.     

Regression‐based model for elastic constants of 2D braided/woven open mesh angle‐ply composites

The elastic constants of closed mesh braided/woven fabrics are generally obtained from finite element analysis, fabric geometry model, and modified classical laminate plate theory. These models are complex and often impractical for industrial design purposes and do not address the cases of open mesh braided/woven fabrics. This paper proposes an alternative to existing models and software packages. Simple regression‐based empirical equations were developed to obtain E_x, E_y, G_xy, and ν_xy of braided/woven fabrics at any angle‐ply angle using the braid/weave unit cell volume fraction (V_f0), the fiber volume fraction (V_f), and the elastic constants of an equivalent angle‐ply laminate (E, E, G, ν). Design equation predictions were verified by comparing them to a previously validated modified classical laminate plate theory (CLPT) model using various fiber/resin combinations. Excellent agreement was found for each set of results. POLYM. COMPOS., 26:152–164, 2005. © 2005 Society of Plastics Engineers     

The viscoelastic properties of rubber–resin blends. III. The effect of resin concentration

The viscoelastic properties of a rubber–resin blend, which influences performance of the blend as a pressure-sensitive adhesive, depend upon the structure of the resin as well as its molecular weight. The effect of the concentration of a compatible resin in the blend was examined using a mechanical spectrometer. Four types of resins were used. These are the rosin esters, polyterpenes, pure monomer resins such as polystyrene and poly(vinyl cyclohexane), and petroleum stream resins. Each was examined in blends with both natural rubber and styrene–butadiene rubber over a range of concentrations. It is shown that the temperature of the tan δ peak for compatible systems can be predicted by the Fox equation, T = W₁T + W₂T, where W₁ and W₂ are the weight fractions of the resin and rubber, respectively, and the T_g's are the tan δ peak temperatures in K. The plateau modulus G for a blend can be identified as the G′ value in the rubbery plateau at the point where tan δ is at a minimum. The relationship between G and G, the plateau modulus for the undiluted elastomer, is shown to be proportional to the volume fraction of the elastomer raised to the 2.3–2.4 power for natural rubber with six different compatible resins. The exponent for styrene–butadiene rubber is 2.5–2.6 with four different resins. Using these relationships, both the tan δ peak temperature and plateau modulus can be predicted for a rubber–resin system from data on the unmodified elastomer and on one typical rubber–resin blend.     

Relationship in polypropylene melt between its linear viscoelasticity and its steady capillary flow properties

It is the object of the present study to obtain clear knowledge of the relations in the polypropylene melt between its linear viscoelasticity and its nonlinear steady capillary flow, paying particular attention to the elastic properties in its capillary flow. By representing the linear viscoelasticity numerically with zero-shear viscosity, η₀, and steady-state compliance, J, evaluation has been made of the properties concerning the elasticity of polymer melt in the capillary flow, such as non-Newtonianity, the entrance pressure loss, the end correction, the Barus effect, and the melt fracture. The steady flow viscosity η, the entrance pressure loss P₀, the critical shear stress, τ_c, and the critical shear rate $\dot \gamma _c$ at which melt fracture begins to occur are subject to η₀ as follows: From the well-known relationship between η and the weight-average molecular weight M?_w, these quantities are governed by M?_w. Meanwhile, for such quantities as structural viscosity index N, end correction coefficient ν, and elastic pressure loss ratio P₀/P, following correlations hold: As η₀ and J are respectively determined mainly by M?_w and the molecular weight distribution MWD, these quantities are governed by both M?_w and MWD. Physical meanings of η₀·J and η₀² · J are, respectively, mean relaxation time and a measure of stored energy in steady flow. The Barus effect has a positive correlation to J, ν, and P₀/P. (The symbol ∝ employed here means positive correlation.)     

Study of crosslinking density in polydimethylsiloxane networks by DSC

A calorimetric study for estimating crosslinking densities of polydimethylsiloxane (PDMS) networks is presented. It involves the experimental determination of the heat capacities of the polymer with (C) and without (C) crosslinking. The theoretical basis of the method is described as well as the procedure used for the determination of the C_ps. The crosslinking densities of PDMS networks, determined by absorbency (swelling) measurments, using the Flory-Rehner equation, and by the method described here, are compared. The PDMS, obtained by the anionic synthesis of octamethylcyclotetrasiloxane, was analyzed by gel permeation chromatography and infrared spectroscopy. Separate samples of the polymer were further crosslinked at different network densities. The C_ps and the thermal stabilities were determined by DSC and TGA, respectively. The results indicate that the crosslinking density ratios of the polymer networks calculated by the relation ΔC/C are in reasonable agreement with those obtained from absorbency measurements. The crosslinking density can also be obtained from heat capacity measurments if the density of the network is known at the temperature that ΔC_p is obtained. © 1995 John Wiley & Sons, Inc.     

Conversion of SO2 into elemental sulfur by using the RF plasma technique

This study demonstrates a new approach for converting SO₂ into elemental sulfur by adding CH₄ in a radio-frequency (RF) plasma reactor. With the applied power (P) of the RF reactor specified at 90 W and operating pressure set at 4000 N/m², it was found that as the CH₄/SO₂ ratio (R) was increased from 0.3 to 1.0, most sulfur-containing products were in the form of elemental sulfur. While R was increased from 1 to 2, the content of elemental sulfur was decreased significantly, but CS₂ was increased dramatically. While R was increased from 2 to 3, both elemental sulfur and CS₂ contents became quite comparable. Nevertheless, it was found that both H₂ and CO (that is, syngas) were the main nonsulfur-containing products under all testing conditions. These results indicate that the use of the RF plasma technique was not only beneficial to convert SO₂, but also was able to convert CH₄ into useful materials. For R = 0 (that is, no CH₄ was introduced), it was found that the SO₂ conversion (i.e., η) = 0.084, indicating that the RF plasma process was inadequate to convert pure SO₂ without adding CH₄ as a reducing agent. While R was increased to 2, it was found that η was improved significantly to 0.968 accompanied with η = 0.999. But as R was increased from 2 to 3, both η and η were slightly decreased. Both η and η also were sensitive to the applied power (P). As P was increased from 15 W to 90 W at R = 2, it was found that both η and η were increased dramatically from 0.247 and 0.320 to 0.968 and 0.999, respectively. But as P was increased from 90 W to 120 W, the increase on both η and η became very limited. Based on these, this study suggests that the operating condition of R = 2 and P = 90 W would be the most appropriate combination for SO₂ conversion. © 2004 American Institute of Chemical Engineers AIChE J, 50: 524–529, 2004     

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.     

Sensitivity analysis of catalytic conversion of n-C6

The present paper is a case study of an application of sensitivity analysis in chemical kinetics. Emphasis is laid upon chemical interpretation of sensitivity information and on identification of the most important model important model parameters. The kinetic model for reforming of C₆ hydrocarbons proposed by Mobil [14] is extended to the analysis of the behavior of n-hexane conversion in an adiabatic reactor. The importance of six initial conditions (feed composition and initial temperature) is analyzed by the computation of normalized first order sensitivity gradients (y/y) (δy_i/δy). The relative importance of 21 model parameters α_j is estimated by the computation of normalized sensitivity gradients of the type (α_j/y_i) (δy_i/δα_j). The influence of the decisive model parameters ΔH and ΔH (activation enthalpies of benzene hydrogenation and methyl cyclopentane isomerization, respectively) as well as operating parameters is presented. The problem of uncertainly in the value of ΔH and its influence on the model solution is also sown. Finally, some advantages of the application of normalized gradients of the explanation of process behavior are discussed.     

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.     

Composition and temperature effects on air separation through liquid crystalline alkyl cellulose membranes

The air separation through triheptyl cellulose (THC)/ethyl cellulose (EC) blend membranes containing no more than 20 wt % THC at the temperature range from 298 to 358 K was investigated using a variable volume method. The air-separation ability for the THC/EC membranes were greater than that for the THC-free pure EC membrane. P for the THC/EC membranes was between 1.06–8.89 × 10^?9 cm³ (STP) cm/cm² s cmHg and P/P 3.04–3.66. The THC/EC membrane showed a unique trend in its P/P ? P relationship, i.e., the magnitude of P/P increased simultaneously with that of P. The THC/EC membrane yielded a maximum oxygen concentration in the oxygen-enriched air (OEA) of 39.5% at an OEA flux of 6.99 × 10^?4 cm³ (STP)/s cm² for a pressure difference of 0.43 MPa at 358 K. After 300 h of measurement at 0.40 MPa and 313 K, the efficiency of the concentrating oxygen was almost constant. © 1994 John Wiley & Sons, Inc.     

Mechanical properties of polyethylene/ethylene vinyl acetate filled with calcium carbonate

The tensile behavior of polyethylene/ethylene vinyl acetate (PE/EVA) polymer blends filled with calcium carbonate (CaCO₃) was studied using tensile and viscoelastic tests. The relations between tensile properties (modulus, strength, etc) of oriented and unoriented PE/EVA-CaCO₃, and void volume of polymer/CaCO₃ interface, PE/EVA blend ratio, and CaCO₃ content were investigated. The results indicated that the tensile strength and elongation of PE/EVA-CaCO₃ decreased with CaCO₃ content and PE blend ratio for unoriented PE/EVA-CaCO₃ systems. In the case of oriented samples, the relative modulus (E/E, where E and E are the modulus of oriented composites and the modulus of oriented matrix, respectively) of PE/EVA-CaCO₃ is larger than that of PE/CaCO₃ by increasing the EVA content relative to PE and CaCO₃. The value of E/E can be simply expressed as the function of void volume and CaCO₃ modulus to polymer matrix modulus.