Steady-state Shear Compliance Research Articles

Rheological characterization on thermal degradation of ethylene-tetrafluoroethylene copolymer

Oscillatory shear modulus in the molten state is evaluated carefully considering the rheological change during the measurement at high temperature for ethylene-tetrafluoroethylene copolymer (ETFE). The results provide the information on the molecular weight distribution as well as the degradation behaviors, which is affected by the environmental condition, i.e., the existence of oxygen. Even under a nitrogen atmosphere, ETFE is thermally unstable in the molten state; ETFE shows random chain scission reaction without crosslinking. The steady-state shear compliance Je0, which depends on the molecular weight distribution greatly, is not changed during the chain scission. It suggests that the chain scission occurs with keeping the molecular weight distribution. Considering the classical theory on the random scission reaction, the experimental result indicates that Mw/Mn of the initial ETFE sample, prior to the exposure to thermal history, is close to 2. In contrast, under air condition, ETFE shows crosslinking reaction even in the cone-and-plate rheometer. The degree of crosslinking is quantitatively estimated by the plateau modulus G′plateau in the low frequency region. The result suggests that the crosslinking occurs as a first order reaction.

Temperature Dependence of the Linear Steady-State Shear Compliance of Linear and Long-Chain Branched Polyethylenes

The linear steady-state shear compliances Je0 of two linear short-chain branched metallocene-catalyzed polyethylenes (mLLDPE), two long-chain branched metallocene-catalyzed polyethylenes (LCB-mLLDPE), and two classical low density polyethylenes (LDPE) were determined in creep-recovery tests in shear between 130 and 190 °C. In order to investigate the dependence of Je0 on the molecular structure the polyethylenes were characterized by high-temperature size-exclusion chromatography coupled with a multiangle laser light scattering device (SEC−MALLS). For the linear mLLDPE the lowest Je0 independent of temperature were observed. For the LCB-mLLDPE having similar polydispersities as the linear mLLDPE not only an increase of Je0 by about 1 order of magnitude compared to the linear mLLDPE but also a significant decrease in Je0 with increasing temperature was found. For the LDPE possessing long-chain branches as well as higher polydispersities, the highest Je0 values were detected, which were also temperature dependent. For the LDPE, the decrease of Je0 with increasing temperature is less pronounced than for the LCB-mLLDPE. However, for both material types the temperature dependence of Je0 is much stronger than expected from the rubber elastic theory.

Functional properties of five varieties of taro flour, and relationship to creep recovery and sensory characteristics of achu (taro based paste)

Achu is a paste traditionally made from taro corms by boiling, peeling and pounding in a mortar to a smooth and homogeneous consistency. The present study aims to define alternative and rapid methods to evaluate the textural hardness of achu reconstituted from taro flour. The creep recovery behaviour of achu samples made from flour of five varieties of taro was evaluated on a controlled-stress rheometer. The functional properties of the taro flours, the sensory analysis of hardness and the acceptability of reconstituted achu were also evaluated. The results showed significant variation in the functional properties of the flours. The rheological properties of the achu, the sensory hardness and overall acceptability were also significantly influenced by the variety. In general, flour which absorbed more water tended to produce achu with high level of newtonian compliance and retarded elastic compliance. The creep steady state shear compliance and the viscoelasticity index of achu, were significantly ( P < 0.05) correlated to the sensory hardness.

Effects of Concentration on Steady-State Viscometric Properties of Short Chain Polymer Solutions Over the Entire Concentration Range

Relationships between viscometric behavior and concentration are observed and evaluated through a series of nonequilibrium molecular dynamics simulations of the behavior of 20-site polymers in solution with explicit solvent across the full concentration range. The zero-shear viscosities, first normal stress coefficients and steady-state shear compliance of the solutions are examined alongside conformational properties including the excluded volume effect. The variation of viscosity with concentration in these solutions is described by the Huggins equation up to relatively high concentrations. At these high concentrations, the effects on conformation of excluded volume interactions decline, while no clear semi-dilute region is identifiable. Although the steady-state shear compliance of the system appears concentration-independent, the dilute and melt behaviors of this system are accurately described by the theories of Zimm and Rouse, respectively.

Melt Rheology of Dendritically Branched Polystyrenes

Unique rheological properties of combined low melt viscosity and high melt elasticity are reported for a novel series of dendritically branched polystyrenes. Unlike previous studies, dendritically branched materials having different molecular weights but all possessing the same number of generations are studied; this allows the determination of true scaling relationships. Zero shear viscosities scale with the second power of molecular weight until corrected to a state of constant free volume, upon which they scale with the first power of molecular weight. Importantly, the steady state shear compliance for the materials increases with increasing molecular weight and is very large compared to other chain architectures. This finding holds potential technological importance as it may be possible to simultaneously decrease viscosity and increase elasticity by blending with these novel structures. Dynamic light scattering and small-angle neutron scattering studies demonstrate the self-similar nature of these highly branched polymers, thereby establishing that the chain architecture is well-defined. Evidence of entanglements is missing. Remarkably, this implies that it is possible to prepare unentangled polystyrenes having a molecular weight in excess of 1 000 000 (g/mol). Melt dynamics are complex; exhibited behavior encompasses aspects of both classical Rouse−Zimm response and the power-law behavior associated with fractal or gelling systems. Neither Rouse−Zimm nor power-law relaxation time distributions are capable of quantitatively describing the data. However, the corrected viscosity scaling and the viscosity shear thinning behavior are in rough agreement with a theory of polymeric fractals proposed by Muthukumar [J. Chem. Phys. 1985, 83, 3161].

Evolution of the viscoelastic properties of SnO 2 colloidal suspensions during the sol–gel transition

This paper describes the effect of the concentration of electrolyte and pH on the kinetics of aggregation and gelation processes of SnO 2 colloidal suspensions. Creep, creep-recovery, and oscillatory rheological experiments have been done in situ during aggregation and gelation. A phenomenological description of the structure of the colloidal system is given from the time evolution of rheological parameters. The dependence of the equilibrium steady-state shear compliance on the terminal region of clusters or aggregates seems to be a way to determine the beginning of interconnection of aggregates and the gel point. We propose that at this point the equilibrium steady-state compliance is a minimum. The steady-state viscosity determined from creep experiment can be fit with a power law with the extent of the transformation, giving critical exponent s=0.7±0.1. The value of the critical exponent Δ=0.78±0.05 was determined from oscillatory experiment. These results indicate that gelation of SnO 2 colloidal suspension exhibits the typical scale expected from the scalar percolation theory.

Viscoelastic Properties of Narrow-Distribution Poly(methyl methacrylates)

The viscoelastic properties of two series of poly(methyl methacrylates) (PMMA) with different tacticities and very narrow molecular weight distributions were measured in the molten state at different temperatures by means of oscillatory rheometry. Zero-shear viscosity η0, steady-state shear compliance Je°, and plateau modulus GN° were obtained from the resulting master curves for the storage modulus G‘ and loss modulus G‘‘. Relaxation time spectra h(τ) were calculated by a nonlinear regularization method and could be used to determine the terminal relaxation time τ0. The molecular weight and polydispersity dependence of these parameters agrees with existing empirical rules for linear amorphous polymers. Stereoregularity, however, has a great influence on η0 and τ0. The entanglement molecular weight Me and the critical molecular weight Mc seem to vary with the tacticity as well. These results are possible explanations for some contradicting or inconsistent literature data concerning PMMA.

Modeling the dynamic properties of monodisperse linear polymer melts with wedge spectra

A mathematical model of the spectrum of relaxation times for molten linear monodisperse homopolymers has been developed which is the sum of two variations of the well-known wedge spectrum. Adjusting the six parameters of the model allows fitting the storage and loss moduli within experimental error over a range of 10–12 logarithmic decades of frequency which encompass the flow, plateau, transition, and glassy zones of viscoelastic behavior. Model parameters are easily determined with a desktop microcomputer using standard nonlinear least-squares fitting procedures. All six model parameters correspond directly to prominent features of experimental data. The plateau modulus, viscosity, steady-state shear compliance, and the frequency at which the storage and loss moduli cross can all be easily calculated from the model parameters. The limiting low- and high-frequency behaviors of the storage and loss moduli predicted by the model are consistent with experiment and with linear viscoelastic theory. For the transition zone, the model can closely mimic the dynamic behavior predicted by normal-coordinate molecular theories. The model is applied to experimental data for five narrow-distribution polystyrenes having molecular weights in the range of 60 000–540 000.

Pressure and solvent influences on the shear thinning behavior of moderately concentrated solutions of poly(butyl methacrylate)

AbstractThe viscosities of moderately concentrated solutions of poly(butyl methacrylate)—M̄w = 1820 kg/mol–in the thermodynamically good solvent toluene and in the theta solvent 2‐propanol were measured up to pressures of 2000 bar as a function of shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} in the temperature interval from 40 to 70°C. Both systems obey Graessley's equation so that it is possible to obtain the following rheological parameters in addition to the zero‐shear viscosity η0 from the dependences \documentclass{article}\pagestyle{empty}\begin{document}$ \eta (\dot \gamma ) $\end{document}. η can be split into an entanglement part ηent plus a frictional contribution ηfric, and the characteristic viscometric relaxation time τ0 becomes accessible. The present results demonstrate that the application of pressure raises the above parameters much less for good than for bad solvents. In contrast to ηfric (which can react differently to the application of pressure due to special circumstances) η0 and τ0 are always influenced to the same degree as T or p are changed. This result implies that the steady state shear compliance (τ0/η0) is independent of the variables of state irrespective of the thermodynamic quality of the solvent. For the good solvent the effects of temperature can be described by the Arrhenius equation, whereas the WLF equation has to be used for the bad one.

Rheology of Pitches

Rheological behavior of optically isotropic pitches derived from petroleum crude oils and coal tars were reviewed in relation to their dependence on molecular weight and temperature. Studied were the hydrodynamic characteristics (intrinsic viscosity, [η], and diffusion coefficient) of dilute pitch solutions, glass transition behavior, viscoelastic properties, and dielectric dispersion-electric conductivity characteristics of fractionated pitches with different molecular weights, which were prepared using the difference in solubility of the pitches in n-hexane and benzene. The hydrodynamic studies yielded an important information on the shape and dimension of constituent pitch molecules, i. e., oblate ellipsoid with the axial ratio of 1-3, and 10-20Å in equatorial diameter. The glass transition temperature, Tg, which decreased linearly with the inverse of number averaged molecular weight, was found to play an important role on the molecular weight dependence of steady-state shear viscosity, η, and steady-state shear compliance, Je0. The dependence of Je0 on temperature suggests that the elastic process in pitches is enthalpic, not entropic as observed in usual organic polymers. The dielectric behavior of pitches were described well by so-called Cole-Cole relation except prominent energy dissipation due to electrically conductive carriers in the region of low electrical frequency at high temperature. The importance of the rheological studies of mesophase pitches was emphasized in relation to the technical development of anisotropic carbon fibers with high elastic modulus and high strength

Melt rheology of high impact polystyrenes at high shear stresses

AbstractA study of the theological properties of commercial polystyrenes, (PS), and high impact polystyrenes (HIPS), is made in the range of shear stresses of practical interest in industrial polymer processing.A general viscosity‐shear rate‐temperature relationship is defined for these products, with a power law exponent of n = 0.3 and an activation energy of 27 Kcal/mol.The fluid elasticity is studied in terms of steady state shear compliance. An expression relating shear compliance, viscosity and molecular weight distribution is obtained for HIPS. As in other two‐phase systems, a decrease in elasticity with viscosity is observed.

The steady-state shear compliance of regular star polymers

The steady-state shear compliance of regular star polymers

Viscoelastic properties of entangled polymers: Ternary blends of monodisperse homopolymers

In a previous publication from this laboratory, the Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to binary blends of monodisperse polymers with chain entanglements. The dynamics of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings. It was recognized that entanglements not only may form between chains of the same lengths (intracomponent entanglements) but also between those of different lengths (intercomponent entanglements). At a given intercomponent entanglement, the longer chain was assumed to have the frictional coefficient of the shorter chain. Similarly, for blends consisting of several monodisperse components with different molecular weights, such modifications are also required to predict their linear viscoelastic behavior. The frequency of these interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation time spectra. Linear viscoelastic properties such as the dynamic mechanical moduli, stress relaxation moduli, and zero-shear viscosity can then be computed for these systems by linear summation of those of the components. The reduced steady-state shear compliance of the blends can also be computed from the component relaxation times. Results are found to be in good agreement with experimental data on polystyrene ternary blends.

Viscoelastic Properties of Entangled Polymer. IV. Binary Blends of Monodisperse Homopolymers

In a previous publication from this laboratory, the Rouse‐Bueche‐Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to monodisperse polymers with chain entanglements. Effects of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings resulting from the transient entanglement network. For binary blends consisting of two monodisperse polymers with different molecular weights, additional modifications are now required to predict their linear viscoelastic behavior. It is recognized that entanglements not only may form between chains of the same length, but also between those of different lengths. For the latter case, the longer chain will in fact have the frictional coefficient of the shorter chain at the point of entanglement. The frequency of such interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation spectra. Linear viscoelastic parameters such as the dynamic mechanical moduli, stress relaxation moduli, and zero shear viscosity can then be computed for the blends by linear summation of those of the components. The reduced steady state shear compliance of the blends can also be computed from knowledge of the component relaxation times. Results are found to be in excellent agreement with literature data on polystyrene, poly(dimethyl siloxane), and poly(methyl methacrylate).

A Relationship between Steady State Shear Compliance and Molecular Weight Distribution

A Relationship between Steady State Shear Compliance and Molecular Weight Distribution

Viscoelastic parameters of characterized branched polyethylenes

AbstractCertain steady state viscoelastic parameters, including melt viscosities, normal stress coefficients, and shear compliances, are determined for a series of well‐characterized low, density polyethylene samples, and the results are analyzed. The effects of shear rate, temperature, molecular weight, molecular weight distribution, and the degree of long chain branching are demonstrated. The agreement observed between steady state shear compliance values derived from normal stresses and those obtained from die swell measurements is significant.

Viscoelastic properties of entangled polymers: The transient network model

The viscoelastic behavior of entangled polymers is modeled by a three-dimensional transient network where the entangled points are considered to act as temporary crosslinks. Polymer chains are represented by beads and springs. The effects of entanglements on chain dynamics are introduced by assigning enhanced frictional coefficients to selected beads as well as extra elastic couplings between pairs of the entangled beads. The formation and disengagement of the entanglements can be envisioned to be in a dynamic equilibrium. The strength of elastic coupling is set to decrease with increasing distance between the entangled points. The resulting modified Rouse-Bueche-Zimm matrix is solved for the relaxation times from which the dynamic moduli, relaxation moduli, steady-state shear compliance, and zero-shear viscosity are computed. Results are in excellent agreement with experimental data on monodisperse polystyrene, poly(α-methylstyrene), poly(vinyl acetate) and polybutadiene.

Estimation of Long-Chain Branching in Ethylene-Propylene Terpolymers from Infinite-Dilution Viscoelastic Properties

Abstract A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (Mw/Mn&amp;lt;1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge ofMw/Mn and the Mark-Houwink exponent a. The resulting value of S2/S12 (where S1=∑ τp/τ1, S2=∑ (τp/τ1)2, the τp's being the relaxation times and τ1 the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene-propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.

Numerical Calculations of the Viscoelastic Properties of Dilute Solutions of Comb-Shaped Branched Polymers

The viscoelastic properties of dilute solutions of comb-shaped branched polymers have been calculated from the bead-spring model, following the Zimm and Zimm-Kilb theories, with exact numerical evaluation of eigenvalues by the method of Lodge and Wu. Eigenvalues, relaxation times, and frequency dependence of the reduced intrinsic shear moduli [G′]R and [G″]R have been obtained for various combinations of number of branch points (f) 1 to 10, beads per branch (Nb) 1 to 37, backbone beads between branches (Na) 1 to 22, and the reduced hydrodynamic interaction parameter (h*) 0 to 0.25. Since the total number of beads (f+1) Na+fNa+fNb−1 is restricted to an unrealistically small value of 111 by computer limitations, attention is focused on the low-frequency behavior where this restriction will have the least influence. Here, the behavior is characterized by the reduced steady-state shear compliance. This quantity is quite sensitive to f when the mass backbone fraction λ is small (approaching starshaped geometry); and for larger λ, it can detect the presence of a small number of branches.

Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties

A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (Mw/Mn <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of Mw/Mn and the Mark-Houwink exponent a. The resulting value of S2/S (where S1 = Στp/τ1, S2 = Σ(τp/τ1)2, the τp's being the relaxation times and τ1 the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.