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Journal of RheologyVolume 45, Issue 4 (July-August 2001) |
Contents
On the scaling of molecular weight distribution functionalsR. S. Anderssena) and R. J. Loyb) a) CSIRO
Mathematical and Information Sciences b) Mathematics
Department, School of Mathematical Sciencs AbstractWhen formulating a constitutive equation model or a mixing rule for some synthetic or biological polymer, one is essentially solving an inverse problem. However, the data will not only include the results obtained from simple step strain, oscillatory shear, elongational and other experiments, but also information about the molecular weight scaling of key rheological parameters (i.e. molecular weight distribution functionals) such as zero-shear viscosity, steady-state compliance and the normal stress differences. In terms of incorporating such scaling information into the formulation of models, there is a need to understand the relationship between various models and their molecular weight scaling, since such information identifies the ways in which molecular weight scaling constrains the choice of possible models. In Anderssen and Mead [J. Non-Newtonian Fluid Mech. 76 (1998), 299- 306], it was established formally that the members of a quite general class of reptation mixing rules all had the same molecular weight scaling. The purpose of this paper is to first introduce the concept of a generalized reptation mixing rule, which greatly extends the class examined by Anderssen and Mead, and then show that all such rules have the same molecular weight scaling. The proof is similar to that give by Anderssen and Mead, but uses the implicit function theorem to establish the uniqueness of the mean-values which arise when invoking various integral mean-value representations for the molecular weight distribution functionals considered. The rheological significance of the new generalized two-parameter mixing rule, proposed in this paper, is examined in some detail in the conclusions. In particular, it is used to established how one must construct a mixing rule for a general polydispersed polymer where the molecular dynamics involves some single, some double and some higher levels of multiple reptation. The work of Maier et al. [J. Rheol. 42 (1998), 1153-1173] and Thimm et al. [J. Rheol. 44 (2000), 429-438] is then utilized to illustrate and validate this proposal. Rheology of fiber suspensions in viscoelastic media: Experiments and model predictionsA. Ramazani S. A., A. Ait-Kadib) and M. Grmelaa) Chemical Engineering Department and CERSIM a) Chemical Engineering Department and GRASP AbstractThe rheological behavior of suspensions of short glass fibers in different fluids has been studied. Transient tests on pre-sheared samples of fiber suspensions in Boger fluids showed that orientation of fibers does not only depends on the strain, but also on the rate-of -strain. The experimental results show that upon increasing fiber concentration and/or fiber aspect ratio, the steady shear material functions of fiber suspensions increase at low shear rates, whereas at high shear rates, these material functions approach those of the matrix and become almost independent of fiber characteristics. A rheological model based on the modified Jeffery equation for the fiber motion and a Hookean energy model, formulated within the GENERIC framework, for the matrix has been developed to quantitatively predict experimental data for suspensions of fibers in different fluids. A quantitative comparison of experimental data with model predictions shows the ability of the model to predict the rheological behavior of fiber suspensions in viscoelastic media b) To whom correspondence should be sent. Viscoelastic properties of a cross-linked polysiloxane near the sol-gel transitionP. Tordjemana,c), C. Fargettea), and P .H. Mutinb) a) Laboratoire des Verres, CC 69,
Universíté Montpellier II b) Laboratoire de Chímíe Moléculaire et
Organisation du Solide AbstractExperimental results are presented concerning the zero frequency and dynamic properties of a cross-linked polysiloxane near gelation threshold. It is prepared by hydrosilation of a di-functional vinyl-terminated polydimethylsiloxane prepolymer and a 7-functional poly(dimethylsiloxane-co-methy1hydrogenosiloxane) prepolymer. The zero frequency and dynamic properties during cross-linking have been studied by rheological experiments in the framework of the linear viscoelasticity .The material at the gelation threshold follows a power law viscoelastic behavior, G* µ w" with u = 0.77. The zero frequency exponents s and t ( h µ es ; G µ et ) were determined from the rheological data (s = 0.76 and t = 2.54). This study shows that the zero frequency and dynamic exponents obey to the scaling relation u = t / (s + t) and are not universal. Above the gelation threshold, a rheological master curve could be built showing that the viscoelastic properties of the gel are governed by the molecular structure of the prepolymers and the self-similarity of the mass distribution of clusters. In this way, this system follows the percolation theory. Assuming that the non-reacted prepolymers swell the network, the molecular weight between cross-links was estimated. c) To whom correspondence should be addressed. E-mail : tordjeman@ldv.univ-montp2.fr Two-dimensional simulation of melt spinning with a microstructural model for flow-induced crystallizationAntonios K. Doufasa) and Anthony J. McHughb) AbstractThe constitutive model for flow-induced crystallization (FIC) developed by the present authors [Doufas et al. (1999), (2000a), (2000b), Doufas and McHugh (2001)], coupling polymer microstructure (chain extension, molecular orientation, and crystallinity) with the macroscopic transport equations (mass, momentum, and energy), was applied to a two-dimensional simulation of melt spinning. The model predicts the radial variation of tensile stress and microstructure driven by the radial variation of the temperature, which is caused by low polymer thermal conductivity. In the limit of infinite thermal conductivity , radially uniform profiles for the temperature and the microstructure are consistently predicted. The formation of a skin-core structure observed experimentally is also predicted, where the molecular orientation, crystallinity, and tensile stress are highest at the surface of the fiber and lowest at the centerline. The microstrucuure is predicted to lock in below the freeze point preserving its radial variation despite the collapse of the temperature radial variation at large distances below the spinneret. Under the conditions investigated, for both nylon and polyethylene teraphythalate systems, the cross-sectionally averaged variables do not deviate significantly from the respective uniform quantities of the one-dimensional formulation at the freeze point. We suggest that the model can be used as an optimization tool for melt spinning processes predicting the final fiber properties through the radial variation of the microstructural variables. a) Current address: The Dow Chemical Company,
M.E. Pruitt Research Center, 1702 Building, Midland MI 48674. Annular Poiseuille flow of ER and MR materialsHenri P. Gavin AbstractElectro- and magneto-rheological materials exhibit substantial increases in yield stress when subjected to strong electric or magnetic fields. The applied electric/magnetic field satisfies Laplace's equations in the ER/MR material. In annular geometries, the resulting spatial variation of the electric/magnetic field results in a yield stress inhomogeneity. The analysis of annular Poiseuille flow of ER/MR materials herein assumes a power-law relationship between the field and the yield stress, and includes the effects of the inhomogeneous yield stresses and hyperbolic shear stress distributions. The approximation of the solution to this problem by flow through an appropriately-defined rectangular duct (in which the yield stress is constant and the shear stresses are linearly distributed) can be remarkably accurate, even for non-slender ducts. Thermoreversible gelation in aqueous dispersions of colloidal particles bearing grafted poly(ethylene oxide) chainsJennifer S. Shaya), Srinivasa R. Raghavanb), and Saad A. Khana,c) a) Dept. of Chemical Engineering b) Dept. of Chemical Engineering AbstractColloidal interactions between particles in a dispersion can be tuned by grafting polymeric chains onto the surface of the particles. The affinity between the polymeric chains and the continuous-phase liquid controls the strength of these interactions. In our system the polymer-liquid affinity is strongly influenced by temperature, and as a result, dramatic changes occur in the dispersion microstructure on heating. The system is an aqueous dispersion of polystyrene (PS) particles bearing grafted poly(ethylene oxide) (PEO) chains of low molecular weight (ca. 2000). At room temperature, water is a good solvent for PEO chains, and the dispersion is a stable, low-viscosity sol. As temperature is increased, water becomes a progressively worse solvent for PEO. Beyond a temperature Tc there is a sharp transition in microstructure from a stable sol to a volume-filling gel. The sol-gel transition is reversible and the transition temperature Tc can be pinpointed using tan d vs. temperature plots. Remarkably, Tc is more than 100°C lower than the q-temperature for PEO (2000) in water, i.e., the gelation occurs under significantly better-than-q conditions. Tc is independent of particle concentration, but is strongly influenced by the graft density of PEO chains on the particles. The higher the graft density, the higher the Tc for gelation; conversely, at very low graft density, the samples are gels even at room temperature. Above Tc, the elastic modulus (G') of the gels reveals a power law dependence with particle volume fraction (f), i.e. G' µ fn. The power law exponent n is independent of the PEO graft density, implying that the various gels have a similar microstructure. We suggest that gelation is the result of a weak secondary minimum in the interparticle potential that can develop in the case of short stabilizing moieties and moderate solvent conditions. c) Corresponding author: 919-515-4519 (phone), 919-515-3465 (fax), khan@eos.ncsu.edu (email). Exploration of the slip phenomenon in the capillary flow of linear low-density polyethylene via electrical measurementsJosé Pérez-González AbstractThe slip phenomenon and the electrification occurring in the capillary flow of a linear low-density polyethylene melt were studied in this work using dies made up of stainless steel and brass, respectively. The experiments were carried out in a torque driven capillary rheometer at a temperature of 200 °C and spanned the different flow regimes observed in capillary flow, including stable and unstable conditions. Flow enhancement or slip was generated in the brass die, as compared to the stainless steel one, after an appropriate cleaning treatment. The melt exhibited electrostatic charge and sharkskin distortions were eliminated during the processing with the brass die in the stable flow regime prior to the stick-slip. Electrification and elimination of sharkskin distortions on the extrudates were observed when the slip velocity was a significant part of the whole average melt velocity (more than 50% in this work). The observations in this work point to a. tribological origin for the electrification of the melt. Finally, electric charge of different sign was measured on the extrudates obtained from the stainless steel and brass dies, respectively, during the stick-slip, which suggests a detachment mechanism for slip in this flow regime. An apparatus for measuring the effect of pressure on the time-dependent properties of polymersAles Kralj,
Ted Prodan and Igor Emria) AbstractWe improved and upgraded the apparatus that Fillers, Moonan, and Tschoegl used several years ago to investigate the influence of pressure and temperature on the mechanical properties of time dependent polymeric materials. The new apparatus can measure the volume and the shear relaxation module of solid polymer specimens, subjected to a combination of temperatures from -60°C to +110°C, and pressures from atmospheric to 360 MPa. The paper demonstrates the capabilities of the new apparatus from the scientific as well as engineering stand point. Shear relaxation measurements on poly(vinyl acetate) (PVAc), natural rubber (NR), styrene-butadiene rubber (SBR), and ethylene-propylene-diene-monomer rubber (EPDM) are also presented. For PVAc we present also bulk creep compliance, coefficient of thermal expansion and the bulk modulus. a) To whom correspondence should be addressed. E-mail: igor.emri@ki.si Comparison of the effects of dimethyl and dichloro benzoate counterions on drag reduction, rheological behaviors and microstructures of a cationic surfactantZhiqing Lin
and Jacques L. Zakina) Yi Zheng, H.
Ted Davis, L. E. Scriven Yeshayahu
Talmon AbstractArquad 16-50 (commercial CTAC, cetyltrimethylammonium chloride) (5mM) with the counterions 3, 4-dichlorobenzoate (5mM and 10mM), 3, 4-dimethylbenzoate (5mM and 10mM) and 3, 5-dichlorosalicylate (5mM) were studied to compare the effect of concentration of the counterion and its ratio to surfactant concentration (x) on drag reduction, rheological behavior and microstructures. The first four solutions are good drag reducers at different temperature ranges. The 3, 4-dimethylbenzoate system (x = 1) is effective at 5-40 °C and the 3, 4-dichlorobenzoate system (x = 1) at 20-70 °C. Increasing the concentration ratio to x = 2 increased the upper temperature limit 10 °C for each system. The counterion concentration changes affect microstructures in the quiescent state in different ways. The viscoelastic x = 1 solution of 3, 4-dimethylbenzoate has a microstructure of both vesicles and threads in the quiescent state which probably transform to a threadlike micellar network under shear. However, its ratio of apparent extensional viscosity to shear viscosity is very low, unusual for a surfactant drag reducer. Its x = 2 solution has typical surfactant drag reducer properties, viscoelastic, high extensional viscosity, and threadlike micellar networks. The x = 1 solution of 3, 4-Cl-benzoate is like the x = 2 solution of 3, 4-CH3-benzoate while its x = 2 solution is non-viscoelastic with vesicles and spherical micelle microstructures in the quiescent state which also probably transform to a network structure in strong shear fields. The only system tested with a counterion having four-substituent groups, 3, 5- dichlorosalicylate, is not effective as a drag reducer, has water-like behavior, and contains very large vesicles. a) Author to whom correspondence should be addressed; e-mail: zakin.1@osu.edu Effect of compatibilization on the breakup of polymeric drops in shear flowSachin Velankar, Peter Van Puyvelde, Ian Mewis, and
Paula Moldenaersa) AbstractA block copolymer may be added as a compatibilizer during polymer processing in order to promote intimate mixing of thermodynamically immiscible homopolymers. The action of this compatibilizer can only partially be attributed to its effect on the interfacial tension between the immiscible homopolymers. Here the additional contributions of the compatibilizer are directly probed by measuring the capillary number during coalescence experiments. Model blends consisting of PIB and PDMS, compatibilized with various amounts of a PIB-PDMS diblock copolymer, are used for this purpose. The mean capillary number of the droplets is determined from the mechanical frequency response of the blends. With increasing amounts of compatibilizer, a systematic increase in steady shear capillary number is seen, to values well above the critical capillary number for droplet breakup of uncompatibilized systems. This indicates that a simple decrease in interfacial tension is not the only effect of adding the compatibilizer to these immiscible blends. Past simulations suggest that these results are associated with gradients in interfacial tension (Marangoni stresses) induced by the gradients of compatibilizer concentration due to flow. Direct evidence of the presence of such interfacial tension gradients along the surface of compatibilized drops was obtained by optical microscopy. a) Author to whom correspondence should be addressed. Determination of WLF constants for a food polymer system: Effect of water activity and moisture contentM. E. Yildiz
and J. L. Kokini AbstractThe WLF equation is a useful tool in prediction of temperature-induced physical changes in foods that are exposed to specific food processing and storage conditions, because so many deteriorative processes are diffusion-controlled. In food polymers, viscoelastic properties are a strong function of the key plasticizers present in foods, such as water. However, WLF constants as a function of water content and water activity are not available in the food literature. In this research, we investigated the WLF properties of soy flour as a function of water activity and elucidated the effect of water on the magnitude of WLF constants. Based on a time-temperature superposition principle, shift factors (aT) were obtained, which were used to estimate WLF constants. WLF constants for soy flour were shown to be material-specific and different from the "universal values". Differential constitutive equations for polymer melts: The eXtended Pom-Pom modelWilco M. H.
Verbeeten, Gerrit W.M. Peters, and Frank P. T. Baaijens AbstractThe Pom-Pom model, recently introduced by McLeish and Larson [J.Rheol., 42(1), 1998], is a breakthrough in the field of visco-elastic constitutive equations. With this model, a correct non-linear behaviour in both elongation and shear is accomplished. The original differential equations, improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified eXtended Pom-Pom (XPP) model does not show the three problems and is easy for implementation in Finite Element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxial, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial LDPE melts and one HDPE melt. Such a good agreement over a full range of well defined rheometric experiments, i. e. shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional. a) http://www.mate.tue.nl/. Structure formation in moderately concentrated viscoelastic suspensions in simple shear flowM. K. Lyona), D. W. Meadb), R. E. Elliottc), and L. G. Lealc) a) ExxonMobi1 Chemical Company b) Department of Computational Science and
Engineering c) Department of Chemical Engineering AbstractWe report experimental results on the evolution of the particle microstructure for noncolloidal particles that are suspended in a viscoelastic medium. For dilute suspensions consisting of particles having a monodisperse particle size distribution subjected to steady and oscillatory shear flows, as well as suspensions having a bidisperse size distribution subjected to steady shear, we verify previous results reported in the research literature. We also present new results of the particle microstructure for a dilute bidisperse system that was subjected to oscillatory shear. For moderately concentrated suspensions we report the formation of particle strings that correspond to a quantitative reduction in the simultaneously measured shear stress |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |