 |
 |
|
|
 |
Journal of RheologyVolume 49, Issue 5 (Sep-Oct 2005) |
Contents
Development of bead-spring polymer models using the constant extension ensemblePatrick T. Underhill and Patrick S. Doyle Department of Chemical Engineering AbstractWe have examined a new method for generating coarse-grained models of polymers. The resulting models consist of bead-spring chains with the spring force-law taken from the force-extension behavior in the constant extension ensemble. This method, called the Polymer Ensemble Transformation (PET) method, is applied to the freely-jointed chain. The resulting model illustrates why current bead-spring chain models are insufficient in describing polymer behavior at high discretization. Applying the method to the freely-jointed chain with unequal rod lengths showed the effect of varying flexibility in the chain. The method was also used to generate a bead-spring model of F-actin, which shows how the method is not restricted to one molecular model and can even be applied to experimental data. The current limitations of the method are discussed, including the need for approximate bending potentials to model the worm-like chain with a bead-spring chain. We discuss practical issues such as using the bead-spring models in Brownian dynamics simulations and develop a simple spring force-law that can accurately represent a freely-jointed chain with only a few rods per spring. Because of the functional form of this new force-law, existing computer simulations can be easily modified. The scaling of zero-shear viscosities of semidilute polymer solutions with concentrationYoungsuk Heo Ronald G. Larson AbstractTo test the universality of the dependence of zero-shear viscosity on concentration for both flexible and locally semiflexible polymers in good solvents, we collected multiple literature data sets and measured the zero shear viscosity of l-phage DNA over a range of semidilute concentrations. We found that all experimental data above a critical concentration c/ce > 0.5 fall on a single empirical curve given by hp/hRouse = (45 ± 2) × (c/ce)2.95±0.07 and this scaling law is in good agreement with the theoretical one, hp/hRouse ≈ (c/ce)2.4/(3n − 1) with n the excluded volume exponent, hp = h0 − hs the polymer contribution to the zero shear viscosity of the solution with h0 the zero-shear viscosity and hs the solvent viscosity, hRouse the hypothetical Rouse polymer viscosity, and ce the entanglement concentration of the polymer solution (Menezes and Graessley 1982; Raspaud et al. 1995; Osaki et al. 2001). This scaling law provides a basis for estimating viscosities for arbitrary semidilute entangled polymer solutions from a knowledge of the solvent viscosity, the entanglement molecular weight in the melt, the excluded volume exponent, the second virial coefficient, and the intrinsic viscosity. Prediction of coil-stretch hysteresis for dilute polystyrene molecules in extensional flowChih-Chen Hsieh and Ronald G. Larson a) Dept. of Chemical Engineering AbstractThe existence of coil-stretch hysteresis in extensional flows of long-chain polymers in dilute solutions has recently been demonstrated using enormously long DNA molecules [Schroeder et al. (2003)]; however, there is no demonstration of hysteresis for synthetic polymers of more modest molecular size. We here use Brownian dynamics simulations of bead-spring chains to predict that the minimum molecular weight of polystyrene in a dilute theta solvent that can show a “coil-stretch hysteresis” in a uniaxial extensional flow is around 0.5 million Daltons. We find that the threshold value of the ratio of effective drag coefficients in the stretched vs. coiled states, zstretch/zcoil, is about 4.5 for the occurrence of hysteresis, close to the value observed for DNA. a) Corresponding author. Phone: 734-936-0772; Fax: 734-763-0459; Email: rlarson@engin.umich.edu. Kinetics and mechanism of shear banding in an entangled micellar solutionY. T. Hu a) and A. Lips Unilever Research & Development AbstractWe have studied shear banding in Couette flow using a combination of particle tracking velocimetry (PTV), small angle light scattering (SALS), microscopic visualization, and flow birefringence. Time-resolved local shear rate characterization by PTV has been achieved for the first time and has enabled a direct study of the kinetics of shear banding. A first stage, which precedes banding, is tilting of shear rate during which local shear rate increases towards the inner and decreases towards the outer gap surface. A shear banding stage then proceeds with a low shear band growing away from the outer gap surface. Shear rate tilting is found to be due to a coupling of local shear thinning with the non-zero stress gradient of the flow geometry. The low shear band starts when local shear rate at the outer surface touches down to a critical reentanglement shear rate. The effective lifetime of the shear bands is the same as the chain reentanglement time. These two findings lead us to suggest that both the progression from tilt to shear banding and the interface between the low and high shear bands are subject to a common local entanglement / disentanglement criterion. Constitutive curves constructed from local shear rates show that there is not a unique stress – shear rate relation in the shear band coexistence regime, suggesting constitutive instability. The high shear band has fluctuating micellar layers aligned in the flow direction, and is strongly shear thinning. We observe insignificant viscosity differences between adjacent layers, and layer relaxation times are an order of magnitude greater than the effective lifetime of the shear bands. The layers, therefore, do not behave as “sub-shear bands” and are not causative for the shear banding. a) Author to whom correspondence should be addressed; e-mail: thomas.hu@unilever.com. Creep recovery of random ethylene-octene copolymer melts with varying co-monomer contentBhaskar Patham and Krishnamurthy Jayaraman a) Department of Chemical Engineering and Materials Science AbstractThis paper presents an investigation of the effects of varying comonomer content from 20 wt% to 38 wt% in random ethylene-octene copolymers made with a metallocene catalyst on the melt rheology including transients in shear creep recovery from high strains. The copolymer with 20% octene appeared to be the same as that reported to be long chain branched in the literature and was used as a reference material. The materials were characterized in oscillatory shear and shear creep at stresses ranging from 5 Pa to 30000 Pa. Van Gurp-Palmen plots prepared from dynamic modulus data and zero shear viscosity values from creep tests at very low stress confirmed that the reference material was long chain branched and established that long chain branching was absent from the copolymer with the highest comonomer content. The steady state recoverable shear compliance values for the three copolymers were very close. However, following large shear deformations brought about at higher strain rates, strain recovery was reduced most significantly for the copolymer with the highest comonomer content where long chain branching was absent. The reduction in recovery at short times was also most significant for this copolymer. a) Corresponding Author, email: jayarama@egr.msu.edu, Tel (517) 355-5138, Fax (517) 432-1105. The influence of polymer concentration and chain architecture on free surface displacement flows of polymeric fluidsGandharv Bhatara Eric S. G. Shaqfeh Bamin Khomami a) AbstractWe examine the effect of polymer concentration and chain architecture on the steady state displacement of polymeric fluids by air in between two infinitely long closely spaced parallel plates, i.e., Hele-Shaw flow. A stabilized finite element method coupled with a pseudo-solid domain mapping technique is used for carrying out the computations. The constitutive equations employed in this study are the Finitely Extensible Non-linear Elastic- Chilcott Rallison (FENE-CR) and the Finitely Extensible Non-linear Elastic- Peterlin (FENE-P) models for dilute solutions, the Giesekus constitutive equation for dilute, semi-dilute and concentrated solutions, and the Extended Pom-Pom (XPP) constitutive equation for linear and branched polymeric melts. Our study indicates the presence of a recirculation flow at low Ca and a bypass flow at high Ca irrespective of polymer concentration and chain architecture. We show that the interfacial dynamics in both the recirculation and the by-pass flow depend on extensional hardening and shear thinning characteristics of the fluids. In the recirculation flow, we observe the formation of normal elastic stress boundary layers in the capillary transition region, an accompanying increase in the film thickness and a compression of the bubble in the capillary transition region, at moderate Wi. In the bypass flow, in addition to the elastic stress boundary layer in the capillary transition region, an additional stress boundary layer is observed at the tip of the bubble. The amount of film thickening, the magnitude of the stress in the stress boundary layer and the amount of bubble compression are largest for the most extensional hardening fluids and reduce with decreasing extensional hardening and increasing shear thinning. We show that the film thickness is determined by two competing forces, i.e., normal stress gradients in the flow direction, in the capillary transition region (recirculation flow) and the tip region (bypass flow) and shear stress gradients in the gap direction. For both the recirculation and the bypass flow, we show how the film thickness scales with fluid normal stresses and shear viscosities, and develop correlations for the film thickness as a function of Ca and Wi. a) Corresponding author. Fax + 314 935 7211; e-mail: bam@poly1.che.wustl.edu Rheology of highly concentrated planar fiber suspensionsSteven Le Corre a) Pierre Dumont b) Laurent Orgeas and Denis Favier AbstractThe rheology of highly concentrated fibers suspended in power-law fluids is investigated by upscaling the physics at the fiber scale. A deterministic upscaling technique is used, namely the homogenization method for periodic discrete structures. This micro-macro approach is used to carry out a quantitative study of concentrated fiber suspensions with planar fiber orientation, performing “numerical rheometry experiments” on a set of representative elementary volumes of fiber suspensions. The simulations underline the significant influence of the fiber volume fraction and orientation, as well as of the non-Newtonian properties of the suspending fluid on the resulting macroscopic rheological behavior. The predictions of the model are compared with experimental results obtained on an industrial thermoset short fiber-bundle polymer composite (SMC). a)
Electronic address:
Steven.Le-Corre@ec-nantes.fr A simple constitutive model for a polymer flow near a polymer-grafted wallR. Stepanyan a), J. J. M. Slot a,b,e), J. Molenaar c,d), and M. Tchesnokov d) a) Faculty of Science and Technology,
University of Twente, b) Material Science Centre, DSM Research, c) Faculty of Mathematics and Computer Science, d) Faculty of Electrical Engineering,
Mathematics, and Computer Science, AbstractA simple constitutive model is proposed to describe a polymer flow near a polymer-grafted wall. The model is based on a generalization of the Rolie-Poly equation [A. E. Likhtman and R. S. Graham, J. Non-Newton. Fluid Mech. 114 (2003) 1-12] to a “bulk+wall” system combined with a microscopic picture of the relaxation of the tethered chains. Different grafting regimes are considered, varying from non-overlapping to strongly interacting tethered chains. Despite its simplicity, the model allows one to reproduce all the generic features of the flow. Different scaling regimes are predicted, in accord with earlier studies, and the transition between them is quantified. Special attention is paid to a careful comparison to available experimental data: a reasonable agreement is demonstrated and possible shortcomings of the model are discussed. e) Author to whom correspondence should be addressed; e-mail: j.j.m.slot@utwente.nl An invariant based fitted closure of the sixth-order orientation tensor for modeling short-fiber suspensionsD. A. Jack and D. E. Smith a) Mechanical and Aerospace Engineering, University of
Missouri - Columbia AbstractOrientation tensors are commonly used in short-fiber reinforced injection molding simulations of industrial polymer composite products. The evolution equation for each even-order orientation tensor is written in terms of the next higher even-order orientation tensor necessitating the use of a closure. It has been shown that current fourth-order closures approach the fourth-order truncation limit when representing the fiber orientation distribution function so that an increase in accuracy necessitates the development of a robust sixth-order closure. This paper presents a new fitted sixth-order closure formed from a general expression for a fully symmetric sixth-order tensor written as a function of a fourth-order orientation tensor. The components of this sixth-order closure are fit to a linear polynomial of the fourth-order orientation tensor invariants whose coefficients are computed by fitting the sixth-order components obtained from the closure to those computed from distribution function simulations for a variety of flow fields and interaction coefficients. The fitted sixth-order closure is shown to more accurately predict the second-order orientation tensor than simulations that employ existing fourth-order and sixth-order closures. Additionally, it is shown that the sixth-order closure more accurately represents the distribution function of fibers than current closure methods. a) Author to who correspondence should be addressed; e-mail: smithdoug@missouri.edu Rheological behavior of blends from a linear and a long-chain branched polypropyleneJens Stange, Claudia Uhl, and Helmut Münstedt University Erlangen-Nürnberg, Institute of Polymer
Materials AbstractThis paper investigates how the rheological behavior of a linear polypropylene is changed by blending with different amounts of a long-chain branched polypropylene. The zero shear-rate viscosities of the blends followed the logarithmic mixing rule between the two blend partners up to 50wt.% of the long-chain branched polypropylene. For the blend with 75wt.% LCB-PP a deviation from the logarithmic mixing rule was found, which can be referred to a disentanglement of the long-chain branched fraction of molecules during the blend extrusion process similar to the findings for the extruded long-chain branched polypropylene. It is concluded that the linear polypropylene in the blends reduces the extrusion effect on the long-chain branched species in a way that for the blends with 50wt.% of the linear PP and more no influence of the blend preparation process on the rheological behavior occurred. As the branching structure within the blends remains unchanged it could be shown that the dependence of the zero shear-rate viscosity on the mass average molar mass can be used to characterize the branching architecture of blend components. In uniaxial elongation a pronounced strain hardening was already found for blends with less than 10wt.% long-chain branched polypropylene. The dependency of the strain hardening on the strain rate changes with the amount of branched polypropylene. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 15 August 2005 |