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Jul 2004

Volume 48, Issue 4, pp. 711-936


Broad frequency range characterization of molten polymers

Chunxia He, Paula Wood-Adams, and John M. Dealy

J. Rheol. 48, 711 (2004); http://dx.doi.org/10.1122/1.1763943 (14 pages) | Cited 2 times

Online Publication Date: 24 Jun 04

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We report a technique for obtaining the continuous retardation spectrum or relaxation spectrum over a very broad range of relaxation times. The major challenge is to obtain reliable data at the long-time end of the spectrum. It is often not practical to use low-frequency oscillatory shear to obtain the necessary data because of the very long time required for the measurements. Polyolefins pose special problems in long-time characterization, because time-temperature superposition is not very useful. Information about the long-time behavior can be obtained by means of creep experiments, but now another problem arises. If we use a stress sufficiently large to yield precise data, the strain may go beyond the limit of linear viscoelastic behavior before steady state is achieved. This problem can be addressed by eliminating the stress well before nonlinearity becomes a problem and tracking the resulting recovery. Using a method proposed by Meissner, the combined creep and recovery data can be used to construct the entire creep curve. The final challenge is to combine the data from the oscillatory shear and creep experiments to obtain a composite linear spectrum. We propose a new method for accomplishing this. Retardation spectra are inferred from both sets of data and compared to reveal the range of times over which both techniques provide reliable data and the range in which each technique is uniquely reliable. The two spectra can then be combined to form a composite spectrum, which can be used to calculate any linear material function. This procedure is demonstrated for two branched polypropylenes whose terminal zones could not be accessed by means of oscillatory shear. For each of these materials, we found that the spectra obtained by the two experimental techniques superposed perfectly within the region of overlapping experimental windows, making it possible to construct a reliable composite spectrum valid over a wide range of times. The composite continuous spectrum is more directly related to molecular structure than rheological properties, such as the complex modulus, which involve integrals of the spectrum. © 2004 The Society of Rheology.
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83.80.Sg Polymer melts
83.85.St Stress relaxation
83.60.Bc Linear viscoelasticity
83.85.Tz Creep and/or creep recoil

Steady-shear rheological properties of model compatibilized blends

S. Velankar, P. Van Puyvelde, J. Mewis, and P. Moldenaers

J. Rheol. 48, 725 (2004); http://dx.doi.org/10.1122/1.1765662 (20 pages) | Cited 9 times

Online Publication Date: 24 Jun 04

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Block copolymers may be added as surface-active compatibilizers in order to control the morphology of blends of immiscible polymers. The effects of such added compatibilizers on the rheological properties of droplet–matrix blends are investigated experimentally. Model blends composed of polyisobutylene (PIB) droplets in a polydimethylsiloxane (PDMS) matrix, compatibilized with a diblock copolymer of PIB and PDMS, are studied here. The viscosity ratio of the blends, i.e., the ratio of the viscosity of the droplets to that of the matrix, is varied from 0.1 to 2.7. The viscosity and the first normal stress difference under steady shear conditions, and complex moduli after cessation of shear are measured. It is found that addition of the compatibilizer slightly raises the magnitude of the terminal complex viscosity of blends at all ratios of viscosity. Furthermore, with addition of the compatibilizer, the terminal relaxation time is found to increase sharply at high viscosity ratios, whereas the steady shear N1 is found to increase at low viscosity ratios. These experimental observations are consistent with Marangoni stress caused by flow-induced gradients in the compatibilizer concentration on the surface of compatibilized drops. It is shown that, qualitatively, the effects of the Marangoni stress are somewhat analogous to an increase in drop viscosity. © 2004 The Society of Rheology.
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83.80.Tc Polymer blends
83.85.Jn Viscosity measurements
83.50.Ax Steady shear flows, viscometric flow

Visualization of individual DNA molecules in a small-scale coating flow

Rajat Duggal and Matteo Pasquali

J. Rheol. 48, 745 (2004); http://dx.doi.org/10.1122/1.1764825 (20 pages) | Cited 2 times

Online Publication Date: 24 Jun 04

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Individual DNA molecules in an ultradilute solution were observed with a fluorescence microscope as they flow between a scaled-down rotating roll and a stationary glass knife. The roll picks up a thin layer of liquid from a pool and drags it to the knife, establishing a bead delineated by two menisci. At low roll speed the flow is premetered and there is a large recirculation. The DNA experiences nearly rectilinear shear flow at the minimum gap position where there is a zero velocity surface. We report the mean and the distribution of fractional extension of DNA molecules and show that the mean fractional extension asymptotes to 0.5, in agreement with the results of Smith et al. [D. E. Smith et al., Science 283, 1724 (1999)]. Interestingly, no polymer distortion is observed at the two menisci. At high roll speed, capillarity is not strong enough to drive backflow; the big recirculation under the coverslip breaks into two smaller recirculations and two separation surfaces arise upstream and downstream of the location of the minimum gap. At the upstream separation surface, most DNA molecules are extended parallel to the knife as they traverse the field of view. We report the distribution of DNA extension and shape in this flow region. Slow, nodular recirculations are present under the upstream and downstream free surfaces. Notably, most DNA molecules stretch axially as they move in these slow recirculating regions. © 2004 The Society of Rheology.
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87.14.G- Nucleic acids
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
83.50.Jf Extensional flow and combined shear and extension
47.80.-v Instrumentation and measurement methods in fluid dynamics

Stability analysis of injection molding flows

Arjen C. B. Bogaerds, Martien A. Hulsen, Gerrit W. M. Peters, and Frank P. T. Baaijens

J. Rheol. 48, 765 (2004); http://dx.doi.org/10.1122/1.1753276 (21 pages) | Cited 1 time

Online Publication Date: 24 Jun 04

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We numerically investigate the stability problem of the injection molding process. It was indicated by Bulters and Schepens [Bulters and Schepens (2000)] that surface defects of injection molded products may be attributed to a flow instability near the free surface during the filling stage of the mold. We examine the stability of this flow using the extended Pom–Pom constitutive equations. The model allows for controlling the degree of strain hardening of the fluids without affecting the shear behavior considerably. To study the linear stability characteristics of the injection molding process we use a transient finite element algorithm that is able to efficiently handle time dependent viscoelastic flow problems and includes a free surface description to take perturbations of the computational domain into account. It is shown that the fountain flow, which is a model flow for the injection molding process, is subject to a viscoelastic instability. If the various rheologies are compared, we observe that the onset of unstable flow can be delayed by increasing the degree of strain hardening of the fluid (by increasing the number of arms in the Pom–Pom model). The most unstable disturbance which is obtained after exponential growth is a swirling flow near the fountain flow surface which is consistent with the experimental findings. © 2004 The Society of Rheology.
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83.60.Wc Flow instabilities
47.11.-j Computational methods in fluid dynamics
83.50.Uv Material processing (extension, molding, etc.)
83.50.Ax Steady shear flows, viscometric flow

Rheo-nuclear magnetic resonance of emulsion systems

K. G. Hollingsworth and M. L. Johns

J. Rheol. 48, 787 (2004); http://dx.doi.org/10.1122/1.1753277 (17 pages) | Cited 1 time

Online Publication Date: 24 Jun 04

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This paper uses the technique of rheo-nuclear magnetic resonance (rheo-NMR) [reviewed by P. T. Callaghan, Rep. Prog. Phys. 62, 599–670 (1999)] to perform a systematic study of emulsion rheology. Rheo-NMR uses NMR velocimetry to produce velocity maps, from which it is possible to quantify rheological parameters, with apparent wall slip being measured directly. The study is initially conducted on silicone oil-in-water emulsions. Xanthan gum, an important emulsion thickener and stabilizer in the food industry, is then investigated. Finally, the technique is applied to a commercial mayonnaise, which is a complex product comprising a concentrated oil in water emulsion with various thickeners and stabilizers in the continuous phase. Rheological parameters (based on either a power-law fluid or a Hershel–Bulkley analysis) and apparent slip characteristics are extracted from the velocity maps for these materials, across a wide range of shear rates. Comparison with conventional rheological measurement and analysis is presented; reasonably good agreement is produced between the two methods. © 2004 The Society of Rheology.
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83.80.Iz Emulsions and foams
83.50.Rp Wall slip and apparent slip
83.85.Fg NMR/magnetic resonance imaging

Monte Carlo simulation of steady extensional flows

Xianfeng Li and Morton M. Denn

J. Rheol. 48, 805 (2004); http://dx.doi.org/10.1122/1.1763945 (17 pages) | Cited 3 times

Online Publication Date: 24 Jun 04

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An efficient nonequilibrium Monte Carlo method using the Bond fluctuation model is used to simulate uniaxial and planar extension of dilute polymer solutions. The time scale is obtained from the stress relaxation of a fully stretched chain and can be related to the longest relaxation time of a real molecule, while the length scale is taken to be the statistical Kuhn segment length. The method leads to τ1∼N2.16 and D∼N−1.02 for a freely draining chain with an excluded volume constraint, where τ1, N, and D are the longest relaxation time, chain length, and diffusion coefficient, respectively. The finite extensibility of the bond causes extension thinning following the coil-stretch transition. The Monte Carlo predictions for the transient extension of isolated DNA molecules in a planar extensional flow agree reasonably well with published experimental measurements and Brownian dynamics simulations. “Molecular individualism” is observed in the unraveling of the polymer chain. © 2004 The Society of Rheology.
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47.11.-j Computational methods in fluid dynamics
83.50.Jf Extensional flow and combined shear and extension
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)

A model for post-flow induced crystallization: General equations and predictions

R. Zheng and P. K. Kennedy

J. Rheol. 48, 823 (2004); http://dx.doi.org/10.1122/1.1763944 (20 pages) | Cited 1 time

Online Publication Date: 24 Jun 04

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The aim of this work is to model the flow-enhanced crystallization and the flow-induced morphological changes of semi-crystalline materials during and after shearing flow. A FENE-P dumbbell model and a rigid dumbbell model are used to describe the molecular chain conformation and the orientation evolution for the amorphous phase and the semi-crystalline phase, respectively. The effect of flow on crystallization is considered by relating excess free energy and flow-induced orientation to crystallization kinetics. The crystallization of the material couples back to influence the solidification rheology of the crystallizing system. An isotactic polypropylene is used as an example to illustrate model predictions. We predict a pronounced effect of short-term shear treatments in accelerating nucleation and changing rheological behavior. Results are compared with available experimental data. © 2004 The Society of Rheology.
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83.10.Tv Structural and phase changes
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
47.11.-j Computational methods in fluid dynamics

Influence of dispersed-phase elasticity on steady-state deformation and breakup of droplets in simple shearing flow of immiscible polymer blends

Wanchai Lerdwijitjarud, Anuvat Sirivat, and Ronald G. Larson

J. Rheol. 48, 843 (2004); http://dx.doi.org/10.1122/1.1753275 (20 pages) | Cited 5 times

Online Publication Date: 24 Jun 04

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The effect of dispersed-phase elasticity on steady-state deformation and breakup of isolated droplets for polybutadiene/poly(dimethyl siloxane) blends in simple shearing flow is investigated systematically for values of the dispersed-phase Weissenberg number (Wid) ranging up to around 3, where the Weissenberg number is defined as the ratio of the first normal stress difference to twice the shear stress at the imposed shear rate. The dependence on droplet elasticity of steady-state morphology for 10%-dispersed phase blends is also studied. The polybutadiene droplet phase is an elastic “Boger” fluid prepared by dissolving a high-molecular-weight polybutadiene into a low-molecular-weight Newtonian polybutadiene melt. To isolate the contribution of droplet elasticity, all experiments were done at a fixed viscosity ratio of around unity, achieved by adjusting the temperature appropriately for each blend. When the droplet elasticity increases, the steady-state deformation of isolated droplets decreases for fixed capillary number. The critical capillary number for breakup (Cacrit) increases linearly with the Weissenberg number of the droplet phase (Wid) up to a value of Wid of around unity. When Wid is greater than unity, Cacrit seems to approach an asymptotic value of 0.95 for high values of Wid. For 10%-dispersed phase blends, the steady-state capillary number (Cass) calculated from a volume-averaged droplet diameter is less than the Cacrit for isolated droplets for the same blend. Cass increases monotonically with the first normal stress difference of the droplet phase. Droplet widening in the vorticity direction is not observed even at droplet Weissenberg numbers much in excess of those for which widening is observed in blends of melts, suggesting that widening is strongly influenced by factors other than the first normal stress difference, such as shear thinning or second normal stress differences. © 2004 The Society of Rheology.
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83.80.Tc Polymer blends
83.80.Sg Polymer melts
83.50.Ax Steady shear flows, viscometric flow
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids

Large shear deformation of particle gels studied by Brownian dynamics simulations

A. A. Rzepiela, J. H. J. van Opheusden, and T. van Vliet

J. Rheol. 48, 863 (2004); http://dx.doi.org/10.1122/1.1764824 (18 pages) | Cited 1 time

Online Publication Date: 24 Jun 04

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Brownian dynamics (BD) simulations have been performed to study structure and rheology of particle gels under large shear deformation. The model incorporates soft spherical particles, and reversible flexible bond formation. Two different methods of shear deformation are discussed, namely affine and nonaffine deformation, the second being novel in simulation studies of gels. Also two dynamic descriptions of the model are presented, with and without inertia effects. Nonaffine deformation resulted in a slower increase of the stress at small deformation than affine deformation. At large deformation both models gave similar stress responses, although the inertia model resulted in lower stresses. The particle gels, regardless of the model used, were observed to fracture into lumps that compactified due to local reorganization. A reversible yielding transition, as observed in polymer gels, was not found. Fractal properties of the gels were irreversibly lost at large deformation. © 2004 The Society of Rheology.
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83.80.Kn Physical gels and microgels
83.50.Ax Steady shear flows, viscometric flow
05.40.Jc Brownian motion

Director reorientation of a side-chain liquid crystalline polymer under extensional flow

Ryan J. Cormier, Claudia Schmidt, and Paul T. Callaghan

J. Rheol. 48, 881 (2004); http://dx.doi.org/10.1122/1.1753278 (14 pages)

Online Publication Date: 24 Jun 04

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When a nematic liquid crystal is subject to deformational flow, rotational torques arising from the Leslie viscosities lead to director realignment. In the case when a magnetic field is present these torques compete with the alignment torque associated with magnetic anisotropy. Under purely extensional flow, this competition results in a sudden director flip at a critical rate of strain given by mathc=χaB02/(μ0∣α3+α2∣), where χa is the anisotropy of the magnetic susceptibility per unit volume of the liquid crystalline polymer, and α2 and α3 are viscosity coefficients arising from the anisotropic (or viscous) part of the stress tensor in the Leslie–Ericksen velocity equation. Using a four-roll mill placed in the 7 T magnet of a nuclear magnetic resonance (NMR) spectrometer, we have observed the orientation of the director, as a function of strain rate, for a flow aligning liquid crystalline polymer consisting of a polysiloxane backbone and mesogenic 4-methoxyphenyl-4′-butenyloxybenzoate side chains, the temperature being 348 K, just a few degrees below the nematic to isotropic transition. Director orientations were obtained using 2H NMR spectral splittings from a probe molecule species comprising <10% methyl-(sulfoxide)-d6. A distinct director flip is observed at a value of strain rate measured by NMR velocimetry to be 0.037 s−1. From this value we determine ∣α2+α3∣/χa∼107×107 Pa s. © 2004 The Society of Rheology.
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83.85.Rx Extensional flow measurement
83.85.Fg NMR/magnetic resonance imaging
83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.

Effect of long branches on the rheology of polypropylene

A. D. Gotsis, B. L. F. Zeevenhoven, and C. Tsenoglou

J. Rheol. 48, 895 (2004); http://dx.doi.org/10.1122/1.1764823 (20 pages) | Cited 3 times

Online Publication Date: 24 Jun 04

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In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching. © 2004 The Society of Rheology.
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83.80.Sg Polymer melts
83.50.Jf Extensional flow and combined shear and extension
83.85.Rx Extensional flow measurement
82.35.Lr Physical properties of polymers

A semi-empirical approach for modeling charged soft microgel particles

B. H. Tan, K. C. Tam, Y. C. Lam, and C. B. Tan

J. Rheol. 48, 915 (2004); http://dx.doi.org/10.1122/1.1763942 (12 pages) | Cited 3 times

Online Publication Date: 24 Jun 04

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We describe a unified semi-empirical approach for predicting the viscosity of dilute and concentrated hard and soft sphere systems. A variable specific volume, k was introduced to convert the mass concentration to effective volume fraction. With increasing particle concentration, the concentration of free counter-ions in the solution can be large enough to induce an osmotic de-swelling of soft particles, resulting in the particle shrinkage. The viscosity data for four different microgel systems at different neutralization degree showed excellent agreement with the modified Krieger–Dougherty model. © 2004 The Society of Rheology.
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47.11.-j Computational methods in fluid dynamics
83.80.Kn Physical gels and microgels
66.20.-d Viscosity of liquids; diffusive momentum transport

Thickening effect in soluble hydrogen-bonding interpolymer complexes. Influence of pH and molecular parameters

F. Bossard, M. Sotiropoulou, and G. Staikos

J. Rheol. 48, 927 (2004); http://dx.doi.org/10.1122/1.1763941 (10 pages)

Online Publication Date: 24 Jun 04

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Linear and nonlinear viscoelastic properties of poly(acrylic acid) (PAA) and poly(acrylic acid-co-2-acrylamido-2-methylpropane sulfonic acid)-graft-poly(N,N-dimethylacrylamide) (P(AA-co-AMPSA)-g-PDMAM) mixtures have been investigated as a function of pH, the PDMAM content of the graft copolymer and the molecular weight of PAA. At pH < 3.75, strong hydrogen-bonding interpolymer complexation between PAA and PDMAM side chains in semidilute solution leads to the formation of a transient network, as the considerable increase in viscosity indicates. The sol/gel transition observed at pH=2.0 by increasing the graft copolymer composition in PDMAM is explained by a substantial increase in the number of the junctions (stickers) resulting from the PDMAAM/PAA hydrogen bonding complexation. Moreover, the thickening effect observed is further strengthened by increasing the molecular weight of PAA, due to the interconnection of more copolymer chains. © 2004 The Society of Rheology.
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83.60.Df Nonlinear viscoelasticity
83.80.Rs Polymer solutions
83.60.Rs Shear rate-dependent structure (shear thinning and shear thickening)
83.60.Bc Linear viscoelasticity
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