Volume 51, Issue 6, November 2007
Index of content:
Comprehensive comparisons with nonlinear flow data of a consistently unconstrained Brownian slip-link model51(2007); http://dx.doi.org/10.1122/1.2790460View Description Hide Description
A consistently unconstrained Brownian slip-link model (CUBS) with constant chain friction is used to predict the nonlinear rheological behavior of linear, entangled, polymeric liquids. The model naturally incorporates primitive-path-length fluctuations, segment connectivity, monomer density fluctuations, entanglement fluctuations, and constraint release without making any closure approximations. Constraint release is imposed on the level of the dynamics of the chain, and the relaxation modulus follows from these rigorously. The model is a mean-field, single-chain slip-link model, or temporary network model, with a single phenomenological time constant, , fit by linear viscoelasticity. The nonlinear flow predictions are made without adjusting any additional parameters. We find that the addition of constant chain friction noticeably improves the model predictions in all the flows considered. In contradiction with tube models, the results suggest that the additional physics of constraint release and convective constraint release are not very important in predicting the nonlinear shear properties, except at low shear rates (close to the LVE regime).
Nonlinear viscoelastic response of dendritic (arborescent) polyisobutylenes in single- and reversing double-step shearing flows51(2007); http://dx.doi.org/10.1122/1.2790073View Description Hide Description
Single-step and three types of reversing double-step experiments were conducted on concentrated solutions of a linear and two dendritic (hyperbranched or arborescent) polyisobutylenes (PIBs). The results in reversing double-step experiments further confirm our previous findings on polyethylene melts that the K-BKZ theory provides better predictions for long chain branched polymers than linear ones. The short chain branched material looks more like the linear material in the present experiments. Isochronal derivatives of the strain potential function ( and ) were calculated from torque and normal force responses in single-step parallel plate experiments. The damping function was extracted from and for both linear and branched PIBs. The damping function of the linear PIB falls between two versions of the Doi–Edwards model. The arborescent PIB with longer branches and lower branching frequency shows weak damping behavior, which is a specific behavior for long chain branched polymers. The arborescent PIB with shorter branches, higher branching frequency and low entanglement density, on the other hand, exhibits the same damping behavior as that of the linear PIB, which is consistent with the findings in the reversing double-step experiments in which it behaves more like a linear polymer.
51(2007); http://dx.doi.org/10.1122/1.2789954View Description Hide Description
Phosphate glass (Pglass)/polymer hybrids are a unique material class that promises to help fulfill the growing need for new advanced materials. Rheological investigations into Pglass/polyamide 12 hybrids have shown a strong dependence on temperature and composition. Strong negative deviations from the log-additivity rule are also observed for these materials as well as a reduction in the activation energy for viscous flow. Hybrids containing Pglass are rheologically simple fluids that display temperature independence in plots of storage modulus versus loss modulus. Hybrids containing Pglass are rheologically complex and do not obey the time-temperature superposition principle. Through application of Han plots, we identified a structural change that occurs in hybrids containing Pglass at temperatures in excess of . This microstructural change induces an apparent yield stress in the material at these elevated temperatures. It is believed that the microstructural change is due to enhanced interactions that occur at elevated temperatures between the compatible pure components of the hybrids.
51(2007); http://dx.doi.org/10.1122/1.2790461View Description Hide Description
A mesoscopic rheological model is proposed for polymer/layered silicate nanocomposites. The conformation tensors and are chosen to characterize states of macromolecules and silicate layers (plates), respectively. In the absence of the plates, the model reduces to the well known FENE-P model. The predictions of the model are shown to agree with thermodynamics. Other predictions of the model, obtained by solving numerically its governing equations, are responses of the suspension to transient (start-up and relaxation) and steady shear flows. The results show that the model predictions cover a wide range of the rheological behavior generally observed for polymer/layered silicate nanocomposites.
Flow–induced chain scission in dilute polymer solutions: Algorithm development and results for scission dynamics in elongational flow51(2007); http://dx.doi.org/10.1122/1.2789945View Description Hide Description
Based on covalent bond scission force estimates from single molecule experiments and a statistical analysis of the instantaneous segmental tension (ST) distribution in bead-rod chains, a new algorithm has been developed for the simulation of flow-induced polymer chain scission. This algorithm overcomes the nonphysical time-step dependence inherent in stochastic chain scission simulations that employ instantaneous ST-based criteria to identify scission events. This is accomplished by the use of a normalized ST profile that is independent of the elongation rate for asymptotically large values of the Weissenberg number, defined as the ratio of the longest relaxation time of the chain to . The algorithm is employed to study chain scission in steady and transient elongational flows as well as the effect of hydrodynamic interactions on chain scission in steady elongational flow. Simulation results for steady elongational flow reproduce the experimentally observed scaling law for the critical elongation rate where denotes the molecular weight. Moreover, for , the chains unravel via a coil-to-stretch configurational transition. Since ST attains its maximum at the midpoint of the chain, the midpoint scission hypothesis (MSH) is valid. This leads to a relatively narrow distribution of daughter chains. However, for , sufficiently large ST could develop in the elongated portions of partially coiled chains. Consequently, chain scission could occur farther from the midpoint. MSH is not valid under such conditions, and the resulting distribution of daughter chains is relatively broad. Hydrodynamic interactions are shown to slow down chain unraveling leading to an increase in with the scaling . The effect of polymer residence time on is examined by investigating scission of polymer chains that traverse the centerline of a regularized contraction flow. It is found that the scaling relationship between and remains the same as that for steady elongational flow given that the residence time exceeds 5% of the longest relaxation time of the chain. This result suggests that the inverse proportionality of to observed experimentally in contraction flow might be due to preshearing effects. Finally, the effect of loading rate onscission probability is discussed in the context of an extended thermally activated barrier to scission model.
51(2007); http://dx.doi.org/10.1122/1.2790023View Description Hide Description
The viscoelastic behavior of very concentrated and electrostatically stabilized suspensions of kaolinite particles has been investigated in the linear and nonlinear regime as a function of volume fraction, ionic strength and in the presence of polymer at various concentrations. Material properties such as linear viscoelasticmoduli and cohesive energy density are extensively enhanced by either increasing volume fraction or decreasing ionic strength. Attention has been paid to the large amplitude oscillatory shear behavior of concentrated suspensions of plate-like particles, characterized by a hump in curves. Rheological investigation shows the extreme sensitivity of the intensity of the strain hardening in to excluded volume, electrostatic and steric interactions. A physical interpretation of this nonlinear behavior has been proposed.
51(2007); http://dx.doi.org/10.1122/1.2790462View Description Hide Description
Recently we proposed a constitutive model for structure and total stress in particulate suspensions, in which structural information is represented by a structuretensor that is determined from evolution equations derived from principles of continuum mechanics [Stickel et al., J. Rheol.50, 379–413 (2006)]. The model was tested by comparing its predictions for structure and stress with results obtained from Stokesian dynamics simulations of hard-sphere suspensions in steady shear flow. Here we apply the same model to time-dependent shear flows. We compare our results with Stokesian dynamics simulations for flows with step discontinuities in the shear rate, including startup, step increases and decreases in shear rate, and flow reversal. In addition, comparisons are made with experimental results from the literature, both for shear flows with step discontinuities and sinusoidally varying shear rates. It is shown that the model predictions are in good quantitative agreement with the simulation results. The predictions also show good qualitative agreement with the experimental data. Some experimental observations, such as the plateau in the dynamic viscosity in the limit of low and high strain amplitudes, are reproduced well. In that case, the model also provides structural information that elucidates the underlying cause for the experimental observations. However, immediately after a flow reversal, the model does not capture the incomplete stress recovery, or irreversibility, that is observed experimentally.
51(2007); http://dx.doi.org/10.1122/1.2794759View Description Hide Description
The examination of capillary flow of polymers has resulted in reports of two distinct flow regimes at stresses well below that required for gross melt fracture. The break (kink) between the two regimes has been associated with the onset of sharkskin melt fracture (SSMF), which does not appear to be consistent with the popular hypothesis that SSMF is purely an exit phenomenon. We scrutinized 37 sets of data from 15 laboratories to detect the reported regimes in a systematic and objective fashion using several statistical tests including the Akaike information content method of model discrimination. Many data sets failed to pass one or more of the tests, and several failed all the tests, suggesting the absence of two distinct regimes as opposed to the expected increase in shear-thinning behavior with increasing stress. On the other hand, four out of the 37 sets passed all the tests and 11 out of 37 passed at least 3 of the 4 tests, leaving open the hypothesis of an abrupt change in flow behavior in the capillary itself or in the entrance region. No global correlation of the results with polymer type, capillary geometry, or temperature was found, although with certain resins the abrupt change appeared most prominently with low-aspect-ratio capillaries, suggesting an entrance phenomenon. A method of quantitatively judging the sharpness of the transition from one regime to another was developed. This method, comprising a single nonlinear but explicit generalized Newtonian fluid function with a sharpness parameter, can be easily applied to any data set and is recommended as a method of checking for the presence of a kink.
Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts51(2007); http://dx.doi.org/10.1122/1.2790072View Description Hide Description
Nonlinear response of linear and branched polymers has been investigated under medium strain amplitude oscillatory shear (strain amplitude range from 10% to 100%) with Fourier-transform rheology. A power law relationship was found between the relative third intensity , which is an indicator of nonlinearity, and the strain amplitude at low and medium strain amplitudes. On a log-log plot, the intercept and slope of were investigated at different excitation frequencies and temperatures. Simulation results with three different constitutive equations [Giesekus, exponential Phan-Thien Tanner (E-PTT), pom-pom model] were also compared. Experimental results show that the intercept was affected by the excitation frequency and temperature, and the slope of for linear polymer remained constant regardless of molecular weight, molecular weight distribution, and excitation frequency in accordance with the predictions of the constitutive equations (Giesekus and E-PTT). It should be noted that the slope of for branched polymer was lower than that of linear polymer, unlike the prediction of the pom-pom model. Among the molecular architecture and processing parameters (e.g., molecular weight, molecular weight distribution, frequency, and temperature), the slope of under medium amplitude oscillatory shear was found to depend only on the long chain branching, which means that it can be used as a measure of the degree of branching. The failure of the pom-pom model in predicting the nonlinear shear behavior was also pointed out.
Axisymmetric two-sphere sedimentation in a shear thinning viscoelastic fluid: Particle interactions and induced fluid velocity fields51(2007); http://dx.doi.org/10.1122/1.2780799View Description Hide Description
We investigate the link between particle interactions and induced flow patterns around two identical spheres sedimenting along their centerline in a polymeric fluid. The fluid is strongly shear thinning and, in agreement with previous results, the spheres are observed to chain even at large initial separation distances. The wake of a single particle displays an upward motion of fluid, i.e., a “negative wake” that is commonly observed in fluids with low extensional viscosities. We show that the features of this negative wake vary only weakly with the Deborah number. In the two-sphere case, the pattern of the induced flow depends on the sphere separation distance. The change in the flow pattern does not, however, induce any significant qualitative change in the sphere interactions. Upstream of the leading sphere and downstream of the trailing one along the sedimentation axis, the variations of the fluid velocity are well described by a single master curve for different values of the sphere separation distance. The existence of such a curve indicates that non-Newtonian effects near each particle are dominated by local conditions near the sphere surfaces, and are only weakly influenced by the presence of a second sphere.