Index of content:
Volume 55, Issue 3, May 2011
Slip-link simulations of entangled polymers in planar extensional flow: Disentanglement modified extensional thinning55(2011); http://dx.doi.org/10.1122/1.3549296View Description Hide Description
In the present work, we have extended a slip-link based model, originally proposed by Masubuchi et al. [J. Chem. Phys.115, 4387 (2001)], to simulate planar extensional flow. The salient features of the extended model are (i) an unrestricted simulation time for planar extensional flow using Kraynik–Reinelt periodic boundary conditions, (ii) an implicit time stepping scheme to enhance numerical stability, and (iii) a mesh-free Lagrangian method for the evaluation of the osmotic force. With the new code, we have simulated both the static and dynamic responses of monodisperse linear worm-like and inverse Langevin chains and compared the simulations results with the experimental data reported by Bach et al. [J. Rheol.47, 429 (2003)]. The simulations were run for monodisperse linear chains including up to 50 entanglements. The model is able to reasonably capture the rheological behavior of entangled systems in the nonlinear range. Based on our simulations, we also present an alternative explanation for the dynamics behind extensional thinning based on disentanglement and a physical explanation for the failure of standard models, i.e., Doi-Edwards (DE)/Doi-Edwards-Marrucci-Grizzuti (DEMG) (which predict a thinning exponent of −1) in predicting the extensional thinning exponent of near −0.5 (as seen in various experiments [Bach et al., J. Rheol.47, 429 (2003); Luap et al., Rheol. Acta45, 83 (2005)]).
55(2011); http://dx.doi.org/10.1122/1.3553032View Description Hide Description
Solution rheology of cellulose in 1-butyl-3-methyl imidazolium chloride ([BMIm]Cl) is reported using oscillatory and steady shear for cellulose concentrations from 0.1 to 10 wt %, spanning the dilute, semidilute unentangled, and entangled regimes. Although pure [BMIm]Cl is a crystalline solid at room temperature with a melting temperature of , all solutions prepared at are transparent and visually homogenous at , and these supercooled solutions, with of order 0.1 wt % water, show no sign of crystallizing for months in either calorimetry or rheology measurements, allowing the potential for room temperature solution processing of native cellulose, such as fiber spinning. The overlap concentration of our cellulose in [BMIm]Cl is 0.5 wt % and the entanglement concentration is a factor of 4 larger (2 wt %). For semidilute unentangled solutions (between 0.5 and 2 wt %), the specific viscosity,relaxation time, and terminal modulus exhibit concentration dependences , , and , respectively, while for entangled solutions (between 2 and 10 wt %) we find , , and , consistent with scaling predictions for neutral polymers in a solvent. However, failure of the Cox–Merz rule with steady shear viscositylarger than complex viscosity and the observed internal mode structure of dilute and semidilute unentangled solutions suggest that cellulose in [BMIm]Cl is not simply a flexible polymer in a solvent.
55(2011); http://dx.doi.org/10.1122/1.3553031View Description Hide Description
Studying the mechanical response of nearly monodisperse linear and comb polystyrene (PS) melts to medium amplitude oscillatory shear (MAOS), Hyun and Wilhelm [Macromolecules42, 411 (2009)] identified two important scaling relations: (1) The relative intensity of the third harmonic compared to the first harmonic scales with the strain amplitude according to . Consequently, a new nonlinear coefficient as well as the so-called intrinsic nonlinearity was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity scales with and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi–Edwards model without (DE) and with (DE IA) independent alignment assumption as well as the molecular stress function (MSF) model, confirms both scaling relations. We show that the nonlinear viscoelastic moduli can be expressed as sums of their linear-viscolelastic counterparts at frequencies of , , and . The absolute value of depends on the difference between the third order orientational effect (parameter ) according to the DE or DE IA model and the second order isotropic stretching effect (parameter ) according to the MSF model. When comparing MAOS data to constitutive models, the apparent values of measured in parallel-plate geometry have to be rescaled in order to take the non-uniform shear deformation into account. Both the DE and DE IA models fail to describe the experimental data. The data of four linear PS melts are quantitatively described by the MSF model with nonlinear parameters (corresponding to the DE IA model) and in the terminal relaxation regime. For the comb polymers, with the same orientational parameter of , stretch parameters of for a polymer with unentangled branches and of for two polymers with entangled branches are found. However, the model predicts a plateau at the level of the maximum of the experimental data, while the experimental values of decrease with increasing frequency. For the comb polymers with entangled branches, a minimum in is observed, and a second increase of at higher frequencies, which correspond to the terminal relaxation times of the branches. Surprisingly, these features can be modeled quantitatively if only the terminal relaxation modes of the backbone and, if present, the branches are assumed to deforming non-affinely and responding to the nonlinearity. The shorter modes seem to be deforming affinely and are excited only in the regime of finite linear viscoelasticity. We are presently not aware of any molecular mechanism that could explain this behavior.
55(2011); http://dx.doi.org/10.1122/1.3568814View Description Hide Description
A rheological model for a short fiber suspension in polymeric liquid is proposed according to irreversible thermodynamics of viscoelastic deformation of polymers with the effect of fiber orientation taken into account. In this model, the evolution of elastic deformation tensor, namely, reversible Finger strain tensor, is governed by not only the reversible Finger strain tensor but also the fiber orientation tensor in a manner of a positive entropy production. The final form of stress tensor combines the viscoelasticity of polymeric matrix of the Leonov model and the fiber contribution of the Dinh–Armstrong model. The Folgar–Tucker model is employed for fiber orientation kinematics along with an invariant-based optimal fitting closure approximation. The rheological behavior of the model is comprehensively studied using steady and transient shear flows.
55(2011); http://dx.doi.org/10.1122/1.3569136View Description Hide Description
The characteristics of van Gurp–Palmen (vGP) plot for long-chain branching polymer with well-defined topological structures, including symmetric star, asymmetric star, H-shaped, and comb polymers, have been calculated by “branch-on-branch” constitutive model. It is indicated that there is only one characteristic transition in the vGP plot for nearly symmetric star polymers, but more for other chain topologies, which were deeply dependent on the topology and the molecular parameters such as side-arm length, backbone length, and number of side arms. The theoretically calculated characteristic transition points were used to construct a topology map. A feasible protocol to distinguish the topological structures of branched polymer was put forward to quantify the chain structure qualitatively and quantitatively. Such a method has been successfully proved by its application on the available data in the literature.
55(2011); http://dx.doi.org/10.1122/1.3568816View Description Hide Description
Numerical computations of the extension of circular cylindrical shaped samples in a dual wind-up drum rheometer of Sentmanat extensional rheometer type [M. L. Sentmanat, Rheol. Acta43, 657 (2004); R. Garritano and H. Berting, US Patent No. 7,096,728 (08/29/2006)] are presented. These time-dependent computations are fully three dimensional and based on theoretically ideal configurations. If necking or sample rupture does not occur, the elongation will resemble as ideal uni-axial if the initial sample diameter is decreased sufficiently. An initial diameter larger than 0.5 mm may result in large deviations from ideal uni-axial deformation.
Dynamics of the orientation behavior and its connection with rheology in sheared non-Brownian suspensions of anisotropic dicolloidal particles55(2011); http://dx.doi.org/10.1122/1.3569585View Description Hide Description
The orientation, microstructure, and rheology in non-Brownian shear flow were studied for suspensions of dicolloidal particles using a novel particle mesh Ewald Stokesian dynamics algorithm for anisotropic particles. Four different particle shapes were studied with dicolloids modeled as the union of two intersecting spheres. Dynamic simulations were conducted for periodic systems of 1000 particles for volume fractions . The suspension microstructure was disordered for all particle shapes at , with some systems showing ordered microstructure at . The viscosity in the disordered state was similar for all particle shapes at equal volume fraction. Negative first and second normal-stress differences were found for , but positive values were observed for certain ordered systems at . Complex orientation behavior was observed as a function of volume fraction and particle shape. All particles showed an orientation shift toward the vorticity axis for . Certain shapes showed a shift away from the vorticity axis for . The high orientation dynamics were consistent with predictions based on the mobility tensor relating the angular velocity to particle stresslet. The orientation dynamics were dominated by the second normal-stress difference. The shift away from the vorticity axis for small was induced by migration away from orientations with large orientation fluctuations.
55(2011); http://dx.doi.org/10.1122/1.3570340View Description Hide Description
In a previous paper [T. S. K. Ng and G. H. McKinley, J. Rheol.52(2), 417–449 (2008)], we demonstrated that gluten gels can best be understood as a polymericnetwork with a power-law frequency response that reflects the fractal structure of the gluten network. Large deformation tests in both transient shear and extension show that in the absence of rigid starch fillers these networks are also time-strain factorizable up to very large strain amplitudes . In the present work, we further explore the nonlinear rheological behavior of these critical gels by considering the material response obtained in large amplitude oscillatory shear over a wide range of strains and frequencies. We use a Lissajous representation to compare the measured material response with the predictions of a network theory that is consistent with the proposed molecular structure of gluten gels. In the linear viscoelastic regime, the Lissajous figures are elliptical as expected and can be quantitatively described by the same power-law relaxation parameters determined independently from earlier experiments. In the nonlinear regime, the Lissajous curves show two prominent additional features. First is a gradual softening of the network indicated by the rotation of the major axis of the stress ellipse. This feature is accounted for in the model by the inclusion of a simple nonlinear network destruction term that reflects the reduction in network connectivity as the polymer chains are increasingly stretched. Second, a distinct upturn in the viscoelastic stress is discernable at large strains. We show that this phenomenon can be modeled by considering the effects of finitely extensible segments in the elasticnetwork. We use this model to quantitatively predict the material response in other large amplitude transient flows such as the start-up of steady shear and transient uniaxial extension up until the onset of strongly nonlinear unsteady phenomena such as edge fracture in shear and sample rupture during extension.
55(2011); http://dx.doi.org/10.1122/1.3573828View Description Hide Description
An engineering model for the thixotropic rheology of alumina concentrated colloidalgels is proposed and compared to rheological experimental results. Concentrated colloidalgels used in extrusion-based solid freeform fabrication are often modeled as simple shear-thinning fluids with finite yield stress such that their rheological properties depend only on instantaneous shear rate and not on shear history. Although this is a satisfactory view for steady state flow, it lacks the detail to consider phenomena associated with transient processes such as die entry and exit in extrusion processes or the shape evolution of an extruded filament as it comes to rest in a low shear environment. The rheological model proposed here considers that both elastic and viscousproperties of an aqueous gel vary with microstructure changes of colloidal aggregates and that the aggregate structure is a function of both shear rate and time. A first-order structural kinetics assumption is used to quantify the microstructure evolution of the gel network during shear flow, where shear-induced attrition and diffusion limited aggregation are the rate limiting mechanisms. A constitutive flow equation is developed by incorporating the structural kinetics to describe unsteady shear-thinning behavior. The data collected through shear rate step-change measurements are used to determine 12 model parameters in the proposed rheological model. The model is compared and validated through hysteresis-loop experiments with satisfactory agreement. This model is quasiempirical in the sense that details of interparticle pair-potentials are not used in the formulation. Nevertheless, the model could have practical uses in simulation of the macroscopic flow behavior of colloidalgels during extrusion processes. Specifically, the model offers predictions of elastic and viscousproperty evolution of colloidalgels as a function of shear history.
55(2011); http://dx.doi.org/10.1122/1.3571554View Description Hide Description
The depletion attraction, induced upon addition of a nonadsorbing polymer to a colloidal solution, can lead to gel formation at sufficiently high polymer concentrations, which corresponds to strong attractive interactions. We have investigated the nonlinear rheological response, in particular the yielding, of colloidalgels with an intermediate volume fraction and variable interparticle attraction. Two distinct yielding processes are observed in both oscillatory experiments, namely, dynamic strain sweeps and transient experiments, here step rate, creep, and recovery tests. The first yielding process occurs at strains similar to the range of the interparticle potential and is interpreted as the breaking of bonds, which destroys the particle network and leads to individual clusters. The process of bond breaking is successfully modeled as the escape of a particle from the potential well of its nearest neighbor. The second yield point occurs at larger strains and is related to the deformation and fragmentation of clusters, consistent with the observed dependence of the yield strain on attraction. Both yield stresses exhibit a power-law dependence on attraction strength in agreement with observations of other systems and theoretical predictions. Furthermore, the observed two-step yielding reveals similarities, and also differences, to the rheology of attractive colloidalglasses.