Volume 54, Issue 2, March 2010
Index of content:
Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials54(2010); http://dx.doi.org/10.1122/1.3301247View Description Hide Description
A strain-rate frequency superposition (SRFS) technique, recently proposed to analyze the low-frequency behavior of soft materials, is evaluated. The application of SRFS to an emulsion and multiarm star polymer solution produces master curves that, while promising in appearance, do not match the anticipated linear response as they seem inconsistent with dynamic frequency sweep data and the Kramers–Kronig relation. While the raw unscaled frequency sweep data are well described using the generalized Maxwell model, strong discrepancies appear when the same procedure is applied to SRFS data. These inconsistencies appear to be generic and are observed in other materials as well. An examination of Lissajous curves obtained from large amplitude oscillatory strain shows that nonlinear contributions, such as solvent-mediated convective flow, strongly affect SRFS master curves. Based on these findings, SRFS should be approached with caution when applied to soft materials.
Rheological properties and microstructural evolution of semi-flexible fiber suspensions under shear flow54(2010); http://dx.doi.org/10.1122/1.3301245View Description Hide Description
The mechanical properties of fiber-reinforced polymers are highly dependent on fiber orientation. A key factor is fiber flexibility, which varies with the intrinsic properties of the fiber, its aspect ratio, and the force of the flow field. In this work, the rheological behavior of model suspensions consisting of a Newtonian silicone oil and fibers with different flexibilities has been studied in transient shear flow. The viscous and elastic properties of the fiber suspensions were shown to increase markedly with fiber flexibility. The suspensions exhibited a viscosity overshoot in stress growth experiments and the magnitude and width of the overshoot became larger as the fiber flexibility increased. The evolution of the suspensions microstructure has also been monitored at different shear rates. The components of the second-order orientation tensor at different times (or strain) were calculated using the images obtained from the visualization experiments. Those experiments showed that fiber orientation was dependent on shear rate and magnitude of applied strain. At low shear rates, rigid fibers oriented to a larger extent in the flow direction as compared to more flexible fibers and their orientation was also faster. Finally, a mesoscopic model in the framework of the general equation for non-equilibrium reversible-irreversible coupling (GENERIC) has been used to predict the rheological behavior of semi-flexible fiber suspensions as well as their microstructure. The model takes into account fiber-fiber interactions and also the semi-flexible nature of the fibers. The predictions of the model are in good qualitative agreement with the rheological and visualization data.
54(2010); http://dx.doi.org/10.1122/1.3301246View Description Hide Description
The hierarchical and “bob” (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent and the factor which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.
Evaluation of the inkjet fluid’s performance using the “Cambridge Trimaster” filament stretch and break-up device54(2010); http://dx.doi.org/10.1122/1.3302451View Description Hide Description
This paper describes the design and initial results from the “Cambridge Trimaster,” a recently developed high speed filament stretch and break-up device that can be used for viscoelastic fluids with shear viscosities as low as . Extensional viscosity and filament break-up behavior were studied optically using a high speed camera and extensional viscosity values determined for a series of mono-disperse polystyrene solutions up to a weight concentration of were measured as a function of the polymer loading. The transient stretching and break-up profiles recorded with the apparatus were observed and correlated with drop formation for drop-on-demand inkjet printing fluids. This allowed the filament break-up behavior to be ranked in terms of satellite drop and droplet filament behavior. Correlation with previous work on the jetting of similar low viscosityviscoelasticpolymer solutions demonstrated the ability of this apparatus to characterize inkjet fluids.
Dynamics of individual molecules of linear polyethylene liquids under shear: Atomistic simulation and comparison with a free-draining bead-rod chain54(2010); http://dx.doi.org/10.1122/1.3314298View Description Hide Description
Nonequilibrium molecular dynamics (NEMD) simulations of a dense liquid composed of linear polyethylene chains were performed to investigate the chain dynamics under shear. Brownian dynamics (BD) simulations of a freely jointed chain with equivalent contour length were also performed in the case of a dilute solution. This allowed for a close comparison of the chain dynamics of similar molecules for two very different types of liquids. Both simulations exhibited a distribution of the end-to-end vector, , with Gaussian behavior at low Weissenberg number . At high , the NEMD distribution was bimodal, with two peaks associated with rotation and stretching of the individual molecules. BD simulations of a dilute solution did not display a bimodal character; distributions of ranged from tightly coiled to fully stretched configurations. The simulations revealed a tumbling behavior of the chains and correlations between the components of exhibited characteristic frequencies of tumbling, which scaled as . Furthermore, after a critical of approximately 2, another characteristic time scale appeared which scaled as . Although the free-draining solution is very different than the dense liquid, the BD simulations revealed a similar behavior, with the characteristic time scales mentioned above scaling as and .
54(2010); http://dx.doi.org/10.1122/1.3302803View Description Hide Description
The pressure-driven flow of a suspension of spinning particles in a rectangular channel is studied using an acoustic method. The suspension is made of insulating particles [poly(methyl methacrylate)] dispersed in a slightly conducting oil and is subjected to a direct current electric field. In such a case, the particles are polarized in the direction opposite to that of the electric field and begin to rotate in order to flip their dipoles in the field direction. Such a rotation of the particles is known as Quincke rotation and is responsible for an important decrease of the effective viscosity of the suspension. Indeed, due to the electric torque exerted on the particles, the stress tensor in the suspension is not symmetric anymore and a driving effect arises from the anti-symmetric part. When such a suspensionflows through a rectangular channel, the velocity profile is expected to deviate from the usual Poiseuille flow. In this paper, the velocity profiles are measured using pulsed ultrasound Doppler velocimetry technique. They compare well to those that are computed from the otherwise measured rheological law.
54(2010); http://dx.doi.org/10.1122/1.3302804View Description Hide Description
A twin gap magnetorheometer—based on a modified Anton Paar magnetocell MRD180/1T—using plate-plate gaps on both sides of the rotor plate, all plates consisting of ferromagnetic steel, is presented and compared to corresponding single plate-plate magnetorheometry. The twin gap arrangement uses a nonmagnetic housing at the rim, thus allowing nominal shear rates up to without sample loss due to centrifugal forces. Shear stresses in a range of 0.001–105 kPa are accessible. Finite element modeling (FEM) using MAXWELL®2D verified the homogeneity of the flux density field in both shear gaps. The magnetic flux density in the magnetorheological fluid reaches up to 1.5 T and is obtained from an online Hall probe signal using a calibration factor from FEM. The radially constant flux density prevents radial carbonyl iron powder migration. Normal forces acting on both sides of the rotor compensate each other. Gap opening due to large normal forces as observed for the single gap geometry—requiring additional corrections for the effective flux density and shear stress—is not relevant. The apparent shear stress versus flux density characteristics from the twin gap and single gap magnetorheometry agree over the full range investigated (0–1.1 T), as shown for samples containing 90 and iron. Flow curves measured in a range of are presented as true shear stresses versus shear rate. The twin gap design (patent pending) has been licensed to the magnetocell manufacturer.
The matching of 3D Rolie-Poly viscoelastic numerical simulations with experimental polymer melt flow within a slit and a cross-slot geometry54(2010); http://dx.doi.org/10.1122/1.3306572View Description Hide Description
This paper is concerned with matching a fully three-dimensional (3D) viscoelastic numerical simulation with experimental results obtained using a multi-pass rheometer for both an entry-exit slit flow and a cross-slot geometry. The 3D code simulates the time evolution of steady flows using a multi-mode Rolie-Poly constitutive equation. A test polydisperse polystyrene was characterized for both its linear and non-linear viscoelastic response and the rheological parameters were used for the simulation with matching boundary conditions for the flow. Both overall pressure difference and flowbirefringence were compared for the entry-exit slit flow and good matching between simulation and experiment was found for the three different depth geometries tested. The 10 mm depth results (depth to width aspect ratio of 6.7:1) also showed that a 2D simulation gave a close match to both 3D simulation and experimental results. The flowbirefringence fit between experiment and simulation for the cross-slot case, while reasonable, did not match as well as the slit and the results demonstrate that the cross-slot geometry is very sensitive to the extensional behavior of the melt. In addition, examples of the application of the 3D code are given for a monodisperse polystyrene, where the match to experiment proved as good as that of the test polydisperse polystyrene.
54(2010); http://dx.doi.org/10.1122/1.3308643View Description Hide Description
The growth or absence of elastic secondary flows is documented for flows of dilute and semi-dilute polymer solutions in sharp 90° micro-bends in channels of rectangular cross-section; secondary flows are not present for Newtonian flows under similar conditions. Flow visualization shows that a vortex is present in the inner, upstream corner of the bend and grows with increasing Reynolds (Re) and Weissenberg (Wi) numbers for flows of shear-thinning, semi-dilute polymeric solutions containing (, ) or high molecular weight poly(ethylene) oxide (PEO) (, ). Rheological differences, likely due to differences in the flexibility of DNA and PEO, influence the degree of vortex enhancement with increasing Wi. The vortex is absent for flow of a dilute, non-shear-thinning PEO solution over a large Re and Wi range (, ) that includes conditions where vortices are observed for the semi-dilute, shear-thinningsolutions. Hence, shear-thinning appears to be central to the presence of an elastic secondary flow in this geometry.
54(2010); http://dx.doi.org/10.1122/1.3305721View Description Hide Description
We propose a method of obtaining all three key “tube” model parameters, namely, the plateau modulus , the entanglement molecular weight, , and the frictional equilibration time , from the molecular weight per backbone bond of -olefin copolymers with longer comonomers, ranging from C4 (butylene) to C26 (hexacosene). is obtained from a correlation by Fetters et al. [Macromolecules35, 10096–10101 (2002)] and is obtained from this using the standard tube-model formula, . The equilibration time is obtained from a remarkable finding by Stadler and Münstedt [J. Rheol.52, 697–712 (2008)] that, at fixed weight-average molecular weight, the zero-shear viscosity of linear -olefin copolymers is independent of comonomer type and content over a wide range of -olefin comonomers. From this observation, and from the values of and , we use the tube theory to construct a method for obtaining from the comonomer type and content. We show that these a priori values of the tube model parameters, when used in two publicly available models (“hierarchical model” and “branch-on-branch” model) for predicting linear rheology, yield accurate predictions for a wide range of polydisperse copolymers. These results show that a priori predictions of linear rheology of complex commercial polyolefin copolymers are now possible.
Investigations on the quality of dispersion of nanofillers in poly(methyl methacrylate) composites by creep-recovery experiments54(2010); http://dx.doi.org/10.1122/1.3314291View Description Hide Description
Nanocomposites with poly(methyl methacrylate) as the matrix and three different types of fillers, namely, nanoclay, nanosilica, and multiwalled carbon nanotubes, were prepared using various methods for the dispersion of the particular fillers. The morphology was analyzed using light and transmission electron microscopy. The composites were investigated by creep-recovery experiments, in addition to conventional dynamic-mechanical measurements. While the changes of the storage modulus are not very distinctive for low filler concentrations, the differences in the recoverable compliance measured by creep-recovery experiments become significant. The better the quality of dispersion, the higher is the recoverable compliance. This finding is explained by an interaction of macromolecules with the particle surface which is more pronounced for well dispersed particles as they offer a larger surface area. Therefore, creep-recovery measurements can very sensitively be used for the determination of the quality of dispersion. This rheological method integrates over the state of the whole sample, whereas transmission electron microscopy analyses only a tiny part of it.
Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology54(2010); http://dx.doi.org/10.1122/1.3314295View Description Hide Description
We investigate the structural, dynamical, and rheological properties of colloid-polymer mixtures in a volume fraction range of . Our systems are density-matched, residual charges are screened, and the polymer-colloid size ratio is . For these systems, the transition to kinetically arrested states, including disconnected clusters and gels, coincides with the fluid-fluid phase separation boundary. Structural investigations reveal that the characteristic length, , of the networks is a strong function of the quench depth: for shallow quenches, is significantly larger than that obtained for deep quenches. By contrast, is for a given quench depth almost independent of ; this indicates that the strand thickness increases with . The strand thickness determines the linear rheology: the final relaxation time exhibits a strong dependence on , whereas the high frequency modulus does not. We present a simple model based on estimates of the strand breaking time and shear modulus that semiquantitatively describes the observed behavior.