Volume 53, Issue 4, July 2009
Index of content:
53(2009); http://dx.doi.org/10.1122/1.3119056View Description Hide Description
Viscoelasticmeasurements made with a stress-controlled rheometer are affected by system inertia. Of all contributors to system inertia, motor inertia is the largest. Its value is usually determined empirically and precision is rarely if ever specified. Inertia uncertainty has negligible effects on rheologic measurements below the coupled motor/plate/sample resonant frequency. But above the resonant frequency, values of soft viscoelastic materials, such as dispersions, gels, biomaterials, and non-Newtonian polymers, err quadratically due to inertia uncertainty. In the present investigation, valid rheologic measurements were achieved near and above the coupled resonant frequency for a non-Newtonian reference material. At these elevated frequencies, accuracy in motor inertia is critical. Here we compare two methods for determining motor inertia accurately. For the first (commercially used) phase method, frequency responses of standard fluids were measured. Phase between and was analyzed at 5–70 Hz for motor inertia values of 50–150% of the manufacturer’s nominal value. For a newly devised two-plate method (10 and 60 mm parallel plates), dynamic measurements of a non-Newtonian standard were collected. Using a linear equation of motion with inertia, viscosity, and elasticity coefficients, expressions for both plates were equated and motor inertia was determined to be accurate (by comparison to the phase method) with a precision of ±3%. The newly developed two-plate method had advantages of expressly eliminating dependence on gap, was explicitly derived from basic principles, quantified the error, and required fewer experiments than the commercially used phase method.
53(2009); http://dx.doi.org/10.1122/1.3119023View Description Hide Description
Non-reversing and reversing double-step strain flows on concentrated entangled polystyrene in diethyl phthalate or tricresyl phosphate were employed to characterize transient entanglement properties affecting subsequent chain stretch and relaxation. An extended Doi-Edwards tube theory for double-step strain flows was employed to retrieve the phenomenological stretch relaxation function following a second large probe strain imposed on specially selected time scales that permit a direct assessment of the modified chain stretch with varying transient entanglement structure. Compared with single-step strain result, the maximum mean-square segmental stretch was noted to reduce by as much as 33% and 48% for non-reversing and reversing flows, respectively, with a probe strain .
Determination of the viscoelastic behavior of sodium hyaluronate in phosphate buffered saline with rheo-mechanical and rheo-optical methods53(2009); http://dx.doi.org/10.1122/1.3122985View Description Hide Description
Aqueous solutions of microbially produced sodium hyaluronate in phosphate buffered saline (, ) were characterized with regard to their molecular parameters and viscoelastic behavior. The weight-average molar mass , -average radius of gyration , and their distributions were determined using a hyphenated assembly of size exclusion chromatography, multi-angle light scattering, and a differential refractive index detector. Correlation of the obtained results with viscometric data enabled the establishment of and relationships (; ). Viscoelastic behavior was investigated by steady state shear experiments. The viscosity yield was determined for varying concentrations and molar masses using shear rates from to . The elastic behavior in shear flow, represented by the first normal stress difference , has been detected on one hand via rheo-mechanical experiments and on the other hand being correlated from the rheo-optical material functions flow birefringence and its orientation utilizing the stress-optical rule. This correlation enabled the extension of the measurement range toward lower absolute values of of more than two decades. The correlated values were in good agreement with the data obtained by rheo-mechanical measurements.
53(2009); http://dx.doi.org/10.1122/1.3143788View Description Hide Description
We study nematodynamics of a mesoscopic system consisting of sheared biaxial liquid crystalline polymers using a hydrodynamical kinetic theory, in which the biaxial liquid crystal polymer is modeled as a rigid, biaxial, ellipsoidal molecule immersed in viscoussolvent. The governing Smoluchowski equation in the model is solved in selected regions of the material parameter space and a range of accessible shear rates using a Wigner–Galerkin spectral method. In addition to the truly biaxial flow-aligning steady states, log-rolling steady states, and out-of-plane steady states, we report the presence of two new time-periodic motions, chaotic motion and associated phase transitions in a range of shear rates and selected material parameters. Rheological signatures of the sheared mesoscopic system are identified with predominant shear thinning in all phases and alternating signs between the normal stress differences in steady vs time-dependent motions.
Experimental observations and matching viscoelastic specific work predictions of flow-induced crystallization for molten polyethylene within two flow geometries53(2009); http://dx.doi.org/10.1122/1.3123209View Description Hide Description
Flow-induced crystallization (FIC) behavior of a high-density polyethylene melt in two entry-exit flow geometries was investigated by direct optical observation using a multi-pass rheometer and the results compared with a viscoelasticflow simulation. A set of experiments was performed at several piston speeds using a sharp and a rounded entry-exit slit and the region of onset for visible FIC was identified in both cases. During flow narrow crystal filament regions localized at the sidewalls and in a downstream “fang” region of stress accumulation were identified. A melt flow two-dimensional numerical simulation using a Lagrangian solver, FLOWSOLVE, and an 11-mode Pom-Pom model satisfactorily matched experimental pressure difference and birefringence fringe distribution for the flow. An algorithm to calculate the specific work accumulated by each fluid element in the complex flow field was implemented within FLOWSOLVE and a method was proposed to estimate the critical specific work for the onset of visible oriented FIC. The concept of specific work applied to the numerical simulations was capable of successfully predicting the experimental regions where FIC occurred.
53(2009); http://dx.doi.org/10.1122/1.3143878View Description Hide Description
Biomass slurries, such as dilute-acid pretreated corn stover (PCS), will be a common process stream in biorefineries designed to convert agricultural residues into biofuels such as ethanol. In this work, the advantages and disadvantages of several rheological techniques are evaluated for PCS suspensions. Three flow regimes were evaluated: (i) shear flow using a vane, (ii) torsional flow between parallel plates, and (iii) biaxial extensional flow between plates. The vane provided the simplest methodology and the most reproducible results. Four experiments were conducted using the vane: (i) transient flow, (ii) stress ramps, (iii) creep, and (iv) oscillatory shear. PCS slurries with fractions of insoluble solids (FIS) ranging from 5% to 17% by weight exhibited soft-solid characteristics, including an apparent yield stress.Yield stresses were highly dependent on stover concentration, scaling with FIS to the sixth power, and ranged from 0.2–5000 Pa between 5% and 17% FIS. PCS suspensions were strongly shear thinning, with flow and dynamic viscosities that were highly dependent on FIS. Last, as with many concentrated suspensions, the Cox–Merz rule was not followed, although flow and dynamic viscosities were coincident when plotted versus an effective shear rate.
53(2009); http://dx.doi.org/10.1122/1.3114370View Description Hide Description
Significant slip can occur in the flow of a blend of two immiscible polymers due to reduced entanglements at their interface. The slip is of practical importance because of its effect on morphology and adhesion in, for example, disordered two-phase blends or multilayer films. Interfacial slip was quantified using two polymer pairs each with closely matched viscosity and elasticity but different miscibility : polypropylene (PP)/polystyrene (PS) and polyethylene (PE)/fluoropolymer (FP) . To control the amount of interfacial area, we prepared alternating layers by coextrusion. The number of layers of PP/PS ranged from 20 to 640 while that for PE/FP was 80. Nominal viscosity of the multilayer samples was measured with three types of rheometers: an in-line slit-die rheometer, rotational parallel-disks, and sliding plate. Good agreement was found between the three methods. The nominal viscosity as well as shear normal stresses of the multilayer samples decreased with the number of layers. From the viscosity reduction, an apparent interfacial slip velocity was calculated. The detectable slip, about , occurred at the same level of stress normalized by average plateau modulus for both pairs. However, did not show a sudden increase at a critical shear stress as predicted by Brochard-Wyart and de Gennes [C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers317, 13 (1993)] but rather increased , where for PS/PP and for PE/FP. The steeper dependence of slip on stress for PE/FP may be related to its higher value and with its narrower molecular weight distribution.
53(2009); http://dx.doi.org/10.1122/1.3143794View Description Hide Description
Long-chain branched polymer melts such as low density polyethylene (LDPE) and branched metallocene polyethylenes show strong time-strain separability in step strain. Constitutive models of the multi-mode Pom-pom form are highly successful in modeling the stress generated by general flow histories for these materials. However, a single Pom-pom mode is not time-strain separable and reconciling this to the step-strain phenomenon has been a challenge. We investigate multi-mode integral Pom-pom models and a differential approximation to compare time-strain separation, with respect to mode density. Here we show that for a wide class of branched distributions, a family of damping functions can be derived with a response that is very close to separable. We evaluate the family for both LDPE and branched high density polyethylene melts and show that a damping function derived from the multi-mode Pom-pom model gives an accurate prediction of the damping behavior in step-strain experiments.
53(2009); http://dx.doi.org/10.1122/1.3123216View Description Hide Description
The deformation and break-up of a droplet of suspension of swollen-in-water starch granules placed in an immiscible fluid, silicon oil, are investigated. The study was carried out on a physically modified waxy maize starch suspension with a theoretical granule volume fraction of 100%. Granules were swollen to their maximum; they were highly deformable. Measurements were carried out using a counter rotating shear cell. The starch suspension was shear thinning above a yield stress of about 90–100 Pa showing elasticity (first normal stress difference) above 300 Pa. The rheo-optical experiments were carried out by stepping up the stress from zero to a constant value and deformation of suspensiondroplets of various sizes was observed with time. Critical break-up capillary numbers were calculated and correlated with droplet-to-matrix viscosity ratio . At low values were found to be smaller or close to those determined for Newtonian fluids. No break-up was observed for viscosity ratios above 0.1, a limit that is roughly 40 times lower than that for the Newtonian fluids. This result was assumed to be due to the fact that internal stress in the droplet is lower than the mean one applied, because of inter-particle interactions and friction, thus shifting suspension from low to extremely high viscosity fluid if applied stress is close to the yield transition.
53(2009); http://dx.doi.org/10.1122/1.3119084View Description Hide Description
A microscopic approach is presented for calculating general properties of interacting Brownian particles under steady shearing. We start from exact expressions for shear-dependent steady-state averages, such as correlation and structure functions, in the form of generalized Green–Kubo relations. To these we apply approximations inspired by the mode coupling theory (MCT) for the quiescent system, accessing steady-state properties by integration through the transient dynamics after startup of steady shear. Exact equations of motion, with memory effects, for the required transient density correlation functions are derived next; these can also be approximated within an MCT-like approach. This results in closed equations for the nonequilibrium stationary state of sheared dense colloidal dispersions, with the equilibrium structure factor of the unsheared system as the only input. In three dimensions, these equations currently require further approximation prior to numerical solution. However, some universal aspects can be analyzed exactly, including the discontinuous onset of a yield stress at the ideal glass transition predicted by MCT. Using these methods we additionally discuss the distorted microstructure of a sheared hard-sphere colloid near the glass transition, and consider how this relates to the shear stress. Time-dependent fluctuations around the stationary state are then approximated and compared to data from experiment and simulation; the correlators for yielding glassy states obey a “time-shear-superposition” principle. The work presented here fully develops an approach first outlined previously [Fuchs and Cates, Phys. Rev. Lett.89, 248304 (2002)], while incorporating a significant technical change from that work in the choice of mode coupling approximation used, whose advantages are discussed.
Determination of method-invariant activation energies of long-chain branched low-density polyethylenes53(2009); http://dx.doi.org/10.1122/1.3124682View Description Hide Description
The idea to use the temperature dependence of rheological properties, especially the flow activation energy, as a tool to investigate branching structures is well-known from literature. However, there is no common method to obtain activation energies, which are independent of the measuring quantity chosen, particularly, in the case of slightly thermorheologically complex polymers like low-density polyethylene (LDPE). Hence, differing activation energies result, which cannot unequivocally be correlated with the branching structure. This paper describes a method for the determination of method-independent activation energies for thermorheologically complex polymers like LDPE. From a generalized approach to the time-temperature superposition principle, a vertical shift factor is introduced, which is related to the temperature dependence of the linear steady-state compliance. In the case of the complex LDPE, a decrease in the linear steady-state compliance with temperature is found. Taking this experimentally determined shift factor into account leads to activation energies independent of the rheological quantity chosen. These values can be taken to analyze differences of the branching architecture.