Index of content:
Volume 47, Issue 2, March 2003
Characterizing complex fluids with high frequency rheology using torsional resonators at multiple frequencies47(2003); http://dx.doi.org/10.1122/1.1538608View Description Hide Description
A set of torsional resonators is used to characterize the linear viscoelastic behavior of complex fluids in the kilohertz range. The frequency dependence of the elastic and loss modulus of a hard sphere dispersion, electrostatically and electrosterically stabilized particles, worm-like micelles, polystyrene microgels, and polymer solutions is studied. The results are compared to theoretical predictions for these systems. The utility of the instrument for characterizing the high frequency rheology of complex fluids is demonstrated. This is especially relevant for suspensions or dilute solutions and gels, where time-temperature superposition often fails and the relaxation spectrum is inaccessible from conventional oscillatory shear rotational rheometry.
Rheo-optical studies of barley (1→3)(1→4)-β-glucan solution: Detection of the flow behavior of aggregates in the sol state47(2003); http://dx.doi.org/10.1122/1.1538609View Description Hide Description
The unbranched homopolymer (1→3)(1→4)-β-D-glucan shows a spontaneous gelation in aqueous solution above a critical concentration Detection of form birefringence,dichroism, as well as their respective orientation, and θ, in steady shear experiments with rheo-optical methods indicate the presence of aggregates in the sol state before the onset of the gelation. Transient dichroism experiments show that these aggregates are stable to shear forces. The aggregates show a finite deformability, their number is directly proportional to the polymer concentration, whereas the structure and deformability as well as the size of the aggregates is independent of concentration and molar mass above the critical concentration Below a change in the plateau level of the reduced dichroism and therefore in the aggregate structure can be detected that coincides with the onset of a stable, nongelating state of the solution. From the intrinsic birefringence, which dominates at high shear rates, the stress optical coefficient C was determined to
47(2003); http://dx.doi.org/10.1122/1.1538606View Description Hide Description
The problem of converting capillary viscometry data with wall slip into a shear stress versus shear rate relationship and a wall shear stress versus slip velocity relationship is formulated as an integral equation of the first kind. This reveals the ill-posed nature of the problem. A procedure based on Tikhonov regularization is applied to find an approximate solution to this equation. This way of processing capillary viscometry data has the advantage that it does not require the assumption of a rheological model to relate the shear rate and the slip velocity to the local shear stress. Since Tikhonov regularization allows for the ill-posed nature of the problem, it can be expected to give reliable results in the presence of experimental noise. The performance of this method is demonstrated by applying it to the capillary data for a linear low-density polyethylene, a high-density polyethylene, a suspension of ammonium sulfate particles in a viscous Newtonian carrying fluid, and a mineral-based aqueous paper coating color. In each case, Tikhonov regularization has succeeded in obtaining the maximum amount of information regarding the rheological properties of the material and these properties are in good or reasonable agreement with published data.
Transient and steady state three-dimensional drop shapes and dimensions under planar extensional flow47(2003); http://dx.doi.org/10.1122/1.1545078View Description Hide Description
Drop shapes and dimensions in transient and steady states have been studied using a four-roll mill flow apparatus with three-dimensional imaging and real-time derivative edge detection. The deformed drops are approximately ellipsoidal for viscosity ratios of with about 4% maximum deviation of actual drop volume from ellipsoidal volume. For drops retain their ellipsoidal shape up to deformation of above which they show progressive deviation from the ellipsoidal shape. The measured length, breadth, and width of deformed drops were compared to predictions of various drop deformation theories. The limit of deformation within which theories predict drop dimensions with 5% accuracy has been tested for The ellipsoidal model of Maffettone and Minale (1998) gives the best prediction for while the second order theory of Barthes-Biesel and Acrivos (1973) gives the best overall prediction for The application of some theories to the determination of interfacial tension and drop viscosity is discussed.
47(2003); http://dx.doi.org/10.1122/1.1545071View Description Hide Description
The orientation dynamics of a lyotropic colloidalsuspension of sepiolite clay under extensional flow have been explored by combined dichroism and small angle light scatteringmeasurements.Extensional flow was applied using a four-roll mill to a thin film of sepiolite suspension (rigid rods 1 μm long and 0.010 μm in diameter). Analysis of transient extensional flow reversals revealed important characteristics of the orientation dynamics of these suspensions: (i) the existence of a critical volume fraction separating isotropic behavior, where no orientation persists after stretching, from nematic behavior, where permanent orientations persist during the relaxation phase; and (ii) in the nematic domain, a critical strain rate separates two flow regimes corresponding to a stable, so-called strong flow regime above the critical strain rate and an unstable, so-called weak flow regime below it. These experimental observations agree with the theoretical predictions of the model proposed by Marrucci and Maffettone (1989, 1990) who have examined the two-dimensional form of the simple molecular model of Hess (1976) and Doi (1981). What is new in the present case is that the colloidalsuspension is a three-dimensional system, whereas previous experimental validations of the model concerned only two-dimensional rodlike polymers systems [Maffettone et al. (1996)] [Maruyama et al. (1998a, 1998b)].
Formulation effects on magnetic mix microstructure based on rheological, magnetic susceptability, and particle size measurements47(2003); http://dx.doi.org/10.1122/1.1538607View Description Hide Description
Steady and oscillatory shear rheological, magnetic susceptibility, and particle size measurements are used to characterize the microstructure of metal particles dispersions in organic solvents with respect to changes induced by milled-in polymer only and A hierarchical structure built of inseparable clusters, aggregates with their size fixed during mix preparation, and a volume-filling network of these aggregates is consistent with our observations. As polymer-to-particles ratio and/or number of active groups in the polymer increase, the aggregates decrease in size and the network becomes weaker and less brittle. For each polymer-to-particles ratio an optimum level of dispersant is established. Below the optimum dispersant level aggregates are too large, while above it aggregates appear to interact too strongly. A plateau at intermediate shear rates occurs unless an optimum dispersant level is maintained along with sufficient polymer. This plateau is attributed to wall-slip and may be used to discriminate dispersion quality.
47(2003); http://dx.doi.org/10.1122/1.1538610View Description Hide Description
The behavior of a low-density polyethylene (LDPE) melt in double-step strain flows is examined. Here emphasis is on double-step shear strains where the second step is reversed, either half way or completely. Data are compared with the “pom–pom” model of McLeish and Larson, which is a molecular theory for the nonlinear rheology of branched polymers. Both integral and differential versions of the pom–pom with molecular drag-strain coupling are used. Semianalytical model predictions are obtained for the stresses in double-step shear flows, and comparison is made with double-step shear strain flows on a LDPE melt. Predictions from the well-known K–BKZ equation are also compared. It is observed that the K–BKZ and the differential version of the pom–pom model give better predictions than the integral version in both types of reversing flows considered. The K–BKZ model performs better than the two versions of the pom–pom in the data-theory comparison of the first normal stress difference. It is concluded that all of the models are in general qualitatively, but not quantitatively, consistent with the experiments and no clear advantage is found among the different models in reversing double step. The better data-theory comparisons for the pom–pom model in reversing flows is explained with the help of a physical picture of backbone stretch and retraction suggesting that the arms preserve the backbone tube orientation.
47(2003); http://dx.doi.org/10.1122/1.1545072View Description Hide Description
A new filament stretching rheometer has been constructed to measure the elongational viscosity of polymer melts at high temperatures. Two polymer melts, a LDPE and a LLDPE, were investigated with this rheometer. A constant elongational rate has been obtained by an iterative application of the Orr–Sridhar method for specification of the end-plate movement. Agreement has been found with linear viscoelasticmeasurements performed in shear. Hencky strains up to about 6 have been reached. Steady values of the viscosity have been sustained in some cases for about two Hencky strain units.
47(2003); http://dx.doi.org/10.1122/1.1545079View Description Hide Description
A filament stretching rheometer is used to study a series of monodisperse and bidisperse polystyrene solutions and to test predictions of the simplified Mead–Larson–Doi (MLD) “toy” model. This model incorporates convective constraint release, diffusive constraint release, and chain stretching into the reptation-based theory of Doi and Edwards but ignores contour length fluctuations (CLFs). The model parameters are the plateau modulus and the two time constants, the Rouse time and the reptation time for each monodisperse component. In order to artificially incorporate CLFs into the toy model, we relate the constants of the toy model to parameters of the Milner–McLeish model obtained using dynamic data. The predictions of this toy MLD model are in good agreement with experimental data for monodisperse solutions in steady shear, startup of shear, and steady state and transient extensional flow. At high strain rates in extensional flow, good agreement is only obtained if the extensibility of the chains is arbitrarily reduced by a factor of 2 below the molecularly derived value, perhaps reflecting the limitations of a single mode model. Without any additional parameters, the model also yields reasonable agreement with experimental data for bidisperse solutions. The study illustrates the advantages of extensional data in justifying parameter estimates and also the sensitivity of extensional measurements to the high molecular weight component of blends.
47(2003); http://dx.doi.org/10.1122/1.1545075View Description Hide Description
Rheology and stress relaxationdynamics of a well-characterized, entangled polystyrene/diethylphthalate solution are investigated during start-up and following cessation of steady shear flow.Rheological measurements designed to probe the effect of flow-induced changes in polymerrelaxation time on properties form the main focus of this study. At shear rates intermediate between the reciprocal terminal relaxation time and reciprocal longest Rouse relaxation time we find that both convective and nonconvective processes accelerate molecular relaxation in entangled polymer liquids. The former processes are described well by the multimode convective constraint release model of Ianniruberto and Marrucci (2002), but the latter ones are not. At shear rates the nonconvective processes give rise to a two-stage relaxation mechanism following cessation of steady shear flow. The first stage of relaxation is characterized by a time constant that is over an order of magnitude greater than and is a decreasing function of shear rate while the second stage is characterized by a shear-independent characteristic time We also find that overshoots in first normal stress difference begin at shear rates substantially lower than and that the effect of shear rate on the size of overshoots is qualitatively different from theoretical predictions.
47(2003); http://dx.doi.org/10.1122/1.1545074View Description Hide Description
This work explores the rheological behavior of exfoliated dispersions of montmorillonite clay in xylene. The clay-based nanodispersions elucidate how the incorporation of silicate particles produces networking upon ultrasound induced exfoliation, thus offering useful insight into the reinforcement mechanism in actual polymernanocomposites. These dispersions exhibit a storage modulus plateau ranging from to over and a yield stress ranging from 4 to over as the clay loading increases from 1 to 10 wt %. Creep and recovery measurements show that these nanodispersions possess (a) a viscosity η ranging from 4000 to nearly (b) a quasisteady state compliance whose reciprocal is comparable to and (c) a retardation time over in agreement with the stress relaxation experiment. Upon the stress-induced sol-gel transition, the dispersion viscosity may drop by a factor of Consistent with the yield behavior, the dispersion displays a steady shear viscosity in the controlled rate mode that scales reciprocally with the applied shear rate. Finally, these dispersions suffer from apparent wall slip at a critical stress proportionally lower than the yield stress at different clay loadings. This wall slip is preventable by attaching sandpapers onto the parallel plate surfaces of the flow cell.
Solution rheology of hydrophobically modified associative polymers: Solvent quality and hydrophobic interactions47(2003); http://dx.doi.org/10.1122/1.1545076View Description Hide Description
The rheological behavior of a model hydrophobically modified alkali solubleemulsion (HASE) polymer, comprised of a random copolymer backbone of methacrylic acid and ethylacrylate and pendant hydrophobic macromonomers, is examined in cosolvents of water and propylene glycol (PG) of different proportions. We find the solventsolubility parameter to have a direct impact on both the steady and dynamic behavior of the polymer solutions. In particular, scaling of the relative viscosity and the elastic modulus at a fixed frequency with the solventsolubility parameter reveals the presence of two distinct regimes with different dependences on In “water-rich” solvents, both and show a strong dependence on in contrast to “PG-rich” solvents, in which there is slight or no dependence on The concentration dependences of both and are also found to be different in water-rich solvents from that in PG-rich solvents. In water-rich solvents, and reveal power-law dependences with exponents of 2.5 and 3.2, respectively, compared to exponents of 1.4 and 2.3 in PG-rich solvents. The different behavior in PG-rich solvents is ascribed to the presence of minimal hydrophobic associations, with the polymer behavior analogous to that of unmodified polymers without hydrophobes. This hypothesis is supported by the similarity in scaling with concentration observed for both the HASE polymer in PG-rich solvents and a similar polymer without the hydrophobes in both solvents. The lack of hydrophobic interactions in the PG-rich solvents may be attributed to the observed decrease in polymer coil dimension together with a lower tendency of the hydrophobes to form micelles in less polar media.
Shear-induced elastification of concentrated emulsions probed by sinusoidal amplitude variation rheometry47(2003); http://dx.doi.org/10.1122/1.1545439View Description Hide Description
We study how concentrated emulsions elastify, or become increasingly elastic, through droplet rupturing induced by a strong applied shear. To do so, we have developed a novel method, sinusoidal amplitude variation (SAV) rheometry, for probing the emulsion’s frequency-dependent storage and loss moduli during the emulsification process. A discrete number of high strain amplitude sinusoidal oscillations at a fixed frequency, which cause droplet rupturing, are followed by frequency sweeps at purturbative strain amplitudes which probe the impact of the rupturing on the moduli. We show that the plateau elastic modulus of a concentrated emulsion grows rapidly after only several oscillations and saturates after many oscillations. We measure how the yield properties of emulsions change during emulsification, and show that a critical rupturing strain must be exceeded in order for the emulsion to elastify. The rapid increase in the elastic modulus and subsequent saturation as a function of the number of driving oscillations point to a mechanism of positive feedback in emulsification that is cutoff by local nonaffine shear.
Fokker–Planck simulations of fast flows of melts and concentrated polymer solutions in complex geometries47(2003); http://dx.doi.org/10.1122/1.1545440View Description Hide Description
In 1999, Öttinger introduced a thermodynamically admissible reptationmodel incorporating chain stretching, anisotropic tube cross sections, double reptation, and the convective constraint release mechanism. In this paper, we describe and use a new high-order Fokker–Planck-based numerical method for the simulation of the Öttinger model in complex geometries. Evidence, in the case of startup homogeneous flows, of the significant CPU time advantage (for comparable levels of accuracy) of our method over a stochastic simulation [Fang et al. (2000)], is presented. For the confined cylinder benchmark problem, differences in the drag behavior observed between the Öttinger model and those of Doi and Edwards (1978a, 1978b, 1978c) and Mead et al. (1998) are explained in terms of double reptation and the differing relaxation spectra.
Measurements of the rheological behavior of a crystallizing polymer by an “inverse quenching” technique47(2003); http://dx.doi.org/10.1122/1.1545080View Description Hide Description
In this paper we show that a suitable thermal history can be used to produce a polymer melt in which a fixed amount of crystalline phase has been frozen. We call this novel method “inverse quenching,” since a stable amorphous/crystalline system is obtained by heating up the sample rather than cooling it down. If the inverse quenchingtemperature is suitably chosen, the polymer can remain stable for a long time, thus allowing different types of experimental measurements. Here we first prove the validity of the inverse quenching method in quiescent crystallization conditions, and then we use the inverse quenching method to perform rheological measurements on an isotactic polypropylene at a constant degree of crystallization. In particular, steady-state viscosity measurements in the early crystallization stages are reported for the first time, showing that the viscosity at low shear rates is much larger than that of the purely amorphous melt even for small values of crystallinity. The technique is also used to study the liquid-to-solid transitional behavior of the crystallizingpolymer, which can be seen as a gelation process, at temperatures that are forbidden to traditional techniques. Such measurements are shown to provide further, robust validation of this novel method.
47(2003); http://dx.doi.org/10.1122/1.1545077View Description Hide Description
In this paper, the linear and nonlinear rheological behavior of semidilute aqueous solutions of a recently synthesized thermoassociative graft copolymer was investigated, as a function of temperature and polymer concentration. The polymer, namely CMC–g–PNIPAM, is based on a carboxymethylcellulose (CMC) backbone bearing thermosensitive poly(N-isopropylacrylamide) (PNIPAM) sidechains. The samples have been submitted to steady shear, oscillatory shear, and step-strain experiments, mainly at temperatures above the threshold temperature to observe thermothickening. The linear and nonlinear rheological data clearly show the existence of two temperature regimes, separated by a transition temperature At temperatures below the solutions behave like a soft critical gel, corresponding to weak PNIPAM segregation. At temperatures above the solutions behave like a stiff critical gel, corresponding to strong PNIPAM segregation.