Index of content:
Volume 48, Issue 5, September 2004
Continuous shear thickening transitions in model concentrated colloids—The role of interparticle forces48(2004); http://dx.doi.org/10.1122/1.1784783View Description Hide Description
The role of interactions between close particles in the shear thickening of concentrated colloids is examined by using a Stokesian dynamics simulation of model systems. The interactions are repulsive thermodynamic forces and lubrication forces. Three different models are contrasted in their thickening behavior: Brownian spheres, polymer coated spheres, and Hookian spheres. Respectively, they show: a “mild” continuous thickening, a “strong” continuous thickening, and a strain thickening with loss of steady state. The relationship of order-disorder transitions and thickening is examined. Depending on the volume fraction and range of repulsive forces, thickening can be observed with or without an order-disorder transition at its onset. The different thickening responses arise from the dependence of the relaxation time of close particle contacts on interparticle gap. A time-scale based criterion for strong thickening is proposed and supported by the simulations. A simple theoretical model based the motion of a pair of particles leads to this criterion, but also predicts the mild thickening of Brownian spheres. It gives a simple fitting of flow curves which includes the details of the interparticle interactions.
48(2004); http://dx.doi.org/10.1122/1.1784784View Description Hide Description
Many body effects that occur in continuous shear thickening of concentrated colloidsuspensions are examined by using a Stokesian dynamics simulation of model systems of polymer coated particles. The shear thickening state is probed in a number of ways: computed scattering intensities, imaging of density variation using Voronoi constructions, examination of the distribution of interparticle forces, and computation of the fabric of contacts. The shear thickening transition in these systems is found to be associated with the growth of a network of close particle contacts and shear induced density variations. This paper focuses on the network of contacts. The distributions of force magnitude are found to be exponential. The network directly relates to the normal stress differences. Both the data and simple physical argument suggest that thickening can be viewed as an approach to “jamming.”
Solution rheology of hydrophobically modified associative polymers: Effects of backbone composition and hydrophobe concentration48(2004); http://dx.doi.org/10.1122/1.1773781View Description Hide Description
We investigate the effects of polymermolecular structure on the solution rheology of a hydrophobically modified associative polymer comprised of macromonomers with alkyl hydrophobes attached to a poly(ethyl acrylate-co-methacrylic acid) backbone. In particular, the effect of polymer backbone composition with variable proportions of methacrylic acid (MAA) and ethyl acrylate (EA) are examined. We find that the concentration of the MAA monomer has a large impact on polymerviscoelasticity.Polymers with low MAA content have smaller hydrodynamic size that result in lower viscosities and dynamic elastic moduli compared to polymers with high MAA content. Moreover, the balance between the polymerhydrodynamic size, the chain flexibility, and the aggregation of the EA blocks yield maxima in these material functions with respect to the MAA concentration. The scaling of shear viscosity, high frequency elastic modulus, and creep compliance with polymer concentration exhibits power-law behavior with different exponents. In all cases, three power-law regimes, regardless of the MAA content, are observed that can be attributed to the presence of different modes of hydrophobic interaction. However, the transitions shift to lower concentrations as the MAA content increases. With regards to the effects of the macromonomer side-chain concentration, we observe a substantial increase in viscosity at intermediate macromonomer content (1 mol %), possibly due to an increase in the number of intermolecular junctions as the number of hydrophobes per chain increases. This is in contrast to (i) low macromonomer concentration (0.3 mol %) behavior that reveals low viscosity due to weak hydrophobic associations, and (ii) high macromonomer concentration (1.9 mol %) behavior that favors more intramolecular association resulting in lower viscoelastic properties compared to intermediate macromonomer concentrations.
Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional and shear flows of dilute solutions of high molecular weight polystyrene48(2004); http://dx.doi.org/10.1122/1.1781171View Description Hide Description
The nonlinear transient extensional and steady-state shear rheological properties of dilute polystyrene solutions of molecular weight 3.9 and 10.2 million in a theta solvent are predicted using Brownian dynamics (BD) simulations with the bead-spring model. Full hydrodynamic interaction is incorporated into BD simulations using the Rotne–Prager tensor. The hydrodynamic interaction parameter is obtained a priori by matching the drag force from a fully extended bead-spring model in extensional flow with that from Batchelor’s theory for a cylindrical rod [Hsieh et al. (2003)]. The agreement between experimental data [Gupta et al. (2000)] and simulation results for the transient Trouton ratio versus strain is good from low to medium strains. However, the plateaus at high strains predicted by the simulations are higher than measured. We also find that hydrodynamic interaction hinders the unraveling of a polymer chain in strong extensional flow due to the hydrodynamicclustering of beads. In steady shear flows, the combination of hydrodynamic interaction and finite spring extensibility results in a shearthinning-thickening-thinning behavior with an increasing shear rate. For polystyrene of molecular weight 3.9 million, the simulated first normal stress coefficient does not quantitatively match the experimental results, in part because the number of beads N required to represent the hydrodynamic interactions accurately exceeds which is much higher than we can afford to use, namely We also predict a negative value of the second normal stress coefficient.
48(2004); http://dx.doi.org/10.1122/1.1773783View Description Hide Description
The rheological behavior of two series of model suspensions containing the same glass fibers in a Newtonian polybutene and in a Boger fluid has also been investigated. The steady-state shear viscosity of both supensions increased with fiber content, but the suspensions in the Boger fluid became shear thinning. Both types of suspension exhibited non-negligible normal stresses. The steady-state viscosity and normal stress difference of the supensions in the polybutene are well predicted by the Lipscomb (1987) equation coupled with the Folgar–Tucker (1984) model. Both types of fiber suspensions were shown to exhibit shear and normal stress overshoots in stress growth experiments. Under flow reversal, a shear stress overshoot was observed at a larger deformation compared to the primary overshoot. The reverse overshoot has been attributed to tumbling of fibers that are not totally aligned in the flow direction even after a very long time. When the flow was reversed, the normal stress difference took initially mimimum values (negative values in the polybutene case) and then depicted a smaller positive overshoot before reaching a steady-state value. The normal stress undershoot has been attributed to a transient fiber-oriented structure. The shape and the magnitude of these overshoots depend on the fiber content, nature of the matrix, and time delay between consecutive experiments.
48(2004); http://dx.doi.org/10.1122/1.1773780View Description Hide Description
The equilibrium rheological properties of a range of isotropic exfoliated and intercalated hyperbranched polymer (HBP)/montmorillonite (MMT) clay nanocomposites have been investigated using low strain oscillating shear measurements at temperatures above the glass transitiontemperature of the HBP. Predominantly exfoliated nanocomposites showed a sharp increase in shear viscosity at about 0.8 wt % MMT, associated with a transition from Newtonian to solid-like behavior, which was characterized in terms of a limiting shear modulus at low frequencies and a limiting viscosity at high frequencies, both of which were strongly dependent on the MMT content. Intercalated HBP/organically modified MMT nanocomposites showed qualitatively similar behavior, but the increase in viscosity with MMT content was far weaker. This was argued to reflect a significantly lower effective particle aspect ratio than in the exfoliated nanocomposites.
48(2004); http://dx.doi.org/10.1122/1.1773784View Description Hide Description
The linear viscoleasticity of seven lyotropic and thermotropic liquid crystalline polymers is characterized using the Leslie–Ericksen equations of defect-free nematodynamics for small amplitude oscillatory capillary Poiseuille flow, using analytical, numerical, and scaling methods. The experimentally measured seven data sets correspond to shear flow-aligning and shear nonaligning materials. The predicted equivalent rheological responses between these two classes of polymers demonstrate the universality of nematodynamics. Principles of superposition are developed, applied, and shown to be accurate in collapsing the data sets for aligning and non-aligning polymers. The scaled resonance peak in the loss tangent is shown to be a universal constant for monodomain nematics.
48(2004); http://dx.doi.org/10.1122/1.1773829View Description Hide Description
We explore the nonlinear rheological response of a soft gel formed by a crowded colloidal star polymer and focus on the occurrence of a stress plateau, marked hysteresis, and yield stress in its flow curve. With the aid of nuclear magnetic resonance velocimetry we find evidence for fluctuations in the flow behavior across the gap of the concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The time scale of the these fluctuations appears rapid (with respect to the measurement time per shear rate in the flow curve), on the order of tens to hundreds of milliseconds, with the speed of fluctuations associated with the flow history of the sample. Our velocity profile analysis suggests a qualitative model in which intermittent changes due to jamming/unjamming transitions occur, analogous to cage dynamics in colloidalglasses.
Interplay of rheology and morphology in melt elongation and subsequent recovery of polystyrene/poly(methyl methacrylate) blends48(2004); http://dx.doi.org/10.1122/1.1773782View Description Hide Description
In this study, blends of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are investigated in melt elongation and subsequent recovery using the uniaxial elongational rheometer RME. The volume concentration Φ of the PS phase ranges from 15% to 85% so that the full range of morphology from PS drops to cocontinuous structures to PMMA drops is spanned. A small and a large Hencky strain rate are chosen which cover the cases of small and large capillary numbers and lead to small and large drop extensions. In simple elongation, the elongational viscosity of the blends is mainly determined by the volume fraction of the PS phase. In recovery, our experimental data clearly reveal that the molecular recovery portions of the blend components superpose to the total recovery of the blend at short recovery times. At large recovery times, the interfacial tension contributes to the recovered stretch for blends with droplet as well as cocontinuous morphologies. The time scale of the interfacial tension driven recovery attains a maximum for the blend with a cocontinuous structure (Φ=50%). We compare our experimental data of the recovered stretch with the results of a model that is based on an effective medium approximation. Our model reproduces the experimental results for the transient recovered stretch and agrees well with the experimental data for large capillary numbers.
48(2004); http://dx.doi.org/10.1122/1.1781168View Description Hide Description
The frequency dependence of the shear modulus of heat denatured β-lactoglobulin gels at 7 at 0.1 M NaCl was studied during the gelation process. It can be characterized by two modes. The fast mode at different protein concentrations is successfully described in terms of the fractalgel model. The slow mode is characterized by a power law frequency dependence and is attributed to structural relaxation of the elastic backbone. The power law exponent is independent of heating time and decreases linearly with decreasing concentration. The evolution of the dynamic mechanical properties during gelation is independent of the heating temperature although the gelation rate increases strongly with increasing temperature.
Network formation and elasticity evolution in dibenzylidene sorbitol/poly(propylene oxide) physical gels48(2004); http://dx.doi.org/10.1122/1.1781169View Description Hide Description
We have investigated dibenzylidene sorbitol (DBS) physical gels with different gelator concentrations in a poly(propylene oxide) (PPO) matrix by frequency dependent rheological measurements. Defining the gel point according to the Winter and Chambon criterion, we have obtained the critical gel concentration Analyzing the experimental data in the plot for samples very close to the gel point, we found that a critical gelation concentration range would be more appropriate for describing the gelation process in DBS/PPO system rather than a single concentration value. By extrapolation from the plot we obtained a characteristic modulus for the samples above the gel point. The analysis of elasticity evolution with increasing gelator concentration revealed the existence of two distinct regimes. A critical domain is identified between and a turn-over DBS concentration of about 0.5 wt % in which exhibits power-law dependence on the relative distance from the gel point. Above 0.5 wt % DBS the characteristic modulus is found to scale with the DBS concentration. The results are discussed within the framework of different models describing physically gelling systems.
48(2004); http://dx.doi.org/10.1122/1.1781170View Description Hide Description
In this paper, we discuss the rheological properties of aqueous solutions of a rigid triple-helical polysaccharide, schizophyllan (SPG), in isotropic, biphasic, and fully anisotropic phases. Both steady shear and dynamic rheological behaviors reveal remarkable changes when SPG solutions pass through the three phases. The steady shear flow exhibits shear thickening at low shear rates for anisotropic SPG liquid crystalline samples, which is attributed to the shear-induced cholesteric to nematic transformation. The first normal stress difference and transient rheological experiments demonstrate that director tumbling is absent or negligible in SPG liquid crystals in the range of examined shear rates. Additionally, the stress relaxation of SPG liquid crystals after flow cessation shows an inverse relation between the relaxation time and preshear rate, as expected by Larson and Mead’s theory [Larson and Mead (1989)]. Small amplitude oscillation measurements following flow cessation show decreasing complex modulus with time for SPG liquid crystals, which is probably related to an increase of molecular orientation after flow cessation. The evolutions of complex modulus after flow cessation are discussed in terms of chain persistence length.
Particle–particle and particle-matrix interactions in calcite filled high-density polyethylene—steady shear48(2004); http://dx.doi.org/10.1122/1.1784782View Description Hide Description
The rheological properties of surfacetreated and untreated -high-density polyethylene composites were studied and related to particle–particle and particle-matrix interactions. Steady shear rheological measurements on composites with different loading (0–30 vol %) were carried out with preshear treatment prior to the measurements, duration of kneading during compounding, and surface treatment (stearic acid) of the filler as variable parameters. The steady state shear viscosity massively increased with increasing filler volume fraction due to the presence of a small number of agglomerates. Although no polymer was entrapped within the agglomerates, their presence led to massive increase in shear viscosity. The rheological response proved to be a more sensitive test for filler dispersion than scanning electron microscopy and shear thinning beyond that of the polymer matrix was observed, due to deagglomeration of the filler. The presence of agglomerates also led to a stress overshoot in the step shear rate experiments. Up to 0.3 filler volume fraction the particles agglomerated in form of clusters and no evidence for the presence of a space-filling particle network was found in this system. The apparent unbound viscosity observed at low shear stress in the high loaded composite and its fast decrease with increasing stress does not indicate yielding and can be attributed to gradual disintegration of the agglomerates. Preshearing the samples at a shear rate of prior to the measurements destroyed many of the agglomerates. Surface treatment of the particles decreased their surface energy and their tendency to agglomerate. It did not only decrease the particle–particle interactions but also decreased the adhesion of the polymer to the filler surface, resulting in a remarkable decrease in shear viscosity. The organic monolayer on the particulate surface lubricated the polymer flow, leading to an additional shear thinning at high shear rates. The maximum packing fraction was estimated by fitting the relative viscosity data to the Krieger–Dougherty equation. Reliable values could only be obtained, when the data set contained values larger than 3.