A rheological criterion to determine the percolation threshold in polymer nano-composites

In this work, the effect of multi-walled carbon nanotube (CNT) and montmorillonite nanoclay on polymer chain dynamics is investigated around the percolation concentration for systems based on ethylene vinyl acetate (EVA) copolymer. Then, the results obtained are compared with literature data to determine if, regardless of particle characteristics, a universal rheological behavior can be detected at percolation. To do so, rheological analyses are performed under small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and transient shear step. SAOS data showed that, while the dynamics related to the Rouse relaxation time (τ _R) were not significantly influenced, the reptation relaxation time (τ _D) was strongly increased by the presence of nanoparticles. In step shear transient tests, the critical shear rate \( \left({\dot{\upgamma}}_{\mathrm{cr}}\right) \) for overshoot appearance was decreased due to chain confinement, and the formation of particle network strongly increased the level of stress overshoot. Particle networks increased significantly the nonlinear parameters (I ₃/I ₁ and Q ₀) obtained under LAOS and quantified by FT-rheology. In all measurements, due to the higher surface area associated to its size and density as well as hollow structure, CNT showed stronger effects compared to clay. Moreover, while the percolation concentration was different for CNT and clay, both systems showed similar behavior at percolation: a 0.5 scaling for G′ indicating a Rouse-dominated behavior.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Rheological behavior of PS-melts containing surface modified PMMA-particles

The rheological properties of polystyrene (PS) compounds containing cross-linked PMMA particles are characterized by oscillatory shear experiments, while the amount of covalently grafted carboxylic-acid terminated polystyrene (CT-PS) on their surface is varied. All samples show an additional relaxation process with a long relaxation time in the frequency range where the matrix flows. The strength of this process depends strongly on the amount of particles, i.e., on the degree of filling and, to the same extent, on the different “coverage” of the particles surface, i.e., the degree of grafting. For the highest degrees of filling and in dependence on the degree of grafting a particle network is formed which is characterized by an evolving equilibrium modulus. Moreover, compatibilization by grafting CT-PS onto the PMMA particles' surface reduces the strength of the additional relaxation process remarkably. This surprising effect is related qualitatively to the balance of the interaction between particles and the interaction between the particles and the matrix due to PS grafts. Some of these results can be understood quantitatively on the basis of the sticky hard-sphere model. Received: 3 January 2000 Accepted: 14 August 2000     

Rheological behaviour of vitreous humour

The vitreous humour (VH) is a complex biofluid that occupies a large portion of the eyeball between the lens and the retina, and exhibits non-Newtonian rheological properties that are key for its function in the eye. It is often possible to distinguish two different phases in VH, known as liquid and gel phases (Sebag J Eye 1: 254–262, 1987). In this work, we present a detailed rheological characterisation of the two phases of the VH under shear and extensional flow conditions. Healthy New Zealand rabbit eyes were used to measure the surface tension and the shear and extensional rheological properties of VH in different phase conformations and at different times after dissection. The results show that VH liquid phase exhibits a surface tension of 47.8 mN/m, a shear thinning behaviour reaching a viscosity plateau around 10^?3 Pa s for shear rates above ~1000 s^?1, and an average relaxation time of 9.7 ms in extensional flow. Interestingly, both VH phases present higher storage modulus than loss modulus, and the measurements performed with VH gel phase 4?±?1 h after dissection exhibit the highest moduli values. The compliance measurements for the gel phase show a viscoelastic gel behaviour and that compliance values decrease substantially with time after dissection. Our results show that the two VH phases exhibit viscoelastic behaviour, but with distinct rheological characteristics, consistent with a gel phase mostly composed of collagen entangled by hyaluronan and a second phase mainly composed of hyaluronan in aqueous solution.     

Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow

Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model.     

Non-linear viscoelastic response of magnetic fiber suspensions in oscillatory shear

This paper reports the first study on the large amplitude oscillatory shear flow for magnetic fiber suspensions subject to a magnetic field perpendicular to the flow. The suspensions used in our experiments consisted of cobalt microfibers of the average length of 37 μm and diameter of 4.9 μm, dispersed in a silicon oil. Rheological measurements have been carried out at imposed stress using a controlled stress magnetorheometer. The stress dependence of the shear moduli presented a staircase-like decrease with, at least, two viscoelastic quasi-plateaus corresponding to the onset of microscopic and macroscopic scale rearrangement of the suspension structure, respectively. The frequency behavior of the shear moduli followed a power-law trend at low frequencies and the storage modulus showed a high-frequency plateau, typical for Maxwell behavior. Our simple single relaxation time model fitted reasonably well the rheological data. To explain a relatively high viscous response of the fiber suspension, we supposed a coexistence of percolating and pivoting aggregates. Our simulations revealed that the former became unstable beyond some critical stress and broke in their middle part. At high stresses, the free aggregates were progressively destroyed by shear forces that contributed to a drastic decrease of the moduli. We have also measured and predicted the output strain waveforms and stress–strain hysteresis loops. With the growing stress, the shape of the stress–strain loops changed progressively from near-ellipsoidal one to the rounded-end rectangular one due to a progressive transition from a linear viscoelastic to a viscoplastic Bingham-like behavior.     

Effects of compatibilization on rheological properties of PS/PB blends and investigation of Doi–Ohta scaling relationship in double start-up of shear experiments

The rheological properties for the blends of polystyrene and polybutadiene were investigated and the effect of compatibilizer styrene butadiene rubber (SBR), on the blends were studied and the results compared with the non-compatibilized blends. The frequency sweep, step shear strain and shear stress growth experiments were carried out for the blends. The results showed that with addition of compatibilizer the changes in behavior of the rheological properties of blends are observed. These rheological variations could be related to the reduction of interfacial tension and size of dispersed phase. Furthermore, the validity of Doi–Ohta scaling relationship in double start-up experiments was studied. It is shown that this scaling relationship becomes more reliable with increasing the amount of PB and compatibilizer.     

Dynamic rheological properties of a fumed silica grease

The thermo-rheological characteristics of a fumed silica lubricating grease in linear and nonlinear oscillatory experiments have been investigated. The material rheological behavior represents a soft solid being thermo-rheologically complex. There is an abnormal temperature dependency in the range of ??10 to 10 °C which is related to the phase transition of the base oil. The dynamic moduli data in linear viscoelastic envelop (LVE) have been modeled using mode-coupling theory (MCT) in the whole temperature range. Two main relaxation mechanisms can be identified through linear and nonlinear viscoelastic properties related to interaction of the primary particle and its neighbor particles as well as a slow relaxation process which represents the escape of this particle from its “cage”. Finally, it is demonstrated that the dominant yielding process in large amplitude oscillatory experiments can be explained based on either particle cage rupture (consistent with MCT framework) or particle “hopping” out of its cage proposed in soft glassy rheology (SGR) model. It will be discussed that the governing mechanism depends on the applied frequency.     

Impact of reinforcing filler on the dynamic moduli of elastomer compounds under shear deformation in relation to wet sliding friction

In pursuit of a better understanding of the relationship between wet sliding friction and bulk viscoelastic properties of elastomer compounds, especially the contribution from different reinforcing fillers, the linear thermorheological behavior, the nonlinear dynamic moduli under shear deformation (for strain up to about 140%), and the wet sliding friction have been characterized in detail for crosslinked compounds of low-cis polybutadiene filled with different reinforcing fillers including carbon black, graphitized carbon black, and precipitated silica. We examine the scenario of possible extra energy dissipation via higher harmonic excitation in rubber compounds coupled with dynamic deformation consisting of components at many frequencies during sliding of rubber on a rough surface. While no straightforward explanation is identified relating the observed difference in wet sliding friction arising from different fillers to the bulk viscoelastic properties, some unexpected viscoelastic features arising from the compounds are observed.     

Step planar extension of polymer melts using a lubricated channel

A technique to do step planar extension on polymer melts has been developed using a rectangular channel with lubricated walls and the linear motor of the Rheometrics System Four rheometer. Using this method we probe the stress relaxation of two polymer melts, a linear low density polyethylene (LLDPE) and a highly branched low density polyethylene (IUPAC X), and compare the step planar extensional data to step shear data. Since a step planar deformation is theoretically equivalent to a step shear in a rotating frame of reference, we expect that the nonlinear modulus for step planar extension should be equivalent to that for step shear. Although we find the time dependence of the stress relaxation modulus to be the same in both shear and planar extension, the strain dependence is surprisingly different for the two experiments.     

Surface rheology

This review article approaches the subject of surface rheology from a phenomenological point of view. Operational definitions are given for the four surface rheological parameters: modulus and viscosity in either dilation or shear. Results of recent measurements are discussed. Observed non-Newtonian or viscoelastic behaviour has in some cases been interpreted in terms of known relaxation processes. The surface rheological behaviour affects the flow of bulk liquid near the surface; coupling occurs through the tangential stress boundary condition.     

Rheological and foaming behavior of linear and branched polylactides

In this work, a chain extender (CE) was added to polylactide (PLA) to improve its foamability. The steady and transient rheological properties of neat PLA and CE-treated PLA revealed that the introduction of the CE profoundly affected the melt viscosity and elasticity. The linear viscoelastic properties of CE-enriched PLA suggested that a long-chain branching (LCB) structure was formed from the reaction with the CE. LCB-PLA exhibited an increased viscosity, more shear sensitivity, and longer relaxation time in comparison with the linear PLA. The LCB structure was also found to affect the transient shear stress growth and elongational flow behavior. LCB-PLA exhibited a pronounced strain hardening, whereas no strain hardening was observed for the linear PLA. Batch foaming of the linear and LCB-PLAs was also examined at foaming temperatures of 130, 140, and 155 °C. The LCB structure significantly increased the integrity of the cells, cell density, and void fraction.     

Rheological characterization in shear of a model dumbbell polymer concentrated solution

We investigate the linear and non-linear rheological behavior in shear of a concentrated solution of ??dumbbell?? polystyrene with long linear backbone and dense short brushes at both ends and compare it with corresponding linear polymers. This type of dumbbells has never been rheologically characterized before. In linear viscoelasticity, the dumbbell polymers show significant differences with conventional linear polymers. In particular, the reptation relaxation of the dumbbell is strongly slowed down. Furthermore, the addition of the side chains increases the friction so that the dumbbell lies above the ?? ₀ vs. number of entanglements relation of linear samples. Transient shear rheology experiments on weakly entangled solutions show a retardation of the chain stretch relaxation of the dumbbell by a factor 2.5 vs. a linear polymer with the same Rouse time. Additionally, a second peak in the transient viscosity is observed at high shear rates.     

Rheological characterization of commercial highly viscous alginate solutions in shear and extensional flows

The rheological properties of sodium alginate in salt-free solutions were studied by steady shear, dynamic oscillatory and extensional measurements. This biopolymer consists of mannuronic and guluronic acid residues that give a polyelectrolyte character. We applied the scaling theories and checked their accordance with polyelectrolyte behaviour for low concentrations with a shift to neutral polymer behaviour at larger concentrations. This nature was supported by the effect of the concentration on the specific viscosity, the relaxation times from steady shear and the longest relaxation times from small amplitude oscillatory shear (SAOS) measurements. To analyze the extensional behaviour of the samples, we conducted a study of dimensionless numbers and time scales where filament thinning driven by viscous, capillary or elastic forces is at play. We conclude that an exponential filament thinning followed by breakup results in the best regimes that describe the experimental data. Besides, the data pointed out that alginate in salt-free concentrated solutions shows strain thinning of the extensional viscosity and chain rigidity, behaviours that cannot be inferred from the shear rheometry.     

The influence of dewetting in filled elastomers on the changes of their mechanical properties

Summary The changes of mechanical properties of filled polymers and their dependence on deformation history are the subject of this paper. For most of filled polymers in practical use, the theory of linear viscoelasticity cannot be applied, even at small deformations. In this work, samples of glass bead filled polybutadiene rubber with different filler levels were investigated at small strains (<10%). The evolution of the relaxation modulus and Poisson's ratio was observed in cyclic experiments, which were also applied in inducing a defined deformation history for the succeeding relaxation experiments. In these experiments, the relaxation modulus and Poisson's ratio were measured as functions of time, with strain, strain rate, filler level and the preceeding deformation history as parameters. The results indicate dewetting as the main reason for the changes of the mechanical properties of the filled materials.The financial support of this work by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.     

High frequency rheology of hard sphere colloidal dispersions measured with a torsional resonator

The high frequency rheology of model, hard sphere dispersions of charge-neutralized, coated silica particles in tetrahydrofurfuryl alcohol (THFA) was measured using two torsional resonators at five frequencies. The resulting elastic modulus shows ω^1/2 limiting behavior at high frequencies and is in quantitative agreement with the theoretical predictions of Lionberger and Russel [J. Rheol. 38 (1994) 1885]. The lack of a high frequency plateau is a signature of weaker hydrodynamic interactions acting at very small separations. Calculations verify that despite the lack of a high frequency plateau, these dispersions can exhibit reversible shear thickening at high shear rates, in agreement with experiment. Thus, the experiments verify the unique sensitivity of high frequency rheology to hydrodynamic properties at the particle surface.     

Dynamic rheology of the immiscible blends of liquid crystalline polymers and flexible chain polymers

Immiscible blends containing liquid crystalline polymers (LCP) as dispersed phases show different dynamic rheological properties than those composed of flexible polymers. The widely used Palierne’s model was shown by many authors to be insufficient to describe the frequency dependence of dynamic modulus of such blends. A new model was presented to describe the dynamic rheology of the immiscible blend containing LCP as a dispersed phase. The flexible chain polymer matrix was assumed to be a linear viscoelastic material under small amplitude oscillatory shear flow, and the LCP was assumed to be an Ericksen’s transversely isotropic fluid. The Rapini-Papoular equation of anisotropic interfacial energy was used to account for the effect of nematic orientation on the interfacial tension. It was found that the orientation of the director and the anchoring energy greatly influenced the storage modulus at the “shoulder” regime. The overall dynamic modulus of the blend can be well described by the model with suitable choice of the orientation of the director and anchoring energy of LCP.     

The influence of epoxy resin on the morphological and rheological properties of PET/PA66 blend

Interfacial reactions have dominant effects on the morphological and rheological properties of compatibilized polymer blends. This work aims to investigate the effect of epoxy resin, as a coupling agent, on the interface properties and subsequent influences on the morphological and rheological properties of polyethylene terephthalate/polyamide66 (PET/PA66) blend. PET/PA66 70/30 blends with different amount of bisphenol A epoxy resin (0, 1, 3, and 5 wt.%) were prepared. SEM micrographs show reduction in droplet size with increasing epoxy resin concentration, confirming the reactive compatibilizing effect of the epoxy resin. Reactions at the interface of the PET-EP-PA66 blend are confirmed by FTIR spectra. Shear viscosity results demonstrates that adding epoxy resin could suppress the interfacial slip at the blend interphase. Obtained results from storage modulus (G′) curves show the presence of one plateau for the blends at low frequency region; nevertheless, relaxation spectra indicate the presence of two more relaxation mechanisms than precursors which are related to the shape relaxation of droplets and the interface relaxation. The presence of the interface relaxation time in the blend without epoxy resin can prove the presence of reactions between two condensation polymers; however, adding the epoxy resin results in reducing both relaxation time and interfacial tension and increasing interfacial shear modulus. These observations indicate that the epoxy resin has been successful to boost the reactions at the interface between two polymers. Fitting the obtained experimental data using Palierne model indicates that the general Palierne model could describe rheological properties of the blends very well.     

Rheology and structure of precipitated silica and poly(dimethyl siloxane) system

The reinforcing capability of precipitated silica in poly(dimethyl siloxane: PDMS) was characterized by means of bound rubber formation, solvent swelling, yield stress, rheological and dynamic properties. Volume concentration of precipitated silica in PDMS was varied from 0 to 0.16. The homogeneity of the compounds after mixing was confirmed by studying a uniformity of dispersion of silica particles in PDMS via SEM morphology of vulcanizates. Bound rubber measurements of the compounds and solvent swelling studies of vulcanizates showed that the precipitated silica exhibited much stronger interaction with PDMS than that of typical carbon black with rubbers but less than that of fumed silica with PDMS. At high volume concentrations of silica (0.128 and 0.160), a yield behavior was evident from the storage modulus measurements. The network formation due to an interaction between the precipitated silica and PDMS was visualized via dynamic property measurements.