Elasticity and dynamics of particle gels in non-Newtonian melts

We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO₂) nanoparticles and polypropylene. Above a critical volume fraction, Φ _c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition, the elasticity of the hybrids shows critical behavior around Φ _c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters. For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G^′, scaling with frequency, ω, as G^′∼ω ^0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of the components could be superimposed.     

Field-induced gelation, yield stress, and fragility of an electro-rheological suspension

 Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress, the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in steady shear where the rate of structure formation equals the rate of internal breaking. Received: 1 May 2001 Accepted: 11 August 2001     

High-frequency viscoelasticity of crosslinked actin filament networks measured by diffusing wave spectroscopy

We study the short-time relaxation dynamics of crosslinked and uncrosslinked networks of semi-flexible polymers using diffusing wave spectroscopy (DWS). The networks consist of concentrated solutions of actin filaments, crosslinked with increasing amounts of α-actinin. Actin filaments (F-actin) are long semi-flexible polymers with a contour length 1–100μm and a persistence length of 5–15μm; α-actinin is a small 200kDa homodimer with two actin-binding sites. Using the large bandwidth of DWS, we measure the mean-square-displacement of 0.96μm diameter microspheres imbedded in the polymer network, from which we extract the frequency-dependent viscoelastic moduli via a generalized Langevin equation. DWS measurements yield, in a single measurement, viscoelastic moduli at frequencies up to 10⁵Hz, almost three decades higher in frequency than probed by conventional mechanical rheology. Our measurements show that the magnitude of the small-frequency plateau modulus of F-actin is greatly enhanced in the presence of α-actinin, and that the frequency dependence of the viscoelastic moduli is much stronger at intermediate frequencies. However, the frequency-dependence of loss and storage moduli become similar for both crosslinked and uncrosslinked networks at large frequencies, G′(ω)∝G′′(ω)∝ω^0.75±0.08. This high-frequency behavior is due to the small-amplitude, large-frequency lateral fluctuations of actin filaments between entanglements. Received: 20 January 1998 Accepted: 12 February 1998     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001     

Time- and temperature-dependent crosslinking behaviour of a silicone resin

The crosslinking behaviour of a silicone resin which is interesting from a technical point of view was investigated by means of rheology. In order to accelerate the crosslinking process, zinc acetylacetonate and aluminium acetylacetonate were applied as latent catalysts. The effect of the type of catalyst, its concentration, and the temperature on crosslinking was determined by isothermal dynamic-mechanical measurements. A radial gradient in crosslinking causes the gel point to be reached earlier at the outer edge of the sample in the rheometer. This radial gradient is averaged when measuring G′ and G″. Therefore, since the physically well-defined state of critical gelation (gel point) could not be obtained from the data, the time at which a distinct crosslinking state is reached was determined by the crossover of the moduli G′ and G″. For this distinguished point, the denotation gelation index GI is introduced. The gelation indices measured at different temperatures follow an Arrhenius-type relationship. Activation energies between 89 and 126 kJ/mol were determined. They were found to be dependent on the type of catalyst used but independent of its concentration. The activation energies of the crosslinking processes enable the calculation of the gelation index at temperatures not measured directly.     

Orthogonal and parallel superposition measurements on lyotropic liquid crystalline polymers

 Mechanical spectroscopy is used to probe the structure of lyotropic liquid crystalline polymers during flow and after the cessation of flow. The oscillatory flow is either parallel or perpendicular to the steady-state flow. The resulting moduli provide information about the time- and shear-dependent microstructure, including anisotropy. Two different concentrations of poly(benzylglutamate) (PBG) in m-cresol and a concentrated hydroxypropylcellulose (HPC) solution, also in m-cresol, are investigated. In all cases, the orthogonal superposition moduli evolve differently from the parallel ones. The former are less sensitive to the flow-induced changes in structure than the latter ones. Together with the lack of sensitivity of the superposition moduli to texture refinement during flow, this suggests a strong relation between director orientation and superposition moduli. After the cessation of flow the parallel moduli decrease for the PBG solutions, whereas the opposite is observed in the HPC solutions. A comparison with the orthogonal moduli provides a direct measure of anisotropy. At rest, the PBG solutions tend toward a higher degree of anisotropy while the HPC solutions become more isotropic. In the latter systems, all moduli are much larger, reflecting a larger contribution from the texture. Received: 8 July 1999/Accepted: 1 October 1999     

Microstructural effects on the dynamic rheology of a discotic mesophase pitch

The dynamic rheology and accompanying microstructure of a synthetic mesophase pitch (AR-HP) is reported. The loss modulus (G″) was found to be higher than the storage modulus (G′) at all frequencies (∼0.1 to ∼100 rad/s) and temperatures (280–305 °C) tested. The slope of the low-frequency terminal zone for G′ was found to be approximately 0.8, much lower than a value of 2 that is observed for flexible chain polymers. Cross-polarized optical microscopy with full-wave retardation plate confirmed the presence of different textures of mesophase pitch processed under different conditions. While loss moduli remained fairly unchanged, finer textures led to significantly lower storage moduli. Consistent with this trend, coarsening of the microstructure during textural relaxation led to an increase in storage moduli. Therefore, for the discotic mesophase pitch, the viscous component was found to remain unaffected by the microstructure, but the elastic modulus was dependent on the orientation of layer-planes and size of the texture.     

Exact Connections of Warping Fields and Torsional Rigidities of Symmetric Composite Bars

Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ₁ and μ₂ are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ₁ ^′ and μ₂ ^′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T(μ₁,μ₂) and T(μ₁ ^′,μ₂ ^′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ₁ ^′′,μ₂ ^′′) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ^′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well. This revised version was published online in June 2006 with corrections to the Cover Date.     

Using oscillatory squeezing flow to measure the viscoelastic properties of dental composite resin cements during curing

We have investigated the rheological changes in two particulate-filled dental composite resin cements during the curing process using a Micro-Fourier Rheometer (MFR). In the MFR, the sample was sandwiched between two parallel plates, and pseudorandom small amplitude squeezing was applied by oscillating the upper plate over a range of frequencies. Fourier transforms of the displacement signal and the resulting time dependent force signal enabled the rapid determination of the dynamic properties G′ and G′′ over the frequency range 2π–200π rad/s . This technique permitted us to follow changes in the rheological properties of the resin cements through the setting period. A typical result was that G′ increased from 2×10³ Pa to 2×10⁵ Pa after about 120 s, and that G′′ changed from 4×10³ Pa to 4×10⁴ Pa over the same period at frequency 40π rad/s. We also found that the dental composite resin cements show linear viscoelastic behaviour over a range of strain amplitudes before curing, but the response becomes distinctly non-linear at the later stages of curing for strain amplitudes γ>0.067%.     

Gelation behavior of polysaccharide-based interpenetrating polymer network (IPN) hydrogels

We report the preparation and rheological characterization of interpenetrating polymer network (IPN) hydrogels made from alginate and hydrophobically modified ethyl hydroxyl ethyl cellulose (HMEHEC). To our knowledge, there have been no studies of the gelation behavior of IPNs. We found that the rheology of these systems can be easily tuned, with the elastic modulus of the IPN strongly dependent on the relative ratio of HMEHEC to alginate. The sol–gel transition of these systems was found to satisfy the Winter–Chambon criterion for gelation at various crosslinker densities. From the power law relationship of the dynamic moduli (G ^′ ~G ^″ ~ω ⁿ), the exponent n appears to be dependent on both the crosslinker density and relative amount of two polymers. The value of n was found to be ~0.5 for all samples for stoichiometric amounts of crosslinker. The effect of molecular weight of HMEHEC on the gel point and viscoelastic exponent has also been reported. Alginate seems to dominate the kinetics of the process but the effect of high molecular weight HMEHEC on the gel point, especially at lower proportion was also evident.     

Rheological characterization of a solder paste for surface mount applications

Solder pastes used in surface mount soldering techniques (SMT) are very complex suspensions containing high volumes of metallic powder in a carrier fluid. The rheological complexity results largely from the carrier fluid itself, which is a suspension of colloidal particles. In this work, we have characterized the rheological properties of a typical carrier fluid and its solder paste containing 64 vol.% metallic powder. A six-blade vane geometry was used to avoid wall slip and sample fracture. All measurements were carried out following pre-shearing and rest time in order to obtain reproducible results. Steady shear experiments showed that the solder paste was highly shear-thinning and thixotropic. In oscillatory shear, the linear viscoelastic domain was found to be very narrow for both the suspending fluid and the paste. Frequency sweep tests in the linear domain revealed a gel-like structure with a nearly constant G′ for the suspending fluid and a slightly increasing G′ for the solder paste. From creep experiments, a yield stress of about 40 Pa was determined for the suspending fluid at temperatures between 25 and 40°C, and of 100 Pa at 4°C. A much larger yield stress, 480 Pa, was determined for the solder paste at 25°C.     

A rheological approach to drill-in fluids optimization

The aim of this work is to propose design criteria, based on rheological characterisation for improving drill-in fluids performance. In particular, it reports an example in which rheological approaches helped improve drill-in fluids resistance to temperature. As a starting system a commercial drill-in fluid containing xanthan gum and calcium carbonate was chosen and evaluated. Different samples were then prepared by changing the initial formulation in order to increase the system's stability to temperature. Drill-in fluids' performance have been compared by considering their “damaging potential”, filtration properties and, “cakes”. All drill-in fluids have been tested before and after aging at a given temperature with “hot rolling tests”. The systems' gel structure was characterized by measuring dynamic moduli (G′ and G′′) in the linear viscoelastic range and all samples were compared by evaluating their “melting” temperature and gel network strength during time cure tests. The results obtained from this work suggest that the rheological tests carried out on the whole drill-in fluid can provide insights into fluids' damaging potential and “cake” structure. In particular, rheology proved to be able to provide quantitative information about gel strength and temperature stability that permitted one to improve drill-in fluids' formulation in order to preclude formation damage and to meet industrial requirements. Received: 6 February 2000 Accepted: 15 November 2000     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Phase morphology and rheological behavior of polymer/layered silicate nanocomposites

Rheological behavior of polymer/layered silicate nanocomposites are strongly dependent not only upon their microstructure but also upon the interfacial characteristics. Different phase morphology (intercalated or exfoliated) of polymer/clay is obtained according to interfacial characteristics between polymer chains and clay. In intercalated structure, the presence of randomly oriented anisotropic stacks of silicate layers is responsible for the enhancement of both moduli. The PS/clay nanocomposites exhibit a slight enhancement at low frequency because of its simple intercalated structure and little interaction. On the other hand, the PS-co-ma/clay nanocomposites have a similar intercalated structure but exhibit a distinct plateau-like behavior at low frequency since the PS-co-ma has a strong attractive interaction with the silicate layers. Finally, PE-g-ma/clay nanocomposites display an exfoliated structure, which exhibit both a distinct plateau-like behavior at low frequency and enhanced moduli at high frequency. Percolation structure as well as large interfacial area between polymer chains and clay are responsible for the rheological behavior. Received: 20 March 2000   Accepted: 11 September 2000     

A rheological approach to the stability of humic acid/clay colloidal suspensions

Steady-state, oscillatory, and transient rheological determinations were used to assess the stability of homoionic sodium montmorillonite (NaMt) suspensions at constant ionic strength (10^–2 mol/l NaCl) and different pH values, after adsorption of humic acid (HA) on the particles. The adsorption of the latter was first spectrophotometrically determined, at pH 3 and 9. While at pH 9 adsorption saturation was observed, at pH 3 the adsorption density continued to grow up to the maximum equilibrium HA concentration reached (∼200 mg/l). Considering the similarity between the structure of edge surfaces of NaMt particles and the surfaces of silica and alumina, the adsorption of HA was also investigated on the latter solids. The results suggest that at pH 3 humic acids adsorb preferentially on edge surfaces, mainly through electrostatic attraction with positively charged aluminol groups. This hypothesis is indirectly confirmed by zeta potential, ζ, values: while HA concentration has little effect on ζ for silica, the addition of HA yields the zeta potential of alumina increasingly negative for all pH values. Using shear stress vs shear rate plots, the yield stress of NaMt was determined as a function of particle concentration, C, for pH 3, 5, 7, and 9, with and without addition of 50 mg/l HA. The yield stress, σ_y, was fitted with a power law σ_y∝C ⁿ ; it was found that n values as high as 12 are characteristic of NaMt suspensions at pH 9 in the presence of HA. This indicates a strong stabilizing effect of humic acid. This stabilization was confirmed by oscillometric measurements, as the storage modulus G′ in the viscoelastic linear region also scales with C, displaying large n values at neutral and basic pHs in the presence of HA. The modulus (in the viscoelastic linear region, for a frequency ν=1 Hz) was found to increase with time, but G′ was lower at any time when HA was added, a consequence of the stabilization provided by HA. Similarly, creep-recovery experiments demonstrated that NaMt suspensions containing HA displayed a less elastic behavior, and a permanent deformation. Modeling the results as a Kelvin-Voigt model allowed one to establish a new scaling law of the reciprocal instantaneous deformation with C. As before, high values of n were found for suspensions at pH 9 in the presence of HA.     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Incremental Magnetoelastic Deformations,with Application to Surface Instability

In this paper the equations governing the deformations of infinitesimal (incremental) disturbances superimposed on finite static deformation fields involving magnetic and elastic interactions are presented. The coupling between the equations of mechanical equilibrium and Maxwell’s equations complicates the incremental formulation and particular attention is therefore paid to the derivation of the incremental equations, of the tensors of magnetoelastic moduli and of the incremental boundary conditions at a magnetoelastic/vacuum interface. The problem of surface stability for a solid half-space under plane strain with a magnetic field normal to its surface is used to illustrate the general results. The analysis involved leads to the simultaneous resolution of a bicubic and vanishing of a 7×7 determinant. In order to provide specific demonstration of the effect of the magnetic field, the material model is specialized to that of a “magnetoelastic Mooney–Rivlin solid”. Depending on the magnitudes of the magnetic field and the magnetoelastic coupling parameters, this shows that the half-space may become either more stable or less stable than in the absence of a magnetic field.      

A rheological approach to the study of concentrated milk clotting

The aim of the present work is to analyze the complex phenomena involved in the concentrated milk clotting process in order to define general criteria applicable to the design of a continuous coagulator. A full characterization of the rheological properties of completely hydrolyzed milk as a function of two different parameters, i.e., the coagulator temperature and the concentration degree of the milk, is presented. The dynamic evolution of loss, G′′, and storage, G′, moduli has been obtained at different frequency values and for different concentration degrees during the clotting process. Time cure tests have been performed on completely hydrolyzed milk samples showing that the rate of curing is very high and that the time for rheological experiments is much too short for testing Winter's theory of gelation. To overcome this problem, the intersect of loss and storage moduli was used for estimating the coagulation. Coagulation is faster when higher temperatures are used and the consistency of the final curd is greater if a more concentrated milk is used. A tentative physical explanation based on the network theories is presented. If an observation time far enough from the crossover point is chosen it can be seen that the curd strength estimated at 40 °C is about 50 times higher than that one evaluated at 25 °C. Among the considered temperatures, a good processing value was evaluated at 40 °C. Received: 6 February 2000 Accepted: 24 October 2000     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Extensional and shear rheometry of oriented triblock copolymers

 The effects of extensional flow orientation on the rheological properties of two poly(styrene)-poly(ethylene-co-butylene)-poly (styrene) (PS-PEB-PS) triblock copolymers containing either spherical or cylindrical PS microdomains were studied by oscillatory shear and oscillatory extensional experiments. Extensional measurements revealed that below the PS block glass transition temperature pre-oriented triblocks display highly anisotropic mechanical properties. For both polymers, the storage modulus E ′ is higher along the flow direction. Above the PS glass transition temperature the materials are no longer anisotropic and the same storage moduli are obtained along the flow direction and perpendicular to it. Above the PS glass transition temperature the rheological behaviour parallel and perpendicular to the flow direction was also probed in pre-oriented and non-oriented samples by oscillatory shear rheometry. At high frequencies, the mechanical response of the triblocks was found to be independent of the orientation for both copolymers while at low frequencies a strong effect of the flow orientation could be observed. For both polymers the value of the storage modulus was found to be lower along the flow direction that perpendicular to it. This was explained by the ability of PS blocks to relax more easily along the flow direction. Received: 10 September 1999/Accepted: 1 October 1999