Effect of fillers on the steady state rheological behaviour of liquid crystalline polymers

The effect of fillers on the flow curves of polymeric liquid crystals is investigated. Suspensions of polystyrene particles in liquid crystalline solutions of hydroxypropylcellulose (HPC) in water are used. By reducing the HPC concentration an isotropic solution can be prepared. It serves as a reference to isolate the effect of the isotropic/anisotropic structure of the suspending medium on the rheological behaviour. Suspensions in the isotropic solution behave as expected for filled viscoelastic matrices in general. In the anisotropic medium the shear rate rather than the shear stress seems to govern the changes in the relative viscosity. This behaviour is clearly different from isotropic viscoelastic media. The most dramatic effect however is that even small amounts of particles eliminate or drastically shift the region of negative normal stress differences. As far as the structure is concerned, microscopic observations show that particles align in anisotropic as well as in isotropic media. At rest or at relatively low shear stresses the liquid crystalline structure is, in the present case, hardly affected by the presence of the particles. If anything, it becomes more homogeneous. Received: 28 April 1998 Accepted: 28 July 1998     

Linear and non-linear rheological behaviour of cement and silica suspensions. Effect of polymer addition

Oil well cement pastes and model silica suspensions demonstrate similar rheology: in oscillatory shear, beyond a critical stress, a sharp transition is ob- served between gel and liquid behaviour. In creep tests, an apparent yield stress and shear-thinning are followed by the appearance of shear thickening. The minimum viscosity measured in steady shear is close in value to the complex viscosity obtained from oscillatory measurements. The observations can be explained by the formation of liquid trapping aggregates whose compactness may be estimated by fitting the Tsenoglou model, and whose cohesion is reflected in the rigidity of the gel and in the critical strain (or stress) of gel dissolution. Substituting cement or silica particles by polymer redispersible powder causes a decrease of the storage modulus in the gel state and a lower viscosity, while leaving the general features of the flow curve unchanged. Decrease in material rigidity may be due to a weaker inter-particle attraction generated by the polymer presence. The decrease in viscosity is explained by a lessening of water entrapped within the aggregates, which now contain polymer particles which are less hydrophilic than either cement or silica.     

The rheological behaviour of Ca(OH)2 suspensions

The rheological behaviour of Ca(OH)₂ suspensions is investigated, predominantly at a solid volume fraction of 0.25. The influence of standing without being subject to shear (“contact time”) is distinguished from that of being sheared (“shearing time”). The results are interpreted on the basis of the “elastic floc” model of energy dissipation during flow, with a view to the problem whether, in addition to an energy dissipation term related to the viscous drag experienced by particles moving within flocs, there should be an independent energy dissipation term related to fluid movement in the flocs when they change volume or shape. It appears that this additional energy dissipation term is not necessary, if the increase in viscous friction, experienced by two particles which are close together, is taken into account. Paper, presented at the First Conference of European Rheologists at Graz, April 14–16, 1982. A short version has been published in [18].     

The rheological behaviour of Ca(OH)2 suspensions in water

The rheological characteristics of Ca(OH)₂ suspensions are investigated in order to check the elastic floc model for energy dissipation during flow. It is found that the energy, required to overcome the viscous drag experienced by particles moving within flocs, can account for the total energy dissipation.     

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.     

Electrical double layer and rheological properties of yttria-stabilized zirconia suspensions in solutions of high molecular weight polyacrylic acid polymers

This work deals with the effect of the adsorption of two high molecular weight polyacrylic acid polymers (Carbopol) on the interfacial properties, and the rheology of aqueous zirconia suspensions. Since the Carbopol-covered particles can be thought of as soft colloids, Ohshimas theory was used to gain information on the surface potential and the charge density of the polymer layer (Ohshima H (1995) Electrophoretic mobility of soft particles. Colloids Surf A Physicochem Eng Aspects 103:249–255). The effect of the pH of the solution on the double layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The electrokinetic properties of the suspensions are studied for different pH and Carbopol concentrations in solution in order to investigate the possible stabilization of the suspensions by electrostatic repulsion between the particles. The rheological behavior of the suspensions was investigated in steady-state and dynamic conditions, and the corresponding yield stress and storage modulus were obtained in absence and presence of polymer in solution. The competition between bridging flocculation provoked by polymer adsorption and electrosteric stabilization determines the rheological properties of the suspensions. In the pH range investigated, bridging flocculation predominates at the neutral pH because of the graft of the uncoiled polymer to more than one particle, while at the extreme pH values (pH 3, pH 9) steric or electrosteric stabilization seems to be the predominant mechanism that explains the rheological results. These facts were confirmed by estimating the zirconia particle (or aggregate) diameter in the liquid medium by means of light scattering measurements.     

A numerical study of various rheological polydispersity measures

Model calculations were performed in order to investigate the sensitivity of various rheological polydispersity parameters for variations in the moments of the molar mass distribution (MMD) of linear polymers. Molar mass distributions were generated with the Gaussian and the Generalised exponential distribution functions, using a fixed weight average molar mass M _w and variable M _w /M _n and M _z /M _n . Assuming linear entangled polymeric chains, the linear viscoelastic properties were predicted by calculating the stress relaxation modulus of the consecutive monodisperse fractions with the BSW relaxation time spectrum and blending these curves with the double reptation blending rule. BSW relaxation parameters appropriate for polypropylene were used.  It was found that both the zero-shear viscosity and the so-called cross-over frequency, at which and are equal, depend mostly on M _w but also significantly on both M _w /M _n and M _z /M _w . By contrast, the steady-state compliance depends mainly on M _z /M _w , its functional dependence on moments of the MMD being best described by the Ferry equation.  None of the polydispersity parameters PI (from the modulus cross-over), MODSEP (the modulus separation) or PDR (from the shape of the flow curve), as introduced in literature depends solely on the polydispersity M _w /M _n . PI is the most sensitive indicator for this purpose. Finally, the parameters ER ( at a fixed low value of , MODSEP en DRI (from the shape of the flow curve) are shown to be good indicators for the weight (M _z /M _w ) of the high molar mass tail of the molar mass distribution. Received: 5 May 1998 Accepted: 30 July 1998     

A rheological theory for liquid crystal thin films

A macroscopic rheological theory for compressible isothermal nematic liquid crystal films is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the film stress tensor includes elastic and viscous components. The asymmetric film viscous stress tensor takes into account the nematic ordering and is given in terms of the film rate of deformation and the surface Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic film tension, which includes the film tension and dilational viscosities. Viscous dissipation due to film compressibility is described by the anisotropic dilational viscosity. Three characteristic film shear viscosities are defined according to whether the nematic orientation is along the velocity direction, the velocity gradient, or the unit normal. In addition the dependence of the rheological functions on curvature and film thickness has been identified. The rheological theory provides a theoretical framework to future studies of thin liquid crystal film stability and hydrodynamics, and liquid crystal foam rheology. Received: 9 October 2000 Accepted: 6 April 2001     

Effect of polymer bridging on rheological properties of dispersions of charged silica particles in the presence of low-molecular-weight physically adsorbed poly(ethylene oxide)

 The effect of a low-molecular-weight physically adsorbed poly(ethylene oxide) on the rheological behavior of aqueous dispersions of silica particles (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing polymer concentration in the system at different volume fractions of the particles. Experiments were performed in the absence of salt and just the pH of the dispersion was adjusted to 9.5, a condition at which the system is electrostatically stable and electrostatic repulsive forces are long range in nature. It was observed that the shear viscosity and the linear viscoelastic functions of the dispersion at 55 vol% increase initially through the addition of polymer, reach a maximum, and then decrease to a minimum with further addition of polymer to the system. At higher polymer concentrations, there may be an increase in the viscosity of the dispersion owing to an increase in the concentration of free polymer chains in the medium causing depletion flocculation in the system. The increase in the rheological behavior of the dispersion at low polymer coverage is attributed to polymer bridging flocculation caused by a low-molecular-weight poly(ethylene oxide) in the system. Comparison of the data given here with the results of earlier studies on the viscosity behavior of the system in the presence of salt (0.01 M) indicates that the range of the electrostatic repulsion has a significant role in the rheological behavior of the system. Received: 7 February 2001 Accepted: 18 October 2001     

Transient Heat Transport in Gas Flow Through Granular Porous Media

Models are developed to describe the time-evolution of gas and solid temperature profiles in a class of granular porous media; this time-dependence being the result of a heat source supplying energy uniformly to the gas as it flows into the medium. The solid-phase is treated as a fixed, axi-symmetric bed of randomly packed spheres of uniform size and material properties. An analytic expression for the locally averaged surface temperature of the solid phase is formulated in terms of the time history of the corresponding local gas temperature. This approach avoids the need to assume locally uniform temperatures within the solid phase, and provides a coupled model for the thermal energy transport in the system. A numerical scheme for treating the resulting transport equations is outlined, and results presented. A quasi-steady approximation is proposed, and this approximation is assessed by reference to numerical results obtained from the numerical scheme. One application of the work is to fixed-bed catalytic reactors and absorbers, and results are presented indicating how the regeneration times of such systems depend on operating parameters.     

Transient rheological behavior of lyotropic solutions of ethyl cellulose in m-cresol

Transient rheological features of anisotropic 30 and 40 wt.% ethyl-cellulose/m-cresol solutions were investigated, taking as a reference other lyotropes like poly(γ-benzylglutamate) in m-cresol, poly(p-phenylene-terephthalamide) in sulfuric acid and hydroxypropylcellulose in water. Strain scaling oscillations before reaching steady state, with a half-period of 20 strain units for 30 wt.% and 22.5 strain units for 40 wt.% in both stress growth and transient viscosity in creep, revealed that director tumbling takes place for ethylcellulose solutions. Large strain recoveries (2–3 strain units) obtained in recoil experiments confirmed the hypothesis of a tumbling regime. In contrast to the majority of reported lyotropes, we did not observe a master curve of strain recovery versus the product of preshear rate by time. This result appears to be associated with the existence of another mechanism of relaxation, in addition to unwinding of the defect texture created by tumbling. Dynamic viscoelastic results after cessation of flow suggest that a slower mechanism of relaxation, associated with texture or polydomain coarsening, takes place. Received: 28 July 1998 Accepted: 10 December 1998     

The peculiarities of the rheological behaviour of coal tars

The results are discussed of rheological studies of coal tars with different concentrations of substances insoluble in toluene at periodical, steady-state and combined periodical-steady shear deformations in a wide range of deformation frequencies, rates and amplitudes in the temperature region from 223 to 333 K. The temperatures of structural and mechanical glassingT _g , the activation energies of viscous flow and initial viscoelastic constants of these systems have been determined. Temperature and temperature-frequency dependencies of dynamical parameters have been obtained, the pre-steady-state and the steady-state flow modes of permanent deformation have been studied and thixotropic parameters have been evaluated at the combined action of vibration and permanent deformation.     

Investigation of the band texture occurring in hydroxypropylcellulose solutions using rheo-optical, rheological and small angle light scattering techniques

The band texture occurs in lyotropic and thermotropic main-chain polymers after cessation of flow. This paper begins with a review of work concerned with band texture formation following shear and is followed by the presentation of original results obtained during a recent investigation. The evolution of band texture formation in a Klucel EF, 50% hydroxypropylcellulose (HPC) water solution, has been observed using polarized optical microscopy. The relationship determined between the primary shear rate and the rate of evolution of the band texture is complex and three different behaviours have been observed corresponding to three shear rate regions. Both steady flow and dynamic rheological investigations have been conducted on the HPC solution, the results of which have been related to the optical behaviour of the band texture. Data from steady flow investigations suggest that the viscosity of the solution when the band texture is present, decreases following increasing primary shear rates, is shear thinning and increases linearly with the time following its formation. Dynamic investigations suggest a definite link between the band texture evolution and the evolution of both G′ and G′′. In addition, the perfection of the band texture versus the primary shear rate has been quantified by studying the evolution of tan(δ) following the cessation of the primary shear. Dynamic experiments show that the structure of the band texture remains longer than suggested by the optical aspect of the texture. Small angle light scattering patterns have been correlated with the development of the band texture and confirm the continuing presence of the band texture structure following its optical disappearance. Received: 2 March 1999/Accepted: 26 July 1999     

A rheological method for selecting nano-kaolin powder as filler in SBR rubber

This paper shows that the stiffness of styrene-butadiene solid rubber with added kaolin powder is related to the yield stress of kaolin dispersion in liquid polybutadiene rubber up to the percolation threshold.For five kinds of kaolin powder,the value of τ spans the range of 100-430Pa,while the corresponding compressive elastic constant of SBR varies from 12 to 21MPa.A relationship between τ° and ΔE*i/E*R is proposed.Critical examination of these data infers that kaolin powder dispersed in solid rubber matrix acts as an additive which decreases the random movement of the polybutadiene chains.Consequently,dispersions of nano-particles in liquid and in solid SBR are considered to be related,thus leading to a rheological method for selecting nano-particles as fillers in solid SBR.     

Phase separation effects in the rheology of aqueous solutions of hydroxypropylcellulose

Aqueous solutions of hydroxypropylcellulose (HPC) have been widely used as a model system to study liquid crystalline behavior in polymers. The HPC limiting concentration for mesophase formation in water is about 40% wt, quite independent of molecular weight. Most rheo-optical investigations have been carried out in the concentration range from 50% to 65% wt, on the assumption that only the liquid crystalline phase was present. In this study, by using video-enhanced contrast light microscopy, we show that an isotropic phase in form of tiny droplets is also present at concentrations up to 60% wt, both in quiescent and in sheared samples at room temperature. The isotropic phase can be made to disappear by lowering the temperature. The effects of phase separation on the rheology of the HPC/water system are studied by measuring viscosity as a function of temperature and concentration. A slope of Region I of the viscosity curve close to –0.5 is found only at low temperatures, when the sample is fully anisotropic, whereas an anomalous dependence of the viscosity on temperature is observed when phase separation is significant. This study shows that special care is needed when interpreting experimental results from the HPC/water system in terms of theories for liquid crystalline polymers.     

Investigation of the band texture occurring in acetoxypropylcellulose thermotropic liquid crystalline polymer using rheo-optical, rheological and light scattering techniques

The optical evolution of the band texture occurring in acetoxypropylcellulose thermotropic polymer has been investigated as a function of temperature and primary shear rate. Two distinct kinds of band texture were observed which are referred to here as the `fast' and `slow' band textures with regard to their rate of evolution. The fast band texture appears very quickly following the cessation of shear and then disappears. The slow band texture is much finer than the fast band texture and appears to exist both during and after the appearance of the fast band texture. The evolution behaviour of the fast band texture is interpreted in terms of the shifting of a three-region evolution curve. Particular attention has been paid to investigating the influence of temperature on the formation of the fast band texture. Rheo-optical experiments show that the minimum shear rate required to form the fast band texture increases as a power-law function of the temperature. By subsequently performing steady flow measurements over a range of temperatures, the minimum shear stress required to form the fast band texture has been found to be independent of temperature and to increase linearly with the molecular weight of the sample. Results obtained from dynamic tests are compared with similar tests conducted previously on a lyotropic hydroxypropylcellulose water solution (Harrison and Navard 1999). The results of the comparison provide evidence in support of a connection between the behaviour of the dynamic functions and the optical evolution of the slow band texture. These results suggest that nematic and cholesteric fluids can relax through several different possible mechanisms, each of which results in a periodic band texture following the cessation of shear. Received: 2 March 1999/Accepted: 26 July 1999     

A transient-network model describing the rheological behaviour of concentrated dispersions

Attractive forces acting between particles in dispersions may cause a three-dimensional structure to be built up. A temporary-network model is postulated that describes the rheological behaviour of such systems. Chains of particles are assumed to be created and broken by thermal actions and by applied deformation. The relation between the network structure and the macroscopic stress tensor is deduced. One of the main model features is that no use is made of the common assumption of affinity of the motion of the chain vectors with the gradient of the macroscopic velocity field. Instead, the chain deformations are assumed to depend on the forces acting on them, i.e. their deformations depend on their stiffness and on the applied deformation, whereas fracture of chains may cause stress relaxation in the rest of the network. The chains may behave as highly non-linear springs, whereas the probability that the chains will break in some time interval may be an explicit function of the chain length itself. Integral equations are derived, from which the stress-tensor components can be calculated in any flow experiment, that obeys creeping-flow conditions. Analytical expressions are obtained for the relaxation spectrum of such systems in terms of the microscopic parameters.     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

Dynamic rheological analysis of the gelation behaviour of waxy crude oils

In this work we have characterised the viscoelastic behaviour of paraffin crystals in three different complex crude oils, close to the gelation threshold and after curing the gels under quiescent isothermal conditions, by means of oscillatory shear measurements. An increase in gelation temperature is observed with increasing oils molecular weight. The interactions between wax crystals and the formation of the space-filling network of interlocking wax crystals are thus facilitated by the presence of paraffins with higher molecular weight. The apparent gelation time, obtained from isothermal curing experiments, decreases as the curing temperature was decreased, and it is highly temperature-dependent.The presence and the importance of the ageing of the wax were established under isothermal conditions. It must result from a coarsening of the crystallites presents in the oil and it is, more important, close to the gel point where its full development is very slow taking several days to occur. After ageing the gels, the connective domains or junction zones linking the crystal arrays fail when relatively small strains are applied to the system and the mechanical spectra of the gels reveal an imperfect elastic network, typical rheological characteristics of a particle gel. Despite the compositional differences among the samples, the similarity of their mechanical behaviour is quite remarkable indicating that in all cases the gel-like organisation of the waxy material results from the formation of identical structures in the different oils, which is related not only to the wax content but also to the presence of other material that may reduce the crystallinity of the structure.The low fractal dimensionality obtained indicates elongated substructures. These results, together with the very high elastic modulus obtained at low volume fractions of crystallised material, are indicative of network structures with high degree of porosity: a lattice of wax crystals with large spaces among them filled by the oil and non-precipitated material.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.