Electrorheological properties of PDMS/carbon black suspensions under shear flow

Suspensions of polydimethylsiloxane (PDMS) containing low amounts (1 wt.% or less) of a highly conducting carbon black (CB) filler are rendered conductive and exhibit electrorheological (ER) responses under shear flow when exposed to an externally applied AC electric field. The presence of columnar structures, consisting of CB particles aligned in the direction of the electric field is evidenced through optical microscopy experiments. The appearance of yielding behavior and positive ER response, manifested by an increase in the viscosity of the suspensions, depend strongly on the filler loading, strength of the electric field, magnitude of the shear field, and viscosity of the medium. The responses are stronger at low filler loadings, below the percolation threshold, and at very low shear rates, where the microstructure of the dispersed phase remains intact. At higher shear rates, corresponding to Mason numbers (Mn) above 1, the structure is disrupted and thus does not contribute to the observed shear stress. The rheological characterization is accompanied with admittance measurements, to demonstrate that the induced polarization forces between particles lead to the formation of electrically conductive structures within the polymer matrix. A critical comparison with the qualitative predictions based on the theory of induced dipole–dipole interactions shows that the theory is valid for these dilute systems.     

Shear viscosity of polybutyleneterephthalate/liquid crystal polymer blends

Viscosity measurements have been carried out on blends of polybuty-leneterephthalate (PBT) and a liquid crystalline copolyesteramide (LCP). The flow curves of the blends with LCP content larger than 20%, show a behavior similar to that of the pure LCP, with a rapid rise of the viscosity at low shear rates. The viscosity-composition curves exhibit a deep minimum at low LCP content which may be mainly attributed to the lack of interactions between the two phases.     

Electrorheology of dielectric liquids

Dielectric liquids that show striking electrorheological (ER) effects are formulated by controlling the conductivity. Although the viscosity is increased on the application of a d.c. field, the flow of electrified fluids is Newtonian in the plain electrodes with smooth surfaces. When the liquids are sandwiched between the electrodes with flocked fabrics, the viscosity behavior is converted from Newtonian to shear-thinning flow. In electric fields, the convective flow is induced over the system due to the electrohydrodynamic(EHD) effect. The interactions between EHD convection and external shear give rise to the additional energy dissipation and in turn the increase in viscosity. The ER effects of simple liquids are very attractive in application to new fluid devices.     

Isothermal elongational behavior of liquid-crystalline polymers and LCPs based blends

The rheological behavior of two flexible thermoplastics, Nylon-6 (Ny) and bisphenol-A polysulfone (PSu), and two wholly aromatic liquid crystalline polymers, Vectra-A900 (VA) and Vectra-B950 (VB), as well as that of Ny/VB and PSu/VA blends with 10% LCP, has been investigated by the use of capillary viscometers equipped with cylindrical dies having different length-to-diameter ratios. The elongational viscosity of all materials was calculated, from the results of isothermal measurements carried out at 290°C, by means of the Cogswell's analysis, based on the estimation of the pressure drop due to the converging flow at the die inlet. The behavior in elongational flow was compared with the rheological behavior in shear flow conditions. It was found that the elongational viscosities of VA and VB are very large and account for a fairly marked pressure drop at the die entrance, due to the orientation of the LCP domains taking place in the converging flow zone. For these materials, the ratio of the elongational viscosity to the Newtonian shear viscosity is up to two orders of magnitude higher than the value expected on the basis of the Trouton rule. For the flexible resins, the Trouton ratio is 3 and ca. 3–10, are common values for high molar mass linear polymers. The addition of 10% LCP into the flexible resins strongly increases their elongational viscosity and makes the blends resemble neat LCPs in their extensional flow behavior. In shear flow, on the contrary, the addition of LCP was shown to induce a marked reduction of the melt viscosity, even when, as for the Ny/VB blend, the LCP is more viscous than the matrix.     

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

Viscoelasticity of a dielectric fluid in nonuniform electric fields generated by electrodes with flocked fabrics

The rheological behavior of a dielectric fluid is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabrics. Although no electrorheological (ER) effects are observed in uniform fields between metal electrodes with smooth surfaces, striking increases in viscosity and elastic response are induced by the electrode with flocked fabrics. The presence of flocked fabrics does not have a significant effect on the fluid rheology without electric fields. The ER behavior and current density are influenced by the fiber length even at a constant field strength. When a very small amount of fine particles is introduced in the electrified fluid without shear, we can see the rapid and large-scale motion of particles between the tips of fibers and plate electrode. In high DC fields, the Coulomb force acting on a free charge often gives rise to the secondary motion of fluid. The local motion of fluid in high electric fields is refereed to as electrohydrodynamic (EHD) convection. The additional energy may be required to change the periodic patterns of EHD convection by forced shear. Therefore, the ER effect demonstrated by the modification of electrode with flocked fabrics can be attributed to a combined effect of EHD convection and external shear. Received: 10 March 1998 Accepted: 1 June 1998     

Polypropylene-polyethylene blends

Summary Die swell behaviour and morphology of melt blends of isotactic polypropylene (PP) and high density polyethylene for pure polymers and blends with 25, 50 and 75 weight % PP are described in the present study. A light interference contrast microscopy technique was used for the morphological characterization of melt blends and extrudate samples of the blends obtained with an Instron capillary rheometer. The results indicate that the domains from blends where the dispersed phase has higher viscosity than the continuous phase remain as continuous domains in the extrudate whereas domain destruction takes place when blends where the continuous phase has the higher viscosity are extruded.The die swell behaviour as well as the fiber forming properties of extrudates of melts having unstable domains extruded at high shear stresses resemble the behaviour of homopolymers, whereas samples with stable domains are significantly different, die swell increases with temperature at constant shear stress and stable fibers cannot be obtained after necking.With 10 figures and 1 table     

Electrorheology of dilute suspensions induced by hydrodynamic instability

The viscosity behavior in electric fields was measured for dilute suspensions of p-[perfluoro(2-isopropyl-1,3-dimethyl-1-butenyl)oxy]benzoic acid particles (PFNA) in silicone oils. The application of electric fields causes a viscosity increase in a wide range of shear rates. Since the electrorheological (ER) effect is much stronger at low shear rates, the flow becomes shear-thinning. However, contrary to conventional ER suspensions which are reversibly converted between Newtonian fluids and Bingham solids, the PFNA suspensions are fluids even in electric fields. When the particle concentration is increased to 5 wt.%, the ER effect reaches saturation. Further increase does not contribute to additional viscosity enhancement. These results cannot be explained through the chain formation mechanism established for conventional systems. After the ER experiments, the bob surface of the rheometer is covered with several stripes of aggregated particles. Although the strength of electric and shear fields is constant in the rheometer, the periodic structure may be formed in the flow of electrified suspensions. When a dielectric liquid is subjected to high electric fields, the secondary motion of liquid can be induced by the Coulomb force acting on free charge. The electrohydrodynamic (EHD) convection is responsible for the periodic distribution of particles concentration. The ER effect of PFNA suspensions may be generated by a combined effect of EHD convection and external shear.     

Uniaxial extensional flow behavior of immiscible and compatibilized polypropylene/liquid crystalline polymer blends

In this work liquid crystalline polymer (LCP) and thermoplastic (TP) blends with and without compatibilizer were studied with respect to their elongational flow behavior, under uniaxial extensional flow. This knowledge is important because in processes involving dominantly extensional deformations, like the case of the formation of the LCP fibrillation, transient extensional flow properties become more important than transient or steady-shear properties. In systems characterized by disperse phase morphologies (10 and 20 wt%) the LCP acts as a plasticizer, decreasing the viscosity of the system and increasing its durability with respect to that of the matrix. On the other hand, for a system in which a co-continuous morphology is present (40 wt% LCP) fibrils and droplets deformation occurs simultaneously, leading to a much higher strain hardening and durability. Moreover, the addition of compatibilizers to the blends gives rise to an increase of the strain hardening and to a decrease of the durability, which is in accordance with the mechanical properties, namely a higher Young’s modulus and lower elongation at break, in comparison with noncompatibilized systems.     

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.     

Specific rheology – morphology relationships for some blends containing LCPs

For the blend melts of isotropic polysulfone (PSF) and LC polyester (PES), differing in viscosity more than 10 times, the flow curves with maxima were observed in cone and plate geometry. The low shear rate branch is located near the PSF flow curve, and the high shear rate branch is close to the PES flow curve. At high strains, the formation of the ring-like morphology of the blend sample, accompanied by appearance of maximum on flow curve, was registered. The scaling analysis of the reasons for the ring morphology formation was based on stretching of the large, low-viscous LC droplet, embedded to the high-viscous polymer matrix, in a homogeneous shear field. It was shown that, if the critical Taylor radius is not exceeded, the droplet may form the closed torus. Under strong flows, the PSF melt manifests the “spurt effect”, consisting of a drastic increase of the shear rate when the critical value of the shear stress is reached. The pattern of the blend flow curves with maxima may be explained by a vanishing PSF input to the total shear stress, inherent for blends, while the PES melt continues to be in a liquid state and, consequently, is responsible for the blend viscosity at the high shear rates. The presence of regular heterogeneities in the blend in the form of LC rings may initiate the rupture of the entanglements network of the matrix PSF (close to LC rings) under strong shear flows. The appearance of the low-viscous “cracks” at the critical shear stress will diminish the contribution of the PSF to the blends rheological response. Received: 20 April 1999 Accepted: 28 January 2000     

Shape and structure recovery of an LCP droplet under a large step strain: observation and stress calculation

Shape recovery of a droplet of liquid crystalline polymer (LCP) hydroxypropylcellulose in a matrix of poly(dimethyl siloxane) subjected to a step shear strain has been studied via optical microscopy. Just after application of a large strain, the LCP droplet shape is flat ellipsoid, and then the droplet takes cylindrical shape and band texture perpendicular to the flow direction appears. The band texture fades away before emergence of poly-domain structure. In the final process with the shape of spheroid, poly-domain structure recovers very slowly. Except for the final process, the shape change is identical with that of isotropic droplet at strains smaller than 3, when the LCP viscosity in Region II is taken as an equivalent viscosity for normalization. For a 20:80 blend, the excess relaxation modulus is calculated based on the Doi-Ohta theory, taking account of the distribution of droplet size and compared with experimental modulus data.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

A parameter investigation of shear-induced coalescence in semidilute PIB–PDMS polymer blends: effects of shear rate, shear stress volume fraction, and viscosity

In this work, drop coalescence of polymer blends under shear flow in a parallel flow apparatus was investigated by optical sectioning microscopy. In each experiment, shear rate was set at values low enough to avoid any break-up phenomena. The time evolution of the drop size distribution was determined by motorized sample scanning and iterative acquisition of stacks of images along sample depth. Drop size and location in the acquired images was found by automated image analysis techniques. A systematic experimental campaign to investigate the effects of shear rate (in the range 0.1–0.5 s⁻¹), volume fraction (2.5–10%), and viscosity of the two phases (3–63 Pa s) at different viscosity ratio (0.1–2.3) was carried out. By comparing data from different experiments, it was found that at any strain value, the average drop size decreases monotonically with the shear stress, calculated as the product of shear rate and matrix viscosity. Furthermore, the coalescence rate slowed down with increasing viscosity ratio. Overall, these results provide an extensive set of data, which can be used as a benchmark for modeling shear-induced coalescence in polymer blends.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Viscosity change in aqueous hectorite suspension activated by DC electric field

The change in the viscosity of deionized aqueous hectorite suspensions by applying an electric field was investigated. The deionized suspensions had low viscosity, which was almost the same as that of its solvent, water. Upon applying a DC electric field of the order of a few volt per millimeter to the deionized suspension, the viscosity started to increase gradually and reached a constant value that was high enough relative to the original value. Regarding the mechanism of the electrically induced stress increase, it is highly plausible that a three-dimensional network structure formed under the electric field due to a deformation of the electrical double layer.     

Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

In this paper, the problems of non-slipping contact, non-slipping adhesive contact, and non-slipping adhesive contact with a stretched substrate are sequentially studied under the plane strain theory. The main results are obtained as follows:(i) The explicit solutions for a kind of singular integrals frequently encountered in contact mechanics (and fracture mechanics) are derived, which enables a comprehensive analysis of non-slipping contacts. (ii) The non-slipping contact problems are formulated in terms of the Kolosov–Muskhelishvili complex potential formulae and their exact solutions are obtained in closed or explicit forms. The relative tangential displacement within a non-slipping contact is found in a compact form. (iii) The spatial derivative of this relative displacement will be referred to in this study as the interface mismatch eigenstrain. Taking into account the interface mismatch eigenstrain, a new non-slipping adhesive contact model is proposed and its solution is obtained. It is shown that the pull-off force and the half-width of the non-slipping adhesive contact are smaller than the corresponding solutions of the JKR model (Johnson et al., 1971). The maximum difference can reach 9% for pull-off force and 17% for pull-off width, respectively. In contrast, the new model may be more accurate in modeling the non-slipping adhesion. (iv) The non-slipping adhesions with a stretch strain (S-strain) imposed to one of contact counterparts are re-examined and the analytical solutions are obtained. The accurate analysis shows that under small values of the S-strain both the natural adhesive contact half-width and the pull-off force may be augmented, but for the larger S-strain values they are always reduced. It is also found that Dundurs’ parameter β may exert a considerable effect on the solution of the pull-off problem under the S-strain.These solutions may be used to study contacts at macro-, micro-, and nano-scales.     

On constitutive equations for electrorheological materials

Constitutive equations for electrorheological (ER) fluids have been based on experimental results for steady shearing flows and constant electric fields. The fluids have been modeled as being rigid until a yield stress is reached. Additional stress is then proportional to the shear rate. Recent experimental results indicate that ER materials have a regime of solid-like response when deformed from a rest state. They behave in a viscoelastic-like manner under sinusoidal shearing and exhibit time-dependent response under sudden changes in shear rate or electric field. In this work, a constitutive theory for ER materials is presented which accounts for these recent experimental observations. The stress is given by a functional of the deformation gradient history and the electric field vector. Using the methods of continuum mechanics, a general three-dimensional constitutive equation is obtained. A sample constitutive equation is introduced which is then used to determine the response of an ER material for different shear histories. The calculated shear response is shown to be qualitatively similar to that observed experimentally.     

Rheological properties of disperse systems at low shear stresses

Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions.Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity.At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent.These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.     

Stress relaxation behavior of co-continuous PS/PMMA blends after step shear strain

Stress relaxation probing on the immiscible blends is an attractive route to reveal the time-dependent morphology–viscoelasticity correlations under/after flow. However, a comprehensive understanding on the stress relaxation of co-continuous blends, especially after subjected to a shear strain, is still lacking. In this work, the stress relaxation behavior of co-continuous polystyrene/poly(methyl methacrylate) (50/50) blends with different annealing times, strain levels, and temperatures was examined under step shear strain and was correlated with the development of their morphologies. It was found that co-continuous blends display a fast relaxation process which corresponded to the relaxation of bulk polymer and a second slower relaxation process due to the recovery of co-continuous morphology. The stress relaxation rates of co-continuous blends tend to decrease due to the coarsening of instable co-continuous structure during annealing. Furthermore, the stress relaxation of the co-continuous blends is strongly affected by the change of viscosity and interfacial tension caused by the temperature. The contribution of morphological coarsening, viscosity, and interfacial tension variation on the stress relaxation behavior of co-continuous blends was discussed based on the Lee–Park model and time–temperature superposition principle, respectively.