Rheology of SiO 2 /(acrylic polymer/epoxy) suspensions. III. Uniaxial elongational viscosity

Uniaxial elongational viscosity of SiO₂/(acrylic polymer/epoxy (AP/EP)) suspensions with various SiO₂ volume fractions (?) in a blend of acrylic polymer and epoxy was investigated at various temperatures (T). The matrix polymer ((AP/EP) blend) contained 70?vol.% of EP. At ?????35?vol.% at T????80°C, where the suspensions were in sol state, strain-hardening behavior was observed. This strain hardening of the suspensions is attributable to the elongational flow properties of (AP/EP) medium. At critical gel state (??=?35?vol.% and T?=?100°C) and in gel state (?????40?vol.%), the elongational viscosity exhibited the strain-softening behavior. These results strongly suggest that the strain softening results from the strain-induced disruption of the network structure of the SiO₂ particles therein.     

Rheology of SiO2/(acrylic polymer/epoxy) suspensions. II. Nonlinear stress relaxation

Large deformation, nonlinear stress relaxation modulus G(t, γ) was examined for the SiO₂ suspensions in a blend of acrylic polymer (AP) and epoxy (EP) with various SiO₂ volume fractions (?) at various temperatures (T). The AP/EP contained 70 vol.% of EP. At ??≤?30 vol.%, the SiO₂/(AP/EP) suspensions behaved as a viscoelastic liquid, and the time-strain separability, G(t, γ)?=?G(t)h(γ), was applicable at long time. The h(γ) of the suspensions was more strongly dependent on γ than that of the matrix (AP/EP). At ??=?35 vol.% and T?=?100°C, and ??≥?40 vol.%, the time-strain separability was not applicable. The suspensions exhibited a critical gel behavior at ??=?35 vol.% and T?=?100°C characterized with a power law relationship between G(t) and t; G(t)?∝?t ^???n . The relaxation exponent n was estimated to be about 0.45, which was in good agreement with the result of linear dynamic viscoelasticity reported previously. G(t, γ) also could be approximately expressed by the relation $G(t,\gamma) \propto t^{-n^{\prime}}$ at ??=?40 vol.%. The exponent n ^′ increased with increasing γ. This nonlinear stress relaxation behavior is attributable to strain-induced disruption of the network structure formed by the SiO₂ particles therein.     

Rheology of carbon black suspensions. I. Three types of viscoelastic behavior

Dynamic viscoelastic properties were investigated for carbon black (CB) suspensions in three suspending media, an alkyd resin (AR), a rosin-modified phenol resin (PR), and a polystyrene/dibutyl phthalate solution (PS/DBP). The affinity of the medium toward the CB particles decreased in this order, and different types of rheological behavior were observed accordingly. In AR having a high affinity, the CB particles were well dispersed to form no agglomerates. These particles exhibited a slow relaxation process attributable to their diffusion. In PR having a moderate affinity, the suspension showed a sol-gel transition with increasing CB concentration, and the critical gel behavior characterized with a power-law relationship between the modulus and frequency (P), G' = G"/tan(n?/2)œPⁿ with n=0.71, was observed at a critical concentration. This behavior suggested formation of a self-similar, fractal agglomerate of the CB particles in PR. These two suspensions in AR and PR exhibited a moderate nonlinearity. In contrast, in PS/DBP, the suspension exhibited a strong nonlinearity attributable to strain-induced disruption of a fully developed three-dimensional (3D) network structure of the CB particles therein. Thus, the structure and rheology of the CB particles changed with the affinity of the suspending medium. This result in turn posed a caution to a conventional structural interpretation that the CB particles in the actually used ink/paint (always) form the fully developed 3D agglomerates.     

Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution

A Hamiltonian framework of non-equilibrium thermodynamics is adopted to construct a set of dynamical continuum equations for a polymer blend with matrix viscoelasticity and a narrow droplet size distribution that is assumed to obey a Weibull distribution function. The microstructure of the matrix is described in terms of a conformation tensor. The variable droplet distribution is described in terms of two thermodynamic variables: the droplet shape tensor and the number density of representative droplets. A Hamiltonian functional in terms of the thermodynamic variables is introduced and a set of time evolution equations for the system variables is derived. Sample calculations for homogenous flows and constant droplet distribution are compared with data of a PIB/PDMS blend and a HPC/PDMS blend with high viscoelastic contrast. For the PIB/PDMS blend, satisfactory predictions of the flow curves are obtained. Sample calculations for a blend with variable droplet distribution are performed and the effect of flow on the rheology, droplet morphology, and on the droplet distribution are discussed. It is found that deformation can increase or decrease the dispersity of the droplet morphology for the flows investigated herein.     

Strain-induced low-frequency relaxation in colloidal DGEBA/SiO2 suspensions

Diglycidyl ether of bisphenol A (DGEBA) is widely exploited as an epoxy resin in adhesives and coatings. In this paper, it is used as an oligomer matrix for silica-filled nanocomposites. Rheological measurements show that the pure matrix obeys power-law relaxation dynamics in the vicinity of the dynamic glass transition of this low-molecular-weight glass former. In the filled systems, a low-frequency relaxation appears additionally to the structural α-process of the matrix. Considering the nanocomposites as Newtonian hard-sphere suspensions at low angular frequencies (or high temperatures), the modified terminal regime behavior of the matrix can be linked to strain-induced perturbations of the isotropic filler distributions. While in the low-frequency regime hydrodynamic stresses relax instantaneously, the Brownian stress relaxation is viscoelastic and can be evidenced by dynamic rheological measurements. At higher angular frequencies, the α-process of the matrix superimposes on the Brownian stress relaxation. In particular, we were able to depict the low-frequency anomaly for concentrated, semi-dilute, and even for dilute suspensions.     

Relaxational interactions and viscoelasticity of polymer melts. Part I: model development

Rheological equations of state for the concentrated solutions and melts of high polymers are derived by applying a structural approach. The dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model. The drag forces describing correlations of motion macromolecules are determined by means of the relaxation equations. The oscillatory shearing flow of the melts is studied on the basis of the equations derived. Expressions for the dynamic modulus and relaxation times are determined. As can be judged from the form of the dependence of the dynamic modulus on frequency, the relaxation time distribution is the same as in real materials. The relaxation spectrum of high polymers has a terminal zone with abnormally long relaxation times.     

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.     

Rheology of carbon black suspensions. III. Sol-gel transition system

Linear viscoelastic properties of carbon black (CB) suspensions with various CB volume fractions () in a rosin-modified phenol resin type varnish (Varnish-1) were investigated at various temperatures (T). The CB/Varnish-1 suspensions exhibited a sol-gel transition on an increase in , and the _gel value at the gelation point decreased with increasing T. This T dependence of _gel, being opposite to the dependence seen for usual gelling systems, can be related to a phenol resin type polymeric component included in the Varnish-1. At low T, this polymeric component appeared to be rather well solvated in the Varnish-1 thereby allowing the gelation due to bare attraction between the CB particles at large . In contrast, at high T, the polymeric component appeared to have been less solvated, as evidence from a moderate failure of the time-temperature superposition of pure Varnish-1 and a decrease of its elasticity (in a shifted frequency scale) with increasing T. This less solvated polymeric component would have been adsorbed on the CB particles, thereby allowing the agglomeration of the particles at small _gel at high T.     

Rheology of carbon black suspensions. II. Well dispersed system

Linear viscoelastic properties were investigated for the suspensions of carbon black (CB) particles having covalently-fused aggregate structures of an average diameter a=120 nm. The suspending medium, an alkyd resin (AR), had a high affinity toward the CB particles, and the aggregates of these particles were well dispersed to form no higher-order agglomerates. Consequently, the suspensions obeyed the time-temperature superposition and their Arrhenius-type activation energy was identical to that of the medium. From comparison of the zero shear viscosity η₀ for the CB suspensions and hard-sphere silica suspensions, an effective volume fraction φ_eff of the CB particles was found to be 2.7 times larger than the bare volume fraction of the particles. The CB particles exhibited a slow relaxation process, and the terminal relaxation time of this process was close to the Peclet time (Brownian diffusion time) evaluated from the aggregate size a and a high frequency viscosity. Furthermore, the terminal relaxation mode distribution of the CB suspensions was well scaled with an intensity factor H_t that was evaluated from the φ_eff in a way utilized for the hard-sphere silica suspensions. These results demonstrated that the slow relaxation in the CB suspensions was dominated by the Brownian diffusion of the CB aggregates, as similar to the situation for the silica suspensions.     

Linear viscoelasticity of thermoassociative chitosan-g-poly(N-isopropylacrylamide) copolymer

Chitosan-g-poly(N-isopropylacrylamide) (chitosan-g-PNIPAM) was synthesized and characterized rheologically in aqueous solutions. The copolymer solution exhibits a thermoassociative behavior in which its elastic response dramatically increases when temperature is above the critical temperature or the association temperature, T _assoc. The copolymer at low concentration shows typical solution property. When the temperature is increased up to the critical temperature, the copolymer exhibits a gel-like characteristic due to the formation of physical cross-links between chitosan backbones through the self-aggregation of PNIPAM side chains. At high concentration, the system exhibits a weak elastic response due to the entanglement of the copolymer at 25°C. As temperature is raised above T _assoc, the system shows a strong elastic behavior due to the formation of additional physical cross-links via the aggregation of PNIPAM side chains. Chitosan-g-PNIPAM offers an attractive associating behavior in aqueous solution at temperature close to the body temperature, thus providing potential applications in pharmaceutical and medical industries.     

Linear viscoelasticity of ZrO 2 nanoparticle dispersions with associative polymers

ZrO₂ nanoparticle dispersions containing associative polymers exhibit two relaxation modes: Maxwellian behavior at high frequency imparted by the associating polymers and a power law spectrum at low frequency generated by the particle dynamics. The timescales and volume fraction dependence of the dispersions reflect weak attractions between particles with adsorbed polymer layers dispersed in a percolated network of associative polymer. The Baxter stickiness parameter extracted from the high frequency viscosity data indicates strong attractions, whereas the high frequency modulus reveals three sources of elasticity: micelle–micelle associations in the solution, rigidity of the particles and adsorbed layer, and adsorbed layer–adsorbed layer interactions. The sol-gel transition of the dispersions occurs around 12–14% particle loading. Comparison with latex dispersions suggests a slower relaxation mode and greater rigidity with the ZrO₂ particles.     

Rheology and morphology of starch/synthetic polymer blends

Corn starch and maleic anhydride functionalized synthetic polymers were melt blended in a Haake twin-screw extruder. The amount of starch in the blends was 60 and 70% by weight. The synthetic polymer used was either styrene maleic anhydride (SMA) or ethylene propylene maleic anhydride copolymer (EPMA). The blends did not exhibit normal thermoplastic behavior; and hence, rheological data was obtained by extrusion feeding the material through a slit die or cylindrical tube viscometer. The starch/SMA blends were extruded through a slit viscometer with a 45% half entry angle, while the starch/EPMA blends were extruded through a cylindrical tube viscometer with a half entry angle of 37.5°. For the blends, data could be obtained at low to moderate shear rates (10< _app<200s^–1). At higher shear rates, blends exhibited slip and/or degradation of starch. The viscosity of the blends exhibited shear-thinning properties. Regrinding and re-extruding through the viscometer a second time showed a significant reduction in shear viscosity for starch/SMA blends. Gel permeation chromatography data indicated that starch macromolecules degraded upon successive extrusion. Extensional viscosity, as estimated from entrance pressure drop method for starch/EPMA blends showed stretch thinning properties. Regrinding and re-extruding showed that the samples were more sensitive to changes in extensional viscosity as observed from the Trouton ratio versus extension rate plot. Optical microscopy showed the presence of starch granules after melt blending, the size of which was related to the torque (or stress) generated during extrusion. The higher the torque, the smaller the size of the starch granules. Successive extrusion runs reduced the number of unmelted granules.Nomenclature A,B Constants associated with power law fluids (Pa s^{m or n}) - e Entrance correction - H Height of slit die (m) - m, n Flow behavior index in shear and extension flow respectively - P _s Shear component of the entrance pressure drop (Pa) - P _e Extensional component of the entrance pressure drop (Pa) - Q volumetric flow rate (m³S^–1) - R _o radius of barrel exit (m) - R ₁ radius of cylindrical die (m) - T _r Trouton ratio - w width of slit die (m) - pressure gradient (Pam^–1) - half die entry angle - P _en Entrance Pressure Drop (Pa) - apparent extension rate (s^–1) - apparent shear rate (s^–1) - _w wall shear stress (Pa) - first normal stress difference in uniaxial extension (Pa)     

Rheology of particle suspensions in viscoelastic media. Wood flour-polypropylene melt

The dynamic mechanical behavior of suspensions of wood flour in polypropylene (PP) melts was investigated at varying filler concentrations. The main observed features were related to the viscoelastic nature of the polymer and to the filler aggregation, where the process of formation and destruction of particle clusters is governed by the polymer chain dynamics. The effect of the wood flour particles at low and large deformations was analyzed. The sample containing a wood flour concentration of 50% (by weight) showed a solid like behavior at low frequencies and was identified as the sample closer to a liquid-solid transition (LST). The values of the Newtonian viscosity obtained from sinusoidal oscillations at low frequencies were related to the concentration of filler in the suspensions. Moreover, a filler concentration scaling was found, that allows to obtain a master curve using the neat polymer as the reference and from which it is possible to calculate the dynamic mechanical behavior of all the suspensions. Apparently, for this system, the relaxation mechanisms of the neat polymer are not changed by the presence of the filler. However, the corresponding relaxation times are increased as a function of the filler concentration.     

Rheology of carbon black suspensions. V. Heat-induced gelation and its reversibility

Linear viscoelastic properties of carbon black (CB) suspensions in a mixture of a rosin-modified phenol resin-type varnish (Varnish-1)/an alkyd resin-type varnish (Varnish-2), which exhibited a sol?Cgel transition on an increase in CB concentration, were investigated from 30°C to 80°C. The viscoelastic properties were reversible from 30°C to 60°C. In contrast, at temperatures above 60°C, the storage (G??) and loss (G??) moduli were irreversible and increased significantly with increasing temperature. This increase in the moduli is due to a change of the dispersion state to agglomerated state by heating. The agglomerated state was held, when the suspensions were lowered at 30°C. However, the G?? and G?? recovered to the original values upon shearing. This heat-induced gelation should be a universal feature for suspensions of weakly attractive particles. The temperature and shearing histories of the suspensions were discussed in relation to adsorption of polymeric component in the varnish on the CB particles.     

The rheology of suspensions of vinylon fibers in polymer liquids. I. Suspensions in silicone oil

Summary The steady shear flow properties of suspensions of vinylon fibers in silicone oil were measured by means of a cone-plate type rheometer. Three kinds of vinylon fibers used had no distributions of length and were more flexible than glass fibers and the like. The content of the fibers ranged from 0 to 7 wt.%. Shear viscosity, the first normal-stress difference, yield stress, and relative viscosity were discussed. Shear viscosity and relative viscosity increased with the fiber concentration and the aspect ratio, and depended upon the shear rate. The applicability of Ziegel's equation of viscosity for fiber suspensions was investigated. The first normal-stress difference increased with the fiber concentration, aspect ratio, and shear rate and its relative increase was much larger than for shear stress and viscosity depending on the properties of the characteristic time, The yield stress could be determined by Casson plots for large aspect ratio fiber suspensions even in low concentration comparing with the suspensions of spherical particles or powder. The influence of the flexibility of the fibers for the rheological properties of the fiber suspensions can not be ignored.With 12 figures and 2 tables     

Spatially periodic suspensions of convex particles in linear shear flows. II. Rheology

Following the purely kinematical developments of Part 1, a rigorous analysis is presented of the “almost” time-periodic low Reynolds number hydrodynamics of a spatially periodic suspension of identical convex particles in a Newtonian liquid undergoing a macroscopically homogeneous linear shear flow. By considering the case of a single particle within a unit cell of the instantaneous spatially periodic configuration, the quasistatic dynamical analysis of this infinite-particle system is effected in much the same way as for a single particle suspended in an unbounded fluid. This is accomplished via the introduction of a partitioned hydrodynamic Stokes resistance matrix, linearly relating the force, couple and stresslet on the particle in the unit cell to the translational and rotational particle-(mean) suspension slip velocities and the mean rate-of-strain of the suspension. In contrast with the unbounded fluid case for a given geometry of the individual particles, the (purely geometric) elements of the resistance matrix depend upon the instantaneous lattice configuration.These dynamic quasistatic calculations for a given instantaneous lattice conformation, in particular that for the stresslet, are then appropriately averaged over both space and time for the class of almost time-periodic, lattice-reproducing, flows discussed in Part I. (In actually performing the time average, an important distinction is drawn between the ergodic and deterministic shear processes whose kinematical basis was laid in Part I.) In turn, this averaged dynamical information is translated into knowledge of the rheological properties of the macroscopically homogeneous suspension.A rigorous asymptotic, lubrication-theory analysis is performed during the course of an illustrative calculation of the rheological properties of a concentrated suspension of almost-touching spheres in a simple shear flow. Contrary to the findings of a previous heuristic treatment of this same lubrication-theory problem—one that ignores evolutionary variations in the instantaneous geometrical configuration of the spatially periodic suspension as the shear proceeds—the time-average properties of the suspension are found to be nonsingular in the limit.Finally, brief comments are offered on potential extensions of the scheme to include nonlinear phenomena, such as nonNewtonian fluids and inertial effects.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table