Rheological Modeling of Dispersion System of Nano/Microsized Polymer Particles Considering Swelling Behavior

Rheological behavior of dispersion system containing nano/microsized cross-linked polymer particle was studied considering particle hydration and swelling. Viscosity of the dispersion system depends on swelling kinetics of polymer particles. Under shear flow, dispersion of swollen polymer particles is shear thinning. According to experimental results, kinetics of particle swelling and hydration was described well by second-order kinetic equation. Relational expression between equilibrium particle size and influencing factors of swelling such as salt concentration and temperature was presented. Assume that swollen polymer particles are uniform and have a simple core-shell structure, interacting through a repulsive steric potential. The rheological modeling of such dispersion system at low shear rate was presented using the concept of effective volume fraction, which depends on swelling kinetics and interparticle potential. Cross model was introduced to describe shear-thinning behavior. The viscosity equation allows correlation of experimental data of relative viscosity versus shear rate or hydration time; accounting for effect of temperature and salt concentration on viscosity. Predictions of the model have a good agreement with experimental results.     

On the viscosity of composite suspensions of aluminum and ammonium perchlorate particles dispersed in hydroxyl terminated polybutadiene--New empirical model

The rheological properties of fuel suspensions with various solid loadings up to close their maximum packing fraction and suspending media having different viscosities are investigated using the rotational viscometer at relatively low shear rates in which suspensions behave as Newtonian fluids. Aluminum (Al) and ammonium perchlorate (AP) particles are major solid components of any solid fuel system which should be distributed uniformly inside a polymeric binder based on hydroxyl terminated polybutadiene (HTPB). The experimental data generated in this investigation indicates that the relative viscosity of the suspensions is independent of viscosity of polymer binder, but in addition to solid content, geometrical aspects of the solid particles affect strongly the relative viscosity of suspensions. Maximum packing fraction of filler is found to be suitable quantitative measure of filler characteristics such as size, size distribution, shape and structure. Consequently, it is revealed that the relative viscosity of fuel suspension is a unique function of reduced volume fraction (Phi). Based on analogy of viscosity enhancement of reactive resin with cure conversion and suspension with filler content, an empirical model with two adjustable parameters originated from resin gelation model is suggested. According to this model and experimental results obtained in this investigation, a generalized model is proposed to describe the relative viscosity as a function of solid content in which the adjustable parameters are found to be general constants. The generalized model which is expressed as mu(r) = (1-Phi)(0.3 Phi-2) is found to be quite accurate to predict the experimental data. Furthermore, the applicability and accuracy of the generalized model are evaluated using the viscosity data of some suspension systems reported in the literature.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

Analysis of the debonding process in polypropylene model composites

Polypropylene (PP) model composites were prepared using cross-linked PMMA particles with a very narrow particle size distribution as filler in order to study the micromechanical processes, which take place during deformation. Composites containing a commercial CaCO₃ filler with a broad particle size distribution were also prepared and studied for comparison. The filler loading of the composites was changed from 0 to 0.3 volume fraction in 0.05 volume fraction steps. Measurements of acoustic emission signals during the elongation of PP/PMMA model composites allowed us to assign the debonding process, including its initiation, unambiguously to a well-defined section of the stress vs. strain curve. The number and intensity of the acoustic signals detected during the deformation of the matrix polymer and the composite, respectively, differed considerably, which made possible the separation of the various micromechanical deformation processes occurring in them. At low extensions the composite is deformed elastically, then debonding takes place in a very narrow deformation range, followed by the plastic deformation of the matrix. At small particle content debonding occurs at relatively low stresses, which differ significantly from the yield stress. Considerable plastic deformation of the matrix begins at the yield point. At larger filler content debonding and shear yielding occur simultaneously. Micromechanical deformation processes cannot be separated as clearly in composites prepared from the commercial CaCO₃ filler with a broad particle size distribution. The debonding of particles with different size occurs in a wide deformation range because of the particle size dependence of debonding stress. The analysis of characteristic values derived from acoustic emission experiments proved that the interacting stress fields of neighboring particles influence the deformation process and that even large particles may aggregate or at least associate at large filler content.     

Model filled rubber. II. Particle composition dependence of suspension rheology

Monodisperse size colloidal particles varying in chemical composition were synthesized by emulsifier‐free emulsion polymerization. Using a stress‐controlled rheometer, the rheological behavior of colloidal suspensions in a low molecular weight liquid polysulfide was investigated. All suspensions exhibited shear thinning behavior. The shear viscosity, dynamic moduli, and yield stress increased as interactions between particles and matrix increased. The rheological properties associated with network buildup in the suspensions were sensitively monitored by a kinetic recovery experiment. We propose that interfacial interactions by polar and hydrogen bonding between particles and matrix strongly promote affinity of matrix polymer to the filler particles, resulting in adsorption or entanglement of polymer chains on the filler surface. A network structure was formed consisting of particles with an immobilized polymer layer on the particle surface with each particle floc acting as a temporary physical crosslinking site. As the interfacial interaction increases, the adsorbed layer thickness on the filler particles, hence, the effective particle volume fraction, increases. As a result, the rheological properties were enhanced in the order PS < PMMA < PSVP. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 815–824, 1999     

The Viscosity of Solutions of Poly(propylene imine) Dendrimers in Methanol

The viscosity of solutions of poly(propylene imine) dendrimers in methanol has been determined. An Ubbelohde and a low-shear rotational viscometer have been used. The viscosity was Newtonian for every concentration and shear rate used. The value of the Huggins coefficient indicates soft sphere behavior. The viscosity of the lower generations as a function of the volume fraction can be described with a single exponent, where the exponent is comparable to the intrinsic viscosity. The viscosity of the 4th and 5th generation dendrimers shows a stronger increase from a volume fraction of about 0.15 to 0.30. This increase is much smaller than that expected, using the Krieger-Dougherty formula for hard spheres with the hydrodynamic radius determined from the intrinsic viscosity. This smaller increase and the small value of the Huggins coefficient are interpreted in terms of a breakdown of the solvation layer. At a volume fraction of 0.3 the dendrimers, using the radius of gyration as the radius, start to touch each other. From the dependence of the viscosity on the concentration and the dependence of the viscosity on the molar weight, it can be concluded that dendrimers do not interpenetrate. It is concluded that they deform (collapse). Copyright 2001 Academic Press.     

Rheology of polystyrene latexes with adsorbed and free gelatin

The rheology of monodisperse polystyrene latex particles of two different particle radii (26 and 67 nm) has been studied with a range of concentrations of the polyampholyte gelatin. Gelatin contributes to the rheology by adsorption to the particles and by thickening the continuous phase. High viscosities and strong shear thinning are measured for low volume fractions of latex. A procedure is presented to deconvolute the effects of free and bound gelatin by applying simple hard-sphere models. This procedure allows us to estimate the effective size of the gelatin-covered particles as well as the continuous-phase gelatin concentration and viscosity. The layer thicknesses from rheology agree well with those from PCS. The effect of varying particle volume fraction, ionic strength, pH and gelatin and surfactant concentration on the rheology of these suspensions is presented. For the smaller latex, the adsorbed layer occupies a greater fraction of the effective volume. Increasing free polymer concentration reduces the adsorbed-layer thickness. The reduced critical shear stress increases with the suspension viscosity for suspensions of the 26 nm latex but is constant for the 67 nm latex. At very high shear (>2000 s⁻¹), the suspensions show excess shear thinning over that expected from a hard-sphere model. This excess thinning is attributed to deformation of the adsorbed gelatin layer under high shear stress and interpreted in terms of an empirical interparticle potential.     

Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging

The steady-shear viscosity, dynamic viscoelasticity, and stress relaxation behavior were measured for suspensions of silica nanoparticles dispersed in aqueous solutions of poly(ethylene oxide) (PEO). The suspensions of silica with diameters of 8-25 nm show striking shear-thickening profiles in steady shear and highly elastic responses under large strains in oscillatory shear. Since the silica particles are much smaller than the polymer coils, one molecule can extend through several particles by intrachain bridging. Each polymer coil may remain isolated as a floc unit and the silica particles hardly connect two flocs. Therefore, the flow of suspensions is Newtonian with low viscosity at low shear rates. When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. The shear-thickening flow may arise from the elastic forces of extended bridges. But, the polymer chain is easily detached from particle surface by thermal energy because of large curvature of particles. As a result, the network structures are reversibly broken down in a quiescent state and the suspensions behaves as viscoelastic fluids with the zero-shear viscosity.     

Rheological properties of deionized Chinese ink

Rheological properties for Chinese ink in exhaustively deionized aqueous media were carefully examined. In the steady shear measurement, the shear viscosities of the ink could be well explained by considering the “effective” volume fraction of the particles in the ink including the electrical double layers and by using Einstein's equation for dilute suspension viscosity, when the particle volume fraction was substantially low. In the case that the volume fraction was higher, the shear viscosities showed extremely higher than those from Einstein's prediction, though the ink remained a Newtonian liquid. In the stress-strain measurement, the shear moduli were observed at strain smaller than 0.2. The “weak” aggregation among the particles in the ink under no shear or low shear rates was supported. It should be noted that the glue in the suspension plays an important role for the good liquidity of the ink and for the “weak” bridges among the particles resulting its good dispersion stability.     

Dynamic yielding, shear thinning, and stress rheology of polymer-particle suspensions and gels

The nonlinear rheological version of our barrier hopping theory for particle-polymer suspensions and gels has been employed to study the effect of steady shear and constant stress on the alpha relaxation time, yielding process, viscosity, and non-Newtonian flow curves. The role of particle volume fraction, polymer-particle size asymmetry ratio, and polymer concentration have been systematically explored. The dynamic yield stress decreases in a polymer-concentration- and volume-fraction-dependent manner that can be described as apparent power laws with effective exponents that monotonically increase with observation time. Stress- or shear-induced thinning of the viscosity becomes more abrupt with increasing magnitude of the quiescent viscosity. Flow curves show an intermediate shear rate dependence of an effective power-law form, becoming more solidlike with increasing depletion attraction. The influence of polymer concentration, particle volume fraction, and polymer-particle size asymmetry ratio on all properties is controlled to a first approximation by how far the system is from the gelation boundary of ideal mode-coupling theory (MCT). This emphasizes the importance of the MCT nonergodicity transition despite its ultimate destruction by activated barrier hopping processes. Comparison of the theoretical results with limited experimental studies is encouraging.     

高分子/棒状纳米粒子复合物的分子动力学模拟

采用非平衡态分子动力学模拟研究了剪切场下棒状纳米粒子对高分子基体的结构、 动力学和流变性质的影响. 通过比较多种体积分数(0.8%~10%)的纳米复合物及纯熔体的模拟结果发现, 随着纳米粒子的增加, 高分子链的扩散和松弛逐渐受到抑制, 而链尺寸几乎保持不变. 从Weissenberg number(W_i)角度看, 在剪切流场下, 高分子链的结构性质(如归一化的均方回转半径、 回转张量和取向抑制参数)几乎与纳米粒子的体积分数无关, 而高分子链的Tumbling运动受到抑制. 研究还发现, 纳米复合物与纯熔体的剪切黏度曲线趋势基本一致, 即W_i=1将曲线分为平台区和剪切变稀区. 纳米棒的加入仅定量地改变了流体的剪切黏度.     

Miscibility of small colloidal spheres with large polymers in good solvent

Nearly athermal colloid-polymer mixtures were studied in the "protein limit." A fluid-fluid transition was observed in mixtures of stearyl-alcohol-coated silica particles and large polystyrene coils in toluene. The ratios of the polymer radius of gyration to the particle radii were q=4.1 and q=5.2. The binodal curves and the critical points were determined. Turbidity measurements and analysis for one set of particles allowed the systems to be mapped onto hard sphere-polymer mixtures. A comparison with recent predictions for the miscibility of model mixtures shows that the experimental binodals lie between the two extreme results for ideal and interacting polymers. The critical colloid volume fraction is also found to decrease with increasing size ratios.     

Rheology of a reversible supramolecular polymer studied by comparison of the effects of temperature and chain stoppers

The rheology of a reversible supramolecular polymer is studied by comparing the effects of an increase in temperature and the addition of chain stoppers. The dependence of the zero-shear viscosity and the terminal relaxation time on temperature is exponential, and the activation energy for viscous flow can be calculated. Above a critical stopper fraction, power laws describe the stopper dependence of the viscosity and relaxation time. A simple model for the effect of the addition of chain stoppers on the average degree of polymerization adequately describes the results. A comparison of flow curves at several temperatures and stopper fractions reveals considerable differences between solutions with the same zero-shear viscosity. These are mainly associated with differences in the terminal relaxation time. A mechanism of shear-induced alignment and subsequent elongation of chains is proposed, with which the experimental results are consistent.     

Effect of Particle Size Distribution on the Rheology of Dispersed Systems

The rheological properties of aqueous polystyrene latex dispersions from three synthetic batches, with nearly the same z-average particle sizes, 400 nm, but varying degrees of polydispersity, 0.085, 0.301, and 0.485, respectively, were systematically investigated using steady-state shear and oscillatory shear measurements. The particles were sized with photon correlation spectroscopy and transmission electron microscopy and were stabilized sterically with PEO–PPO–PEO triblock copolymer (Synperonic F127). Results from steady-state shear measurements show that the viscosities of the systems exhibit shear-thinning behavior at high solid fractions. However, the degree of shear thinning depends on the breadth of particle size distribution, with the narrowest distribution suspension exhibiting the highest degree of shear thinning. The Herschel–Bulkley relationship best describes the flow curves. The relative viscosities as a function of volume fraction data were compared, and it was found that the broadest distribution suspension had the lowest viscosity for a given volume fraction. In addition, the data were fitted to the Krieger–Dougherty equation for hard spheres. A reasonable agreement of theory with experiment is observed, particularly and surprisingly for the very broad distribution. However, when the contribution to the volume due to the adsorbed polymer layer is considered, the agreement between experiment and theory becomes closer for all the suspensions, although the agreement for the broad distribution suspension is now worse. Fitting the Dougherty–Krieger theory to the experimental data based on our experimental maximum packing fractions gives very good agreement for all the systems studied. From oscillatory shear measurements, the moduli were obtained as a function of frequency at various latex volume fractions. The results show general change of the dispersions from viscous (G" > G′) at low volume fractions (0.25–0.30) to moderately elastic (G′ > G") at moderately high volume fractions (0.41–0.45). The change at this concentration level is likely due to some compression and interpenetration of the stabilizing polymer chain at the periphery, indicating the dominance of the interparticle forces. Overall, the very broad distribution was found to have the lowest elastic modulus for a given volume fraction.     

Normal stress and shear stress in a viscoelastic liquid under steady shear flow: Effect of molecular weight heterogeneity

Under steady shear flow, the normal stress and the shear stress in both dilute and concentrated solutions of monodisperse poly-α-methylstyrenes and their blends were measured. It was confirmed that the molecular theories of Rouse and Zimm extended to concentrated solutions can explain the relation between the zero-shear normal stress coefficient and the zero-shear steady-flow viscosity for both monodisperse and polydisperse systems. Shear-rate dependence of steady-flow viscosity can be understood fairly well by the molecular entanglement concept proposed by Graessley so long as the polymer is monodisperse or the amount of the higher molecular weight component is high. However, zero-shear viscosity of blended systems cannot be explained quantitatively by the theory of Graessley. The shear-rate dependence of steady-state compliance of blended systems was also observed, and it can well be explained by the theory of Tanaka, Yamamoto, and Takano which interpreted the shear rate-dependent steady-state compliance in terms of the relaxation time spectrum and its variation with shear rate.     

A novel procedure able to predict the rheological behavior of trifunctional epoxy resin/hyperbranched aliphatic polyester mixtures

A hyperbranched polymer (HBP), based on a highly branched polyester, was added to a trifunctional triglycidyl-p-aminophenol (TGAP) epoxy resin as a possible route to increase the toughness of the resin. Different amounts of the HBP, up to 26.5% wt. of resin, were dispersed in the TGAP resin. The rheological behavior of the formulations produced was studied as function of the shear rate and the filler content using a cone and plate rheometer. The rheological behavior of the TGAP resin, initially Newtonian, was modified displaying a pseudo-plastic trend when the hyperbranched polymer was added. An increase in the viscosity of the resin was observed with increasing volume fraction of the filler. The Cross equation was used to predict the viscosity of each formulation as a function of the shear rate. A novel procedure was developed to predict the viscosity of each mixture as a function of the filler volume fraction. This could be employed to provide quantitative information on the filler volume fraction in epoxy/HBP systems, necessary to achieve the characteristic viscosity values corresponding to the typical shear rates for a specific processing technology.     

Influence of cross-link density on rheological properties of temperature-sensitive microgel suspensions

The influence of the cross-link density on rheological properties of thermosensitive microgels was investigated. The temperature-sensitive hydrogel particles consisted of poly (N-isopropylacrylamide) (PNiPAM) chemically cross-linked with several different molar ratios of N,N′-methylenebisacrylamide. The variation of cross-link density leads to soft spheres that possess a different particle interaction potential and a different swelling ratio. With increasing temperature the microgel particles decrease in size and with it the effective volume fraction, which leads to strong changes in rheological properties. The relative zero-shear viscosity and the plateau modulus at different temperatures superpose to mastercurves when plotted versus the effective volume fraction. Up to an effective volume fraction of 0.5 the microgels behaved like hard spheres and the maximum volume fraction, as determined from the divergence of the zero-shear viscosity, was mainly dominated by the polydispersity of the spheres and not by the cross-link density. The plateau modulus, on the other hand, revealed soft-sphere behavior and the interaction potential became softer with decreasing cross-linker content. Received: 15 December 1999 Accepted: 15 February 2000     

Noncontinuum effects in nanoparticle dynamics in polymers

We propose a continuum model for the dynamics of particles in polymer matrices which encompasses arbitrary size ratios of the polymer and particle. We present analytical and computer simulation results for the mobility of the particles and the viscosity of the suspension for the case of unentangled polymer melts. Our results indicate strong dependencies of the particle mobility upon the polymer-particle size ratios and much reduced intrinsic viscosities for the suspensions. These predictions rationalize some recent experimental observations on the dynamics of nanoparticles in polymer melts.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.