The rheology of filled polymers

The flow properties of polymer melts containing fillers of various shapes and sizes have been examined. If there is no failure of either the filler or polymer in the solid state, then the modulus enhancement for randomly distributed filler is equal to the melt viscosity enhancement under medium shear stress conditions (10⁴ Nm^?2) in simple shear flow or in oscillatory shear flow. Submicron-size fillers, in particular, can form weak structures in the melt that greatly increase the low shear rate viscosity without changing the modulus of the solid proportionately. The highly pseudo-plastic nature of polymer melts at shear stresses of 10⁶ Nm^?2 means that, even without orientation of filler particles toward the flow direction, the viscosity enhancement is less than at lower shear stresses.     

Model filled polymers. XIV: Effect of modifications of filler composition on rheology

Steady shear vxiscosity, dynamic moduli and the appearance of fracture surfaces of model composites, consisting of monodisperse crosslinked polymeric spheres of varied composition in a polymethyl-methacrylate matrix, depend on the compatibility of filler particle and matrix. After intensive mixing, “compatible” systems form uniform and stable dispersions. Filler particles cluster in incompatible composites producing a highly non-Newtonian response. At 40 w% filler, yield behavior results, with a yield stress of 3100 Pa for polystyrene particles and 1900 Pa for copolystyrene-acetoxystyrene particles. The flow properties of compositionally complex particles from seeding are determined by particle surface composition.     

Model filled polymers: The effect of particle size on the rheology of filled poly(methyl methacrylate) composites

The effect of size of crosslinked monodisperse spherical polymer particles on the steady shear and dynamic rheology of filled poly(methyl methacrylate) (PMMA) composites was studied for PMMA and polystyrene (PS) particles in the range from 0.1 to 1.3 micron particle size. For PMMA matrices filled with crosslinked PS particles, reduction in filler size increases non‐Newtonian behavior. Particle size effects on the rheology of filled PMMA were much less pronounced for PMMA filler. The rate of growth of steady shear viscosity with aging time was much larger for PMMA filled with PS particles than with PMMA particles. The apparent yield stress of filled PMMA composites was estimated from Casson plots. The yield stress was negligible for PMMA filler but increased with decreasing particle size for PS filler. We suggest that PS particles are rejected by the PMMA matrix and form clusters, causing large enhancements in viscosity and moduli. Polym. Eng. Sci. 44:452–462, 2004. © 2004 Society of Plastics Engineers.     

Model filled rubber. I: Effect of particle morphology on suspension rheology

Monodispersed polystyrene (PS) particels, crosslinked with divinylbenzene (DVB), were prepared by emulsifier-free emulsion polymerization. The colloidal-suspension rheology of a low-molecular-weight liquid polysulfide, which is used in commercial sealants, filled with these PS particles varying in size and particle-crosslink density, was studied. At low frequencies or shear rates, the dynamic moduli and viscosity increased as particle diameter decreased from 1.25 to 0.315 μm or particle crosslink density increased from 0 to 5 mole% DVB. We suggest that particle-particle interactions are dominant and lead to the formation of clusters in the concentrated suspension. Rheological properties associated with network buildup in suspensions were most sensitively monitored by a kinetic-recovery experiment. The strength of, as well as the tendency for, cluster network formation in the colloidal suspensions increases with decreasing particle size, and increasing particle-crosslink density, or decreasing surface roughness.     

The effect of molecular weight blending on PVC melt rheology

The effect of molecular weight blending on melt flow characteristics has been studied with a 50/50 mixture of suspension PVC resins with the respective M _w of 56,300 and 123,000. The dynamic shear measurements were made with the Rheometrics Visco-Elastic Tester at angular frequencies of 0.1 to 40 radians/s. In the temperature range of 160 to 215° C, all samples showed three distinct flow regions marked by three different values of the activation energy. The high molecular weight fraction introduced a relatively strong influence on the melt flow characteristics of the blend due to the effect of its relatively high crystalline content. These samples also failed to show a Newtonian flow behavior at 190°C at an extremely low shear rate corresponding to 10^?4 radians/s., possibly reflecting the effect of the remnant crystallinity of the material.     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.     

The effect of molecular weight and weight distribution upon polymer melt rheology

A major objective in polymer rheology is to predict a fluid's response to a general deformation from molecular information. A method has been developed which allows one to predict the viscoelastic properties of polymer melts from a limited amount of rheological and molecular data for the polymer. The input parameters are: (a) zero-shear viscosity; (b) molecular weight distribution; (c) temperature and density; and (d) constants relating Graessley's relaxation time to the Rouse relaxation time. The technique then “simulates” a discrete relaxation spectrum using G′ and G″ data from the Rouse theory and finally requires that a continuum model of polymer viscoelasticity be fit to shear viscosity data predicted by Graessley's theory. Examples of the utility of the procedure are given to illustrate the role of molecular weight and weight distribution in determining rheological behavior.     

Interfacial interactions and the properties of filled polymers: I. Dynamic-mechanical responses

The dynamic mechanical responses of rutile-filled, chlorinated polyethylene (CPE) were studied as a function of temperature, of filler loading, and of filler surface condition. An objective was to establish the influence of matrix-filler interactions on mechanical properties. Necessary information on potential interactions between matrix and filler was obtained from inverse gas chromatographic data, in the form of an acid-base interaction parameter, Ω. The damping peak in filled CPE compounds was depressed by the pigment, as called for by theoretical models. The magnitude of the effect exceeded expectations, however, and clearly depended on the strength of interfacial interactions. These were consistent with the acid-base ranking of CPE and the various rutiles, as given by Ω. It has been postulated that in the presence of acid-base interactions, an immobilized layer of polymer in the vicinity of solid particles increases the effective particle dimension, thereby accounting for the observed variations in relative damping. Additional effects of matrix-filler interaction were noted in the variation of storage moduli with loading and temperature. Again, the effects tend to be more pronounced when significant specific interactions between matrix and solid are operative. These observations point to the inadequacy of existing models as interpretative bases for dynamic mechanical properties in systems with significant specifie interactions among their components.     

Surface interactions and some properties of filled polymers

Inverse chromatography was applied to evaluate interaction parameters for polyethylene (PE), polyvinyl chloride (PVC), and CaCO₃, these parameters being based on retention volumes of proton-donor, -acceptor, and neutral vapors. The acid/base characteristics of CaCO₃ were controllably altered by exposing the particulate to microwave plasmas sustained by acidic and basic vapors. It was shown that the ease-of-dispersion of fillers in the polymer matrixes related with the acid–base interaction balance in the polymer-filler pair, and varied widely with the surface treatment given to the filler. Mechanical properties at large deformation of the filled polymers and their durability also were shown to depend on surface interactions. Optimization of properties in PVC compounds was favored when strong acid-base interactions could take place with the plasma-modified filler. In the case of PE, properties were superior when unmodified filler was used; imparting strongly acidic or basic surface properties to the filler diminished its “compatibility” and usefulness with this nonpolar matrix.     

The influence of molecular weight on the melt rheology of polypropylene

Melt viscosity and melt elasticity data were obtained over a broad range of temperatures and shear rates on a series of four polypropylenes of different molecular weight but approximately the same molecular weight distribution. The superposition technique was used with both temperature and molecular weight to shift flow curves for all four materials at three temperatures each along the shear rate axis to generate a master flow curve at a given temperature and molecular weight. For polypropylenes of this type, and molecular weight distribution shift, factors which can be used to extend the useful range of experimentally obtained flow data were determined. The dependency of apparent viscosity on weight average molecular weight at shear stresses as high as 10⁶ dynes/cm² is shown. The dependency of melt elasticity on molecular weight and temperature is discussed.     

Interfacial interactions and properties of filled polymers. II: Dispersion of filler particles

The specific interaction characteristics and the inherent agglomeration of variously surface coated rutile pigments have been assessed, respectively, by inverse gas chromatographic and powder rheological methods. Standardized methods were used to disperse the pigments in polyethylene and chlorinated polyethylene. Measurements were made of energy requirements for dispersion and of the quality of dispersion attained. It was found that in the non-polar polyethylene matrix, dispersion processes depended on the strength of pigment agglomerates, but not on the specific interaction potential of the solids. Conversely, in the acidic chlorinated polyethylene, acid/base interactions influenced dispersion but the process was independent of inherent pigment agglomeration.     

Model filled polymers. VII: Flow behavior of polymers containing monodisperse crosslinked polymeric beads

Steady shear viscosities and dynamic moduli of polymer composites, consisting of combinations of crosslinked beads and matrices of polystyrene (PS) and polymethacrylates (PMA), are measured in a cone and plate rheometer. Viscosities and moduli were very sensitive to chemical composition. Crosslinked beads of identical composition to the matrix exhibited the lowest viscosity enhancements at low shear rates and the lowest moduli in dynamic mechanical analysis. The effects of bead concentration on rheological behavior were compared for PS and PMMA beads in a PMMA matrix. PMMA beads produce small effects, whereas PS beads yield highly non-Newtonian systems in PMMA, showing a yield stress of 1100 Pa at 30 wt% filler loading and dynamic moduli independent of frequency. We suggest that rheological behavior reflects the state of dispersion of beads in the matrix. Beads identical in composition to the matrix yield uniform dispersions. We propose that uniform and stable bead dispersions exhibit the lowest viscosity and moduli. Beads that cluster in the matrix, such as PS beads in PMMA, exhibit highly non-Newtonian behavior.     

Controlled rheology of polypropylene: Modeling of molecular weight distributions

A mathematical model for the controlled degradation of polypropylene is presented in this article. A previous model of this process was extended to predict the whole molecular weight distribution of the modified resin. Probability generating functions were applied to transform the infinite set of mass balance equations of both polymer and radicals. The integration of the transformed set of equations yielded the probability generating function transforms. These transforms were then inverted with two different inversion algorithms, recovering the molecular weight distributions of the polymer. The model predictions were compared with our experimental data and other information taken from the literature. Good agreement was obtained. The approach presented here is also useful for other polymerization and postpolymerization processes. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1676–1685, 2003     

Melt rheology of ion-containing polymers. I. Effect of molecular weight and excess neutralizing agent in model elastomeric sulfonated polyisobutylene-based ionomers

Melt rheology of elastomeric triarm sulfonated polyisobutylene model ionomers has been studied. The molecular weights (M _n) of the polymers have been varied from 8300 to 34,000. The sulfonated materials were neutralized with potassium hydroxide either to the exact stoichiometric equivalence point or to twice this amount, i.e., 100% excess neutralizing agent was added. For comparison one nonsulfonated precursor of M _n = 8300 was also studied. It was observed that the introduction of one sulfonate group at each chain end of the triarm poly-isobutylene molecule changes the state of matter at room temperature. Specifically, the unsulfonated materials are viscous liquids while the sulfonated ionomers are solid elastomers at room temperature. The zero-shear melt viscosity of the unsulfonated precursor is 900 poise (90 Pa·s), at room temperature while for those materials neutralized with potassium hydroxide to the exact stoichiometric point it is above 9 × 10³ poise (900 Pa·s) at 180°C. As expected, the zero shear viscosity increases with an increase in the molecular weight. Significant ionic interactions still persist at 180°C as evident by the high viscosity of the ionomers. However, at higher frequencies (～600 rad/s), the melt viscosity decreases to about 5 × 10³ poise for the different molecular weight materials. The melt viscosity of ionomers containing 100% excess neutralizing agent shows a dramatic increase. The excess KOH is speculated to be incorporated into the ionic domains rather than uniformly distributed throughout the matrix. This results in an increased strength of the ionic aggregates, thereby increasing the melt viscosities. Thus, due to the very pronounced effect on rheological properties it is important to know not only the extent of neutralization (up to full neutralization) but also the amount of excess neutralizing agent, if any, which is present in the sample.     

Influence of molecular weight and molecular weight distribution on the tensile properties of amorphous polymers

Tensile property data for polystyrene samples of varying polydispersity are correlated with various parametric measures of molecular weight. Traditional measures of molecular weight, such as M?_n, M?_w, and M?_z, are shown to be unable to account for the variation of tensile properties with molecular weight. However, a new molecular weight parameter, termed the failure property parameter, is able to provide a single relationship between tensile strength and the parameter for both the broad and narrow distribution polymers. The form of this parameter is consistent with its having origins in the view that it is the entanglement network in an amorphous polymer that provides the observed strength properties. Specifically for polystyrene, the failure property parameter results indicate that material below 60,000 molecular weight does not contribute to polymer strength. Although the results of this investigation are specifically for polystyrene, the arguments used to develop the failure property parameter are not dependent on polymer chemical structure. Consequently, we believe that both the concepts and definition of this new parameter are applicable to all amorphous polymers.     

Melt rheology of segmented polyamides: Effect of block molecular weight

Segmented polyamides, also known as polyether‐ester‐amides, are composed of polyether and polyamide structural units. The rheological behavior of segmented polyamides with respect to the variations in the molecular weight of hard and soft blocks has been studied using a Monsanto Processability Tester. These systems exhibit pseudoplastic flow behavior. The shear viscosity of the segmented polyamides decreases with a decrease in hard block molecular weight up to 1500. However, at low shear rates, the shear viscosity shows marginal change with an increase in soft segment molecular weight. The equilibrium die swell increases with an increase in shear rate, but decreases with increasing temperature. The stress relaxation study of the segmented polyamides reveals that the stress developed during extrusion relaxes exponentially for all the systems. The equilibrium die swell at a fixed temperature and shear rate, the time required to relax a fixed amount of stress and the stress developed after a certain time interval decrease with a decrease in hard block molecular weight up to 1500, but increase with an increase in soft segment molecular weight. The activation energy of the melt flow process increases with the rate of shear in most of the cases. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1739–1747, 1999     

PVC melt rheology III: The effect of order and molecular weight on the shear rate dependence

The effect of polymerization temperature on the melt flow behavior of PVC of varying molecular weights has been studied over a wide shear rate range. For the same molecular weight, higher melt viscosities are observed for polymers prepared at lower temperatures. The shear rate dependence of the viscosity vs molecular weight plot is shown to be nonlinear over the shear rates examined. The inability to achieve a limiting zero-shear viscosity is discussed.     

Effect of polymer matrix on the rheology of hydroxyapatite‐filled polyethylene composites

The effect of matrix polymer and filler content on the rheological behavior of hydroxyapatite‐filled injection molding grade high‐density polyethylene (HDPE) has been studied. Studies of the flow curves revealed that the matrix and the composite exhibit three distinct regions in the flow curve, namely, a pseudoplastic region at low to moderate shear rates, a plateau and a second pseudoplastic region at high shear rates. The shear stress corresponding to the plateau (τ_c) is dependent on both the filler concentration and the melt temperature. Addition of HA in the HDPE matrix increases the value of τ_c and decreases compressibility of the melt. An increase in temperature also raises the value of τ_c. From the nature of flow curves it is concluded that the matrix polymer largely decides the rheology of the composite.     

Heat-resistant polymers containing the low molecular weight closo-carboranes. III. The preparation of polycarboranesiloxane polymers by alcoholysis

A new synthesis for carboranesiloxane polymers has been discovered. It involves the alcoholysis of the bischlorodimethylsilylcarborane monomers and the generation of the HCl catalyst in situ. Alcoholysis is applicable to the synthesis of most carborane-siloxane polymers, with the probable exception of the SiB-1 homopolymers of the larger carboranes. The attack of the B? H moieties in the carborane cage can be minimized both by the utilization of a tertiary alcohol and by the addition of excess acid when a primary alcohol is employed.