Linear Rheological Data Research Articles

On the Correlation of Rheology and Morphology of Bimodal Polypropylene Reactor Blends Synthesized by Homogeneous Binary Metallocene/Metallocene Catalysts

ABSTRACTIn this study, morphological and rheological characteristics of bimodal polypropylene reactor blends synthesized by binary catalysts based on I: rac-Me2Si(2-Me-4-PhInd)2ZrCl2 and II: (2-PhInd)2ZrCl2 at different molar ratios were investigated. Gel permeation chromatography, scanning electron microscopy, and rheometry analysis were performed to evaluate the effect of molar ratio of catalyst II, responsible for the formation of elastomeric stereoblock polypropylene with low molecular weight, to catalyst I, responsible for production of high molecular weight isotactic (i) polypropylene, on the molecular weight, molecular weight distribution, morphological characteristics and rheological behavior of the synthesized products. The gel permeation chromatography results indicated that once a hybrid of the two catalysts is used, a broad and bimodal molecular weight distribution would be obtained, and the molar ratio of the catalysts governs the values of molecular weight and molecular weight distribution. 13C NMR results suggest that the different polypropylene tacticity resulting from the two catalysts (stereoblock vs. isotactic) is hardly influenced using a binary system. The effect of molecular weight enhancement and molecular weight distribution broadening was confirmed through the linear rheological data (G′ at lower frequencies, crossover modulus and crossover frequency) due to the impeded molecular motions of chains with high molecular weights which play an important role in the elasticity of chains. The zero shear rate viscosity and relaxation time, determined by fitting the Carreau–Yasuda model, are in great conformity with the experimental data at low-frequency region. Likewise, the miscibility and increased level of heterogeneity of microstructure, which is a result of changing the molar ratios of catalysts II/I, are confirmed through the Cole–Cole and Han plots and were further corroborated through the obtained scanning electron microscopy results.

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag–Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shear-thinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting Mittag–Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox–Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule, which is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shear-thinning Cross-type or Carreau-type flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

Investigation of the rheological behavior of industrial tubular and autoclave LDPEs under SAOS, LAOS, transient shear, and elongational flows compared with predictions from the MSF theory

The molecular structure of two different types of industrial low-density polyethylenes (LDPE), i.e., tubular and autoclave, was investigated by gel permeation chromatography and different rheological methods and then compared with predictions from theoretical modeling. Linear rheological data generated from small amplitude oscillatory shear (SAOS) are presented using the framework of a Van Gurp-Palmen plot while nonlinear rheological data obtained from either transient shear, transient extension, or medium amplitude oscillatory shear (MAOS) are compared with simulations using a generalized form of the molecular stress function theory with only three nonlinear material parameters: a2, β, and fmax which represent the dissipation in simple shear flow, the ratio of molar mass of the branched polymer to the molar mass of the backbone, and the maximum stretching of the polymer chain before chains slip past one another without further stretch, respectively. The effect of these parameters on the predictions is investigated for the aforementioned nonlinear deformations. As a result of these comparisons, a2 was found to have a constant value within experimental error (a2 = 0.07 ± 0.03) when simulating the shear stress growth coefficient. Next, β was defined by fitting the extensional data with this model resulting in a constant value of 1.8 for tubular LDPEs and a value between 1.6 and 2.1 for autoclave LDPEs depending on the molecular structure. The universality of these β values was found by simulating the intrinsic nonlinearity Q0(ω)≡limγ0→0I3/1/γ02 (defined by Fourier transform rheology method) in the MAOS region. Finally, fmax was evaluated by fitting the model to tensile stress growth coefficient data. It was found that fmax is independent of the extensional rate for tubular LDPEs but exhibits a power law behavior with the extensional rate for autoclave LDPEs. Our investigations demonstrated that nonlinear deformations instead of SAOS deformations are the preferred method for characterizing the molecular structure of these polymers due to its sensitivity to the complex structure of LCB present in these materials along with their broad molecular weight distribution.

The effect of inkjet ink composition on rheology and jetting behaviour

This work presents recent results on the way linear and non linear viscoelastic properties of the fluids affect the jetting mechanism. Recent progress on quantitative characterising both high frequency linear (LVE) and non-linear (NLVE) viscoelasticity of fluids allows fluids to be assessed for their jettability before using such materials in a DoD print head. In term of linear viscoelastic measurements, the Piezo Axial Vibrator (PAV) was used to probe the rheology of the fluids on a frequency range between 10Hz and 10000Hz. A filament stretching apparatus, called the “Cambridge Trimaster”, was used in combination with high speed cinematography, to characterize the fluids high speed stretching and break-up behaviour. The series of fluids investigated here consist in dilutions of mono disperse polystyrene with different molecular weight (110, 210, 306 and 488 kg/mol respectively) diluted in diethyl phthalate. The choice of polymer weights and concentrations were chosen to match both the complex viscosity and the LVE. However, non linear rheological data experiments exhibit differences in the fluid relaxation time and filament break-up mechanism. Ultra-high speed cinematography of DoD jetting events were correlated with filament break-up experiments and demonstrated that fluid rheology provides valuable information on the jetting quality of the fluids.

Entangled Dendritic Polymers and Beyond: Rheology of Symmetric Cayley-Tree Polymers and Macromolecular Self-Assemblies

We present linear rheological data on a series of anionically synthesized, model symmetric Cayleytree polybutadienes having 2 or 3 generations with entangled branches. The signature of each layer relaxation is evident, in both the plateau modulus (that scales with the volume fraction of the unrelaxed layers) and the terminal relaxation as a distinct contribution, well-separated in time. Using a robust tube-model analysis of the viscoelastic relaxation of entangled polymers of given architecture, which is based on the concept of hierarchy of motion in branched structures, we describe quantitatively the frequency spectra without adjustable parameters; the needed plateau modulus, entanglement molecular weight, and Rouse time of an entanglement segment are taken from the data. Last, but not least, we show that this approach can be successfully applied to account for the rheology of macromolecular self-assemblies, such as the Cayley-tree-like associations of telechelic, mono-o-functionalized star polymers. The implications of the latter findings in providing pathways for the analysis of complex soft superstructures are evident.

Viscoelasticity of Monodisperse Comb Polymer Melts

The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic variation due to the topological arrangements of the branches in branched polymer melts. The position of the branch points, the arm length, and number of the arms are essential to defining the rheological behavior. Recent advances in molecular tube models have led to a much greater understanding of the linear rheology of linear, star, H-shaped, pom-pom, and comb polymers. We correct and extend existing molecular theories for the linear viscoelasticity of comb polymer melts, especially in accounting for (1) polydispersity and (2) the path length of backbone extremities. We compare the predictions with linear rheological data of nearly monodisperse polybutadiene combs. We then predict the zero-shear viscosity for monodisperse comb polyethylenes with varying arm lengths, backbone lengths, and number of arms. For a fixed molecular weight, we find that combs with the longest arms but few branch points give the highest predicted zero-shear viscosities and that they obey an exponential dependence on the length of the arms in the same way as star polymers. We find that combs with short arms, under four entanglements, lie below the 3.4 power law obeyed by linear polymers. All other comb topologies are bounded by these extremes.

Rheology of Viscoelastic Mixed Surfactant Solutions: Effect of Scission on Nonlinear Flow and Rheochaos

The linear and nonlinear rheology of viscoelastic mixed anionic-zwitterionic surfactant solutions has been systematically investigated. In the linear viscoelastic regime, these systems display nearly Maxwellian behavior with a unique relaxation time, tau0, and a characteristic elastic plateau modulus, G0. Linear rheological data were used to calculate the repitation and breaking times of the micelles, tau(rep) and tau(b), respectively. Surprisingly, the elastic modulus G0 significantly increases with salt concentration c(s), whereas tau(b) decreases by 1 order of magnitude. The strong effect of c(s) on the material parameters and microstructure of rodlike micelles allowed for the systematic investigation of the effect of these parameters on nonlinear flow. For samples with relatively long tau(b), the quasi-static flow diagram (stress vs shear rate) shows a stress peak followed by a metastable branch (a region of decreasing shear stress), whereas for samples with relatively short tau(b), this phenomenon is not observed. Transient flow responses corroborate quasi-static flow findings and further reveal the significance of microscopic dynamic parameters on flow behavior. Shear stress time series were recorded at constant shear rates, and above a critical shear rate, gamma(c2), stress fluctuations are observed. The amplitude of these stress fluctuations, Delta sigma, was found to scale as Delta sigma approximately equal to G0(tau(b)| gamma - gamma(c2)|)beta with beta approximately 0.5. This scaling is observed for micellar systems with tau(b) ranging from 0.12 to 0.01 s and G0 ranging from 1 x 10(3) to 7 x 10(3) dyn/cm2.

Small-Angle Neutron Scattering Study of the Relaxation of a Melt of Polybutadiene H-Polymers Following a Large Step Strain

We present scattering data from a melt of H-shaped polybutadiene polymers, in which the central crossbar of the polymers is wholly labeled with deuterium. The melt was uniaxially stretched by a factor of 2, and using careful temperature control of the sample, the neutron scattering pattern was measured after several different times of relaxation. The scattering data are compared against the predictions of a new theory, based upon the tube model but which includes the additional effect of elastic inhomogeneities in the entanglement network. We find that with this new theory one can obtain a good representation of the data, using parameters that are consistent with relaxation times obtained from a tube model description of the linear rheological data. The most important aspect of these data is an increasing anisotropy of the correlation hole peak, and this appears to be directly related to the elastic inhomogeneities. One further aspect of the comparison to theory is that the best fits are obtained using a Warner−Edwards tube diameter that deforms in a manner consistent with recent predictions for polymer networks.