Determination of Plateau Moduli and Entanglement Molecular Weights of Isotactic, Syndiotactic, and Atactic Polypropylenes Synthesized with Metallocene Catalysts

Copolymerisation with non-conjugated dienes offers an attractive route for introducing long-chain branching in polypropylene. From a simplified set of rate equations for such copolymerisation with a metallocene catalyst, we derive the probabilities of branch formation at different stages of the reaction in a semi-batch reactor. Using these probabilities, we generate an ensemble of molecules via a Monte Carlo sampling.The knowledge of the branching topology and segment lengths allows us to compute the flow properties of the resins from computational rheology. We compare our model predictions with existing experimental data, namely the molar mass distribution and small angle oscillatory shear response, for a set of resins with varying diene content. * To whom correspondence should be addressed 1The rheology data suggests that the entanglement time τ e depends sensitively and in a well-defined fashion on the diene content.

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“…6a). With the same choice of M e and τ e , we can describe the viscoelastic moduli of the iPP linear resin in 39 .…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Modeling of Synthesis and Flow Properties of Propylene–Diene Copolymers

et al. 2014

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“…The causal links between viscoelasticity and microstructure are explored in various viscoelastic tests. The viscoelastic behavior of polymers and related composites is usually characterized in creep test (whereby the creep strain is measured in time under a constant load) or dynamic mechanical test, where the variation in storage and loss moduli is observed as a function of the temperature, (Xia et al, 2007;Eckstein et al, 1998). To describe the creep results, phenomenological models, composed of spring and dashpot elements, are frequently used.…”

Section: Structure -Property Relationshipsmentioning

confidence: 99%

Nano-Scale Reinforcing and Toughening Thermoplastics: Processing, Structure and Mechanical Properties

Siengchin¹

2011

Nanofibers - Production, Properties and Functional Applications

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“…In a viscoelastic fluid, such as the cytoplasm of a living cell, is not a constant and is time scale dependent, thereby giving rise to a time scale-dependent diffusion coefficient. We can however instead approximate as the product of the relaxation time (the time scale at which the viscous to elastic crossover occurs; Figure 2) and the plateau value of the elastic modulus (Eckstein et al, 1998). It is important to note that the diffusion coefficient calculated from twodimensional particle trajectories can be approximated as the three-dimensional diffusion coefficient assuming that the local environment surrounding each microsphere is isotropic in three dimensions.…”

Section: Cytomechanics From Multiple Particle Trackingmentioning

confidence: 99%

“…Intracellular viscosity is obtained from the product of the relaxation time (inverse of the cross-over frequency, ␦ ϭ45°) and the plateau modulus (the value of the elastic modulus evaluated at the frequency where the minimum of ␦ occurs) (Eckstein et al, 1998). Intracellular viscosity increased from 8.1 Ϯ 10.0 to 94.1 Ϯ 22.1 Poise upon Rho activation ( Figure 2D).…”

Section: Cytomechanical Response To Rho Activationmentioning

confidence: 99%

“…In LPA-treated cells, the loss tangent crosses over to the elastic regime (␦ Ͻ 45°) at a much lower frequency than control cells ( Figure 2C), suggesting that activation of Rho enables the cell to elastically resist a wider range of rates of deformations compared with quiescent cells. These viscoelastic profiles, which are reminiscent of those found in polymeric fluids (Ferry, 1980) and reconstituted actin networks cross-linked with ␣-actinin (Sato et al, 1987;Xu et al, 1998b), describe the cytoplasm as a complex fluid that when sheared rapidly, resists deformations and is therefore elastic, and when sheared slowly, relaxes rapidly via viscous diffusion and thereby offers less resistance to mechanical stresses.Intracellular viscosity is obtained from the product of the relaxation time (inverse of the cross-over frequency, ␦ ϭ45°) and the plateau modulus (the value of the elastic modulus evaluated at the frequency where the minimum of ␦ occurs) (Eckstein et al, 1998). Intracellular viscosity increased from 8.1 Ϯ 10.0 to 94.1 Ϯ 22.1 Poise upon Rho activation ( Figure 2D).…”

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confidence: 99%

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Rho Kinase Regulates the Intracellular Micromechanical Response of Adherent Cells to Rho Activation

Kole

Tseng

Huang

et al. 2004

MBoC

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Local sol-gel transitions of the cytoskeleton modulate cell shape changes, which are required for essential cellular functions, including motility and adhesion. In vitro studies using purified cytoskeletal proteins have suggested molecular mechanisms of regulation of cytoskeleton mechanics; however, the mechanical behavior of living cells and the signaling pathways by which it is regulated remains largely unknown. To address this issue, we used a nanoscale sensing method, intracellular microrheology, to examine the mechanical response of the cell to activation of the small GTPase Rho. We observe that the cytoplasmic stiffness and viscosity of serum-starved Swiss 3T3 cells transiently and locally enhances upon treatment with lysophosphatidic acid, and this mechanical behavior follows a trend similar to Rho activity. Furthermore, the time-dependent activation of Rho decreases the degree of microheterogeneity of the cytoplasm. Our results reveal fundamental differences between intracellular elasticity and cellular tension and suggest a critical role for Rho kinase in the regulation of intracellular mechanics. INTRODUCTIONCytoskeletal rearrangements are closely correlated with key cellular processes such as cell shape changes during mitosis, the separation of daughter cells by the contractile ring during cytokinesis, cell-cell and cell-substrate interactions, transmembrane signaling, endocytosis, secretion, and motility (Schmidt and Hall, 1998). These processes involve the coordinated assembly, disassembly, cross-linking, and bundling of cytoskeletal filaments, which are mediated by auxiliary proteins and are believed to regulate the mechanical properties of the cell. In vitro studies using purified cytoskeletal proteins have suggested molecular mechanisms of regulation of cytoskeleton mechanics (Sato et al., 1987;Janmey et al., 1990;Pollard et al., 1992); however, the mechanical behavior of living cells and the molecular signaling pathways by which it is regulated remains largely unknown.It is well established that members of the Rho family of small GTPases play a central role in cytoskeletal assembly and architecture Van Aelst and D'Souza-Schorey, 1997;Rottner et al., 1999;Bishop and Hall, 2000). The roles of Rho proteins in controlling actin filament dynamics and network organization are fairly well understood at the biochemical level (Ballestrem et al., 2001). However, fundamental questions still exist regarding the downstream intracellular mechanical response of the cytoskeleton to Rho GTPase activation (Heidemann and Wirtz, 2004). For instance, upon activation of Rho, what are the intracellular viscoelastic properties that modulate the intracellular transport of organelles and engineered particles (Suh et al., 2003), and how does Rho activation affect the ability of the cell to resist deformation? Using a novel functional assay, intracellular microrheology (Tseng et al., 2002b), we directly measure the micromechanical response of Swiss 3T3 fibroblasts subjected to Rho activation by lysophosphatidic acid (LPA) ...

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Determination of Plateau Moduli and Entanglement Molecular Weights of Isotactic, Syndiotactic, and Atactic Polypropylenes Synthesized with Metallocene Catalysts

Cited by 258 publications

References 26 publications

Modeling of Synthesis and Flow Properties of Propylene–Diene Copolymers

Modeling of Synthesis and Flow Properties of Propylene–Diene Copolymers

Nano-Scale Reinforcing and Toughening Thermoplastics: Processing, Structure and Mechanical Properties

Rho Kinase Regulates the Intracellular Micromechanical Response of Adherent Cells to Rho Activation

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