Viscoelasticity of randomly branched polymers in the critical percolation class

Lusignan, Charles P.; Mourey, Thomas H.; Wilson, James T.; Colby, Ralph H.

doi:10.1103/physreve.52.6271

Cited by 70 publications

(90 citation statements)

References 60 publications

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“…The scaling exponents are very sensitive to small changes in |p -p c | as recently confirmed by Lusignan et al 18 Our method of determining the gel point from the tan δ crossover and the distance from the gel point by matching our data sets is very precise. Calculations of the largest possible error when using…”

Section: Discussionsupporting

confidence: 52%

“…Experimentally, it has been shown that eq 9 holds for cross-linking of very low molecular weight precursors. 18 Several models for the relaxation behavior of nearly critical and critical gels have been presented. 4,[19][20][21][22][23][24] None of these models was able to describe all experimental observations in the vicinity of the gel point.…”

Section: Introductionmentioning

confidence: 99%

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Relaxation Patterns of Nearly Critical Gels

Mours¹,

Winter²

1996

Macromolecules

142

116

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We measure the complex rheological behavior of nearly critical gels and analyze the data by searching for characteristic patterns and abstracting those patterns into a self-consistent model. The sample is a linear, flexible, nearly monodisperse polybutadiene which gets cross-linked on its vinyl side groups. The dynamic mechanical storage and loss moduli of cross-linking polymers change smoothly during the liquid-solid transition, while equilibrium rheological properties (e.g., zero-shear viscosity and equilibrium compliance) diverge. During gelation, the relaxation occurs in a distinct pattern which can be described in a quantitative way with a minimum number of parameters. The pattern can be understood as a combination of the BSW spectrum (representing the precursor relaxation behavior) and the selfsimilar Chambon-Winter gel spectrum (modeling the terminal relaxation due to growing clusters). The spectrum is cut off at the material's longest relaxation time, λmax. Our model parameters, λmax and Ge (equilibrium modulus), exhibit characteristic scaling behavior with respect to the distance from the gel point, |p -pc|. The relaxation exponent, n, in the terminal zone is a function of the extent of reaction. Hence, dynamic scaling (requires constant n values) is not valid for our system. The proposed model passes the self-consistency test by predicting the mechanical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol-gel transition.

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Section: Discussionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Relaxation Patterns of Nearly Critical Gels

Mours¹,

Winter²

1996

Macromolecules

142

116

View full text Add to dashboard Cite

show abstract

“…Recently, Lussignan and co-workers [159,160] analysed the effects of branching on η o values in polyesters. In particular, by constraining the molecular weight between branch points M bb , they systematically varied M w .…”

Section: Quantitative Prediction Of Lcb From Rheological Data: Rheolomentioning

confidence: 99%

“…These authors present a semiempirical method of determining the level of LCB almost entirely from η o values. The method relies on a formula that relates η o to M w and a 'branching exponent' s/γ, obtained by making empirical adjustments to the theory developed for the rheological behaviour of fractal gelation clusters approaching the critical gel point [159,160].…”

Section: State-of-the-artmentioning

confidence: 99%

Effect of long chain branching on linear-viscoelastic melt properties of polyolefins

et al. 2002

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Abstract:The aim of this review is to provide evidence that rheological testing is a potent tool for characterising polymers in the melt. An effort has been made in order to gather results in conventional and model polyolefins, and correlating them with phenomena occurring at the molecular level. We have focused our interest on long chain branching (LCB). In the case of materials containing long side-chain branches, strong effects on viscosity, elastic character and activation energy of flow are general features. Literature results mostly indicate that the effect of polydispersity on these parameters could be very similar to that expected due to the presence of LCB -notwithstanding that the effects of LCB seem to be stronger than those due to polydispersity for a given molecular weight. Different relaxation processes appear as a consequence of the presence of LCB: slower terminal relaxation behaviour than of linear counterparts, and faster additional branch relaxation at higher frequencies, clearly distinguishable from polydispersity effects. To measure the amount of LCB from limited viscoelastic data and molecular properties seems to be a suitable instrument to explain the rheological features of the different polymers, but it fails when the results are compared with measured values of LCB density in model polymers. The actual framework leads us to say that the number of branches is less important than the topology itself. Therefore, the position and architecture of the branches along the polymer main chain are the main factors that control the rheology of the material.

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“…Moreover, ρ 0 stands for the monomer concentration and F i (t) := −∂V /∂R i (t) is the net spring force acting on monomer i at time t. Using the transformation (13) and the solution (15), it is readily shown 3,4 that the stress tensor (19) is given by…”

Section: Observables a Shear Stressmentioning

confidence: 99%

Rheology of gelling polymers in the Zimm model

Löwe

Müller

Zippelius

2004

The Journal of Chemical Physics

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In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model for randomly crosslinked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erdős-Rényi random graphs or three-dimensional bond percolation. Within this model the critical behaviour of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size n with n. We investigate these Mark-Houwink like scaling relations numerically and conclude that the scaling exponents are independent of the hydrodynamic interaction strength. The numerically determined exponents agree well with experimental data for branched polymers. However, we show that this traditional model of polymer physics is not able to yield a critical divergence at the gel point of the viscosity for a polydisperse dilute solution of gelation clusters. A generally accepted scaling relation for the Zimm exponent of the viscosity is thereby disproved.

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Viscoelasticity of randomly branched polymers in the critical percolation class

Cited by 70 publications

References 60 publications

Relaxation Patterns of Nearly Critical Gels

Relaxation Patterns of Nearly Critical Gels

Effect of long chain branching on linear-viscoelastic melt properties of polyolefins

Rheology of gelling polymers in the Zimm model

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