The relaxation of polymers with linear flexible chains of uniform length

Baumgaertel, M.; Schausberger, A.; Winter, H. Henning

doi:10.1007/bf01376790

Cited by 283 publications

(221 citation statements)

References 11 publications

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“…The new spectrum, eq 12, has a very simple functional form since it only consists of a superposition of several power laws. It therefore represents an extension of successful power law relaxation time spectra as applied to nearly monodisperse linear flexible polymers, 31 bimodal blends of such polymers, 37 and branched polymers with uniform arm lengths. 38 Besides this inherent simplicity, the parameters of our new model show interesting p-dependence.…”

Section: Discussionmentioning

confidence: 99%

“…The relaxation behavior of the nearly monodisperse polymer precursor follows a distinct pattern which can be described by the BSW relaxation time spectrum. 31,32 The spectrum consists of a superposition of two power laws with slopes -n g and n e describing the glass transition and entanglement regime, respectively: …”

Section: Relaxation Patterns and Model Spectrummentioning

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: Discussionmentioning

confidence: 99%

Section: Relaxation Patterns and Model Spectrummentioning

confidence: 99%

Relaxation Patterns of Nearly Critical Gels

Mours¹,

Winter²

1996

Macromolecules

142

116

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“…Therefore, rheological measurements have now become a common and basic analytical tool of polymer characterization. [1][2][3] Microscopically, the viscoelasticity of polymers is apparently well described by the reptational tube model with corrections for timedependent topological fluctuations. Also, it is a wellknown fact that the melt flow behavior of polymers is very sensitive to their molecular weight and their molecular weight distribution.…”

Section: Introductionmentioning

confidence: 99%

Rheological Properties of 1,4-Polyisoprene over a Large Molecular Weight Range

et al. 2004

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The dynamic viscoelastic properties of anionically polymerized model 1,4-polyisoprene (PI) with 6-8% 3,4 microstructure and in the range of molecular weights between 1.5 × 10 3 and 3.2 × 10 6 g/mol were reanalyzed using linear rheology. Viscosities obtained in the zero shear-rate limit, η0, up to sufficiently high molecular weight PI samples indicated a clear transition to the pure reptation regime. All characteristic molecular weights, dividing the [η 0,M]-interval in three different regimes could be obtained in high accuracy and a new "triangle" is proposed. The experimental data were analyzed in terms of the empirical Winter-relaxation BSW-model description for both dynamic moduli. The BSW parameters are determined and interpreted in terms of the packing model where possible. Limitations of the packing model are detected and discussed. Additionally, the parameters of the assumed distribution of relaxation times are compared to predictions of microscopic dynamic theories and useful correlations made. The publication deals, in part, with a misconception in the literature for estimates of the constraint release contribution. The monomeric friction coefficient 0, determined in this study for the first time rheologically for anionic PI itself agrees with the natural rubber analogue.

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“…represents the broadened power law spectrum (BSW model; Baumgaertel et al (1990)). While in the vicinity of the dynamic glass transition, all of the systems can be adequately described by the fits, deviations of the G 0 ω ð Þ data from the broadened BSW models are observed at small modulus values.…”

Section: Experimental Methodsmentioning

confidence: 99%

Influence of suspension viscosity on Brownian relaxation of filler particles

et al. 2017

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Brownian relaxation caused by Brownian movement of particles in suspensions can macroscopically be probed by small-amplitude oscillatory shear experiments. Phenomenological considerations suggest a direct proportionality between suspension viscosity and Brownian relaxation times. To verify this relation experimentally, a set of nanocomposite suspensions with viscosities varying over five decades is presented. The suspensions are chosen in a way to ensure that particle-particle interactions and average particle-particle distances are identical so that they can be used as a model system to study the mere influence of suspension viscosity on Brownian relaxation. The suggested linear relationship between suspension viscosity and Brownian relaxation time can be confirmed. Moreover, a verification of a recently introduced characteristic timescale for Brownian relaxation is presented.

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The relaxation of polymers with linear flexible chains of uniform length

Cited by 283 publications

References 11 publications

Relaxation Patterns of Nearly Critical Gels

Relaxation Patterns of Nearly Critical Gels

Rheological Properties of 1,4-Polyisoprene over a Large Molecular Weight Range

Influence of suspension viscosity on Brownian relaxation of filler particles

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