The effect of entanglements on the rheological behavior of polybutadiene critical gels

Rosa, Michael E. De; Winter, H. Henning

doi:10.1007/bf00437307

Cited by 118 publications

(75 citation statements)

References 37 publications

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“…This longest relaxation time increases with growing cluster size (increasing extent of reaction) and, at the gel point, diverges to infinity. The relaxation exponent n can also be a function of p. 19,20 When modeling the relaxation spectrum of critical gels of high molecular weight model polybutadiene precursors with a combination of BSW and CW spectra, De Rosa and Winter 4 found it necessary to decrease the slope of the entanglement power law, n e , which is a possibility also considered in the present work by introducing a modified slope, An e , in this region.…”

Section: Relaxation Patterns and Model Spectrummentioning

confidence: 77%

“…This is probably due to the small number of chemical cross-links added compared to the number of entanglements (temporary cross-links) already present in the precursor material. 4 Using GELPRO software, 25 frequency-dependent dynamic moduli from the time-resolved rheometry experiment could be interpolated at discrete times, t i . Each interpolated data set can be viewed as a "snapshot" of the material at a certain intermediate reaction stage.…”

Section: Resultsmentioning

confidence: 99%

“…The characterization of the polybutadiene precursors is given elsewhere. 4 The cross-linking reaction was catalyzed by a platinum compound, cis-dichlorobis(diethylsulfide)platinum(II), which was applied as an 8 × 10 -6 M solution in toluene. Samples were prepared by mixing 0.6 g of polymer precursor with 0.03 mL of catalyst solution in a ceramic crucible using a microspatula.…”

Section: Methodsmentioning

confidence: 99%

“…In the case of low molecular weight precursors (M w < M e ), this is the crossover to the glass transition; for higher molecular weight precursors (M w > M e ), λ 0 characterizes the crossover to entanglement relaxation. 4 Since the longest relaxation time diverges at the gel point, the selfsimilar relaxation is valid to infinite time. The selfsimilar relaxation behavior can also be expressed by the power law relaxation time spectrum (CW spectrum): [1][2][3] The relaxation exponent may adopt values 0 < n < 1.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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: Relaxation Patterns and Model Spectrummentioning

confidence: 77%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relaxation Patterns of Nearly Critical Gels

Mours¹,

Winter²

1996

Macromolecules

142

116

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show abstract

“…Consecuentemente, una representación más generalizada de la respuesta en cizalla oscilatoria sería: una región pseudo-terminal a bajas frecuencias, una región «plateau» intermedia y el comienzo de la región de transición a altas frecuencias. Los espectros de relajación calculados a partir de las funciones viscoelásticas dinámicas, bien por métodos aproximados Franco et al, 1997) o por técnicas de regularización (Madiedo, 1996;Madiedo et al, 1996), pueden ser satisfactoriamente definidos por el modelo BSW-CW (De Rosa et al, 1994). Este modelo predice una transición brusca entre la región «plateau» y la pseudo-terminal del espectro .…”

Section: Introductionunclassified

Reología de emulsiones estabilizadas por biopolímeros

Madiedo¹,

Bower²,

Mackley³

et al. 1997

Grasas y Aceites

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RESUMEN Reología de emulsiones estabilizadas por biopolímerosEn este trabajo se estudian las respuestas viscosa y viscoelás-tica de emulsiones alimentarias estabilizadas por proteínas. La función de amortiguación determinada desde el módulo de relajación ha permitido, junto con el espectro de relajación calculado a partir de los módulos dinámicos, predecir la respuesta del material en condiciones de cizalla estacionaria mediante la aplicación del modelo de Wagner. Por otra parte, el estudio de la evolución de la microestructura de estos sistemas con la cizalla permite explicar el comportamiento observado en ensayos de flujo estacionario, así como la falta de concordancia entre los resultados experimentales y los predichos. PALABRAS-CLAVE: BiopolímeroViscoelasticidad. SUMMARY Emulsión -Espectro Rheology of biopolymer stabilized emulsionsIn this work, the viscous and viscoelastic responses of food emulsions stabilized by proteins are studied. The damping function determined from the relaxation modulus, together with the relaxation spectrum calculated from the dynamic tnoduli, allowed a prediction of the material response under steady-state conditions by applying the Wagner model. On the other hand, the study of the evolution of the microstructure of these systems under shear allows to explain the behavior observed in steady-flow tests, as well as the lack of concordance between experimental an predicted values.

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A rheological study of the gelling of UF polycondensates

Halász¹,

Vorster²,

Pizzi

et al. 2000

J. Appl. Polym. Sci.

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The gelling process of urea-formaldehyde resins has been investigated by rheological methods. The gel point values were determined by three methods, and compared with those obtained by low resolution impulsional 1 H-nuclear magnetic resonance. The activation energy of the curing process was determined and the effect of the molar ratio was investigated. In addition, the critical power exponents were calculated and the parameters of the relaxation modulus function were also determined. Equations describing the gel time as a function of degree of conversion and reactants molar ratio are presented.

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The effect of entanglements on the rheological behavior of polybutadiene critical gels

Cited by 118 publications

References 37 publications

Relaxation Patterns of Nearly Critical Gels

Relaxation Patterns of Nearly Critical Gels

Reología de emulsiones estabilizadas por biopolímeros

A rheological study of the gelling of UF polycondensates

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