Long‐chain branching in low‐density polyethylene

Côté, Jules; Shida, Mitsuzo

doi:10.1002/pol.1971.160090303

Cited by 41 publications

(12 citation statements)

References 6 publications

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“…The molecular weight data for the low-density samples have been corrected for the long-chain branching with the branching model based on Flory-Zimm-Stockmayer distribution. The weight average number of branch points per molecule N, given in Table I was obtained [7] from combined GPC and intrinsic viscosity data.…”

Section: Resultsmentioning

confidence: 99%

“…Thus, the spectrum representation can be considered good [ I ] . In order to avoid the spectral oscillation in deriving H (7) from G"(w) by any method it was necessary to extrapolate smoothly these data at higher frequencies as shown by the dotted line. Good agreement was also observed for the high-density sample HD 190 between experimental and regenerated Gyo) and C"(o) as shown in Figure 2.…”

Section: Resultsmentioning

confidence: 99%

“…The first approximation to the spectrum H, (T) is given by the equation HI (7) = ( 2 l d [? X v(?.>l. Insertion of H, (7) in eqs. (5) and (1) gives vl(?).…”

Section: Conversion From Q ( I ) To H(t)mentioning

confidence: 99%

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Shear rate dependent relaxation spectrum for polyethylene melts

Shroff¹,

Shida²

1971

J. polym. sci., C Polym. symp.

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Many of the familiar relations in the theory of linear viscoelasticity which relate the relaxation spectrum H(τ) to the experimentally measured quantities were extended to embrace the concept of shear dependent relaxation spectrum H(τ, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}). The concept is based on the relation H(τ, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) = H(τ)h(θ)g(θ)3/2, where θ = c \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document} τ and c = 0.5. Here \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document} is the shear rate and τ is the relaxation time. The replacement of H(τ) by H(τ',\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) in the integral relations of the linear theory produced the corresponding nonlinear parameters, e.g., the shear rate dependent viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}), the shear stress relaxation following cessation of steady‐state flow σ(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document},t) and the dynamic parameters under parallel superimposed rotation η'(ω) and G'(ω, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}). The concept was used successfully for several high‐density polyethylene melts in interconversion between η(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}), c(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document},t) and the dynamic viscosity η'(ω) without involving coordinate shifts or empirical parameters. The failure of this approach for interconversion between η(ω) and η(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) for the highly branched polyethylenes was ascribed to the level of long‐chain branching. For the high‐density resins, the agreement between measured η'(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) and G'(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) and those calculated using H(τ,\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document}) was not quantitative since the parallel superimposed experiments require an additional term in ∂H(τ,\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ $\end{document})/∂ \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^ ^2 $\end{document} inside the integral.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Shear rate dependent relaxation spectrum for polyethylene melts

Shroff¹,

Shida²

1971

J. polym. sci., C Polym. symp.

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“…The value G at M, = Mo in the log Glog M , plot was taken as the real value of the branching degree for the polymer. (8) and ( 9 ) to yield two series of values for M, and M,, respectively. Plotting Mw and M n against M, (as shown in Fig.…”

Section: Theorymentioning

confidence: 99%

“…(8) and ( 9 ) to yield two series of values for M, and M,, respectively. Plotting Mw and M n against M, (as shown in Fig.…”

Section: The Valuesmentioning

confidence: 99%

A new method for rapid evaluation of long‐chain branching in polymers

Chunshan

Guo

1990

J of Applied Polymer Sci

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SynopsisA new method for rapid evaluation of long-chain branching (LCB) in polymers was developed. The crude GPC chromatogram and the measured value of intrinsic viscosity of the whole polymer are the only data required. By using trial and error in combination with graphic analysis, the threshold value Mo and average molecular weights M w and Mn, as well as LCB can be simultaneously evaluated. The advantage of this method lies in avoiding predetermination of the Mo for a given resin. The results obtained by this method for NBS Branched Polyethylene Standard Reference Material SRM 1476 and for a branched cis-1,4-polybutadiene sample were in good agreement with those given by the conventional Ram-Miltz method.

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Fractionation of Polymers

Barrales‐Rienda

Bello

et al. 1999

The Wiley Database of Polymer Properties

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Long‐chain branching in low‐density polyethylene

Cited by 41 publications

References 6 publications

Shear rate dependent relaxation spectrum for polyethylene melts

Shear rate dependent relaxation spectrum for polyethylene melts

A new method for rapid evaluation of long‐chain branching in polymers

Fractionation of Polymers

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