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Journal of Rheology / Volume 54 / Issue 2

J. Rheol. 54, 393 (2010); http://dx.doi.org/10.1122/1.3305721 (14 pages)

Method for obtaining tube model parameters for commercial ethene/α-olefin copolymers

Xue Chen and Ronald G. Larson

Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109

Florian J. Stadler and Helmut Münstedt

Institute of Polymer Materials, Friedrich-Alexander-University Erlangen-Nürnberg, Martensstr. 7, 91058 Erlangen, Germany

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We propose a method of obtaining all three key “tube” model parameters, namely, the plateau modulus GN0, the entanglement molecular weight, Me, and the frictional equilibration time τe, from the molecular weight per backbone bond of ethene/α-olefin copolymers with longer comonomers, ranging from C4 (butylene) to C26 (hexacosene). GN0 is obtained from a correlation by Fetters et al. [Macromolecules 35, 10096–10101 (2002)] and Me is obtained from this using the standard tube-model formula, Me = (4/5)(ρRT/GN0). The equilibration time τe is obtained from a remarkable finding by Stadler and Münstedt [J. Rheol. 52, 697–712 (2008)] that, at fixed weight-average molecular weight, the zero-shear viscosity of linear ethene/α-olefin copolymers is independent of comonomer type and content over a wide range of α-olefin comonomers. From this observation, and from the values of GN0 and Me, we use the tube theory to construct a method for obtaining τe from the comonomer type and content. We show that these a priori values of the tube model parameters, when used in two publicly available models (“hierarchical model” and “branch-on-branch” model) for predicting linear rheology, yield accurate predictions for a wide range of polydisperse copolymers. These results show that a priori predictions of linear rheology of complex commercial polyolefin copolymers are now possible.

© 2010 The Society of Rheology

ACKNOWLEDGMENTS

The authors grateful for the Exxon Exact 3132 sample provided by Cesar Garcia-Franco of Exxon-Mobil. The authors would also like to acknowledge Dr. Christian Zimmermann and Professor Wolfgang Pechold for their characterization of F26F with their piezo-oscillator. The authors acknowledge support from NSF under Grant No. DMR 0604965. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

Article Outline

  1. INTRODUCTION
  2. EXPERIMENTS
    1. Materials
    2. Rheological measurements
  3. THEORY
    1. Models
    2. Model input parameters
  4. MODELING RESULTS AND COMPARISONS TO EXPERIMENTAL DATA
  5. CONCLUSIONS

KEYWORDS and PACS

Keywords

molecular weight, organic compounds, polymer blends, rheology, Copolymer, Frictional equilibration time, Hierarchical model, Plateau modulus, Rheology, Tube model

PACS

  • 61.41.+e

    Polymers, elastomers, and plastics

PUBLICATION DATA

ISSN

0148-6055 (print)  
1520-8516 (online)

Publisher

The Society of Rheology

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ARTICLE DATA

History
Received 12 Jul 09
Revised 23 Dec 09
Published online 12 Mar 10
Digital Object Identifier
http://dx.doi.org/10.1122/1.3305721

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