Skip to main content
SpringerLink
Log in

What is the flow activation volume of entangled polymer melts?

  • Original Contribution
  • Published:
Colloid and Polymer Science Aims and scope Submit manuscript

Abstract

We evaluate the flow activation volume in polymer melts of isotactic polypropylene and atactic polystyrene with step-shear experiments at different melt temperatures. The melt is initially sheared with constant shear rate until the attainment of a melt state with nearly constant viscosity. Perturbations to this experiment, involving shear steps in short-time intervals with decreasing rates, are induced next. Measurements of the shear stress value at each shear rate step allow the evaluation of an experimental (apparent) flow activation volume. The true flow activation volume is evaluated by extrapolating the experimental data to infinite shear stress values. The value obtained is larger than the physical volume of the chain and agrees with the volume of a tube confining chains with a molecular weight between M n and M w. Besides supporting the validity of tube model, experiments based on this protocol may be used on model polymer samples, in composites with nanoparticles and in polymer blends to access the validity of mechanisms considered by flow models.

Symbols in the figure represent the apparent values of flow activation volume of atactic polystyrene evaluated from the step shear experiments. Fitting of the data with an equation derived from the rate theory of plastic deformation, allows the true flow activation volume to be evaluated by extrapolating the data to an infinite shear stress value. The true flow activation volume compares to the volume a tube confining the polymer chains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Moe NE, Qiu X, Ediger MD (2000) Macromolecules 33:2145–2152

    Article  CAS  Google Scholar 

  2. Qiu X, Ediger MD (2000) Macromolecules 33:490–498

    Article  CAS  Google Scholar 

  3. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York

    Google Scholar 

  4. de Gennes PG (1971) J Chem Phys 55:572–579

    Article  Google Scholar 

  5. Schleger P, Farago B, Lartigue C, Kollmar A, Richter D (1998) Phys Rev Lett 81:124–127

    Article  CAS  Google Scholar 

  6. Vaca Chávez F, Saalwächter K (2011) Macromolecules 44:1549–1559

    Google Scholar 

  7. Likhtman AE (2009) J Non-Newtonian Fluid Mech 157:158–161

    Article  CAS  Google Scholar 

  8. Gao J, Weiner JH (1989) Macromolecules 22:979–984

    Article  CAS  Google Scholar 

  9. Krausz AS, Eyring H (1975) Deformation kinetics. Wiley, New York

    Google Scholar 

  10. Caillard D, Martin JL (2003) Thermally activated mechanisms in crystal plasticity, Pergamon Materials Series, vol 8. Elsevier, Lausanne

    Google Scholar 

  11. McGrum NG, Buckley CP, Bucknall CB (1997) Principles of polymer engineering, 2nd edn. Oxford University Press, New York

    Google Scholar 

  12. Kazmierczak T, Galeski A, Argon AS (2005) Polymer 46:8926–8936

    Article  CAS  Google Scholar 

  13. Fetters LJ et al (1994) Macromolecules 27:4639–4647

    Article  CAS  Google Scholar 

  14. Lin YH (1987) Macromolecules 20:3080–3083

    Article  CAS  Google Scholar 

  15. Alefeld GZ (1962) Naturforsh A 17:899

    Google Scholar 

  16. Martins JA, Zhang W, Brito AM (2006) Macromolecules 39:7626–7634

    Article  CAS  Google Scholar 

  17. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, Oxford

    Google Scholar 

Download references

Acknowledgments

We thank Andrzej Galeski for pointing us ref. [10]. We acknowledge the Portuguese Foundation of Science and Technology for funding the project FCOMP-01-0124-FEDER-007151 (PTDC/CTM/68614/2006). This work was supported by the European Community fund FEDER and project 3599/PPCDT.

Author information

Authors and Affiliations

  1. Departamento de Engenharia de Polímeros, Universidade do Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    José A. Martins, Vera S. Cruz, Joanna Krakowiak & Weidong Zhang

  2. CICECO, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    José A. Martins, Vera S. Cruz, Joanna Krakowiak & Weidong Zhang

Authors
  1. José A. Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vera S. Cruz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joanna Krakowiak
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weidong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José A. Martins.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martins, J.A., Cruz, V.S., Krakowiak, J. et al. What is the flow activation volume of entangled polymer melts?. Colloid Polym Sci 290, 23–29 (2012). https://doi.org/10.1007/s00396-011-2519-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00396-011-2519-4

Keywords

Search

Navigation