- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Rigidity percolation in dispersions with a structured viscoelastic matrix

M. W. L. Wilbrink and M. A. J. Michels

W. P. Vellinga and H. E. H. Meijer

  • Technische Universiteit Eindhoven, Group Polymer Physics, Department of Applied Physics, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Technische Universiteit Eindhoven, Materials Technology, Department of Mechanical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

PDF

Phys. Rev. E 71, 031402 – Published 22 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.031402

Abstract

This paper deals with rigidity percolation in composite materials consisting of a dispersion of mineral particles in a microstructured viscoelastic matrix. The viscoelastic matrix in this specific case is a hydrocarbon refinery residue. In a set of model random composites the mean interparticle surface-to-surface distance was controlled, changing particle volume fraction φ and particle number density independently. This was achieved by mixing two sets of monodisperse particles with widely differing radii (0.35μm and 17.5μm) with the matrix. A scaling exponent of 3.9±0.6 for the storage modulus G′ vs φ−φc was observed above a threshold φc, in good agreement with theoretical values for rigidity percolation. It is found that at the rigidity-percolation threshold the pore structure, as characterized by the mean surface-to-surface distance for the filler, rather than the filler volume fraction, is similar for different types of composites. This behavior is explained from the internal structure of the viscoelastic matrix, which consists of fractal solid aggregates dissolved in a viscous medium; the effective radius of these aggregates and the mean surface-to-surface distance together determine whether or not the aggregates are capable of providing rigidity to the composite. The explanation is further supported by a qualitative comparison with effective-medium calculations. These indicate that the observed breakdown of time-temperature superposition near φc is due to the appearance of a time scale characteristic for the mechanical interplay between the viscous binder phase and the purely elastic solid particles.

View figure in article

Article Text

References (26)

  1. Asphaltenes and Asphalts, edited by T. F. Yen and G. V. Chilingarian (Elsevier, Amsterdam, 1994), Vol. 1.
  2. D. Lesueur et al., J. Rheol. 40, 813 (1996).
  3. J. Ph. Pfeiffer, The Properties of Asphaltic Bitumen, Elsevier Polymer Series (Elsevier, Amsterdam, 1950).
  4. H. C. A. Brandt, E. M. Hendriks, M. A. J. Michels, and F. Visser, J. Phys. Chem. 99, 10430 (1995).
  5. A. J. Markvoort, Master’s thesis, TU Eindhoven, 1996.
  6. A. J. Markvoort, H. C. A. Brandt, R. Haswell, and M. A. J. Michels (unpublished).
  7. Shell Internationale Research Maatschappij B.V., M. Reijnhout, Patent No. WO 00/46164, August 10, 2000; M. W. L. Wilbrink, Master’s thesis, TU Eindhoven, 2002.
  8. V. Trappe and D. A. Weitz, Phys. Rev. Lett. 85, 449 (2000).
  9. M. C. Grant and W. B. Russel, Phys. Rev. E 47, 2606 (1993).
  10. Rheometrics Ares 3LS-4A, Rheometrics Inc.
  11. G. Strobl, The Physics of Polymers, 2nd ed. (Springer, Berlin, 1997).
  12. See, e.g., M. O. Marasteanu and D. A. Anderson, Transp. Res. Rec. 1766, 32 (2001).
  13. C. van der Poel, J. Appl. Chem. 4, 221 (1954).
  14. S. Torquato, Random Heterogeneous Materials (Springer, New York, 2002).
  15. S. Roux, J. Phys. A 19, L351 (1986).
  16. M. Sahimi, J. Phys. C 19, L79 (1986).
  17. A. Hansen and S. Roux, Phys. Rev. B 40, 749 (1989).
  18. C. Moukarzel and P. M. Duxbury, Phys. Rev. E 59, 2614 (1999).
  19. In [14] this graph is shown, but the source of the points quoted is in error. S. Torquato (personal communication) remarks that two of the points are from S. Torquato[25], two from [26], and two from unpublished work by . The following values are shown in the graph: {0, 0.29}, {0.2, 0.29}, {0.6, 0.31}, {0.67, 0.32}, {0.8, 0.33}, {0.91, 0.41}, {1, 0.64}.
  20. S. B. Lee and S. Torquato, J. Chem. Phys. 89, 3258 (1988).
  21. D. He, N. N. Ekere, and L. Cai, Phys. Rev. E 65, 061304 (2002).
  22. B. Lu and S. Torquato, Phys. Rev. A 45, 5530 (1992).
  23. D. Bruggeman, Ann. Phys. 24, 636 (1935).
  24. R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneous Media, edited by J. C. Garland and D. B. Tanner (AIP, New York, 1978).
  25. E. M. Sevick, P. A. Monson, and J. M. Ottino, J. Chem. Phys. 88, 1198 (1988).
  26. M. D. Rintoul and S. Torquato, Phys. Rev. Lett. 77, 4198 (1996).

Outline

Information

Phys. Rev. E 71, 031402– Published 22 March, 2005
  • Received 17 May 2004

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation