Skip to main content
SpringerLink
Log in

Recent Advances in the Theory of Filler Networking in Elastomers

  • Chapter
  • First Online:
Filled Elastomers Drug Delivery Systems

Part of the book series: Advances in Polymer Science ((POLYMER,volume 160))

Abstract

The viscoelastic properties of (mostly carbon black) filled elastomers are reviewed with emphasis on the strain-dependence of the complex dynamic modulus (Payne effect). Considerable progress has been made in the past in relating the typical dynamical behavior at low strain amplitudes to a cyclic breakdown and reagglomeration of physical filler-filler bonds in typical clusters of varying size, including the infinite filler network. Common features between the phenomenological agglomeration/deagglomeration Kraus approach and very recent semi-microscopical networking approaches (two aggregate VTG model, links-nodes-blobs model, kinetical cluster-cluster aggregation) are discussed. All semi-microscopical models contain the assumption of geometrical arrangements of sub-units (aggregates) in particular filler network structures, resulting for example from percolation or kinetical cluster-cluster aggregation. These concepts predict some features of the Payne effect that are independent of the specific types of filler. These features are in good agreement with experimental studies. For example, the shape exponent m of the storage modulus, G′, drop with increasing deformation is determined by the structure of the cluster network. Another example is a scaling relation predicting a specific power law behavior of the elastic modulus as a function of the filler volume fraction. The exponent reflects the characteristic structure of the fractal filler clusters and of the corresponding filler network. The existing concepts of the filler network breakdown and reformation appear to be adequate in describing the deformation-dependence of dynamic mechanical properties of filled rubbers. The different approaches suggest in a common manner that there is a change of filler structure with increasing dynamic strain. However, in all cases additional assumptions are made about the accompanying energy dissipation process, imparting higher hysteresis to the filled rubber. This process may be slippage of entanglements (slip-links) in the transition layer between bound rubber layer and mobile rubber phase, and/or partially release of elastically ‘dead’ immobilized rubber trapped within the filler network or agglomerates.

The theoretical understanding of filled elastomers has been improved to the extent that now a connection can be made between the filler structures on larger length scales and the viscoelastic properties of rubbery materials.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Payne AR (1962) J Appl Polym Sci 6:57

    Article  CAS  Google Scholar 

  2. Payne AR (1963) J Appl Polym Sci 7:873

    Article  CAS  Google Scholar 

  3. Payne AR (1964) J Appl Polym Sci 8:2661

    Article  Google Scholar 

  4. Payne AR (1964) Trans IRI40:T135

    Google Scholar 

  5. Payne AR (1965) In: Kraus G (ed) Reinforcement of elastomers. Interscience Publisher, New York, chap 3

    Google Scholar 

  6. Payne AR (1972) J Appl Polym Sci 16:1191

    Article  CAS  Google Scholar 

  7. Payne AR (1963) Rubber Chem Technol 36:432

    CAS  Google Scholar 

  8. Medalia AI (1973) Rubber Chem Technol 46:877

    CAS  Google Scholar 

  9. Medalia AI ( 1974) Rubber Chem Technol 47:411

    CAS  Google Scholar 

  10. Voet A, Cook FR (1967) Rubber Chem Technol 40:1364

    CAS  Google Scholar 

  11. Voet A, Cook FR (1968) Rubber Chem Technol 41:1215

    CAS  Google Scholar 

  12. Dutta NK, Tripathy DK (1989) Kautsch Gummi Kunstst 42:665

    CAS  Google Scholar 

  13. Dutta NK, Tripathy DK (1992) J Appl Polym Sci 44:1635

    Article  CAS  Google Scholar 

  14. Dutta NK, Tripathy DK (1990) Polym Test 9:3

    Article  CAS  Google Scholar 

  15. Ulmer JD, Hergenrother WL, Lawson DF (1998) Rubber Chem Technol 71:637

    CAS  Google Scholar 

  16. Wang M-J, Patterson WJ, Ouyang GB (1998) Kautsch Gummi Kunstst 51:106

    CAS  Google Scholar 

  17. Freund B, Niedermeier W (1998) Kautsch Gummi Kunstst 51:444

    CAS  Google Scholar 

  18. Mukhopadhyay K, Tripathy DK (1992) J Elastomers Plast 24:203

    Article  CAS  Google Scholar 

  19. Wang M-J (1998) Rubber Chem Technol 71:520

    CAS  Google Scholar 

  20. Bischoff A, Klüppel M, Schuster RH (1998) Polym Bull 40:283

    Article  CAS  Google Scholar 

  21. Vieweg S, Unger R, Heinrich G, Donth E (1999) J Appl Polym Sci 73:495

    Article  CAS  Google Scholar 

  22. Payne AR, Watson WF (1963) Rubber Chem Technol 36:147

    Google Scholar 

  23. Amari T, Mesugi K, Suzuki H (1997) Prog Org Coat 31:171

    Article  CAS  Google Scholar 

  24. Payne AR, Wittaker RE (1970) Rheol Acta 9:91

    Article  CAS  Google Scholar 

  25. Payne AR, Wittaker RE (1970) Rheol Acta 9:97

    Article  Google Scholar 

  26. Brown JD ( 1997) Nonlinear dynamic behavior of filled elastomers at small strain amplitudes. PhD Thesis, Rensselaer Polytechnic Institute, Troy, New York; Chazeau L, Brown JD,Yanyo LC, Sternstein SS (2000) Polym Compos 21:202

    Google Scholar 

  27. Wilhelm M, Reinheimer P, Orteifer M (1999) Rheol Acta 38:349; (1999) Kautsch Gummi Kunstst 52:754

    Article  CAS  Google Scholar 

  28. Voet A, Morawski JC (1974) Rubber Chem Technol 47:765

    CAS  Google Scholar 

  29. Giuliani G, Volpi A (1985) Developments in dynamic testing procedures. Paper No 79, ACS Rubber Division Meeting, Cleveland, Ohio

    Google Scholar 

  30. Dutta NK, Tripathy DK, Medalia AI ( 1973) Rubber World 168:49

    Google Scholar 

  31. Lion A (1998) J Mech Phys Solids 46:895

    Article  CAS  Google Scholar 

  32. Lion A (1999) Rubber Chem Technol 72:410

    CAS  Google Scholar 

  33. Medalia AI (1978) Rubber Chem Technol 51:437

    CAS  Google Scholar 

  34. Medalia AI, Laube SG (1978) Rubber Chem Technol 51:89

    CAS  Google Scholar 

  35. Sircar AK, Lamond TG (1975) Rubber Chem Technol 48:79,89

    Google Scholar 

  36. Kraus G (1984) J App Polym Sci, Appl Polym Symp 39:75

    CAS  Google Scholar 

  37. Ouyang GB, Tokita N, Wang M-J (1995) Paper No 108, ACS Rubber Division Meeting, Cleveland, Ohio

    Google Scholar 

  38. Payne AR, Wittaker RE (1971) Rubber Chem Technol 44:440

    CAS  Google Scholar 

  39. Roland CM, Lee GF (1989) NTIS Rep AD-A2 12824

    Google Scholar 

  40. Ulmer JD, Hess WM, Chirico VE (1974) Rubber Chem Technol 47:729

    CAS  Google Scholar 

  41. Gui KE, Wilkinson CS Jr, Gehmann SD (1952) Ind Eng Chem 44:720

    Article  CAS  Google Scholar 

  42. Smit PPA (1966) Rheol Acta 5:277

    Article  CAS  Google Scholar 

  43. Maier P, Göritz D (1998) Kautsch Gummi Kunstst 49:18

    Google Scholar 

  44. Dean GD, Duncan JC, Johnson AF (1984) Polym Test 4:225

    Article  CAS  Google Scholar 

  45. Martin RE, Malguarnera SC (1981) J Elastomers Plast 13:139

    Article  CAS  Google Scholar 

  46. Ahmadi HR, Muhr AH (1997) Plast Rubber Compos Process Appl 26:451

    CAS  Google Scholar 

  47. Resh WF (Sept 1990) SAE Tech Paper Ser 901757, Passenger Car Meeting and Exposition, Dearborn, Michigan

    Google Scholar 

  48. Fujita T, Suzuki S, Fujita S (1989) ASME, PVP, Seismic Shock Vibration Isolation 181:23

    Google Scholar 

  49. Iwan WD (1967) J Appl Mech (ASME) 612

    Google Scholar 

  50. Turner DM (1988) Plast Rubber Compos Process Appl 9:197

    CAS  Google Scholar 

  51. Coveney VA, Johnson DE, Turner DM (1995) Rubber Chem Technol 68:660

    CAS  Google Scholar 

  52. Coveney VA, Johnson DE (2000) Rubber Chem Technol 73:565

    CAS  Google Scholar 

  53. Coveney VA, Johnson DE (1999) Rubber Chem Technol 72:673

    CAS  Google Scholar 

  54. Tschoegl NW (1989) The phenomenological theory of linear viscoelasticity. Springer, Berlin Heidelberg New York

    Google Scholar 

  55. Harris JA (1987) Rubber Chem Technol 60:870

    CAS  Google Scholar 

  56. Heinrich G, Vilgis TA (1995) Macromol Chem Phys Macromol Symp 93:253

    CAS  Google Scholar 

  57. Vieweg S, Unger R, Schröter K, Donth E, Heinrich G (1995) Polym Network Blends 5:199

    CAS  Google Scholar 

  58. Huber G, Vilgis TA (1999) Kautsch Gummi Kunstst 52:102

    CAS  Google Scholar 

  59. Huber G (1997) PhD thesis, University of Mainz, Germany

    Google Scholar 

  60. Witten TA, Rubinstein M, Colby RH (1993) J Phys II (France) 3:367

    Article  CAS  Google Scholar 

  61. De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca, London

    Google Scholar 

  62. Bunde A, Havlin S (1996) (eds) Fractals and disordered systems. Springer, Berlin Heidelberg New York

    Google Scholar 

  63. Klüppel M, Heinrich G (1995) Rubber Chem Technol 68:623

    Google Scholar 

  64. Klüppel M, Schuster RH, Heinrich G (1997) Rubber Chem Technol 70:243

    Google Scholar 

  65. Huber G, Vilgis TA, Heinrich G (1996) J Phys Condens Matter 8:409

    Article  Google Scholar 

  66. Ulmer JD (1996) Rubber Chem Technol 69:15

    CAS  Google Scholar 

  67. Wang M-J, Patterson WJ, Ouyang GB (1996) Paper No 33, ACS Rubber Division Meeting, Montreal, Canada

    Google Scholar 

  68. Gerspacher M, O’Farrell CP (1992) Kautsch Gummi Kunstst 45:97; Gerspacher M (1993) Dynamic viscoelastic properties of loaded elastomers. In: Donnet J-B, Bansal RC, Wang M-J (eds) Carbon black. science and technology. Marcel Dekker, New York Basel Hong Kong

    CAS  Google Scholar 

  69. Le Méhauté A (1991) Fractal geometries. Theory and applications. CRC Press, Boca Raton Ann Arbor London; Le Méhauté A, Crepy G (1983) Solid State Ionics 9/10:17

    Google Scholar 

  70. Sapoval B (1991) Fractal electrodes, fractal membranes, and fractal catalysts. In: Bunde A, Havlin S (eds) Fractals and disordered system. Springer, Berlin Heidelberg New York

    Google Scholar 

  71. Liu SH (1985) Phys Rev Lett 55:529

    Article  CAS  Google Scholar 

  72. Blunt M (1989) J Phys A: Math Gen 22:1179

    Article  Google Scholar 

  73. Sapoval B (1994) Phys Rev Lett 73:3314

    Article  CAS  Google Scholar 

  74. Le Méhauté A, Gerspacher M, Tricot C (1993) Fractal geometry. In: Donnet J-B, Bansal RC, Wang M-J (eds) Carbon black. Science and technology. Marcel Dekker, New York Basel Hong Kong

    Google Scholar 

  75. Le Méhauté A (1984) J Stat Phys 36:665

    Article  Google Scholar 

  76. Zerda TW, Yang H, Gerspacher M (1992) Rubber Chem Technol 65:130

    CAS  Google Scholar 

  77. Schröder A, Klüppel M, Schuster RH (1999) Kautsch Gummi Kunstst 52:814; (2000) Kautsch Gummi Kunstst 53:257

    Google Scholar 

  78. Klüppel M, Schramm J (2000) Macromol Theory Simul 9:742

    Article  Google Scholar 

  79. Klüppel M, Schramm J (1999) An advanced micromechanical model of hyperelasticity and stress softening of reinforced rubbers. In: Dorfmann A, Muhr A (eds) Constitutive models for rubber. A.A. Balkema,, Rotterdam

    Google Scholar 

  80. Van de Walle A, Tricot C, Gerspacher M (1994) Paper No 10, ACS Rubber Division Meeting, Pittsburgh, Pennsylvania

    Google Scholar 

  81. Gerspacher M, O’Farrell CP, Tricot C, Nikiel L, Yang HA (1996) Paper No 74, ACS Rubber Division Meeting, Louisiana, Kentucky

    Google Scholar 

  82. Van de Walle A, Tricot C, Gerspacher M (1996) Kautsch Gummi Kunstst 49:172

    Google Scholar 

  83. Welsh FE, Richmond BR, Keach CB, Emerson RJ (1995) Paper No 59, ACS Rubber Division Meeting, Philadelphia

    Google Scholar 

  84. Yamaguchi T, Kurimoto I, Ohashi K, Okita T (1989) Kautsch Gummi Kunstst 42:403

    CAS  Google Scholar 

  85. Wolff S, Wang M-J, Tan E-H (1994) Kautsch Gummi Kunstst 47:102

    CAS  Google Scholar 

  86. Gent AN, Hwang Y-C (1988) Rubber Chem Technol 61:630

    CAS  Google Scholar 

  87. Gent AN, Park B (1986) Rubber Chem Technol 59:77

    CAS  Google Scholar 

  88. Heinrich G, Vilgis TA (1993) Macromolecules 26:1109

    Article  CAS  Google Scholar 

  89. Wolff S, Wang M-J, Tan E-H (1993) Rubber Chem Technol 61:102

    Google Scholar 

  90. Lin C-R, Lee Y-D (1996) Macromol Theory Simul 5:1075; (1997) Macromol Theory Simul 6:339

    Article  CAS  Google Scholar 

  91. Kantor Y, Webman I (1984) Phys Rev Lett 52:1891

    Article  Google Scholar 

  92. Schuster RH, Klüppel M, Schramm J, Heinrich G (1998) Paper No 56, ACS Rubber Division Meeting, Indianapolis

    Google Scholar 

  93. Meakin P (1990) Prog Solid State Chem 20:135; (1988) Adv Colloid Interface Sci 28:249

    Article  Google Scholar 

  94. Vieweg S (1997) PhD thesis, University of Halle, Germany

    Google Scholar 

  95. Vieweg S, Unger R, Hempel E, Donth E (1998) J Non-Cryst Solids 235/237:470

    Article  Google Scholar 

  96. Litvinov VM, Steeman PAM (1999) Macromolecules 32:8476

    Article  CAS  Google Scholar 

  97. Dutta NK, Roy Choudhury N, Haidar B, Vidal A, Donnet J-B (1994) Polymer 35:4293

    Article  CAS  Google Scholar 

  98. Früh T (1996) PhD thesis, University of Hannover, Germany

    Google Scholar 

  99. Hofmann W (1989) Rubber technology handbook. Hanser Publishers, München Wien New York

    Google Scholar 

  100. Raos G, Allegra G, Assecondi L, Croci C (2000) Comput Theor Polym Sci 10:149

    Article  CAS  Google Scholar 

  101. Wang M-J (1999) Rubber Chem Technol 72:430

    CAS  Google Scholar 

  102. Kastner A, Alig I, Heinrich G, Klüppel M (2002) Polym Bull (in preparation)

    Google Scholar 

  103. Fitzgerald ER (1982) Polym Bull 8:331

    CAS  Google Scholar 

  104. Fitzgerald ER (1982) Rubber Chem Technol 55:1547

    CAS  Google Scholar 

  105. Heinrich G (1997) Gummi Fasern Kunstst 50:775

    CAS  Google Scholar 

  106. Heinrich G (1992) Filler-filler interaction. Internal Research Report Continental AG AN92/4.3/20 (unpublished)

    Google Scholar 

  107. Susteric Z (1989) Makromol Chem Makromol Symp 23:329

    CAS  Google Scholar 

  108. Cai JJ, Salovey R (1999) J Mat Sci 34:4719

    Article  CAS  Google Scholar 

  109. Lanzl T, Ludwig J, Kreitmeier S, Göritz D (2000) Kautsch Gummi Kunstst 53:623

    Google Scholar 

  110. Karásek L, Meissner B, Asai S, Sumita M (1996) Polym J 28:121

    Article  Google Scholar 

  111. Lin C-R, Chen Y-C, Chang C-Y (2001) Macromol Theory Simul (in press)

    Google Scholar 

  112. Niedermeier W (1998) Paper No 28, ACS Rubber Division Meeting, Nashville, Tennessee

    Google Scholar 

  113. Eggers H, Schümer P (1996) Rubber Chem Technol 69:253

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Continental AG, Strategic Technology, P.O. Box 169, 30001, Hannover, Germany

    Gert Heinrich

  2. Deutsches Institut für Kautschuktechnologie e. V., Eupener Strasse 33, 30519, Hannover, Germany

    Manfred Klüppel

Authors
  1. Gert Heinrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manfred Klüppel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Heinrich, G., Klüppel, M. (2002). Recent Advances in the Theory of Filler Networking in Elastomers. In: Filled Elastomers Drug Delivery Systems. Advances in Polymer Science, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45362-8_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-45362-8_1

  • Received:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43052-0

  • Online ISBN: 978-3-540-45362-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation