Skip to main content

Multiscale Modeling Approach to Dynamic-Mechanical Behavior of Elastomer Nanocomposites

  • Chapter
  • First Online:
Designing of Elastomer Nanocomposites: From Theory to Applications

Part of the book series: Advances in Polymer Science ((POLYMER,volume 275))

Abstract

Rubber composites based on an elastomeric matrix filled with rigid fillers such as carbon black or silica remain important materials for technical applications and everyday life. Targeted improvement of the mechanical properties of these materials requires a deep understanding of the molecular mobility over broad time and temperature scales. We focus here on recent studies of the dynamic properties of rubber composites with the aid of a physically motivated multiscale theoretical approach. Rubber compounds, based on a solution-polymerized styrene butadiene rubber filled with precipitated silica, have been investigated. The construction of master curves for the storage and loss moduli over more than 15 decades of frequencies is presented. The master curves over the whole frequency range are analyzed with the aid of a new multiscale approach, which includes contributions from the relaxation processes described in rigorous theoretical studies for different scales of motion. It takes into account the long-scale motions of dangling chain ends, Rouse-like dynamics and bending motions of semiflexible chain fragments in the intermediate frequency range, and the specific nonpolymeric relaxation at very high frequencies. The modification of molecular mobility of polymer chains on the surfaces of filler particles and the contribution of the percolation network built by the filler are discussed. The proposed theoretical approach allows fitting of the dynamic moduli of filled and unfilled rubbers in the linear viscoelastic regime with a limited set of parameters (relaxation times, scaling exponents, molar mass of the Kuhn segment, etc.) having reasonable values. The slowing down of the relaxation processes in the vicinity of the filler particles is demonstrated.

The authors declare no competing financial interests.

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

Access this chapter

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 EPUB and 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 299.99
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

References

  1. Saphiannikova M, Toshchevikov V, Gazuz I, Petry F, Westermann S, Heinrich G (2014) Macromolecules 47:4813–4823

    Article  CAS  Google Scholar 

  2. Ivaneiko I, Toshchevikov V, Saphiannikova M, Stöckelhuber K, Petry F, Westermann S, Heinrich G (2016) Polymer 82:356–365

    Article  CAS  Google Scholar 

  3. Vilgis TA, Heinrich G, Klüppel M (2009) Reinforcement of polymer nanocomposites: theory, experiments and applications. Cambridge University Press, Cambridge

    Book  Google Scholar 

  4. Grellmann W, Heinrich G, Kaliske M, Klüppel M, Schneider K, Vilgis T (2013) Fracture mechanics and statistical mechanics of reinforced elastomeric blends. Springer, Heidelberg, New York, Dordrecht, and London

    Book  Google Scholar 

  5. Heinrich G (1997) Rubber Chem Technol 70:1–14

    Article  CAS  Google Scholar 

  6. Klüppel M, Heinrich G (2000) Rubber Chem Technol 73:578–606

    Article  Google Scholar 

  7. Heinrich G, Vilgis TA (2015) Poly Lett 9:291–299

    Article  CAS  Google Scholar 

  8. Heinrich G, Dumler BD (1998) Rubber Chem Technol 71:53–61

    Article  CAS  Google Scholar 

  9. Heinrich G, Vilgis TA (2008) Kautschuk Gummi Kunststoffe 61:368–376

    CAS  Google Scholar 

  10. Westermann S, Petry F, Boes R, Thielen G (2004) Tire Technology International: Annual review. p 68

    Google Scholar 

  11. Westermann S, Petry F, Boes R, Thielen G (2004) Kautschuk Gummi Kunststoffe 57:645–650

    CAS  Google Scholar 

  12. Stöckelhuber KW, Svistkov AS, Pelevin AG, Heinrich G (2011) Macromolecules 44:4366–4381

    Article  Google Scholar 

  13. Mooney M (1959) J Polym Sci 34:599–626

    Article  Google Scholar 

  14. Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York

    Google Scholar 

  15. Morse DC (1998) Macromolecules 31:7044–7067

    Article  CAS  Google Scholar 

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

    Google Scholar 

  17. Shore JE, Zwanzig RJ (1975) Chem Phys 63:5445–5458

    CAS  Google Scholar 

  18. Mansfield MJ (1983) Polym Sci Polym Phys Ed 21:773–786

    Article  CAS  Google Scholar 

  19. Gotlib YY, Toshchevikov VP (2001) Polym Sci A 43:525–534

    Google Scholar 

  20. Gotlib YY, Toshchevikov VP (2001) Polym Sci A 43:1074–1083

    Google Scholar 

  21. Gurtovenko AA, Gotlib YY (2000) Macromolecules 33:6578–6587

    Article  CAS  Google Scholar 

  22. Gurtovenko AA, Blumen A (2005) Adv Polym Sci 182:171–282

    Article  CAS  Google Scholar 

  23. Toshchevikov VP, Blumen A, Gotlib YY (2007) Macromol Theory Simul 16:359–377

    Article  CAS  Google Scholar 

  24. Toshchevikov VP, Gotlib YY (2009) Macromolecules 42:3417–3429

    Article  CAS  Google Scholar 

  25. Edwards SF, Takano H, Terentjev EMJ (2000) Chem Phys 113:5531–5538

    CAS  Google Scholar 

  26. Curro JG, Pincus P (1983) Macromolecules 16:559–562

    Article  CAS  Google Scholar 

  27. Curro JG, Pearson DS, Helfand E (1985) Macromolecules 18:1157–1162

    Article  CAS  Google Scholar 

  28. Heinrich G, Straube E, Helmis G (1988) Adv Polym Sci 85:33–87

    Article  CAS  Google Scholar 

  29. Edwards SF, Vilgis TA (1988) Rep Prog Phys 51:243–297

    Article  Google Scholar 

  30. Kaliske M, Heinrich G (1999) Rubber Chem Technol 72:602–632

    Article  CAS  Google Scholar 

  31. Migliorin IG, Rostiashvili VG, Vilgis TA (2003) Eur Phys J B 33:61–73

    Article  Google Scholar 

  32. Vilgis TA (2005) Polymer 46:4223–4229

    Article  CAS  Google Scholar 

  33. Klüppel M (2003) Adv Polym Sci 164:1–86

    Article  Google Scholar 

  34. Leblanc JL (2010) Filled polymers: science and industrial applications. CRC, Boca Raton

    Google Scholar 

  35. Rooj S, Das A, Stöckelhuber KW, Wang D-Y, Galiatsatos V, Heinrich G (2011) Soft Matter 9:3798–3808

    Article  Google Scholar 

  36. Doi M, Edwards SF (1988) The theory of polymer dynamics. Oxford University Press, Oxford

    Google Scholar 

  37. Klüppel M (2009) J Phys Condens Matter 21:035104

    Article  Google Scholar 

  38. Otegui J, Schwartz G, Cerveny S, Colmenero J, Loichen J, Westermann S (2013) Macromolecules 46:2407–2416

    Article  CAS  Google Scholar 

  39. Kummali M, Miccio L, Schwartz G, Alegria A, Colmenero J, Otegui J, Petzold A, Westermann S (2013) Polymer 54:4980–4986

    Article  CAS  Google Scholar 

  40. Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Hansa, Cincinnati

    Book  Google Scholar 

  41. Williams G, Watts DC (1970) Trans Faraday Soc 66:80–85

    Article  CAS  Google Scholar 

  42. Toshchevikov VP, Heinrich G, Gotlib YY (2010) Macromol Theory Simul 19:195–209

    Article  CAS  Google Scholar 

  43. Sommer J-U, Schulz M, Trautenberg HLJ (1993) Chem Phys 98:7515–7520

    CAS  Google Scholar 

  44. Lang M, Göritz D, Kreitmeier S (2003) Macromolecules 36:4646–4658

    Article  CAS  Google Scholar 

  45. Chasse W, Lang M, Sommer J-U, Saalwächter K (2012) Macromolecules 45:899–912

    Article  CAS  Google Scholar 

  46. Marzocca AJ, Steren CA, Raimondo RB, Cerveny S (2004) Polym Int 53:646–655

    Article  CAS  Google Scholar 

  47. Chatenay D, Cocco S, Monasson R, Thieffry D, Dalibard J (eds) (2005) Multiple aspects of DNA and RNA: from biophysics to bioinformatics. Lecture notes of the Les Houches Summer School 2004, session LXXXII. Elsevier, Amsterdam

    Google Scholar 

  48. Westermann S, Kreitschmann M, Pyckhout-Hintzen W, Richter D, Straube E, Farago B, Goerigk G (1999) Macromolecules 32:5793–5802

    Article  CAS  Google Scholar 

  49. Domurath J, Saphiannikova M, Ausias G, Heinrich G (2012) J Non-Newtonian Fluid Mech 171–172:8–16

    Article  Google Scholar 

  50. Domurath J, Saphiannikova M, Férec J, Ausias G, Heinrich G (2015) J Non-Newtonian Fluid Mech 221:95–102

    Article  CAS  Google Scholar 

  51. Chen HS, Acrivos A (1978) Int J Solids Struct 14:349–364

    Article  Google Scholar 

  52. Gold O (1936) Beiträge zur Hydrodynamik der zähen Flssigkeiten. Dissertation, Wien University

    Google Scholar 

  53. Guth E, Gold O (1938) Phys Rev 53:322–324

    CAS  Google Scholar 

  54. Guth E (1945) J Appl Phys 16:20–25

    Article  CAS  Google Scholar 

  55. Huber G, Vilgis TA (1999) KGK, Kautschuk Gummi Kunststoffe 52:102–107

    CAS  Google Scholar 

  56. Simhambhatla M, Leonov A (1995) Rheol Acta 34:329–338

    Article  CAS  Google Scholar 

  57. Sarvestani AS, Jabbari E (2007) Macromol Theory Simul 16:378–385

    Article  CAS  Google Scholar 

  58. Li Y, Kröger M, Liu W (2012) Phys Rev Lett 109:118001

    Article  Google Scholar 

  59. Glomann T, Schneider G, Allgaier J, Radulescu A, Lohstroh W, Farago B, Richter D (2013) Phys Rev Lett 110:178001

    Article  CAS  Google Scholar 

  60. Kalathi J, Kumar S, Rubinstein M, Grest G (2015) Soft Matter 11:4123–4132

    Article  CAS  Google Scholar 

  61. Sobhanie M, Isayev A (1999) J Non-Newtonian Fluid Mech 85:189–212

    Article  CAS  Google Scholar 

  62. Costa F, Saphiannikova M, Wagenknecht U, Heinrich G (2008) Layered double hydroxide based polymer nanocomposites. Adv. Polym. Sci. 210:101–168

    Google Scholar 

  63. Odegard G, Clancy T, Gates T (2005) Polymer 46:553–562

    Article  CAS  Google Scholar 

  64. Richter S, Saphiannikova M, Jehnichen D, Bierdel M, Heinrich G (2009) Express Polym Lett 3:753–768

    Article  CAS  Google Scholar 

  65. Richter S, Saphiannikova M, Stöckelhuber K, Heinrich G (2010) Macromol Symp 291–292:193–201

    Article  Google Scholar 

  66. Richter S, Kreyenschulte H, Saphiannikova M, Götze T, Heinrich G (2011) Macromol Symp 306–307:141–149

    Article  Google Scholar 

  67. Toshchevikov V, Gotlib Y (2006) Polym Sci Ser A 48:649–663

    Article  Google Scholar 

  68. Toshchevikov V, Gotlib Y (2013) Polym Sci Ser A 55:556–569

    Article  CAS  Google Scholar 

  69. Heinrich G, Vilgis T (1993) Macromolecules 26:1109–1119

    Article  CAS  Google Scholar 

  70. Heinrich G, Vilgis T (1993) Kautschuk Gummi Kunstoffe 46:283–289

    CAS  Google Scholar 

  71. Schneider G, Nusser K, Willner L, Falus P, Richter D (2011) Macromolecules 44:5857–5860

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge a technical support from T. Götze, K. Scheibe, and R. Jurk (Leibniz-Institut für Polymerforschung Dresden e.V.).

We wish to thank Dr. K. W. Stöckelhuber (Leibniz-Institut für Polymerforschung Dresden e.V.) for inspiring discussions, Dr. F. Petry (Goodyear Innovation Center Luxembourg) for his outstanding support and collaboration, and the Goodyear Tire and Rubber Company for permission to publish this paper.

The authors would like to cordially express their gratitude to Prof. Dr. G. Heinrich for all the outstanding collaborations and discussions during the past years. Be it in conjunction with elastomer physics, polymer and rubber viscoelasticity, rubber friction, contact mechanics, fracture mechanics, or any other scientific subject, the discussions were always shaped by respect, honesty, integrity and an impressive level of scientific competence. Prof. Heinrich is an undisputed authority in his field, from fundamental science and polymer theory up to the tire-related applications of rubber technology. He unifies the leadership traits of a scientific director, academic teacher, and institutional manager. It has always been a great pleasure to collaborate and work with him.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marina Saphiannikova .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ivaneiko, I., Toshchevikov, V., Westermann, S., Saphiannikova, M. (2016). Multiscale Modeling Approach to Dynamic-Mechanical Behavior of Elastomer Nanocomposites. In: Stöckelhuber, K., Das, A., Klüppel, M. (eds) Designing of Elastomer Nanocomposites: From Theory to Applications. Advances in Polymer Science, vol 275. Springer, Cham. https://doi.org/10.1007/12_2016_3

Download citation

Publish with us

Policies and ethics