Advertisement

Multiscale Modeling Approach to Dynamic-Mechanical Behavior of Elastomer Nanocomposites

  • Ievgeniia Ivaneiko
  • Vladimir Toshchevikov
  • Stephan Westermann
  • Marina Saphiannikova
Chapter
Part of the Advances in Polymer Science book series (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.

Keywords

Dynamic moduli Multiscale theoretical approach Polymer localization Rigid fillers Rubber composites 

Notes

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.

References

  1. 1.
    Saphiannikova M, Toshchevikov V, Gazuz I, Petry F, Westermann S, Heinrich G (2014) Macromolecules 47:4813–4823CrossRefGoogle Scholar
  2. 2.
    Ivaneiko I, Toshchevikov V, Saphiannikova M, Stöckelhuber K, Petry F, Westermann S, Heinrich G (2016) Polymer 82:356–365CrossRefGoogle Scholar
  3. 3.
    Vilgis TA, Heinrich G, Klüppel M (2009) Reinforcement of polymer nanocomposites: theory, experiments and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  4. 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 LondonCrossRefGoogle Scholar
  5. 5.
    Heinrich G (1997) Rubber Chem Technol 70:1–14CrossRefGoogle Scholar
  6. 6.
    Klüppel M, Heinrich G (2000) Rubber Chem Technol 73:578–606CrossRefGoogle Scholar
  7. 7.
    Heinrich G, Vilgis TA (2015) Poly Lett 9:291–299CrossRefGoogle Scholar
  8. 8.
    Heinrich G, Dumler BD (1998) Rubber Chem Technol 71:53–61CrossRefGoogle Scholar
  9. 9.
    Heinrich G, Vilgis TA (2008) Kautschuk Gummi Kunststoffe 61:368–376Google Scholar
  10. 10.
    Westermann S, Petry F, Boes R, Thielen G (2004) Tire Technology International: Annual review. p 68Google Scholar
  11. 11.
    Westermann S, Petry F, Boes R, Thielen G (2004) Kautschuk Gummi Kunststoffe 57:645–650Google Scholar
  12. 12.
    Stöckelhuber KW, Svistkov AS, Pelevin AG, Heinrich G (2011) Macromolecules 44:4366–4381CrossRefGoogle Scholar
  13. 13.
    Mooney M (1959) J Polym Sci 34:599–626CrossRefGoogle Scholar
  14. 14.
    Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New YorkGoogle Scholar
  15. 15.
    Morse DC (1998) Macromolecules 31:7044–7067CrossRefGoogle Scholar
  16. 16.
    Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, OxfordGoogle Scholar
  17. 17.
    Shore JE, Zwanzig RJ (1975) Chem Phys 63:5445–5458Google Scholar
  18. 18.
    Mansfield MJ (1983) Polym Sci Polym Phys Ed 21:773–786CrossRefGoogle Scholar
  19. 19.
    Gotlib YY, Toshchevikov VP (2001) Polym Sci A 43:525–534Google Scholar
  20. 20.
    Gotlib YY, Toshchevikov VP (2001) Polym Sci A 43:1074–1083Google Scholar
  21. 21.
    Gurtovenko AA, Gotlib YY (2000) Macromolecules 33:6578–6587CrossRefGoogle Scholar
  22. 22.
    Gurtovenko AA, Blumen A (2005) Adv Polym Sci 182:171–282CrossRefGoogle Scholar
  23. 23.
    Toshchevikov VP, Blumen A, Gotlib YY (2007) Macromol Theory Simul 16:359–377CrossRefGoogle Scholar
  24. 24.
    Toshchevikov VP, Gotlib YY (2009) Macromolecules 42:3417–3429CrossRefGoogle Scholar
  25. 25.
    Edwards SF, Takano H, Terentjev EMJ (2000) Chem Phys 113:5531–5538Google Scholar
  26. 26.
    Curro JG, Pincus P (1983) Macromolecules 16:559–562CrossRefGoogle Scholar
  27. 27.
    Curro JG, Pearson DS, Helfand E (1985) Macromolecules 18:1157–1162CrossRefGoogle Scholar
  28. 28.
    Heinrich G, Straube E, Helmis G (1988) Adv Polym Sci 85:33–87CrossRefGoogle Scholar
  29. 29.
    Edwards SF, Vilgis TA (1988) Rep Prog Phys 51:243–297CrossRefGoogle Scholar
  30. 30.
    Kaliske M, Heinrich G (1999) Rubber Chem Technol 72:602–632CrossRefGoogle Scholar
  31. 31.
    Migliorin IG, Rostiashvili VG, Vilgis TA (2003) Eur Phys J B 33:61–73CrossRefGoogle Scholar
  32. 32.
    Vilgis TA (2005) Polymer 46:4223–4229CrossRefGoogle Scholar
  33. 33.
    Klüppel M (2003) Adv Polym Sci 164:1–86CrossRefGoogle Scholar
  34. 34.
    Leblanc JL (2010) Filled polymers: science and industrial applications. CRC, Boca RatonGoogle Scholar
  35. 35.
    Rooj S, Das A, Stöckelhuber KW, Wang D-Y, Galiatsatos V, Heinrich G (2011) Soft Matter 9:3798–3808CrossRefGoogle Scholar
  36. 36.
    Doi M, Edwards SF (1988) The theory of polymer dynamics. Oxford University Press, OxfordGoogle Scholar
  37. 37.
    Klüppel M (2009) J Phys Condens Matter 21:035104CrossRefGoogle Scholar
  38. 38.
    Otegui J, Schwartz G, Cerveny S, Colmenero J, Loichen J, Westermann S (2013) Macromolecules 46:2407–2416CrossRefGoogle Scholar
  39. 39.
    Kummali M, Miccio L, Schwartz G, Alegria A, Colmenero J, Otegui J, Petzold A, Westermann S (2013) Polymer 54:4980–4986CrossRefGoogle Scholar
  40. 40.
    Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Hansa, CincinnatiCrossRefGoogle Scholar
  41. 41.
    Williams G, Watts DC (1970) Trans Faraday Soc 66:80–85CrossRefGoogle Scholar
  42. 42.
    Toshchevikov VP, Heinrich G, Gotlib YY (2010) Macromol Theory Simul 19:195–209CrossRefGoogle Scholar
  43. 43.
    Sommer J-U, Schulz M, Trautenberg HLJ (1993) Chem Phys 98:7515–7520Google Scholar
  44. 44.
    Lang M, Göritz D, Kreitmeier S (2003) Macromolecules 36:4646–4658CrossRefGoogle Scholar
  45. 45.
    Chasse W, Lang M, Sommer J-U, Saalwächter K (2012) Macromolecules 45:899–912CrossRefGoogle Scholar
  46. 46.
    Marzocca AJ, Steren CA, Raimondo RB, Cerveny S (2004) Polym Int 53:646–655CrossRefGoogle Scholar
  47. 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, AmsterdamGoogle Scholar
  48. 48.
    Westermann S, Kreitschmann M, Pyckhout-Hintzen W, Richter D, Straube E, Farago B, Goerigk G (1999) Macromolecules 32:5793–5802CrossRefGoogle Scholar
  49. 49.
    Domurath J, Saphiannikova M, Ausias G, Heinrich G (2012) J Non-Newtonian Fluid Mech 171–172:8–16CrossRefGoogle Scholar
  50. 50.
    Domurath J, Saphiannikova M, Férec J, Ausias G, Heinrich G (2015) J Non-Newtonian Fluid Mech 221:95–102CrossRefGoogle Scholar
  51. 51.
    Chen HS, Acrivos A (1978) Int J Solids Struct 14:349–364CrossRefGoogle Scholar
  52. 52.
    Gold O (1936) Beiträge zur Hydrodynamik der zähen Flssigkeiten. Dissertation, Wien UniversityGoogle Scholar
  53. 53.
    Guth E, Gold O (1938) Phys Rev 53:322–324Google Scholar
  54. 54.
    Guth E (1945) J Appl Phys 16:20–25CrossRefGoogle Scholar
  55. 55.
    Huber G, Vilgis TA (1999) KGK, Kautschuk Gummi Kunststoffe 52:102–107Google Scholar
  56. 56.
    Simhambhatla M, Leonov A (1995) Rheol Acta 34:329–338CrossRefGoogle Scholar
  57. 57.
    Sarvestani AS, Jabbari E (2007) Macromol Theory Simul 16:378–385CrossRefGoogle Scholar
  58. 58.
    Li Y, Kröger M, Liu W (2012) Phys Rev Lett 109:118001CrossRefGoogle Scholar
  59. 59.
    Glomann T, Schneider G, Allgaier J, Radulescu A, Lohstroh W, Farago B, Richter D (2013) Phys Rev Lett 110:178001CrossRefGoogle Scholar
  60. 60.
    Kalathi J, Kumar S, Rubinstein M, Grest G (2015) Soft Matter 11:4123–4132CrossRefGoogle Scholar
  61. 61.
    Sobhanie M, Isayev A (1999) J Non-Newtonian Fluid Mech 85:189–212CrossRefGoogle Scholar
  62. 62.
    Costa F, Saphiannikova M, Wagenknecht U, Heinrich G (2008) Layered double hydroxide based polymer nanocomposites. Adv. Polym. Sci. 210:101–168Google Scholar
  63. 63.
    Odegard G, Clancy T, Gates T (2005) Polymer 46:553–562CrossRefGoogle Scholar
  64. 64.
    Richter S, Saphiannikova M, Jehnichen D, Bierdel M, Heinrich G (2009) Express Polym Lett 3:753–768CrossRefGoogle Scholar
  65. 65.
    Richter S, Saphiannikova M, Stöckelhuber K, Heinrich G (2010) Macromol Symp 291–292:193–201CrossRefGoogle Scholar
  66. 66.
    Richter S, Kreyenschulte H, Saphiannikova M, Götze T, Heinrich G (2011) Macromol Symp 306–307:141–149CrossRefGoogle Scholar
  67. 67.
    Toshchevikov V, Gotlib Y (2006) Polym Sci Ser A 48:649–663CrossRefGoogle Scholar
  68. 68.
    Toshchevikov V, Gotlib Y (2013) Polym Sci Ser A 55:556–569CrossRefGoogle Scholar
  69. 69.
    Heinrich G, Vilgis T (1993) Macromolecules 26:1109–1119CrossRefGoogle Scholar
  70. 70.
    Heinrich G, Vilgis T (1993) Kautschuk Gummi Kunstoffe 46:283–289Google Scholar
  71. 71.
    Schneider G, Nusser K, Willner L, Falus P, Richter D (2011) Macromolecules 44:5857–5860CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ievgeniia Ivaneiko
    • 1
  • Vladimir Toshchevikov
    • 1
  • Stephan Westermann
    • 2
  • Marina Saphiannikova
    • 1
  1. 1.Leibniz-Institut für Polymerforschung Dresden e. V.DresdenGermany
  2. 2.Goodyear Innovation Center LuxembourgColmar-BergLuxembourg

Personalised recommendations