11. Robertson CG, Lin CJ, Rackaitis M, Roland CM (2008) Macromolecules 41:2727–2731
12. Kraus G (1984) J Appl Polym Sci 39:75–92
13. Medalia AI (1973) Rubber World 168:49
14. Wang M (1998) Rubber Chem Technol 71:520–589
15. Kraus G (1984) Mechanical losses in carbon-black-filled rubbers. In: Applied polymer
symposia, 75–92, Phillips Petroleum Co, Bartlesville, OK, USA, Phillips Petroleum Co,
Bartlesville, OK, USA
16. Huber G, Vilgis TA (2002) On the mechanism of hydrodynamic reinforcement in elastic
composites. Macromolecules 35:9204–9210
17. Witten TA, Rubinstein M, Colby RH (1993) Reinforcement of rubber by fractal aggregates.
J Phys II 3:367–383
18. Heinrich G, Klu ¨ppel M, Vilgis TA (2002) Reinforcement of elastomers. Curr Opin Sol Stat
Mater Sci 6:195–203
19. Kluppel M, Schuster R, Heinrich G (1997) Rubber Chem Technol 70:243–255
20. Funt JM (1999) Rubber Chem Technol 4:657–675
21. Maier PG, Goritz D (1996) Kautsch. Gummi Kunstst 49, Jahrgang.Nr. 1/96
22. Zhu AJ, Sternstein SS (2003) Nonlinear viscoelasticity of nanofilled polymers: interfaces,
chain statistics and properties recovery kinetics. Compos Sci Technol 63:1113–1126
23. Sternstein SS, Zhu AJ (2002) Reinforcement mechanism of nanofilled polymer melts as
elucidated by nonlinear viscoelastic behavior. Macromolecules 35:7262–7273
24. Marrone M, Montanari T, Busca G, Conzatti L, Costa G, Castellano M, Turturro A (2004)
J Phys Chem B 108:3563–3572
25. Bokobza L (2004) The reinforcement of elastomeric networks by fillers. Macromol Mater
Eng 289:607–621
26. Castellano M, Conzatti L, Turturro A, Costa G, Busca G (2007) J Phys Chem B
111:4495–502
27. Clement F, Bokobza L, Monnerie L (2005) Investigation of the Payne effect and its temperature dependence on silica-filled polydimethylsiloxane networks. Part I: Experimental
results. Rubber Chem Technol 78:211
28. Paquien JN, Galy J, Gerard JF, Pouchelon A (2005) Rheological studies of fumed silica–
polydimethylsiloxane suspensions. Colloids Surf A 260:165–172
29. Ramier J, Gauthier C, Chazeau L, Stelandre L, Guy L (2007) J Polym Sci B Polym Phys
45:286–298
30. Maier PG, Goritz D (1993) Kautsch Gummi Kunstst 46, Jahrgang. Nr. 11/93
31. Maier PG, Goritz D (2000) Kautsch Gummi Kunstst 53, Jahrgang. Nr. 12/2000
32. Cassagnau P (2003) Payne effect and shear elasticity of silica-filled polymers in concentrated
solutions and in molten state. Polymer 44:2455–2462
33. Cassagnau P (2008) Melt rheology of organoclay and fumed silica nanocomposites. Polymer
49:2183–2196
34. Sun J, Song Y, Zheng Q, Tan H, Yu J, Li H (2007) J Polym Sci B Polym Phys 45:2594–2602
35. Yatsuyanagi F, Kaidou H, Ito M (1999) Rubber Chem Technol 4:657–672
36. Berriot J, Montes H, Lequeux F, Long D, Sotta P (2003) Europhys Lett 64:50–56
37. Berriot J, Lequeux F, Montes H, Monnerie L, Long D, Sotta PJ (2002) Non-Cryst Solids
719:307–310
38. Montes H, Lequeux F, Berriot J (2003) Influence of the glass transition temperature gradient
on the nonlinear viscoelastic behavior in reinforced elastomers. Macromolecules
36:8107–8118
39. Merabia S, Sotta P, Long DR (2008) A microscopic model for the reinforcement and the
nonlinear behavior of filled elastomers and thermoplastic elastomers (Payne and Mullins
Effects). Macromolecules 41:8252–8266
40. Ferry JD (1980) Viscoelasticity properties of polymer, 3rd edn. Wiley, New York
41. Callister W (2007) Materials science and engineering. Wiley, City
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
265
12. Kraus G (1984) J Appl Polym Sci 39:75–92
13. Medalia AI (1973) Rubber World 168:49
14. Wang M (1998) Rubber Chem Technol 71:520–589
15. Kraus G (1984) Mechanical losses in carbon-black-filled rubbers. In: Applied polymer
symposia, 75–92, Phillips Petroleum Co, Bartlesville, OK, USA, Phillips Petroleum Co,
Bartlesville, OK, USA
16. Huber G, Vilgis TA (2002) On the mechanism of hydrodynamic reinforcement in elastic
composites. Macromolecules 35:9204–9210
17. Witten TA, Rubinstein M, Colby RH (1993) Reinforcement of rubber by fractal aggregates.
J Phys II 3:367–383
18. Heinrich G, Klu ¨ppel M, Vilgis TA (2002) Reinforcement of elastomers. Curr Opin Sol Stat
Mater Sci 6:195–203
19. Kluppel M, Schuster R, Heinrich G (1997) Rubber Chem Technol 70:243–255
20. Funt JM (1999) Rubber Chem Technol 4:657–675
21. Maier PG, Goritz D (1996) Kautsch. Gummi Kunstst 49, Jahrgang.Nr. 1/96
22. Zhu AJ, Sternstein SS (2003) Nonlinear viscoelasticity of nanofilled polymers: interfaces,
chain statistics and properties recovery kinetics. Compos Sci Technol 63:1113–1126
23. Sternstein SS, Zhu AJ (2002) Reinforcement mechanism of nanofilled polymer melts as
elucidated by nonlinear viscoelastic behavior. Macromolecules 35:7262–7273
24. Marrone M, Montanari T, Busca G, Conzatti L, Costa G, Castellano M, Turturro A (2004)
J Phys Chem B 108:3563–3572
25. Bokobza L (2004) The reinforcement of elastomeric networks by fillers. Macromol Mater
Eng 289:607–621
26. Castellano M, Conzatti L, Turturro A, Costa G, Busca G (2007) J Phys Chem B
111:4495–502
27. Clement F, Bokobza L, Monnerie L (2005) Investigation of the Payne effect and its temperature dependence on silica-filled polydimethylsiloxane networks. Part I: Experimental
results. Rubber Chem Technol 78:211
28. Paquien JN, Galy J, Gerard JF, Pouchelon A (2005) Rheological studies of fumed silica–
polydimethylsiloxane suspensions. Colloids Surf A 260:165–172
29. Ramier J, Gauthier C, Chazeau L, Stelandre L, Guy L (2007) J Polym Sci B Polym Phys
45:286–298
30. Maier PG, Goritz D (1993) Kautsch Gummi Kunstst 46, Jahrgang. Nr. 11/93
31. Maier PG, Goritz D (2000) Kautsch Gummi Kunstst 53, Jahrgang. Nr. 12/2000
32. Cassagnau P (2003) Payne effect and shear elasticity of silica-filled polymers in concentrated
solutions and in molten state. Polymer 44:2455–2462
33. Cassagnau P (2008) Melt rheology of organoclay and fumed silica nanocomposites. Polymer
49:2183–2196
34. Sun J, Song Y, Zheng Q, Tan H, Yu J, Li H (2007) J Polym Sci B Polym Phys 45:2594–2602
35. Yatsuyanagi F, Kaidou H, Ito M (1999) Rubber Chem Technol 4:657–672
36. Berriot J, Montes H, Lequeux F, Long D, Sotta P (2003) Europhys Lett 64:50–56
37. Berriot J, Lequeux F, Montes H, Monnerie L, Long D, Sotta PJ (2002) Non-Cryst Solids
719:307–310
38. Montes H, Lequeux F, Berriot J (2003) Influence of the glass transition temperature gradient
on the nonlinear viscoelastic behavior in reinforced elastomers. Macromolecules
36:8107–8118
39. Merabia S, Sotta P, Long DR (2008) A microscopic model for the reinforcement and the
nonlinear behavior of filled elastomers and thermoplastic elastomers (Payne and Mullins
Effects). Macromolecules 41:8252–8266
40. Ferry JD (1980) Viscoelasticity properties of polymer, 3rd edn. Wiley, New York
41. Callister W (2007) Materials science and engineering. Wiley, City
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
265