J Mater Sci(2008)43:6747-6757 6757 to the individual fiber. These models are far less successfull 13. Fantner GE, Rabinovych O, Schitter G, Thurner P, Kindt JH in translating the properties of the interphase on an indi- Finch MM, Weaver JC, Golde LS, Morse DE, Lipman EA vidual fiber into the performance of a multifiber composite angelo Iw, Hansma PK(2006)Compos Sci Technol 66: 1205 14. Kim J-K, Mai Y-w(1998)Engineered interfaces in fiber rein 16. Cave NG, Kinloch AJ(1992)Polymer 33: 1167 nG forced composites, Ch 3. Elsevier, Amsterdam, p On the nano-scale, the discrete molecular structure of 15. Droste dh, DiBenedetto AT(1969)J Appl Polym Sci 13: 2149 the polymer has to be considered. The segmental im bilization seems to be the primary reinforcing mechanism 18.Kim -K, Mai Y-w (1998)Engineered interfaces in fiber rein in true polymer nanocomposites at temperatures near and forced composites, Ch 4. Elsevier, Amsterdam, p 93 above the Tg. Reptation model and simple percolation 19 Pluedemann EP(982)Silane coupling agents. Plenum Press, model were used to describe immobilization of chains near 20 DiBenedetto AT, Huang SI, Birch D, Gomes J, Lee WC(1994) solid nano-particles and to explain the peculiarities in the Compos Struct 27: 73 viscoleastic response of polymers near solid surfaces of 21. Jancar J(2008)Polym Compos 28: large polymer-inclusion contact area. The"interphase "in 22 Jancar J(2006)Comp Sci Technol 66: 3144 the col m sense does not exist at the nano-scale when 3. Maranganti R, Sharma P(2007)J Mech Phys Solids 55: 1823 relaxation processes in individual discrete chains are taken 25. Narayanan RA, Thiyagarajan P, Zhu A-, Ash BI, Shofner M into account and the chains with retarded reptation can be Schadler LS, Kumar SK, Sternstein Ss(2007) Polymer 48: 5734 considered forming the"interphase "analogue in the dis- 26. Eitan A, Fisher FT, Andrews R, Brinson LC, Schadler Ls(2006) crete matter. For a common polymer, all the chains in the omposite become effectively immobilized when the 27. Yu T, Lin J, Xu J, Chen T, Lin S, Tian X (2007) Comp Sci Technol 67: 3219 internal filler-polymer interface area equals approximately 28. Drozdov AD. Jensen EA. Christiansen JC(2008)Int J Eng Sci In polymers at very low temperatures, the classical Ber- 29. Ha SR, Rhee KY, Kim HC, Kim JT (2008)Coll houlli-Euler continuum elasticity becomes not valid below 30. Cosoli P. Scocchi G. Pricl S. Fermeglia M(2008) Micro approximately 5 nm. The size of this characteristic volume Mesopor Mater 107: 169 increases with increasing temperature and higher-order 31. Jiang L, Zhang J, Wolcott MP (2007)Polymer 48:7632 strain elasticity along with molecular dynamics approach 32. Stemstein SS, Zhu AJ(2002)Macromolecules 35: 7262 has to be used as the bridging law to connect behavior of the 33. Kalfus J, Jancar J(2007) Polym Compos 28: 365 4. Kalfus J, Jancar J(2007)J Polym Sci: Part B: Polym Phys discrete matter at nano-scale with mechanical response of ontinuous matter at larger length scales 35. Kalfus J, Jancar J(2007)Polym Compos 28: 743 Bettye L et al (1999)Nature 399: 761 Acknowledgement Financial support from the Czech Ministry of 37. Zidek J, Jancar J(2006)Key Eng Mater 334-33.5:857 Education, Youth and Sports under grant MsM 002163050l is great 38. Doi M, Edwards SF(2003)Theory of polymer dynamics. Oxford 39. Lin Y-H (1985) Macromolecules 18: 2779 40. Zheng x. Sauer BB, van Alsten JG, Schwarz SA, Rafail References 41. Yoon DY Suter UW. Sund L. Pukanszky B(2005)Eur Polym J 41: 645 42. Subbotin A, Semenov A, Doi M(1997) Phys Rev E 56:56 2. DiBenedetto AT(2001) Mater Sci Eng A302: 74 43. deGennes P-G(1979)Scaling concepts in polymer physics 3. Hashin Z(2002)J Mech Phys Solids 50: 2509 Cornell University Press, London 4. 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Nikolov S, Han CS, Rabbe d(2007)J Solids Struct 44: 1582 12. Fantner G, Oroudjev e, Schitter G, Golde Ls, Thumer P, MM. Turner P, Gutmann T Morse DE, Hansma H, Hansm (2006) Biophys J 90: 1411 2 Springerto the individual fiber. These models are far less successfull in translating the properties of the interphase on an indi￾vidual fiber into the performance of a multifiber composite parts. On the nano-scale, the discrete molecular structure of the polymer has to be considered. The segmental immo￾bilization seems to be the primary reinforcing mechanism in true polymer nanocomposites at temperatures near and above the Tg. Reptation model and simple percolation model were used to describe immobilization of chains near solid nano-particles and to explain the peculiarities in the viscoleastic response of polymers near solid surfaces of large polymer-inclusion contact area. The ‘‘interphase’’ in the continuum sense does not exist at the nano-scale when relaxation processes in individual discrete chains are taken into account and the chains with retarded reptation can be considered forming the ‘‘interphase’’ analogue in the dis￾crete matter. For a common polymer, all the chains in the composite become effectively immobilized when the internal filler-polymer interface area equals approximately 45 m2 . In polymers at very low temperatures, the classical Ber￾noulli–Euler continuum elasticity becomes not valid below approximately 5 nm. The size of this characteristic volume increases with increasing temperature and higher-order strain elasticity along with molecular dynamics approach has to be used as the bridging law to connect behavior of the discrete matter at nano-scale with mechanical response of continuous matter at larger length scales. 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