Use of Reptation Dynamics in Modelling Molecular Interphase in Polymer Nano-Composite

  • J. Jancar
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 13)


In polymer matrix composites, exhibiting heterogeneous structure at multiple length scales, the interphase phenomena at various length scales were shown to be of pivotal importance for the control of the performance and reliability of such structures. At the micro-scale, the interphase is modelled as a 3D continuum with some average properties most commonly resulting from data fitting procedures. Number of continuum mechanics models was derived over the last 50 years to describe the stress transfer between matrix and an individual fiber, considering the interphase with various chemical structure and thickness the third component of the model composite characterized by some average shear strength, τa, with realtively good success. The observed strong thickness dependence of the elastic modulus of the interphase with thickness smaller than 500 nm suggested presence of its underlying nano-scale molecular sub-structure. On the nano-scale, the discrete molecular structure of the polymer has to be considered. At this length scale, the continuum mechanics can only be used for materials with characteristic length scale greater than approximately 20 nm. Below 20 nm, continuum mechanics becomes not valid and gradient-strain elasticity along with molecular dynamics approach has to be used. The segmental immobilization seems to be the primary mechanism controlling the behavior of nano—scale “interphase”. Modified reptation model was used to describe the dynamics of chains near a solid nano-particles and to explain the peculiarities in the viscoleastic response of polymer nanocomposites. These results reflecting the discrete molecular nature of the nano-scale interphase can be used in gradient-strain elasticity models. Experimental results obtained for model nanocomposites were used to support theoretical predictions.


Polymer Nanocomposites Stress Transfer Couple Stress Theory Polymer Matrix Composite Molecular Dynamic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jancar J (2008), Review of the role of the interphase in the control of composite performance on micro- and nano-length scales, J. Mater. Sci., in print.Google Scholar
  2. 2.
    DiBenedetto AT (2001), Tailoring of interfaces in glass fiber reinforced polymer composites: A review, Materials Science and Engineering A 302, 74–82.CrossRefGoogle Scholar
  3. 3.
    Jancar J (2006), Effect of interfacial shear strength on the mechanical response of polycarbonate and PP reinforced with basalt fibers, Comp. Interfaces 13, 853–864.CrossRefGoogle Scholar
  4. 4.
    Jancar J (2006), Hydrolytic stability of PC/GF composites with engineered interphase of varying elastic modulus, Comp. Sci. Technol. 66, 3144–3152.CrossRefGoogle Scholar
  5. 5.
    Kalfus J, Jancar J (2007), realxation processes in PVAc-HA nanocomposites, J. Polym. Sci.: PartB : Polym. Phys. 45, 1380–1388.CrossRefGoogle Scholar
  6. 6.
    Kalfus J, Jancar J (2007), Viscoelastic response of nanocomposite poly(vynil acetate) hydroxyapatite with varying particle shape — Dynamic strain softening and modulus recovery, Polym. Compos. 28, 743–747.CrossRefGoogle Scholar
  7. 7.
    Vacatello M (2002), Chain dimensions in filled polymers: An intriguing problem, Macromolecules 35, 8191–8193.CrossRefGoogle Scholar
  8. 8.
    Vacatello M (2002), Molecular arrangements in polymer-based nanocomposites, Macromol. Theory Simul. 11, 757–765.CrossRefGoogle Scholar
  9. 9.
    Vacatello M (2003), Phantom chain simulations of polymer-nanofiller systems, Macromole-cules 36, 3411–3416.CrossRefGoogle Scholar
  10. 10.
    Vacatello M (2003), Predicting the molecular arrangements in polymer-based nanocomposites, Macromol. Theory Simul. 12, 86–91.CrossRefGoogle Scholar
  11. 11.
    Starr FW, Schröder TB, Glotzer SC (2002), Molecular dynamics simulation of a polymer melt with a nanoscopic particle, Macromolecules 35, 4481–4492.CrossRefGoogle Scholar
  12. 12.
    Cosoli P, Scocchi G, Pricl S, Fermeglia M (2008), Many-scale molecular simulation for ABS— MMT nanocomposites: Upgrading of industrial scraps, Micropor. Mesopor. Mater. 107 169– 179.CrossRefGoogle Scholar
  13. 13.
    Maranganti R, Sharma P (2007), A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies, J. Mech. Phys. Solids 55, 1823–1852.CrossRefADSGoogle Scholar
  14. 14.
    Park SK, Gao X-L (2006), Bernoulli-Euler beam model based on a modified couple stress theory, J. Micromech. Microengrg. 16, 2355–2359.CrossRefADSGoogle Scholar
  15. 15.
    Sharma P, Ganti S (2004), Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies, J. Appl. Mech. 71: 663–671.zbMATHCrossRefGoogle Scholar
  16. 16.
    Sharma P, Ganti S, Bhate N (2003), Effect of surfaces on the size-dependent elastic state of nano-inhomogeneties, Appl. Phys. Lett. 82, 535–537.CrossRefADSGoogle Scholar
  17. 17.
    Nikolov S., Han C.S., Rabbe D (2007), On the origin of size effects in small-strain elasticity of solid polymers, Int. J. Solids Struct. 44, 1582–1592.zbMATHCrossRefGoogle Scholar
  18. 18.
    Hashin Z (2002), Thin interphase/imperfekt interface in elasticity with application to coated fiber composites, J. Mech. Phys. Solids 50, 2509–2537.zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Nairn JA (2007), Numerical implementation of imperfect interfaces, Comput. Mat. Sci. 40, 525–536.CrossRefGoogle Scholar
  20. 20.
    Droste DH, DiBenedetto AT (1969), The glass transition temperature of filled polymers and its effect on their physical properties, J. Appl. Polym. Sci. 13, 2149–2168.CrossRefGoogle Scholar
  21. 21.
    Cave NG, Kinloch AJ (1992), Self-assembling monolayer silane films as adhesion promoters, Polymer 33, 1162–1170.CrossRefGoogle Scholar
  22. 22.
    Zinc P., Wagner HD, Salmon L, Gerard J-F (2001), Are microcomposites realistic models of the fiber/matrix interface? II. Physico-chemical approach, Polymer 42, 6641–6650.CrossRefGoogle Scholar
  23. 23.
    John A. Nairn (1997), On the use of shear-lag methods for analysis of stress transfer in unidirectional composites, Mech. Mater. 26, 63–80.CrossRefGoogle Scholar
  24. 24.
    Johnson AC, Hayes SA, Jones FR (2005), An improved model including plasticity for the prediction of the stress in fibres with an interface/interphase region, Composites: Part A 36, 263–271.Google Scholar
  25. 25.
    Duan HL, Yi X, Huang ZP, Wang J (2007), A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part I. Theoretical framework, Mech. Mater. 39, 81–93.CrossRefGoogle Scholar
  26. 26.
    Duan HL, Yi X, Huang ZP, Wang J (2007), A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part II. Application and scaling laws, Mech. Mater. 39, 94–103.CrossRefGoogle Scholar
  27. 27.
    Wetherhold RC, Corjon M, Das PK (2007), Multiscale considerations for interface engineering to improve fracture toughness of ductile fiber/thermoset matrix composites, Comp. Sci. Technol. 67, 2428–2437.CrossRefGoogle Scholar
  28. 28.
    Wu ZJ, Ye JQ, Cabrera JG (2000), 3D analysis of stress transfer in the micromechanics of fiber reinforced composites by using an eigen-function expansion method, J. Mech. Phys. Solids 48, 1037–1063.zbMATHCrossRefADSGoogle Scholar
  29. 29.
    Pisanova E, Zhandarov S, Mader E (2001), How can adhesion be determined from micromechanical tests–, Composites: Part A 32, 425–434.CrossRefGoogle Scholar
  30. 30.
    Xia Z, Okabe T, Curtin WA (2002), Shear-lag versus finite element models for stress transfer in fiber-reinforced composites, Comp. Sci. Technol. 62, 1141–1149.CrossRefGoogle Scholar
  31. 31.
    Goh KL, Aspden RL, Hukins DWL (2004), Review: Finite element analysis of stress transfer in short-fibre composite materials, Comp. Sci. Technol. 64, 1091–1100.CrossRefGoogle Scholar
  32. 32.
    Xie X-Q, Ranade SV, DiBenedetto AT (1999), A solid state NMR study of polycarbonate oligomer grafted onto the surface of amorphous silica, Polymer 40, 6297–6306.CrossRefGoogle Scholar
  33. 33.
    Kim J-K, Mai Y-W (1998), Micromechanics of stress transfer across the interface, in Engineered Interfaces in Fiber Reinforced Composites, Elsevier, Amsterdam, Ch. 4, pp. 93–164.CrossRefGoogle Scholar
  34. 34.
    DiAnselmo A, Jancar J, DiBenedetto AT, Kenny JM (1992), Finite element analysis of the effect of an interphase on the mechanical properties of polymeric composite materials, in Composite Materials, A.T. DiBenedetto, L. Nicolais, R Watanabe (Eds.), Elsevier Science Publ., pp. 49–59.Google Scholar
  35. 35.
    Cammarata RC (1997), Surface and interface stress effects on interfacial and nanostructured materials, Mater. Sci. Engrg. A 237, 180–184.CrossRefGoogle Scholar
  36. 36.
    Kalfus J, Jancar J (2007), Immobilization of polyvinylacetate macromolecules on hydroxyapatite nanoparticles, Polymer 48, 3935–3938.CrossRefGoogle Scholar
  37. 37.
    Sternstein SS, Zhu AJ (2002), Reinforcement mechanism of nanofilled polymer melts as elucidated by nonlinear viscoelastic behavior, Macromolecules 35, 7262–7273.CrossRefGoogle Scholar
  38. 38.
    Kalfus J, Jancar J (2007), Elastic response of nanocomposite poly(vinylacetate)/ hydroxyapatite with varying particle shape, Polym. Compos. 28, 365–371.CrossRefGoogle Scholar
  39. 39.
    Zhu AJ, Sternstein SS (2003), Nonlinear viscoelasticity of nanofilled polymers: Interfaces, chain statistics and properties recovery kinetics, Comp. Sci. Technol. 63, 1113–1126.CrossRefGoogle Scholar
  40. 40.
    Ozmusul MS, Picu CR, Sternstein SS, Kumar SK (2005), Lattice Monte Carlo simulations of chain conformations in polymer nanocomposites, Macromolecules 38, 4495–4500.CrossRefGoogle Scholar
  41. 41.
    Liu ZH, Li Y, Kowk KW (2001), Mean interparticle distances between hard particles in one to three dimensions, Polymer42, 2701–2706.CrossRefGoogle Scholar
  42. 42.
    Sargsyan A, Tonoyan A, Davtyan S, Schick C (2007), The amount of immobilized polymer in PMMA/SiO2 nanocomposites determined from calorimetric data, Eur. Polymer J. 43 3113– 3127.CrossRefGoogle Scholar
  43. 43.
    Doi M, Edwards SF (2003), Theory of Polymer Dynamics, Oxford University Press, London.Google Scholar
  44. 44.
    Lin, Y-H (1985), Comparison of the pure reptational times calculated from linear viscoelasticity and diffusion motion data of nearly monodisperse polymers, Macromolecules 18, 2779– 2781.CrossRefGoogle Scholar
  45. 45.
    Zheng, X, Sauer BB, van Alsten JG, Schwarz SA, Rafailovich MH, Sokolov J, Rubinstein M (1995), Repatation dynamics of a polymer melt near an attractive solid interface, Phys. Rev. Lett. 74, 407–415.CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, B.V. 2009

Authors and Affiliations

  • J. Jancar
    • 1
  1. 1.Institute of Materials ChemistryBrno University of TechnologyCzech Republic

Personalised recommendations