Skip to main content

Modeling of Tensile Modulus for Recycled PET/Clay Nanocomposites


The present study is devoted to tensile modulus of recycle PET/clay nanocomposites based on the various conventional models. Some models such as Paul and Takayanagi provide good results, when compared with the experimental data. Hirsch model predicts more accurate data by the x value of 0.1 revealing that the tensile modulus of current nanocomposites conforms to the inverse rule of mixture model. The comparison between experimental and theoretical results of Guth models confirm the necessity for taking account of stiffening factors such as aspect ratio of silicate layers. The theoretical data present a good agreement with experimental data considering the aspect ratio of 8 for silicate layers. In addition, the orientation and 3D random dispersion of the nanoclay platelets should be assumed according to Halpin–Tsai model. Further, some simplifications and modifications are carried out on the several models to enhance their predictability. The modified models are too simple, because they only require to Young’s modulus and volume fraction of components for prediction.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.


  1. 1

    Mitchell, S. and O’Brien, S., Asymptotic, Numerical and Approximate Techniques for a Free Boundary Problem Arising in the Diffusion of Glassy Polymers, Appl. Math. Comput., 2012, vol. 219, no. 1, pp. 376–388.

    MathSciNet  Google Scholar 

  2. 2

  3. 3

    Paci, M. and La Mantia, F., Competition between Degradation and Chain Extension during Processing of Reclaimed Poly (Ethylene Terephthalate), Polym. Degr. Stability, 1998, vol. 61, pp. 417–420.

    Article  Google Scholar 

  4. 4

    Spinace, M. and De Paoli, M., Characterization of Poly (Ethylene Terephtalate) after Multiple Processing Cycles, J. Appl. Polym. Sci., 2001, vol. 80, pp. 20–25.

    Article  Google Scholar 

  5. 5

    Farahmand, F., Shokrollahi, P., and Mehrabzadeh, M., Recycling of Commingled Plastics Waste Containing Polyvinylchloride, Polypropylene, Polyethylene and Paper, Iran. Polym. J., 2003, vol. 12, pp. 185–190.

    Google Scholar 

  6. 6

    Nikje, M.M.A., Haghshenas, M., and Garmarudi, A.B., Preparation and Application of Glycolysed Polyurethane Integral Skin Foams Recyclate from Automotive Wastes, Polym. Bullet., 2006, vol. 56, pp. 257–265.

    Article  Google Scholar 

  7. 7

    Vakili, M. and Fard, M.H., Chemical Recycling of Poly Ethylene Terephthalate Wastes, World Appl. Sci. J., 2010, vol. 8, pp. 839–846.

    Google Scholar 

  8. 8

    Argon, A. and Cohen, R., Toughenability of Polymers, Polymer., 2003, vol. 44, pp. 6013–6032.

    Article  Google Scholar 

  9. 9

    Elloumi, A., Pimbert, S., Bourmaud, A., and Bradai, C., Thermomechanical Properties of Virgin and Recycled Polypropylene Impact Copolymer/CaCO3 Nanocomposites, Polym. Eng. Sci., 2010, vol. 50, pp. 1904–1913.

    Article  Google Scholar 

  10. 10

    Panin, V.E., Surikova, N.S., Panin, S.V., Shugurov, A.R., and Vlasov, I.V., Effect of Nanoscale Mesoscopic Structural States Associated with Lattice Curvature on the Mechanical Behavior of Fe–Cr–Mn Austenitic Steel, Phys. Mesomech., 2019, vol. 22, no. 5, pp. 382–391.

    Article  Google Scholar 

  11. 11

    Bochkarev, A.O. and Grekov, M.A., Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem, Phys. Mesomech., 2019, vol. 22, no. 3, pp. 209–223.

    Article  Google Scholar 

  12. 12

    Cherepanov, G.P., Theory of Superplasticity and Fatigue of Polycrystalline Materials Based on Nanomechanics of Fracturing and Failure, Phys. Mesomech., 2019, vol. 22, no. 1, pp. 52–64.

    Article  Google Scholar 

  13. 13

    Bharadiya, P.S., Singh, M.K., and Mishra, S., Influence of Graphene Oxide on Mechanical and Hydrophilic Properties of Epoxy/Banana Fiber Composites, JOM, 2019, vol. 71, pp. 838–843.

    Article  Google Scholar 

  14. 14

    Zare, Y. and Rhee, K.Y., A Simulation Work for the Influences of Aggregation/Agglomeration of Clay Layers on the Tensile Properties of Nanocomposites, JOM, 2019, pp. 3989–3995.

  15. 15

    Panin, V.E., Surikova, N.S., Smirnova, A.S., and Pochivalov, Yu.I., Mesoscopic Structural States in Plastically Deformed Nanostructured Metal Materials, Phys. Mesomech., 2018, vol. 21, no. 5, pp. 396–400.

    Article  Google Scholar 

  16. 16

    Golovnev, I.F. and Golovneva, E.I., Numerical Study of the Kinetic Aspects of Fracture of Metal Nanocrystals, Phys. Mesomech., 2019, vol. 22, no. 3, pp. 195–202.

    Article  Google Scholar 

  17. 17

    Korotaev, A.D., Litovchenko, I.Yu., and Ovchinnikov, S.V., Structural-Phase State, Elastic Stress, and Functional Properties of Nanocomposite Coatings Based on Amorphous Carbon, Phys. Mesomech., 2019, vol. 22, no. 6, pp. 488–495.

    Article  Google Scholar 

  18. 18

    Van der Wal, A. and Gaymans, R., Polypropylene–Rubber Blends: 5. Deformation Mechanism during Fracture, Polymer, 1999, vol. 40, pp. 6067–6075.

    Article  Google Scholar 

  19. 19

    Bizarria, M., Giraldi, A.L.F.M., de Carvalho, C.M., Velasco, J.I., d'Ávila, M.A., and Mei, L.H.I., Morphology and Thermomechanical Properties of Recycled PET–Organoclay Nanocomposites, J. Appl. Polymer Sci., 2007, vol. 104, pp. 1839–1844.

    Article  Google Scholar 

  20. 20

    Zare, Y. and Rhee, K., A Core–Shell Structure for Interphase Regions Surrounding Nanoparticles to Predict the Shear, Bulk and Young’s Polymer Moduli of Particulate Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 1, pp. 89–96.

    Article  Google Scholar 

  21. 21

    Zare, Y. and Rhee, K.Y., Evaluation and Development of Expanded Equations Based on Takayanagi Model for Tensile Modulus of Polymer Nanocomposites Assuming the Formation of Percolating Networks, Phys. Mesomech., 2018, vol. 21, no. 4, pp. 351–357.

    Article  Google Scholar 

  22. 22

    Zare, Y. and Rhee, K.Y., A Modeling Approach for Young’s Modulus of Interphase Layers in Polymer Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 2, pp. 176–181.

    Article  Google Scholar 

  23. 23

    Zare, Y., Rhee, K., and Park, S.-J., Simple Models for Interphase Characteristics in Polypropylene/Montmorillonite/CaCO3 Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 2, pp. 182–188.

    Article  Google Scholar 

  24. 24

    Sisakht Mohsen, R., Saied, N.K., Ali, Z., Hosein, E.M., and Hasan, P., Theoretical and Experimental Determination of Tensile Properties of Nanosized and Micron-sized CaCO3/PA66 Composites, Polymer Compos., 2009, vol. 30, pp. 274–280.

    Article  Google Scholar 

  25. 25

    Broutman, L.J. and Krock, R.H., Modern Composite Materials, Reading, Mass.: Addison-Wesley, 1967.

  26. 26

    Haghighat, M., Zadhoush, A., and Khorasani, S.N., Physicomechanical Properties of α-Cellulose-Filled Styrene–Butadiene Rubber Composites, J. Appl. Polymer Sci., 2005, vol. 96, pp. 2203–2211.

    Article  Google Scholar 

  27. 27

    Guth, E., Theory of Filler Reinforcement, J. Appl. Phys., 1945, vol. 16, pp. 20–25.

    ADS  Article  Google Scholar 

  28. 28

    Guth, E. and Gold, O., On the Hydrodynamical Theory of the Viscosity of Suspensions, Phys. Rev., 1938, vol. 53, p. 2.

    Google Scholar 

  29. 29

    Wu, Y.P., Jia, Q.X., Yu, D.S., and Zhang, L.Q., Modeling Young’s Modulus of Rubber–Clay Nanocomposites Using Composite Theories, Polymer Test., 2004, vol. 23, pp. 903–909.

    Article  Google Scholar 

  30. 30

    Ahmed, S. and Jones, F., A Review of Particulate Reinforcement Theories for Polymer Composites, J. Mater. Sci., 1990, vol. 25, pp. 4933–4942.

    ADS  Article  Google Scholar 

  31. 31

    Nuñez, A.J., Sturm, P.C., Kenny, J.M., Aranguren, M., Marcovich, N.E., and Reboredo, M.M., Mechanical Characterization of Polypropylene–Wood Flour Composites, J. Appl. Polymer Sci., 2003, vol. 88, pp. 1420–1428.

    Article  Google Scholar 

  32. 32

    Kalaprasad, G., Joseph, K., Thomas, S., and Pavithran, C., Theoretical Modelling of Tensile Properties of Short Sisal Fibre-Reinforced Low-Density Polyethylene Composites, J. Mater. Sci., 1997, vol. 32, pp. 4261–4267.

    ADS  Article  Google Scholar 

  33. 33

    Borse, N.K. and Kamal, M.R., Melt Processing Effects on the Structure and Mechanical Properties of PA-6/Clay Nanocomposites, Polymer Eng. Sci., 2006, vol. 46, pp. 1094–1103.

    Article  Google Scholar 

  34. 34

    Dong, Y. and Bhattacharyya, D., Mapping the Real Micro/Nanostructures for the Prediction of Elastic Moduli of Polypropylene/Clay Nanocomposites, Polymer, 2010, vol. 51, pp. 816–824.

    Article  Google Scholar 

  35. 35

    Grunlan, J.C., Kim, Y.S., Ziaee, S., Wei, X., Abdel-Magid, B., and Tao, K., Thermal and Mechanical Behavior of Carbon-Nanotube-Filled Latex, Macromolecular Mater. Eng., 2006, vol. 291, pp. 1035–1043.

    Article  Google Scholar 

  36. 36

    Affdl, J. and Kardos, J., The Halpin–Tsai Equations: A Review, Polymer Eng. Sci., 1976, vol. 16, pp. 344–352.

    Article  Google Scholar 

  37. 37

    Putz, K.W., Mitchell, C.A., Krishnamoorti, R., and Green, P.F., Elastic Modulus of Single-Walled Carbon Nanotube/Poly (Methyl Methacrylate) Nanocomposites, J. Polymer Sci. B. Polymer Phys., 2004, vol. 42, pp. 2286–2293.

    ADS  Article  Google Scholar 

  38. 38

    Bilotti, E., Zhang, R., Deng, H., Quero, F., Fischer, H., and Peijs, T., Sepiolite Needle-Like Clay for PA6 Nanocomposites: An Alternative to Layered Silicates?, Compos. Sci. Technol., 2009, vol. 69, pp. 2587–2595.

    Article  Google Scholar 

  39. 39

    Wong, E.W., Sheehan, P.E., and Lieber, C.M., Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes, Science, 1997, vol. 277, p. 1971.

    Article  Google Scholar 

  40. 40

    Nielsen, L.E. and Landel, R.F., Mechanical Properties of Polymers and Composites, New York: CRC Press, 1994.

  41. 41

    Nielsen, L.E., Morphology and the Elastic Modulus of Block Polymers and Polyblends, Rheolog. Acta, 1974, vol. 13, pp. 86–92.

    Article  Google Scholar 

  42. 42

    Lewis, T. and Nielsen, L., Dynamic Mechanical Properties of Particulate-Filled Composites, J. Appl. Polymer Sci., 1970, vol. 14, pp. 1449–1471.

    Article  Google Scholar 

  43. 43

    Kerner, E., The Elastic and Thermo-Elastic Properties of Composite Media, Proc. Phys. Soc. B, 1956, vol. 69, p. 808.

    ADS  Article  Google Scholar 

  44. 44

    Bliznakov, E.D., White, C.C., and Shaw, M.T., Mechanical Properties of Blends of HDPE and Recycled Urea-Formaldehyde Resin, J. Appl. Polymer Sci., 2000, vol. 77, pp. 3220–3227.

    Article  Google Scholar 

  45. 45

    Albano, C., Perera, R., Catano, L., Karam, A., and Gonzalez, G., Prediction of Mechanical Properties of Composites of HDPE/HA/EAA, J. Mech. Behavior Biomed. Mater., 2011, vol. 4(3), pp. 467–475.

    Article  Google Scholar 

  46. 46

    Hui, C. and Shia, D., Simple Formulae for the Effective Moduli of Unidirectional Aligned Composites, Polymer Eng. Sci., 1998, vol. 38, pp. 774–782.

    Article  Google Scholar 

  47. 47

    Shia, D., Hui, C., Burnside, S., and Giannelis, E., An Interface Model for the Prediction of Young’s Modulus of Layered Silicate–Elastomer Nanocomposites, Polymer Compos., 1998, vol. 19, pp. 608–617.

    Article  Google Scholar 

  48. 48

    Ji, X.L., Jing, J.K., Jiang, W., and Jiang, B.Z., Tensile Modulus of Polymer Nanocomposites, Polymer Eng. Sci., 2002, vol. 42, pp. 983–993.

    Article  Google Scholar 

  49. 49

    Cauvin, L., Kondo, D., Brieu, M., Bhatnagar, N., Mechanical Properties of Polypropylene Layered Silicate Nanocomposites: Characterization and Micro-Macro Modelling, Polymer Test., 2010, vol. 29, pp. 245–250.

    Article  Google Scholar 

  50. 50

    Pegoretti, A., Kolarik, J., Peroni, C., and Migliaresi, C., Recycled Poly (Ethylene Terephthalate)/Layered Silicate Nanocomposites: Morphology and Tensile Mechanical Properties, Polymer, 2004, vol. 45, pp. 2751–2759.

    Article  Google Scholar 

  51. 51

    Zare, Y. and Garmabi, H., Analysis of Tensile Modulus of PP/Nanoclay/CaCO3 Ternary Nanocomposite Using Composite Theories, J. Appl. Polymer Sci., 2012, vol. 123, pp. 2309–2319.

    Article  Google Scholar 

  52. 52

    Aït Hocine, N., Médéric, P., and Aubry, T., Mechanical Properties of Polyamide-12 Layered Silicate Nanocomposites and Their Relations with Structure, Polymer Test., 2008, vol. 27, pp. 330–339.

    Article  Google Scholar 

  53. 53

    Kalaitzidou, K., Fukushima, H., Miyagawa, H., Drzal, L.T., Flexural and Tensile Moduli of Polypropylene Nanocomposites and Comparison of Experimental Data to Halpin–Tsai and Tandon–Weng Models, Polymer Eng. Sci., 2007, vol. 47, pp. 1796–1803.

    Article  Google Scholar 

  54. 54

    Hedayati, A. and Arefazar, A., Study on Dispersion and Intercalation of Organoclay in PP and PP-g-MA Matrices, Polymer Compos., 2009, vol. 30, pp. 1717–1731.

    Article  Google Scholar 

  55. 55

    Mirmohseni, A. and Zavareh, S., Epoxy/Acrylonitrile-Butadiene-Styrene Copolymer/Clay Ternary Nanocomposite as Impact Toughened Epoxy, J. Polymer Res., 2010, vol. 17, pp. 191–201.

    Article  Google Scholar 

  56. 56

    Ahmadi, S.J., Yudong, H., and Li, W., Synthesis of EPDM/Organoclay Nanocomposites: Effect of the Clay Exfoliation on Structure and Physical Properties, Iran. Polymer J., 2004, vol. 13, pp. 415–422.

    Google Scholar 

  57. 57

    Mirzataheri, M., Mahdavian, A.R., and Atai, M., Nanocomposite Particles with Core-Shell Morphology IV: An Efficient Approach to the Encapsulation of Cloisite 30B by Poly (Styrene-co-Butyl Acrylate) and Preparation of Its Nanocomposite Latex via Miniemulsion Polymerization, Colloid Polymer Sci., 2009, vol. 287, pp. 725–732.

    Article  Google Scholar 

  58. 58

    Dayma, N. and Satapathy, B.K., Morphological Interpretations and Micromechanical Properties of Polyamide-6/Polypropylene-Grafted-Maleic Anhydride/Nanoclay Ternary Nanocomposites, Mater. Design, 2010, vol. 31, pp. 4693–4703.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to K.-Y. Rhee.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zare, Y., Rhee, KY. Modeling of Tensile Modulus for Recycled PET/Clay Nanocomposites. Phys Mesomech 24, 282–290 (2021).

Download citation


  • recycling
  • polymer nanocomposites
  • mechanical properties