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Rheological Properties of Polymer–Carbon Composites

  • Sayan Ganguly
  • Narayan Ch Das
Chapter
Part of the Springer Series on Polymer and Composite Materials book series (SSPCM)

Abstract

Polymer rheology is an enormously sensitive indicator of polymer long-chain branching, and consequently can be exploited as a tool to evaluate polymer structures. Carbonaceous fillers are most abundantly used filler due to its reinforcing nature and its low cost. Among the carbon filler family, the most widely uttered names are carbon black and carbon nanotubes (CNTs) because of their relatively low cost, ease of processing, surprising dispersibility and mechanical strength. Several researchers did work on the polymer solution or polymer melt-based composite processing methods in order to distribute the fillers at a greater extent. It has been noticed by the various researchers that carbon black is easier to distribute than CNTs due to low aspect ratio of CNTs. Several rheological models have been discussed for filler-polymer composite systems. The relation among the rheological parameters is discussed also in light of yield stress value, shear rates and steady-state shear character of composites. We also discussed how the polymer/filler ratio affects the rheological nature of nanocomposites. Basically, dilute domains (rheology dominated by polymer concentration) and semi-dilute domains (dominated by the filler particles, filler fractals/cluster, filler agglomerates, etc.) have been analysed by various hypothesizes as told by researchers. However, we tried to contextualize the rheological resultant effects of carbonaceous filler impregnated polymer composites through the underlying structure-dispersion relationship and cultivate the interplay of different filler-polymer forces in the nanocomposites.

Keywords

Carbonaceous fillers Rheological models Carbon black Carbon nanotubes Shear rate 

Abbreviations

CNTs

Carbon nanotubes

SPM

Scanning probe microscopy

Tg

Glass transition temperature

MC

Monte Carlo

–CH2

Methylene

–CH3

Methyl

PE

Polyethylene

G*

Complex modulus

WLF

Williams–Landel–Ferry

PTT

Phan–Thein–Tanner

UCM

Upper-Convected Maxwell

K-BKZ

Kaye and Bernstein

EPDM

Ethylene propylene diene monomer

SWCNT

Single wall carbon nanotubes

MWCNT

Multi wall carbon nanotubes

GPa

Giga pascal

η*

Complex viscosity

fc

Percolation threshold

σmax

Maximum stress

References

  1. 1.
    Sheldon RP (1982) Composite polymeric materials: applied science. Elsevier Science distributorGoogle Scholar
  2. 2.
    McCabe KA, Rassenti SJ, Smith VL (1990) Auction design for composite goods: the natural gas industry. J Econ Behav Organ 14(1):127–149CrossRefGoogle Scholar
  3. 3.
    Almomen A, Cho S, Yang C-H, Li Z, Jarboe EA, Peterson CM et al (2015) Thermosensitive progesterone hydrogel: a safe and effective new formulation for vaginal application. Pharm Res 32(7):2266–2279CrossRefGoogle Scholar
  4. 4.
    Robeson LM (2007) Polymer blends. A comprehensive review. LeseprobeGoogle Scholar
  5. 5.
    Nichetti D, Manas-Zloczower I (1998) Viscosity model for polydisperse polymer melts. J Rheol (1978-present) 42(4):951–969CrossRefGoogle Scholar
  6. 6.
    Takahashi M, Isaki T, Takigawa T, Masuda T (1993) Measurement of biaxial and uniaxial extensional flow behavior of polymer melts at constant strain rates. J Rheol (1978-present) 37(5):827–846CrossRefGoogle Scholar
  7. 7.
    Seemann R, Herminghaus S, Neto C, Schlagowski S, Podzimek D, Konrad R et al (2005) Dynamics and structure formation in thin polymer melt films. J Phys: Condens Matter 17(9):S267Google Scholar
  8. 8.
    Daoulas KC, Harmandaris VA, Mavrantzas VG (2005) Detailed atomistic simulation of a polymer melt/solid interface: structure, density, and conformation of a thin film of polyethylene melt adsorbed on graphite. Macromolecules 38(13):5780–5795CrossRefGoogle Scholar
  9. 9.
    Bojan MJ, Steele WA (1987) Interactions of diatomic molecules with graphite. Langmuir 3(6):1123–1127CrossRefGoogle Scholar
  10. 10.
    Xanthos M, Dagli S (1991) Compatibilization of polymer blends by reactive processing. Polym Eng Sci 31(13):929–935CrossRefGoogle Scholar
  11. 11.
    Ferry JD (1980) Viscoelastic properties of polymers. WileyGoogle Scholar
  12. 12.
    Prest W, Porter RS (1972) Rheological properties of poly (2, 6-dimethylphenylene oxide)—polystyrene blends. J Polym Sci Part A-2: Polym Phys 10(9):1639–1655CrossRefGoogle Scholar
  13. 13.
    Ogah AO, Afiukwa JN, Nduji A (2014) Characterization and comparison of rheological properties of agro fiber filled high-density polyethylene bio-composites. Open J Polym ChemGoogle Scholar
  14. 14.
    Moutee M, Fortin Y, Fafard M (2007) A global rheological model of wood cantilever as applied to wood drying. Wood Sci Technol 41(3):209–234CrossRefGoogle Scholar
  15. 15.
    Xie F, Halley PJ, Avérous L (2012) Rheology to understand and optimize processibility, structures and properties of starch polymeric materials. Prog Polym Sci 37(4):595–623CrossRefGoogle Scholar
  16. 16.
    Qiao X, Li W, Watanabe H, Sun K, Chen X (2009) Rheological behavior of biocomposites of silk fibroin fiber and poly (ε-caprolactone): effect of fiber network. J Polym Sci, Part B: Polym Phys 47(20):1957–1970CrossRefGoogle Scholar
  17. 17.
    Zhang Y, Lim CT, Ramakrishna S, Huang Z-M (2005) Recent development of polymer nanofibers for biomedical and biotechnological applications. J Mater Sci—Mater Med 16(10):933–946CrossRefGoogle Scholar
  18. 18.
    Marynowski K (2006) Two-dimensional rheological element in modelling of axially moving viscoelastic web. Eur J Mech-A/Solids 25(5):729–744CrossRefGoogle Scholar
  19. 19.
    Dealy JM, Wissbrun KF (2012) Melt rheology and its role in plastics processing: theory and applications. Springer Science & Business MediaGoogle Scholar
  20. 20.
    Ansari M, Hatzikiriakos SG, Mitsoulis E (2012) Slip effects in HDPE flows. J Nonnewton Fluid Mech 167:18–29Google Scholar
  21. 21.
    Ansari M, Alabbas A, Hatzikiriakos S, Mitsoulis E (2010) Entry flow of polyethylene melts in tapered dies. Int Polym Proc 25(4):287–296CrossRefGoogle Scholar
  22. 22.
    Phillips T, Owens R (2002) Computational rheology. Imperial College Press, London, UKGoogle Scholar
  23. 23.
    Willett J, Jasberg B, Swanson C (1995) Rheology of thermoplastic starch: effects of temperature, moisture content, and additives on melt viscosity. Polym Eng Sci 35(2):202–210CrossRefGoogle Scholar
  24. 24.
    James DF (2009) Boger fluids. Annu Rev Fluid Mech 41:129–142CrossRefGoogle Scholar
  25. 25.
    Jarecki L, Lewandowski Z (2009) Mathematical modelling of pneumatic melt spinning of isotactic polypropylene. Part III. Computations of the process dynamics. Fibres Text Eastern Eur 17(1):75–80Google Scholar
  26. 26.
    Higashitani K, Pritchard W (1972) A kinematic calculation of intrinsic errors in pressure measurements made with holes. Trans Soc Rheol (1957–1977) 16(4):687–696CrossRefGoogle Scholar
  27. 27.
    Cherizol R, Sain M, Tjong J (2015) Review of non-Newtonian mathematical models for rheological characteristics of viscoelastic composites. Green Sustain Chem 5(01):6CrossRefGoogle Scholar
  28. 28.
    Crochet M, Legat V (1992) The consistent streamline-upwind/Petrov-Galerkin method for viscoelastic flow revisited. J Nonnewton Fluid Mech 42(3):283–299CrossRefGoogle Scholar
  29. 29.
    Bird RB, Armstrong R, Hassager O (1987) Dynamics of polymeric liquids, vol 1. Fluid mechanicsGoogle Scholar
  30. 30.
    Tucker C, Dessenberger R (1994) Flow and rheology in polymer composites manufacturing, chapter 8. Elsevier ScienceGoogle Scholar
  31. 31.
    Grafe T, Graham K (2003) Polymeric nanofibers and nanofiber webs: a new class of nonwovens. Nonwoven Technol Rev 12:51–55Google Scholar
  32. 32.
    Zhou C, Kumar S (2010) Thermal instabilities in melt spinning of viscoelastic fibers. J Nonnewton Fluid Mech 165(15):879–891CrossRefGoogle Scholar
  33. 33.
    da Silva LJ, Panzera TH, Velloso VR, Christoforo AL, Scarpa F (2012) Hybrid polymeric composites reinforced with sisal fibres and silica microparticles. Compos B Eng 43(8):3436–3444CrossRefGoogle Scholar
  34. 34.
    Devereux BM, Denn MM (1994) Frequency response analysis of polymer melt spinning. Ind Eng Chem Res 33(10):2384–2390CrossRefGoogle Scholar
  35. 35.
    Ellison CJ, Phatak A, Giles DW, Macosko CW, Bates FS (2007) Melt blown nanofibers: fiber diameter distributions and onset of fiber breakup. Polymer 48(11):3306–3316CrossRefGoogle Scholar
  36. 36.
    Ellyin F, Vaziri R, Bigot L (2007) Predictions of two nonlinear viscoelastic constitutive relations for polymers under multiaxial loadings. Polym Eng Sci 47(5):593–607CrossRefGoogle Scholar
  37. 37.
    Burghardt W, Fuller G (1989) Note: end effects in flow birefringence measurements. J Rheol (1978-present) 33(5):771–779CrossRefGoogle Scholar
  38. 38.
    Maders H, Vergnes B, Demay Y, Agassant J (1992) Steady flow of a White-Metzner fluid in a 2-D abrupt contraction: computation and experiments. J Nonnewton Fluid Mech 45(1):63–80CrossRefGoogle Scholar
  39. 39.
    Thien NP, Tanner RI (1977) A new constitutive equation derived from network theory. J Nonnewton Fluid Mech 2(4):353–365CrossRefGoogle Scholar
  40. 40.
    Brondani WM, Coradin HT, Franco AT, Morales RE, Martins AL (2007) Numerical study of a PTT visco elastic fluid flow through a concentric annular. In: Proceedings of COBEM (Brasillia)Google Scholar
  41. 41.
    Phan‐Thien N (1978) A nonlinear network viscoelastic model. J Rheol (1978-present) 22(3):259–283CrossRefGoogle Scholar
  42. 42.
    Giesekus H (1982) A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J Nonnewton Fluid Mech 11(1–2):69–109CrossRefGoogle Scholar
  43. 43.
    Giesekus H (1985) Constitutive equations for polymer fluids based on the concept of configuration-dependent molecular mobility: a generalized mean-configuration model. J Nonnewton Fluid Mech 17(3):349–372CrossRefGoogle Scholar
  44. 44.
    Mostafaiyan M, Khodabandehlou K, Sharif F (2004) Analysis of a viscoelastic fluid in an annulus using Giesekus model. J Nonnewton Fluid Mech 118(1):49–55CrossRefGoogle Scholar
  45. 45.
    Isaki T, Takahashi M, Takigawa T, Masuda T (1991) Comparison between uniaxial and biaxial elongational flow behavior of viscoelastic fluids as predicted by differential constitutive equations. Rheol Acta 30(6):530–539CrossRefGoogle Scholar
  46. 46.
    Yarin AL, Sinha-Ray S, Pourdeyhimi B (2010) Meltblowing: II-linear and nonlinear waves on viscoelastic polymer jets. J Appl Phys 108(3):034913CrossRefGoogle Scholar
  47. 47.
    Luo X-L, Tanner R (1987) A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation. Rheol Acta 26(6):499–507CrossRefGoogle Scholar
  48. 48.
    Chauvière C, Owens RG (2002) A robust spectral element method for simulations of time-dependent viscoelastic flows, derived from the Brownian configuration field method. J Sci Comput 17(1–4):191–199CrossRefGoogle Scholar
  49. 49.
    Cirulis JT, Keeley FW, James DF (2009) Viscoelastic properties and gelation of an elastin-like polypeptide. J Rheol (1978-present) 53(5):1215–1228CrossRefGoogle Scholar
  50. 50.
    Oldroyd J (1950) On the formulation of rheological equations of state. Proc Roy Soc Lond A 200:523–541CrossRefGoogle Scholar
  51. 51.
    Scott J (1935) Theory and application of the parallel-plate plastimeter. Part 2. Rubber Chem Technol 8(4):587–596CrossRefGoogle Scholar
  52. 52.
    Dillon J, Johnston N (1933) The plastic properties of several types of unvulcanized rubber stocks at high rates of shear. J Appl Phys 4(6):225–235Google Scholar
  53. 53.
    Mullins L (1969) Softening of rubber by deformation. Rubber Chem Technol 42(1):339–362CrossRefGoogle Scholar
  54. 54.
    White JL, Soos I (1993) The development of elastomer rheological processability quality control instruments. Rubber Chem Technol 66(3):435–454CrossRefGoogle Scholar
  55. 55.
    Zakharenko N, Tolstukhina F, Bartenev G (1962) Flow of rubberlike polymers with and without carbon black. Rubber Chem Technol 35(2):326–334CrossRefGoogle Scholar
  56. 56.
    Bershtein V, Yegorov V, Marikhin V, Myasnikova L (1985) Specific features of molecular motion in lamellar polyethylene between 100 and 400 K. Polym Sci USSR 27(4):864–874CrossRefGoogle Scholar
  57. 57.
    Toki S, White JL (1982) Rheological and solid wall boundary condition characterization of unvulcanized elastomers and their compounds. J Appl Polym Sci 27(8):3171–3184CrossRefGoogle Scholar
  58. 58.
    Lobe VM, White JL (1979) An experimental study of the influence of carbon black on the rheological properties of a polystyrene melt. Polym Eng Sci 19(9):617–624CrossRefGoogle Scholar
  59. 59.
    Tanaka H, White JL (1980) Experimental investigations of shear and elongational flow properties of polystyrene melts reinforced with calcium carbonate, titanium dioxide, and carbon black. Polym Eng Sci 20(14):949–956CrossRefGoogle Scholar
  60. 60.
    Suetsugu Y, White JL (1983) The influence of particle size and surface coating of calcium carbonate on the rheological properties of its suspensions in molten polystyrene. J Appl Polym Sci 28(4):1481–1501CrossRefGoogle Scholar
  61. 61.
    Suh CH, White JL (1996) Talc-thermoplastic compounds: particle orientation in flow and rheological properties. J Nonnewton Fluid Mech 62(2):175–206CrossRefGoogle Scholar
  62. 62.
    Osanaiye GJ, Leonov AI, White JL (1993) Investigations of the rheological behavior of rubber-carbon black compounds over a wide range of stresses including very low stresses. J Nonnewton Fluid Mech 49(1):87–101CrossRefGoogle Scholar
  63. 63.
    Subramoney S (1998) Novel nanocarbons—structure, properties, and potential applications. Adv Mater 10(15):1157–1171CrossRefGoogle Scholar
  64. 64.
    Haggenmueller R, Gommans H, Rinzler A, Fischer JE, Winey K (2000) Aligned single-wall carbon nanotubes in composites by melt processing methods. Chem Phys Lett 330(3):219–225CrossRefGoogle Scholar
  65. 65.
    Lozano K, Barrera E (2001) Nanofiber-reinforced thermoplastic composites. I. Thermoanalytical and mechanical analyses. J Appl Polym Sci 79(1):125–133CrossRefGoogle Scholar
  66. 66.
    Lozano K, Bonilla-Rios J, Barrera E (2001) A study on nanofiber-reinforced thermoplastic composites (II): investigation of the mixing rheology and conduction properties. J Appl Polym Sci 80(8):1162–1172CrossRefGoogle Scholar
  67. 67.
    Qian D, Dickey EC, Andrews R, Rantell T (2000) Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl Phys Lett 76(20):2868–2870CrossRefGoogle Scholar
  68. 68.
    Salvetat J-P, Briggs GAD, Bonard J-M, Bacsa RR, Kulik AJ, Stöckli T et al (1999) Elastic and shear moduli of single-walled carbon nanotube ropes. Phys Rev Lett 82(5):944CrossRefGoogle Scholar
  69. 69.
    Walters D, Ericson L, Casavant M, Liu J, Colbert D, Smith K et al (1999) Elastic strain of freely suspended single-wall carbon nanotube ropes. Appl Phys Lett 74(25):3803–3805CrossRefGoogle Scholar
  70. 70.
    Li F, Cheng H, Bai S, Su G, Dresselhaus M (2000) Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes. Appl Phys Lett 77(20):3161–3163CrossRefGoogle Scholar
  71. 71.
    Pötschke P, Fornes T, Paul D (2002) Rheological behavior of multiwalled carbon nanotube/polycarbonate composites. Polymer 43(11):3247–3255CrossRefGoogle Scholar
  72. 72.
    Chatterjee T, Krishnamoorti R (2013) Rheology of polymer carbon nanotubes composites. Soft Matter 9(40):9515–9529CrossRefGoogle Scholar
  73. 73.
    Du F, Scogna RC, Zhou W, Brand S, Fischer JE, Winey KI (2004) Nanotube networks in polymer nanocomposites: rheology and electrical conductivity. Macromolecules 37(24):9048–9055CrossRefGoogle Scholar
  74. 74.
    Chatterjee T, Krishnamoorti R (2008) Steady shear response of carbon nanotube networks dispersed in poly (ethylene oxide). Macromolecules 41(14):5333–5338CrossRefGoogle Scholar
  75. 75.
    Moreira L, Fulchiron R, Seytre G, Dubois P, Cassagnau P (2010) Aggregation of carbon nanotubes in semidilute suspension. Macromolecules 43(3):1467–1472CrossRefGoogle Scholar
  76. 76.
    Whittle M, Dickinson E (1997) Stress overshoot in a model particle gel. J Chem Phys 107(23):10191–10200CrossRefGoogle Scholar
  77. 77.
    Silbert L, Farr R, Melrose JR, Ball R (1999) Stress distributions in flowing aggregated colloidal suspensions. J Chem Phys 111(10):4780–4789CrossRefGoogle Scholar
  78. 78.
    Thomin JD, Keblinski P, Kumar SK (2008) Network effects on the nonlinear rheology of polymer nanocomposites. Macromolecules 16(41):5988–5991CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Rubber Technology CentreIndian Institute of Technology KharagpurKharagpurIndia

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