Primitive chain network simulations for comb-branched polymer under step shear deformations

Abstract

The damping of the relaxation modulus under step shear deformation is weaker for multi-branched polymers such as comb polymers than for linear polymers. This weak damping has been related to the hierarchical relaxation, the branched arm relaxation occurring prior to the backbone relaxation and dilating the entanglement network for the backbone relaxation/contraction. A corresponding model has been proposed and favorably compared with the data for the damping function. However, the enhancement of dilation due to large deformation, known to occur for linear polymers to affect the chain contraction rate, was not considered in the model. Thus, in this paper, we investigated the dilation for a comb polymer under deformation with the aid of a 3D multichain sliplink simulation that naturally accounts for the dilation due to the constraint release through the many chain dynamics. The simulation was confirmed, to the first time, to reproduce the linear and nonlinear viscoelastic data for a comb polyisoprene (Kirkwood et al., Macromolecules 42:9592–9608, 2009). A magnitude of dilation under deformation was examined for the survival probability of the sliplinks. It turned out that the dilation for the comb backbone activated by the arm relaxation is enhanced by the deformation at short times but not at long times where the backbone relaxes and the damping function is defined. This result lends support to the conventional model.

This is a preview of subscription content, log in to check access.

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

References

  1. Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31:6348–6355

    Article  CAS  Google Scholar 

  2. Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410

    Article  Google Scholar 

  3. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, Oxford

    Google Scholar 

  4. Furuichi K, Nonomura C, Masubuchi Y, Watanabe H, Ianniruberto G, Greco F, Marrucci G (2008) Entangled polymer orientation and stretch under large step shear deformations in primitive chain network simulations. Rheol Acta 47:591–599

    Article  CAS  Google Scholar 

  5. Furuichi K, Nonomura C, Masubuchi Y, Watanabe H (2010) Chain contraction and nonlinear stress damping in primitive chain network simulations. J Chem Phys 133:174902

    Article  Google Scholar 

  6. Heinrich M, Pyckhout-Hintzen W, Allgaier J, Richter D, Straube E, Read DJ, McLeish TCB, Groves DJ, Blackwell RJ, Wiedenmann A (2002) Arm relaxation in deformed H-polymers in elongational flow by SANS. Macromolecules 35:6650–6664

    Article  CAS  Google Scholar 

  7. Ianniruberto G, Brasiello A, Marrucci G (2011) Friction Coefficient does not stay constant in nonlinear viscoelasticity. In: Proc. 7th Annual European Rheology Conference, p 61

  8. Islam MT, Sanchez-Reyes J, Archer LA (2001) Nonlinear rheology of highly entangled polymer liquids: step shear damping function. J Rheol 45:61–82

    Article  CAS  Google Scholar 

  9. Kapnistos M, Kirkwood KM, Ramirez J, Vlassopoulos D, Leal LG (2009) Nonlinear rheology of model comb polymers. J Rheol 53:1133–1153

    Article  CAS  Google Scholar 

  10. Kirkwood KM, Leal LG, Vlassopoulos D, Driva P, Hadjichristidis N (2009) Stress relaxation of comb polymers with short branches. Macromolecules 42:9592–9608

    Article  CAS  Google Scholar 

  11. Laun HM (1978) Description of nonlinear shear behavior of a low-density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17:1–15

    Article  CAS  Google Scholar 

  12. Lees AW, Edwards SF (1972) The computer study of transport processes under extreme conditions. J Phys C Solid State Phys 5:1921–1929

    Article  Google Scholar 

  13. Likhtman AE (2005) Single-chain slip-link model of entangled polymers: simultaneous description of neutron spin-echo, rheology, and diffusion. Macromolecules 38:6128–6139

    Article  CAS  Google Scholar 

  14. Magatti D, Ferri F (2001) Fast multi-tau real-time software correlator for dynamic light scattering. Appl Opt 40:4011–4021

    Article  CAS  Google Scholar 

  15. Masubuchi Y, Takimoto JI, Koyama K, Ianniruberto G, Marrucci G, Greco F (2001) Brownian simulations of a network of reptating primitive chains. J Chem Phys 115:4387–4394

    Article  CAS  Google Scholar 

  16. Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2003) Entanglement molecular weight and frequency response of sliplink networks. J Chem Phys 119:6925–6930

    Article  CAS  Google Scholar 

  17. Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2004) Molecular simulations of the long-time behaviour of entangled polymeric liquids by the primitive chain network model. Model Simul Mat Sci Eng 12:S91–S100

    Article  Google Scholar 

  18. Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2006) Primitive chain network simulations for branched polymers. Rheol Acta 46:297–303

    Article  CAS  Google Scholar 

  19. Masubuchi Y, Lanniruberto G, Greco F, Marrucci G (2008) Quantitative comparison of primitive chain network simulations with literature data of linear viscoelasticity for polymer melts. J Non-Newton Fluid Mech 149:87–92

    Article  CAS  Google Scholar 

  20. Masubuchi Y, Yaoita T, Matsumiya Y, Watanabe H (2011) Primitive chain network simulations for asymmetric star polymers. J Chem Phys 134:194905

    Article  Google Scholar 

  21. Matsumiya Y, Watanabe H, Osaki K (2000) Comparison of dielectric and viscoelastic relaxation functions of cis-polyisoprenes: test of tube dilation molecular picture. Macromolecules 33:499–506

    Article  CAS  Google Scholar 

  22. McLeish TCB (1988) Hierarchical-relaxation in tube models of branched polymers. Europhysics Letters 6:511–516

    Article  CAS  Google Scholar 

  23. McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: the pom-pom polymer. J Rheol 42:81–110

    Article  CAS  Google Scholar 

  24. Mead DW, Larson RG, Doi M (1998) A molecular theory for fast flows of entangled polymers. Macromolecules 31:7895–7914

    Article  CAS  Google Scholar 

  25. Osaki K (1993) On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta 32:429–437

    Article  CAS  Google Scholar 

  26. Osaki K, Takatori E, Shibasaki S, Kurata M (1988) Stress-relaxation of semidilute polystyrene solutions—a new observation with theta-solvent and with blends containing very short chains. Polym J 20:511–513

    Article  CAS  Google Scholar 

  27. Sanchez-Reyes J, Archer LA (2002), Step shear dynamics of entangled polymer liquids, Macromolecules 35:5194–5202

    Article  CAS  Google Scholar 

  28. Shanbhag S, Larson RG (2004) A slip link model of branch-point motion in entangled polymers. Macromolecules 37:8160–8166

    Article  CAS  Google Scholar 

  29. Tadmor Z, Gogos CG (2006) Principles of polymer processing. Wiley, New Jersey

    Google Scholar 

  30. Vega DA, Milner ST (2007) Shear damping function measurements for branched polymers. J Polym Sci Part B-Polymer Physics 45:3117–3136

    Article  CAS  Google Scholar 

Download references

Acknowledgement

This study was supported by Grant-in-Aid for Scientific Research (B) No 20340111.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yuichi Masubuchi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Masubuchi, Y., Matsumiya, Y., Watanabe, H. et al. Primitive chain network simulations for comb-branched polymer under step shear deformations. Rheol Acta 51, 193–200 (2012). https://doi.org/10.1007/s00397-011-0574-x

Download citation

Keywords

  • Entanglement
  • Stress relaxation
  • Nonlinear viscoelasticity
  • Polymer melt
  • Damping function
  • Brownian dynamics