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.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31:6348–6355
Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410
Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, Oxford
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
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
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
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
Islam MT, Sanchez-Reyes J, Archer LA (2001) Nonlinear rheology of highly entangled polymer liquids: step shear damping function. J Rheol 45:61–82
Kapnistos M, Kirkwood KM, Ramirez J, Vlassopoulos D, Leal LG (2009) Nonlinear rheology of model comb polymers. J Rheol 53:1133–1153
Kirkwood KM, Leal LG, Vlassopoulos D, Driva P, Hadjichristidis N (2009) Stress relaxation of comb polymers with short branches. Macromolecules 42:9592–9608
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
Lees AW, Edwards SF (1972) The computer study of transport processes under extreme conditions. J Phys C Solid State Phys 5:1921–1929
Likhtman AE (2005) Single-chain slip-link model of entangled polymers: simultaneous description of neutron spin-echo, rheology, and diffusion. Macromolecules 38:6128–6139
Magatti D, Ferri F (2001) Fast multi-tau real-time software correlator for dynamic light scattering. Appl Opt 40:4011–4021
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
Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2003) Entanglement molecular weight and frequency response of sliplink networks. J Chem Phys 119:6925–6930
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
Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2006) Primitive chain network simulations for branched polymers. Rheol Acta 46:297–303
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
Masubuchi Y, Yaoita T, Matsumiya Y, Watanabe H (2011) Primitive chain network simulations for asymmetric star polymers. J Chem Phys 134:194905
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
McLeish TCB (1988) Hierarchical-relaxation in tube models of branched polymers. Europhysics Letters 6:511–516
McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: the pom-pom polymer. J Rheol 42:81–110
Mead DW, Larson RG, Doi M (1998) A molecular theory for fast flows of entangled polymers. Macromolecules 31:7895–7914
Osaki K (1993) On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta 32:429–437
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
Sanchez-Reyes J, Archer LA (2002), Step shear dynamics of entangled polymer liquids, Macromolecules 35:5194–5202
Shanbhag S, Larson RG (2004) A slip link model of branch-point motion in entangled polymers. Macromolecules 37:8160–8166
Tadmor Z, Gogos CG (2006) Principles of polymer processing. Wiley, New Jersey
Vega DA, Milner ST (2007) Shear damping function measurements for branched polymers. J Polym Sci Part B-Polymer Physics 45:3117–3136
This study was supported by Grant-in-Aid for Scientific Research (B) No 20340111.
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
- Stress relaxation
- Nonlinear viscoelasticity
- Polymer melt
- Damping function
- Brownian dynamics