Skip to main content
Log in

A hierarchical multi-mode MSF model for long-chain branched polymer melts part II: multiaxial extensional flows

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

In part I, a novel hierarchical multi-mode molecular stress function (HMMSF) model for long-chain branched (LCB) polymer melts has been proposed, which implements the basic ideas of (i) the pom-pom model, (ii) hierarchal relaxation, (iii) dynamic dilution, and (iv) interchain pressure. Here, the capability of this approach is demonstrated in modelling the extensional viscosity data of a broadly distributed long-chain branched polymer melt in uniaxial, equibiaxial, and planar extensional deformations with only a single non-linear parameter, the dilution modulus, which quantifies the fraction of dynamically diluted chain segments.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Bernstein B, Kearsley E, Zapas L (1963) A study of stress relaxation with finite strain. Transactions of The Society of Rheology (1957–1977) 7:391–410. doi:10.1122/1.548963

    Article  Google Scholar 

  • Chatraei S, Macosko C, Winter H (1981) Lubricated squeezing flow: a new biaxial extensional rheometer. J Rheology 25:433–443. doi:10.1122/1.549648

    Article  Google Scholar 

  • Demarmels A, Meissner J (1985) Multiaxial elongation of polyisobutylene with various and changing strain rate ratios. Rheol Acta 24:253–259. doi:10.1007/BF01332605

    Article  Google Scholar 

  • Denson C, Hylton D (1980) A rheometer for measuring the viscoelastic response of polymer melts in arbitrary planar and biaxial extensional flow fields. Poly Eng & Sci 20:535–539. doi:10.1002/pen.760200804

    Article  Google Scholar 

  • Denson CD, Gallo R (1971) Measurements on the biaxial extension viscosity of bulk polymers: the inflation of a thin polymer sheet. Poly Eng & Sci 11:174–176. doi:10.1002/pen.760110213

    Article  Google Scholar 

  • Doi M, Edwards SF (1986) The Theory of Polymer Dynamics. Oxford University Press, Oxford

    Google Scholar 

  • Gupta M (2002) Estimation of elongational viscosity of polymers from entrance loss data using individual parameter optimization. Adv Polym Tech 21:98–107. doi:10.1002/adv.10017

    Article  Google Scholar 

  • Hachmann P (1996) Multiaxiale Dehnung von Polymerschmelzen. Ph. D. thesis, ETH Zurich

    Google Scholar 

  • Hachmann P, Meissner J (2003) Rheometer for equibiaxial and planar elongations of polymer melts. J Rheology 47:989–1010. doi:10.1122/1.1574021

    Article  Google Scholar 

  • Hingmann R, Marczinke B (1994) Shear and elongational flow properties of polypropylene meltsa). J Rheology 38:573–587 doi:10.1122/1.550475

    Article  Google Scholar 

  • Ianniruberto G, Marrucci G (2012) Entangled melts of branched PS behave like linear PS in the steady state of fast elongational flows. Macromolecules 46:267–275. doi:10.1021/ma302131b

    Article  Google Scholar 

  • Ishizuka O, Koyama K (1980) Elongational viscosity at a constant elongational strain rate of polypropylene melt. Polymer 21:164–170. doi:10.1016/0032-3861(80)90055-5

    Article  Google Scholar 

  • Kashyap T, Venerus DC (2010) Stress relaxation in polymer melts following equibiaxial step strain. Macromolecules 43:5874–5880. doi:10.1021/ma100689y

    Article  Google Scholar 

  • Kaye A (1962) Non-Newtonian flow in incompressible fluids. College of Aeronautics Cranfield,

    Google Scholar 

  • Khan S, Prud’homme R, Larson R (1987) Comparison of the rheology of polymer melts in shear, and biaxial and uniaxial extensions. Rheol Acta 26:144–151. doi:10.1007/BF01331972

    Article  Google Scholar 

  • Laun HM, Schuch H (1989) Transient elongational viscosities and drawability of polymer melts. J Rheology 33:119–175. doi:10.1122/1.550058

    Article  Google Scholar 

  • Masubuchi Y, Matsumiya Y, Watanabe H, Marrucci G, Ianniruberto G (2014) Primitive chain network simulations for Pom-Pom polymers in uniaxial elongational flows. Macromolecules 47:3511–3519. doi:10.1021/ma500357g

    Article  Google Scholar 

  • McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: The pom-pom polymer. J Rheol 42:81–110. doi:10.1122/1.550933

    Article  Google Scholar 

  • Meissner J, Hostettler J (1994) A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheol Acta 33:1–21. doi:10.1007/BF00453459

    Article  Google Scholar 

  • Meissner J, Raible T, Stephenson SE (1981) Rotary clamp in uniaxial and biaxial extensional rheometry of polymer melts. J Rheology 25:1–28. doi:10.1122/1.549612

    Article  Google Scholar 

  • Meissner J, Stephenson SE, Demarmels A, Portman P (1982) Multiaxial elongational flows of polymer melts-classification and experimental realization. J Non-Newtonian Fluid Mech 11:221–237. doi:10.1016/0377-0257(82)80031-1

    Article  Google Scholar 

  • Münstedt H (1979) New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample. J Rheol 24:847–867. doi:10.1122/1.549544

    Google Scholar 

  • Narimissa E, Gupta RK, Kao N, Nguyen DA, Bhattacharya SN (2014) Extensional Rheological Investigation of Biodegradable Polylactide-Nanographite Platelet Composites via Constitutive Equation Modeling. Macromol Mat & Eng 299:851–868. doi:10.1002/mame.201300382

    Article  Google Scholar 

  • Narimissa E, Rolón-Garrido VH, Wagner MH (2015) A hierarchical multi-mode MSF model for long-chain branched polymer melts part i: elongational flow. Rheol Acta 54:779–791. doi:10.1007/s00397-015-0879-2

    Article  Google Scholar 

  • Nguyen DA, Bhattacharjee PK, Sridhar T (2015) Response of an entangled polymer solution to uniaxial and planar deformation. J Rheology 59:821–833. doi:10.1122/1.4917544

    Article  Google Scholar 

  • Nishioka A, Takahashi T, Masubuchi Y, Takimoto JI, Koyama K (2000) Description of uniaxial, biaxial, and planar elongational viscosities of polystyrene melt by the K-BKZ model. J Non-Newtonian Fluid Mech 89:287–301. doi:10.1016/S0377-0257(99)00047-6

    Article  Google Scholar 

  • Osaki K, Watanabe H, Inoue T (1999) Stress overshoot in shear flow of an entangled polymer with bimodal molecular weight distribution. J Soc Rheol, Jpn 27:63–64. doi:10.1678/rheology.27.63

    Article  Google Scholar 

  • Padmanabhan M, Macosko CW (1997) Extensional viscosity from entrance pressure drop measurements. Rheol Acta 36:144–151. doi:10.1007/BF00366820

    Article  Google Scholar 

  • Revenu P, Guillet J, Carrot C (1993) Elongational flow of polyethylenes in isothermal melt spinning. J Rheol 37:1041–1056. doi:10.1122/1.550408

    Article  Google Scholar 

  • Sampers J, Leblans PJR (1988) An experimental and theoretical study of the effect of the elongational history on the dynamics of isothermal melt spinning. J Non-Newtonian Fluid Mech 30:325–342. doi:10.1016/0377-0257(88)85032-8

    Article  Google Scholar 

  • Samurkas T, Dealy J, Larson R (1989) Strong extensional and shearing flows of a branched polyethylene. J Rheology 33:559–578. doi:10.1122/1.550028

    Article  Google Scholar 

  • Soon KH, Harkin-Jones E, Rajeev RS, Menary G, McNally T, Martin PJ, Armstrong C (2009) Characterisation of melt-processed poly(ethylene terephthalate)/syntheticmica nanocomposite sheet and its biaxial deformation behaviour. Polym Inter 58:1134–1141. doi:10.1002/pi.2641

    Article  Google Scholar 

  • Soskey PR, Winter HH (1985) Equibiaxial extension of two polymer melts: polystyrene and low density polyethylene. J Rheology 29:493–517. doi:10.1122/1.549799

    Article  Google Scholar 

  • Stephenson SE (1980) Biaxial extensional flow of polymer melts and its realization in a newly developed rheometer. ETH Zürich

    Google Scholar 

  • Sugimoto M, Masubuchi Y, Takimoto J, Koyama K (2001) Melt rheology of polypropylene containing small amounts of high-molecular-weight chain. 2. Uniaxial and biaxial extensional flow. Macromolecules 34:6056–6063. doi:10.1021/ma0015525

    Article  Google Scholar 

  • 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 37:827–846. doi:10.1122/1.550397

    Article  Google Scholar 

  • Tanner R (1988) From A to (BK) Z in constitutive relations. J Rheology 32:673–702. doi:10.1122/1.549986

    Article  Google Scholar 

  • Van Aken J, Janeschitz-Kriegl H (1980) New apparatus for the simultaneous measurement of stresses and flow birefringence in biaxial extension of polymer melts. Rheol Acta 19:744–752. doi:10.1007/BF01521867

    Article  Google Scholar 

  • Van Aken J, Janeschitz-Kriegl H (1981) Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt. Rheol Acta 20:419–432. doi:10.1007/BF01503263

    Article  Google Scholar 

  • Wagner M, Bastian H, Ehrecke P, Hachmann P, Meissner J (1998) A constitutive analysis of uniaxial, equibiaxial and planar extension of linear and branched polyethylene melts. Progress and Trends in Rheology V. Springer, In, pp. 4–7 doi:10.1007/978-3-642-51062-5_2

    Google Scholar 

  • Wagner MH (1976) Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt. Rheol Acta 15:136–142. doi:10.1007/bf01517505

  • Wagner MH (1999) Constitutive equations for polymer melts and rubbers: lessons from the 20th century. Korea-Australia Rheol J 11:293–304

    Google Scholar 

  • Wagner MH, Hepperle J, Münstedt H (2004) Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory. J Rheology 48:489–503. doi:10.1122/1.1687786

    Article  Google Scholar 

  • Wagner MH, Rubio P, Bastian H (2001) The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheology 45:1387–1412. doi:10.1122/1.1413503

    Article  Google Scholar 

  • Wagner MH, Schaeffer J (1992) Nonlinear strain measures for general biaxial extension of polymer melts. J Rheol 36:1–26. doi:10.1122/1.550338

    Article  Google Scholar 

  • Wagner MH, Schaeffer J (1993) Rubbers and polymer melts: Universal aspects of nonlinear stress-strain relations. J Rheol 37:643-661. doi:10.1122/1.550388

  • Wagner MH, Yamaguchi M, Takahashi M (2003) Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model. J Rheol 47:779–793. doi:10.1122/1.1562155

    Article  Google Scholar 

  • Winter H, Macosko C, Bennett K (1979) Orthogonal stagnation flow, a framework for steady extensional flow experiments. Rheol Acta 18:323–334. doi:10.1007/BF01515825

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Esmaeil Narimissa.

Additional information

Víctor H. Rolón-Garrido passed away on June 8, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narimissa, E., Rolón-Garrido, V.H. & Wagner, M.H. A hierarchical multi-mode MSF model for long-chain branched polymer melts part II: multiaxial extensional flows. Rheol Acta 55, 327–333 (2016). https://doi.org/10.1007/s00397-016-0922-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-016-0922-y

Keywords

Navigation