Abstract.
The pom-pom rheological constitutive equation for branched polymers proposed by McLeish and Larson is evaluated in step shear strain flows. Semianalytic expressions for the shear-stress relaxation modulus are derived for both the integral and approximate differential versions of the pom-pom model. Predictions from the thermodynamically motivated differential pompon model of Öttinger are also examined. Single-mode integral and differential pom-pom models are found to give qualitatively different predictions, the former displays time–strain factorability after the backbone stretch is relaxed, while the latter does not. We also find that the differential pompon model gives quantitatively similar predictions to the integral pom-pom model in step strain flows. Predictions from multimode integral and differential pom-pom models are compared with experimental data on a widely characterized, low-density polyethylene known as 1810H. The experiments strongly support time–strain factorability, while the multimode pom-pom model predictions show deviations from this behavior over the entire range of time that is experimentally accessible.
Similar content being viewed by others
References
Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31:6348–6355
Bick DK, McLeish TCB (1996) Topological contributions to nonlinear elasticity in branched polymers. Phys Rev Lett 76:2587–2590
Bishko G, McLeish TCB, Harlen OG, Larson RG (1997) Theoretical molecular rheology of branched polymers in simple and complex flows: The pom-pom model. Phys Rev Lett 79:2352–2355
Blackwell RJ, McLeish TCB Harlen OG (2000) Molecular drag-strain coupling in branched polymer melts. J Rheol 44:121–136
Bruker I (1986) Measurements of the first normal stress difference in a new rheo-dilatometer for molten polymers: Triple-step strain tests for all K-BKZ constitutive equations. Rheol Acta 25:501–506
Doi M (1980a) Molecular rheology of concentrated polymer systems. I, J. Poly. Sci., Polym. Phys., 18:1005–1020
Doi M (1980b) Stress relaxation of polymeric liquids after double step strain. J Polym Sci Part B Polym Phys 18:1891–1905
Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York
Gevgilili H, Kalyon DM (2001) Step strain flow: Wall slip effects and other error sources. J Rheol 45:467–475
Graham RS, McLeish TCB, Harlen OG (2001) Using the pom-pom equations to analyze polymer melts in exponential shear. J Rheol 45:275–290
Hachmann P (1996) Multiaxiale Dehnung von Polymerschmelzen. PhD thesis. ETH Zürich
Inkson NJ, McLeish TCB, Harlen OG, Grove DJ (1999) Predicting low density polyethylene melt rheology in elongational and shear flows with "pom-pom" constitutive equation. J Rheol 43:873–896
Kimura S, Osaki K, Kurata M (1981) Stress relaxation of polybutadiene at large deformation. J Polym Sci, Polym Phys Ed 19:151–163
Kraft M (1996) Untersuchungen zur schernduzierten rheologischen Anisotropie von verschiedenen Polyethylen Schmelzen. PhD thesis. ETH Zürich
Laun HM (1978) Description of the non-linear shear behavior of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17:1–15
Lodge AS, Meissner J (1973) Comparison of network theory predictions with stress/time data in shear and elongation for a low-density polyethylene melt. Rheol Acta 12:41–47
McKinley GH, Hassager O (1999) The Considère condition and rapid stretching of linear and branched polymer melts. J Rheol 43:1195–1212
McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: The pom-pom polymer. J Rheol 42:81–110
McLeish TCB, Milner ST (1999) Entangled dynamics and melt flow of branched polymers. Adv Polym Sci 143:195–256
McLeish TCB, Allgaier J, Bick DK, Bishko G, Biswas P, Blackwell R, Blottière B, Clarke N, Gibbs B, Groves DJ, Hakiki A, Heenan RK, Johnson JM, Kant R, Read DJ, Young RN (1999) Dynamics of entangled H-polymers: theory, rheology and neutron scattering. Macromolecules 32:6734–6758
Meissner J, Garbella RW, Hostettler J (1989) Measuring normal stress differences in polymer melt shear flow. J Rheol 33:843–864
Olson DJ, Brown EF, Burghardt WR (1998) Second normal stress difference relaxation in a linear polymer melt following step strain. J Polym Sci Part B Polym Phys 36:2671–2675
Osaki K (1993) On the damping function of shear relaxation modulus of entangled polymers. Rheol Acta 32:429–437
Öttinger HC (2001) Thermodynamic admissibility of the pom-pom model for branched polymers. Rheol Acta 40:317–321
Rubio P, Wagner MH (1999) Letter to the editor: A note added to "Molecular constitutive equations for a class of branched polymers: the pom-pom polymer". J Rheol 43:1709–1710
Rubio P, Wagner MH (2000) LDPE melt rheology and the pom-pom model. J Non-Newtonian Fluid Mech 92:245–259
Samurkas T, Larson RG, Dealy JM (1989) Strong extensional and shearing flows of a branched polyethylene. J Rheol 33:559–645
Soskey PR, Winter H (1984) Large step shear strain experiments with parallel-disk rotational rheometers. J Rheol 28:625–645
Vrentas CM, Graessley WW (1981) Relaxation of shear and normal stress components in step-strain experments, J Non-Newtonian Fluid Mech 9:339–355
Venerus DC, Brown EF, Burghardt WR (1998) The nonlinear response of a polydisperse polymer solution to step strain deformations. Macromolecules 31:9206–9212
Venerus DC (2000) Exponential shear flow of branched polymer melts. Rheol Acta 39:71–79
Verbeeten WMH, GWM Peters, FPT Baaijens (2001) Differential constitutive equations for polymer melts: the extended pom-pom model. J Rheol 45:823–843
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chodankar, C.D., Schieber, J.D. & Venerus, D.C. Evaluation of rheological constitutive equations for branched polymers in step shear strain flows. Rheol Acta 42, 123–131 (2003). https://doi.org/10.1007/s00397-002-0263-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-002-0263-x