Nonlinear viscoelastic properties of branched polyethylene in reversing flows

Journal of Rheology

Volumn 51, Issue 3, 2007, Pages 341-365

  Sui, Changping ^a   McKenna, Gregory B ^a  

^a Texas Tech University   (United States)

Author keywords

Branched polymers; Cox Merz rule; Damping function; K BKZ theory; Nonlinear viscoelasticity; Normal stress ratio; Polyethylene; Reversing flows; Rheology; Step strains; Strain energy function

Indexed keywords

BRANCHED POLYMERS; COX-MERZ RULES; K-BKZ THEORY; NONLINEAR VISCOELASTICITY; REVERSING FLOWS; STEP STRAINS; STRAIN ENERGY FUNCTIONS;

NONLINEAR ANALYSIS; POLYMER MELTS; POLYSTYRENES; VISCOELASTICITY;

POLYETHYLENES;

EID: 34247849249     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.2711962     Document Type: Article

References (76)

1. Archer, L. A., J. Sanchez-Reyes, and Juliani, " Relaxation dynamics of polymer liquids in nonlinear step strain., " Macromolecules 35, 10216-10224 (2002).
2. Bernstein, B., E. A. Kearsley, and L. J. Zapas, " A study of stress relaxation with finite strain., " Trans. Soc. Rheol. 7, 391-410 (1963).
3. Bernstein, B., " Time-dependent behavior of an incompressible elastic fluid. Some homogeneous deformation histories., " Acta Mech. II, 329-354 (1966).
4. Bird, R. B., R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1977).
5. Booij, H. C., P. Leblans, J. Palmen, and G. Tiemersma-Thoone, " Nonlinear viscoelasity and the Cox-Merz relations for polymeric fluids., " J. Polym. Sci., Polym. Phys. Ed. 21, 1703-1711 (1983).
6. Brown, E. F., W. R. Burghardt, H. Hahvand, and D. C. Venerus, " Comparison of optical and mechanical measurements of second stress difference relaxation following step strain., " Rheol. Acta 34, 221-234 (1995).
7. Brown, E. F., and W. R. Burghardt, " First and second normal stress difference relaxation in reversing double-step strain flows., " J. Rheol. 40, 37-54 (1996).
8. Chang, W. V., R. Bloch, and N. W. Tschoegl, " Study of the viscoelastic behavior of uncrosslinked (Gum) rubbers in moderately large deformations., " J. Polym. Sci., Polym. Phys. Ed. 15, 923-944 (1977).
9. Cox, W. P., and E. H. Merz, " Correlation of dynamic and steady state flow viscosities., " J. Polym. Sci. 28, 619-622 (1958).
10. Chodankar, C. D., J. D. Schieber, and D. C. Venerus, " Pom-pom theory evaluation in double-step strain flows., " J. Rheol. 47, 413-427 (2003a).
11. Chodankar, C. D., J. D. Schieber, and D. C. Venerus, " Evaluation of rheological constitutive equations for branched polymers in step shear strain flows., " Rheol. Acta 42, 123-131 (2003b).
12. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Parts 1 and 2., " J. Chem. Soc., Faraday Trans. 2 74, 1789-1817 (1978).
13. Doi, M., " Stress relaxation of polymeric liquids after double-step strain., " J. Polym. Sci., Polym. Phys. Ed. 18, 1891-1905 (1980).
14. Doi, M., and S. F. Edwards, The Theory of Polymer Dynamics (Oxford Scientific, Clarendon, Oxford, 1986).
15. Ferri, D., and P. Lomellini, " Melt rheology of randomly branched polystyrenes., " J. Rheol. 43, 1355-1372 (1999).
16. Ferry, J. D., Viscoelastic Properties of Polymers (Wiley, New York, 1980).
17. Flory, A., and G. B. McKenna, " Finite step rate corrections in stress relaxation experiments: Comparison of two methods., " Mech. Time-Depend. Mater. 8, 17-37 (2004).
18. Fukuda, M., K. Osaki, and M. Kurata, " Nonlinear viscoelasticity of polystyrene solutions I. Strain-dependent relaxation modulus., " J. Polym. Sci. A 13, 1563-1576 (1975a).
19. Fukuda, M., K. Osaki, and M. Kurata, " Nonlinear viscoelasticity of polystyrene solutions I., " J. Polym. Sci., Polym. Phys. Ed. 13, 1563-1567 (1975b).
20. Hua, C. C., " Investigation on several empirical rules for entangled polymers based on a self-consistent full-chain reptation theory., " J. Chem. Phys. 112, 8176-8186 (2000).
21. Inn, Y. W., K. F. Wissbrun, and M. M. Denn, " Effect of edge fracture on constant torque rheometery of entangled polymer solutions., " Macromolecules 38, 9385-9388 (2005).
22. Kawabata, S., M. Masuda, K. Tei, and H. Kawai, " Experimental survey of the strain energy density function of isoprene rubber vulcanizate., " Macromolecules 14, 154-162 (1981).
23. Kaye, A., " Non-Newtonian flow of incompressible fluids., " Note No. 134, College of Aeronautics, Cranfield, UK, 1962.
24. Kearsley, E. A., and L. J. Zapas, " Some method of measurement of an elastic strain-energy function of the Valanis-Landel type., " J. Rheol. 24, 483-500 (1980).
25. Kulicke, W. M., and R. S. Porter, " Relation between steady shear flow and dynamic rheology., " Rheol. Acta 19, 601-605 (1980).
26. Khanna, Y. P., " Dynamic melt rheology. I: Re-examining dynamic viscosity in relationship to the steady shear flow., " Polym. Eng. Sci. 31, 440-444 (1991).
27. Larson, R. G., " Nonlinear shear relaxation modulus for a linear low density polyethylene., " J. Rheol. 29, 823-831 (1985).
28. Larson, R. G., Constitutive Equations for Polymer Melts and Solutions (Butterworth, Stoneham, MA, 1988).
29. Larson, R. G., S. A. Khan, and V. R. Raju, " Relaxation of stress and birefringence in polymers of high molecular weight., " J. Rheol. 32, 145-161 (1988).
30. Laun, H. M., " Description of the nonlinear shear behavior of a low density polyethylene melt by means of experimentally determined strain dependent memory function., " Rheol. Acta 17, 1-15 (1978).
31. Lee, C. S., J. J. Magda, and K. L. DeVries, " Measurements of the second normal stress difference for star polymers with highly entangled branches., " Macromolecules 25, 4744-4750 (1992).
32. Lee, S., and W. G. Knauss, " A note on the determination of the relaxation and creep data from ramp tests., " Mech. Time-Depend. Mater. 4, 1-7 (2000).
33. Magda, J. J., J. Lou, S. G. Baek, and K. L. Devries, " Second normal stress difference of a Boger fluid., " Polymer 32, 2000-2009 (1991).
34. Magda, J. J., C. S. Lee, S. J. Muller, and R. G. Larson, " Rheology, flow instability, and shear-induced diffusion in polystyrene solutions., " Macromolecules 26, 1696-1706 (1993).
35. Marrucci, G., " The free energy function of the Doi and Edwards theory: Analysis of the instability in stress relaxation., " J. Rheol. 27, 433-450 (1983).
36. McKenna, G. B., and L. J. Zapas, " Nonlinear viscoelastic behavior of poly (methyl methacrylate)., " J. Rheol. 23, 151-166 (1979).
37. McKenna, G. B., and L. J. Zapas, " Viscoelastic behavior of poly (methyl methacrylate): Prediction of extensional response from torsional data., " in Rheology, edited by, G. Astarita, G. Marrucci, and, L. Nicolas, (Plenum, New York, 1980a), Vol. 3, pp. 299-307.
38. McKenna, G. B., and L. J. Zapas, " The normal stress response in nonlinear viscoelastic materials: Some experimental findings., " J. Rheol. 24, 367-377 (1980b).
39. McKenna, G. B., and L. J. Zapas, " Experiments on the small strain behavior of cross-linked natural rubber., " Polymer 24, 1495-1501 (1983).
40. McLeish, T. C. B., and R. G. Larson, " Molecular constitutive equations for a class of branched polymers: The pom-pom polymer., " J. Rheol. 42, 81-110 (1998).
41. Meissner, J., R. W. Garbella, and J. Hostettler, " Measuring normal stress differences in polymer melt shear flow., " Macromolecules 33, 843-864 (1989).
42. Morrison, F. A., and R. G. Larson, " A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrene., " J. Polym. Sci., Part B: Polym. Phys. 30, 943-950 (1992).
43. Osaki, K., Y. Einaga, N. Yamada, and M. Tamura, " Stress relaxation of polymer solutions under large strain. Application of double-step strain., " Polym. J. (Singapore) 5, 283-287 (1973).
44. Osaki, K., M. Fukuda, S. Ohta, B. S. Kim, and M. Kurata, " Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity., " J. Polym. Sci., Polym. Phys. Ed. 13, 1577-1589 (1975).
45. Osaki, K., S. Ohta, M. Fukuda, and M. Kurata, " Applications of ESCA to polymer chemistry. XI. Core and valence energy levels of a series of polymethacrylates., " J. Polym. Sci. A 14, 1701-1713 (1976).
46. Osaki, K., S. Kimura, and M. Kurata, " Relaxation of shear and normal stress in double-step shear deformation for a polystyrene solution. A test of the Doi and Edwards theory for polymer rheology., " J. Rheol. 25, 549-562 (1981a).
47. Osaki, K., S. Kimura, and M. Kurata, " Relaxation of shear and normal stresses in step-strain deformation of a polystyrene solution. Comparison with the predictions of the Doi and Edwards theory., " J. Polym. Sci., Polym. Phys. Ed. 19, 517-527 (1981b).
48. Osaki, K., and M. Kurata, " Experimental appraisal of the Doi and Edwards theory for polymer rheology based on the data for polystyrene solutions., " Macromolecules 13, 671-676 (1980).
49. Osaki, K., " On the damping function of shear relaxation modulus for entangled polymers., " Rheol. Acta 32, 429-437 (1993).
50. Papanastasiou, A. C., L. E. Scriven, and C. W. Macosko, " An integral constitutive equation for mixed fluids: Viscoelastic characterization., " J. Rheol. 27, 387-410 (1983).
51. Pattamaprom, C., and R. G. Larson, " Constraint release effects in monodisperse and bidisperse polystyrenes in fast transient shearing flow., " Macromolecules 34, 5229-5237 (2001).
52. Penn, R. W., and E. A. Kearsley, " The scaling law for finite torsion of elastic cylinders., " Trans. Soc. Rheol. 20, 227-238 (1976).
53. Rivlin, R. S., " Stress relaxation in incompressible elastic materials at constant deformation., " Q. Appl. Math. 14, 83-89 (1956).
54. Rubio, P., and M. H. Wagner, " LDPE melt rheology and the pom-pom model., " J. Non-Newtonian Fluid Mech. 92, 245-259 (2000).
55. Samurkas, T., R. G. Larson, and J. M. Dealy, " Strong extensional and shearing flows of a branched polyethylene., " J. Rheol. 33, 559-578 (1989).
56. Sanchez-Reyes, J., M. T. Islam, and L. A. Archer, " Step shear dynamics of highly entangled polymer liquids., " Macromolecules 35, 5194-5202 (2002).
57. Soskey, P. R., and H. H. Winter, " Large step shear strain experiments with parallel-disk rotational rheometer., " J. Rheol. 28, 625-645 (1984).
58. Takahashi, M., T. Masuda, and S. Onogi, " A stress dependent constitutive equation-Comments., " J. Rheol. 22, 285-291 (1978).
59. Tapadia, P., and S. Q. Wang, " Direct visualization of continuous simple shear in non-Newtonian polymeric fluids., " Phys. Rev. Lett. 96, 016001-016004 (2006).
60. Utracki, L. A., and R. Gendron, " Pressure oscillations during extrusion of polyethylene. II., " J. Rheol. 28, 601-623 (1984).
61. Venerus, D. C., C. M. Vrentas, and J. S. Vrentas, " Step strain deformations for viscoelastic fluids: experiment., " J. Rheol. 34, 657-683 (1990).
62. Venerus, D. C., and H. Kahvand, " Doi and Edwards theory evaluation in double-step strain flows., " J. Polym. Sci., Part B: Polym. Phys. 32, 1531-1542 (1994a).
63. Venerus, D. C., and H. Kahvand, " Normal stress relaxation in reversing double-step strain flows., " J. Rheol. 38, 1279-1315 (1994b).
64. Venerus, D. C., " A critical evaluation of step strain flows of entangled linear polymer liquids., " J. Rheol. 49, 277-295 (2005).
65. Venerus, D. C., and N. Ritesh, " Stress relaxation dynamics of an entangled polystyrene solution following step strain flow., " J. Rheol. 50, 59-75 (2006).
66. Venkatraman, S., M. Okano, and A. Nixon, " A comparison of torsional and capillary rheometry for polymer melts: The Cox-Merz rule revisited., " Polym. Eng. Sci. 30, 308-313 (1990).
67. Vrentas, C. M., and W. W. Graessley, " Study of shear stress relaxation in well-characterized polymer liquids., " J. Rheol. 26, 359-371 (1982).
68. Wagner, M. H., " Analysis of time-dependent non-linear sress-growth data for shear and elongational flow of a low-density branched polyethylene melt., " Rheol. Acta 15, 136-142 (1976).
69. Wagner, M. H., P. Rubio, and H. Bastain, " The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release., " J. Rheol. 45, 1387-1412 (2001).
70. Wagner, M. H., J. Hepperle, and H. Munstedt, " Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory., " J. Rheol. 48, 489-503 (2004).
71. Wagner, M. H., " Challenges in nonlinear rheology of linear and long-chain branched polymer melts., " Proc. XIVth Int. Congr. On Rheology, 2004, pp. PL04-1-PL04-7.
72. Wen, Y. H., H. C. Lin, C. H. Li, and C. C. Hua, " An experimental appraisal of the Cox-Merz rule and Laun's rule based on bidisperse entangled polystyrene solutions., " Polymer 45, 8551-8559 (2004).
73. Woods-Adams, P. M., " The effect of long chain branches on the shear flow behavior of polyethelene., " J. Rheol. 45, 203-210 (2001).
74. Zapas, L. J., " Viscoelastic behavior under large deformations., " J. Res. Natl. Bur. Stand., Sect. A 70A, 525-539 (1966).
75. Zapas, L. J., and T. Craft, " Correlation of large longitudinal deformations with different strain histories., " J. Res. Natl. Bur. Stand., Sect. A 69A, 541-546 (1965).
76. Zapas, L. J., G. B. McKenna, and A. Bernna, " An analysis of the corrections to the normal force response for the cone and plate geometry in single-step stress relaxation experiments., " J. Rheol. 33, 69-91 (1989).