Comprehensive comparisons with nonlinear flow data of a consistently unconstrained Brownian slip-link model

Journal of Rheology

Volumn 51, Issue 6, 2007, Pages 1111-1141

  Schieber, Jay D ^a   Nair, Deepa M ^a   Kitkrailard, Thidaporn ^a  

^a Illinois Institute of Technology   (United States)

Author keywords

Data comparison; Elongation flow; Entangled polymers; Molecular modeling; Shear flow; Slip links

Indexed keywords

DATA COMPARISON; ELONGATION FLOW; ENTANGLED POLYMERS; SLIP-LINKS;

APPROXIMATION THEORY; ELONGATION; MOLECULAR MODELING; NONLINEAR ANALYSIS; RHEOLOGY; SHEAR FLOW;

BROWNIAN MOVEMENT;

EID: 36749015698     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.2790460     Document Type: Article

References (75)

1. Bach, A., K. Almdal, H. K. Rasmussen, and O. Hassager, " Elongational viscosity of narrow molar mass distribution polystyrene., " Macromolecules 36, 5174-5179 (2003).
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. Bhattacharjee, P., D. Nguyen, G. McKinley, and T. Sridhar, " Extensional stress growth and stress relaxation in entangled polymer solutions., " J. Rheol. 47, 269-290 (2003).
4. Bird, R. B., C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids Vol. II: Kinetic Theory, 2nd ed. (Wiley-Interscience, New York, 1987).
5. 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).
6. Collis, M. W., A. K. Lele, M. R. Mackley, R. S. Graham, A. E. Groves, A. E. Likhtman, T. M. Nicholson, O. G. Harlen, T. C. B. McLeish, L. R. Hutchings, C. M. Fernyhough, and R. N. Young, " Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization., " J. Rheol. 49, 501-522 (2005).
7. Demarquette, N. R., and J. M. Dealy, " Nonlinear viscoelasticity of concentrated polystyrene solutions: Sliding plate rheometer studies., " J. Rheol. 36, 1007-1032 (1992).
8. Doi, M., " Stress relaxation of polymeric liquids after double-step strain., " J. Polym. Sci., Polym. Phys. Ed. 18, 1891-1901 (1980).
9. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Part 1. Brownian motions in the equilibrium state., " J. Chem. Soc., Faraday Trans. 2 74, 1789-1800 (1978a).
10. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Part 2. Molecular motion under flow., " J. Chem. Soc., Faraday Trans. 2 74, 1802-1817 (1978b).
11. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Part 3. The constitutive equation., " J. Chem. Soc., Faraday Trans. 2 74, 1818-1832 (1978c).
12. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Part 4. Rheological properties., " J. Chem. Soc., Faraday Trans. 2 75, 38-54 (1979).
13. Doi, M., and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
14. Doi, M., and J.-I. Takimoto, " Molecular modelling of entanglement., " Philos. Trans. R. Soc. London, Ser. A 361, 641-652 (2003).
15. Doshi, S. R., and J. M. Dealy, " Exponential shear: A strong flow., " J. Rheol. 31, 563-582 (1987).
16. Eskandari, M., " Optimization of the solid-state shear extrusion process for low-cross-link density natural rubber with a proposed Gaussian slip-link model., " Ph.D. thesis, Illinois Institute of Technology, Chicago, 2006.
17. Everaers, R., S. K. Sukumaran, G. S. Grest, C. Svaneborg, A. Sivasubramanian, and K. Kremer, " Rheology and microscopic topology of entangled polymeric liquids., " Science 303, 823-826 (2004).
18. Fang, J., M. Kröger, and H. C. Öttinger, " A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows., " J. Rheol. 44, 1293-1317 (2000).
19. Ferry, J. L., Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1980).
20. Fetters, L. J., D. J. Lohse, S. Milner, and W. W. Graessley, " Packing length influence in linear polymer melts on the entanglement, critical and reptation molecular weights., " Macromolecules 32, 6847-6851 (1999a).
21. Fetters, L. J., D. J. Lohse, and W. W. Graessley, " Chain dimensions and entanglement spacings in dense macromolecular systems., " J. Polym. Sci., Part B: Polym. Phys. 37, 1023-1033 (1999b).
22. Foteinopoulou, K., N. Karayiannis, V. Mavrantzas, and M. Kroger, " Primitive path identification and entanglement statistics in polymer melts: Results from direct topological analysis on atomistic polyethylene models., " Macromolecules 39, 4207-4216 (2006).
23. Gardiner, C. W., Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd ed. (Springer, Berlin, 1982).
24. Gigras, P. G., and B. Khomami, " Adaptive configuration fields: A new multiscale simulation technique for reptation-based models with a stochastic strain measure and local variations of life span distribution., " J. Non-Newtonian Fluid Mech. 108, 99-122 (2002).
25. Graham, R. S., A. Likhtman, T. C. B. McLeish, and S. T. Milner, " Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release., " J. Rheol. 47, 1171-1200 (2003).
26. Graham, R. S., T. C. B. McLeish, and O. G. Harlen, " Using the pom-pom equations to analyze polymer melts in exponential shear., " J. Rheol. 45, 275-290 (2001).
27. Greco, F., " The stress tensor in entangled polymers., " Phys. Rev. Lett. 88, 108301 (2002).
28. Honerkamp, J., Stochastische Dynamische Systeme (VCH, Berlin, 1983).
29. Hua, C. C., and J. D. Schieber, " Segment connectivity, chainlength breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions., " J. Chem. Phys. 109, 10018-10027 (1998a).
30. Hua, C.-C., and J. D. Schieber, " Viscoelastic flow through fibrous media using the CONNFFESSIT approach., " J. Rheol. 42, 477-491 (1998b).
31. Hua, C. C., J. D. Schieber, and D. C. Venerus, " Segment connectivity, chainlength breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions., " J. Chem. Phys. 109, 10028-10032 (1998).
32. Hua, C. C., J. D. Schieber, and D. C. Venerus, " Segment connectivity, chain length breathing, segmental stretch, and constraint release in reptation models. III. Shear flows., " J. Rheol. 43, 701-717 (1999).
33. Ianniruberto, G., and G. Marrucci, " On compatibility of the Cox-Merz rule with the model of Doi and Edwards., " J. Non-Newtonian Fluid Mech. 65, 241-246 (1996).
34. Ianniruberto, G., and G. Marrucci, " Convective orientational renewal in entangled polymers., " J. Non-Newtonian Fluid Mech. 95, 363-374 (2000).
35. Ianniruberto, G., and G. Marrucci, " A simple constitutive equation for entangled polymers with chain stretch., " J. Rheol. 45, 1305-1318 (2001).
36. Kahvand, H., " Strain coupling effects in polymer rheology., " Ph.D. thesis, Illinois Institute of Technology, Chicago, 1995.
37. Kaye, A., " Non-Newtonian flow of incompressible fluids., " Note No. 134, College of Aeronautics, Cranfield, UK, 1962.
38. Kitkrailard, T., " Dynamics of semi-flexible entangled polymers., " Master's thesis, Illinois Institute of Technology, Chicago, Illinois, 2005.
39. Kwan, T. C. B., and E. Shaqfeh, " Brownian dynamics simulations of the stress and molecular configurations of polymers in exponential and linearly-ramped shear flow., " J. Non-Newtonian Fluid Mech. 82, 139-165 (1999).
40. Leygue, A., C. Bailly, and R. Keunings, " A tube-based constitutive equation for polydisperse entangled linear polymers., " J. Non-Newtonian Fluid Mech. 136, 1-16 (2006).
41. Likhtman, A., " Single-chain slip-link model of entangled polymers: Simultaneous description of neutron spin-echo, rheology, and diffusion., " Macromolecules 38, 6128-6139 (2005).
42. Marko, J. F., and E. D. Siggia, " Stretching DNA., " Macromolecules 28, 8759-8770 (1995).
43. Marrucci, G., " Dynamics of entanglements: A nonlinear model consistent with the Cox-Merz rule., " J. Non-Newtonian Fluid Mech. 62, 279-289 (1996).
44. Marrucci, G., and G. Ianniruberto, " Flow-induced orientation and stretching of entangled polymers., " Philos. Trans. R. Soc. London, Ser. A 361, 677-688 (2003).
45. Masubuchi, Y., G. Ianniruberto, F. Greco, and G. Marrucci, " Entanglement molecular weight and frequency response of sliplink networks., " J. Chem. Phys. 119, 6925-6930 (2003).
46. Masubuchi, Y., J. Ichi Takimoto, K. Koyama, G. Ianniruberto, G. Marrucci, and F. Greco, " Brownian simulations of a network of reptating primitive chains., " J. Chem. Phys. 115, 4387-4394 (2001).
47. Mead, D. W., R. G. Larson, and M. Doi, " A molecular theory for fast flows of entangled polymers., " Macromolecules 31, 7895-7914 (1998).
48. Menezes, E. V., and W. W. Graessley, " Nonlinear rheological behavior of polymer systems for several shear-flow histories., " J. Polym. Sci., Polym. Phys. Ed. 20, 1817-1833 (1980).
49. Milner, S. T., T. C. B. McLeish, and A. E. Likhtman, " Microscopic theory of convective constraint release., " J. Rheol. 45, 539-563 (2001).
50. Nair, D., " Brownian dynamics simulation of consistently unconstrainted Brownian sliplinks., " Master's thesis, Illinois Institute of Technology, Chicago, 2004.
51. Nair, D. M., and J. D. Schieber, " Linear viscoelastic predictions of a consistently unconstrained Brownian slip-link model., " Macromolecules 39, 3386-3397 (2006).
52. Neergaard, J., K. Park, D. C. Venerus, and J. D. Schieber, " Exponential shear flow of linear, entangled polymeric liquids., " J. Rheol. 44, 1043-1054 (2000).
53. Neergaard, J., and J. D. Schieber, " A full chain network model with sliplinks and binary constraint release., " XIIIth International Congress on Rheology, Cambridge, United Kingdom, 2000, Vol. 2, pp. 120-122.
54. Osaki, K., S. Kimura, and M. Kurata, " Relaxation of shear and normal stresses in double-step shear deformations for a polystyrene solution. A test of the Doi-Edwards theory for polymer rheology., " J. Rheol. 25, 549-562 (1981).
55. Osaki, K., and M. Kurata, " Stress relaxation of a polymer solution in double-step shear deformations: A separate evaluation of the stress components due to entangled segments of different orientations., " J. Polym. Sci., Part A-2 20, 623-632 (1982).
56. Öttinger, H. C., " Modified reptation model., " Phys. Rev. E 50, 4891-4895 (1994).
57. Öttinger, H. C., Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996).
58. Öttinger, H. C., " A thermodynamically admissible reptation model for fast flows of entangled polymers., " J. Rheol. 43, 1461-1493 (1999).
59. Rault, J., " Space filling an entanglements in polymeric systems., " J. Non-Newtonian Fluid Mech. 23, 229-247 (1987).
60. Rubinstein, M., " Discretized model of entangled-polymer dynamics., " Phys. Rev. Lett. 59, 1946-1949 (1987).
61. Rubinstein, M., and S. Panyukov, " Elasticity of polymer networks., " Macromolecules 35, 6670-6686 (2002).
62. Samurkas, T., R. G. Larson, and J. M. Dealy, " Strong extensional and shearing flows of a branched polyethylene., " J. Rheol. 33, 559-578 (1989).
63. Schieber, J. D., " Fluctuations in entanglements of polymer liquids., " J. Chem. Phys. 118, 5162-5166 (2003a).
64. Schieber, J. D., " GENERIC compliance of a temporary network model with sliplinks, chain-length fluctuations, segment-connectivity and constraint release., " J. Non-Equil. Thermodyn. 28, 179-188 (2003b).
65. Schieber, J. D., J. Neergaard, and S. Gupta, " A full-chain, temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching., " J. Rheol. 47, 213-233 (2003). Although all dynamical calculations were verified to agree with analytic results at equilibrium, we later discovered that stress calculations contained a bug. Hence, stress curves in this manuscript should be ignored.
66. Schweizer, T., J. van Meerveld, and H. C. Öttinger, " Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution experiment and theory., " J. Rheol. 48, 1345-1363 (2004).
67. Shanbhag, S., and M. Kroger, " Primitive path networks generated by annealing and geometrical methods: Insights into differences., " Macromolecules 40, 2897-2903 (2007).
68. Sivashinsky, N., A. T. Tsai, T. J. Moon, and D. S. Soong, " Some new transient test results from a parallel-plate rheometer., " J. Rheol. 28, 287-301 (1984).
69. Tzoumanekas, C., and D. N. Theodorou, " Topological analysis of linear polymer melts: A statistical approach., " Macromolecules 39, 4592-4604 (2006).
70. Venerus, D. C., " Exponential shear flow of polymer melts., " Rheol. Acta 39, 71-79 (2000).
71. Venerus, D. C., and H. Kahvand, " Doi-Edwards theory evaluation in double-step strain flows., " J. Polym. Sci., Part B: Polym. Phys. 32, 1531-1542 (1994a).
72. Venerus, D. C., and H. Kahvand, " Normal stress relaxation in reversing double-step strain flows., " J. Rheol. 38, 1297-1315 (1994b).
73. Venerus, D. C., C. M. Vrentas, and J. S. Vrentas, " Step strain deformations for viscoelastic fluids: Experiment., " J. Rheol. 34, 657-684 (1990).
74. Zhou, Q., and R. Larson, " Primitive path identification and statistics in molecular dynamics simulations of entangled polymer melts., " Macromolecules 38, 5761-5765 (2005).
75. Zülle, B., J. J. Linster, J. Meissner, and H. P. Hürlimann, " Deformation hardening and thinning in both elongation and shear of a low density polyetyhylene melt., " J. Rheol. 31, 583-598 (1987).