Self-consistent modeling of entangled network strands and linear dangling structures in a single-strand mean-field slip-link model

Rheologica Acta

Volumn 51, Issue 1, 2012, Pages 21-35

  Jensen, Mette Krog ^a   Khaliullin, Renat ^b   Schieber, Jay D ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b Illinois Institute of Technology   (United States)

Author keywords

BSW spectrum; Entanglement; Polymer network

Indexed keywords

EID: 84855323677     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-011-0568-8     Document Type: Article

References (31)

1. Baumgaertel M, Schausberger A, Winter H (1990) The relaxation of polymers with linear flexible chains of uniform length. Rheol Acta 29(5): 400-408.
2. Doi M, Takimoto J (2003) Molecular modelling of entanglement. Philos Trans: Math Phys Eng Sci 361(1805): 641-652.
3. Fetters L, Lohse D, Richter D, Witten T, Zirkel A (1994) Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties. Macromolecules 27(17): 4639-4647.
4. Flory P (1941) Molecular size distribution in three dimensional polymers. III. Tetrafunctional branching units. J Am Chem Soc 63(11): 3096-3100.
5. Graessley W (2008) Polymeric liquids and networks: dynamics and rheology. Garland Science, London.
6. Jensen M, Bach A, Hassager O, Skov A (2009) Linear rheology of cross-linked polypropylene oxide as a pressure sensitive adhesive. Int J Adhes Adhes 29: 687-693.
7. Jensen M, Hassager O, Rasmussen H, Skov A, Bach A, Koldbech H (2010) Planar elongation of soft polymeric networks. Rheol Acta 49(1): 1-13.
8. Kawamura T, Urayama K, Kohjiya S (2002) Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. III. Effect of entanglement density on strain-energy density function. J Polym Sci B Polym Phys 40(24): 2780-2790.
9. Khaliullin R, Schieber J (2008) Analytic expressions for the statistics of the primitive-path length in entangled polymers. Phys Rev Lett 100(18): 188302-188304.
10. Khaliullin R, Schieber J (2009) Self-consistent modeling of constraint release in a single-chain mean-field slip-link model. Macromolecules 42(19): 7504-7517.
11. Khaliullin R, Schieber J (2010) Application of the slip-link model to bidisperse systems. Macromolecules 159-177.
12. Larsen AL, Hansen K, Sommer-Larsen P, Hassager O, Bach A, Ndoni S, Jørgensen M (2003) Elastic properties of nonstoichiometric reacted PDMS networks. Macromolecules 36: 10063.
13. Macosko CW, Miller DR (1976) A new derivation of average molecular weights of nonlinear polymers. Macromolecules 9(2): 199.
14. Marcelo A, Villar M, Vallés E (1996) Influence of pendant chains on mechanical properties of model poly(dimethylsiloxane) networks. 2. Viscoelastic properties. Macromolecules 29: 4081-4089.
15. Mark J (1981) Elastic properties of model polymer networks. Pure Appl Chem 53: 1495-1503.
16. Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2003) Entanglement molecular weight and frequency response of sliplink networks. J Chem Phys 119: 6925.
17. Miller DR, Macosko CW (1976) A new derivation of post gel properties of network polymers. Macromolecules 9(2): 206.
18. Milner ST, McLeish TCB (1998) Reptation and contour-length fluctuations in melts of linear polymers. Phys Rev Lett 81(3): 725-728.
19. Mortensen K (1993) PEO-PPO-PEO block polymer in aqueous solution: Micelle formation and crystallization. Prog Colloid Polym Sci 91: 69.
20. Read D, McLeish T (2001) Molecular rheology and statistics of long chain branched metallocene-catalyzed polyolefins. Macromolecules 34(6): 1928-1945.
21. Rubinstein M, Colby R (2006) Polymer physics. Oxford University Press, Oxford.
22. Rubinstein M, Panyukov S (2002) Elasticity of polymer networks. Macromolecules 35(17): 6670-6686.
23. Schieber J (2003) Fluctuations in entanglements of polymer liquids. J Chem Phys 118(11): 5162-5166.
24. Schieber J, Neergaard J, Gupta S (2003) A full-chain, temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching. J Rheol 47(1): 213-233.
25. n. X. crystal structure of poly (ethylene oxide). Macromolecules 6(5): 672-675.
26. Tsenoglou C (1989) Rubber elasticity of cross-linked networks with trapped entanglements and dangling chains. Macromolecules 22(1): 284-289.
27. Urayama K, Kawamura T, Kohjiya S (2009) Structure-mechanical property correlations of model siloxane elastomers with controlled network topology. Polymer 50(2): 347-356.
28. Vallés E, Macosko C (1976) The effect of network structure in the equation of rubber elasticity. Rubber Chem Technol 49: 1232-1237.
29. Villar M, Bibbó M, Vallés E (1996) Influence of pendant chains on mechanical properties of model poly(dimethylsiloxane) networks. 1. Analysis of the molecular structure of the network. Macromolecules 29: 4072-4080.
30. Wang S, Mark JE (1992) Unimodal and bimodal networks of poly(dimethyl siloxane) in pure shear. J Polym Sci Part B Polym Phys 30: 801-807.
31. Winter HH, Chambon F (1986) Analysis of linear viscoelasticity of a cross-linking polymer at the gel point. J Rheol 30(2): 367.