Molecular dynamics study of the vulcanization transition

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 3, 1998, Pages 3347-3352

  Plischke, Michael ^a   Barsky, Sandra J ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011791387     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.3347     Document Type: Article

References (34)

1. L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, Oxford, 1975).
2. H. M. James and E. Guth, J. Chem. Phys. 11, 455 (1943); JCPSA6
3. P. J. Flory, J. Am. Chem. Soc. 63, 3083 (1941)
4. J. Am. Chem. Soc.P. J. Flory63, 3091 (1941)
5. J. Am. Chem. Soc.P. J. Flory63, 3096 (1941)
6. W. H. Stockmayer, J. Chem. Phys. 11, 45 (1943); JCPSA6
7. M. Gordon and S. B. Ross-Murphy, Pure Appl. Chem. 43, 1 (1975).PACHAS
8. P. G. de Gennes, J. Phys. (France) Lett. 37, L1 (1976)
9. J. Phys. (France) Lett.P. G. de Gennes38, L355 (1977).
10. See P. M. Goldbart, H. E. Castillo, and A. Zippelius, Adv. Phys. 45, 393 (1996) for a recent review of this work.ADPHAH
11. R. T. Deam and S. F. Edwards, Philos. Trans. R. Soc. London, Ser. A 280, 317 (1976)
12. R. C. Ball and S. F. Edwards, Macromolecules 13, 748 (1980)
13. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 22, 1010 (1981).POLMAG
14. S. J. Barsky and M. Plischke, Phys. Rev. E 53, 871 (1996); PLEEE8
15. Sandra J. Barsky, Ph.D. dissertation, Simon Fraser University (1996).
16. S. J. Barsky, M. Plischke, B. Joós, and Z. Zhou, Phys. Rev. E 54, 5370 (1996).PLEEE8
17. K. Kremer and G. S. Grest, J. Chem. Phys. 92, 5057 (1990); JCPSA6
18. J. Chem. Phys.K. KremerG. S. Grest94, 4103 (1991)
19. K. KremerG. S. GrestJ. Chem. Soc., Faraday Trans. 88, 1707 (1992)
20. E. R. Duering, K. Kremer, and G. S. Grest, Macromolecules 26, 3241 (1993).MAMOBX
21. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1977), Vol. 1.
22. M. Allen and D. Tildesley, Computer Simulations of Liquids (Oxford University Press, Oxford, 1987).
23. There is no a priori reason for excluding self-linkages since they would certainly occur in real vulcanization processes. However, there are indications [B. Joós (private communication)] that excluding self-linkages reduces fluctuations in measured quantities and narrows the critical region. Therefore, this may be a useful modification of the model.
24. The entanglement length for polymer melts at density ρσ3=0.85 has been estimated by 8 to be Ne≈35.
25. C. P. Lusignan, T. H. Mourey, J. C. Wilson, and R. H. Colby, Phys. Rev. E 52, 6271 (1995).PLEEE8
26. The order parameter q as defined in 4 is obviously positive semi-definite. However, the partial time averages q(n,t) are noisy functions due to the Brownian dynamics and the random nature of the cross-linking process. Therefore, it is possible for the extrapolation procedure to produce an estimate q0<0.
27. It is well known that at T=0, diluted central force networks have a separate rigidity percolation point at a substantially higher concentration of sites or bonds than is necessary for geometric percolation. [See, for example, S. Feng and P. N. Sen, Phys. Rev. Lett. 52, 216 (1984) or
28. D. J. Jacobs and M. F. Thorpe, Phys. Rev. E 53, 3682 (1996) for more recent developments.] However, at zero temperature rigidity is a purely energetic effect whereas at finite T there is generically an entropic contribution to the elastic constants. In diluted central-force networks at finite T, geometric and rigidity percolation coincide [PLEEE8
29. M. Plischke and B. Joós, Phys. Rev. Lett.80, 4907 (1998)].PRLTAO
30. S. J. Barsky and M. Plischke (unpublished).
31. G. Grest and K. Kremer, J. Phys. (France) 51, 2829 (1990).JOPQAG
32. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1992).
33. R. H. Colby, M. Rubinstein, J. R. Gillmor, and T. H. Mourey, Macromolecules 25, 7180 (1992). These authors estimate that for their system the prefactor a in the Ginzburg criterion is roughly 0.1 and that critical versus mean field behavior sets in at δn/nc≈0.01N-1/3.MAMOBX
34. R. H. Colby, J. R. Gillmor, and M. Rubinstein, Phys. Rev. E 48, 3712 (1993). PLEEE8