Model for gelation with explicit solvent effects: Structure and dynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 1 1, 2003, Pages 114011-114016

  Plischke, Michael ^a   Vernon, D C ^a   Joós, Béla ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b Université d Ottawa et Institut de Physique Ottawa Carleton   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONCENTRATION (PROCESS); CROSSLINKING; GELATION; GELS; PERCOLATION (FLUIDS); SOLVENTS; VISCOSITY OF LIQUIDS;

SOLVENT EFFECTS;

MONOMERS;

EID: 0037717168     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. See, for example, D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1994).
2. See, D. Stauffer, A. Coniglio, and M. Adam, Adv. Polym. Sci. 44, 103 (1982) for a review.
3. D. Vernon, M. Plischke, and B. Joós, Phys, Rev. E 64, 031505 (2001).
4. P.O. de Gennes, J. Phys. (France) 40, L197 (1979).
5. K. Broderix, H. Löwe, P. Müller, and A. Zippelius, Europhys. Lett. 48, 421 (1999); Phys. Rev. E 63, 011510 (2001).
6. K. Broderix, H. Löwe, P. Müller, and A. Zippelius, Europhys. Lett. 48, 421 (1999); Phys. Rev. E 63, 011510 (2001).
7. M. Adam, M. Delsanti, D. Durand, G. Hild, and J.P. Munch, Pure Appl. Chem. 53, 1489 (1981); M. Adam, M. Delsanti, and D. Durand, Macromolecules 18, 2285 (1985); D. Durand, M. Delsanti, and J.M. Luck, Europhys. Lett. 3, 297 (1987).
8. M. Adam, M. Delsanti, D. Durand, G. Hild, and J.P. Munch, Pure Appl. Chem. 53, 1489 (1981); M. Adam, M. Delsanti, and D. Durand, Macromolecules 18, 2285 (1985); D. Durand, M. Delsanti, and J.M. Luck, Europhys. Lett. 3, 297 (1987).
9. M. Adam, M. Delsanti, D. Durand, G. Hild, and J.P. Munch, Pure Appl. Chem. 53, 1489 (1981); M. Adam, M. Delsanti, and D. Durand, Macromolecules 18, 2285 (1985); D. Durand, M. Delsanti, and J.M. Luck, Europhys. Lett. 3, 297 (1987).
10. C.P. Lusignan, T.H. Mourey, J.C. Wilson, and R.H. Colby, Phys. Rev. E 52, 6271 (1995); J.E. Martin and J. Wilcoxon, Phys. Rev. Lett. 61, 373 (1988); D. Adolf and J.E. Martin, Macromolecules 23, 3700 (1990); J.E. Martin, J. Wilcoxon, and J. Odinek, Phys. Rev. A 43, 838 (1991); J.E. Martin, D. Adolf, and J. Wilcoxon, Phys. Rev. Lett. 61, 2620 (1988).
11. C.P. Lusignan, T.H. Mourey, J.C. Wilson, and R.H. Colby, Phys. Rev. E 52, 6271 (1995); J.E. Martin and J. Wilcoxon, Phys. Rev. Lett. 61, 373 (1988); D. Adolf and J.E. Martin, Macromolecules 23, 3700 (1990); J.E. Martin, J. Wilcoxon, and J. Odinek, Phys. Rev. A 43, 838 (1991); J.E. Martin, D. Adolf, and J. Wilcoxon, Phys. Rev. Lett. 61, 2620 (1988).
12. C.P. Lusignan, T.H. Mourey, J.C. Wilson, and R.H. Colby, Phys. Rev. E 52, 6271 (1995); J.E. Martin and J. Wilcoxon, Phys. Rev. Lett. 61, 373 (1988); D. Adolf and J.E. Martin, Macromolecules 23, 3700 (1990); J.E. Martin, J. Wilcoxon, and J. Odinek, Phys. Rev. A 43, 838 (1991); J.E. Martin, D. Adolf, and J. Wilcoxon, Phys. Rev. Lett. 61, 2620 (1988).
13. C.P. Lusignan, T.H. Mourey, J.C. Wilson, and R.H. Colby, Phys. Rev. E 52, 6271 (1995); J.E. Martin and J. Wilcoxon, Phys. Rev. Lett. 61, 373 (1988); D. Adolf and J.E. Martin, Macromolecules 23, 3700 (1990); J.E. Martin, J. Wilcoxon, and J. Odinek, Phys. Rev. A 43, 838 (1991); J.E. Martin, D. Adolf, and J. Wilcoxon, Phys. Rev. Lett. 61, 2620 (1988).
14. C.P. Lusignan, T.H. Mourey, J.C. Wilson, and R.H. Colby, Phys. Rev. E 52, 6271 (1995); J.E. Martin and J. Wilcoxon, Phys. Rev. Lett. 61, 373 (1988); D. Adolf and J.E. Martin, Macromolecules 23, 3700 (1990); J.E. Martin, J. Wilcoxon, and J. Odinek, Phys. Rev. A 43, 838 (1991); J.E. Martin, D. Adolf, and J. Wilcoxon, Phys. Rev. Lett. 61, 2620 (1988).
15. n for 12≤ n ≤ 288, including our case n = 36.
16. The choice of a time interval of 100 integration steps between cross-linking events is arbitrary and corresponds to roughly a collision time in the simple liquid at our volume fraction and temperature. Other possible choices for this time interval are zero (instantaneous cross linking) or a time delay corresponding to the relaxation time of a typical cluster for a given value of p. For instantaneous cross linking, one expects standard three-dimensional percolation results since the situation is very similar to the site-bond percolation process [1]. In future work, we expect to investigate the effects of different time delays on the scaling properties at the percolation point.
17. J.C. Gimel, D. Durand, and T. Nicolai, Phys. Rev. B 51, 11 348 (1995).
18. A. Hasmy and R. Jullien, Phys. Rev. E 53, 1789 (1996).
19. M. Plischke, S. Jespersen, and B. Joós (unpublished).
20. A critical volume fraction appears in the model of Gimel, et al. [10], albeit in a rather trivial way: When the volume fraction is increased above 0.31, the system percolates instantaneously (in the thermodynamic limit) and the features associated with cluster-cluster aggregation disappear.
21. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1987), Chap. 2; J.P. Hansen and I.R. MacDonald, Theory of Simple Liquids, 2nd ed. (Academic Press, New York, 1986).
22. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1987), Chap. 2; J.P. Hansen and I.R. MacDonald, Theory of Simple Liquids, 2nd ed. (Academic Press, New York, 1986).
23. c and with the finite-size scaling analysis reported above.
24. For a review, see M. Adam and D. Lairez, in The Physical Properties of Polymeric Gels, edited by J.P. Cohen Addad (Wiley, New York, 1996), p. 87.