Thermoreversible gelation in solutions of associating polymers. 2. Linear dynamics

Macromolecules

Volumn 31, Issue 4, 1998, Pages 1386-1397

  Rubinstein, Michael ^a   Semenov, Alexander N ^b,c  

^a University of North Carolina at Chapel Hill   (United States)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c A N NESMEYANOV INSTITUTE OF ORGANOELEMENT COMPOUNDS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVATION ENERGY; BINDING ENERGY; DISSOCIATION; ELASTIC MODULI; GELATION; PERCOLATION (FLUIDS); VISCOELASTICITY;

ASSOCIATING POLYMERS; ROUSE-ZIMM REGIME; THERMOREVERSIBLE GELATION;

INTERPENETRATING POLYMER NETWORKS;

EID: 0031998985     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma970617+     Document Type: Article

References (32)

1. Part 1. Semenov, A. N.; Rubinstein, M. Macromolecules 1998, 31, 1373-1385.
2. The effects of entanglements will be analyzed in a future publication.
3. 26-28
4. De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell Univ. Press: Ithaca, NY, 1985.
5. 4,29). The critical regime is considered in section 4.3.
6. Flory, P. J. Principles of Polymer Chemistry; Cornell Univ. Press: Ithaca, NY, 1971.
7. Rubinstein, M.; Colby, R. H. Macromolecules 1990, 23, 2753.
8. Actually we should consider here slightly different process: two smaller clusters combining into a chosen M-cluster. However the rates of the two processes are of the same order of magnitude.
9. Stauffer, D. Introduction to Percolation Theory; Taylor and Francis: London, 1985.
10. Hermann, H. Phys. Rep. 1986, 136, 153.
11. Coniglio, A, Phys. Rev. Lett. 1981, 46, 250.
12. Gelation and Associating Polymers. Cates, M. E. NATO ASI Ser. 1989, 211, 319. Cates, M. E.; McLeish, T. C. B.; Rubinstein, M. J. Phys. C 1990, 2, 749.
13. Gelation and Associating Polymers. Cates, M. E. NATO ASI Ser. 1989, 211, 319. Cates, M. E.; McLeish, T. C. B.; Rubinstein, M. J. Phys. C 1990, 2, 749.
14. This statement is true for treelike clusters which are formed in the classical gelation regime considered here. In the critical (percolation) regime, i.e., in a close vicinity to the gel point, the cluster structure is more complicated. In particular, clusters might include closed cycles (loops) of connected chains. In this regime the fraction of red bonds is lower than in the classical gelation regime. The percolation regime is considered in section 4.3. We are grateful to the reviewer who commented on this point.
15. Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Claredon Press: Oxford, England, 1986.
16. The scaling law, eq 3.13, is valid up to logarithmic corrections which are entirely neglected here and below.
17. Tobolsky, A. V. Properties and Structure of Polymers; Wiley: New York, 1960.
18. Green, M. S.; Tobolsky, A. V. J. Chem. Phys. 1946, 14, 80.
19. 1 = 1 - p*, where p* is the fraction of all closed stickers defined by eq 5.1. Although this method leads to the same result, eq 4.2, it is less preferable since applicability of eq 5.1 in the regime where p* is dominated by local pairs is not obvious.
20. Hence three- or four-sticker aggregates are not considered here; i.e., these states are assumed to be unfavorable.
21. 1/2. This condition is assumed below.
22. 15,31
23. We assume Rouse dynamics of clusters also in the percolation regime.
24. perc, which is always true if ∈ is large enough; see eqs 4.23 and 4.26.
25. Des Cloizeaux, J.; Jannink, G. Polymers in Solution; Clarendon Bress: Oxford, England, 1990; Section 13.1.6.
26. Des Cloizeaux, J. J. Phys. Fr. 1980, 41, 223.
27. Schaefer, L.; Kappeler, Ch. J. Phys. Fr. 1985, 46, 1853. Kosmas, M. J. Phys. Lett. 1984, 45, L889. Broseta, D.; Leibler L.; Joanny, J. F. Macromolecules 1987, 20, 1935.
28. Schaefer, L.; Kappeler, Ch. J. Phys. Fr. 1985, 46, 1853. Kosmas, M. J. Phys. Lett. 1984, 45, L889. Broseta, D.; Leibler L.; Joanny, J. F. Macromolecules 1987, 20, 1935.
29. Schaefer, L.; Kappeler, Ch. J. Phys. Fr. 1985, 46, 1853. Kosmas, M. J. Phys. Lett. 1984, 45, L889. Broseta, D.; Leibler L.; Joanny, J. F. Macromolecules 1987, 20, 1935.
30. Daoud, M. J. Phys. A 1988, 21, L237.
31. O'Shaughnessy, B.; Yu, J. Phys. Rev. Lett. 1995, 74, 4329.
32. Alexander, S.; Pincus, P. Phys. Rev. B 1978, 18, 2011.