Lattice cluster theory for pedestrians: The incompressible limit and the miscibility of polyolefin blends

Macromolecules

Volumn 31, Issue 19, 1998, Pages 6681-6690

  Freed, Karl F ^a   Dudowicz, Jacek ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ENTROPY; FREE ENERGY; MIXING; MOLECULAR STRUCTURE; MOLECULAR WEIGHT; MONOMERS; NEUTRON SCATTERING; PHASE DIAGRAMS; POLYBUTENES; REACTION KINETICS; SOLUBILITY;

FLORY-HUGGINS THEORY; LATTICE CLUSTER THEORY; LOWER CRITICAL SOLUTION TEMPERATURE (LCST); NONRANDOM MIXING EFFECTS; POLYISOBUTYLENE;

POLYMER BLENDS;

EID: 0032166680     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma980702x     Document Type: Article

References (57)

1. Flory, P. J. J. Chem. Phys. 1941, 9, 660; Principles of Polymer Chemistry; Cornell Press: Ithaca, NY, 1953.
2. Flory, P. J. J. Chem. Phys. 1941, 9, 660; Principles of Polymer Chemistry; Cornell Press: Ithaca, NY, 1953.
3. Janssen, S.; Schwahn, D.; Mortensen, K.; Springer, T. Macromolecules 1993, 26, 5589. Hammouda, B.; Bauer, B. J. Macromolecules 1995, 28, 4505.
4. Janssen, S.; Schwahn, D.; Mortensen, K.; Springer, T. Macromolecules 1993, 26, 5589. Hammouda, B.; Bauer, B. J. Macromolecules 1995, 28, 4505.
5. Freed, K. F.; Dudowicz, J. Trends Polym. Sci. 1995, 3, 248.
6. Dudowicz, J.; Freed, K. F. Macromolecules 1991, 24, 5076.
7. Nemirovsky, A. M.; Bawendi, M. G.; Freed, K. F. J. Chem. Phys. 1987, 87, 7272.
8. (a) Freed, K. F.; Bawendi, M. G. J. Phys. Chem. 1989, 93, 2194.
9. (b) Dudowicz, J.; Freed, K. F.; Madden, W. G. Macromolecules 1990, 23, 4803.
10. Freed, K. F.; Pesci, A. I. J. Chem. Phys. 1987, 87, 7342.
11. Dudowicz, J.; Freed, M. S.; Freed, K. F. Macromolecules 1991, 24, 5096. Dudowicz, J.; Freed, K. F. Macromolecules 1991, 24, 5112. Freed, K. F.; Dudowicz, J. Theor. Chim. Acta 1992, 82, 357.
12. Dudowicz, J.; Freed, M. S.; Freed, K. F. Macromolecules 1991, 24, 5096. Dudowicz, J.; Freed, K. F. Macromolecules 1991, 24, 5112. Freed, K. F.; Dudowicz, J. Theor. Chim. Acta 1992, 82, 357.
13. Dudowicz, J.; Freed, M. S.; Freed, K. F. Macromolecules 1991, 24, 5096. Dudowicz, J.; Freed, K. F. Macromolecules 1991, 24, 5112. Freed, K. F.; Dudowicz, J. Theor. Chim. Acta 1992, 82, 357.
14. Freed, K. F.; Dudowicz, J. Macromolecules 1996, 29, 625.
15. Dudowicz, J.; Freed, K. F. Macromolecules 1996, 29, 7826.
16. Dudowicz, J.; Freed, K. F. Macromolecules 1993, 26, 213.
17. This behavior has subsequently been observed by: Russell, T. P.; Karis, T. E.; Gallot, Y.; Mayes, A. M. Nature 1994, 368, 729. Karis, T. E.; Russell, T. P.; Gallot, Y.; Mayes, A. M. Macromolecules 1995, 28, 1129.
18. This behavior has subsequently been observed by: Russell, T. P.; Karis, T. E.; Gallot, Y.; Mayes, A. M. Nature 1994, 368, 729. Karis, T. E.; Russell, T. P.; Gallot, Y.; Mayes, A. M. Macromolecules 1995, 28, 1129.
19. Freed, K. F.; Dudowicz, J.; Foreman, K. W. J. Chem. Phys. 1998, 108, 7881.
20. Graessley, W. W.; Krishnamoorti, R.; Reichart, G. C.; Balsara, N. P.; Fetters, L. J.; Lohse, D. J. Macromolecules 1995, 28, 1260.
21. Kumar, S. K. Macromolecules 1994, 27, 260. Kumar, S. K.; Veytsman, B. A.; Maranas, J. K.; Crist, B. Phys. Rev. Lett. 1997, 79, 2265.
22. Kumar, S. K. Macromolecules 1994, 27, 260. Kumar, S. K.; Veytsman, B. A.; Maranas, J. K.; Crist, B. Phys. Rev. Lett. 1997, 79, 2265.
23. Joanny, J.-F.; Benoit, H. Macromolecules 1997, 30, 3704.
24. Higgins, J.; Benoit, H. Polymers and Neutron Scattering; Clarendon Press: Oxford, England 1994; Taylor, J. K.; Debenedetti, P. G.; Graessley, W. W.; Kumar, S. K. Macromolecules 1996, 29, 764.
25. Higgins, J.; Benoit, H. Polymers and Neutron Scattering; Clarendon Press: Oxford, England 1994; Taylor, J. K.; Debenedetti, P. G.; Graessley, W. W.; Kumar, S. K. Macromolecules 1996, 29, 764.
26. We note in this regard that all atomistic off-lattice computations of polymer properties with Monte Carlo, molecular dynamics, and integral equation methods, of necessity, describe these systems as compressible, i.e., with densities lower than those corresponding to close packing.
27. Tang, H.; Freed, K. F. Macromolecules 1991, 24, 958. Hammouda, B. J. Non-Cryst. Solids 1994, 172-174, 928; Bidkar, U. R.; Sanchez, I. C. Macromolecules 1995, 28, 3963.
28. Tang, H.; Freed, K. F. Macromolecules 1991, 24, 958. Hammouda, B. J. Non-Cryst. Solids 1994, 172-174, 928; Bidkar, U. R.; Sanchez, I. C. Macromolecules 1995, 28, 3963.
29. Tang, H.; Freed, K. F. Macromolecules 1991, 24, 958. Hammouda, B. J. Non-Cryst. Solids 1994, 172-174, 928; Bidkar, U. R.; Sanchez, I. C. Macromolecules 1995, 28, 3963.
30. Dudowicz, J.; Freed, K. F., Macromolecules 1990, 23, 1519.
31. Sanchez, I. C.; Lacomb, R. H. Macromolecules 1978, 11, 1145.
32. Flory, P. J.; Orwoll, R. A.; Vrij, A. J. Am. Chem. Soc. 1964, 86, 3507.
33. Dee, G. T.; Walsh, D. J. Macromolecules 1988, 21, 811, Lipson, J. E. G.; Andrews, S. S. J. Chem. Phys. 1992, 96, 1426.
34. Dee, G. T.; Walsh, D. J. Macromolecules 1988, 21, 811, Lipson, J. E. G.; Andrews, S. S. J. Chem. Phys. 1992, 96, 1426.
35. Bates, F. S.; Fredrickson, G. H., Macromolecules 1994, 27, 1065. Fredrickson, G. H.; Liu, A. J.; Bates, F. S., Macromolecules 1994, 27, 2503.
36. Bates, F. S.; Fredrickson, G. H., Macromolecules 1994, 27, 1065. Fredrickson, G. H.; Liu, A. J.; Bates, F. S., Macromolecules 1994, 27, 2503.
37. (a) Foreman, K. W.; Freed, K. F. Macromolecules 1997, 30, 7295.
38. (b) Foreman, K. W.; Freed, K. F. Adv. Chem. Phys. 1998, 103, 335.
39. Madden, W. G. J. Chem. Phys. 1990, 92, 2055.
40. Nemirovsky, A. M.; Dudowicz, J.; Freed, K. F. Phys. Rev. A 1992, 45, 7111.
41. We assume here that there no penta-or higher functional groups are present.
42. (a) Freed, K. F.; Dudowicz, J. Macromolecules 1996, 29, 625.
43. (b) Dudowicz, J.; Freed, K. F. Macromolecules 1997, 30, 5506.
44. The simplifications arise when all subchains in the side groups have at least a pair of sequential bonds. See appendix in ref 27.
45. From Table 3 of ref 6b, using the relation in the Appendix of ref 27.
46. Sariban, A.; Binder, K. J. Chem. Phys. 1997, 86, 5859.
47. Foreman, K. W.; Freed, K. F.; Ngola, I. M. J. Chem. Phys. 1997, 107, 4688.
48. Guggenheim, E. A. Proc. R. Soc. London, A 1944, 183, 203, 213; Mixtures; Oxford University Press: Oxford, England 1952.
49. Guggenheim, E. A. Proc. R. Soc. London, A 1944, 183, 203, 213; Mixtures; Oxford University Press: Oxford, England 1952.
50. Foreman, K. W.; Freed, K. F., J. Chem. Phys. 1995, 102, 4663.
51. Krishnamoorti, R.; Graessley, W. W.; Fetters, L. J.; Garner, R. T.; Lohse, D. J. Macromolecules 1995, 28, 1252.
52. Singh, C.; Schweizer, K. S. Macromolecules 1995, 28, 8692; J. Chem. Phys. 1995, 103, 5814; 1997, 30, 1490.
53. Singh, C.; Schweizer, K. S. Macromolecules 1995, 28, 8692; J. Chem. Phys. 1995, 103, 5814; 1997, 30, 1490.
54. Singh, C.; Schweizer, K. S. Macromolecules 1995, 28, 8692; J. Chem. Phys. 1995, 103, 5814; 1997, 30, 1490.
55. Dudowicz, J.; Freed, K. F. Macromolecules, submitted for publication.
56. This point is evident from Table 2 of ref 29a and has also been noted by Schweizer, K. S.; Curro, J. C. Adv. Polym. Sci. 1994, 116, 319.
57. Ruzette, A.-V.; Mayes, A. M.; Banerjee, P.; Russell, T. P.; Pollard, M.; Jerome, R. Bull. Am. Phys. Soc. 1998, 43, 450.