Structural aspects of the glass transition in three-dimensional polymer melts

Abstract

We discuss structural aspects of three-dimensional polymer melts undergoing glass transition. Our Monte Carlo study is based on the well known bond-fluctuation model including van der Waals interaction and bond-length potential. Results are presented for different cooling rates and a wide range of temperatures. The glass-transition temperature, T_g, was determined by the significant change in various static and dynamic quantities, such as the static structure factor of individual polymer chains and the incoherent scattering function. Below T_g, the latter is characterized by division into a Debye-like short-time regime and two separate time regimes with stretched-exponential behaviour. Further investigation by means of block density distribution analysis revealed an inhomogeneous, non-Gaussian distribution of mass below T_g. A direct proof for the existence of cavities and clusters of effective monomers has been given by visualization via a two-dimensional projection technique.

References

1. A. Kolinski, J. Skolnick and R. Yaris, J. Chem. Phys., 1986, 84, 1922; 1987, 86, 1567; 1987, 86, 7164; 1987, 86, 7174; J. Skolnick, R. Yaris and A. Kolinski, J. Chem. Phys., 1988, 88, 1407.
2. B. Frick, D. Richter, W. Petry and U. Buchenau, Z. Phys. B, 1988, 70, 73; B. Frick, D. Richter and C. L. Ritter, Europhys. Lett., 1989, 9, 557; D. Richter, R. Zorn, B. Farago, B. Frick and L. J. Fetters, Phys. Rev. Lett., 1992, 68, 71; J. Colmenero, A. Algería, A. Arbe and B. Frick, Phys. Rev. Lett., 1992, 69, 478.
3. C. A. Angell, J. Non-Cryst. Solids, 1991, 131–133, 13.
4. D. J. Plazek, E. Schlosser, A. Schönhals and K. L. Ngai, J. Chem. Phys., 1993, 98, 6488.
5. K. Zemke, K. Schmidt-Rohr and H. W. Spiess, Acta Polym., 1994, 45, 148.
6. I. Bahar, B. Erman, G. Fytas and W. Steffen, Macromolecules, 1994, 27, 5200.
7. C. Dasgupta, A. V. Indrani, S. Ramaswamy and M. K. Phani, Europhys. Lett., 1991, 15, 307.
8. P. Harrowell, Phys. Rev. E, 1993, 48, 4359.
9. H. Sillescu, Acta Polym., 1994, 45, 2.
10. T. G. F. Schoon, Br. Polym. J., 1970, 2, 89.
11. J. J. Klement and P. H. Geil, J. Macromol. Sci. B, 1971, 5, 535; G. S. Y. Yeh, J. Macromol. Sci. B, 1972, 6, 451, 465; P. H. Geil, J. Macromol. Sci. B, 1976, 12, 173; R. Lam and P. H. Geil, J. Macromol. Sci. B, 1981, 20, 37; R. Lee, H. Miyaji and P. H. Geil, J. Macromol. Sci. B, 1983, 22, 489.
12. J. H. Wendorff, Polymer, 1982, 23, 543.
13. M. Wittkop, Th. Hölzl, S. Kreitmeier and D. Göritz, J. NonCryst. Solids, 1996, 201, 199.
14. Th. Hölzl, M. Wittkop, S. Kreitmeier and D. Göritz, in Overview of Research Projects on the Cray Y-MP at the Leibniz-Rechenzentrum München, ed. Ch. Schaller and M. Brehm, Leibniz-Rechenzentrum, München, 1996, p. 167.
15. M. Wittkop, S. Kreitmeier and D. Göritz, Comput. Polym. Sci., 1995, 5, 187; Phys. Rev. E, 1996, 53, 838; J. Chem. Soc., Faraday Trans., 1996, 92, 1375; Comput. Theoret. Polym. Sci., 1996, 6, 41.
16. M. Bishop, D. Ceperley, H. L. Frisch and M. H. Kalos, J. Chem. Phys., 1982, 76, 1557; M. Bishop, M. H. Kalos and H. L. Frisch, J. Chem. Phys., 1983, 79, 3500.
17. K. Kremer, Macromolecules, 1983, 16, 1632; K. Kremer and G. S. Grest, J. Chem. Phys., 1990, 92, 5057.
18. A. Baumgärtner, Annu. Rev. Phys. Chem., 1984, 35, 419.
19. D. N. Theodorou and U. W. Suter, Macromolecules, 1985, 18, 1467; 1986, 19, 379; A. S. Argon, P. H. Mott and U. W. Suter, Phys. Stat. Sol. (b), 1992, 172, 193; P. H. Mott, A. S. Argon and U. W. Suter, Philos. Mag. A, 1993, 67, 931; Philos. Mag. A, 1993, 68, 537.
20. D. Rigby and R.-J. Roe, J. Chem. Phys., 1987, 87, 7285; 1988, 89, 5280; Macromolecules, 1989, 22, 2259; H. Takeuchi and R.-J. Roe, J. Chem. Phys., 1991, 94, 7446, 7458; R.-J. Roe, J. Chem. Phys., 1994, 100, 1610.
21. D. Brown and J. H. R. Clarke, Macromolecules, 1991, 24, 2075; D. Brown, J. H. R. Clarke, M. Okuda and T. Yamazaki, J. Chem. Phys., 1994, 100, 1684, 6011.
22. W. Paul, K. Binder, K. Kremer and D. W. Heermann, Macromolecules, 1991, 24, 6332.
23. H.-P. Wittmann, K. Kremer and K. Binder, J. Chem. Phys., 1992, 96, 6291.
24. J. Baschnagel, K. Binder and H.-P. Wittmann, J. Phys.: Condens. Matter, 1993, 5, 1597; P. Ray, J. Baschnagel and K. Binder, J. Phys.: Condens. Matter, 1993, 5, 5731; J. Baschnagel and K. Binder, Physica A, 1994, 204, 47; B. Lobe, J. Baschnagel and K. Binder, Macromolecules, 1994, 27, 3658; J. Baschnagel and B. Lobe, Macromol. Symp., 1994, 81, 63; J. Baschnagel and R. Dickman, J. Chem. Phys., 1994, 101, 3326.
25. J. Baschnagel, Phys. Rev. B, 1994, 49, 135.
26. J. Baschnagel and K. Binder, Macromol. Theory Simul., 1996, 5, 417.
27. H. L. Trautenberg, J.-U. Sommer and D. Göritz, J. Chem. Soc., Faraday Trans., 1995, 91, 2649.
28. W. Paul, K. Binder, D. W. Heermann and K. Kremer, J. Phys. II, 1991, 1, 37; J. Chem. Phys., 1991, 95, 7726.
29. H.-P. Deutsch and R. Dickman, J. Chem. Phys., 1990, 93, 8983; R. Dickman, Comput. Polym. Sci., 1991, 1, 206; A. Yethiraj and R. Dickman, J. Chem. Phys., 1992, 97, 4468.
30. H. L. Trautenberg, M. Wittkop, Th. Hölzl and D. Göritz, Phys. Rev. Lett., 1996, 76, 4448.
31. R. Zallen, The Physics of Amorphous Solids, Wiley, New York, 1983.
32. H. P. Deutsch and K. Binder, J. Chem. Phys., 1991, 94, 2294.
33. H. L. Trautenberg, Th. Hölzl and D. Göritz, Comput. Theoret. Polym. Sci., 1996, 6, 135.
34. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys., 1953, 21, 1087.
35. S. Kreitmeier, M. Wittkop, H. L. Trautenberg, Th. Hölzl and D. Göritz, J. Comput. Phys., in the press.
36. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, New York, 1986.
37. H. R. Wendt and F. F. Abraham, Phys. Rev. Lett., 1978, 41, 1244.
38. N. Pistoor and K. Kremer, Prog. Colloid Polym. Sci., 1990, 81, 184.
39. J. Ullo and S. Yip, Phys. Rev. A, 1989, 39, 5877.
40. S. Yashonath, K. J. Rao and C. N. R. Rao, Phys. Rev. B, 1985, 31, 3196.
41. R. H. Boyd and P. V. K. Pant, Macromolecules, 1991, 24, 4073; 1991, 24, 4078.
42. G. F. Signorini, J.-L. Barrat and M. L. Klein, J. Chem. Phys., 1990, 92, 1294.
43. P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York, 1969.
44. G. Beaucage, J. Appl. Cryst., 1996, 29, 134.
45. W. Götze and L. Sjögren, Rep. Prog. Phys., 1992, 55, 241.
46. M. Fuchs, W. Götze, S. Hildebrand and A. Latz, J. Phys.: Condens. Matter, 1992, 4, 7709.
47. W. Paul and J. Baschnagel, in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, ed. K. Binder, Oxford University Press, New York, 1995.
48. G. Williams and D. C. Watts, Trans. Faraday Soc., 1970, 66, 80.
49. J. E. Shore and R. Zwanzig, J. Chem. Phys., 1975, 63, 5445.
50. R. J. Glauber, J. Math. Phys., 1963, 4, 294.
51. C. K. Hall and E. Helfand, J. Chem. Phys., 1982, 77, 3275.
52. K. Kaski, K. Binder and J. D. Gunton, Phys. Rev. B, 1984, 29, 3996.
53. N. G. van Kempen, Phys. Rev. A, 1964, 135, 362.
54. L. P. Kadanoff, Ann. Phys. (N.Y.), 1966, 2, 263.
55. M. Rovere, D. W. Heermann and K. Binder, Europhys. Lett., 1988, 6, 585.
56. H. J. Hölle, R. G. Kirste, B. R. Lehnen and M. Steinbach, Prog. Colloid Polym. Sci., 1975, 58, 30.
57. T. Hölzl, C. Mesner, M. Wittkop and D. Göritz, in preparation.
58. M. Wittkop, S. Kreitmeier and D. Göritz, J. Chem. Phys., 1996, 104, 3373.