Polymer dynamics in solution Universal properties vs. individual behaviour in a unified approach

Abstract

The main factors affecting the dynamics of polymer chains in dilute solution are reviewed. We consider both the collective properties of the chain that follow relatively simple universal laws and the local properties related to the chain stereochemistry. Good-solvent expansion and hydrodynamic interaction are discussed for chains of different architecture, in particular linear and regular star polymers, starting from the usual Rouse–Zimm approach. We also include in the dynamic equations the effect of the local chain stiffness, arising from (i) the equilibrium configurational properties of the chain and (ii) the energy barriers to skeletal rotations hindering the propagation of conformational rearrangements along the chain backbone. The quantities taken into consideration are the intrinsic viscosity and the hydrodynamic radius, compared with the radius of gyration, as well as the complex modulus measured under an oscillating shear deformation, and the dynamic structure factor measured through quasi-elastic scattering. As an example of non-equilibrium behaviour, we discuss a theoretical investigation of the kinetics of chain contraction to a compact globular state following a sudden change in solvent quality.

References

1. J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1970.
2. H. Yamakawa, Modern Theory of Polymer Solutions, Harper & Row, New York, 1971.
3. G. Allegra and F. Ganazzoli, Adv. Chem. Phys., 1989, 75, 265.
4. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Scientific Publications, Oxford, 1986.
5. P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
6. B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics, Wiley-Interscience, New York, 1976.
7. J. S. Higgins and H. C. Benoît, Polymers and Neutron Scattering, Oxford Scientific Publications, Oxford, 1994.
8. G. Allegra, J. S. Higgins, F. Ganazzoli, E. Lucchelli and S. Brückner, Macromolecules, 1984, 17, 1253; F. Ganazzoli, G. Allegra, J. S. Higgins, J. Roots, S. Brückner and E. Lucchelli, Macromolecules, 1985, 18, 435.
9. P. E. Rouse, J. Chem. Phys., 1953, 21, 1272.
10. B. H. Zimm, J. Chem. Phys., 1956, 24, 269.
11. A. Keller and J. A. Odell, Colloid Polym. Sci., 1985, 263, 181.
12. G. Allegra and F. Ganazzoli, J. Chem. Phys., 1981, 74, 1310.
13. J. G. Kirkwood, Rec. Trav. Chim., 1949, 68, 649.
14. J. G. Kirkwood and J. Riseman, J. Chem. Phys., 1948, 16, 565.
15. M. L. Mansfield and L. I. Klushin, J. Phys. Chem., 1992, 96, 3994.
16. S. F. Edwards and K. F. Freed, J. Chem. Phys., 1974, 61, 1189.
17. J. Rotne and S. Prager, J. Chem. Phys., 1969, 50, 4831.
18. Y. Hu, K. Kostov, A. Perico, S. Smithline and K. F. Freed, J. Chem. Phys., 1995, 103, 9090.
19. B. Dünweg and K. Kremer, J. Chem. Phys., 1993, 99, 6983.
20. B. H. Zimm and R. W. Kilb, J. Polym. Sci., 1959, 37, 19.
21. F. Ganazzoli, G. Allegra, E. Colombo and M. De Vitis, Macromolecules, 1995, 28, 1076.
22. G. Allegra and F. Ganazzoli, J. Chem. Phys., 1985, 83, 397.
23. I. M. Lifshitz, A. Y. Grosberg and A. R. Khokhlov, Rev. Mod. Phys., 1978, 50, 683.
24. G. Allegra and F. Ganazzoli, Prog. Polym. Sci., 1991, 16, 463.
25. F. Ganazzoli, Macromolecules, 1992, 25, 7357.
26. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett., 1977, 39, 95.
27. J. Des Cloizeaux, J. Phys. (Paris), 1980, 41, 223.
28. A. Baumgärtner, Z. Phys., 1981, 42, 265.
29. G. Allegra, E. Colombo and F. Ganazzoli, Macromolecules, 1993, 26, 330.
30. A. Forni, F. Ganazzoli and M. Vacatello, Macromolecules, 1996, 29, 2994.
31. M. Daoud and J. P. Cotton, J. Phys., 1982, 43, 531.
32. G. Weill and J. Des Cloizeaux, J. Phys. (Paris), 1979, 40, 99.
33. Polymer Handbook, ed. J. Brandrup and E. H. Immergut, Wiley Interscience, New York, 1989.
34. Y. Tsunashima, Polymer, 1989, 30, 2284.
35. B. H. Zimm, Macromolecules, 1980, 13, 592; 1984, 17, 795.
36. J. J. Freire, A. Rey, M. Bishop and J. H. R. Clarke, Macromolecules, 1991, 24, 6494.
37. P. J. Flory, Statistical Mechanics of Chain Molecules, Wiley, New York, 1969.
38. W. L. Mattice and U. W. Suter, Conformational Theory of Large Molecules, Wiley, New York, 1994.
39. G. Allegra, J. Chem. Phys., 1978, 68, 3600.
40. M. Bixon and R. Zwanzig, J. Chem. Phys., 1978, 68, 1896.
41. A. Perico, F. Ganazzoli and G. Allegra, J. Chem. Phys., 1987, 87, 3677.
42. R. A. Harris and J. E. Hearst, J. Chem. Phys., 1966, 44, 2595.
43. J. E. Hearst, R. A. Harris and E. Beals, J. Chem. Phys., 1966, 45, 3106.
44. G. Allegra, J. Chem. Phys., 1983, 79, 6382.
45. W. Kuhn and H. Kuhn, Helv. Chim. Acta, 1945, 28, 1533; 1946, 29, 7, 609, 830.
46. G. Cerf, J. Polym. Sci., 1957, 23, 125.
47. A. Peterlin, J. Polym. Sci. Part A-2, 1967, 5, 179.
48. W. H. Stockmayer, Ber. Bunsen-Ges. Phys. Chem., 1979, 83, 374.
49. G. Allegra, J. Chem. Phys., 1986, 84, 5881.
50. G. Allegra, J. Chem. Phys., 1974, 61, 4910.
51. Here R_x° and R_x are taken as precise values, whereas in previous Papers^50,52,53 they were regarded as average values.
52. G. Allegra and F. Ganazzoli, Macromolecules, 1981, 14, 1110.
53. M. A. Fontelos, F. Ganazzoli and G. Allegra, Macromolecules, 1989, 22, 4517.
54. H. A. Kramers, Physica, 1940, 7, 284.
55. D. T.-L. Chen and H. Morawetz, Macromolecules, 1976, 9, 463; T.-P. Liao and H. Morawetz, Macromolecules, 1980, 13, 1228.
56. E. Helfand, J. Chem. Phys., 1971, 54, 4651.
57. D. J. Massa, J. L. Schrag and J. D. Ferry, Macromolecules, 1971, 4, 210.
58. F. Ganazzoli, J. Chem. Phys., in the press.
59. T. P. Lodge, J. Chem. Phys., 1993, 97, 1480; T. P. Lodge and J. L. Schrag, Macromolecules, 1984, 17, 352.
60. A. Z. Akcasu, M. Benmouna and C. C. Han, Polymer, 1980, 21, 866.
61. P.-G. de Gennes, Physics, 1967, 3, 37; E. Dubois-Violette and P.-G. de Gennes, Physics, 1967, 3, 181.
62. A. Z. Akcasu and H. Gurol, J. Polym. Sci., Pol. Phys. Ed., 1976, 14, 1.
63. G. Allen, J. S. Higgins, A. Maconnachie and R. E. Ghosh, J. Chem. Soc., Faraday Trans., 1982, 78, 2117.
64. A. Z. Akcasu and J. S. Higgins, J. Polym. Sci., Pol. Phys. Ed., 1977, 15, 1745.
65. G. Allegra and F. Ganazzoli, Gazz. Chim. Ital., 1987, 117, 599.
66. F. Ganazzoli, R. La Ferla and G. Allegra, Macromolecules, 1995, 28, 5285.
67. E. G. Timoshenko, Y. A. Kuznetsov and K. A. Dawson, J. Chem. Phys., 1995, 102, 1816.
68. J. Yu, Z. Wang and B. Chu, Macromolecules, 1992, 25, 1618; B. Chu, Q. Ying and A. Yu. Grosberg, Macromolecules, 1995, 28, 180.
69. P.-G. de Gennes, J. Phys. Lett., 1985, 46, L639.
70. A. Y. Grosberg, S. K. Neachaev and E. I. Shakhnovich, J. Phys. (Paris), 1988, 49, 2095; A. Y. Grosberg and D. V. Kuznetsov, Macromolecules, 1993, 26, 4249.
71. G. Raos and G. Allegra, Macromolecules, 1996, 29, 8565.
72. J. F. Douglas and K. F. Freed, Macromolecules, 1994, 27, 6088.
73. A. Perico, Biopolymers, 1989, 28, 1527; A. Perico, Acc. Chem. Res., 1989, 22, 336.
74. Y. Hu, J. M. MacInnis, B. J. Cherayil, G. R. Fleming, K. F. Freed and A. Perico, J. Chem. Phys., 1990, 93, 822.
75. G. D. Smith and D. Y. Yoon, J. Chem. Phys., 1994, 100, 649; W. Paul, D. Y. Yoon and G. D. Smith, J. Chem. Phys., 1995, 103, 1702.