Large-Scale Molecular Systems pp 453-469 | Cite as

# The Coupling Scheme for Relaxations in Complex Correlated Systems

## Abstract

In this NATO Advanced Study Institute many different problems of large-scale molecular systems were discussed. The range of topics covered in this ASI is immensely broad. In view of the very nature of this ASI, what I addressed in lecture and elaborated further here is only a subset of all the large-scale molecular systems discussed in the Proceedings. I am primarily concerned with irreversible processes (relaxation) in correlated systems in which some identical constituents, molecules, ions, or their analogues, are interacting in either the quantum or classical mechanical sense, whichever is appropriate. Additional randomness caused by possible factors such as the presence of not identical constituents and fluctuations of local environments makes the problem even more complex. Correlated systems with additional complications such as distribution and randomness will be referred to as complex correlated systems. I am interested in the dynamics of irreversible processes in these systems which require solutions to these many body problems that give the time developments of either macroscopic (e.g. stress, strain, and electric polarization) or microscopic (e.g. orientation of tagged molecules, center-of-mass vector of a probe polymer chain in a polymer matrix) dynamical variables. When interactions between the constituents are strong, the system becomes highly correlated and solution is extremely difficult. In this paper I shall focus on three examples of such highly correlated systems. These are: (1) a glass forming viscous liquid that is made up of molecular units that are densely packed together and hence interacting strongly with each other (e.g. (O-terphenyl, 1,3,5 trinaphthalbenzene, and toulouene); (2) a vitreous ionic conductor (e.g. the alkali oxide trisilicate and triborate glasses, Na_{2}O-3SiO_{2} and Li_{2}O-3B_{2}O_{3} respectively and also defect crystalline ionic conductors (e.g. Na β-alumina) that contain a propensity of interacting ions; and (3) polymer melts of long linear or star branched macromolecules that are fully entangled with each other and noncrossability of these densely packed macromolecules implies strong interaction.

## Keywords

Relaxation Function Coupling Scheme Continuous Time Random Walk Entangle Polymer NATO Advance Study Institute## Preview

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## References

- 1.
- 2.A. K. Rajagopal and K. L. Ngai in Relaxations in Complex Systems. (Eds. K. L. Ngai and G. B. Wright) National Technical Information Service, Springfield, V (1984) 275.Google Scholar
- 3.A.K. Rajagopal, R.W. Rendell, K.L. Ngai, and S. Teitler, Ann. N.Y. Acad. Sci. 484. (1986) 321.CrossRefGoogle Scholar
- 4.A.K. Rajagopal, K.L. Ngai, R.W. Rendell and S. Teitler, Physica 149, (1988) 358.CrossRefGoogle Scholar
- 5.K.L. Ngai, R.W. Rendell, A.K. Rajagopal, and S. Teitler, N.Y. Acad. Sci. 484, (1986) 150.CrossRefGoogle Scholar
- 6.A.K. Rajagopal, S. Teitler, and K.L. Ngai, J. Phys. C.: Solid State Phys. 17, (1984) 6611.Google Scholar
- 7.K.L. Ngai, A.K. Rajagopal, and S. Teitler, J. Chem. Phys. 88, (1988) 5086.Google Scholar
- 8.A.K. Rajagopal, K.L. Ngai and S. Teitler, Nucl. Phys. (B) 5A, (1988) 97 and also K.L. Ngai, A.K. Rajagopal and S. Teitler, Ibid, 103.Google Scholar
- 9.A. Blumen, J. Klafter and G. Zumofen, in Optical Spectroscopy of Glasses (I. Zschakke ed.) D. Reidel Publ. Co. (1986), p. 199.CrossRefGoogle Scholar
- 10.See lecture notes by A. Blumen and J. Klafter in this Proceeding.Google Scholar
- 11.A. Kolinski, J. Skolnick and R. Yaris, J. Chem. Phys. 86, 1567, (1987); ibid 7164.CrossRefGoogle Scholar
- 12.T. Pakula and S. Geyler, Macromolecules 20, 2909 (1987).CrossRefGoogle Scholar
- 13.K. Kremer and G. Grest, J. Chem. Phys.(1990).Google Scholar
- 14.W. Dieterich, J. Peterson, A. Bunde and H.E. Roman, to appear in Solid State Ionics (1990).Google Scholar
- 15.A. Bunde, in Proc. 3rd Bar-Ilan Conference on Frontiers in Condensed Matter Physics, Physica A (1990).Google Scholar
- 16.E.W. Montroll and M.F. Shlesinger, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).CrossRefGoogle Scholar
- 17.J.T. Bendler and M.F. Shlesinger, Macromolecules.Google Scholar
- 18.E.W. Montroll and G. Weiss, J. Math. Phys. 6, 167 (1965).Google Scholar
- 19.See J.D. Ferry, “Viscoelastic Properties of Polymers”, John Wiley & Sons, NY (1980).Google Scholar
- 20.C. A. Angell in “Relaxations in Complex Systems”, (Eds. K.L. Ngai and G.B. Wright) National Technical Information Service, Port Royal Road, Springfield, VA 1984) 3.Google Scholar
- 21.K.L. Ngai, J. Non-Cryst. Solids 95, & 96, 969 (1987); K.L. Ngai, R.W. Rendell and D.J. Plazek, J. Chem. Phys. (in press).CrossRefGoogle Scholar
- 22.K. L. Ngai, R.W. Rendell and H. Jain, Phys. Rev. B 30, 2133 (1984).CrossRefGoogle Scholar
- 23.For a review see M. V. Berry, Proc. R. Soc. Lond. A413, 183 (1987).Google Scholar
- 24.N. G. van Kampen in “Fundamental Problems in Statistical Mechanics” (Ed. E.G.D. Cohen) North-Holland (1962) 173.Google Scholar
- 25.Y. Nambu, “Quarks”, World Scientific 1985.Google Scholar
- K.L. Ngai and J. Skolnick to be published.Google Scholar
- 27.P. G. DeGennes, “Scaling Concepts in Polymer Physics” Cornell University, Ithaca, (1979).Google Scholar
- 28.K.L. Ngai and F.S. Liu, Phys. Rev. B24, 1049 (1981).Google Scholar
- 29.G.B. McKenna, K.L. Ngai and D.J. Plazek Polymer 26 1651 (1985).CrossRefGoogle Scholar
- 30.S. Chandrasekhar, Nature 344, 285 (1990).CrossRefGoogle Scholar