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Polymer Electrolytes: Hopping, Domain Structures and Frequency-Dependent Conductivity

Published online by Cambridge University Press:  28 February 2011

Mark A. Ratner
Affiliation:
Department of Chemistry and Materials Research Center, Northwestern University, Evanston, Illinois 60208
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Abstract

The dynamic bond percolation model was developed to deal with dynamic disorder, treating ion mobility by a percolation model in which the assignment of any site-to-site jump as allowed or forbidden changes on a timescale related to the local reorganizational dynamics of the polymer segments (the renewal time). Here we discuss the special cases of highfrequency spectra and partially crystalline electrolytes. At high frequencies, the present hopping model yields unphysical behavior (frequencyindependent response); we trace this back to the incorrect treatment of short-time dynamics, and show how it can be corrected. For partially crystalline materials, we show that a rollover feature in the spectrum, in the microwave range, can be expected when ions are trapped in isolated regions of high conductivity, such as amorphous pockets in largely crystalline PEO.

Type
Research Article
Copyright
Copyright © Materials Research Society 1991

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References

1. MacCallum, J. R. and Vincent, C. A., eds., Polymer Electrolyte Reviews, vols. I, II (London, Elsevier).Google Scholar
2. Tonge, J. S. and Shriver, D. F., in Lay, J., ed., Polymers for Electronic Applications (CRC, Boca Raton, 1989).Google Scholar
3. Ratner, M. A. and Shriver, D. F., Chem., Revs. 80, 109 (1988).Google Scholar
4. Br. Polymer, J. 20, #13 (1988); G. A. Nazri, R. A. Huggins and D. F. Shriver, eds., MRS vol. 135 (Mat. Res. Soc., Pittsburgh, 1989).Google Scholar
5. Scrosati, B., ed., Second International Symposium on Polymer Electrolytes (Elsevier, London, 1990).Google Scholar
6. Armand, M. B., Faraday Disc. Chem. Soc., 88, 65 (1989).Google Scholar
7. Angell, C. A., Solid State lonics, 9/10, 3 (1983); 18/19, 72 (1986).Google Scholar
8. Torell, L. M. and Angell, C. A., Br. Polymer J., 20, 173 (1988).Google Scholar
9. Killis, A., LeNest, J. F., Cheradame, H. and Gandini, A., Makromol. Chem., 183, 2835 (1982).Google Scholar
10. Watanabe, M. and Ogata, N. in ref. (1), p. 39.Google Scholar
11. Williams, M. L., Landel, R. F. and Ferry, J. D., J. Am. Chem. Soc., 77, 3701 (1955).Google Scholar
12. Ratner, M. A., in ref. 1, p. 173.Google Scholar
13. Ratner, M. A. and Nitzan, A., Faraday Disc. Chem. Soc., 88, 19 (1989).Google Scholar
14. Cheradame, H., in IUPAC Macromolecules, ed. Benoit, H. and Rempp, P. (Pergamon, New York, 1982).Google Scholar
15. Druger, S. D., Nitzan, A. and Ratner, M. A., J. Chem. Phys., 79, 3133 (1983).Google Scholar
16. Druger, S. D., Ratner, M. A. and Nitzan, A., Phys. Rev., B31, 3939 (1985); Solid State lonics, 18/19, 106 (1986).Google Scholar
17. Druger, S. D., in Transport and Relaxation Processes in Random Materials, ed. Klafter, J., Rubin, R. J. and Shlesinger, M. F. (World Scientific, Singapore, 1986).Google Scholar
18. Ratner, M. A. and Nitzan, A., Solid State lonics, 28–30, 3 (1988); R. Granek, A. Nitzan, S. D. Druger and Ratner, M. A., Solid State Ionics, 28-30, 120 (1988).Google Scholar
19. Nitzan, A., Druger, S. D. and Ratner, M. A., Philos. Mag., B56, 853 (1987).Google Scholar
20. Druger, S. D. and Ratner, M. A., Phys. Rev. B, 38, 12589 (1988); Chem. Phys. Lett., 151, 434 (1988). R. Kubo, J. Phys. Soc. Jap. 12, 570 (1957).Google Scholar
21. Ansari, S. M., Brodwin, M., Stainer, M., Druger, S. D., Ratner, M. A. and Shriver, D. F., Solid State lonics, 17, 101 (1985).Google Scholar
22. Harris, C., Nitzan, A., Ratner, M. A. and Shriver, D. F., Solid State Ionics, 18/19, 151.Google Scholar
23. Granek, R., Nitzan, A. and Ratner, M. A., J. Non-Cryst. Sol, in press.Google Scholar
24. Hilfer, R. and Orbach, R., Chem. Phys., 128, 275 (1988).Google Scholar
25. Nitzan, A., Druger, S. D. and Ratner, M. A., Solid State lonics, 9/10, 1115 (1983).Google Scholar
26. Ratner, M. A. and Druger, S. D., Mol. Cryst. Liq. Cryst., 190, 171 (1990)Google Scholar
27. cf. e.g., Stauffer, D., Introduction to Percolation Theory (Taylor and Francis, London, 1975).Google Scholar
28. e.g. Zallen, R., The Physics of Amorphous Solids (Wiley, New York, 1983).Google Scholar
29. Kakihana, M., Sandahl, J., S. Schantz and Torell, L. M., in ref. 5, p.1.Google Scholar
30. e.g. Ferry, J. D., Viscoelastic Properties of Polymers (Wiley, New York, 1961).Google Scholar
31. Lee, Y. T. and Crist, B., J. Appl. Phys. 60, 2603 (1986); P. R. Sfrensen and T. Jacobsen, Polym. Bull., 9, 47 (1983); L. C. Hardy, Ph.D. Thesis, Northwestern University, 1986.Google Scholar
32. Minier, M., Berthier, C. and Gorecki, W., J. Phys. (Paris) 45, 739 (1984).CrossRefGoogle Scholar
33. Druger, S. D., Ratner, M. A., Nitzan, A. and Skinner, D. W., J. Chem. Phys., 92, 4491 (1990).Google Scholar
34. Scher, H. and Lax, M., Phys. Rev. B, 7, 4491 (1973); M. Lax, Phys. Rev., 109, 1921 (1958).Google Scholar
35. Harrison, A. K. and Zwanzig, R., Phys. Rev., A32, 1072 (1985).Google Scholar