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Fractal Structure and Fractal Time in Silica Sol-Gels

Published online by Cambridge University Press:  28 February 2011

James E. Martin  and
Jess Wilcoxon
James E. Martin
Affiliation:
Sandia National Laboratories,Albuquerque,NM 87185
Jess Wilcoxon
Affiliation:
Sandia National Laboratories,Albuquerque,NM 87185
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Abstract

Near the gel point, light scattering studies of silica sol-gels reveal fractal clusters whose size diverges as a power law, in accord with the predictions of percolation theory. More surprising is the appearance of a fractal time description of the dynamics of these clusters. This novel dynamics has recently been revealed by quasielastic light scattering from the density fluctuations that occur at the sol-gel transition. Since the relaxation of fluctuations in these branched polymer systems is self-similar, decay processes occur on all time scales (fractal time), and average decay times diverge. An interpretation of this observation will be presented that relies on a length-scale-dependent viscosity and the geometrical self-similarity of the sol-gel transition. The scattering theory is extended to the calculation of time- and frequency-dependent viscoelastic properties, as well as mechanical properties such as the shear modulus, steady state creep compliance, and viscosity. The viscoelastic predictions are found to be in good agreement with experimental data.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 180: Symposium A – Better Ceramics Through Chemistry IV , 1990 , 199
Copyright
Copyright © Materials Research Society 1990

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References

REFERENCES

1. Stauffer, D., Introduction to Percolation Theory (Taylor & Francis, London, 1985).Google Scholar
2. Daoud, M. and Martin, J. E., in The Fractal Approach to the Chemistry of Disordered Systems: Polymers, Colloids, Surfaces, edited by Avnir, D..Google Scholar
3. Stauffer, D., Coniglio, A. and Adam, M., in Advances in Polymer Science 44 (Springer-Verlag, Berlin, 1982).Google Scholar
4. de Gennes, P. G., Scaling Concepts in Polymer Physics, (Cornell, New York, 1979).Google Scholar
5. Martin, J. E. and Wilcoxon, J. P., Phys. Rev A 39, 252 (1989).Google Scholar
6. Martin, J. E. and Wilcoxon, J. P., Phys. Rev. Lett. 61, 373 (1988).Google Scholar
7. Martin, J. E. and Ackerson, B. J., Phys. Rev. A 31, 1180 (1985).Google Scholar
8. Martin, J. E., J. Appl. Cryst. 19, 25 (1986);Google Scholar
8a also Martin, J. E. and Hurd, A. J., J. Appl. Cryst. 20, 61 (1986).Google Scholar
9. Schaefer, D. W. and Keefer, K. D., Phys. Rev. Lett. 53, 1383 (1984).Google Scholar
10. Isaacson, J. and Lubensky, T. C., J. Phys. (Paris) 41, L469 (1980).Google Scholar
11. de Gennes, P. -G., Acad., C. R. Sci. Paris 291, 17 (1980).Google Scholar
12. Martin, J. E., in Time Dependent Effects in Disordered Materials, edited by Pynn, R. and Riste, Tormod, NATO ASI Series, Physics Vol. 167 (Plenum, New York, 1987).Google Scholar
13. Martin, J. E. and Keefer, K. D., Phys. Rev. A 34, 4988 (1986).Google Scholar
14. Martin, J. E., Wilcoxon, J. P., and Odinek, J., to appear in Phys. Rev. A.Google Scholar
15. Martin, J. E., Sullivan, J. and Wilcoxon, J. P., unpublished results.Google Scholar
16. Martin, J. E., Wilcoxon, J. P. and Adolf, D., Phys. Rev. A 36 1803 (1987).Google Scholar
17. Daoud, M., Family, F. and Jannink, G., J. Physique Lett. 45, 199 (1984).Google Scholar
18. Daoud, M. and Leibler, L., Macromol. 21, 1497 (1988).Google Scholar
19. Martin, J. E. and Odinek, J., preprint.Google Scholar
20. Assink, R. A. and Kay, B. D., J. Non-Cryst. Solids 107, 35 (1988).Google Scholar
21. Kay, B. D. and Assink, R. A., J. Non-Cryst. Solids 104, 112 (1988).Google Scholar
22. Martin, J. E., J. Phys. A: Math. Gen. 18, L207 (1985).Google Scholar
23. Chambon, F. and Winter, H. H., Polym. Bull. 13, 499 (1985);Google Scholar
23a also Winter, H. H., Morganelli, P. and Chambon, R., Macromol. 21, 532 (1988).Google Scholar
24. Martin, J. E., Adolf, D., and Wilcoxon, J. P., Phys. Rev. Lett. 61, 2620 (1988);Google Scholar
24a also Martin, J. E., Adolf, D., and Wilcoxon, J. P., Phys. Rev. A 39, 1325 (1989).Google Scholar
26. Martin, J. E., inAtomic and Molecular Processing of Electronic and Ceramic Materials, Proc. of the Twenty-Third Conference on Ceramic Science, editors Aksay, I., Stoebe, T., McVay, G. and Wager, J., Mats. Res. Soc. (1987).Google Scholar
27. Mandelbrot, B. B., in The Fractal Geometry of Nature, pg. 247 (Freeman, New York, 1983).Google Scholar
28. Martin, J. E. and Leyvraz, F., Phys. Rev. A 34, 2346 (1986).Google Scholar