Dynamics of Nonlinear Tenuous Structures
The vibrational dynamics of tenuous structures is developed using extended and localized states. A phonon-fracton model is used for explicit computations. It is shown that the localized states can contribute to thermal transport via hopping processes, assisted by absorption of extended state vibrations. This “phonon assisted-fracton hopping” is the vibrational analog of Mott’s variable range hopping contribution to electical conductivity. Comparison with thermal conductivity experiments on amorphous materials allows an estimate of the magnitude of the anharmonicity coefficient. It is found to be (roughly) two orders of magnitude larger than the acoustic limit. This enhancement is attributed to the “openness” of the geometry for fracton excitations, and could have profound effects on the vibrational and conformational excitations of tenuous structures.
KeywordsSilica Aerogel Thermal Transport Vibrational Excitation Localization Length Plateau Temperature
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- 1.S. Alexander and R. Orbach: J. Phys. (Paris) Lett. 43, L-62S (1982)Google Scholar
- 2.S. Alexander, O. Entin-Wohlman, and R. Orbach: J. Phys. (Paris) Lett. 46, L- S49 (198S); ibid L-SSS (198S); ibid Phys. Rev. B32, 6447 (198S); ibid Phys. Rev. B33, 393S (1986)Google Scholar
- 3.O. Entin-Wohlman, S. Alexander, and R. Orbach: Phys. Rev. B32, 8007 (1985)Google Scholar
- 4.S. Alexander, O. Entin-Wohlman, and R. Orbach: Phys. Rev. B35, 1166 (1987)Google Scholar
- 5.S. Alexander, O. Entin-Wohlman, and R. Orbach: Phys. Rev. B34, 2726 (1986)Google Scholar
- 6.R. Vacher, T. Woignier, J. Pelous, and E. Courtens: Phys. Rev. B37, 6500 (1988); E. Courtens, J. Pelous, J. Phalippou, R. Vacher, and T. Woignier: Phys. Rev. Lett. 58, 128 (1987); E. Courtens, R. Vacher, J. Pelous, and T. Woignier: Europhys. Lett. 6, 245 (1988); Y. Tsujimi, E. Courtens, J. Pelous, and R. Vacher: Phys. Rev. Lett. 60, 2757 (1988)Google Scholar
- 9.A. Jagannathan, R. Orbach, and O. Entin-Wohlman: submitted for publicationGoogle Scholar
- 11.R.C. Zeller and R.O. Pohl: Phys. Rev. B4, 2029 (1971); D.G. Cahill and R.O. Pohl: Phys. Rev. B3S, 4067 (1987); S. Kelham and H.M. Rosenberg: J. Phys. C14, 1737 (1981); R. Orbach and H.M. Rosenberg: In Proceedings of the 17th International Conference on Low Temperature Physics, ed. by U. Eckern, A. Schmid, W. Weber, and H. Wuhl (Elsevier, Amsterdam, 1984) p.375; J.E. de Oliveira, J. Page, and H.M. Rosenberg: submitted for publication.ADSGoogle Scholar
- 12.S. Simons: Proc. Phys. Soc. 83, 749 (1964)Google Scholar
- XIV. R. O. Pohl: private communicationGoogle Scholar